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href="//www.newsama.com/journals/amse/" aria-label="Advances in Materials Science and Engineering">材料科学与工程进展据/一种>/据一种class="sc-htpNat bUhGXt link sc-gGCbJM eslOan breadCrumb" href="//www.newsama.com/journals/amse/contents/year/2020/" aria-label="2020">2020据/一种>/据span class="sc-lcpuFF dIyyAR">文章据/span> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 comSpQ threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-jeCdPy julqxU section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分据/button> <div class="sc-gtfDJT eVAVoo static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-GMQeP fMysxi sc-eInJlc cfvYGB left_section_menu"> <p>在这一页上据/p> <span class="sc-hzDEsm gxpLsG grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-fOICqy 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article_header_class"> <p class="sc-hzNEM exLcDH article_type">研究文章|据!-- -->开放获取据/p> <div class="sc-chbbiW kzNyka article_citation"> 体积据!-- --> 2020据!-- --> <span class="sc-cooIXK hCCmjz">|据/span>文章ID.据!-- --> 9527836.据!-- --> <span class="sc-cooIXK hCCmjz">|据/span> <a class="sc-htpNat bUhGXt link sc-fcdeBU dJIaji" href="https://doi.org/10.1155/2020/9527836" aria-label="Doi-link">https://doi.org/10.1155/2020/9527836.据/一种> </div> <div class="sc-bmyXtO gDNLQN article_full_citation"> <div class="sc-jtggT bycqoT isHide"> <p>永美浩，伊菲马，金胜江，张翔兴，雷尼，建阳据!-- -->那据!-- --> “据span class="adjust-article-svg-size">基于马尔可夫定量判断的逆瞬态非金属管道泄漏诊断方法据/span>“，据!-- --><i>材料科学与工程进展据/一世>那据!-- --> 卷。据!-- -->2020据!-- -->那据!-- --> 文章ID.据!-- -->9527836.据!-- -->那据!-- --> 11.据!-- -->   页面据!-- -->那据!-- --> 2020据!-- -->．据!-- --> https://doi.org/10.1155/2020/9527836.据/p> </div> <button class="sc-iAyFgw irxuxk sc-dEoRIm jkPgtr" color="">显示引文据/button> </div> <h1 class="sc-gPEVay iUuzmH sc-kxynE eYDjPA article_title adjust-article-svg-size heading-title">基于马尔可夫定量判断的逆瞬态非金属管道泄漏诊断方法据/h1> </div> <div class="sc-gpHHfC cdKJIh article_authors"> <hr class="sc-gPzReC jVvWtU hr__author"> <span class="">永美浩据一种class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0001-6453-5037" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-eXNvrr jzSEeN" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIGlkPSJMYXllcl8xIiBkYXRhLW5hbWU9IkxheWVyIDEiIHZpZXdCb3g9IjAgMCAyOTkuNSAyNTkuNSI+PGRlZnM+PHN0eWxlPi5jbHMtMXtmaWxsOiNhNmNlMzk7fS5jbHMtMntmaWxsOiNmZmY7fS5jbHMtM3tmaWxsOm5vbmU7fTwvc3R5bGU+PC9kZWZzPjx0aXRsZT5vcmNoaWQ8L3RpdGxlPjxwYXRoIGNsYXNzPSJjbHMtMSIgZD0iTTI4Ny41LDEyOS41YTEyOCwxMjgsMCwxLDEtMTI4LTEyOEExMjgsMTI4LDAsMCwxLDI4Ny41LDEyOS41WiIvPjxwYXRoIGNsYXNzPSJjbHMtMiIgZD0iTTExNy44LDE4Ny43SDEwMi40VjgwLjZoMTUuNFYxODcuN1oiLz48cGF0aCBjbGFzcz0iY2xzLTIiIGQ9Ik0xNDAuNCw4MC42SDE4MmMzOS42LDAsNTcsMjguMyw1Nyw1My42LDAsMjcuNS0yMS41LDUzLjYtNTYuOCw1My42SDE0MC40Wm0xNS40LDkzLjNoMjQuNWMzNC45LDAsNDIuOS0yNi41LDQyLjktMzkuNywwLTIxLjUtMTMuNy0zOS43LTQzLjctMzkuN0gxNTUuOHY3OS40WiIvPjxwYXRoIGNsYXNzPSJjbHMtMiIgZD0iTTEyMC4yLDU4LjNhMTAuMSwxMC4xLDAsMSwxLTEwLjEtMTAuMUExMC4xNCwxMC4xNCwwLDAsMSwxMjAuMiw1OC4zWiIvPjxyZWN0IGNsYXNzPSJjbHMtMyIgd2lkdGg9IjI5OS41IiBoZWlnaHQ9IjI1OS41Ii8+PC9zdmc+" height="16"></a>那据sup>1据/sup></span> <span class="">艾菲马据一种class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0002-1405-7812" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-eXNvrr jzSEeN" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a>那据sup>1据/sup></span> <span class="">Juncheng江据!-- -->那据sup>1据/sup></span> <span class=""><b>Zhixiang兴据/b><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-gVyKpa kNPCsS icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><a class="sc-htpNat bUhGXt link" href="https://orcid.org/0000-0002-0191-1733" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-eXNvrr jzSEeN" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a>那据sup>1据/sup></span> <span class="">雷尼据!-- -->那据sup>2据/sup> 和据/span> <span class="">剑阳据sup>3.据/sup></span> <div class="sc-kQsIoO lnoGXA isHide"> <p><sup>1据/sup><span>常州大学环境与安全工程学院，江苏常州213164据/span></p> <p><sup>2据/sup><span>南京江北鑫桂，南京科技大学，南京，江苏，211816据/span></p> <p><sup>3.据/sup><span>常州市港华燃气有限公司，江苏常州213161据/span></p> </div> <button class="sc-iAyFgw irxuxk sc-cpmKsF dxqSPm" color="">显示更多据/button> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑：据/b>弗朗西斯科·哈维尔Fernández Fernández据/D.一世v> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">已收到据/span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">20月13日据/span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">公认据/span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2020年3月02日据/span> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表据/span> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">20月22日据/span> </div> </div> </div> <article class="sc-hgHYgh hYIwYm article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">摘要据/h4> <p>针对城市非金属管道早期泄漏监测的问题及大型定位误差，提出了基于马尔可夫定量判断的反向瞬态城市非金属气体管道泄漏定位方法。基于通过实验获得的不同压力下的流量数据建立马尔可夫流动状态转换概率矩阵，以定量地确定管道泄漏状态。在此基础上，根据实际构造适用于城市非金属气体管道泄漏位置的反向瞬态泄漏控制方程。对目标函数寻求压力和计算压力之间的差异。最后，目标函数与顺序二次编程（SQP）方法结合优化，以获得实际泄漏参数并计算泄漏源的尺寸和位置。结果表明，基于马尔可夫的定量判断的逆瞬态泄漏定位方法可以更准确地确定管道的泄漏状态，并计算燃气管道的早期泄漏参数和泄漏位置，从而提高了定位精度。据/p> <span class="end-abs"></span> <h4 id="introduction">1.介绍据/h4> <p>非金属管道因其耐腐蚀、耐高温、低摩擦、耐磨损等特点，近年来已成为城市交通管道的主要材料。它们逐渐取代了金属管道。据相关统计，非金属管道目前占城市燃气管道的70%以上。非金属管道虽然具有较强的耐腐蚀性能，但也存在管道接头泄漏断裂、管身断裂、管道内胆收缩变形等引起的管道泄漏问题。目前，大多数城市的地埋管道泄漏监测还处于人工检测的水平。同时，由于管道材料的不同，许多金属管道的检漏方法已不再适用于非金属管道。因此，有必要研究一种适用于城市非金属管道的泄漏诊断方法和技术，以加强城市非金属管道的风险监测。据/p> <p>埋地管道的泄漏测量一直是一个难以解决的主题，特别是在城市非金属管道中。在泄漏检测和定位技术中仍有许多问题，这导致了普遍关注并实现了一些结果。2007年，李恒等人。应用马尔可夫链法预测气体管道抗腐蚀层的老化。实验证明，通过长期验证和常规摘要，验证的准确性可以大大提高，但提取的功能不能准确地表示原始数据中的所有有用信息[据一种href="#B1">1据/一种>];2008年，Jung和Karney比较和指出，遗传算法和粒子群优化（PSO）算法往往提供相对精确的泄漏校准，但摩擦系数值的校准很差[据一种href="#B2">2据/一种>］.2008年，Karney等人将逆瞬态方法与系统响应的频域分析、反射瞬态信号分析等不依赖瞬态模型的方法相结合。通过数值模拟，验证了逆瞬态法在管网中的可行性。提出瞬态逆方法的定位精度与模型的建立有关[据一种href="#B3">3.据/一种>］.2011年，Soares等人。通过对非金属管泄漏监测反瞬态分析的优化模型组合液压瞬态分析，提出了定位的关键因素是瞬态求解器的精确校准。结果表明，随着系统模型的分散，泄漏位置的准确性为管道总长度的4-15％[据一种href="#B4">4.据/一种>］.2012年，Haghhighi等人。施加的中央启发式优化（CFO）元启发式方法来检测管道泄漏的规格和管道摩擦系数，这证实了该方法优于遗传算法（GA），粒子群算法（PSO），和蚁群算法（ACO）[据一种href="#B5">5.据/一种>］.2015年，黄等人。组合瞬态流动仿真和模拟退火（SA）方法，用于开发泄漏检测模拟退火方法（LDSA）并将其应用于现实生活管道和数值模拟的合成管网，以验证其识别泄漏的能力。结果表明，该方法可以准确地检测毛孔的泄漏[据一种href="#B6">6.据/一种>］.2016年，Yu等将灰色理论与马尔可夫理论相结合，对管道腐蚀状态进行预测。结果表明，该方法计算简单，精度高，但在工程应用中仍有很大的局限性[据一种href="#B7">7.据/一种>］.2016年，Zhihong和Baomin旨在城市管道网络泄漏率数据的非线性和随机波动的特点。基于灰色马尔可夫链模型，2005年至2012年的管道泄漏率是研究对象。用灰色马尔可夫链进行比较分析。预测结果表明，修改的马尔可夫链模型获得的预测精度更高[据一种href="#B8">8.据/一种>］.2017年，Liu将相关函数法与ITA结合，通过计算节点灵敏度系数确定泄漏点位置，然后应用GA算法通过瞬态逆模型得到泄漏量。通过大量实验验证了两种方法结合的可行性[据一种href="#B9">9.据/一种>］.2017年，蔡永桥等。建立了基于双流体模型的气液两相流量泄漏系统的数学模型，并确认系统的数值计算结果与实验数据趋势一致，证明该模型具有良好的适用性[据一种href="#B10">10.据/一种>］.2017年，Abdulshaheed证明，使用逆瞬态方法的最大问题是系统中瞬态的建模不能准确反映实际情况，并且计算的数据和测量的实验数据非常不同。差异主要是因为该模型不能准确地考虑不稳定摩擦的多维效果[据一种href="#B11">11.据/一种>］.2017年，陈等人。通过特征线法测试了管道泄漏的瞬态模型，并确认了使用起始和结束压力和流量在管道泄漏后稳定状态计算的定位结果接近真实值[据一种href="#B12">12.据/一种>］.2019年，Liu等人提出了一种基于马尔可夫特征提取和两阶段法的泄漏检测新方法。实验结果表明，该方法具有较高的准确率和较低的虚警率，但计算模型需要根据不同的管道进行调整，适应性不强[据一种href="#B13">13.据/一种>］.据/p> <p>上述研究促进了非金属管道泄漏监测的研究，但其中大部分仍处于实验室研究阶段，并且还存在许多问题，如不完全获取管道泄漏信息，无法定量分析和判断管道泄漏状态，逆瞬态模型的不准确性导致大型计算误差，适用性差。本文探讨了城市中的气体管道，探讨了基于定量判断的定位逆瞬态非金属管道的方法。通过建立马尔可夫流动状态转变概率矩阵定量地确定管道泄漏，在此基础上，适用于城市燃气管道定位分析的逆的瞬时泄漏控制方程被构造，并且目标函数是基于所述实际压力之间的差建立了计算的压力并最终结合顺序二次编程（SQP）方法来精确计算流水线泄漏源的位置。据/p> <h4 id="markov-chain-quantitative-judgment-principle">马尔可夫链定量判断原则据/h4> <p>马尔可夫链方法可以通过管道当前状态的数据来预测管道未来状态是否会泄漏。由于泄漏状态是不可逆的，该方法可用于管道泄漏监测。的想法应用到判断管道泄漏是原始流数据转换成一个马尔可夫链和提取的参数向量马尔可夫链的转移特点建立状态转移概率矩阵预测管道流动的趋势。将流量变化率与管道实际流量变化率进行比较，判断管道是否泄漏。据/p> <h5 id="sec2.1">2.1。建立国家转换概率矩阵据/h5> <p>第一组流量数据通过管道上的流量传感器收集据一世>K.据/一世>流量(据span class="nowrap"> <svg height="9.39034pt" id="M1" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 100.286 9.39034" width="100.286pt" 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)"> <path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 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xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.223,0)"> <use xlink:href="#g113-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,55.541,3.132)"> <path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path> </g> <g transform="matrix(.013,0,0,-0.013,60.487,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.63,0)"> <path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path> </g> <g transform="matrix(.013,0,0,-0.013,70.773,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.916,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.093,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.236,0)"> <use xlink:href="#g113-114"></use> </g> <g 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39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z" id="g113-76"></path> </g> <g transform="matrix(.013,0,0,-0.013,121.85,17.671)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> </g> <g transform="matrix(.013,0,0,-0.013,128.8,17.488)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="52.0198pt" id="I2" version="1.1" viewbox="0 0 226.51 52.0198" width="226.51pt" 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="#B2-1"></use> <use transform="matrix(1 0 0 1 94.7 30.57)" xlink:href="#B2-2"></use> </svg></span></span><span class="right_break" id="R2"> <svg class="label" height="11.44pt" id="M2-3" 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="B2-3"> <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="52.0198pt" id="IL2" version="1.1" viewbox="0 0 13.45 52.0198" 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 20.08)" xlink:href="#B2-3"></use> </svg></span></span></p> <p>他们之中，据一世>一世据/一世>是收集的订购据一世>K.据/一世>流量变化率，△据一世>问：据/一世><sub><i>N据/一世></sub>是时间点的流量的变化量据一世>T.据/一世><sub>N据/sub>以及在时间点的流动据一世>T.据/一世><sub><i>N据/一世>-1据/sub>，和据一世>问：据/一世><sub><i>N据/一世></sub>是时间段的实时流动据一世>T.据/一世>．的据一世>问：据/一世><sub><i>一世据/一世></sub>包括四个变化状态。在第一个州，价值据一世>问：据/一世><sub><i>一世据/一世></sub>是0，表示非曝光状态;在第二个州，价值据一世>问：据/一世><sub><i>一世据/一世></sub>是0-1（％），表明漏电小;在第三州，价值据一世>问：据/一世><sub><i>一世据/一世></sub>为1-3(%)，表示泄漏膨胀状态;在第四种状态中，价值据一世>问：据/一世><sub><i>一世据/一世></sub>是3-100（％），表示泄漏状态大。第一组流动变化率的国家根据上述四个州进行分类，以及从一个州转换到另一个国家的概率据一世>K.据/一世>流量变化率是按时间顺序计算的据一世>P.据/一世>矩阵。据/p> <p>四种状态的流量变化率为据一世>N据/一世>1，据一世>N据/一世>2，据一世>N据/一世>3，和据一世>N据/一世>4;从第一个状态到第一个、第二个、第三和第四个状态的转换次数分别为:据一世>N据/一世>11，据一世>N据/一世>12，据一世>N据/一世>13,据一世>N据/一世>14，过渡概率是据span class="nowrap"> <svg height="12.7178pt" id="M3" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 66.6962 12.7178" width="66.6962pt" 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="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="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.853,0)"> <path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,40.314,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.745,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.708,0)"> <path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path> </g> <g transform="matrix(.013,0,0,-0.013,55.069,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,61.53,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="12.7178pt" id="M4" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="12.7178pt" id="M5" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>那据/span>和据span class="nowrap"> <svg height="12.7178pt" id="M6" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-50"></use> </g> </svg>;据/span>从第二状态到第二个，第三和第四个状态的转换次数分别是据一世>N据/一世>22，据一世>N据/一世>23，和据一世>N据/一世>24，过渡概率是据span class="nowrap"> <svg height="12.7178pt" id="M7" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="12.7178pt" id="M8" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>那据/span>和据span class="nowrap"> <svg height="12.7178pt" id="M9" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-51"></use> </g> </svg>;据/span>从第三种状态到第二种、第三种和第四种状态的转换次数分别为:据一世>N据/一世>32，据一世>N据/一世>33，和据一世>N据/一世>34，过渡概率是据span class="nowrap"> <svg height="12.7178pt" id="M10" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="12.7178pt" id="M11" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span>和据span class="nowrap"> <svg height="12.7178pt" id="M12" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-52"></use> </g> </svg>;据/span>从第四状态到第二个，第三和第四个州的转换次数分别为，据一世>N据/一世>42，据一世>N据/一世>43，和据一世>N据/一世>44，过渡概率是据span class="nowrap"> <svg height="12.7178pt" id="M13" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 59.3488 12.7178" width="59.3488pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-53"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="12.7178pt" id="M14" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 64.5171 12.7178" width="64.5171pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.351,3.132)"> <use xlink:href="#g50-53"></use> </g> </svg>那据/span>和据span class="nowrap"> <svg height="12.7178pt" id="M15" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 59.3488 12.7178" width="59.3488pt" 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="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.384,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,11.816,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.411,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.674,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,38.134,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.566,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.529,0)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.89,0)"> <use xlink:href="#g113-53"></use> </g> </svg>．