比较性能Surrogate-Assisted MOEAs Pin-Fin散热器的几何设计</t我tle> <link rel="preload stylesheet" as="style" type="text/css" href="https://cdn.bibblio.org/rcm/4.28.0/bib-related-content.min.css"> <link rel="preload" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" as="style"> <link rel="stylesheet" href="https://static.hindawi.com/new/next_assets/2023-08-03-0017a694320dbe69a559e8120be98c/_next/static/css/b2661f2cd4bd618b.css" data-n-g=""> <style id="__jsx-903e4b2e5d3241e4">div#__next{display:-webkit-box;display:-webkit-flex;display:-moz-box;display:-ms-flexbox;display:flex;min-height:100vh;-webkit-box-orient:vertical;-webkit-box-direction:normal;-webkit-flex-direction:column;-moz-box-orient:vertical;-moz-box-direction:normal;-ms-flex-direction:column;flex-direction:column}</style> </head> <body> <div id="__next"> <section class="ant-layout"> <div> <header class="ant-layout-header"> <div class="header__width-wrapper"> 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<div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</d我v> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#results-and-discussion">结果与讨论</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conclusions">结论</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#acknowledgments">确认</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</一个> </div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div 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<span class="articleHeader__authors_author">和<年代trong>Sujin Bureerat</年代trong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><sup>2</年代up></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</button> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong> <span>挂林(史蒂夫)严</年代p一个n> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2012年1月16日</年代p一个n> </div> <div class="articleHeader__timeline_item "> <strong>修改后的</年代trong> <span>2012年2月21日</年代p一个n> </div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2012年3月06</年代p一个n> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>2012年5月13日</年代p一个n> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>介绍了比较性能的几个surrogate-assisted多目标进化算法(MOEAs)的几何设计pin-fin散热器(PFHS)。的surrogate-assisted MOEAs是通过整合多目标人群为基础的增量学习(PBIL)和二次响应面模型(QRS)、径向基函数(RBF)插值技术,和克里格(库尔德斯坦地区政府)或高斯过程模型。混合整数/连续多目标设计问题的PFHS目的减少结温度和风扇抽运功率同时构成。最优结果使用原多目标PBIL和混合PBIL的三个版本进行了比较。结果表明,混合使用库尔德斯坦地区政府PBIL是最好的演员。混合PBILs需要更少数量的超过原始PBIL功能评估。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>风冷散热器是一个最有效的和流行的电子冷却设备包因其可靠性高,简单,安全,低成本。操作以这样一种方式,散热器相连的设备需要冷却,如中央处理单元(CPU)芯片。然后,用风扇散热是通过生成空气流过散热器。因此,设计这样的冷却装置需要找到一个最佳的几何形状,冷却性能优化。最小化之间的温度散热器基地和电子设备,叫做结温度,是一种最常用的设计目标为最大化热力性能(<一个href="#B1">1</一个>- - - - - -<一个href="#B5">5</一个>]。然而,在传热设计,增加热性能通常会导致整个冷却装置的压降增加。这需要高抽运功率,因此高运营成本。因此,散热器的设计过程通常有两个设计目标结温度和风扇抽运功率为这个研究。</p> <p>使用多目标当今对散热器的几何和分级设计近年来调查。我们的以前的工作表明,使用多目标设计MOEAs pin-fin和铝制散热片优于经典设计方法(<一个href="#B1">1</一个>- - - - - -<一个href="#B5">5</一个>]。其他工作相关的数值模拟和优化设计的某些类型的pin-fin散热片可以在找到<一个href="#B6">6</一个>- - - - - -<一个href="#B12">12</一个>]。然而,还发现,由于昂贵耗时的函数优化过程评估从执行有限体积分析(FVA);因此,性能增强MOEA设计过程始终是必需的。使用径向基函数响应面模型(RSM)结合强度帕累托进化算法为铝制散热器设计研究[<一个href="#B1">1</一个>]。发现,包含RBF代理模型的进化设计过程,说的性能大大提高。在pin-fin散热器设计的情况下,调查使用集成的克里格模型和PBIL求解散热器设计问题了(<一个href="#B5">5</一个>]。结果表明,混合优化器性能是可以接受的。</p> <p>这项工作旨在增强性能的多目标进化优化器将进化搜索的代理模型。尽管众所周知,过去通过代孕MOEAs模型可以提高搜索性能,性能测试的几个代理模型为特定设计情况下仍然需要研究由于设计问题的本质可以影响代理模型的预测性能。设计问题是对找到的几何参数PFHS减少其结温度和风扇抽运功率。基于增量学习是选为优化器,因为它给最好的结果所示(<一个href="#B2">2</一个>,<一个href="#B4">4</一个>]。设计过程中精炼出来的工作提出了(<一个href="#B5">5</一个>]。代理模型与PBIL采用克里格方法或高斯过程模型(<一个href="#B13">13</一个>),一个径向基函数(<一个href="#B1">1</一个>),和一个二次响应面模型。比较结果表明,性能的surrogate-assisted PBIL优于nonsurrogate PBIL尽管前者使用低数量的评价函数。这种类型的设计的最佳代理模型问题是库尔德斯坦地区政府。</p> <h4 id="surrogate-assisted-pbil">2。Surrogate-Assisted PBIL</h4> <p>一个特定的多目标优化问题可以表示如下。<年代p一个ncl一个年代年代="equation" id="eq1"> <svg height="46.1875" id="M1" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 46.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,46.1875)"> <g transform="translate(72,-35.05)"> <text transform="matrix(1,0,0,-1,115.64,61.13)"> <tspan style="font-size: 12.50px; " x="87.160004" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="94.349998" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.115167" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> n</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.842501" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.318335" y="0"> 米</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.04567" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.521503" y="0"> 年代</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.38517" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.888889" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="70.954529" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.93,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,223.89,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.279146" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.071396" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.285145" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,273.12,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,280.45,61.14)"> <tspan style="font-size: 12.50px; " x="14.83" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.652556" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="-166.16" y="22.290001"> 年代</t年代p一个n> <tspan style="font-size: 12.50px; " x="-161.29633" y="22.290001"> u</t年代p一个n> <tspan style="font-size: 12.50px; " x="-155.04483" y="22.290001"> b</t年代p一个n> <tspan style="font-size: 12.50px; " x="-148.79333" y="22.290001"> j</t年代p一个n> <tspan style="font-size: 12.50px; " x="-145.3175" y="22.290001"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="-139.76617" y="22.290001"> c</t年代p一个n> <tspan style="font-size: 12.50px; " x="-134.21483" y="22.290001"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="-126.5755" y="22.290001"> t</t年代p一个n> <tspan style="font-size: 12.50px; " x="-123.11217" y="22.290001"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="-106.92078" y="22.290001"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,179.69,35.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,185,38.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.652556" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.455387" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.659275" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="44.910774" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="279.75" y="-11.54"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="283.91351" y="-11.54"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="290.16501" y="-11.54"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="293.29074" y="-11.54"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="299.54224" y="-11.54"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="14.4875" id="M2" style="vertical-align:-3.22282pt;width:75.212502px;" version="1.1" viewbox="0 0 75.212502 14.4875" width="75.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4875)"> <g transform="translate(72,-60.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> ∈</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-39.77,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-36.32,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.3772497" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-20.69,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-16.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> </g> </g> </svg>是一个向量的<年代vg height="7.1374998" id="M3" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>设计变量和<年代vg height="11.05" id="M4" style="vertical-align:-3.2316pt;width:11.8375px;" version="1.1" viewbox="0 0 11.8375 11.05" width="11.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.8,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>(<年代vg height="7.3249998" id="M5" style="vertical-align:-0.0pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 7.3249998" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.325)"> <g transform="translate(72,-66.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>)设计不等式约束。<年代vg height="12.3" id="M6" style="vertical-align:-1.29163pt;width:46.212502px;" version="1.1" viewbox="0 0 46.212502 12.3" width="46.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="14.415959" y="0"> ≥</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.619846" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>目标函数<年代vg height="14.7125" id="M7" style="vertical-align:-3.2316pt;width:42.25px;" version="1.1" viewbox="0 0 42.25 14.7125" width="42.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-67.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-60.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-57.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n> </text> </g> </g> </svg>旨在同时最小化。图<一个href="//www.newsama.com/journals/jam/2012/534783/fig1/" target="_blank">1</一个>显示任意biobjective最小化问题。可行的设计方案的设置是绘制在目标域(<年代vg height="14.475" id="M8" style="vertical-align:-3.13504pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.475" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>和<年代vg height="14.475" id="M9" style="vertical-align:-3.13504pt;width:14.8875px;" version="1.1" viewbox="0 0 14.8875 14.475" width="14.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>坐标)。最优点是位于前如图所示。这叫做nondominated或帕累托的设计问题的成员帕累托前面是同样好优化的观点。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-9e216bce1a83e064ed823c16ea00bcad"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-9e216bce1a83e064ed823c16ea00bcad partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-9e216bce1a83e064ed823c16ea00bcad partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>帕累托最优。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>PBIL进化优化器是一个基于二进制搜索空间提出Baluja [<一个href="#B14">14</一个>]1994年,而它是由Bureerat延长多目标情况下,Sriworamas [<一个href="#B15">15</一个>]。对于单目标情况,PBIL搜索过程始于一个初始的概率向量<年代vg height="14.3625" id="M10" style="vertical-align:-3.2316pt;width:13.4375px;" version="1.1" viewbox="0 0 13.4375 14.3625" width="13.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>)中每个元素的概率向量决定在每一列的一个二进制“1”人口,人口中的每一行是一个设计方案。概率向量的样本如表所示<一个href="//www.newsama.com/journals/jam/2012/534783/tab2/" target="_blank">2</一个>。表明一个概率向量可能导致各种各样的人群,和这个特性PBIL导致令人印象深刻的人口多样性繁殖在多目标优化设计过程(<一个href="#B15">15</一个>]。</p> <p>取得一个概率向量二进制人口,然后使用最好的二进制设计方案修改概率向量使用以下关系:<年代p一个ncl一个年代年代="equation" id="EEq1"> <svg height="19.549999" id="M11" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.549999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.55)"> <g transform="translate(72,-56.36)"> <text transform="matrix(1,0,0,-1,131.94,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,141.24,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> n</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.104352" y="0"> w</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,139.37,57.