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<div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</d我v> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conclusions">结论</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#data-availability">数据可用性</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conflicts-of-interest">的利益冲突</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#acknowledgments">确认</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</一个> </div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <div class="articleHeader__specialIssue"> <span class="articleHeader__specialIssue_tag">特殊的问题</span> <h2 class="articleHeader__specialIssue_title">学习和适应复杂的可再生能源系统的优化和控制</h2> <a href="//www.newsama.com/journals/complexity/si/253828/" class="articleHeader__specialIssue_url" target="_blank" rel="noreferrer">把这个特殊的问题</一个> </div> <strong>研究文章|开放获取</strong> <div class="articleHeader__meta"> <span>体积2020年|</span> <span>文章的ID6046729|</span> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2020/6046729" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2020/6046729</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</button> </div> <h1 class="articleHeader__title">Multimodel异常识别和控制在石灰石-石膏湿法烟气脱硫系统</h1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>李小丽</strong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><a href="https://orcid.org/0000-0002-8627-6221" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>1、2、3</sup></span> <span class="articleHeader__authors_author">Quanbo刘<一个href="https://orcid.org/0000-0002-6974-0125" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>1</sup></span> <span class="articleHeader__authors_author">康王<一个href="https://orcid.org/0000-0002-8403-7606" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a>,<sup>1</sup></span> <span class="articleHeader__authors_author">富强王,<sup>4</sup></span> <span class="articleHeader__authors_author">Guimei崔,<sup>5</sup></span> <span class="articleHeader__authors_author">和杨李<一个href="https://orcid.org/0000-0002-5164-5568" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a><sup>6</sup></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</button> </div> <div class="articleHeader__academicEditor"> <strong>客座编辑:</strong> <span>京娜</span> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</strong> <span>2020年6月24日</span> </div> <div class="articleHeader__timeline_item "> <strong>接受</strong> <span>2020年8月3日</span> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</strong> <span>2020年10月12日</span> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>二氧化硫,最常见的一种空气污染物气体,带来数量可观的对人类健康和环境的危害。为了减少它带来的不利影响,是迫切需要控制电厂排放的烟气,因为大部分大气中二氧化硫源于在整个生产过程中产生的烟气发电。然而,环境的复杂性和不确定性增加出现的异常在实际烟气脱硫系统。在工业脱硫系统异常会引起严重的后果,对高性能控制与传统控制策略构成挑战。在本文中,基于过程数据采样1000 MW机组燃煤电厂烟气脱硫系统,与多层平行multimodel控制策略动态神经网络(MPDNN)是用于解决控制问题在不同的异常。此外,仿真结果表明提出的控制方法的适用性和有效性通过比较不同的情况。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>朦胧的增加出现天气在过去的几年中,在中国环境恶化引起了极大关注。二氧化硫,担任的主要贡献者之一导致大气污染,对人体健康有负面影响以及环境(<一个href="#B1">1</一个>- - - - - -<一个href="#B3">3</一个>]。此外,化石燃料的燃烧,尤其是煤炭、电厂的主要原因是大气中二氧化硫的存在(<一个href="#B4">4</一个>]。因此,去除二氧化硫的烟气从燃煤电厂具有重要意义,已逐渐成为最重要的公众关注。在各种各样的烟气脱硫方法,石灰石-石膏湿法烟气脱硫(WLFGD)大多数电厂的首要任务是由于它的特点是低运营成本和相对高的吸收利用试剂(<一个href="#B5">5</一个>,<一个href="#B6">6</一个>]。为了抑制二氧化硫带来的污染,出口烟气的浓度以及泥浆pH值作为控制变量选择在我们的案例研究,和前这是一个直接反映脱硫性能的指标。同时,通过验证,浆槽中的pH值对脱硫效率有重大的影响(<一个href="#B7">7</一个>]。</p> <p>异常检测(或异常值检测)是识别意想不到的观察或事件的过程中,大部分数据差别很大的<一个href="#B8">8</一个>]。由于异常检测领域应用价值高,它已经扩展到各个领域,尤其是在这个行业。在这项工作中,我们关注的情况下烟气脱硫中异常条件。完善,工业过程和设施在过去几年不断增加的复杂性,从而导致更大的机会出现明显的缺点。此外,鉴于烟气脱硫是一种化学工程过程中,存在一些独特的缺点,从而诱导异常比传统工业的其他条件,如催化剂失活,阀堵塞,或压缩机故障(<一个href="#B9">9</一个>]。因此,关于化学系统,特别注意必须放在系统的可靠性和稳定性在整个操作,这需要检测异常条件和对系统进行有效的控制。在过去的几十年中,有相当多的出版物包括异常检测的主题。然而,很少有出版物包括脱硫系统中的异常检测,更不用说应用控制技术在异常条件下。我们所知,几乎所有的贡献涉及故障检测和诊断问题。在文献[<一个href="#B10">10</一个>,<一个href="#B11">11</一个>),主成分分析(PCA)与监测指标霍特林的T2和平方预测误差是用来找到确切的故障出现在指定的时间内烟气脱硫系统。内核的不同应用PCA在后者的工作,和混合预测模型,其中包含自回归综合移动平均模型和最小二乘支持向量机模型,建议在<一个href="#B12">12</一个>),使泥浆pH值的预测,然后设计了故障诊断系统定位pH传感器的缺点。另外,燃烧模型基于物理特性介绍了烟气脱硫(<一个href="#B13">13</一个>]。在这种方法中,烟气评估模型构建和用于识别过程异常和传感器故障。</p> <p>至于出版物上面所提到的,存在一个共性,提出故障检测或诊断方法的实现是由标记的情况下,也就是说,包含各种异常的显式标签使用的所有实例。然而,从实用的角度来看,它是具有挑战性的向多个类别(即组异常。,f一个ults of different types) accurately in WLFGD system, as the malfunction of certain part in system may trigger successive faults in other components. Accordingly, the classification results depend critically upon individual experience in practice. In this case, the usage of exploring and grouping method is more advantageous for the extraction of underlying anomalous conditions in practical applications. Therefore, in this article, the integration of isolation forest and adaptive mean shift clustering are employed to determine types of anomalous conditions existing in our system. Another issue that has to be taken into account is what kind of control strategy should we apply in this context. Here, multimodel control is utilized in our case study due to complicacy and diversity of operating environments in the whole desulphurization process. More specifically, as a fair number of devices and plants are employed on-site, there are many possibilities for occurrences of anomalies, which are actually one of the major reasons for variations in the environment. Moreover, since many subprocesses in flue gas desulphurization are interactive, the presence of unknown and discontinuous anomalous conditions in any subprocess, even caused by some unnoticeable devices, may bring about parameter changes in controlled actual system. Given that multimodel control is particularly suited to cope with a class of control problems, which caused by parameter uncertainties due to changes of operating environments, it is selected as the control strategy in our case study.</p> <p>这个工作的主要贡献可以概括如下:(1)一种新的探索和提出了成组技术在异常环境中提供一个详细的分析在工业领域。(2)MPDNN-based提出了自适应控制和扩展multimodel首次。(3)控制方式的不同组合对MPDNN初始化自适应模型进行比较和讨论。</p> <p>本文的其余部分组织如下:部分<一个href="#sec2">2</一个>描述了湿法烟气脱硫的原理和过程。然后,综合异常检测技术基于隔离和介绍了聚类算法<一个href="#sec3">第三节</一个>。<一个href="#sec4">第四节</一个>讨论了理论知识与MPDNN multimodel系统识别和控制过程。在<一个href="#sec5">第五节</一个>,仿真研究表明,提出的控制策略的有效性对数值进行比较。最后,<一个href="#sec6">第六节</一个>本文总结并给出我们的未来的工作。</p> <h4 id="the-introduction-of-flue-gas-desulphurization-system">2。烟气脱硫系统的引入</h4> <p>事实上,整个过程的二氧化硫减排WLFGD系统很复杂,虽然化学方程式是看似简单的形式。WLFGD可以表达的整体反应的化学方程式如下:<span class="equation_break" id="EEq1"><span class="left_break" id="L1"></span><span class="middle_break"><span class="center_break" id="M1"> <svg height="13.8661pt" id="M1-1" version="1.1" viewbox="0 0 176.221 13.8661" 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transform="matrix(.0091,0,0,-0.0091,138.99,12.316)"> <use xlink:href="#g50-51"></use> </g> </g> </svg> <svg class="alt_equation" height="34.1673pt" id="I1" version="1.1" viewbox="0 0 176.42 34.1673" width="176.42pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B1-1"></use> <use transform="matrix(1 0 0 1 13.6 21.02)" xlink:href="#B1-2"></use> </svg></span></span><span class="right_break" id="R1"> <svg class="label" height="11.44pt" id="M1-3" version="1.1" viewbox="0 0 13.398 11.44" width="13.398pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B1-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 611 70 451 70 272V271C70 90 136 -71 282 -169L300 -147Z" id="g190-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M311 0V25C221 32 216 41 216 113V635C162 613 103 594 39 583V559L88 556C131 552 135 546 135 500V113C135 41 131 32 40 25V0H311Z" id="g190-213"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.26)"> <path d="M275 271C275 451 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 269V271Z" id="g190-42"></path> </g> </g> </svg> <svg class="alt_label" height="34.1673pt" id="IL1" version="1.1" viewbox="0 0 13.45 34.1673" width="13.45pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 11.15)" xlink:href="#B1-3"></use> </svg></span></span></p> <p>基本反应原理可以从上面的总反应方程式。即石灰石泥浆作为吸收剂的反应在烟气二氧化硫,和有限公司<sub>2</sub>随着石膏(卡索<sub>4</sub>·H<sub>2</sub>O)终于产生。在下面,列出的湿法烟气脱硫过程。为了清晰、WLFGD系统的一般结构呈现在图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig1/" target="_blank">1</一个>,它提供了一个例子在脱硫过程。石灰石泥浆作为吸收剂被用来喂养浆槽的吸收器。在这个过程中,泥浆的密度和流量可以通过密度计测量和流量计安装在管。同时,循环泵利用起来浆,以便它可以从吸收器的顶部掉下来。相反,烟气经过加热换热器从进气导管进入吸收器之前为了降低气体的温度。随着进气导管位于低吸收器的一部分,它将导致逆流接触烟气和石灰石泥浆。接下来,两个组件之间的重要的化学反应去除烟气二氧化硫含量。最后,使脱硫烟气排放从堆栈和石膏,坚实的副产品,在吸收剂浆了,可以应用在墙板和水泥等领域<一个href="#B14">14</一个>,<一个href="#B15">15</一个>]。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-d735dbc8e216dfed92cfa3eac00c18bc"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-d735dbc8e216dfed92cfa3eac00c18bc partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-d735dbc8e216dfed92cfa3eac00c18bc partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 湿法烟气脱硫系统的原理图。</d我v> </div> </div> </div> <h4 id="extraction-of-anomalous-conditions-in-wlfgd-system">3所示。提取WLFGD系统中的异常情况</h4> <p>在WLFGD的操作系统,操作数据与测量变量的数组收集从一个1000 MW火力发电厂机组每一分钟。在本节中,执行一些相关变量的初步分析首先,这对异常条件提取奠定了基础之后在这一节中。然后,相关技术利用的过程中寻找异常详细。</p> <h5 id="sec3.1">3.1。预赛</h5> <p>在这里,四个输出变量在系统中选择对异常进行分析。他们是出口啊<sub>2</sub>二氧化硫浓度,浓度,出口出口烟气温度、泥浆pH值。之前寻找异常情况下,变量之间的皮尔逊相关系数计算,并可视化相关矩阵的形式(图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig2/" target="_blank">2</一个>)。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-de3491a587804b5e1f990fc7a247baee"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.002.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-de3491a587804b5e1f990fc7a247baee partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-de3491a587804b5e1f990fc7a247baee partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 四个输出变量的相关矩阵。</d我v> </div> </div> </div> <p>相关矩阵是对称、单位对角,semidefiniteness [<一个href="#B16">16</一个>),矩阵中的每个条目表示两个变量之间的相关系数。上述矩阵显式表示的程度每一对变量之间的关系。每个变量的符号简单,上面提到的用部分相关矩阵获得的全名。因为它是图所示<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig2/" target="_blank">2</一个>,关于四个变量的皮尔森相关系数的绝对值都超过0.50,其中一些甚至超过0.92,反映出高水平的相关性在WLFGD四个输出变量系统。由(<一个href="#B17">17</一个>),变量有高相关规定限制异常检测的性能,从正常的轻微异常相关变量的范围可能产生相对更大的异常。此外,高维数据会带来问题的维数的诅咒(<一个href="#B18">18</一个>,<一个href="#B19">19</一个>]。PCA,作为一种最常用的特征提取技术,降低维度通过生成更少的主成分(pc)代替原来的变量。相反,个人电脑是彼此不相关的<一个href="#B20">20.</一个>]。从这个意义上讲,高维数据和相关变量出现的问题在异常条件下可以解决通过PCA提取。此外,组件保留的数量是另一个需要考虑的问题降维。确定电脑的数量可以参考标准如下(<一个href="#B21">21</一个>):(1)每个电脑应该大于1的特征值;每个组件(2)解释了至少5%的方差;和(3)解释方差累计达到70%。特征值的总结,解释方差的比例,累积解释方差对个人电脑不同的数字计算了以上四个输出变量列在下表中<一个href="//www.newsama.com/journals/complexity/2020/6046729/tab1/" target="_blank">1</一个>。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 特征值和方差的pc。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2020/6046729/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <p>如表所示<一个href="//www.newsama.com/journals/complexity/2020/6046729/tab1/" target="_blank">1</一个>个人电脑,前两个特征值为3.068和1.247,然而第三个人电脑的特征值只有0.465。同时,方差解释为前两个电脑是62.3%和25.3%,分别解释方差累计达到87.6%。在上述标准的基础上,保留两个电脑是更可取的。因此,上述四个输出变量简化为两个原则组件进行进一步分析下面的异常情况。</p> <h5 id="sec3.2">3.2。异常条件的提取</h5> <p>在WLFGD减少维数的实际测量数据系统,异常条件将检测并提取之后,可以进行必要的准备建设multimodel控制系统在下一节。在本节中,集成isolation-based和clustering-based异常条件的方法来执行任务的上下文中提取WLFGD。</p> <p>从实用的角度,计算效率异常检测至关重要,尤其是在工业场景中,由于初始的需求促使行动维护系统稳定。隔离森林(如果)是一种ensemble-based刘等人提出的异常检测方法(<一个href="#B22">22</一个>],它的特点是精度高、成本低内存和计算复杂性(<一个href="#B23">23</一个>),从而能保证及时性寻找异常的系统。此外,隔离森林算法,在训练过程中异常情况下不需要(<一个href="#B24">24</一个>]。因此,适合在工业环境中实现。使用如果检测异常的基本原理的基础上,异常的固有属性,也就是说,倾斜的数据的数量很小,正常细胞形成鲜明对比。在此基础上,利用树结构来描述数据的递归过程空间分区,异常数据更容易被分离在树的上方位置与正常点。更具体地说,让<span class="inline_break"> <svg height="16.2017pt" id="M2" style="vertical-align:-3.943501pt" version="1.1" viewbox="-0.0498162 -12.2582 47.866 16.2017" width="47.866pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z" id="g113-124"></path> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,11.713,3.132)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> </g> <g transform="matrix(.013,0,0,-0.013,16.888,0)"> <path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,21.399,-5.741)"> <path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,21.399,3.784)"> <use xlink:href="#g50-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.058,3.784)"> <path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,31.618,3.784)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> </g> <g transform="matrix(.013,0,0,-0.013,40.235,0)"> <path d="M512 1V51H381C244 51 133 142 133 255S244 459 381 459H512V509H382C213 509 75 395 75 255S213 1 382 1H512Z" id="g117-77"></path> </g> </svg><span class="irelop"></span> <svg height="16.2017pt" style="vertical-align:-3.943501pt" version="1.1" viewbox="51.448183799999995 -12.2582 15.677 16.2017" width="15.677pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,51.498,0)"> <path d="M378 16V19L193 101V573L189 575L64 511V497C112 490 117 487 117 401V85C117 65 122 58 143 49L273 -9C281 -13 290 -15 300 -15C311 -15 322 -12 331 -8L378 16ZM701 30L693 44C684 39 674 35 663 35C642 35 625 36 617 48L441 312V315C512 355 581 413 581 494C581 549 543 595 492 617L420 650C405 657 391 665 375 665C349 665 329 647 306 635L235 599V127H239C273 140 282 148 282 167V586L335 613L425 573C470 552 505 511 505 462C505 397 447 353 387 322C375 316 363 308 363 295C363 279 375 261 386 245L541 13C552 -4 572 -15 595 -15C606 -15 617 -12 626 -8L701 30Z" id="g113-21"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,61.3,-5.741)"> <path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z" id="g50-101"></path> </g> </svg></span>感兴趣的点,在那里<我>N</我>和<我>d</我>分别表示实例的数量和属性;形成一个隔离森林的过程总结如下:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">建立通过选择一个子集<我>k</我>(<我>k</我><<我>N</我>随机从)实例<我>N</我>情况下,和一个<我>iTree</我>递归地将由分区这个子集。</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">首先,任意选择的属性子集。然后,分割点是选为内任意点选择的属性子集。</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">空间构成的数据子集划分为两个子空间,这对应于左和右子树,选择的分割点。数据将被分配到相应的子树之后,比较他们的价值观和分割点在指定的属性,和更小的和更大的对应左和右子树,分别。</span></span><span class="list-item"><span class="list-label">(4)</span><span class="list-content">重复第二个和第三个步骤为每个新子空间,直到只有一个单点的子空间,或高度限制<我>h</我>的<我>iTree</我>满足了。<我>h</我>是一个参数的大小取决于子集的形式<span class="inline_break"> <svg height="16.3284pt" id="M3" style="vertical-align:-3.8679pt" version="1.1" viewbox="-0.0498162 -12.4605 17.971 16.3284" width="17.971pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z" id="g113-105"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.34,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="16.3284pt" style="vertical-align:-3.8679pt" version="1.1" viewbox="21.553183800000003 -12.4605 30.367 16.3284" width="30.367pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,21.603,0)"> <path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path> </g> <g transform="matrix(.013,0,0,-0.013,26.088,0)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path> </g> <g transform="matrix(.013,0,0,-0.013,29.377,0)"> <path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g121-109"></path> </g> <g transform="matrix(.013,0,0,-0.013,36.007,0)"> <path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 203 -257C336 -257 452 -160 452 -59C452 39 371 59 309 59C275 59 240 58 203 58C158 58 140 77 140 96C140 110 157 129 170 138C186 135 205 133 221 133C306 133 396 185 396 293C396 328 384 360 366 381L423 378C439 387 459 413 468 429L463 437ZM219 418C277 418 314 362 314 284C314 205 275 166 231 165C176 165 137 221 137 299C137 376 177 418 219 418ZM241 -11C285 -11 314 -14 339 -24C367 -36 384 -61 384 -95C384 -157 335 -206 240 -206C166 -206 108 -165 108 -110C108 -82 128 -54 154 -32C172 -17 195 -11 241 -11Z" id="g121-101"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,42.151,-5.944)"> <path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,42.151,3.818)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.298,0)"> <path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path> </g> </svg>。</span></span>通过这种方式,一个<我>iTree</我>建立了。</span></span><span class="list-item"><span class="list-label">(5)</span><span class="list-content">构建<我>n iTree</我>根据上面说的步骤,这样隔离森林{<我>T</我><sub>1</sub>、…<我>T</我><sub><i>n</我></sub>可以形成}。</span></span></span></p> <p>至于任何点<我>x</我>点的,分区隔离<我>我</我>th<我>iTree</我>可以称为路径长度<我>l</我>(<我>x</我><sub><i>我</我></sub>为判断),它提供了参考<我>x</我>是一个异常。