据/span></p> <p>然后，得到状态转移概率矩阵据一世>P.据/一世>的马尔可夫链据span class="equation_break" id="EEq2"><span class="left_break" id="L16"></span><span class="middle_break"><span class="center_break" id="M16"> <svg height="67.5095pt" id="M16-1" version="1.1" viewbox="0 0 137.204 67.5095" width="137.204pt" 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,-0.013,0,37.082)"> <path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.65,37.082)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.92,22.663)"> <path d="M525 1652V1724H212V0H293V1488C293 1639 296 1652 402 1652H525Z" id="g119-41"></path> </g> <g transform="matrix(.013,0,0,-0.013,22.92,30.232)"> <path d="M293 0V620H212V0H293Z" id="g119-49"></path> </g> <g transform="matrix(.013,0,0,-0.013,22.92,37.8)"> <use xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.92,45.368)"> <use xlink:href="#g119-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.92,67.46)"> <path d="M525 39V111H402C295 111 293 124 293 230V1733H212V39H525Z" id="g119-57"></path> </g> <g transform="matrix(.013,0,0,-0.013,34.91,9.319)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.29,12.451)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.73,12.451)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.69,9.319)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.08,12.451)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.51,12.451)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.48,9.319)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.86,12.451)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,92.29,12.451)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,103.26,9.319)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.65,12.451)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.08,12.451)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.18,27.35)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.69,27.35)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.08,30.481)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.51,30.481)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.48,27.35)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.86,30.481)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,92.29,30.481)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,103.26,27.35)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.65,30.481)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.08,30.481)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.18,45.379)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.69,45.379)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.08,48.511)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.51,48.511)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.48,45.379)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.86,48.511)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,92.29,48.511)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,103.26,45.379)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.65,48.511)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.08,48.511)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.18,63.41)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.69,63.41)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.08,66.541)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.51,66.541)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.48,63.41)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.86,66.541)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,92.29,66.541)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,103.26,63.41)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.65,66.541)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,115.08,66.541)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.06,22.663)"> <path d="M478 0V1724H165V1652H288C394 1652 397 1639 397 1488V0H478Z" id="g119-42"></path> </g> <g transform="matrix(.013,0,0,-0.013,123.06,30.232)"> <path d="M478 0V620H397V0H478Z" id="g119-50"></path> </g> <g transform="matrix(.013,0,0,-0.013,123.06,37.8)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.06,45.368)"> <use xlink:href="#g119-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.06,67.46)"> <path d="M478 39V1733H397V230C397 124 395 111 288 111H165V39H478Z" id="g119-58"></path> </g> <g transform="matrix(.013,0,0,-0.013,134.24,37.082)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R16"> <svg class="label" height="11.44pt" id="M16-2" version="1.1" viewbox="0 0 15.038 11.44" width="15.038pt" 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,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 495L63 476C89 515 130 568 198 568C274 568 316 519 316 436C316 347 251 264 191 192C142 134 85 76 30 21V0H403C415 45 425 89 438 131L411 139Z" id="g190-243"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>并满足：据span class="nowrap"> <svg height="11.927pt" id="M17" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 111.013 11.927" width="111.013pt" 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="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.313,0)"> <path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path> </g> <g transform="matrix(.013,0,0,-0.013,24.849,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.31,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,39.162,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.699,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,56.16,3.132)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.012,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.548,0)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.009,3.132)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.588,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,100.85,0)"> <use xlink:href="#g113-76"></use> </g> </svg>．据/span></p> <h5 id="sec2.2">2.2。管道泄漏的定量判断据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">在节据一种href="#sec2.1">2.1据/一种>在相同的环境条件下，采集第二组流量数据，设此时每个间隔内的实际流量变化数为据一世>α据/一世><sub>1据/sub>参数向量如下：据/span></span></span><span class="equation_break" id="EEq3"><span class="left_break" id="L18"></span><span class="middle_break"><span class="center_break" id="M18"> <svg height="18.3157pt" id="M18-1" version="1.1" viewbox="0 0 160.214 18.3157" width="160.214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B18-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.06,15.617)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.64,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.89,12.485)"> <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,-0.013,38.24,13.432)"> <path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,49.15,7.383)"> <path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z" id="g50-41"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,52.41,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,56.84,7.383)"> <path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z" id="g50-42"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,48.3,17.29)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.65,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,77.56,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,80.82,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,85.25,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.72,17.29)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.07,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,105.98,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,109.23,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,113.67,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,105.13,17.29)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.48,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,134.39,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,137.65,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,142.08,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,133.54,17.29)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,148.9,12.485)"> <path d="M273 -404V944H76V909L99 908C205 900 208 895 208 751V-249C208 -355 206 -360 99 -368L76 -369V-404H273Z" id="g119-130"></path> </g> <g transform="matrix(.013,0,0,-0.013,157.25,12.485)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R18"> <svg class="label" height="11.44pt" id="M18-2" version="1.1" viewbox="0 0 14.868 11.44" width="14.868pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B18-2"> <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="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.37,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">他们之中，据一世>α据/一世><sub>1据/sub>表示第一个参数矢量，和据span class="nowrap"> <svg height="16.4744pt" id="M19" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 22.534 16.4744" width="22.534pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.91,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.168,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.6,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.858)"> <use xlink:href="#g50-50"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="16.4744pt" id="M20" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 22.534 16.4744" width="22.534pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.91,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.168,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.6,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.858)"> <use xlink:href="#g50-51"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="16.584pt" id="M21" style="vertical-align:-4.0179pt" version="1.1" viewbox="-0.0498162 -12.5661 22.534 16.584" width="22.534pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.91,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.168,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.6,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.858)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span>和据svg height="16.4744pt" id="M22" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 22.534 16.4744" width="22.534pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.91,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.168,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.6,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.858)"> <use xlink:href="#g50-53"></use> </g> </svg>代表流量变化率的数量据一世>K.据/一世>第一状态的流量变化率分别在第一状态，第二状态，第三状态和第四状态。据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">计算马尔可夫链以获得a据一世>β据/一世><sub>1据/sub>基于预测流量变化率的参数向量基于Markov链在未来的时间段，其公式给出据/span></span></span><span class="equation_break" id="EEq4"><span class="left_break" id="L23"></span><span class="middle_break"><span class="center_break" id="M23"> <svg height="18.3157pt" id="M23-1" version="1.1" viewbox="0 0 60.541 18.3157" width="60.541pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B23-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.23,15.617)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.81,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.07,12.485)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.13,15.617)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.98,12.485)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.52,12.485)"> <use xlink:href="#g113-81"></use> </g> </g> </svg> <svg height="18.3157pt" id="M23-2" version="1.1" viewbox="0 0 147.944 18.3157" width="147.944pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B23-2"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.24,12.485)"> <use xlink:href="#g119-129"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.59,13.432)"> <path d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,35.85,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,39.11,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,43.54,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.78,17.29)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.35,13.432)"> <use xlink:href="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.61,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,66.87,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,71.3,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.54,17.29)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.11,13.432)"> <use xlink:href="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,91.37,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,94.62,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,99.06,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,91.3,17.29)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.87,13.432)"> <use xlink:href="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,119.13,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,122.38,7.383)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,126.82,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,119.06,17.29)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.64,12.485)"> <use xlink:href="#g119-130"></use> </g> <g transform="matrix(.013,0,0,-0.013,144.98,12.485)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="40.4353pt" id="I23" version="1.1" viewbox="0 