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,159.63,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,180.97,65.97)"> <tspan style="font-size: 8.75px; " x="0" y="0"> o</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> l</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.8090558" y="0"> d</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,179.09,57.19)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,194.74,58.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="5.8499999" y="-2.51"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.877166" y="-2.51"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.217386" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.81,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.79,58.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.6300001" y="-2.51"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.970221" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,262.64,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,265.86,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.71,57.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,281.68,60.97)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="183.07001" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="187.23351" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="193.485" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="196.61075" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="202.86224" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M12" style="vertical-align:-3.2316pt;width:21.9125px;" version="1.1" viewbox="0 0 21.9125 14.5875" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-67.78,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.91,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>的元素是二进制的解决方案和最好<年代vg height="14.2375" id="M13" style="vertical-align:-3.13504pt;width:30.325001px;" version="1.1" viewbox="0 0 30.325001 14.2375" width="30.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-67.78,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.93,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是学习速率,在这个工作中,被定义为<年代p一个ncl一个年代年代="equation" id="EEq2"> <svg height="15.75" id="M14" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,119.05,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,127.91,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,138.35,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.444805" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.785027" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.936024" y="0"> 一个</t年代p一个n> <tspan style="font-size: 12.50px; " x="51.487354" y="0"> n</t年代p一个n> <tspan style="font-size: 12.50px; " x="57.738853" y="0"> d</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.753517" y="0"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="73.105042" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="77.268539" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="85.833092" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="92.084595" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="95.210342" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="105.63785" y="0"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="111.88934" y="0"> r</t年代p一个n> <tspan style="font-size: 12.50px; " x="122.99201" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="134.34474" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="140.59624" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="143.72198" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="149.97348" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="156.21248" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="326.39999" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="330.56351" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="336.815" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="339.94073" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="346.19226" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在兰德<年代vg height="13.125" id="M15" style="vertical-align:-1.95624pt;width:47.724998px;" version="1.1" viewbox="0 0 47.724998 13.125" width="47.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.191385" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.442884" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> ]</t年代p一个n> </text> </g> </g> </svg>是一个随机数。</p> <p>PBIL的多目标版本,一组概率向量,它们被称为一个概率矩阵,而不是只使用一个向量,以产生一个更加多样化的二进制人口。搜索过程具有初始概率矩阵,和帕累托档案收集nondominated解决方案。二进制的人口可以获得来自联盟的创建群体概率矩阵的每一行。nondominated解决方案通过排序nondominated解决方案的结合上一代和成员在当前的人口。如果nondominated解决方案的数量超过了预定义的档案大小,法线的方法(<一个href="#B2">2</一个>是用来从帕累托档案删除一些解决方案。重复这个过程,直到停止标准是实现。中可以看到更多细节的多目标PBIL [<一个href="#B2">2</一个>,<一个href="#B15">15</一个>]。</p> <p>在这部作品中,杂交PBIL和代理模型是在这样一种方式进行,培训设计点和相应的客观价值生成使用拉丁超立方体抽样(lh)技术。然后,代理模型(库尔德斯坦地区政府、QRS或RBF)。PBIL用于找到nondominated前面的设计问题,基于代理模型预测功能评估。之后,几个nondominated前线的设计方案选择的集群技术(<一个href="#B16">16</一个>),而他们的实际功能评估。选择二进制解决方案集作为初始种群,并用于生成PBIL概率矩阵。然后,通常PBIL过程激活几个迭代改善nondominated前面。从混合策略,预计的数量函数所使用的评价低于nonsurrogate PBIL。计算过程可以分为三个阶段,详细如下。</p> <p>第一阶段:初始化<年代p一个ncl一个年代年代="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><span class="list-content">使用一个拉丁超立方体技术生成训练点。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">执行实际功能评估。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">构造一个代理模型(库尔德斯坦地区政府、QRS或RBF)。</年代p一个n></span></span></p> <p>第二阶段:优化使用代理模式<年代p一个ncl一个年代年代="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><span class="list-content">生成一个初始概率矩阵<年代vg height="16.2875" id="M16" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>= 0.5和帕累托存档<年代vg height="13.575" id="M17" style="vertical-align:-2.26974pt;width:45.724998px;" version="1.1" viewbox="0 0 45.724998 13.575" width="45.724998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.427982" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.46837" y="0"> {</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.46981" y="0"> }</t年代p一个n> </text> </g> </g> </svg>。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">如果终止条件满足,停止。否则,进入步骤3。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">生成一个二进制人口<年代vg height="10.325" id="M18" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>根据<年代vg height="16.2875" id="M19" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>。</年代p一个n></span><span class="list-item"><span class="list-label">(4)</年代p一个n><span class="list-content">功能评价基于代理的预测。</年代p一个n></span><span class="list-item"><span class="list-label">(5)</年代p一个n><span class="list-content">找到nondominated解决方案<年代vg height="11.0375" id="M20" style="vertical-align:-0.38873pt;width:39.474998px;" version="1.1" viewbox="0 0 39.474998 11.0375" width="39.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.740317" y="0"> ∪</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代p一个n> </text> </g> </g> </svg><i>,</我>和替换<年代vg height="10.55" id="M21" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>与解决方案。</年代p一个n></span><span class="list-item"><span class="list-label">(6)</年代p一个n><span class="list-content">如果<年代vg height="10.55" id="M22" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>太大,去除它的一些成员使用法线技术。</年代p一个n></span><span class="list-item"><span class="list-label">(7)</年代p一个n><span class="list-content">使用成员<年代vg height="10.55" id="M23" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>更新<年代vg height="16.2875" id="M24" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>使用(<一个href="#EEq1">2.2</一个>),<年代vg height="14.2375" id="M25" style="vertical-align:-3.13504pt;width:19.9125px;" version="1.1" viewbox="0 0 19.9125 14.2375" width="19.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>计算使用(<一个href="#EEq2">2.3</一个>)。</年代p一个n></span><span class="list-item"><span class="list-label">(8)</年代p一个n><span class="list-content">去2。</年代p一个n></span></span></p> <p>第三阶段:优化实际功能评估<年代p一个ncl一个年代年代="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><span class="list-content">选择一些成员<年代vg height="10.55" id="M26" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>在前一阶段使用集群技术,发现他们的实际函数值。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">生成一个初始概率矩阵<年代vg height="16.2875" id="M27" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>= 0.5和帕累托存档<年代vg height="10.55" id="M28" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>从排序第三阶段的设计方案在步骤1中。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">更新<年代vg height="16.2875" id="M29" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>使用成员<年代vg height="10.55" id="M30" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>。</年代p一个n></span><span class="list-item"><span class="list-label">(4)</年代p一个n><span class="list-content">如果终止条件满足,停止。否则,转到步骤5。</年代p一个n></span><span class="list-item"><span class="list-label">(5)</年代p一个n><span class="list-content">生成一个二进制人口<年代vg height="10.325" id="M31" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>根据<年代vg height="16.2875" id="M32" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>。</年代p一个n></span><span class="list-item"><span class="list-label">(6)</年代p一个n><span class="list-content">基于有限体积分析实际功能评价。</年代p一个n></span><span class="list-item"><span class="list-label">(7)</年代p一个n><span class="list-content">找到nondominated解决方案<年代vg height="11.0375" id="M33" style="vertical-align:-0.38873pt;width:39.474998px;" version="1.1" viewbox="0 0 39.474998 11.0375" width="39.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.740317" y="0"> ∪</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.267843" y="0"> </t年代p一个n> </text> </g> </g> </svg><i>,</我>和替换<年代vg height="10.55" id="M34" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>与解决方案。</年代p一个n></span><span class="list-item"><span class="list-label">(8)</年代p一个n><span class="list-content">如果<年代vg height="10.55" id="M35" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>太大,去除它的一些成员使用法线技术。</年代p一个n></span><span class="list-item"><span class="list-label">(9)</年代p一个n><span class="list-content">使用成员<年代vg height="10.55" id="M36" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.55)"> <g transform="translate(72,-63.56)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>更新<年代vg height="16.2875" id="M37" style="vertical-align:-4.77652pt;width:18.35px;" version="1.1" viewbox="0 0 18.35 16.2875" width="18.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n> </text> </g> </g> </svg>使用(<一个href="#EEq1">2.2</一个>),<年代vg height="14.2375" id="M38" style="vertical-align:-3.13504pt;width:19.9125px;" version="1.1" viewbox="0 0 19.9125 14.2375" width="19.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-63.1,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>计算使用(<一个href="#EEq2">2.3</一个>)。</年代p一个n></span><span class="list-item"><span class="list-label">(10)</年代p一个n><span class="list-content">去4。</年代p一个n></span></span></p> <h4 id="surrogate-models">3所示。代理模型</h4> <p>让<年代vg height="13.6125" id="M39" style="vertical-align:-2.34499pt;width:54.162498px;" version="1.1" viewbox="0 0 54.162498 13.6125" width="54.