在这种情况下,<我>n</我>路径长度可以被收购,每一种都对应于一个<我>iTree</我>在{<我>T</我><sub>1</sub>、…<我>T</我><sub><i>n</我></sub>}。然后,路径长度<我>x</我>在一个隔离森林通过的平均值计算<我>n</我>路径的长度,也就是说,<span class="equation_break" id="EEq2"><span class="left_break" id="L4"></span><span class="middle_break"><span class="center_break" id="M4"> <svg height="35.6587pt" id="M4-1" version="1.1" viewbox="0 0 116.784 35.6587" width="116.784pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B4-1"> <g transform="matrix(.013,0,0,-0.013,0,20.415)"> <path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 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xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="29.6681pt" id="I6" version="1.1" viewbox="0 0 176.29 29.6681" width="176.29pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B6-1"></use> </svg></span></span><span class="right_break" id="R6"> <svg class="label" height="11.44pt" id="M6-2" version="1.1" viewbox="0 0 15.458 11.44" width="15.458pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B6-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.96,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="29.6681pt" id="IL6" version="1.1" viewbox="0 0 15.52 29.6681" width="15.52pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 8.9)" xlink:href="#B6-2"></use> </svg></span></span>与<我>H</我>(<我>x</我>)表示谐波数,可以估计由欧拉常数<我>H</我>(<我>x</我>)= ln (<我>x</我>)+ 0.5772156649。考虑到两种极端情况下,最小和最大距离的地方<我>x</我>每一个成年的根源<我>iTree</我>分别实现。在这一点上,<我>E</我>(<我>l</我>(<我>x</我>)到达最小值0,最大值<我>n</我>−1。用两个极端值<我>E</我>(<我>l</我>(<我>x</我>))(<一个href="#EEq3">3</一个>),它可以断定的异常分数<我>x</我>在[0,1]的经营范围内。一旦异常分数计算每个样本,异常可以寻找基于阈值的异常分数,而且接近1,<我>x</我>更有可能是一个异常。作为一个经验法则,阈值的异常分数为0.6分。在我们的案例中,实例中包含的子集和树的数量设置为256年和100年,分别已被证明是最优参数,产生最佳的性能异常检测(<一个href="#B22">22</一个>]。在此基础上,异常点搜索缩小操作数据。为了简化表示,一段时间的结果是给定的图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig3/" target="_blank">3</一个>。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-ffae3d835f9b69622ceec75175e91a1f"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.003.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-ffae3d835f9b69622ceec75175e91a1f partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-ffae3d835f9b69622ceec75175e91a1f partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 如果在WLFGD系统异常检测到。</d我v> </div> </div> </div> <p>如图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig3/" target="_blank">3</一个>,部分检测到异常的红点和剩余的点被认为是正常的。同样,异常点在不同的时间可以收集和汇聚在一起。尽管所有的异常被发现在这个阶段,需要确定类型的异常状况进行进一步的研究。然而,由于操作条件在实际WLFGD场景的复杂性,很难知道特定数量的异常情况,并合理分区也是一个棘手的问题。这里,适应性转变是应用于解决遇到的问题。</p> <p>意味着转变(MS)是一种非参数模式寻求算法基于核密度估计,这是能够找到集群与任何形状的数据(<一个href="#B25">25</一个>]。女士的主要缺点是它的高计算复杂度高维度[<一个href="#B26">26</一个>]。然而,在我们的案例研究中,特征空间的维数减少,避免它带来的计算问题。与此同时,模式的数量(即。,clustering numbers) can be automatically determined by the algorithm; therefore, MS is of practical significance for determining the type of anomaly in our case study. The principle of MS clustering is outlined as the process of moving each point towards the direction of maximum local density, and the direction is determined via kernel density estimate. The movements of each point are repeated until the point converges to another point with local maxima of density (i.e., mode). Lastly, points with the same mode are classified as the identical cluster. The bandwidth of a kernel function is the unique and key parameter in MS which affects the clustering result of the MS significantly [<一个href="#B27">27</一个>,<一个href="#B28">28</一个>]。基于带宽是否变量在点的转移,女士可以分为两组,即。、常数和自适应意味着转变。至于恒带宽,太小或太大带宽可能会导致不适当的聚类。相比之下,自适应意味着转变(AMS)可以为集群产生更好的结果。假设<span class="inline_break"> <svg height="15.5493pt" id="M7" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -12.2582 20.754 15.5493" width="20.754pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.89,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> </g> </svg><span class="irelop"></span> <svg height="15.5493pt" 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</svg></span></span></p> <p>让函数<span class="inline_break"> <svg height="14.8655pt" id="M10" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 34.924 14.8655" width="34.924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path> </g> <g 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</svg></span></span>在最右边的部分(7)被称为均值移位向量,收益率最大密度增加的方向。特征空间中的每个点移动到当地密度最大值逐渐与梯度的方向,即意味着转变的方向向量。现在,出现的问题是如何确定自适应带宽<我>h</我><sub><i>我</我></sub>。在这里,<我>k</我>最近邻居法(<一个href="#B26">26</一个>采用。的带宽<我>x</我><sub><i>我</我></sub>依赖于其<我>k</我>th遥远的点<我>x</我><sub><i>我</我>,<我>k</我></sub>,<我>h</我><sub><i>我</我></sub>的形式<span class="equation_break" id="EEq8"><span class="left_break" id="L12"></span><span class="middle_break"><span class="center_break" id="M12"> <svg height="14.9308pt" id="M12-1" version="1.1" viewbox="0 0 81.314 14.9308" width="81.314pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B12-1"> <g transform="matrix(.013,0,0,-0.013,0,10.58)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.64,13.712)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.33,10.58)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.59,3.912)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.59,7.514)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.59,11.115)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.59,14.717)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.96,10.58)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.16,13.712)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.12,10.58)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.66,10.58)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.86,13.712)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.41,13.712)"> <path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,65.56,13.712)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.73,3.912)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.73,7.514)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.73,11.115)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.73,14.717)"> <use xlink:href="#g119-35"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.35,10.58)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R12"> <svg class="label" height="11.44pt" id="M12-2" version="1.1" viewbox="0 0 15.168 11.44" width="15.168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B12-2"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <path d="M246 635C138 635 67 554 67 471C67 401 116 348 178 315C143 296 103 268 87 252C65 231 42 203 42 157C42 50 128 -12 234 -12C319 -12 432 52 432 169C432 256 370 303 299 344C347 376 373 399 381 408C399 430 408 459 408 487C408 569 341 635 246 635ZM235 603C284 603 334 567 334 483C334 420 306 383 273 358C202 393 142 427 142 503C142 552 173 603 235 603ZM245 21C179 21 122 70 122 163C122 219 155 270 204 300C279 263 352 219 352 144C352 66 308 21 245 21Z" id="g190-152"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.67,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>它遵循从(<一个href="#EEq8">8</一个>)的价值<我>k</我>极大地影响聚类的结果通过改变每个点的带宽。的基础上发现异常点,集群是由自适应的意思是不同的<我>k</我>。同时,介绍了轮廓系数作为衡量聚类的性能来选择最优<我>k</我>价值。至于集群轮廓系数,值的范围(−1,1)和聚类结果的合理性是其价值的比例。如果收集的异常,轮廓系数计算和绘制<我>k</我>的间隔50;结果呈现在图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig4/" target="_blank">4</一个>。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-07fac0461e49aaae73d6057fbaaa865a"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.004.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-07fac0461e49aaae73d6057fbaaa865a partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.004_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-07fac0461e49aaae73d6057fbaaa865a partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 集群轮廓系数不同<我>k</我>。</d我v> </div> </div> </div> <p>图中所示<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig4/" target="_blank">4</一个>,很明显,集群轮廓系数达到最大值时<我>k</我>等于100。在这个意义上,可以实现最优聚类效果<我>k</我>= 100。因此,异常条件的细分WLFGD系统是由AMS在这个上下文。提高聚类的准确性,两个维度得到异常比例在聚类前(−1、2),结果显示在图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig5/" target="_blank">5</一个>。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-0d6f002a585d4f6775bce07a50faab69"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.005.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-0d6f002a585d4f6775bce07a50faab69 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.005_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-0d6f002a585d4f6775bce07a50faab69 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 提取不同的异常条件的结果。</d我v> </div> </div> </div> <p>如图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig5/" target="_blank">5</一个>,异常分为三个类别,每个由点构成的某种颜色。与此同时,每个类别的模式是,一个坚实的圆,分别。在这个阶段,各种异常条件的数据可以通过上述聚类结果中提取。然后,数据集对应于每种类型的异常条件随机分为两部分,其中70%为模型训练和30%控制测试、培训和控制过程将明确表示,在接下来的部分。</p> <h4 id="identification-and-multimodel-adaptive-control-in-anomalous-conditions">4所示。在异常条件下识别和Multimodel自适应控制</h4> <p>实际上,异常提取条件为控制自适应multimodel提供做过使本节介绍。整个控制过程可以简要地概括为两个步骤。首先,模型建立了描述不同类型的异常提取的条件。然后,multimodel控制策略应用于连接与模型。上述两个步骤分别对应于以下两个部分。此外,在这项工作的第一部分指出,在石灰石泥浆pH值和出口二氧化硫浓度(即选为控制变量。系统的输出变量)。第二,石灰石浆液的流量和密度,这很容易可以通过传感器对系统输出,同时产生相当大的影响(即被选中作为控制变量。系统的输入变量)。</p> <h5 id="sec4.1">4.1。系统识别</h5> <p>动态神经网络吸引了越来越多的关注和被利用在许多领域,由于它的更好的能力表示非线性系统与静态。此外,动态神经网络用于非线性系统识别可以进一步分为串并联模型和并行模型(<一个href="#B29">29日</一个>]。鉴于这一事实的反应发生在吸收高水平的复杂性,因此存在很大的障碍与化学机理模型系统。与此同时,高非线性和延迟现有的泥浆pH值变化的过程中进一步添加系统识别的困难WLFGD的上下文。由于上述优点的动态神经网络,在这里,并行形式它用于标识系统在我们的案例研究。这种类型的神经网络的优势可以概括如下:(1)实际系统的输出不受偏见产生的噪声(<一个href="#B30">30.</一个>),(2)识别模型特别适合使用离线。随着并行动态神经网络没有隐层(详细描述<一个href="#B31">31日</一个>- - - - - -<一个href="#B33">33</一个>),接下来,MPDNN是我们主要关注的描述。</p> <p>给出了考虑非线性系统识别<span class="equation_break" id="EEq9"><span class="left_break" id="L13"></span><span class="middle_break"><span class="center_break" id="M13"> <svg height="14.5707pt" id="M13-1" version="1.1" viewbox="0 0 87.794 14.5707" width="87.794pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B13-1"> <g transform="matrix(.013,0,0,-0.013,7.27,10.371)"> <path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z" id="g117-11"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.21,13.725)"> <path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path> </g> <g transform="matrix(.013,0,0,-0.013,14.53,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.8,10.593)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.33,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.35,10.593)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.55,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.22,10.593)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.36,10.593)"> <path d="M515 96L502 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transform="matrix(.013,0,0,-0.013,84.83,10.593)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R13"> <svg class="label" height="11.44pt" id="M13-2" version="1.1" viewbox="0 0 15.338 11.44" width="15.338pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B13-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M247 635C117 635 41 518 41 422C41 317 114 239 220 239C239 239 256 244 278 255L348 290C315 139 207 37 63 13L67 -15C93 -15 155 -5 207 17C343 71 443 203 443 385C443 520 371 635 247 635ZM231 602C331 602 355 476 355 390C355 371 354 349 351 325C334 310 298 294 261 294C177 294 128 369 128 457C128 516 155 602 231 602Z" id="g190-193"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.84,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>的状态<span class="inline_break"> <svg height="13.2475pt" id="M14" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -9.95639 21.366 13.2475" width="21.366pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.502,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="13.2475pt" style="vertical-align:-3.29111pt" version="1.1" viewbox="24.9471838 -9.95639 15.166 13.2475" width="15.166pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,24.997,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.799,-5.741)"> <use xlink:href="#g50-111"></use> </g> </svg></span>和输入<span class="inline_break"> <svg height="13.2475pt" id="M15" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -9.95639 21.092 13.2475" width="21.092pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.929,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.228,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="13.2475pt" style="vertical-align:-3.29111pt" version="1.1" viewbox="24.6741838 -9.95639 17.842 13.2475" width="17.842pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,24.724,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.526,-5.741)"> <path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path> </g> </svg>,</span></span>和以下表格的动态神经网络用于识别系统:<span class="equation_break" id="EEq10"><span class="left_break" id="L16"></span><span class="middle_break"><span class="center_break" id="M16"> <svg height="16.3923pt" id="M16-1" version="1.1" viewbox="0 0 128.455 16.3923" width="128.455pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B16-1"> <g transform="matrix(.013,0,0,-0.013,6.41,8.532)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,0.58,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.29,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.59,12.042)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.86,12.042)"> <path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path> </g> <g transform="matrix(.013,0,0,-0.013,36.42,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.99,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.19,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.79,12.042)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.33,12.042)"> <path d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z" id="g113-88"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,70.11,15.173)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.54,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.7,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.39,12.042)"> <path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path> </g> <g transform="matrix(.013,0,0,-0.013,89.91,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.94,12.042)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z" id="g113-87"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,102.27,15.173)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,106.7,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,108.86,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,113.98,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,112.55,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,119.75,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.45,12.042)"> <use xlink:href="#g119-6"></use> </g> </g> </svg> <svg height="16.3923pt" id="M16-2" version="1.1" viewbox="0 0 116.394 16.3923" width="116.394pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B16-2"> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,12.042)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.32,15.173)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,25.75,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.91,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.6,12.042)"> <path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z" id="g113-243"></path> </g> <g transform="matrix(.013,0,0,-0.013,41.12,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,46.15,12.042)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.48,15.173)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.91,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.07,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.19,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.76,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,70.96,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.66,12.042)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.89,12.042)"> <path d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z" id="g113-225"></path> </g> <g transform="matrix(.013,0,0,-0.013,90.58,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.61,12.042)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.53,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.2,12.042)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,113.43,12.042)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R16"> <svg class="label" height="11.44pt" id="M16-3" version="1.1" viewbox="0 0 19.728 11.44" width="19.728pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B16-3"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.82,9.25)"> <path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.23,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>与<span class="inline_break"> <svg height="13.2475pt" id="M17" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -9.95639 21.392 13.2475" width="21.392pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.429,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.528,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="13.2475pt" style="vertical-align:-3.29111pt" version="1.1" viewbox="24.974183800000002 -9.95639 14.461 13.2475" width="14.461pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,25.024,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.826,-5.741)"> <use xlink:href="#g50-111"></use> </g> </svg></span>被估计的状态。