0 163.82 40.4353" width="163.82pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -3.2)" xlink:href="#B23-1"></use> <use transform="matrix(1 0 0 1 15.84 22.12)" xlink:href="#B23-2"></use> </svg></span></span><span class="right_break" id="R23"> <svg class="label" height="11.44pt" id="M23-3" 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="B23-3"> <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)"> <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,-0.013,10.96,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="40.4353pt" id="IL23" version="1.1" viewbox="0 0 15.52 40.4353" 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 14.29)" xlink:href="#B23-3"></use> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里据span class="nowrap"> <svg height="16.4744pt" id="M24" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 21.8815 16.4744" width="21.8815pt" 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="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.257,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.515,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.947,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.192,3.858)"> <use xlink:href="#g50-50"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="16.4744pt" id="M25" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 21.8815 16.4744" width="21.8815pt" 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="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.257,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.515,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.947,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.192,3.858)"> <use xlink:href="#g50-51"></use> </g> </svg>那据/span><span class="nowrap"> <svg height="16.584pt" id="M26" style="vertical-align:-4.0179pt" version="1.1" viewbox="-0.0498162 -12.5661 21.8815 16.584" width="21.8815pt" 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="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.257,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.515,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.947,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.192,3.858)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span>和据span class="nowrap"> <svg height="16.4744pt" id="M27" style="vertical-align:-3.908299pt" version="1.1" viewbox="-0.0498162 -12.5661 21.8815 16.4744" width="21.8815pt" 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="#g113-110"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.257,-6.049)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.515,-6.049)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.947,-6.049)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.192,3.858)"> <use xlink:href="#g50-53"></use> </g> </svg>那据/span>分别表示通过预测获得的第一状态，第二状态，第三状态和第四状态的流动变化率的量。据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在这些当中据一世>K.据/一世>流程参数，据一世>S.据/一世>用作预测状态序列号，（据一世>S.据/一世>= 1、2、3、4)，选择流量参数个数最多的状态，即据svg height="13.9998pt" id="M28" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 27.012 13.9998" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <path d="M463 633C453 636 427 644 417 648C388 660 349 667 316 667C183 667 100 592 100 483C100 398 176 335 223 305L259 282C321 242 358 203 358 149C358 66 301 22 234 22C110 22 70 131 57 208L24 205L28 48C51 23 128 -17 215 -17C342 -17 446 60 446 174C446 262 394 310 317 361L284 383C229 420 183 455 183 515C183 569 222 628 298 628C384 628 418 563 428 481L461 487C459 527 458 593 463 633Z" id="g50-84"></path> </g> <g transform="matrix(.0065,0,0,-0.0065,14.366,5.233)"> <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(.0065,0,0,-0.0065,19.768,5.233)"> <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(.0065,0,0,-0.0065,22.686,5.233)"> <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> </svg>为此时预测的管道状态，表示为据span class="nowrap"> <svg height="11.9316pt" id="M29" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 22.7858 11.9316" width="22.7858pt" 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="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.071,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.633,3.132)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.719,3.132)"> <use xlink:href="#g58-118"></use> </g> </svg>-据/span>国家。据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">与[据一种href="#B2">2据/一种>[收集第三组流量数据。重复部分中描述的过程据一种href="#sec2.1">2.1据/一种>，此时每个间隔内的实际流量变化率数设为据一世>α据/一世><sub>2据/sub>参数向量如下：据/span></span></span><span class="equation_break" id="EEq5"><span class="left_break" id="L30"></span><span class="middle_break"><span class="center_break" id="M30"> <svg height="18.3157pt" id="M30-1" version="1.1" viewbox="0 0 156.414 18.3157" width="156.414pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B30-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.06,15.617)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.64,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.9,12.485)"> <use xlink:href="#g119-129"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.25,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,46.16,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,49.42,7.383)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.85,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.31,17.29)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.66,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.57,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,77.83,7.383)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.26,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,73.73,17.29)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.08,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.99,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,106.24,7.383)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,110.68,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,102.14,17.29)"> <use xlink:href="#g50-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,120.49,13.432)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,131.4,7.383)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,134.66,7.383)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,139.09,7.383)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,130.55,17.29)"> <use xlink:href="#g50-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,145.91,12.485)"> <use xlink:href="#g119-130"></use> </g> <g transform="matrix(.013,0,0,-0.013,153.45,12.485)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R30"> <svg class="label" height="11.44pt" id="M30-2" version="1.1" viewbox="0 0 14.898 11.44" width="14.898pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B30-2"> <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="M130 550H367L393 615L386 623H101L63 323C82 331 123 342 165 342C275 342 328 277 328 188C328 107 283 40 201 40C141 40 99 72 78 91C69 99 59 98 51 91C39 81 30 67 29 58C28 48 33 37 46 24C60 10 104 -12 149 -12C203 -11 269 14 323 59C384 109 412 165 412 225C412 308 347 399 219 399C193 399 146 382 104 367L130 550Z" id="g190-161"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.4,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在这些当中据一世>K.据/一世>流程参数，据一世>W.据/一世>表示为实际的管道状态序列号(据一世>W.据/一世>= 1、2、3、4)，选择流量参数个数最多的状态，即据svg height="13.9998pt" id="M31" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 30.3459 13.9998" width="30.3459pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <path d="M1013 650H775L768 618L793 615C853 608 859 601 837 545C792 433 708 266 639 131H637L537 639H503L251 132H249L190 552C183 602 190 607 235 614L262 618L269 650H25L18 618C92 610 95 608 107 525L184 -9H221L475 494H479L576 -9H613L884 526C928 607 934 609 1005 618L1013 650Z" id="g50-88"></path> </g> <g transform="matrix(.0065,0,0,-0.0065,17.688,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,23.089,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,26.008,5.233)"> <use xlink:href="#g58-118"></use> </g> </svg>被选中为管道在内据span class="nowrap"> <svg height="11.9316pt" id="M32" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 27.5094 11.9316" width="27.5094pt" 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="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,-0.0091,10.777,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.339,3.132)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,22.425,3.132)"> <use xlink:href="#g58-118"></use> </g> </svg>-据/span>国家。据/span></span><span class="list-item"><span class="list-label">（4）据/span><span class="list-content">状态序列号的值据一世>S.据/一世>处于预测状态据svg height="13.9998pt" id="M33" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 27.012 13.9998" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,14.366,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,19.768,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,22.686,5.233)"> <use xlink:href="#g58-118"></use> </g> </svg>与状态序列号的值比较据一世>W.据/一世>在实际状态据span class="nowrap"> <svg height="13.9998pt" id="M34" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 30.3459 13.9998" width="30.3459pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-88"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,17.688,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,23.089,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,26.008,5.233)"> <use xlink:href="#g58-118"></use> </g> </svg>：据/span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">①如果据一世>S.据/一世>=据一世>W.据/一世>=1，一世T.一世s judged that the pipeline is in normal operation据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">②如果据一世>S.据/一世> < 据一世>W.据/一世>，则判断管道处于启动泄漏的早期阶段据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">③如果据一世>S.据/一世>>据一世>W.据/一世>，判断，管道在开始泄漏的后期据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">④如果据一世>S.据/一世>=据一世>W.据/一世> ≠ 1, it is judged that the pipeline is in the leakage stabilization stage据/span></span></span></p> <h4 id="inverse-transient-method-for-nonmetallic-pipeline-leak-location-method">3.非金属管道泄漏定位方法的逆瞬态方法据/h4> <p>基于Markov链方法来定量地确定流水线的泄漏，逆瞬态方法用于进一步确定每个监控节点是否具有泄漏，以便描绘泄漏处于节点或两个节点之间的管道，并连续缩短节点距离以获得精确定位。逆瞬态方法定位的原理如下。据/p> <h5 id="sec3.1">3．1.控制方程据/h5> 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</svg></span></span><span class="right_break" id="R35"> <svg class="label" height="11.44pt" id="M35-4" version="1.1" viewbox="0 0 15.428 11.44" width="15.428pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-4"> <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)"> <path d="M143 344C173 483 265 547 326 576C363 593 402 605 434 611L429 641C389 634 343 623 301 608C195 570 43 456 43 236C43 81 135 -12 245 -12C368 -12 453 88 453 208C453 310 380 393 273 393C253 393 232 386 211 376L143 344ZM234 338C325 338 367 255 367 172C367 102 346 21 264 21C184 21 132 113 132 239C132 267 133 291 138 312C164 327 197 338 234 338Z" id="g190-227"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.93,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M35-6" version="1.1" viewbox="0 0 15.028 11.44" width="15.028pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-6"> <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="M430 623H48C43 580 39 534 30 478H57C80 544 84 550 152 550H369C286 366 187 178 74 -1L81 -12L156 -2C249 201 343 408 438 611L430 623Z" id="g190-223"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里据一世>m据/一世>是气体流量，kg·s据sup>-1据/sup>;据一世>一种据/一世>是管道的横截面积，m据sup>2据/sup>;据一世>P.据/一世>是压力，pa;据一世>ρ据/一世>是气体密度，kg·m据sup>-3据/sup>;据一世>D.据/一世>为管道内径，m;据svg height="9.49473pt" id="M36" 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>是摩擦系数。据/p> 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B37-12"> <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,-0.013,8.9,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.29,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span>在哪里据一世>一种据/一世>为压力波速，m/s，当气管为等温线时，据一世>一种据/一世>是一个固定值。据/p> <p>特征线网格如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig1/" target="_blank">1据/一种>．方程式（据一种href="#EEq8">9.据/一种>）和（据一种href="#EEq8">11.据/一种>)分别为C+和C−特征线AP和BP;方程(据一种href="#EEq8">8.据/一种>）和（据一种href="#EEq8">10.据/一种>)为满足各自特征线的相容方程。这些管子被平均地分成几部分据一世>N据/一世>相等的部分，步长是δ据一世>X据/一世>，时间步长为Δ据一世>T.据/一世>=据一世>一种据/一世>Δ据一世>X据/一世>．方程式（据一种href="#EEq8">8.据/一种>）和（据一种href="#EEq8">10.据/一种>）分别集成在C +特征线AP和C-特征线BP中，其中兼容性方程的第三项是二阶近似，并且获得C +特征线和C-特征线。特征线上的两个非线性方程如下：据span class="equation_break" id="EEq12"><span 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height="11.44pt" id="M38-9" 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="B38-9"> <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></span></span></p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.001" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.001.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 特征网格的示意图。据/D.一世v> </div> </div> </div> <p>城市管道的早期泄漏可视为小孔泄漏，气体泄漏公式取决于泄漏口气体的流速。