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="28.644373" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.807873" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="39.059372" y="0"> )</t年代p一个n> </text> </g> </g> </svg>是一个功能的设计向量<年代vg height="7.3249998" id="M40" style="vertical-align:-0.0pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 7.3249998" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.325)"> <g transform="translate(72,-66.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>大小的<年代vg height="11.075" id="M41" style="vertical-align:-0.3135pt;width:32.650002px;" version="1.1" viewbox="0 0 32.650002 11.075" width="32.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.9896574" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.767242" y="0"> 1</t年代p一个n> </text> </g> </g> </svg>。给定一组设计解决方案(或采样点)<年代vg height="16.2125" id="M42" style="vertical-align:-1.95624pt;width:121.3625px;" version="1.1" viewbox="0 0 121.3625 16.2125" width="121.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2125)"> <g transform="translate(72,-59.03)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.870388" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="37.033886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-28.41,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-23.54,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,12.14,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,20.87,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> </g> </g> </svg>通过使用拉丁hypercute生成技术和相应的函数值<年代vg height="14.6" id="M43" style="vertical-align:-3.13504pt;width:110.1875px;" version="1.1" viewbox="0 0 110.1875 14.6" width="110.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.490497" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.694386" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-37.05,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-32.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,3.2,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,11.94,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> </g> </g> </svg>、代理或近似模型的曲线拟合或插值。本研究中使用如下近似模型。</p> <h5 id="sec3.1">3.1。二次响应面模型</h5> <p>最常用的多项式代理模型或二阶多项式的响应面模型或二次模型,可以表示为<年代p一个ncl一个年代年代="equation" id="EEq3"> <svg height="22.7875" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 22.7875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.7875)"> <g transform="translate(72,-53.77)"> <g> <path d="m 132.94,68.15 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,132.94,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.6773224" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,160.82,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,168.47,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.35" y="6.5500002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="29.58" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.22,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.44,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,214.32,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,220.31,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.35" y="6.5500002"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="29.59" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.06,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,259.28,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,266.16,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,269.38,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,276.25,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,280.68,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="184.07001" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="188.23351" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="194.485" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="197.61075" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="203.86224" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M45" style="vertical-align:-3.2316pt;width:11.85px;" version="1.1" viewbox="0 0 11.85 14.5875" width="11.85" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.79,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>为<年代vg height="13.45" id="M46" style="vertical-align:-2.21957pt;width:173.3125px;" version="1.1" viewbox="0 0 173.3125 13.45" width="173.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.527766" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.731653" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.983154" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.184402" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="53.775402" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.989155" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="63.152653" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="72.142311" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="83.482529" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="89.734032" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.89753" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="98.061028" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="107.05069" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="118.40341" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="124.65491" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="128.81841" y="0"> /</t年代p一个n> <tspan style="font-size: 12.50px; " x="132.29425" y="0"> 2</t年代p一个n> </text> </g> </g> </svg>是确定多项式系数。系数可以发现通过使用回归或最小二乘技术。</p> <h5 id="sec3.2">3.2。克里格模型</h5> <p>克里格模型(也称为高斯过程模型)用于本文是著名的MATLAB工具箱命名计算机实验设计与分析(dac) [<一个href="#B13">13</一个>]。估计的函数可以被认为是全球和当地的近似模型的结合<年代p一个ncl一个年代年代="equation" id="EEq4"> <svg height="20.4125" id="M47" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.4125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4125)"> <g transform="translate(72,-55.67)"> <text transform="matrix(1,0,0,-1,153,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.2769861" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.440485" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.942045" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.581379" y="0"> =</t年代p一个n> </text> <g> <path d="m 191.63,70.71 8.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,191.63,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.515023" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.678522" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="21.180082" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.119247" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.459469" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="52.074993" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.238495" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="62.740055" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="68.991554" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="273.12" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="277.28351" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="283.535" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="286.66074" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="292.91226" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="18.65" id="M48" style="vertical-align:-2.34499pt;width:39.3125px;" version="1.1" viewbox="0 0 39.3125 18.65" width="39.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.65)"> <g transform="translate(72,-57.08)"> <g> <path d="m -67.78,70.71 8.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-67.78,59.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.427022" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.590521" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.842022" y="0"> )</t年代p一个n> </text> </g> </g> </svg>是一个全球性的回归模型<年代vg height="13.45" id="M49" style="vertical-align:-2.21957pt;width:30.4125px;" version="1.1" viewbox="0 0 30.4125 13.45" width="30.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.6523161" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.815815" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代p一个n> </text> </g> </g> </svg>是一个高斯随机过程与零均值和协方差非零表示局部偏差。在这项工作中,线性函数用于全球模型,可以表示为<年代p一个ncl一个年代年代="equation" id="EEq5"> <svg height="48.349998" id="M50" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.35)"> <g transform="translate(72,-33.32)"> <g> <path d="m 146.3,60.91 8.44,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,146.3,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.902856" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.943245" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,176.41,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,184.06,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,201.31,65.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,195.41,43.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,196.94,35.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,213.65,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,219.81,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,223.03,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.91,46.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.6,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.45,54.96)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,263.16,49.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="201.59" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="205.75349" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="212.005" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="215.13075" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="221.38225" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="17.6625" id="M51" style="vertical-align:-3.25793pt;width:112.1125px;" version="1.1" viewbox="0 0 112.1125 17.6625" width="112.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.6625)"> <g transform="translate(72,-57.87)"> <text transform="matrix(1,0,0,-1,-71.95,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.277706" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.318094" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.481594" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-38.3,58.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-33.42,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,1.91,58.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,6.76,61.