<span class="inline_break"> <svg height="11.4337pt" id="M18" style="vertical-align:-0.6370001pt" version="1.1" viewbox="-0.0498162 -10.7967 19.631 11.4337" width="19.631pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.767,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="11.4337pt" style="vertical-align:-0.6370001pt" version="1.1" viewbox="23.213183800000003 -10.7967 25.434 11.4337" width="25.434pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,23.263,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,33.065,-5.741)"> <use xlink:href="#g50-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.724,-5.741)"> <path d="M547 55L345 261L547 468L508 508L306 301L104 508L65 468L267 261L65 55L104 14L306 221L508 14L547 55Z" id="g54-42"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,43.284,-5.741)"> <use xlink:href="#g50-111"></use> </g> </svg></span>是一个对角赫维茨矩阵。假设控制输入函数有界和作为<span class="inline_break"> <svg height="12.7178pt" id="M19" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 37.372 12.7178" width="37.372pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.516,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.014,0)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.943,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.611,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.741,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="40.954183799999996 -9.28833 10.831 12.7178" width="10.831pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,41.004,0)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.933,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span></span>让<我>l</我>隐层的节点数,表示<svg height="12.9866pt" id="M20" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 17.7399 12.9866" width="17.7399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.764,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>和<svg height="12.9866pt" id="M21" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 17.7399 12.9866" width="17.7399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.764,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是<我>l</我>——- - - - - -<我>n</我>权重矩阵和<svg height="12.9866pt" id="M22" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.1978 12.9866" width="21.1978pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>和<svg height="12.9866pt" id="M23" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 21.1978 12.9866" width="21.1978pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>是<我>n</我>——- - - - - -<我>l</我>权重矩阵。<span class="inline_break"> <svg height="14.5263pt" id="M24" style="vertical-align:-2.268101pt" version="1.1" viewbox="-0.0498162 -12.2582 29.803 14.5263" width="29.803pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.347,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.845,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.809,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.939,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="14.5263pt" style="vertical-align:-2.268101pt" version="1.1" viewbox="33.3851838 -12.2582 13.008 14.5263" width="13.008pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.435,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.237,-5.741)"> <path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z" id="g50-109"></path> </g> </svg></span>是一个s形向量函数,<span class="inline_break"> <svg height="15.6876pt" id="M25" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -12.2582 29.802 15.6876" width="29.802pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.346,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.844,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.808,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.938,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="15.6876pt" style="vertical-align:-3.4294pt" version="1.1" viewbox="33.384183799999995 -12.2582 21.065 15.6876" width="21.065pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.434,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.236,-5.741)"> <use xlink:href="#g50-109"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.703,-5.741)"> <use xlink:href="#g54-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.263,-5.741)"> <use xlink:href="#g50-109"></use> </g> </svg></span>是一个对角矩阵由s形向量函数的元素,可以表示成<span class="inline_break"> <svg height="13.6586pt" id="M26" style="vertical-align:-4.350699pt" version="1.1" viewbox="-0.0498162 -9.3079 30.569 13.6586" 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xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,91.267,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.388,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.959,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.161,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.856,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.354,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="13.6586pt" style="vertical-align:-4.350699pt" version="1.1" viewbox="115.4471838 -9.3079 18.427 13.6586" width="18.427pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,115.497,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,120.64,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,125.783,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,130.96,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span><span class="nowrap"> <svg height="13.6586pt" style="vertical-align:-4.350699pt" version="1.1" viewbox="136.0531838 -9.3079 51.984 13.6586" width="51.984pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,136.103,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,143.123,3.132)"> <use xlink:href="#g50-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,146.096,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,150.594,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,157.926,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,162.358,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,164.514,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,169.636,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,168.207,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,175.409,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,179.104,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,183.602,0)"> <use xlink:href="#g113-94"></use> </g> </svg>,</span></span>和组件的s形向量函数的形式<span class="equation_break" id="EEq11"><span class="left_break" id="L27"></span><span class="middle_break"><span class="center_break" id="M27"> <svg height="26.8235pt" id="M27-1" version="1.1" viewbox="0 0 71.748 26.8235" width="71.748pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B27-1"> <g transform="matrix(.013,0,0,-0.013,0,14.469)"> <use 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transform="matrix(.013,0,0,-0.013,24.68,14.469)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.82,14.469)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.06,14.469)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="70.8538pt" id="I27" version="1.1" viewbox="0 0 171.36 70.8538" width="171.36pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -5.28)" xlink:href="#B27-1"></use> <use transform="matrix(1 0 0 1 32.24 22.02)" xlink:href="#B27-2"></use> <use transform="matrix(1 0 0 1 132.22 52.42)" xlink:href="#B27-3"></use> </svg></span></span><span class="right_break" id="R27"> <svg class="label" height="11.44pt" id="M27-4" version="1.1" viewbox="0 0 17.788 11.44" width="17.788pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B27-4"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use 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xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.06,4.361)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.17,14.409)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.14,10.625)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.34,13.756)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.01,10.625)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.27,10.625)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.013,0,0,-0.013,85.96,10.625)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.98,10.625)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,97.91,13.756)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,101.58,10.625)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.81,10.625)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="38.0447pt" id="I29" version="1.1" viewbox="0 0 153.01 38.0447" width="153.01pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B29-1"></use> <use transform="matrix(1 0 0 1 33.39 23.46)" xlink:href="#B29-2"></use> </svg></span></span><span class="right_break" id="R29"> <svg class="label" height="11.44pt" id="M29-3" version="1.1" viewbox="0 0 19.468 11.44" width="19.468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B29-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.93,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="38.0447pt" id="IL29" version="1.1" viewbox="0 0 19.55 38.0447" width="19.55pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 13.09)" xlink:href="#B29-3"></use> </svg></span></span>与<span class="nowrap"> <svg height="13.9365pt" id="M30" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -10.1025 18.8882 13.9365" width="18.8882pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.669,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>,</span><span class="nowrap"> <svg height="13.9365pt" id="M31" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -10.1025 18.8882 13.9365" width="18.8882pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.669,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.784)"> <use xlink:href="#g50-51"></use> </g> </svg>,</span><span class="nowrap"> <svg height="13.9365pt" id="M32" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -10.1025 15.4303 13.9365" width="15.4303pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.224,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>,</span>和<svg height="13.9365pt" id="M33" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -10.1025 15.4303 13.9365" width="15.4303pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.224,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.784)"> <use xlink:href="#g50-51"></use> </g> </svg>任何固定权数矩阵。由于矩阵<我>一个</我>在(<一个href="#EEq10">10</一个>)是稳定的,对(<我>一个</我>,<我>R</我><sup>1/2</sup>)是可控的,两人(<我>问</我><sup>1/2</sup>,<我>一个</我>)是可观察的,当地所表达的频率状态(<一个href="#EEq13">13</一个>)(<一个href="#B34">34</一个>]<span class="equation_break" id="EEq13"><span class="left_break" id="L34"></span><span class="middle_break"><span class="center_break" id="M34"> <svg height="26.1319pt" id="M34-1" version="1.1" viewbox="0 0 66.166 26.1319" width="66.166pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.14,10.593)"> <path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.53,16.857)"> <path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-2"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z" id="g117-94"></path> </g> <g transform="matrix(.013,0,0,-0.013,12.46,8.349)"> <use xlink:href="#g113-50"></use> </g> <rect height="0.65243" width="6.26339" x="12.46" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,12.46,26.082)"> <path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path> </g> <g transform="matrix(.013,0,0,-0.013,22.1,16.857)"> <path d="M335 -404V-369L312 -368C205 -360 203 -355 203 -249V751C203 895 206 900 312 908L335 909V944H138V-404H335Z" id="g119-129"></path> </g> <g transform="matrix(.013,0,0,-0.013,27.46,16.857)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.6,10.593)"> <use 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id="M34-3" version="1.1" viewbox="0 0 2.964 26.1319" width="2.964pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-3"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-46"></use> </g> </g> </svg> <svg height="26.1319pt" id="M34-4" version="1.1" viewbox="0 0 108.214 26.1319" width="108.214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-4"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.33,16.857)"> <use xlink:href="#g119-129"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.69,16.857)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,24.83,10.593)"> <use xlink:href="#g50-85"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.21,16.857)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.37,10.593)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.93,10.593)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.8,16.857)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.34,16.857)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,71.49,10.593)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,77.05,10.593)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.01,16.857)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,91.15,16.857)"> <use xlink:href="#g119-130"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,96.68,7.664)"> <use xlink:href="#g50-85"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.25,16.857)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R34"> <svg class="label" height="11.44pt" id="M34-5" version="1.1" viewbox="0 0 19.258 11.44" width="19.258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-5"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.25)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.76,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>然后,矩阵的黎卡提微分方程形式,<span class="equation_break" id="EEq14"><span class="left_break" id="L35"></span><span class="middle_break"><span class="center_break" id="M35"> <svg height="16.4066pt" id="M35-1" version="1.1" viewbox="0 0 136.374 16.4066" width="136.374pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-1"> <g transform="matrix(.013,0,0,-0.013,0,12.442)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.13,6.179)"> <use 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xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.68,9.26)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.14,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>有一个对称正解<我>P</我>。