由于城市燃气管道的压力比较低，泄漏口气体的流速一般为亚音速流动:据span class="equation_break" id="EEq13"><span class="left_break" id="L39"></span><span class="middle_break"><span class="center_break" id="M39"> <svg height="37.8888pt" id="M39-1" version="1.1" viewbox="0 0 17.489 37.8888" width="17.489pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B39-1"> <g transform="matrix(.013,0,0,-0.013,0,25.867)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.22,28.999)"> <path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 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transform="matrix(.013,0,0,-0.013,159.98,25.867)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="59.904pt" id="I39" version="1.1" viewbox="0 0 174.61 59.904" width="174.61pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -16.68)" xlink:href="#B39-1"></use> <use transform="matrix(1 0 0 1 11.56 22.01)" xlink:href="#B39-2"></use> </svg></span></span><span class="right_break" id="R39"> <svg class="label" height="11.44pt" id="M39-3" 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="B39-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.89,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.76,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="59.904pt" id="IL39" version="1.1" viewbox="0 0 19.34 59.904" width="19.34pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 24.02)" xlink:href="#B39-3"></use> </svg></span></span>在哪里据一世>m据/一世><sub><i>L.据/一世></sub>是泄漏泄漏流量，kg·s据sup>-1据/sup>;据一世>一种据/一世><sub><i>E.据/一世></sub>是有效的泄漏区域，m据sup>2据/sup>, Ae = C×A0;C为孔板系数，与泄漏孔的形状有关;据一世>一种据/一世><sub>0.据/sub>是漏洞区域，m据sup>2据/sup>;据一世>P.据/一世><sub><i>D.据/一世></sub>是管道的起点压力，pa;据一世>K.据/一世>是气体的绝热系数，无量纲;据一世>R.据/一世>气体常数是J·kg吗据sup>-1据/sup>·K据sup>-1据/sup>;据一世>T.据/一世>是气体的温度K。据/p> <p>假设监测节点为泄漏点，建立泄漏控制方程，分析监测节点的压力和流量数据。以泄漏孔为节点，研究了Δ据一世>X据/一世>流入漏孔前的距离满足公式(据一种href="#EEq8">8.据/一种>）和δ内的流动特性据一世>X据/一世>流出泄漏孔后的距离满足公式（据一种href="#EEq8">10.据/一种>)，然后再从漏孔流出。流体参数下标为1，通过漏孔后流体参数下标为2，建立的泄漏控制方程为:据span class="equation_break" id="EEq14"><span class="left_break" id="L40"></span><span 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viewbox="0 0 19.758 11.44" width="19.758pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B40-13"> <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,-0.013,8.83,9.26)"> <use xlink:href="#g190-227"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.26,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M40-15" 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="B40-15"> <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,-0.013,8.81,9.26)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.84,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M40-17" version="1.1" viewbox="0 0 19.498 11.44" width="19.498pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B40-17"> <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,-0.013,8.83,9.26)"> <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> <svg class="alt_label" height="339.984pt" id="IL40" version="1.1" viewbox="0 0 19.84 339.984" width="19.84pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 48.29)" xlink:href="#B40-5"></use> <use transform="matrix(1 0 0 1 0 165.6)" xlink:href="#B40-10"></use> <use transform="matrix(1 0 0 1 0 258.64)" xlink:href="#B40-13"></use> <use transform="matrix(1 0 0 1 0 304.03)" xlink:href="#B40-15"></use> <use transform="matrix(1 0 0 1 0 326.76)" xlink:href="#B40-17"></use> </svg></span></span>在哪里据一世>P.据/一世><sub>1据/sub>和据一世>m据/一世><sub>1据/sub>流体在流入泄漏点前的一段距离压力Pa，流量，kg·s据sup>-1据/sup>;据一世>P.据/一世><sub>2据/sub>和据一世>m据/一世><sub>2据/sub>在泄漏点，Pa，流量，kg·s之后，流体压力是一定距离。据sup>-1据/sup>;据一世>P.据/一世><sub><i>L.据/一世></sub>是泄漏点的压力，pa。据/p> <h5 id="sec3.2">３．２．目标函数的建立据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">最小二乘标准目标函数定义如下：据/span></span></span><span class="equation_break" id="EEq19"><span class="left_break" id="L41"></span><span class="middle_break"><span class="center_break" id="M41"> <svg height="45.4571pt" id="M41-1" version="1.1" viewbox="0 0 125.554 45.4571" width="125.554pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B41-1"> <g transform="matrix(.013,0,0,-0.013,0,27.913)"> <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 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.64,27.913)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.9,27.913)"> <path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g121-107"></path> </g> <g transform="matrix(.013,0,0,-0.013,33.55,27.913)"> <path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z" id="g121-103"></path> </g> <g transform="matrix(.013,0,0,-0.013,37.04,27.913)"> <path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g121-108"></path> </g> <g transform="matrix(.013,0,0,-0.013,46.4,26.382)"> <path d="M767 1968H717L614 -968H612L327 324L133 268L144 227L265 262L644 -1458H646L767 1968Z" id="g119-125"></path> </g> <rect height="0.65243" width="65.3931" x="57.2" y=".702"></rect> <g transform="matrix(.0091,0,0,-0.0091,59.24,13.148)"> <path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z" id="g50-78"></path> </g> <g transform="matrix(.013,0,0,-0.013,57.2,27.919)"> <path d="M956 -188L922 -180C881 -295 847 -317 759 -317H196L640 311L259 873H678C777 873 812 865 833 838C853 816 869 781 885 721L918 727L902 932H77V907L514 253L53 -396V-421H902L956 -188Z" id="g119-73"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,57.49,41.562)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,60.03,41.562)"> <path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,65.59,41.562)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.54,27.913)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.57,27.913)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.22,31.044)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.18,27.913)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,100.72,27.913)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,108.75,23.361)"> <path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,107.38,31.954)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,112.54,27.913)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,117.64,20.612)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,122.59,27.913)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R41"> <svg class="label" height="11.44pt" id="M41-2" 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="B41-2"> <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="#g190-213"></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><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里据一世>E.据/一世>是目标函数;据一世>m据/一世>是时间步;据一世>P.据/一世><sub><i>一世据/一世></sub>是计算的压力，pa;据svg height="15.3797pt" id="M42" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.4361 11.9462 15.3797" width="11.9462pt" 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(.0091,0,0,-0.0091,8.026,-5.741)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.656,3.784)"> <use xlink:href="#g50-106"></use> </g> </svg>是测量的压力，pa。通过最小化目标函数据一世>E.据/一世>为0时，生成最适合实际情况的有效泄漏面积，根据有效面积的取值确定节点是否泄漏。据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">管道中的摩擦系数确定如下：据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">根据来自摩擦计算公式的实验数据计算摩擦系数：据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">Blasius公式：据/span></span></span><span class="equation_break" id="EEq20"><span class="left_break" id="L43"></span><span class="middle_break"><span class="center_break" id="M43"> <svg height="26.954pt" id="M43-1" version="1.1" viewbox="0 0 61.714 26.954" width="61.714pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B43-1"> <g transform="matrix(.013,0,0,-0.013,0,16.857)"> <use xlink:href="#g113-233"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.81,16.857)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.26,8.349)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.5,8.349)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.47,8.349)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.71,8.349)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.95,8.349)"> <path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path> </g> <g transform="matrix(.013,0,0,-0.013,51.19,8.349)"> <use xlink:href="#g113-53"></use> </g> <rect height="0.65243" width="34.2921" x="23.26" y="13.203"></rect> <g transform="matrix(.013,0,0,-0.013,25.5,26.708)"> <path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z" id="g121-80"></path> </g> <g transform="matrix(.013,0,0,-0.013,33.74,26.708)"> <path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g121-99"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,39.32,21.613)"> <path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,43.75,21.613)"> <path d="M117 -12C153 -12 178 12 178 50C178 84 153 110 118 110C84 110 59 84 59 50C59 12 84 -12 117 -12Z" id="g50-47"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,45.9,21.613)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,50.34,21.613)"> <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,-0.013,58.75,16.857)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R43"> <svg class="label" height="11.44pt" id="M43-2" 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="B43-2"> <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)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.61,9.25)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.02,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">其中，在雷诺系数计算公式中使用经验公式。据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">经验公式：据/span></span></span><span class="equation_break" id="EEq21"><span class="left_break" id="L44"></span><span class="middle_break"><span class="center_break" id="M44"> <svg height="63.4114pt" id="M44-1" version="1.1" viewbox="0 0 91.954 63.4114" width="91.954pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B44-1"> <g transform="matrix(.013,0,0,-0.013,0,17.506)"> <use xlink:href="#g121-80"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.24,17.506)"> <use xlink:href="#g121-99"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.45,17.506)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.71,17.506)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.95,17.506)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.92,17.506)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.16,17.506)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.4,17.506)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.54,17.506)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.55,8.636)"> <use xlink:href="#g113-82"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.87,11.767)"> <path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path> </g> <rect height="0.65243" width="16.5197" x="71.27" y="13.853"></rect> <g transform="matrix(.013,0,0,-0.013,71.27,26.732)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.49,26.732)"> <path d="M457 332C457 400 429 448 397 448C384 448 371 441 365 435L366 428C376 413 388 372 388 315C388 152 306 45 220 45C166 45 134 85 158 180L197 332C204 361 207 385 207 402C207 434 196 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C130 383 129 374 122 343L76 156C71 137 69 120 69 105C69 25 125 -12 181 -12C314 -12 457 166 457 332Z" id="g113-242"></path> </g> <g transform="matrix(.013,0,0,-0.013,88.99,17.506)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="63.4114pt" id="M44-2" version="1.1" viewbox="0 0 33.734 63.4114" width="33.734pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B44-2"> <g transform="matrix(.013,0,0,-0.013,0,50.756)"> <use xlink:href="#g113-242"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.88,50.756)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.34,41.766)"> <path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path> </g> <rect height="0.65243" width="7.24204" x="22.34" y="47.103"></rect> <g transform="matrix(.013,0,0,-0.013,22.44,59.982)"> <use xlink:href="#g113-239"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.77,50.756)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R44"> <svg class="label" height="11.44pt" id="M44-3" 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="B44-3"> <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="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.58,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">其中λ是摩擦系数，Re是雷诺系数，据svg height="11.9453pt" id="M45" style="vertical-align:-3.309401pt" version="1.1" viewbox="-0.0498162 -8.6359 14.0732 11.9453" width="14.0732pt" 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(.0091,0,0,-0.0091,9.321,3.132)"> <use xlink:href="#g185-40"></use> </g> </svg>是体积流量，m据sup>3.据/sup>/ s;据一世>D.据/一世>为管道内径，m;据一世>ν据/一世>运动粘度是m吗据sup>2据/sup>/ s;据svg height="9.39034pt" id="M46" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.34167 9.39034" width="7.34167pt" 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="#g113-234"></use> </g> </svg>是动态粘度，PA·S;据svg height="9.39034pt" id="M47" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.13289 9.39034" width="7.13289pt" 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="#g113-239"></use> </g> </svg>是气体密度，kg·m据sup>-3据/sup>．