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,10.93,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>,<年代vg height="17.725" id="M52" style="vertical-align:-3.20526pt;width:198.08749px;" version="1.1" viewbox="0 0 198.08749 17.725" width="198.08749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.725)"> <g transform="translate(72,-57.82)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.994217" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="34.245716" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.885052" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.08894" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.252438" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="68.503937" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="77.881187" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,12.81,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,17.69,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,29.77,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,34.65,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.169498" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,70.7,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,75.55,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,79.71,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>。的协方差<年代vg height="13.45" id="M53" style="vertical-align:-2.21957pt;width:30.4125px;" version="1.1" viewbox="0 0 30.4125 13.45" width="30.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.6523161" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.815815" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代p一个n> </text> </g> </g> </svg>表示为<年代p一个ncl一个年代年代="equation" id="EEq6"> <svg height="19.475" id="M54" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,108.87,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> C</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.3395014" y="0"> o</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.591001" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.943005" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.106504" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="39.722031" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="43.885529" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,159.26,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,164.04,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.238997" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.452748" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.068275" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.231773" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,198.77,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,203.63,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.790329" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.830717" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,234.81,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,239.68,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.11" y="2.51"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="15.9" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="27.227718" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="31.391216" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,277.58,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,282.36,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,294.07,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,298.93,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1599998" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="165.82001" y="0.0099999998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="169.98351" y="0.0099999998"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="176.235" y="0.0099999998"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="179.36075" y="0.0099999998"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="185.61224" y="0.0099999998"> )</t年代p一个n> </text> </g> </g> </svg></span>为<年代vg height="13.55" id="M55" style="vertical-align:-2.29482pt;width:105.025px;" version="1.1" viewbox="0 0 105.025 13.55" width="105.025" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.1139669" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.478714" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="24.680922" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="36.72131" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.972813" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.186562" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="62.76506" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="72.142311" y="0"> </t年代p一个n> </text> </g> </g> </svg>,在那里<年代vg height="10.325" id="M56" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>之间的相关函数的两个吗<年代vg height="10.325" id="M57" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>设计分<年代vg height="10.6875" id="M58" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6875" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是对称的相关矩阵的大小<年代vg height="10.725" id="M59" style="vertical-align:-0.3135pt;width:45.075001px;" version="1.1" viewbox="0 0 45.075001 10.725" width="45.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.415719" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.193304" y="0"> </t年代p一个n> </text> </g> </g> </svg>统一的对角线(<一个href="#B17">17</一个>]。所使用的相关函数<年代p一个ncl一个年代年代="equation" id="EEq7"> <svg height="19.950001" id="M60" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.950001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.95)"> <g transform="translate(72,-56.04)"> <text transform="matrix(1,0,0,-1,99.99,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.491217" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,121.99,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.77,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,138.48,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,143.34,60.66)"> <tspan style="font-size: 12.50px; " x="41.900002" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.667219" y="0"> e</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.218552" y="0"> x</t年代p一个n> <tspan style="font-size: 12.50px; " x="31.470051" y="0"> p</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.75" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="56.314556" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="60.478054" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,210.32,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,217.87,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,235.72,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,240.58,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,244.74,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,251.45,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.1521959" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.315695" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,271.28,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,278.83,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,296.68,65.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,301.53,60.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1700001" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.1" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="163.22" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="167.3835" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="173.63499" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="176.76074" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="183.01225" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M61" style="vertical-align:-3.2316pt;width:11.7125px;" version="1.1" viewbox="0 0 11.7125 14.5875" width="11.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.9,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>未知的相关参数,通过最大似然方法的确定。有发现<年代vg height="14.0375" id="M62" style="vertical-align:-2.5707pt;width:9.8874998px;" version="1.1" viewbox="0 0 9.8874998 14.0375" width="9.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0375)"> <g transform="translate(72,-60.77)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="11" id="M63" style="vertical-align:-0.13794pt;width:8.9750004px;" version="1.1" viewbox="0 0 8.9750004 11" width="8.9750004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11)"> <g transform="translate(72,-63.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>可以实现,克里格预测<年代p一个ncl一个年代年代="equation" id="EEq8"> <svg height="18.674999" id="M64" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.674999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.675)"> <g transform="translate(72,-57.06)"> <g> <path d="m 112.94,69.25 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,112.94,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.29" y="-0.0099999998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.453499" y="-0.0099999998"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.942556" y="-0.0099999998"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.581888" y="-0.0099999998"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="38.622276" y="-0.0099999998"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="44.036076" y="-0.0099999998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="48.199577" y="-0.0099999998"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="54.701138" y="-0.0099999998"> )</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171.81,66.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.52,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.590041" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.930262" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,206.76,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,215.55,60.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.665059" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.904057" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,241.49,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,254.45,60.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="13.178162" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.530886" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.170219" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="39.984592" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.223591" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="210.3" y="0.0099999998"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="214.4635" y="0.0099999998"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="220.715" y="0.0099999998"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="223.84074" y="0.0099999998"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="230.09225" y="0.0099999998"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="19.575001" id="M65" style="vertical-align:-2.21957pt;width:185.5125px;" version="1.1" viewbox="0 0 185.5125 19.575001" width="185.5125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.575)"> <g transform="translate(72,-56.34)"> <text transform="matrix(1,0,0,-1,-71.95,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.102664" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.143053" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.306553" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="31.470051" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="35.633549" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-29.81,63.