然后,它遵循从[<一个href="#B35">35</一个>],权重矩阵法可以给出如下更新:<span class="equation_break" id="EEq15a"><span class="left_break" id="L36"></span><span class="middle_break"><span class="center_break" id="M36"> <svg height="187.294pt" id="M36-1" version="1.1" viewbox="0 0 20.518 187.294" width="20.518pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B36-1"> <g transform="matrix(.013,0,0,-0.013,9.57,19.049)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,21.946)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.77,25.078)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.21,25.078)"> <use xlink:href="#g50-45"></use> 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xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.8,9.26)"> <path d="M152 404V712C115 698 54 683 7 677V654C71 648 73 642 73 579V24C128 -2 179 -12 220 -12C353 -12 471 92 471 238C471 357 381 449 274 449C262 449 249 446 233 439L152 404ZM152 374C170 384 202 393 230 393C313 393 382 326 382 213C382 97 330 26 246 26C194 26 165 62 158 81C154 91 152 101 152 116V374Z" id="g190-99"></path> </g> <g transform="matrix(.013,0,0,-0.013,21.4,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M36-13" version="1.1" viewbox="0 0 24.788 11.44" width="24.788pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B36-13"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.79,9.26)"> <path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path> </g> <g transform="matrix(.013,0,0,-0.013,20.29,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M36-19" version="1.1" viewbox="0 0 26.158 11.44" width="26.158pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B36-19"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.79,9.26)"> <use xlink:href="#g190-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.66,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="334.566pt" id="IL36" version="1.1" viewbox="0 0 26.26 334.566" width="26.26pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 36.56)" xlink:href="#B36-4"></use> <use transform="matrix(1 0 0 1 0 121.26)" xlink:href="#B36-8"></use> <use transform="matrix(1 0 0 1 0 195.45)" xlink:href="#B36-13"></use> <use transform="matrix(1 0 0 1 0 282.47)" xlink:href="#B36-19"></use> </svg></span></span>识别错误<svg height="11.927pt" id="M37" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.7626 11.927" width="13.7626pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-133"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.958,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>表示为<span class="nowrap"> <svg height="12.5403pt" id="M38" style="vertical-align:-3.29109pt" version="1.1" viewbox="-0.0498162 -9.24921 34.699 12.5403" width="34.699pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.429,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.802,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.339,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.541,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>。</span>增益矩阵<span class="inline_break"> <svg height="15.535pt" id="M39" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 44.888 15.535" width="44.888pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-76"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.741,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.797,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.308,-5.741)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.308,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.856,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,29.416,3.784)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.024,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span> <svg height="15.535pt" style="vertical-align:-3.9436pt" version="1.1" viewbox="48.4701838 -11.5914 25.465 15.535" width="25.465pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,48.52,0)"> <use xlink:href="#g113-21"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.322,-5.741)"> <use xlink:href="#g50-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,62.982,-5.741)"> <use xlink:href="#g54-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,68.542,-5.741)"> <use xlink:href="#g50-111"></use> </g> </svg></span>是用来确定神经网络的学习速率。这两个<svg height="11.8174pt" id="M40" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 15.8896 11.8174" width="15.8896pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g 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transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.88,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.037,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.381,0)"> <path d="M535 323V373H52V323H535ZM535 138V188H52V138H535ZM451 524L316 717H271L136 524C143 513 151 502 158 491H429C436 502 444 513 451 524ZM383 535H204L293 663L383 535Z" id="g114-113"></path> </g> </svg><span class="irelop"></span> <svg height="16.2749pt" style="vertical-align:-4.3507pt" version="1.1" viewbox="30.5941838 -11.9242 43.94 16.2749" width="43.94pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,30.644,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.868,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.976,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.853,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.389,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.721,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.27,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,71.426,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg></span>(<我>我</我>= 1,2),当<我>t</我>= 0,<span class="inline_break"> <svg height="14.4532pt" id="M43" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -10.1025 28.264 14.4532" width="28.264pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g 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<g transform="matrix(.013,0,0,-0.013,15.26,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里<我>f</我>是一个非线性的向量值函数。旨在提高收敛速度,所有测量值都为零均值和单位方差比例前的在线识别。在以下,系统识别是有或没有进行神经网络中隐层的存在。此外,隐藏层的情况下,使用两个和三个节点,分别,为了找到与最优识别精度。这里,由于空间限制,只有一个类型的提取异常条件选择。至于没有隐层神经网络,<svg height="12.7178pt" id="M45" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 19.477 12.7178" width="19.477pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.346,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.844,0)"> <use xlink:href="#g113-46"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.808,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和重量矩阵<span class="nowrap"> <svg height="12.9866pt" id="M46" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 17.7399 12.9866" width="17.7399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.764,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>,</span> <svg height="12.9866pt" id="M47" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 17.7399 12.9866" width="17.7399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.764,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,3.132)"> <use xlink:href="#g50-117"></use> </g> </svg>在(<一个href="#EEq10">10</一个>)设置为单位矩阵。在所有这三种情况下,给出了s形函数<span class="equation_break" id="EEq17"><span class="left_break" id="L48"></span><span class="middle_break"><span class="center_break" id="M48"> <svg height="29.2114pt" id="M48-1" version="1.1" viewbox="0 0 71.748 29.2114" width="71.748pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.02,19.988)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.26,17.039)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.77,16.857)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.04,17.039)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.21,16.857)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.47,16.857)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,50.23,19.988)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.47,17.039)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.98,16.857)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.25,17.039)"> <use xlink:href="#g113-42"></use> </g> </g> </svg> <svg height="29.2114pt" id="M48-2" version="1.1" viewbox="0 0 125.474 29.2114" width="125.474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-2"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.7,8.349)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.94,8.349)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.9,8.349)"> <use xlink:href="#g113-51"></use> </g> <rect height="0.65243" width="79.967" x="12.46" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,12.46,26.082)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.61,26.082)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.14,26.082)"> <use xlink:href="#g121-99"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.67,26.082)"> <use xlink:href="#g121-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.83,26.082)"> <use xlink:href="#g121-110"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,26.265)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.41,26.082)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.04,26.082)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.28,26.082)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.24,26.082)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.48,26.082)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.75,26.265)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.53,16.857)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,107.07,16.857)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,113.31,16.857)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,116.27,16.857)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,122.51,16.857)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="29.2114pt" id="M48-3" version="1.1" viewbox="0 0 39.024 29.2114" width="39.024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-3"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.18,16.857)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.44,16.857)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.68,16.857)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.82,16.857)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.06,16.857)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="73.2417pt" id="I48" version="1.1" viewbox="0 0 191.14 73.2417" width="191.14pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -7.67)" xlink:href="#B48-1"></use> <use transform="matrix(1 0 0 1 32.24 22.02)" xlink:href="#B48-2"></use> <use transform="matrix(1 0 0 1 152 52.42)" xlink:href="#B48-3"></use> </svg></span></span><span class="right_break" id="R48"> <svg class="label" height="11.44pt" id="M48-4" version="1.1" viewbox="0 0 19.338 11.44" width="19.338pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B48-4"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.81,9.25)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.84,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="73.2417pt" id="IL48" version="1.1" viewbox="0 0 19.42 73.2417" width="19.42pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 30.69)" xlink:href="#B48-4"></use> </svg></span></span></p> <p>给出了初始权重矩阵<span class="equation_break" id="EEq18"><span class="left_break" id="L49"></span><span class="middle_break"><span class="center_break" id="M49"> <svg height="71.2237pt" id="M49-1" version="1.1" viewbox="0 0 111.724 71.2237" width="111.724pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B49-1"> <g transform="matrix(.013,0,0,-0.013,0,18.917)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.78,22.048)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.21,22.048)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.37,22.048)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.97,18.917)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.23,18.917)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.15,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.39,9.184)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.36,9.184)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.6,9.184)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.65,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.9,27.214)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.89,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.13,27.214)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,84.1,27.214)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.34,27.214)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.65,18.917)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.76,18.917)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="71.2237pt" id="M49-2" version="1.1" viewbox="0 0 99.184 71.2237" width="99.184pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B49-2"> <g transform="matrix(.013,0,0,-0.013,0,58.962)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.77,62.094)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.21,62.094)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.36,62.094)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.96,58.962)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.23,58.962)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.15,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.39,49.229)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.35,49.229)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.24,49.229)"> <use xlink:href="#g113-49"></use> </g> <g 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transform="matrix(.013,0,0,-0.013,8.83,9.26)"> <use xlink:href="#g190-152"></use> </g> <g transform="matrix(.013,0,0,-0.013,15,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>此外,<span class="inline_break"> <svg height="31.1785pt" id="M50" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 20.398 31.1785" width="20.398pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.767,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="31.1785pt" style="vertical-align:-12.2618pt" version="1.1" viewbox="23.980183800000002 -18.9167 66.352 31.1785" width="66.352pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,24.03,2.51347e-05)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.947,-9.733)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.578,-9.733)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.818,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.073,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.909,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.111,8.297)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.742,8.297)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.982,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.286,2.51347e-05)"> <use xlink:href="#g119-154"></use> </g> </svg>,</span></span><span class="inline_break"> <svg height="31.1785pt" id="M51" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 19.414 31.1785" width="19.414pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.783,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="31.1785pt" style="vertical-align:-12.2618pt" version="1.1" viewbox="22.9961838 -18.9167 51.025 31.1785" width="51.025pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,23.046,2.51347e-05)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.964,-9.733)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,39.204,-9.733)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.6,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.095,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.468,8.297)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.708,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.984,2.51347e-05)"> <use xlink:href="#g119-154"></use> </g> </svg>,</span></span>和<span class="inline_break"> <svg height="31.1785pt" id="M52" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 20.649 31.1785" width="20.649pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.018,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="31.1785pt" style="vertical-align:-12.2618pt" version="1.1" viewbox="24.2311838 -18.9167 51.03 31.1785" width="51.03pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,24.281,2.51347e-05)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.199,-9.733)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.439,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.835,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.33,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.703,8.297)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.943,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.219,2.51347e-05)"> <use xlink:href="#g119-154"></use> </g> </svg>。