据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">合理范围的泄漏区域确定如下：据/span></span></span><span class="equation_break" id="EEq22"><span class="left_break" id="L48"></span><span class="middle_break"><span class="center_break" id="M48"> <svg height="13.8661pt" id="M48-1" version="1.1" viewbox="0 0 88.634 13.8661" width="88.634pt" 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,-0.013,0,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.88,9.184)"> <path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z" id="g117-93"></path> </g> <g transform="matrix(.013,0,0,-0.013,21.14,9.184)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.38,12.316)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.47,12.316)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.17,9.184)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.43,9.184)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.68,12.316)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.06,12.316)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.62,12.316)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,80.71,12.316)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,85.67,9.184)"> <use xlink:href="#g113-45"></use> </g> </g> </svg></span></span><span class="right_break" id="R48"> <svg class="label" height="11.44pt" id="M48-2" 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="B48-2"> <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,-0.013,10.61,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.66,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里据svg height="11.927pt" id="M49" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 17.5389 11.927" width="17.5389pt" 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(.0091,0,0,-0.0091,10.244,3.132)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.331,3.132)"> <use xlink:href="#g50-106"></use> </g> </svg>是节点的有效泄漏区域据一世>一世据/一世>;据svg height="11.9316pt" id="M50" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 32.3727 11.9316" width="32.3727pt" 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(.0091,0,0,-0.0091,10.244,3.132)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,15.628,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.19,3.132)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.276,3.132)"> <use xlink:href="#g58-118"></use> </g> </svg>为泄漏面积的最大极限，确定为管道横截面积的合理比例。据/span></span></span></p> <h5 id="sec3.3">３．３．算法优化据/h5> <p>序列二次规划(SQP)算法是处理非线性规划问题最有效的方法之一。该算法具有计算效率高、收敛性好等优点。由于目标函数中包含非线性函数的规划问题，采用SQP算法对其进行优化和收敛。SQP算法步骤如下:据span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">定义目标函数据一世>E.据/一世>（据一世>X据/一世>）。据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">在约束中定义非线性约束。据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">确定初始值据一世>X据/一世><sub>0.据/sub>迭代。据/span></span><span class="list-item"><span class="list-label">（4）据/span><span class="list-content">确定变量的上限和下限，并分别表示为VUB和VLB。据/span></span><span class="list-item"><span class="list-label">（5）据/span><span class="list-content">建立主程序。非线性编程的功能是Fmincon，并运行解决方案。据/span></span><span class="list-item"><span class="list-label">（6）据/span><span class="list-content">在算法优化的最后，如果发现节点的泄漏区域不为零，则将其视为泄漏状态;否则视为无泄漏状态。据/span></span><span class="list-item"><span class="list-label">(7）据/span><span class="list-content">准确定位管道泄漏。据/span></span></span></p> <h4 id="nonmetallic-pipeline-leak-diagnosis-models-and-procedures">4.非金属管道泄漏诊断模型和程序据/h4> <h5 id="sec4.1">4．1.模型建立据/h5> <p>根据城市气体管道的特点，为涉嫌泄漏状态的管道建立Markov链流状态转换概率矩阵，并且将预测的流量状态与实际流动状态进行比较，以定量地确定管道泄漏。建立了适用于城市非金属气体管道泄漏位置的逆瞬态分析模型，基于实际压力和计算压力之间的差异建立了目标函数，并用连续的二次编程方法（SQP）进行了优化，以确保计算效率和融合。具体模型如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig2/" target="_blank">2据/一种>[据一种href="#B15">15据/一种>那据一种href="#B16">16据/一种>］.据/p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.002" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.002.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 城市埋藏非金属管道泄漏诊断分析模型。据/D.一世v> </div> </div> </div> <h5 id="sec4.2">4.2。实施步骤据/h5> <p><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">第一步:马尔可夫定量泄漏测定据/span></span><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">通过逐渐关闭管道阀以产生瞬态流量，收集第一组管道流量以建立马尔可夫状态转换概率矩阵据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">在相同的环境下，采集第二组流量数据，计算参数向量，结合状态转移概率矩阵预测下一时段管道的流动状态据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">将预测的管道流动状态与实际状态进行比较，判断管道是否泄漏据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第2步：划分节点据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">当判断管道存在泄漏时，将泄漏管段划分为多个监测节点，获取节点处的流量和压力参数据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">步骤3:建立瞬态逆定位模型据/span></span><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">建立了瞬态泄漏逆控制方程据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">建立了基于近稳态流动数据的管道泄漏监测目标函数据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第4步：算法优化据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">SQP算法用于汇聚目标函数，以找到每个节点的两端之间的流量差异，并计算监视节点的有效泄漏区域据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第5步：定位计算据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">如果只有单个监视节点的有效泄漏面积是非零，则监控节点被判断为泄漏点。如果多个监视节点的有效泄漏区域是非零，则在非零节点之间继续划分等步骤的监视节点。重复步骤2至4，直到两个节点之间的距离符合定位管道泄漏的要求。据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">定位精度与监控节点的数量密切相关。如果判断出单个节点泄漏，则认为泄漏点位于该节点处。如果计算出存在多个监视节点泄漏，继续在这些监视节点之间的管道部分中排列具有相等距离的多个监控节点，并重复计算，直到达到每个节点之间的距离达到精度要求时达到终止步骤．找到具有非零有效泄漏区域的节点，以便精确定位。据/span></span></span></p> <h4 id="test-flow-field-analysis">5.试验流场分析据/h4> <p>试验管部分的材料是PPC管。管道的总长度为8米，具有U形结构。管的直径为0.0456μm，工作压力为0.3MPa，0.2MPa和0.1MPa。传输介质在室温下是空气。管道结构如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig3/" target="_blank">3.据/一种>．在管道的进口端依次设置有上游流量传感器1、上游压力传感器2和上游次声传感器3。在管道出口端依次设置有下游流量传感器6、下游压力传感器5和下游次声传感器4。结构框图如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig4/" target="_blank">4.据/一种>．据一世>X据/一世><sub>1据/sub>来据一世>X据/一世><sub>6.据/sub>是监控节点，长度据一世>X据/一世><sub>1据/sub>-据一世>X据/一世><sub>2据/sub>管段长度为3.2米据一世>X据/一世><sub>2据/sub>-据一世>X据/一世><sub>3.据/sub>管部分为1.6米，并且长度为1.6米据一世>X据/一世><sub>3.据/sub>-据一世>X据/一世><sub>4.据/sub>管段为3.2米。泄漏孔在距离地面0.6 m以下据一世>X据/一世><sub>3.据/sub>，泄漏孔径为0.004 m。的据一世>X据/一世><sub>1据/sub>是在管道入口和据一世>X据/一世><sub>4.据/sub>在管道出口。的据一世>X据/一世><sub>5.据/sub>和据一世>X据/一世><sub>6.据/sub>0.4米和1.2米在据一世>X据/一世><sub>2据/sub>，分别。测试环境温度为24摄氏度。据/p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.003" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.003.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 测试管道。据/D.一世v> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.004" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.004.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 试验管线结构示意图。据/D.一世v> </div> </div> </div> <p>在0.1MPa的入口压力下，0.2MPa和0.3MPa，收集管道头部和漏极泄漏和非释放条件下的压力和流动变化。收集的数据如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig5/" target="_blank">5.据/一种>-据一种href="//www.newsama.com/journals/amse/2020/9527836/fig7/" target="_blank">7.据/一种>．标有正方形的多边形线代表上游流动，用圆形标记的多边形线是下游流动，标有正三角形的折线是上游压力，并且标有倒三角形的折线是下游压力。据/p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.005" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.005.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 压力和流量数据收集0.1 MPa泄漏。据/D.一世v> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.006" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.006.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 在泄漏0.2 MPa时收集压力和流量数据。据/D.一世v> </div> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="9527836.fig.007" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.007.svgz"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 泄漏0.3 MPa时收集压力和流量数据。据/D.一世v> </div> </div> </div> <p>从数字据一种href="//www.newsama.com/journals/amse/2020/9527836/fig5/" target="_blank">5.据/一种>-据一种href="//www.newsama.com/journals/amse/2020/9527836/fig7/" target="_blank">7.据/一种>(1)管道不泄漏时，管道初、末压力相近，整个管道压力稳定;泄漏时，管道内总压力减小，上下游压力差不明显。(2)当不存在泄漏时，管道头端流速相等，整个管道流速稳定;泄漏时，泄漏孔前端流量显著增加，泄漏孔后端流量略有下降。经过一段时间后，泄漏孔前部的流量减小，而泄漏孔两端的流量保持不变，进口压力越大，流量差越大。据/p> <h4 id="markov-chain-quantitative-leak-judgment">6.马尔可夫链定量泄漏判断据/h4> <h5 id="sec6.1">6.1。建立国家转换概率矩阵据/h5> <p>在部分0.3MPa的入口压力下从泄漏测试中收集第一组流量数据据一种href="#sec5">5.据/一种>其中包括2.66,2.79,2.81,3.16和3.76（m据sup>3.据/sup>/ h)。获得了每次流动变化率据一世>问：据/一世><sub>1据/sub>=0.那据一世>问：据/一世><sub>2据/sub>=4.。6.6.%,据一世>问：据/一世><sub>3.据/sub>=0.。7.1%, and据一世>问：据/一世><sub>4.据/sub>=11.。0.6.%; the flow change rates in the four leakage states were据一世>N据/一世><sub>1据/sub>=1，据一世>N据/一世><sub>2据/sub>=1，据一世>N据/一世><sub>3.据/sub>=0.，和据一世>N据/一世><sub>4.据/sub>= 3。据/p> <p>然后，得到状态转移概率矩阵据一世>P.据/一世>马尔可夫链条如下：据span class="equation_break" id="EEq23"><span class="left_break" id="L51"></span><span class="middle_break"><span class="center_break" id="M51"> <svg height="67.5096pt" id="M51-1" version="1.1" viewbox="0 0 131.254 67.5096" width="131.254pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B51-1"> <g transform="matrix(.013,0,0,-0.013,0,37.082)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.66,37.082)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.92,37.082)"> <path d="M977 -2260C523 -1750 258 -773 258 271C258 1317 519 2291 977 2802L940 2838C397 2253 152 1318 152 272V271C152 -785 397 -1724 940 -2296L977 -2260Z" id="g119-229"></path> </g> <g transform="matrix(.013,0,0,-0.013,41.39,9.267)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.45,9.267)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.51,9.267)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.57,9.267)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.39,27.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.45,27.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.51,27.297)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.57,27.297)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.39,45.327)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.45,45.327)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.51,45.327)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.57,45.327)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.39,63.462)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.63,63.462)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.87,63.462)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.23,63.462)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.51,63.462)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.75,63.462)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.99,63.462)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,101.35,63.462)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.64,37.082)"> <path d="M1034 271V272C1034 1318 789 2253 246 2838L209 2802C667 2291 928 1317 928 271C928 -773 663 -1750 209 -2260L246 -2296C789 -1724 1034 -785 1034 271Z" id="g119-236"></path> </g> <g transform="matrix(.013,0,0,-0.013,128.29,37.082)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R51"> <svg class="label" height="11.44pt" id="M51-2" 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="B51-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <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></span></span></p> <h5 id="sec6.2">6.2。管道泄漏的定量测定据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">在相同的环境条件下，收集了第二组流量数据，其中包括4.36,4.89,5.33,5.71和5.99（m据sup>3.据/sup>/ h)。获得了每次流动变化率据一世>问：据/一世><sub>1据/sub>=13.。6.7.%,据一世>问：据/一世><sub>2据/sub>=10.。8.4.%,据一世>问：据/一世><sub>3.据/sub>=8.26.%,据一世>问：据/一世><sub>4.据/sub>=6.。6.5.%, and据一世>问：据/一世><sub>5.据/sub>= 4.67%;四种泄漏状态下的流量变化率为据一世>N据/一世><sub>1据/sub>=0.那据一世>N据/一世><sub>2据/sub>=0.那据一世>N据/一世><sub>3.据/sub>=0.，和据一世>N据/一世><sub>4.据/sub>= 5。将此时每个区间的实际流量变化数编码为参数向量，得到据/span></span></span><span class="equation_break" id="EEq24"><span class="left_break" id="L52"></span><span class="middle_break"><span class="center_break" id="M52"> <svg height="14.5707pt" id="M52-1" version="1.1" viewbox="0 0 91.224 14.5707" width="91.224pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B52-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.06,13.725)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.63,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.9,10.593)"> <path d="M308 -259V-228H299C192 -219 190 -215 190 -109V616C190 755 193 759 299 768H308V799H127V-259H308Z" id="g119-1"></path> </g> <g transform="matrix(.013,0,0,-0.013,34.74,9.875)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.15,9.875)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.56,9.875)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.97,9.875)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.22,10.593)"> <path d="M244 -259V799H63V768H72C178 759 181 755 181 616V-109C181 -215 179 -219 72 -228H63V-259H244Z" id="g119-2"></path> </g> <g transform="matrix(.013,0,0,-0.013,88.26,10.593)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R52"> <svg class="label" height="11.44pt" id="M52-2" version="1.1" viewbox="0 0 21.318 11.44" width="21.318pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B52-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.36,9.26)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.82,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">从马尔可夫链计算，参数矢量据一世>β据/一世><sub>1据/sub>基于马尔可夫链预测的未来时段流量变化率的据/span></span></span><span class="equation_break" id="EEq25"><span class="left_break" id="L53"></span><span class="middle_break"><span class="center_break" id="M53"> <svg height="14.5707pt" id="M53-1" version="1.1" viewbox="0 0 120.764 14.5707" width="120.