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-24.93,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.528246" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="17.691746" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.855244" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,3.44,63.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,8.31,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.955748" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.332996" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="37.496498" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.659996" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,56.48,63.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,61.32,58.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,69.65,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>和<年代vg height="16.5375" id="M66" style="vertical-align:-2.21957pt;width:258.5625px;" version="1.1" viewbox="0 0 258.5625 16.5375" width="258.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.65,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.94,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="10.414999" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.054333" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.082218" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.245716" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="43.497936" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="47.661434" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="53.912937" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="59.126686" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,6.7,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,11.57,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.616966" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="22.780466" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="29.031965" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="34.245716" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,52.32,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,57.2,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.364747" y="0"> …</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.943245" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="29.156996" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="38.409218" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.572716" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="48.824215" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.037968" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,117.74,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,126.48,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="4.1634989" y="0"> ]</t年代p一个n> </text> </g> </g> </svg>。更多细节,请参阅[<一个href="#B13">13</一个>]。</p> <h5 id="sec3.3">3.3。径向基函数插值</h5> <p>径向基函数插值法被用于广泛的应用,如空气动力学和有限元网格之间的集成气动弹性分析(<一个href="#B18">18</一个>]。这样一个模型的使用surrogate-assisted进化优化是司空见惯的事(<一个href="#B1">1</一个>,<一个href="#B19">19</一个>,<一个href="#B20">20.</一个>]。近似函数可以写成<年代p一个ncl一个年代年代="equation" id="EEq9"> <svg height="50.662498" id="M67" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <g> <path d="m 137.67,56.21 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.67,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="8.2769861" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.440485" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.942045" y="0"> )</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.581379" y="0"> =</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,180.25,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,176.29,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.82,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n> <tspan style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,194.53,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,201.08,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.3,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="12.61" y="2.52"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="18.469999" y="-1.04"> 为</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.469999" y="1.0599999"> 为</t年代p一个n> <tspan style="font-size: 12.50px; " x="25" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="34.027164" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="45.367386" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,256.18,52.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,259.4,48.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n> <tspan style="font-size: 12.50px; " x="0" y="2.0999999"> 为</t年代p一个n> <tspan style="font-size: 12.50px; " x="8.6199999" y="3.5599999"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="16.559999" y="1.04"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="205.35001" y="1.04"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="209.5135" y="1.04"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="215.765" y="1.04"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="218.89075" y="1.04"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="225.14224" y="1.04"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="11.05" id="M68" style="vertical-align:-3.2316pt;width:12.3375px;" version="1.1" viewbox="0 0 12.3375 11.05" width="12.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.4,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>系数确定并吗<年代vg height="10.325" id="M69" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是一个径向基核函数(这里将线性样条函数)。的系数可以找到<年代vg height="10.325" id="M70" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>采样点的详细(<一个href="#B1">1</一个>]。</p> <h4 id="pfhs-design">4所示。PFHS设计</h4> <p>此处pin-fin散热器是一种风冷散热器与广场散热器基础和广场针鳍如图<一个href="//www.newsama.com/journals/jam/2012/534783/fig2/" target="_blank">2</一个>。散热是通过使用一个风扇产生的气流在散热器的顶部。一个方基地(PFHS物理模型<年代vg height="11.325" id="M71" style="vertical-align:-3.22281pt;width:22.5875px;" version="1.1" viewbox="0 0 22.5875 11.325" width="22.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> </g> </g> </svg>)在图给出<一个href="//www.newsama.com/journals/jam/2012/534783/fig2/" target="_blank">2</一个>。参数定义一个散热器几何包括基线长度(<年代vg height="11.325" id="M72" style="vertical-align:-3.22281pt;width:22.5875px;" version="1.1" viewbox="0 0 22.5875 11.325" width="22.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> </g> </g> </svg>),基础厚度<年代vg height="13.0125" id="M73" style="vertical-align:-3.2316pt;width:10.775px;" version="1.1" viewbox="0 0 10.775 13.0125" width="10.775" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0125)"> <g transform="translate(72,-61.59)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-68.04,61.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>翅片的宽度(<年代vg height="11.225" id="M74" style="vertical-align:-3.13504pt;width:24.4375px;" version="1.1" viewbox="0 0 24.4375 11.225" width="24.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.225)"> <g transform="translate(72,-63.02)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.26,63.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> </g> </g> </svg>),数量的鳍<年代vg height="12.975" id="M75" style="vertical-align:-4.77652pt;width:15.9px;" version="1.1" viewbox="0 0 15.9 12.975" width="15.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.74,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>。鳍高度基于16输入参数(是多种多样的<年代vg height="14.3875" id="M76" style="vertical-align:-3.25793pt;width:45.0625px;" version="1.1" viewbox="0 0 45.0625 14.3875" width="45.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.25,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> - - - - - -</t年代p一个n> <tspan style="font-size: 12.50px; " x="2.088001" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-45.25,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 6</t年代p一个n> </text> </g> </g> </svg>)。图<一个href="//www.newsama.com/journals/jam/2012/534783/fig3/" target="_blank">3</一个>显示<年代vg height="10.8625" id="M77" style="vertical-align:-0.3135pt;width:43.125px;" version="1.1" viewbox="0 0 43.125 10.8625" width="43.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8625)"> <g transform="translate(72,-63.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.190665" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="28.144253" y="0"> 7</t年代p一个n> </text> </g> </g> </svg>控制点在16鳍鳍基础上高度参数对称分布。翅片高度可以由使用径向基函数插值。图<一个href="//www.newsama.com/journals/jam/2012/534783/fig4/" target="_blank">4</一个>翅片高度分布的显示了一个示例使用RBF插值(<一个href="#B3">3</一个>]。fin-to-fin空间或鳍针(<年代vg height="10.925" id="M78" style="vertical-align:-3.13504pt;width:19.200001px;" version="1.1" viewbox="0 0 19.200001 10.925" width="19.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-66.45,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> </g> </g> </svg>)是均布。冷却风扇的散热器<年代vg height="16.2875" id="M79" style="vertical-align:-4.77652pt;width:22.325001px;" version="1.1" viewbox="0 0 22.325001 16.2875" width="22.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.76,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>气流速度(米/秒),安装在散热器的顶部。一个统一的热负荷(<年代vg height="12.925" id="M80" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>)生成的散热器交界处,电子设备被设置为120瓦特。材料和空气的属性和假设的热流模拟详细(<一个href="#B1">1</一个>,<一个href="#B2">2</一个>]。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-44919282d94c2a27073319f57f3ce4c5"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.002.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-44919282d94c2a27073319f57f3ce4c5 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-44919282d94c2a27073319f57f3ce4c5 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>pin-fin散热器的物理模型。</td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-81c60320849e1ad527c7bde533a926eb"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.003.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-81c60320849e1ad527c7bde533a926eb partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-81c60320849e1ad527c7bde533a926eb partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>翅片高度分布控制点。</td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-774a5948fa5f83a2d696a3c96535ced2"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.004.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-774a5948fa5f83a2d696a3c96535ced2 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.004_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-774a5948fa5f83a2d696a3c96535ced2 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>翅片高度分布。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>在设计过程中,一个自动化的过程是通过接口CFD软件MATLAB。设计变量包括这些参数用于创建PFHS几何和进气速度。编码/解码过程的更多细节的设计变量,看到<一个href="#B3">3</一个>]。</p> <p>的设计问题,提出了减少biobjective功能的风扇抽运功率和结温pin-fin散热器。风扇抽运功率是用来测量电子的消费能力,而结温度决定了散热器的热性能。散热器长宽比和空间限制装置的设计约束。的多目标设计问题PFHS可以编写如下。</p> <p>目标函数:<年代p一个ncl一个年代年代="equation" id="eq2"> <svg height="102.45" id="M81" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 102.45" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,102.45)"> <g transform="translate(72,9.96)"> <text transform="matrix(1,0,0,-1,170.12,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.727334" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.203168" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.61,53.