</span></span>因此,解决方案<我>P</我>(<一个href="#EEq14">14</一个>)可以很容易地计算<span class="inline_break"> <svg height="31.1785pt" id="M53" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 19.289 31.1785" width="19.289pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.658,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="31.1785pt" style="vertical-align:-12.2618pt" version="1.1" viewbox="22.8711838 -18.9167 38.493 31.1785" width="38.493pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,22.921,2.51347e-05)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.838,-9.733)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.08,-9.733)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.838,8.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.08,8.297)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,54.332,2.51347e-05)"> <use xlink:href="#g119-154"></use> </g> </svg>。</span></span>自适应选择收益<我>K</我><sub>1</sub>=<我>K</我><sub>2</sub>= 15和初始状态设置为<span class="inline_break"> <svg height="15.2113pt" id="M54" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -11.9202 23.438 15.2113" width="23.438pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.429,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.807,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="15.2113pt" style="vertical-align:-3.2911pt" version="1.1" viewbox="27.0201838 -11.9202 32.717 15.2113" width="32.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,27.07,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.555,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.795,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.938,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.178,0)"> <use xlink:href="#g113-94"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.663,-5.741)"> <use xlink:href="#g50-85"></use> </g> </svg>。</span></span>应该注意的是,选择的<我>一个</我>,<我>R,</我>和<我>问</我>应该更好地确保解决方案吗<我>P</我>是一个真正的矩阵,在识别过程中可以减少计算时间。此外,自适应获得可适当增加加快识别过程。在这个基础,识别异常条件的选择训练集得到这个no-hidden-layer动态神经网络权重更新法律在[<一个href="#B32">32</一个>]。同时给出了估计和实际输出图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig6/" target="_blank">6</一个>比较的目的。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-f3f79eea08da9a7a7f3677f215670ca8"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.006a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.006b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-f3f79eea08da9a7a7f3677f215670ca8 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.006a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.006b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-f3f79eea08da9a7a7f3677f215670ca8 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 识别结果的动态神经网络没有隐藏层:(a)出口二氧化硫浓度的结果;(b)泥浆pH值的结果。</d我v> </div> </div> </div> <p>至于MPDNN与一个隐藏层,输出权值是一样的<svg height="12.9866pt" id="M55" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 22.4766 12.9866" width="22.4766pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-49"></use> </g> </svg>和<svg height="12.9866pt" id="M56" style="vertical-align:-4.3507pt" version="1.1" viewbox="-0.0498162 -8.6359 22.4766 12.9866" width="22.4766pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-49"></use> </g> </svg>集以上,体重和输入矩阵的隐层初始化<span class="equation_break" id="EEq19"><span class="left_break" id="L57"></span><span class="middle_break"><span class="center_break" id="M57"> <svg height="71.2237pt" id="M57-1" version="1.1" viewbox="0 0 95.744 71.2237" width="95.744pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B57-1"> <g transform="matrix(.013,0,0,-0.013,0,18.917)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.33,22.048)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.76,22.048)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,22.048)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.52,18.917)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.78,18.917)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.7,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.94,9.184)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.9,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.8,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.32,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.18,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.42,27.214)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.38,27.214)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.67,18.917)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.78,18.917)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="71.2237pt" id="M57-2" version="1.1" viewbox="0 0 86.514 71.2237" width="86.514pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B57-2"> <g transform="matrix(.013,0,0,-0.013,0,58.962)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.34,62.094)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.77,62.094)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.93,62.094)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.53,58.962)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.79,58.962)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.71,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.95,49.229)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.91,49.229)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.19,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.33,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.19,67.259)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.44,58.962)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.55,58.962)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R57"> <svg class="label" height="11.44pt" id="M57-3" version="1.1" viewbox="0 0 19.598 11.44" width="19.598pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B57-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.76,9.26)"> <use xlink:href="#g190-193"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.1,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>在这种情况下,该系统是由MPDNN (<一个href="#EEq10">10</一个>)两个隐层节点,基于(权重更新<一个href="#EEq15a">15</一个>),<我>K</我><sub><i>我</我></sub>= 15 (<我>我</我>= 1,2,3,4),<span class="inline_break"> <svg height="11.8174pt" id="M58" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 27.012 11.8174" width="27.012pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-140"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.803,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.381,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="11.8174pt" style="vertical-align:-3.1815pt" version="1.1" viewbox="30.5941838 -8.6359 27.013 11.8174" width="27.013pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,30.644,0)"> <use xlink:href="#g113-140"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,41.447,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.026,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="11.8174pt" style="vertical-align:-3.1815pt" version="1.1" viewbox="61.238183799999995 -8.6359 5.823 11.8174" width="5.823pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,61.288,0)"> <path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path> </g> </svg>,</span></span>而设置的参数保持不变。图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig7/" target="_blank">7</一个>提出了两种状态的识别结果。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-24a2396be607cb430b7ca1e31a5c2ffe"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.007a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.007b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-24a2396be607cb430b7ca1e31a5c2ffe partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.007a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.007b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-24a2396be607cb430b7ca1e31a5c2ffe partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 识别结果的动态神经网络隐层有两个节点:(a)出口二氧化硫浓度的结果;(b)泥浆pH值的结果。</d我v> </div> </div> </div> <p>同样,如果三个隐层节点,给出初始权重矩阵如下:<span class="equation_break" id="EEq20"><span class="left_break" id="L59"></span><span class="middle_break"><span class="center_break" id="M59"> <svg height="74.11pt" id="M59-1" version="1.1" viewbox="0 0 157.894 74.11" width="157.894pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B59-1"> <g transform="matrix(.013,0,0,-0.013,0,18.917)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.77,22.048)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.21,22.048)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.36,22.048)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.96,18.917)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.23,18.917)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48,22.048)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,52.44,22.048)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.59,22.048)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.2,18.917)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.46,18.917)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,84.38,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.62,9.184)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,93.58,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.48,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,127.34,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.58,9.184)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,136.54,9.184)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,89,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.86,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,112.1,27.214)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.06,27.214)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,127.34,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.58,27.214)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,136.54,27.214)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,145.83,18.917)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.013,0,0,-0.013,154.93,18.917)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="74.11pt" id="M59-2" version="1.1" viewbox="0 0 157.404 74.11" width="157.404pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B59-2"> <g transform="matrix(.013,0,0,-0.013,0,61.848)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.33,64.98)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.76,64.98)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.92,64.98)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.52,61.848)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.79,61.848)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,41.12,64.98)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.55,64.98)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.71,64.98)"> <use xlink:href="#g50-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.31,61.848)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.57,61.848)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.11,52.116)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,98.97,52.116)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.21,52.116)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.17,52.116)"> <path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path> </g> <g transform="matrix(.013,0,0,-0.013,120.45,52.116)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,126.69,52.116)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,129.65,52.116)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.49,70.146)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.73,70.146)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.69,70.146)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,98.97,70.146)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.21,70.146)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.17,70.146)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,125.07,70.146)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,138.94,61.848)"> <use xlink:href="#g119-154"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,145.87,46.224)"> <use xlink:href="#g50-85"></use> </g> <g transform="matrix(.013,0,0,-0.013,154.44,61.848)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="74.11pt" id="I59" version="1.1" viewbox="0 0 160.98 74.11" width="160.98pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B59-1"></use> <use transform="matrix(1 0 0 1 3.46 0)" xlink:href="#B59-2"></use> </svg></span></span><span class="right_break" id="R59"> <svg class="label" height="11.44pt" id="M59-3" version="1.1" viewbox="0 0 21.518 11.44" width="21.518pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B59-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.61,9.26)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.02,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="74.11pt" id="IL59" version="1.1" viewbox="0 0 21.6 74.11" width="21.6pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 31.12)" xlink:href="#B59-3"></use> </svg></span></span></p> <p>剩余的参数选择相同在前两种情况;识别结果如图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig8/" target="_blank">8</一个>。应该提到重量参数矩阵的过多可能造成限制识别速度。因此,上述权重矩阵的某些元素设置为零,在识别过程中保持不变。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-f66403a3c09345a28b608a9b80f92d47"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.008a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.008b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-f66403a3c09345a28b608a9b80f92d47 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.008a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.008b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-f66403a3c09345a28b608a9b80f92d47 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 识别结果与三个节点的动态神经网络隐层:(a)出口二氧化硫浓度的结果;(b)泥浆pH值的结果。</d我v> </div> </div> </div> <p>接下来,识别是进行测试设置相同的参数。由于空间限制,结果并没有显示出来。相反,三种神经网络的识别性能测量的均方误差(MSE)标准,在训练集和测试集和相应的结果展示在表<一个href="//www.newsama.com/journals/complexity/2020/6046729/tab2/" target="_blank">2</一个>。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 在训练集和测试集识别结果。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/complexity/2020/6046729/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <p>从表<一个href="//www.newsama.com/journals/complexity/2020/6046729/tab2/" target="_blank">2</一个>,它可以很容易地得出结论,MPDNN优于no-hidden-layer的训练集和测试集。更具体地说,有三个节点在隐藏层具有最佳的识别性能。因为以下部分的控制方案的设计是基于确定性等价的原则,因此,控制性能主要取决于识别模型的准确性。在这个基地,MPDNN选择隐层的三个节点模型其他两种类型的异常条件基于各自的训练集,他们会提供下面的控制目的。</p> <h5 id="sec4.2">4.2。控制设计</h5> <p>正如在导论部分所讨论的,真的很难施加有效的控制整个脱硫过程;这可以归因于这样一个事实:实际操作环境WLFGD系统是复杂的和多方面的。上述所有因素表明,自适应multimodel控制策略特别适合应对这样的问题,在大型的非线性系统参数不确定性时变环境下需要被控制。然而,也存在一些问题阻碍了multimodel控制的应用程序在实际场景中,我们将在下面进行讨论。</p> <p>为了简化博览会,一些数学符号引入问题的声明。让<我>p</我>的参数向量植物在某一个瞬间,<svg height="13.5007pt" id="M60" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 9.932 13.5007" width="9.932pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>表示的参数<我>我</我>模型在同一时刻多个模型。假设<我>p</我>和<svg height="13.5007pt" id="M61" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 9.932 13.5007" width="9.932pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>躺在<我>d</我>维紧致集<我>U</我>在参数空间。我们的目标是通过多个模型估计每一个瞬间。至于<我>我</我>th固定模型,参数向量<svg height="13.5007pt" id="M62" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 9.932 13.5007" width="9.932pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>位于相同的位置。相反,一个自适应模型近似<我>p</我>逐步由初始值参数调整,因此自适应模型参数时变之前达到收敛。到目前为止,进行了大量的研究,但都在线性和非线性情况下,找到最优的实现multimodel控制,和不同的组合模型进行了研究,其中包括(1)固定模型;(2)自适应模型;(3)固定模型和自由奔跑自适应模型;和(4)固定模型,和自由奔跑自适应模型初始化时。它已经证明过去的控制体系结构,这是这项工作的兴趣,可以产生最佳的性能,读者可以参考(<一个href="#B36">36</一个>,<一个href="#B37">37</一个>为更多的细节。使用这样的结构,只要其中一个固定的模型选择、参数自适应模型将重置为初始化时的选择模型,然后适应参数从初始化的。前提是<我>p</我>坐落在<我>U</我>在某个瞬间,附近的<svg height="15.7176pt" id="M63" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 32.03 15.7176" width="32.03pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,6.292,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.895,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.978,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.489,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.489,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,22.038,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.598,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>可以被视为一个类<svg height="15.7176pt" id="M64" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9343 15.7176" width="33.9343pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <path d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z" id="g113-86"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,13.117,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.173,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.684,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.684,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.232,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.792,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>分布在<我>U</我>。