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B53-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.22,13.725)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.8,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.06,10.593)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.91,9.928)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.32,9.928)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.56,9.928)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.92,9.928)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.2,9.928)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.61,9.928)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.85,9.928)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.09,9.928)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,101.45,9.928)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.76,10.593)"> <use xlink:href="#g119-2"></use> </g> <g transform="matrix(.013,0,0,-0.013,117.8,10.593)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R53"> <svg class="label" height="11.44pt" id="M53-2" version="1.1" viewbox="0 0 21.078 11.44" width="21.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B53-2"> <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,-0.013,10.68,9.26)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.58,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><span class="nowrap"> <svg height="13.9998pt" id="M54" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 56.9815 13.9998" width="56.9815pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,14.366,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,19.768,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,22.686,5.233)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.506,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.769,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.831,3.132)"> <use xlink:href="#g50-53"></use> </g> </svg>那据/span>据预测，管道的状态将在第四州。据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">如上所述，收集第三组流量数据，分别为6.24、6.65、6.81、7.02、7.12 (m)据sup>3.据/sup>/ h)。得到各时刻的流量变化率为据一世>问：据/一世><sub>1据/sub>=4.。0.1%,据一世>问：据/一世><sub>2据/sub>= 6.17%,据一世>问：据/一世><sub>3.据/sub>=2。3.5.%,据一世>问：据/一世><sub>4.据/sub>= 2.99%,据一世>问：据/一世><sub>5.据/sub>= 1.40%;四种泄漏状态下的流量变化率为据一世>N据/一世><sub>1据/sub>=0.那据一世>N据/一世><sub>2据/sub>=0.那据一世>N据/一世><sub>3.据/sub>= 3,据一世>N据/一世><sub>4.据/sub>=2。W.E.obtain:据/span></span></span><span class="equation_break" id="EEq26"><span class="left_break" id="L55"></span><span class="middle_break"><span class="center_break" id="M55"> <svg height="14.5707pt" id="M55-1" version="1.1" viewbox="0 0 91.054 14.5707" width="91.054pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B55-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.06,13.725)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.64,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.9,10.593)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.74,9.875)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.16,9.875)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.57,9.875)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,71.81,9.875)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.06,10.593)"> <use xlink:href="#g119-2"></use> </g> <g transform="matrix(.013,0,0,-0.013,88.09,10.593)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R55"> <svg class="label" height="11.44pt" id="M55-2" version="1.1" viewbox="0 0 21.478 11.44" width="21.478pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B55-2"> <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,-0.013,10.54,9.26)"> <use xlink:href="#g190-227"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.98,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><span class="nowrap"> <svg height="13.9998pt" id="M56" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 60.3154 13.9998" width="60.3154pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-88"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,17.688,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,23.089,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,26.008,5.233)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.84,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.103,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,55.165,3.132)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span>据预测，管道状态将处于第三种状态。据/span></span><span class="list-item"><span class="list-label">（4）据/span><span class="list-content">状态序列号的值据一世>S.据/一世>处于预测状态据svg height="13.9998pt" id="M57" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 27.012 13.9998" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,14.366,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,19.768,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,22.686,5.233)"> <use xlink:href="#g58-118"></use> </g> </svg>与状态序列号的值进行比较据一世>W.据/一世>在实际状态据span class="nowrap"> <svg height="13.9998pt" id="M58" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 30.3459 13.9998" width="30.3459pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-88"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,17.688,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,23.089,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,26.008,5.233)"> <use xlink:href="#g58-118"></use> </g> </svg>：据/span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">由于S > W，判断为启动泄漏后期。同样，对进口压力分别为0.1 MPa和0.2 MPa时的流动数据进行了分析计算，结果如下据svg height="13.9998pt" id="M59" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 56.9815 13.9998" width="56.9815pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,14.366,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,19.768,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,22.686,5.233)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.506,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.769,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.831,3.132)"> <use xlink:href="#g50-53"></use> </g> </svg>和据span class="nowrap"> <svg height="13.9998pt" id="M60" style="vertical-align:-5.3639pt" version="1.1" viewbox="-0.0498162 -8.6359 60.3154 13.9998" width="60.3154pt" 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="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.062,3.132)"> <use xlink:href="#g50-88"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,17.688,5.233)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,23.089,5.233)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0065,0,0,-0.0065,26.008,5.233)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.84,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.103,0)"> <use xlink:href="#g113-79"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,55.165,3.132)"> <use xlink:href="#g50-52"></use> </g> </svg>那据/span>分别。那是，据一世>S.据/一世>>据一世>W.据/一世>，确定试验管道已处于泄漏后期。据/span></span></span></p> <h4 id="calculation-of-pipeline-leakage-location-by-inverse-transient-method">7.通过逆瞬态方法计算管道泄漏位置据/h4> <h5 id="sec7.1">7.1。划分节点据/h5> <p>根据图据一种href="//www.newsama.com/journals/amse/2020/9527836/fig4/" target="_blank">4.据/一种>,四个节点据一世>X据/一世><sub>1据/sub>那据一世>X据/一世><sub>2据/sub>那据一世>X据/一世><sub>3.据/sub>，和据一世>X据/一世><sub>4.据/sub>首先划分，步长为1.6米。分别计算4个节点的泄漏参数。据/p> <h5 id="sec7.2">7.2。目标函数的建立据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">根据泄漏控制方程（据一种href="#EEq14">15据/一种>-据一种href="#EEq19">19据/一种>），节点的计算压力与真正压力之间的差异表示如下[据一种href="#B17">17据/一种>-据一种href="#B19">19据/一种>]：据/span></span></span><span class="equation_break" id="EEq27"><span class="left_break" id="L61"></span><span class="middle_break"><span class="center_break" id="M61"> <svg height="40.4071pt" id="M61-1" version="1.1" viewbox="0 0 32.348 40.4071" width="32.348pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B61-1"> <g 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id="M61-3" version="1.1" viewbox="0 0 24.289 40.4071" width="24.289pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B61-3"> <g transform="matrix(.013,0,0,-0.013,0,23.877)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,23.877)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.91,23.877)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,4.604)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,8.205)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,11.807)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,15.408)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,19.01)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,22.611)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,26.213)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,29.814)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,33.415)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,37.017)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.87,40.618)"> <use xlink:href="#g119-34"></use> </g> </g> </svg> <svg class="alt_equation" height="132.715pt" id="I61" version="1.1" viewbox="0 0 494.71 132.715" width="494.71pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -14.69)" xlink:href="#B61-1"></use> <use transform="matrix(1 0 0 1 13.59 43.03)" xlink:href="#B61-2"></use> <use transform="matrix(1 0 0 1 12.86 92.31)" xlink:href="#B61-3"></use> </svg></span></span><span class="right_break" id="R61"> <svg class="label" height="11.44pt" id="M61-4" 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="B61-4"> <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,-0.013,10.63,9.26)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.66,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="132.715pt" id="IL61" version="1.1" viewbox="0 0 21.24 132.715" width="21.24pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 60.43)" xlink:href="#B61-4"></use> </svg></span></span><span class="list"><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">有效泄漏面积范围的确定:据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">若测试泄漏孔半径为2mm，则以泄漏孔半径为3mm时的有效泄漏面积为泄漏面积的最大极限:据/span></span></span><span class="equation_break" id="EEq28"><span class="left_break" id="L62"></span><span class="middle_break"><span class="center_break" id="M62"> <svg height="15.9225pt" id="M62-1" version="1.1" viewbox="0 0 111.764 15.9225" width="111.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B62-1"> <g transform="matrix(.013,0,0,-0.013,0,11.958)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.87,11.958)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.13,11.958)"> <use xlink:href="#g113-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.38,15.09)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.013,0,0,-0.013,39.36,11.958)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.62,11.958)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.86,11.958)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.83,11.958)"> <path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z" id="g113-57"></path> </g> <g transform="matrix(.013,0,0,-0.013,66.07,11.958)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,75.21,11.958)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,85.75,11.958)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,91.99,11.958)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,98.28,5.695)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,103.84,5.695)"> <use xlink:href="#g50-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.8,11.958)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R62"> <svg class="label" height="11.44pt" id="M62-2" version="1.1" viewbox="0 0 21.298 11.44" width="21.298pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B62-2"> <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,-0.013,10.62,9.26)"> <use xlink:href="#g190-152"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">测定管道中的摩擦系数：据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">24℃时，空气的动态粘度为1.83 × 10据sup>-5据/sup> Pa·s and the kinematic viscosity is 1.4364 × 10据sup>-5据/sup> m据sup>2据/sup>/ s。将无泄漏的稳态数据和参数带入方程(据一种href="#EEq20">20.据/一种>），并发现管道中的摩擦系数约为0.07。据/span></span></span></p> <h5 id="sec7.3">7.3。算法优化据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">节点上的数据据一世>X据/一世><sub>2据/sub>计算了节点的压力和流量数据据一世>X据/一世><sub>2据/sub>，压力和流量数据在△据一世>X据/一世>(1.6米)两端据一世>X据/一世><sub>2据/sub>，并且已知参数被取代成等式（据一种href="#EEq27">27据/一种>）。