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,193.74,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.1900001" y="-2.51"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,207.81,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,212.23,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,224.87,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> f</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.695616" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.5815039" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,236.32,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.2700005" y="-2.51"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-68.470001" y="25.18"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,174.73,30.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,182.63,33.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,201.55,30.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,209.22,33.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="21.092562" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,239.58,30.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,247.86,33.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-74.440002" y="31.379999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,180.84,-1.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> f</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.695616" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.5815039" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,195.76,2.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="20.549999" y="-9.2200003"> ̇</t年代p一个n> <tspan style="font-size: 12.50px; " x="13.248248" y="-9.2200003"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,217.88,8.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,222.77,11.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> </text> <g> <path d="m 209,5.18 32.1,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,218.88,-6.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,226.32,-9.82)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,242.29,2.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="222.46001" y="-25.83"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="226.6235" y="-25.83"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="232.875" y="-25.83"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="236.00075" y="-25.83"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="242.25224" y="-25.83"> )</t年代p一个n> </text> </g> </g> </svg></span></p> <p>设计变量向量:<年代p一个ncl一个年代年代="equation" id="eq3"> <svg height="19.475" id="M82" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.475" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.475)"> <g transform="translate(72,-56.42)"> <text transform="matrix(1,0,0,-1,124.04,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="9.7148314" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.75522" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.918718" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,156.18,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,162.59,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,177.49,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,187.24,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,202.14,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,210.42,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,222.82,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,229.23,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,245.35,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> −</t年代p一个n> <tspan style="font-size: 8.75px; " x="10.37112" y="0"> 1</t年代p一个n> <tspan style="font-size: 8.75px; " x="14.74712" y="0"> 6</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,264.97,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,274.1,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,278.71,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,282.87,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,289.58,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="175.17" y="0"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="179.3335" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="185.58499" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="188.71075" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="194.96225" y="0"> )</t年代p一个n> </text> </g> </g> </svg></span></p> <p>约束:<年代p一个ncl一个年代年代="equation" id="eq4"> <svg height="202.425" id="M83" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 202.425" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,202.425)"> <g transform="translate(72,89.94)"> <text transform="matrix(1,0,0,-1,164.42,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171.3,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,178.5,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n> <tspan style="font-size: 12.50px; " x="11.340221" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="17.591721" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.843222" y="0"> 5</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,208.6,68.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∘</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,212.16,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> K</t年代p一个n> <tspan style="font-size: 12.50px; " x="16.666498" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.870388" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="39.121887" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-60.799999" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-54.5485" y="22.48"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-51.422749" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-45.171249" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-38.91975" y="22.48"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="-32.668251" y="22.48"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="-22.953419" y="22.48"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-10.91303" y="22.48"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,210.95,37.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,224.18,40.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-49.740002" y="20.48"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="-40.012665" y="20.48"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-27.984779" y="20.48"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,206.85,17.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,216.72,20.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="24.543388" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-59.900002" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-53.648499" y="22.48"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-50.522751" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-44.271252" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-38.019749" y="22.48"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="-31.76825" y="22.48"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="-22.040916" y="22.48"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-10.01303" y="22.48"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,210.63,-5.36)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.72,-2.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.159637" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-55.470001" y="20.469999"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-49.218498" y="20.469999"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-46.092751" y="20.469999"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-36.377918" y="20.469999"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-24.33753" y="20.469999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.31,-25.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.54,-22.71)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-48.619999" y="20.469999"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-42.3685" y="20.469999"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-39.242748" y="20.469999"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="-29.52792" y="20.469999"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-17.48753" y="20.469999"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,208.25,-46.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,218.13,-43.18)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-56.650002" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-50.398499" y="22.48"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-47.272751" y="22.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-41.021252" y="22.48"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="-31.306419" y="22.48"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="-19.266029" y="22.48"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,208.56,-68.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,220.31,-65.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.405136" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.656635" y="0"> 6</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.908134" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="-66.849998" y="20.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-60.598499" y="20.48"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="-57.472752" y="20.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-51.221249" y="20.48"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="-44.969749" y="20.48"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="-38.71825" y="20.48"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="-29.00342" y="20.48"> <</t年代p一个n> <tspan style="font-size: 12.50px; " x="-16.96303" y="20.48"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,208.85,-89.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> fi</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.883616" y="0"> n</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,222.08,-86.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代p一个n> <tspan style="font-size: 12.50px; " x="12.040389" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="18.291889" y="0"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="21.417639" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="27.66914" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="33.920639" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="40.172138" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="242.67" y="-74.040001"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="246.8335" y="-74.040001"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="253.08499" y="-74.040001"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="256.21075" y="-74.040001"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="262.46225" y="-74.040001"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="16.2875" id="M84" style="vertical-align:-4.77652pt;width:14.25px;" version="1.1" viewbox="0 0 14.25 16.2875" width="14.