在这种情况下,固定模型作为提供初始参数估计<我>p</我>,使其包含在一定<我>U</我><sub><i>我</我></sub>。然后,优化基础上进行<span class="nowrap"> <svg height="13.5007pt" id="M65" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 9.932 13.5007" width="9.932pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>,</span>也就是说,一个点<我>U</我><sub><i>我</我></sub>渐近收敛于真实的参数<我>p</我>。这一过程的两个阶段可以消除瞬态和稳态误差,分别。显然,这样的控制体系结构是否可以有效地应用在很大程度上取决于参数之间的亲密关系<svg height="13.5007pt" id="M66" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 7.891 13.5007" width="7.891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> </svg>(即固定模型。,在我t我一个lp一个rameters of the adaptive model at switching instant) and<我>p</我>真正的植物在某一个瞬间。事实上,大型初始参数自适应模型的误差会导致贫穷的瞬态响应,并可能需要长时间适应和解决,限制使用multimodel自适应控制实际上在很大程度上。因此,适当的选择<svg height="13.5007pt" id="M67" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -10.0713 7.891 13.5007" width="7.891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,1.781,-1.044)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-113"></use> </g> </svg>对于不同的固定模式,有效优化的先决条件在随后的阶段,是最重要的。</p> <p>除了初始参数的定性问题的决心,一个定量的问题关于固定模型的数量也是强大的。后者的问题强加限制这种控制策略的实际应用,计算开销和效率,处理的数量模型必须考虑。从实用的角度,通常情况下,植物只有几个子集之间切换<我>U</我>。因此,是没有意义的建筑固定模型与参数不当。处理两个,上面提到的问题,足够的知识<我>U</我>应该获得这样的参数固定模型得到;此外,每个子集<我>U</我><sub><i>我</我></sub>(即。,thecorresponding area in which adaptation of parameters takes place) could be determined. To this end, as indicated earlier, anomalous conditions were analyzed and extracted in turn and then subdivided into varied types. In this sense, information regarding anomalous conditions on-site can be obtained thoroughly, based on which the number of fixed models is therefore determined. Our idea is illustrated intuitively in the form of a flow diagram (Figure<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig9/" target="_blank">9</一个>)。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-bcb6e6989188433c3d2de67732ea0321"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.009.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-bcb6e6989188433c3d2de67732ea0321 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.009_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-bcb6e6989188433c3d2de67732ea0321 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 计划的完成控制过程。</d我v> </div> </div> </div> <p>从图中我们可以很清楚地看到<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig9/" target="_blank">9</一个>multimodel控制在我们的工作过程划分为两个部分,在左中场部分详细分析了不同类型的异常条件数据探索和挖掘。通过这种方式,获得的定性和定量信息异常,可以进一步利用提供指导模型组建筑右半边图的一部分<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig9/" target="_blank">9</一个>。控制设计阶段,设计相应的控制器为每个构造模型和控制器<svg height="15.7176pt" id="M68" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9473 15.7176" width="33.9473pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,13.13,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.186,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.697,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.697,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.245,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.805,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>建立了。事实上,模型在模型组<svg height="15.7176pt" id="M69" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 30.0327 15.7176" width="30.0327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,9.23,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.286,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.797,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.797,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.345,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,24.905,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>和控制器<svg height="15.7176pt" id="M70" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9473 15.7176" width="33.9473pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.13,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.186,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.697,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.697,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.245,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.805,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>是成对。也就是说,一对<svg height="15.7176pt" id="M71" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 39.2712 15.7176" width="39.2712pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.817,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.436,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.492,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.003,-5.741)"> <use xlink:href="#g50-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.003,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,28.551,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.111,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>选择在每个瞬间基于切换方案介绍。</p> <p>如上所述在介绍性的部分,这两个控制变量,泥浆pH值,出口烟气浓度是重要的指标,可以测量脱硫的效果。在我们的案例中,监管问题会解决,即。,multimodel adaptive control was carried out to track the reference values we set. The set point of slurry pH value should make trade-off between desulphurization efficiency and safety problems caused by corrosiveness. It has been verified in [<一个href="#B38">38</一个>],pH值为5.5的合理价值在正常操作条件。此外,所需的出口烟气浓度设置为3.6毫克/米<sup>3</sup>根据实际条件和排放标准。此后,所需的状态表示为<span class="inline_break"> <svg height="15.7542pt" id="M72" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.9202 24.609 15.7542" width="24.609pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.267,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.978,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="15.7542pt" style="vertical-align:-3.834pt" version="1.1" viewbox="28.1911838 -11.9202 47.449 15.7542" width="47.449pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,28.241,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.726,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.993,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.928,3.784)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,46.072,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.215,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.483,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.418,3.784)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.562,0)"> <use xlink:href="#g113-94"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.047,-5.741)"> <use xlink:href="#g50-85"></use> </g> </svg></span>和控制误差向量是写成<span class="inline_break"> <svg height="10.4525pt" id="M73" style="vertical-align:-0.3500004pt" version="1.1" viewbox="-0.0498162 -10.1025 16.645 10.4525" width="16.645pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path> </g> <g transform="matrix(.013,0,0,-0.013,9.014,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="10.4525pt" style="vertical-align:-0.3500004pt" version="1.1" viewbox="20.227183800000002 -10.1025 34.327 10.4525" width="34.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.277,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.544,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.529,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,48.494,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.065,0)"> <use xlink:href="#g113-121"></use> </g> </svg>。</span></span>区分<我>e</我>关于<我>t</我>这样可以派生动力学的控制误差,表示为<span class="equation_break" id="EEq21"><span class="left_break" id="L74"></span><span class="middle_break"><span class="center_break" id="M74"> <svg height="16.0061pt" id="M74-1" version="1.1" viewbox="0 0 64.634 16.0061" width="64.634pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B74-1"> <g transform="matrix(.013,0,0,-0.013,6.31,11.82)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.31,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.63,12.042)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.16,11.82)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.9,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.16,5.778)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.1,15.826)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.18,12.042)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.13,8.532)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.29,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.71,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.01,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.67,12.042)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R74"> <svg class="label" height="11.44pt" id="M74-2" version="1.1" viewbox="0 0 19.468 11.44" width="19.468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B74-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.58,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>然后(<一个href="#EEq10">10</一个>)调用重写(<一个href="#EEq21">21</一个>)以下形式:<span class="equation_break" id="EEq22"><span class="left_break" id="L75"></span><span class="middle_break"><span class="center_break" id="M75"> <svg height="16.3923pt" id="M75-1" version="1.1" viewbox="0 0 61.168 16.3923" width="61.168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B75-1"> <g transform="matrix(.013,0,0,-0.013,6.32,11.82)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.32,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.64,12.042)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.16,11.82)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.9,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.17,5.778)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.11,15.826)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.18,12.042)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.13,8.532)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.3,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.72,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.01,15.173)"> <use xlink:href="#g50-117"></use> </g> </g> </svg> <svg height="16.3923pt" id="M75-2" version="1.1" viewbox="0 0 121.495 16.3923" width="121.495pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B75-2"> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,12.042)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.9,12.042)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.46,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.03,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.23,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.83,12.042)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.37,12.042)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.15,15.173)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.58,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.74,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.43,12.042)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.95,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,87.98,12.042)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,95.31,15.173)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,99.74,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,101.9,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,107.02,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.59,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,112.79,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,116.49,12.042)"> <use xlink:href="#g119-6"></use> </g> </g> </svg> <svg height="16.3923pt" id="M75-3" version="1.1" viewbox="0 0 116.394 16.3923" width="116.394pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B75-3"> <g transform="matrix(.013,0,0,-0.013,0,12.042)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,12.042)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.32,15.173)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,25.75,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.91,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.6,12.042)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.12,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,46.15,12.042)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.48,15.173)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.91,15.173)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.07,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.19,11.82)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.76,12.042)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,70.96,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.66,12.042)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.89,12.042)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.58,12.042)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.61,12.042)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.53,15.173)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.2,12.042)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,113.43,12.042)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R75"> <svg class="label" height="11.44pt" id="M75-4" version="1.1" viewbox="0 0 21.158 11.44" width="21.158pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B75-4"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.61,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.66,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <p>如果我们选择的控制输入表单<span class="equation_break" id="EEq23"><span class="left_break" id="L76"></span><span class="middle_break"><span class="center_break" id="M76"> <svg height="16.7067pt" id="M76-1" version="1.1" viewbox="0 0 54.348 16.7067" width="54.348pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B76-1"> <g transform="matrix(.013,0,0,-0.013,0,12.356)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.69,12.356)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.72,12.356)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.65,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.31,12.356)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.99,12.356)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.26,12.356)"> <use xlink:href="#g113-118"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.19,15.488)"> <use xlink:href="#g50-117"></use> </g> </g> </svg> <svg height="16.7067pt" id="M76-2" version="1.1" viewbox="0 0 105.57 16.7067" width="105.57pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B76-2"> <g transform="matrix(.013,0,0,-0.013,0,12.356)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.26,12.356)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.07,12.356)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.92,12.356)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,36.7,15.488)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,41.13,15.488)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.29,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,46.98,12.356)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.51,12.356)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.53,12.356)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,68.86,15.488)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,73.29,15.488)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,75.45,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.57,12.134)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,79.14,12.356)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,86.34,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.04,12.356)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.09,12.356)"> <use xlink:href="#g119-2"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,100.01,5.055)"> <use xlink:href="#g54-36"></use> </g> </g> </svg> <svg height="16.7067pt" id="M76-3" version="1.1" viewbox="0 0 2.964 