以0.3MPa为例，以0.3MPa的测试数据为例，并且瞬态数据进入等式（据一种href="#EEq27">27据/一种>）获得目标函数：据/span></span></span><span class="equation_break" id="EEq29"><span class="left_break" id="L63"></span><span class="middle_break"><span class="center_break" id="M63"> <svg height="40.4071pt" id="M63-1" version="1.1" viewbox="0 0 32.241 40.4071" width="32.241pt" xmlns="http://www.w3.org/2000/svg" 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transform="matrix(.013,0,0,-0.013,63.13,22.611)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.13,26.213)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.13,29.814)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.13,33.415)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.13,37.017)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.13,40.618)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.88,23.877)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="132.715pt" id="I63" version="1.1" viewbox="0 0 202.97 132.715" width="202.97pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -14.69)" xlink:href="#B63-1"></use> <use transform="matrix(1 0 0 1 13.59 43.03)" xlink:href="#B63-2"></use> <use transform="matrix(1 0 0 1 12.87 92.31)" xlink:href="#B63-3"></use> </svg></span></span><span class="right_break" id="R63"> <svg class="label" height="11.44pt" id="M63-4" version="1.1" viewbox="0 0 21.388 11.44" width="21.388pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B63-4"> <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,-0.013,10.54,9.26)"> <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="132.715pt" id="IL63" version="1.1" viewbox="0 0 21.47 132.715" 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 60.43)" xlink:href="#B63-4"></use> </svg></span></span><span class="list"><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">非线性约束的定义：据/span></span></span><span class="equation_break" id="EEq30"><span class="left_break" id="L64"></span><span class="middle_break"><span class="center_break" id="M64"> <svg height="55.1861pt" id="M64-1" version="1.1" viewbox="0 0 71.874 55.1861" width="71.874pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-1"> <g transform="matrix(.013,0,0,-0.013,0,9.184)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.22,12.316)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.08,9.184)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.61,9.184)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.83,12.316)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.41,9.184)"> <path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z" id="g117-94"></path> </g> <g transform="matrix(.013,0,0,-0.013,62.67,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.91,9.184)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="55.1861pt" id="M64-2" version="1.1" viewbox="0 0 48.712 55.1861" width="48.712pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-2"> <g transform="matrix(.013,0,0,-0.013,0,30.203)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.22,33.334)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.8,30.203)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.06,30.203)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,44.28,33.334)"> <use xlink:href="#g50-50"></use> </g> </g> </svg> <svg height="55.1861pt" id="M64-3" version="1.1" viewbox="0 0 96.144 55.1861" width="96.144pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-3"> <g transform="matrix(.013,0,0,-0.013,0,30.203)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.26,30.203)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.48,33.334)"> <use xlink:href="#g50-67"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,29.02,33.334)"> <use xlink:href="#g54-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,34.58,33.334)"> <path d="M610 0V27L347 666L316 657L46 26V0H610ZM504 54H116L310 537L504 54Z" id="g50-133"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,40.52,33.334)"> <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,-0.013,47.16,30.203)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.7,30.203)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.92,33.334)"> <use xlink:href="#g50-77"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,76.57,33.334)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,84.13,33.334)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,88.21,33.334)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.013,0,0,-0.013,93.18,30.203)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="55.1861pt" id="M64-4" version="1.1" viewbox="0 0 93.764 55.1861" width="93.764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-4"> <g transform="matrix(.013,0,0,-0.013,0,51.222)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.24,54.353)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.54,51.222)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.8,51.222)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,37.02,54.353)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.6,51.222)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.86,51.222)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,69.08,54.353)"> <use xlink:href="#g50-66"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,75.55,54.353)"> <use xlink:href="#g54-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,81.11,54.353)"> <use xlink:href="#g50-133"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,87.06,54.353)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.8,51.222)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="76.205pt" id="I64" version="1.1" viewbox="0 0 147.83 76.205" width="147.83pt" 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="#B64-1"></use> <use transform="matrix(1 0 0 1 30.68 0)" xlink:href="#B64-2"></use> <use transform="matrix(1 0 0 1 51.52 21.02)" xlink:href="#B64-3"></use> <use transform="matrix(1 0 0 1 37.96 21.02)" xlink:href="#B64-4"></use> </svg></span></span><span class="right_break" id="R64"> <svg class="label" height="11.44pt" id="M64-5" version="1.1" viewbox="0 0 21.438 11.44" width="21.438pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B64-5"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.26)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.94,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="76.205pt" id="IL64" version="1.1" viewbox="0 0 21.52 76.205" width="21.52pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 32.17)" xlink:href="#B64-5"></use> </svg></span></span><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>m据/一世><sub><i>L.据/一世>最大限度据/sub>为将最大限制泄漏面积代入泄漏量公式(据一种href="#EEq14">16据/一种>），这是0.092千克/秒：据/span></span></span><span class="equation_break" id="EEq31"><span class="left_break" id="L65"></span><span class="middle_break"><span class="center_break" id="M65"> <svg height="71.2237pt" id="M65-1" version="1.1" viewbox="0 0 138.174 71.2237" width="138.174pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B65-1"> <g transform="matrix(.013,0,0,-0.013,0,18.917)"> <path d="M520 -816C310 -597 186 -177 186 271C186 720 307 1139 520 1358L491 1388C219 1134 96 727 96 272V271C96 -188 219 -597 491 -846L520 -816Z" id="g119-157"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.05,9.184)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.68,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.95,9.184)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.88,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,30.95,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.2,18.917)"> <path d="M522 271V272C522 727 399 1134 127 1388L98 1358C311 1139 432 720 432 271C432 -177 308 -597 98 -816L127 -846C399 -597 522 -188 522 271Z" id="g119-158"></path> </g> <g transform="matrix(.013,0,0,-0.013,50.44,18.917)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.5,9.184)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,73.72,12.316)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.5,27.214)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,73.72,30.346)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,81.7,18.917)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,93.39,18.917)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,104.66,18.917)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.71,9.184)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.71,27.214)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,124.96,18.917)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,135.21,18.917)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg height="71.2237pt" id="M65-2" version="1.1" viewbox="0 0 123.104 71.2237" width="123.104pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B65-2"> <g transform="matrix(.013,0,0,-0.013,0,58.962)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.05,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.29,49.229)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.25,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.49,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,32.73,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.97,49.229)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.22,49.229)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.46,49.229)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.33,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.86,58.962)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.55,58.962)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.82,58.962)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.87,49.229)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,107.09,52.361)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.87,67.259)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,107.09,70.391)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.07,58.962)"> <use xlink:href="#g119-158"></use> </g> </g> </svg> <svg height="71.2237pt" id="M65-3" version="1.1" viewbox="0 0 85.324 71.2237" width="85.324pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B65-3"> <g transform="matrix(.013,0,0,-0.013,0,58.962)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.26,58.962)"> <use xlink:href="#g119-157"></use> </g> <g transform="matrix(.013,0,0,-0.013,25.44,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.68,49.229)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,34.65,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.89,49.229)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,47.13,49.229)"> <use xlink:href="#g113-57"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.37,49.229)"> <use xlink:href="#g113-58"></use> </g> <g transform="matrix(.013,0,0,-0.013,59.61,49.229)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.31,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.55,67.259)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.52,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.76,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,44,67.259)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,50.24,67.259)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.48,67.259)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.72,67.259)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.12,58.962)"> <use xlink:href="#g119-158"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.36,58.962)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R65"> <svg class="label" height="11.44pt" id="M65-4" version="1.1" viewbox="0 0 19.078 11.44" width="19.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B65-4"> <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="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.19,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.58,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span><span class="list"><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">流据一世>m据/一世><sub><i>一种据/一世></sub>和据一世>m据/一世><sub><i>B.据/一世></sub>第14组数据被视为初始计算值，具有初始值据一世>X据/一世><sub>0.据/sub>=[0.。0.0.19.8.那0.。0.0.0.6.35].据/span></span><span class="list-item"><span class="list-label">（4）据/span><span class="list-content">确定变量的上限和下限：据/span></span><span class="list-item"><span class="list-label"></span><span class="list-content">根据步骤2：VLB = [0.000635,0]计算数据;Vub = [0.00893,0.000635]。据/span></span><span class="list-item"><span class="list-label">（5）据/span><span class="list-content">流动差异据一世>X据/一世><sub>2据/sub>和据一世>X据/一世><sub>3.据/sub>为0.0033 kg/s，将数据带入公式(据一种href="#EEq14">16据/一种>）获得1.01×10的有效泄漏面积据sup>-5 据/sup>m据sup>2据/sup>．根据上述步骤，节点前后的流动差异据一世>X据/一世><sub>1据/sub>和据一世>X据/一世><sub>4.据/sub>分别为0和0，则有效泄漏面积分别为0和0。4个节点的SQP算法迭代图如图所示据一种href="//www.newsama.com/journals/amse/2020/9527836/fig8/" target="_blank">8（a）据/一种>-据一种href="//www.newsama.com/journals/amse/2020/9527836/fig8/" target="_blank">8 (d)据/一种>．据/span></span></span></p> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="（一种）“N一种mE.="9527836.fig.008a" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008a.svgz"> <br> <strong>（一种）据/strong> </div> <div class="partial-carousel--single-image"> <img alt="(b)“N一种mE.="9527836.fig.008b" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008b.svgz"> <br> <strong>(b)据/strong> </div> <div class="partial-carousel--single-image"> <img alt="(c)“N一种mE.="9527836.fig.008c" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008c.svgz"> <br> <strong>(c)据/strong> </div> <div class="partial-carousel--single-image"> <img alt="(d)“N一种mE.="9527836.fig.008d" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008d.svgz"> <br> <strong>(d)据/strong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig8"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="（一种）“N一种mE.="9527836.fig.008a" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008a.svgz"><br><strong>（一种）据/strong></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)“N一种mE.="9527836.fig.008b" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008b.svgz"><br><strong>(b)据/strong></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)“N一种mE.="9527836.fig.008c" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008c.svgz"><br><strong>(c)据/strong></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)“N一种mE.="9527836.fig.008d" src="https://static-01.hindawi.com/articles/amse/volume-2020/9527836/figures/9527836.fig.008d.svgz"><br><strong>(d)据/strong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig8"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 4个节点算法的迭代图。（一种）据一世>X据/一世> <sub>1据/sub>节点算法迭代，(b)据一世>X据/一世> <sub>2据/sub>节点算法迭代，（c）据一世>X据/一世> <sub>3.据/sub>节点算法迭代，（d）据一世>X据/一世> <sub>4.据/sub>节点算法迭代。