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.2875)"> <g transform="translate(72,-58.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>结温,<年代vg height="14.35" id="M85" style="vertical-align:-3.22281pt;width:23.7125px;" version="1.1" viewbox="0 0 23.7125 14.35" width="23.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-64.52,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> f</t年代p一个n> <tspan style="font-size: 8.75px; " x="2.6868639" y="0"> 一个</t年代p一个n> <tspan style="font-size: 8.75px; " x="6.572752" y="0"> n</t年代p一个n> </text> </g> </g> </svg>风扇抽运功率,<年代vg height="12.925" id="M86" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>热负荷,<年代vg height="14.35" id="M87" style="vertical-align:-3.22281pt;width:22.0375px;" version="1.1" viewbox="0 0 22.0375 14.35" width="22.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> h</t年代p一个n> <tspan style="font-size: 8.75px; " x="4.3759999" y="0"> 年代</t年代p一个n> </text> </g> </g> </svg>散热器热耐药,<年代vg height="10.95" id="M88" style="vertical-align:-0.12538pt;width:38.674999px;" version="1.1" viewbox="0 0 38.674999 10.95" width="38.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="22.492897" y="0"> 我</t年代p一个n> <tspan style="font-size: 12.50px; " x="25.968731" y="0"> 年代</t年代p一个n> </text> </g> </g> </svg>在散热器的压降,<年代vg height="11.0375" id="M89" style="vertical-align:-3.22282pt;width:14.0875px;" version="1.1" viewbox="0 0 14.0875 11.0375" width="14.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-65.67,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>空气密度,<年代vg height="13.8625" id="M90" style="vertical-align:-3.22282pt;width:27.75px;" version="1.1" viewbox="0 0 27.75 13.8625" width="27.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-60.47,64.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̇</t年代p一个n> <tspan style="font-size: 12.50px; " x="-7.3017521" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-58.91,61.05)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>空气质量流率。</p> <p>连续性、动量和能量方程稳态强制对流在牛顿常数性质液体没有热代可以写成<年代p一个ncl一个年代年代="equation" id="EEq10"> <svg height="113.8375" id="M91" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 113.8375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,113.8375)"> <g transform="translate(72,19.07)"> <text transform="matrix(1,0,0,-1,186.44,54.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∇</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.1396933" y="0"> ⋅</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,204.03,65.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,203.21,53.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.77" y="-0.85000002"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.810389" y="-0.85000002"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.06189" y="-0.85000002"> ,</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,142.59,34.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,141.76,22.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.25" y="-0.86000001"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.825858" y="-0.86000001"> ∇</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,170.61,34.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,169.78,22.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="32.029999" y="-8.1099997"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="7.7800002" y="-0.86000001"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="19.807886" y="-0.86000001"> −</t年代p一个n> </text> <g> <path d="m 199.36,26.64 11.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,199.36,14.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,205.63,11.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n> </text> <text transform="matrix(1,0,0,-1,211.72,23.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∇</t年代p一个n> <tspan style="font-size: 12.50px; " x="9.1396933" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="19.34214" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="30.682362" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="36.958866" y="0"> ∇</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,257.82,28.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 8.75px; " x="9.7600002" y="-6.0599999"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,266.76,22.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="7.77" y="-0.86000001"> ,</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171.82,-4.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,171,-16.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="11.25" y="-0.86000001"> ⋅</t年代p一个n> <tspan style="font-size: 12.50px; " x="14.825858" y="-0.86000001"> ∇</t年代p一个n> <tspan style="font-size: 12.50px; " x="23.965551" y="-0.86000001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="34.305531" y="-0.86000001"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="46.345921" y="-0.86000001"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="53.397614" y="-0.86000001"> ∇</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,233.54,-10.27)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,238.42,-15.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> <tspan style="font-size: 12.50px; " x="6.8766499" y="0"> ,</t年代p一个n> <tspan style="font-size: 12.50px; " x="226.33" y="-38.610001"> (</t年代p一个n> <tspan style="font-size: 12.50px; " x="230.4935" y="-38.610001"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="236.745" y="-38.610001"> 。</t年代p一个n> <tspan style="font-size: 12.50px; " x="239.87074" y="-38.610001"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="246.12225" y="-38.610001"> )</t年代p一个n> </text> </g> </g> </svg></span>在哪里<年代vg height="23.762501" id="M92" style="vertical-align:-1.05959pt;width:20.987499px;" version="1.1" viewbox="0 0 20.987499 23.762501" width="20.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.7625)"> <g transform="translate(72,-52.99)"> <text transform="matrix(1,0,0,-1,-70.54,65.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⇀</t年代p一个n> </text> <text transform="matrix(1,0,0,-1,-71.37,53.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是流体的速度,<年代vg height="10.325" id="M93" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>是温度,<年代vg height="7.1750002" id="M94" style="vertical-align:-0.1254pt;width:8.9375px;" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.175)"> <g transform="translate(72,-66.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>热导率,<年代vg height="7.2375002" id="M95" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.2375)"> <g transform="translate(72,-66.21)"> <text transform="matrix(1,0,0,-1,-71.95,66.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>运动粘度。</p> <p>这些控制方程thermofluid分析的强制对流pin-fin散热器。在优化过程中,这三个方程是通过有限体积分析处理,这是一个最强大的计算流体动力学的数值方法。的假设分析如下。<年代p一个ncl一个年代年代="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><span class="list-content">流体流动是层流和稳定。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">常数材料热物理性质的空气和固体材料。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">统一的入口气流速度。</年代p一个n></span><span class="list-item"><span class="list-label">(iv)</年代p一个n><span class="list-content">均匀热流在整个基板底面。</年代p一个n></span></span></p> <p>散热器的身体是用铝做的。固体和液体的物理性质(<一个href="#B1">1</一个>,<一个href="#B2">2</一个>]。环境温度设置为298 K。</p> <p>设计变量的向量<年代vg height="7.3249998" id="M96" style="vertical-align:-0.0pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 7.3249998" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.325)"> <g transform="translate(72,-66.14)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n> </text> </g> </g> </svg>有21个元素。使用国际标准单位在设计目标和约束条件,除非另有说明。在这个工作中,30个采样点同时使用了lh技术,而PBIL 100人口规模和200代surrogate-based函数执行评估。然后,25代理优化的设计方案作为共同PBIL最初的解决方案,用于进一步探索nondominated前25人口规模和19代。这意味着该surrogate-assisted PBIL<年代vg height="11.5125" id="M97" style="vertical-align:-0.51414pt;width:124.4375px;" version="1.1" viewbox="0 0 124.4375 11.5125" width="124.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.5125)"> <g transform="translate(72,-62.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> +</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.618887" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.870388" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="41.897552" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="52.67514" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="58.92664" y="0"> 0</t年代p一个n> <tspan style="font-size: 12.50px; " x="68.653976" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="80.694359" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="86.945862" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="93.197365" y="0"> 0</t年代p一个n> </text> </g> </g> </svg>实际功能评估。原来的PBIL没有使用代理模型,人口规模将是25而代将35。这意味着nonsurrogate PBIL用途<年代vg height="11.2625" id="M98" style="vertical-align:-0.3135pt;width:91.162498px;" version="1.1" viewbox="0 0 91.162498 11.2625" width="91.162498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2625)"> <g transform="translate(72,-62.99)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.056252" y="0"> 3</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.307751" y="0"> 5</t年代p一个n> <tspan style="font-size: 12.50px; " x="42.035088" y="0"> =</t年代p一个n> <tspan style="font-size: 12.50px; " x="54.062973" y="0"> 8</t年代p一个n> <tspan style="font-size: 12.50px; " x="60.314472" y="0"> 7</t年代p一个n> <tspan style="font-size: 12.50px; " x="66.565971" y="0"> 5</t年代p一个n> </text> </g> </g> </svg>实际功能评估。</p> <h4 id="results-and-discussion">5。结果与讨论</h4> <p>图<一个href="//www.newsama.com/journals/jam/2012/534783/fig5/" target="_blank">5</一个>显示nondominated方面获得的各种surrogate-assisted PBILs,定义为PBIL-QRS, PBIL-RBF,和PBIL-KRG混合PBILs使用二次响应面模型,一个径向基函数插值技术,分别和克里格模型。可以清楚地看到,通过使用获得的面前PBIL-KRG优于其他人,而第二个最好是PBIL-RBF。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-667b27f607b32d15f3174b2c0655d3aa"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.005.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-667b27f607b32d15f3174b2c0655d3aa partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.005_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-667b27f607b32d15f3174b2c0655d3aa partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>帕累托方面从surrogate-assisted PBILs。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>最前面的混合方法然后获得使用价格相比nonsurrogate PBIL(称为PBIL-35)如图<一个href="//www.newsama.com/journals/jam/2012/534783/fig6/" target="_blank">6</一个>。除了两个nondominated方面,目前真正的散热器在现实世界中使用模拟那里结温度和风扇抽运功率计算值。圆柱销的真正的散热器鳍片包括以下。<年代p一个ncl一个年代年代="list"><span class="list-item"><span class="list-label">(我)</年代p一个n><span class="list-content">模型17 r 0.0635散热器宽度、恒定的翅片高度0.0424米,直径0.0033 m鳍,散热器底座厚度0.0127米,<年代vg height="11.075" id="M99" style="vertical-align:-0.3135pt;width:48.325001px;" version="1.1" viewbox="0 0 48.325001 11.075" width="48.