16.7067" width="2.964pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B76-3"> <g transform="matrix(.013,0,0,-0.013,0,12.356)"> <use xlink:href="#g113-46"></use> </g> </g> </svg> <svg height="16.7067pt" id="M76-4" version="1.1" viewbox="0 0 120.104 16.7067" width="120.104pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B76-4"> <g transform="matrix(.013,0,0,-0.013,0,12.356)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.85,12.356)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.99,12.356)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.26,6.093)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,21.19,16.14)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.24,12.356)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.78,12.356)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.55,15.488)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,55.99,15.488)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.14,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.83,12.356)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.36,12.356)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,76.38,12.356)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,83.72,15.488)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,88.15,15.488)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,90.31,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.43,12.134)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,94,12.356)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,101.2,15.488)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,104.89,12.356)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,109.95,12.356)"> <use xlink:href="#g119-2"></use> </g> <g transform="matrix(.013,0,0,-0.013,117.14,12.356)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="40.5486pt" id="I76" version="1.1" viewbox="0 0 164.72 40.5486" width="164.72pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B76-1"></use> <use transform="matrix(1 0 0 1 58.49 0)" xlink:href="#B76-2"></use> <use transform="matrix(1 0 0 1 12.87 23.842)" xlink:href="#B76-3"></use> <use transform="matrix(1 0 0 1 18.74 23.84)" xlink:href="#B76-4"></use> </svg></span></span><span class="right_break" id="R76"> <svg class="label" height="11.44pt" id="M76-5" version="1.1" viewbox="0 0 21.018 11.44" width="21.018pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B76-5"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.64,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.52,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="40.5486pt" id="IL76" version="1.1" viewbox="0 0 21.1 40.5486" width="21.1pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 14.34)" xlink:href="#B76-5"></use> </svg></span></span>在右边第一项(<一个href="#EEq23">23</一个>)表示Moore-Penrose逆矩阵<span class="nowrap"> <svg height="13.639pt" id="M77" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 65.909 13.639" width="65.909pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.058,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.404,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.902,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.234,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.666,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.822,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.944,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.515,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.717,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.411,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</span></p> <p><span class="statement" id="assump1"><span class="statement-title"><i class="statement-title">假设1。</我></span>节点的数量<我>l</我>在隐藏层和州的数量<我>n</我>满足<span class="inline_break"> <svg height="10.4081pt" id="M78" style="vertical-align:-1.11977pt" version="1.1" viewbox="-0.0498162 -9.28833 14.761 10.4081" width="14.761pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z" id="g113-109"></path> </g> <g transform="matrix(.013,0,0,-0.013,7.13,0)"> <use xlink:href="#g117-94"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="10.4081pt" style="vertical-align:-1.11977pt" version="1.1" viewbox="18.343183800000002 -9.28833 6.69 10.4081" width="6.69pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,18.393,0)"> <use xlink:href="#g113-111"></use> </g> </svg>。</span></span>此外,<我>n</我>——- - - - - -<我>l</我>矩阵<svg height="13.639pt" id="M79" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 65.909 13.639" width="65.909pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.058,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.404,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.902,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.234,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.666,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.822,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.944,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.515,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.717,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.411,0)"> <use xlink:href="#g113-42"></use> </g> </svg>已经全部行排名,也就是说,<span class="inline_break"> <svg height="13.639pt" id="M80" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 91.631 13.639" width="91.631pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path> </g> <g transform="matrix(.013,0,0,-0.013,5.488,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.973,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.75,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,25.182,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.339,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.031,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.377,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.875,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,50.207,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,54.639,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,56.796,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.917,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.488,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.69,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.385,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.883,0)"> <use xlink:href="#g113-94"></use> </g> <g transform="matrix(.013,0,0,-0.013,84,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="13.639pt" style="vertical-align:-4.35067pt" version="1.1" viewbox="95.2121838 -9.28833 6.526 13.639" width="6.526pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,95.262,0)"> <use xlink:href="#g113-111"></use> </g> </svg>,</span></span>这样的产品<svg height="13.639pt" id="M81" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 65.909 13.639" width="65.909pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.058,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.404,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.902,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.234,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.666,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.822,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.944,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.515,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.717,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.411,0)"> <use xlink:href="#g113-42"></use> </g> </svg>及其Moore-Penrose逆等于单位矩阵。特别是,<svg height="13.639pt" id="M82" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 65.909 13.639" width="65.909pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.058,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.404,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.902,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.234,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.666,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.822,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.944,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.515,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.717,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.411,0)"> <use xlink:href="#g113-42"></use> </g> </svg>是一个方阵什么时候<我>l</我>=<我>n</我>,然后成为矩阵的非奇异性条件<svg height="13.639pt" id="M83" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 65.909 13.639" width="65.909pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.777,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.209,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.365,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.058,0)"> <use xlink:href="#g113-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.404,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.902,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,40.234,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.666,3.132)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.822,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.944,-.222)"> <use xlink:href="#g119-17"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.515,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,57.717,3.132)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.411,0)"> <use xlink:href="#g113-42"></use> </g> </svg>(<一个href="#B39">39</一个>,<一个href="#B40">40</一个>]。<br>假设,用(<一个href="#EEq23">23</一个>)(<一个href="#EEq22">22</一个>),获得的闭环动态误差:<span class="equation_break" id="EEq24"><span class="left_break" id="L84"></span><span class="middle_break"><span class="center_break" id="M84"> <svg height="63.9731pt" id="M84-1" version="1.1" viewbox="0 0 134.125 63.9731" width="134.125pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B84-1"> <g transform="matrix(.013,0,0,-0.013,6.32,10.371)"> <use xlink:href="#g117-11"></use> </g> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,5.32,13.725)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.64,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.9,10.593)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.53,10.593)"> <use 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</svg></span></span>显然,作为<我>一个</我>是一个赫维茨矩阵,控制误差是我们实现渐近稳定的控制输入。此外,开关时间和顺序的多个模型是完全依赖于交换计划。切换方案设计的基础上,每个模型的性能指标。保证切换的准确性、瞬时和累计识别错误都是需要考虑的性能指标<span class="nowrap"> <svg height="15.7176pt" id="M85" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 43.8252 15.7176" width="43.8252pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <path d="M429 650H175L169 622C251 614 259 612 244 532L174 152C163 91 152 37 135 -6C109 -72 67 -101 23 -113L33 -144C45 -143 73 -134 102 -119C186 -76 229 -1 254 133L327 532C341 609 347 613 423 622L429 650Z" id="g113-75"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,9.542,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.598,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.096,0)"> <use 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transform="matrix(.013,0,0,-0.013,41.473,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.906,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.404,0)"> <use xlink:href="#g113-126"></use> </g> </svg>在每一个实例。较小的性能指标<我>J</我><sub><i>我</我></sub>识别的准确性越高吗<我>我</我>模型。在这个基础,相应的控制器<svg height="12.5794pt" id="M91" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 25.286 12.5794" width="25.286pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.675,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.173,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.606,0)"> <use xlink:href="#g113-42"></use> </g> </svg>选择,这样是最好的控制性能可以产生相应的瞬间。</span></p> <h4 id="simulation-studies">5。模拟研究</h4> <p>在本节中,不同multimodel控制模式的设计和分析的基础上,提取异常条件在以前的部分。此外,MPDNN隐藏层的三个节点(没有进一步规范,MPDNN表示这种结构在本节中)用于在下列情况下模型和控制器的设计。</p> <h5 id="sec5.1">5.1。准备工作</h5> <p>在之前的章节中,提取不同类型的异常条件,其中一个对其训练集模型通过MPDNN。神经网络的收敛重量记录<svg height="12.4698pt" id="M92" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 11.2181 12.4698" width="11.2181pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>在这种情况下。同样,其他两种类型的条件可以确定各自的训练集,在相同的技术(包括数据的预处理)和需要选择合适的参数用于MPDNN。通过这种方式,预期的识别精度(MSE为两国在两种情况下小于2<我>e</我>−4),三套参数向量。<span class="equation_break" id="EEq26"><span class="left_break" id="L93"></span><span class="middle_break"><span class="center_break" id="M93"> <svg height="16.1222pt" id="M93-1" version="1.1" viewbox="0 0 128.374 16.1222" width="128.374pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B93-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.14,13.725)"> <path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 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id="g113-107"></path> </g> <g transform="matrix(.013,0,0,-0.013,9.13,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.4,10.593)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.64,10.593)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.78,10.593)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.02,10.593)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.16,10.593)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.4,10.593)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="38.1373pt" id="I93" version="1.1" viewbox="0 0 180.95 38.1373" width="180.95pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B93-1"></use> <use transform="matrix(1 0 0 1 128.43 23.58)" 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</g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>(<我>我</我>= 1,2)如下:<span class="equation_break" id="EEq27"><span class="left_break" id="L97"></span><span class="middle_break"><span class="center_break" id="M97"> <svg height="74.5277pt" id="M97-1" version="1.1" viewbox="0 0 92.204 74.5277" width="92.204pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B97-1"> <g transform="matrix(.013,0,0,-0.013,0,19.021)"> <use xlink:href="#g113-88"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.77,22.153)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.46,19.021)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.72,19.021)"> <use xlink:href="#g119-153"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.64,9.288)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.64,12.42)"> <use 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<p>上述结果权重矩阵用于建立固定模型,分别。测试和验证了该方法的有效性在实际WFLGD系统,仿真平台的异常条件设置在我们的案例研究。在这个平台中,每个类型的异常环境模拟通过MPDNN在上面的形式在各自的测试数据。没有普遍性,正常状态被拟合MPDNN考虑剩余的部分正常运行数据。MPDNN保证模拟的准确性,参数在每个情况下测定试验和错误,这样能够达到最优的识别性能。这样,这两个州的最后均方识别错误在所有四个条件低于1.042<我>e</我>−3。在这个阶段,固定模型和仿真环境WLFGD系统已经建立了。</p> <p>上面的平台建设将模拟三种类型的异常条件和正常操作条件下每30单位的时候,它可以表示为<span class="equation_break" id="EEq29"><span class="left_break" id="L99"></span><span class="middle_break"><span class="center_break" id="M99"> <svg height="77.6774pt" id="M99-1" version="1.1" viewbox="0 0 161.694 77.6774" width="161.694pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B99-1"> <g transform="matrix(.013,0,0,-0.013,0,16.395)"> <path d="M660 1109V1150C557 1150 406 1122 406 886V0H513V923C513 1011 529 1089 660 1109Z" id="g119-47"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,20.179)"> <path d="M513 0V330H406V0H513Z" id="g119-55"></path> </g> <g transform="matrix(.013,0,0,-0.013,0,23.963)"> <use xlink:href="#g119-55"></use> </g> <g 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transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-193"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.89,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="77.6774pt" id="IL99" version="1.1" viewbox="0 0 21.47 77.6774" width="21.47pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 32.91)" xlink:href="#B99-2"></use> </svg></span></span></p> <p><span class="statement" id="rem1"><span class="statement-title"><i class="statement-title">备注1。</我></span>初始权重的模型主要影响multimodel自适应控制的控制性能,尤其是在实际应用。感兴趣的问题本文主要关心的是在异常条件下初始权重的设置;正常操作条件的讨论和分析的范围。因此,我们不安排测试设置和构建模型只有一个正常的状态。<br>所有MPDNN仿真平台的初始状态设置为<span class="inline_break"> <svg height="15.2113pt" id="M100" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -11.9202 23.411 15.2113" width="23.411pt" 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</svg>,</span></span>和<svg height="9.49473pt" id="M102" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.30254 9.49473" width="7.30254pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-233"></use> </g> </svg>被选中的性能指标(<一个href="#EEq21">21</一个>)。