据/D.一世v> </div> </div> </div> <h5 id="sec7.4">7.4。泄漏位置计算据/h5> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">根据四个节点的计算有效泄漏区域，泄漏点位于节点之间据一世>X据/一世><sub>2据/sub>和据一世>X据/一世><sub>3.据/sub>．据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">由于泄漏点在节点之间据一世>X据/一世><sub>2据/sub>和据一世>X据/一世><sub>3.据/sub>，两个监测点据一世>X据/一世><sub>5.据/sub>和据一世>X据/一世><sub>6.据/sub>是否再次设置在节点之间的管道段据一世>X据/一世><sub>2据/sub>和据一世>X据/一世><sub>3.据/sub>和△据一世>X据/一世>被占0.4米。根据上述过程，在之前和之后的流动差异据一世>X据/一世><sub>5.据/sub>和据一世>X据/一世><sub>6.据/sub>计算为0和0.0033kg / s，有效的泄漏区域为0和1.01×10据sup>-5据/sup> m据sup>2据/sup>．根据4.2节点划分的要求和试管素的实际情况，确定泄漏点在管道部分上0.8米以后长据一世>X据/一世><sub>6.据/sub>，即，泄漏点的最终位置是在据一世>X据/一世><sub>6.据/sub>．类似地，根据上述步骤分析了0.2MPa和0.1MPa的入口压力下的数据，最后泄漏点位于据一世>X据/一世><sub>6.据/sub>．此节点的泄漏参数显示在表中据一种href="//www.newsama.com/journals/amse/2020/9527836/tab1/" target="_blank">1据/一种>．据/span></span></span></p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td class="align_left">入口压力（MPa）据/T.D.> <td class="align_center">流动差异（kg / s）据/T.D.> <td class="align_center">节点压力（MPA）据/T.D.> <td class="align_center">有效节点渗漏面积(m据sup>2据/sup>）据/T.D.> <td class="align_center">真正的泄漏面积（m据sup>2据/sup>）据/T.D.> <td class="align_center">绝对误差(m据sup>2据/sup>）据/T.D.> </tr> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td class="align_left">0.3据/T.D.> <td class="align_center">0.0033据/T.D.> <td class="align_center">0.14据/T.D.> <td class="align_center">1.01×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.246×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.2据/T.D.> <td class="align_center">0.0029据/T.D.> <td class="align_center">0.11据/T.D.> <td class="align_center">1.124×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.132×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.1据/T.D.> <td class="align_center">0.0012据/T.D.> <td class="align_center">0.04据/T.D.> <td class="align_center">1.279×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.023×10据sup>-5据/sup></td> </tr> <tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表格1据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 第一次测试据一世>X据/一世> <sub>5.据/sub>不同压力下节点泄漏参数。据/D.一世v> </div> </div> </div> <p>在与第一个测试相同的条件下再次重复测试两次，并且泄漏点的确切计算结果如表所示据一种href="//www.newsama.com/journals/amse/2020/9527836/tab2/" target="_blank">2据/一种>和据一种href="//www.newsama.com/journals/amse/2020/9527836/tab3/" target="_blank">3.据/一种>．在3次测试中获得的不同入口压力下泄漏点处有效泄漏面积的平均绝对计算误差如表所示据一种href="//www.newsama.com/journals/amse/2020/9527836/tab4/" target="_blank">4.据/一种>．据/p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td class="align_left">入口压力（MPa）据/T.D.> <td class="align_center">流动差异（kg / s）据/T.D.> <td class="align_center">节点压力（MPA）据/T.D.> <td class="align_center">有效节点渗漏面积(m据sup>2据/sup>）据/T.D.> <td class="align_center">真正的泄漏面积（m据sup>2据/sup>）据/T.D.> <td class="align_center">绝对误差(m据sup>2据/sup>）据/T.D.> </tr> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td class="align_left">0.3据/T.D.> <td class="align_center">0.0027据/T.D.> <td class="align_center">0.1据/T.D.> <td class="align_center">1.151×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.105×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.2据/T.D.> <td class="align_center">0.0031据/T.D.> <td class="align_center">0.1据/T.D.> <td class="align_center">1.32×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.064×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.1据/T.D.> <td class="align_center">0.0017据/T.D.> <td class="align_center">0.06据/T.D.> <td class="align_center">1.208×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.048×10据sup>-5据/sup></td> </tr> <tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2.据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 第二次测试据一世>X据/一世> <sub>5.据/sub>不同压力下节点泄漏参数。据/D.一世v> </div> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-content fig-content-tab3"> <table class="table-group" id="tab3"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td class="align_left">入口压力（MPa）据/T.D.> <td class="align_center">流动差异（kg / s）据/T.D.> <td class="align_center">节点压力（MPA）据/T.D.> <td class="align_center">有效节点渗漏面积(m据sup>2据/sup>）据/T.D.> <td class="align_center">真正的泄漏面积（m据sup>2据/sup>）据/T.D.> <td class="align_center">绝对误差(m据sup>2据/sup>）据/T.D.> </tr> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td class="align_left">0.3据/T.D.> <td class="align_center">0.0032据/T.D.> <td class="align_center">0.12据/T.D.> <td class="align_center">1.137×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.119×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.2据/T.D.> <td class="align_center">0.0024据/T.D.> <td class="align_center">0.09据/T.D.> <td class="align_center">1.137×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.119×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.1据/T.D.> <td class="align_center">0.0012据/T.D.> <td class="align_center">0.04据/T.D.> <td class="align_center">1.279×10据sup>-5据/sup></td> <td class="align_center">1.256×10据sup>-5据/sup></td> <td class="align_center">0.023×10据sup>-5据/sup></td> </tr> <tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 第三次测试据一世>X据/一世> <sub>5.据/sub>不同压力下节点泄漏参数。据/D.一世v> </div> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-content fig-content-tab4"> <table class="table-group" id="tab4"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr class="thead"> <td class="align_left">入口压力（MPa）据/T.D.> <td class="align_center" colspan="3">绝对误差(m据sup>2据/sup>）据/T.D.> <td class="align_center">平均误差(m据sup>2据/sup>）据/T.D.> </tr> <tr> <td class="thead-hr" colspan="5"> <hr></td> </tr> <tr> <td class="align_left">0.3据/T.D.> <td class="align_center">0.246×10据sup>-5据/sup></td> <td class="align_center">0.105×10据sup>-5据/sup></td> <td class="align_center">0.119×10据sup>-5据/sup></td> <td class="align_center">0.156×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.2据/T.D.> <td class="align_center">0.132×10据sup>-5据/sup></td> <td class="align_center">0.064×10据sup>-5据/sup></td> <td class="align_center">0.119×10据sup>-5据/sup></td> <td class="align_center">0.105×10据sup>-5据/sup></td> </tr> <tr> <td class="align_left">0.1据/T.D.> <td class="align_center">0.023×10据sup>-5据/sup></td> <td class="align_center">0.048×10据sup>-5据/sup></td> <td class="align_center">0.023×10据sup>-5据/sup></td> <td class="align_center">0.031×10据sup>-5据/sup></td> </tr> <tr class="table-tr"> <td colspan="5"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4.据/span> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/amse/2020/9527836/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <div> 三个实验中不同压力下的绝对误差。据/D.一世v> </div> </div> </div> <p>这可以从表中得知据一种href="//www.newsama.com/journals/amse/2020/9527836/tab1/" target="_blank">1据/一种>来据一种href="//www.newsama.com/journals/amse/2020/9527836/tab4/" target="_blank">4.据/一种>管道泄漏有效面积的绝对误差是0.023×10的最低点据sup>-5据/sup> m据sup>2据/sup>最高为0.156 × 10据sup>-5据/sup> m据sup>2据/sup>．在进口压力为0.3 MPa、0.2 MPa和0.1 MPa时，多次试验计算得到的有效泄漏面积的平均绝对误差为0.49 × 10据sup>-5据/sup> m据sup>2据/sup>，0.105×10据sup>-5据/sup> m据sup>2据/sup>，0.031×10据sup>-5据/sup> m据sup>2据/sup>．与通过高斯函数修改的抗衣弧形方法的平均绝对误差相比[据一种href="#B20">20.据/一种>]为0.52×10据sup>-5 据/sup>m据sup>2据/sup>，可以看出，这种方法可以有效地应用于城市非金属天然气管道。然而，管道中的流动介质是可压缩的流体。管道中的压力越大，当发生泄漏时管道中的流体密度的变化越大，导致模型计算中的误差。因此，在实际应用中，应选择接近瞬态过程中稳态的数据以进行计算。据/p> <h4 id="conclusion">8.结论据/h4> <p><span class="list"><span class="list-item"><span class="list-label">（1）据/span><span class="list-content">通过提取马尔可夫链的传递特征，实时获得管道变化的转移概率矩阵，预测管道流量变化的趋势发展。通过比较预测的管道流量变化情况与实际管道流量变化情况，可以判断管道的泄漏情况。马尔可夫链可以实时监测管道流量的变化，通过预测和比较降低误报率。据/span></span><span class="list-item"><span class="list-label">（2）据/span><span class="list-content">根据气体管道气体介质的特性，根据气体运动和连续性方程，给出了特定的边界条件来建立适合于气体管道泄漏监测的逆瞬态定位分析数学模型。选择特征线方法与顺序二次编程方法结合解决管道泄漏模型有一定的收敛性并提高了模型计算的准确性。据/span></span><span class="list-item"><span class="list-label">（3）据/span><span class="list-content">管道泄漏有效面积的判断误差可以达到0.023×10据sup>-5据/sup> − 0.156 × 10据sup>-5 据/sup>m据sup>2据/sup>．这是因为管道中的流动介质是可压缩的流体。管道中的压力越大，在发生泄漏时管道中的流体密度的变化越大，导致模型计算中的误差。因此，在实际应用中，应选择在瞬态过程中靠近稳态的数据进行计算。据/span></span><span class="list-item"><span class="list-label">（4）据/span><span class="list-content">基于马尔可夫定量判断，在进行管道泄漏检测时，为了保证较高的定位精度，需要设置尽可能多的等距节点，提出了瞬态反泄漏检测方法。据/span></span></span></p> <h4 id="data-availability">数据可用性据/h4> <p>用于支持本研究结果的数据可根据要求可从相应的作者获得。据/p> <h4 id="conflicts-of-interest">利益冲突据/h4> <p>作者声明他们没有利益冲突。据/p> <h4 id="authors’-contributions">作者的贡献据/h4> <p>永美昊促成了该研究的概念，进行了数据分析，并写了稿件;Yifei MA进行实验并促进了分析;洪城江促成了稿件的准备和修订;Zhixiang Xing帮助通过建设性讨论进行分析;雷尼和建阳有助于实验准备。据/p> <h4 id="acknowledgments">致谢据/h4> <p>该研究得到了中国天然科学基金（51834007），江苏省（BE2018642），江苏研究和创新项目（KYCX1795），以及常州科技支持计划（CE20185024）。据/p> </div> <div class="xml-content"> <h4 class="references" id="references">参考据/h4> <ol> <li id="B1">H.Li，S. 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Adib&publication_year=2018" target="_blank">谷歌学术据/一种></span></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权据/h4> <p>版权所有©2020 Yongmei Hao等。这是分布下的开放式访问文章据一种rel="license" href="http://creativecommons.org/licenses/by/4.0/">创意公共归因许可证据/一种>如果正确引用了原始工作，则允许在任何媒体中的不受限制使用，分发和再现。据/p> </div> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章据/h4> <div id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 ZTprm"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-dxZgTM lwEtq article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-gFaPwZ hoOvRq sc-iomxrj fOYLEe 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height="24"><span class="text">下载引用据/span></span><span class="sc-htoDjs bqeMOy sc-jzgbtB bcxtxQ fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-gFaPwZ hoOvRq sc-iFMziU bGHCWJ ref_desktop" href="//www.newsama.com/journals/amse/2020/9527836.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-fhYwyz ieulRf" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引文据/span></span><span class="sc-htoDjs bqeMOy sc-jzgbtB bcxtxQ fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-drKuOJ cBpQvD article_bottom_toolbar"> <div class="sc-gRnDUn cZpOzA accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-cHSUfg prPtb" title="" role="presentation" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHhtbG5zOnhsaW5rPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5L3hsaW5rIiB3aWR0aD0iMjAiIGhlaWdodD0iMjIiIHZpZXdCb3g9IjAgMCAyMCAyMiI+PGRlZnM+PGNsaXBQYXRoIGlkPSJhIj48cGF0aCBkPSJNMywyMmEzLDMsMCwwLDEtMy0zVjE2YTEsMSwwLDAsMSwyLDB2M2ExLDEsMCwwLDAsMSwxSDE3YTEsMSwwLDAsMCwxLTFWMTZhMSwxLDAsMSwxLDIsMHYzYTMsMywwLDAsMS0zLDNabTYuMjg4LTYuMy00LTRhMSwxLDAsMCwxLDEuNDE0LTEuNDE0TDksMTIuNTg2VjFhMSwxLDAsMCwxLDIsMFYxMi41ODZsMi4yOTMtMi4yOTNhMSwxLDAsMCwxLDEuNDE0LDEuNDE0bC00LDRhMSwxLDAsMCwxLTEuNDIzLDBaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSgyIDEpIi8+PC9jbGlwUGF0aD48L2RlZnM+PGcgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTIgLTEpIj48cGF0aCBkPSJNMywyMmEzLDMsMCwwLDEtMy0zVjE2YTEsMSwwLDAsMSwyLDB2M2ExLDEsMCwwLDAsMSwxSDE3YTEsMSwwLDAsMCwxLTFWMTZhMSwxLDAsMSwxLDIsMHYzYTMsMywwLDAsMS0zLDNabTYuMjg4LTYuMy00LTRhMSwxLDAsMCwxLDEuNDE0LTEuNDE0TDksMTIuNTg2VjFhMSwxLDAsMCwxLDIsMFYxMi41ODZsMi4yOTMtMi4yOTNhMSwxLDAsMCwxLDEuNDE0LDEuNDE0bC00LDRhMSwxLDAsMCwxLTEuNDIzLDBaIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSgyIDEpIi8+PGcgY2xpcC1wYXRoPSJ1cmwoI2EpIj48cmVjdCB3aWR0aD0iMjQiIGhlaWdodD0iMjQiIGZpbGw9InJnYmEoMCwwLDAsMCkiLz48cmVjdCB3aWR0aD0iMjQiIGhlaWdodD0iMjQiLz48L2c+PC9nPjwvc3ZnPg==" height="24"><span class="sc-cugefK gzkcXu">下载其他格式据/span><span class="sc-fnwBNb iaVowO">更多的据/span></span> <span class="sc-htoDjs bMdQcY sc-cTjmhe jIQcJs icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-cmjSyW cpuiKr"> <a class="sc-htpNat bUhGXt link sc-sdtwF hnolyX open_panel" href="//www.newsama.com/downloads/journals/amse/2020/9527836.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-iYUSvU jmLwpf"> epub.据/D.一世v><img alt="" class="sc-EHOje jOLhQl sc-cHSUfg prPtb" title="" role="presentation" 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height="24"></a> <a class="sc-htpNat bUhGXt link sc-sdtwF hnolyX open_panel" href="//www.newsama.com/downloads/journals/amse/2020/9527836.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-iYUSvU jmLwpf"> XML.据/D.一世v><img alt="" class="sc-EHOje jOLhQl sc-cHSUfg prPtb" title="" role="presentation" 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height="24"><span class="sc-cugefK gzkcXu">订单印刷副本据/span><span class="sc-fnwBNb iaVowO">订单据/span></span><span class="sc-htoDjs kNoiZu sc-cTjmhe jIQcJs right__icon icon-colored _32KP5uexH-Bgs7Kj8Gk1Tz icon-themeable" title="" font-size="16"></span></a> <div class="sc-cBdUnI blbVzE"> <div class="sc-exkUMo bzUZma"> <div> 意见据span>146据/span> </div> <div> 下载据span>237.据/span> </div> </div> <div> <div class="sc-kcDeIU eatOFG"> <span class="__dimensions_badge_embed__" data-doi="10.1155/2020/9527836" data-style="small_circle"></span>引用据/D.一世v> </div> </div> <nav class="sc-Rmtcm hZsedb sc-iNhVCk gOltjj" id="toolbar__iconNav"> <h3 class="sc-csuQGl idXHYp">分享帖子据/h3> <ul class="sc-bRBYWo keayzM"> <li class="iconBorder"><a class="sc-htpNat bUhGXt link" href="https://twitter.com/share?url=https://doi.org/10.1155/2020/9527836&via=Hindawi" aria-label="Sharing on Twitter" rel="noopener noreferrer" target="_blank"><img alt="" class="sc-EHOje jOLhQl socialTwitter" title="" role="presentation" 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