在下面,模拟在不同的情况下会进行序列,与客观的测试的有效性MPDNN multimodel不同组合的固定模型的自适应控制。</span></p> <h5 id="sec5.2">5.2。实验</h5> <p>如前所述,通过验证,固定的模式模型与自适应模型初始化时在multimodel控制最优控制效果。此外,这项工作更侧重于讨论的主题选择的固定模型在实际multimodel控制。因此,组合不同的模型将不会参与下面的情况下。相反,不同的施工方法的固定模型模拟来测试本文中提出的方法的有效性。为了简化符号,在以下情况下,<我>我</我>th MPDNN固定模型来标示<我>如果</我><sub><i>我</我></sub>和传统MPDNN初始化自适应模型表示<我>IA</我><sub>1</sub>和<我>IA</我><sub>2,</sub>分别。<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>案例1</我>。单身自由奔跑自适应模型:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">单一识别模型自适应控制的最基本形式。模型的参数调整与变化的环境。这类自适应控制可以有效减缓环境发生变化,而大型过度会出现在即时意料之外的环境。的初始值<我>IA</我><sub>1</sub>在这种情况下设置<span class="nowrap"> <svg height="12.4698pt" id="M103" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 11.2181 12.4698" width="11.2181pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>。</span>图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig10/" target="_blank">10 ()</一个>显示在不同条件下的反应工厂,和图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig10/" target="_blank">10 (b)</一个>控制误差的绝对值。很明显,存在很大的瞬态错误条件变化时30,60岁,90单位的时间。更糟的是,90年代后,强烈的振荡起来,工厂已经失控,这表明,单一的自适应模型在实际WLFGD场景中不是一个合适的选择。</span></span></span></span></span></span></p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-33b7d6f757b17a4ae8c9c3dc731881bb"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0010a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0010b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-33b7d6f757b17a4ae8c9c3dc731881bb partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0010a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0010b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-33b7d6f757b17a4ae8c9c3dc731881bb partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 控制反应的案例1:(a)系统输出;(b)控制误差的绝对值。</d我v> </div> </div> </div> <span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>例2。</我>三个固定模型,基于时间的一个自适应模型,和一个初始化自适应模型:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在这种情况下,建筑的<svg height="15.535pt" id="M104" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 37.0399 15.535" width="37.0399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.426,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.212,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.267,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.778,-5.741)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.778,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.327,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.887,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>依赖于时间序列的分区。具体而言,所有提取异常点被命令在提升时间序列。点同样分为三个部分,和每一个用来设置一个固定的模式与以前相同的方式融合权重和适当的参数,和两个国家均方识别错误的三个模型都在8.703以下<我>e</我>−4。至于<我>IA</我><sub>1</sub>应用在这种情况下,旨在控制核电站在正常情况下,初始参数设置接近权重对应常态的仿真平台。此外,的重量<我>IA</我><sub>1</sub>将再次被初始化的参数发生变化时的仿真平台。系统响应和控制误差的绝对值数据<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig11/" target="_blank">(11日)</一个>和<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig11/" target="_blank">11 (b)</一个>,分别。凭直觉,而案例2中使用的控制方式,控制性能都得到了极大的改进。看到,在不同的操作条件下植物是可控的。然而,过激的植物参数变化时有点大。特别是90年代在即时,需要较长时间的适应过程。</span></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>例3。</我>三个基于范围固定模型,一个自适应模型,和一个初始化自适应模型:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在之前的章节中,异常操作数据映射到二维特征空间通过主成分分析。在这里,建立<svg height="15.535pt" id="M105" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 37.0399 15.535" width="37.0399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.426,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.212,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.267,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.778,-5.741)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.778,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.327,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.887,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>是通过分区的第一主成分(PC1)。通过这种方式,阈值向量<span class="inline_break"> <svg height="12.7178pt" id="M106" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 17.686 12.7178" width="17.686pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.055,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="21.268183800000003 -9.28833 18.492 12.7178" width="18.492pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,21.318,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.803,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.9,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,36.846,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="41.9401838 -9.28833 15.77 12.7178" width="15.77pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,41.99,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,48.086,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.033,0)"> <use xlink:href="#g113-94"></use> </g> </svg></span>通过均匀地把各种PC1分成三个部分。然后,异常点对应于三个间隔,即<span class="inline_break"> <svg height="12.7178pt" id="M107" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 30.106 12.7178" width="30.106pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.485,0)"> <path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z" id="g113-122"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,11.427,3.132)"> <path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,19.016,3.132)"> <path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,21.519,3.132)"> <path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path> </g> <g transform="matrix(.013,0,0,-0.013,27.142,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span><span class="nowrap"> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="32.2361838 -9.28833 15.734 12.7178" width="15.734pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,32.286,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.383,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.329,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,</span></span><span class="inline_break"> <svg height="12.7178pt" id="M108" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 18.492 12.7178" width="18.492pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.485,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.582,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.528,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span><span class="nowrap"> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="20.622183800000002 -9.28833 15.731 12.7178" width="15.731pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.672,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.769,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.715,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,</span></span>和<span class="inline_break"> <svg height="12.7178pt" id="M109" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 18.492 12.7178" width="18.492pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-92"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.485,0)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.582,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.528,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="20.622183800000002 -9.28833 28.212 12.7178" width="28.212pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.672,0)"> <use xlink:href="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.614,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.176,3.132)"> <path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z" id="g58-95"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,39.261,3.132)"> <path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path> </g> <g transform="matrix(.013,0,0,-0.013,44.206,0)"> <use xlink:href="#g113-94"></use> </g> </svg></span>(<我>y</我><sub>最小值</sub>和<我>y</我><sub>马克斯</sub>是PC1的最小值和最大值),收集并用于构建三个固定模型由MPDNN。<我>IA</我><sub>1</sub>相同的设置,在例2。图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig12/" target="_blank">12</一个>在这种情况下提出了相应的控制响应。通过比较控制误差的绝对值如图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig12/" target="_blank">12 (b)</一个>与其对应的图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig11/" target="_blank">11 (b)</一个>,发现即时30年代的瞬态误差降低。不过,更大的超调90年代发生在参数变化。</span></span></span></span></span></span> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-0db3597276d67fcaa9ad39b26127468c"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0011a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0011b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-0db3597276d67fcaa9ad39b26127468c partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0011a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0011b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-0db3597276d67fcaa9ad39b26127468c partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图11</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 控制的响应情况2:(a)系统输出;(b)控制误差的绝对值。</d我v> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-108f6d5eb711e46af1f04ac3d9b0bb9c"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0012a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0012b.jpg"> <br> <strong>(b)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-108f6d5eb711e46af1f04ac3d9b0bb9c partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0012a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0012b_th.jpg"><br><strong>(b)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-108f6d5eb711e46af1f04ac3d9b0bb9c partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图12</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 控制反应的案例3:(a)系统输出;(b)控制误差的绝对值。</d我v> </div> </div> </div> <span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>例4。</我>三个AMF clustering-based固定模型,一个自适应模型,和一个初始化自适应模型:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">4,固定模型的确定依赖于异常条件的提取结果获得的部分<一个href="#sec3">3</一个>。因此,三个固定模型构建基于权重<span class="nowrap"> <svg height="15.535pt" id="M110" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 31.4681 15.535" width="31.4681pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.511,0)"> <use xlink:href="#g113-230"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.66,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.716,0)"> <use xlink:href="#g113-126"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.227,-5.741)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.227,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.775,3.784)"> <use xlink:href="#g54-34"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,26.335,3.784)"> <use xlink:href="#g50-50"></use> </g> </svg>。</span>与此同时,设置<我>IA</我><sub>1</sub>符合上述情况。由此产生的输出和控制错误的植物中描述的数据<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig13/" target="_blank">(13日)</一个>和<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig13/" target="_blank">13 (b)</一个>,分别。很明显,在这种情况下控制方式可以产生更好的控制性能与上面提到的所有情况。从瞬态响应的角度来看,当参数的变化在不同的瞬间,可以保持小超调的输出。相反,稳态误差可以达到零。这种改进的原因在于减少初始参数错误<我>IA</我><sub>2</sub>。从切换显示序列图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig13/" target="_blank">13 (c)</一个>,每次当异常条件变化的类型,固定模型最少的性能指标会选择降低瞬态错误首先,然后<我>IA</我><sub>2</sub>将接任控制器到下环境出现。作为固定模型的建立,我们可以大致描述实际环境在不同的时间范围,瞬态误差相对较小当切换到一个新的环境。同时,由于固定参数模型之间的亲密和真实的,需要适应的时间<我>IA</我><sub>2</sub>回到集合点。</span></span></span></span></span></span> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-9068ce5f627b67a3974e27129b011b3d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0013a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0013b.jpg"> <br> <strong>(b)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0013c.jpg"> <br> <strong>(c)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-9068ce5f627b67a3974e27129b011b3d partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" 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class="caption-text">图13</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig13/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 控制反应的案例4:(a)系统输出;(b)控制误差的绝对值;(c)切换序列。</d我v> </div> </div> </div> <span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>例5。</我>额外的固定模型的基础上,例4,一个自适应模型,和一个初始化自适应模型:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">例5的设计是建立在过去的情况。进一步验证案例4中固定模型构造的有效性,额外的三个固定的模型<span class="inline_break"> <svg height="12.5794pt" id="M111" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 24.109 12.5794" width="24.109pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.498,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.413,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.199,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.145,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.5794pt" style="vertical-align:-3.29107pt" version="1.1" viewbox="26.2381838 -9.28833 19.611 12.5794" width="19.611pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,26.288,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.203,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.989,3.132)"> <path d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z" id="g50-54"></path> </g> <g transform="matrix(.013,0,0,-0.013,42.935,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.5794pt" style="vertical-align:-3.29107pt" version="1.1" viewbox="48.0291838 -9.28833 21.43 12.5794" width="21.43pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,48.079,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.993,0)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.779,3.132)"> <path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z" id="g50-55"></path> </g> <g transform="matrix(.013,0,0,-0.013,64.726,0)"> <use xlink:href="#g113-42"></use> </g> </svg></span>被认为是。此外,每个额外的固定模型的权重设置的范围内随机−1和1。系统响应和误差大小在每个即时给出数据<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig14/" target="_blank">(14日)</一个>和<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig14/" target="_blank">14 (b)</一个>分开。与同行相比,在图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig13/" target="_blank">13</一个>,很明显,没有多少改善瞬态响应的变化异常条件。事实上,它可以看到,系统响应在正常操作条件下更糟。原因可以总结的切换序列如图<一个href="//www.newsama.com/journals/complexity/2020/6046729/fig14/" target="_blank">14 (c)</一个>。阶段控制在正常条件下,三个额外的固定模型的参数接近真实参数的植物可能会导致出现的频繁切换,导致间歇的时间超过60至90台。此外,在模拟计算成为非常大的数量在这个控制模式,这再一次证明了不合适的型号选择应用multimodel时控制在实际场景中可能引起严重后果。</span></span></span></span></span></span> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-d82c2e1b38fd54a114c4808383a07cd9"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0014a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0014b.jpg"> <br> <strong>(b)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/figures/6046729.fig.0014c.jpg"> <br> <strong>(c)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-d82c2e1b38fd54a114c4808383a07cd9 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0014a_th.jpg"><br><strong>(一)</strong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0014b_th.jpg"><br><strong>(b)</strong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/complexity/volume-2020/6046729/thumbnails/6046729.fig.0014c_th.jpg"><br><strong>(c)</strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-d82c2e1b38fd54a114c4808383a07cd9 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图14</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/complexity/2020/6046729/fig14/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 控制反应的案例4:(a)系统输出;(b)控制误差的绝对值;(c)切换序列。</d我v> </div> </div> </div> <h4 id="conclusions">6。结论</h4> <p>本文关注于解决实际控制问题WLFGD系统通过使用MPDNN multimodel控制策略。multimodel控制应用程序的困难在现实世界中规定<一个href="#sec4">第四节</一个>。的目标实现multimodel控制在异常条件下的背景下,一连串的技术已经采用的搜索和提取不同类型的异常。MPDNN,有一个很好的近似能力不确定的环境中,用于标识这些异常条件,建立相应的模型。表示在<一个href="#sec5">第五节</一个>相比,在其他情况下,控制性能的MPDNN multimodel控制系统,它是建立在过程中,我们提出了工作,为模拟WLFGD系统能产生满意的控制性能。基于这个方向,在我们未来的工作将主要关注组合数据分析技术和自适应控制的上下文中multimodel控制。</p> <h4 id="data-availability">数据可用性</h4> <p>使用的实验数据来支持本研究的结果包括在本文中。</p> <h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者宣称没有利益冲突有关的出版。</p> <h4 id="acknowledgments">确认</h4> <p>这项工作得到了国家自然科学基金(61873006和61873006)和国家重点研究和开发项目(2018 yfc1602704和2018 yfb1702704)。</p> </div> </div> <div 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