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="6.2515001" y="0"> 4</t年代p一个n> <tspan style="font-size: 12.50px; " x="15.278666" y="0"> ×</t年代p一个n> <tspan style="font-size: 12.50px; " x="26.056252" y="0"> 1</t年代p一个n> <tspan style="font-size: 12.50px; " x="32.307751" y="0"> 4</t年代p一个n> </text> </g> </g> </svg>鳍。</年代p一个n></span><span class="list-item"><span class="list-label">(2)</年代p一个n><span class="list-content">模型11米和0.0508米散热器宽度,常数0.0269米翅片高度、翅片直径0.0033米,0.0048米散热器底座厚度,和61的鳍。</年代p一个n></span><span class="list-item"><span class="list-label">(3)</年代p一个n><span class="list-content">模型14米和0.0508米散热器宽度、常数0.0480米翅片高度、翅片直径0.0033米,0.0048米散热器底座厚度,和61的鳍。</年代p一个n></span></span></p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-218620174214716d6247150f7a7e4ffd"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.006.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-218620174214716d6247150f7a7e4ffd partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.006_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-218620174214716d6247150f7a7e4ffd partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>PBIL-KRG20和PBIL35。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>第一个模型称为一个密集的针翅片散热器,而其他人则称为稀疏销翅片散热器。模型模拟的进气速度0.5米/秒,恒定的热负荷120瓦被应用于散热器的底部基础。基于优势理论,设计解决方案从PBIL-KRG和nonsurrogate PBIL远高于实际散热片。</p> <p>的放大的图<一个href="//www.newsama.com/journals/jam/2012/534783/fig6/" target="_blank">6</一个>图中给出了<一个href="//www.newsama.com/journals/jam/2012/534783/fig7/" target="_blank">7</一个>比较PBIL-KRG和PBIL-35。的结果可以看出,使用混合PBIL总体优于nonsurrogate同行。这是由定量评估确认表<一个href="//www.newsama.com/journals/jam/2012/534783/tab1/" target="_blank">1</一个>。从表中,帕累托前沿的超体积值绘制在图<一个href="//www.newsama.com/journals/jam/2012/534783/fig5/" target="_blank">5</一个>和<一个href="//www.newsama.com/journals/jam/2012/534783/fig7/" target="_blank">7</一个>计算参考点在哪里设置(303 K, 0.1瓦)。根据其定义,更大的超体积意味着更好的帕累托或nondominated前面。两种混合方法PBIL-KRG PBIL-RBF可以超越原始PBIL虽然后使用345更多的实际功能评估。一些选定的设计方案从PBIL-KRG绘制在图前面<一个href="//www.newsama.com/journals/jam/2012/534783/fig8/" target="_blank">8</一个>。结果表明,混合优化器在各种PFHS几何图形。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 超体积比较(参考点(303,0.1))。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/jam/2012/534783/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 概率向量和相应的数量。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/jam/2012/534783/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-c1cc194ccebe1e4b2c5ee7ff36d0b9d6"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.007.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-c1cc194ccebe1e4b2c5ee7ff36d0b9d6 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.007_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-c1cc194ccebe1e4b2c5ee7ff36d0b9d6 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>PBIL-KRG20与PBIL35的放大图<一个href="//www.newsama.com/journals/jam/2012/fig6/">6</一个>。</td> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-a39e8f478849e93aad1063e2fd6171c4"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.008.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-a39e8f478849e93aad1063e2fd6171c4 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.008_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-a39e8f478849e93aad1063e2fd6171c4 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>选择PFHSs PBIL-KRG20面前。</td> </tr> </tbody> </table> </div> </div> </div> </div> <p>进一步的调查是由检查使用代理模型的准确性。30个采样点在前一节中用于构建三个代理模型(QRS、RBF和库尔德斯坦地区政府)。第二组采样点30生成设计方案,而其函数值评估基于代理模型和有限体积分析(实际函数值)确定。箱线图,如图<一个href="//www.newsama.com/journals/jam/2012/534783/fig9/" target="_blank">9</一个>显示了错误作为一个实际的函数值之间的差异的绝对值和一个从代孕近似。可以看出,最准确的代理模型接点温度和风扇抽运功率是RBF库尔德斯坦地区政府而第二个最好的。这是重合的,从混合PBILs获得最优结果。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-30a84817e4d7e982894191f4a5aa9352"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/figures/534783.fig.009.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-30a84817e4d7e982894191f4a5aa9352 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/jam/volume-2012/534783/thumbnails/534783.fig.009_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-30a84817e4d7e982894191f4a5aa9352 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</年代p一个n> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/jam/2012/534783/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>代理模型的精度评估。</td> </tr> </tbody> </table> </div> </div> </div> </div> <h4 id="conclusions">6。结论</h4> <p>本文提出了混合PBIL使用三个著名的代理模型作为二次响应面模型,一个径向基函数插值技术,和克里格模型。杂交是在这样一种方式进行,一个拉丁超立方体抽样技术是用来构造一个代理模型的生成训练点。然后,PBIL用于解决设计问题基于代理模型的预测。从这个阶段取得帕累托解,帕累托面前然后进一步提高通过运行与实际功能评估PBIL几代。</p> <p>实现混合PBILs随着nonsurrogate PBIL pin-fin散热片的多目标几何设计。提出的设计问题是找到PFHS几何图形,同时最小化其结温度和风扇抽运功率。计算结果表明,表现最好的是surrogate-assisted PBIL使用库尔德斯坦地区政府。这是重合的准确性预测调查结温度和风扇抽运功率的代理模型。设计方案获得执行提出设计过程是真正优于散热器目前在现实世界中使用。提出的混合策略是有效的。我们的未来的工作是研究替代混合策略以便MOEA搜索性能求解PFHS设计改进。</p> <h4 id="acknowledgments">确认</h4> <p>这项研究受到了高等教育委员会办公室,泰国,根据该计划战略奖学金前沿研究网络(CHE-PhD-THA),可持续基础设施研发中心(孔敬大学),和泰国研究基金(基金会)。</p> </div> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 class="ArticleReferences_references__GH2t_" id="references">引用</h4> <ol class="ArticleReferences_orderedReferences__mJr9M"> <li class="ArticleReferences_articleReference__ouEuh" id="B1"> <div class="referenceContent"> <p class="referenceText">s Srisomporn和美国Bureerat几何设计使用杂交MOEA和RSM铝制散热片,”<我>IEEE事务组件和包装技术</我>没有,卷。31日。2、351 - 360年,2009页。</p>视图: <a href="https://doi.org/10.1109/TCAPT.2008.916799" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Geometrical%20design%20of%20plate-fin%20heat%20sinks%20using%20hybridization%20of%20MOEA%20and%20RSM&author=S.%20Srisomporn&author=S.%20Bureerat&publication_year=2009" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B2"> <div class="referenceContent"> <p class="referenceText">Bureerat和s . Srisomporn“最佳铝制散热片通过使用多目标进化算法,”<我>工程优化</我>,42卷,不。4、305 - 323年,2010页。</p>视图: <a href="https://doi.org/10.1080/03052150903143935" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Optimum%20plate-fin%20heat%20sinks%20by%20using%20a%20multi-objective%20evolutionary%20algorithm&author=S.%20Bureerat&author=S.%20Srisomporn&publication_year=2010" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B3"> <div class="referenceContent"> <p class="referenceText">美国Kanyakam和美国Bureerat Pin-Fin散热器使用进化算法的多目标优化,”<我>诉讼的逆问题,设计和优化研讨会</我>若昂佩索阿,巴西,2010年8月。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Multiobjective%20optimisation%20of%20a%20Pin-Fin%20heat%20sink%20using%20evolutionary%20algorithms&author=S.%20Kanyakam&author=S.%20Bureerat" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B4"> <div class="referenceContent"> <p class="referenceText">Kanyakam和s . Bureerat“多目标进化优化舒展pin-fin散热器、“<我>计算流体力学的工程应用</我>,5卷,不。4、553 - 565年,2011页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Multiobjective%20evolutionary%20optimization%20of%20splayed%20pin-fin%20heat%20sink&author=S.%20Kanyakam&author=S.%20Bureerat&publication_year=2011" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B5"> <div class="referenceContent"> <p class="referenceText">美国Kanyakam和美国Bureerat pin-fin散热器的优化设计使用surrogate-assisted多目标进化算法,”<我>先进材料的研究</我>卷,308 - 310,1122 - 1128年,2011页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Optimal%20design%20of%20a%20pin-fin%20heat%20sink%20using%20a%20surrogate-assisted%20multiobjective%20evolutionary%20algorithm&author=S.%20Kanyakam&author=S.%20Bureerat&publication_year=2011" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B6"> <div class="referenceContent"> <p class="referenceText">如果不是,s . Prasanna, r . Arumugam和n . Sudharsan“多目标优化的平板散热片使用Taguchi-based灰色关联分析,“<我>国际先进制造技术杂志》上</我>,52卷,不。5 - 8,739 - 749年,2010页。</p>视图: <a href="https://doi.org/10.1007/s00170-010-2754-8" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Multi-objective%20optimization%20of%20flat%20plate%20heat%20sink%20using%20Taguchi-based%20Grey%20relation%20analysis&author=S.%20Manivannan&author=S.%20Prasanna&author=R.%20Arumugam&author=N.%20Sudharsan&publication_year=2010" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B7"> <div class="referenceContent"> <p class="referenceText">w·a·汗、j . r .身为Culham和m . m . Yovanovich”优化pin-fin散热器在旁路流使用熵代最小化方法,”<我>电子杂志的包装、ASME的事务</我>,卷130,不。3、0310101 - 0310101、2008页。</p>视图: <a href="https://doi.org/10.1115/1.2965209" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Optimization%20of%20pin-fin%20heat%20sinks%20in%20bypass%20flow%20using%20entropy%20generation%20minimization%20method&author=W.%20A.%20Khan&author=J.%20R.%20Culham&author=M.%20M.%20Yovanovich&publication_year=2008" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B8"> <div class="referenceContent"> <p class="referenceText">h·t·陈,p . l . Chen j . t . Horng黄懿慧挂,“pin-fin散热器优化设计,”<我>电子杂志的包装、ASME的事务</我>,卷127,不。4、397 - 406年,2005页。</p>视图: <a href="https://doi.org/10.1115/1.2056572" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Design%20optimization%20for%20pin-fin%20heat%20sinks&author=H.%20T.%20Chen&author=P.%20L.%20Chen&author=J.%20T.%20Horng&author=Y.%20H.%20Hung&publication_year=2005" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B9"> <div class="referenceContent"> <p class="referenceText">郑胜耀金,人类。古,a . v .“库兹涅佐夫”“各向异性渗透率和有效热导率的影响泡沫铝散热器的热performnce,”<我>数值传热的</我>,40卷,不。1,21-36,2001页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Effect%20of%20anisotropy%20in%20permeability%20and%20effective%20thermal%20conductivity%20on%20thermal%20performnce%20of%20an%20Aluminum%20foam%20heat%20sink&author=S.%20Y.%20Kim&author=J.-M.%20Koo&author=A.%20V.%20Kuznetsov&publication_year=2001" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B10"> <div class="referenceContent"> <p class="referenceText">郑胜耀金,人类。古,a . v .“库兹涅佐夫”“优化pin-fin散热器使用当地热非平衡各向异性多孔模型在飞机撞击频道”<我>数值传热的</我>,44卷,不。8,771 - 787年,2003页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Optimization%20of%20pin-fin%20heat%20sinks%20using%20anisotropic%20local%20thermal%20nonequilibrium%20porous%20model%20in%20a%20jet%20impinging%20channel&author=S.%20Y.%20Kim&author=J.-M.%20Koo&author=A.%20V.%20Kuznetsov&publication_year=2003" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B11"> <div class="referenceContent"> <p class="referenceText">j·g·Maveety h·h·荣格,“设计一个最优pin-fin散热器与空气impingment冷却,”<我>IEEE组件和包装技术</我>,25卷,不。3、459 - 469年,2002页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Design%20of%20an%20optimal%20pin-fin%20heat%20sink%20with%20air%20impingment%20cooling&author=J.%20G.%20Maveety&author=H.%20H.%20Jung&publication_year=2002" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B12"> <div class="referenceContent"> <p class="referenceText">p . k . k . w .公园哦,和h . j . Lim”的应用CFD和克里格方法的优化散热器、“<我>国际期刊的传热传质</我>卷,49号月19日至20日,第3447 - 3439页,2006年。</p>视图: <a href="https://doi.org/10.1016/j.ijheatmasstransfer.2006.03.009" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=The%20application%20of%20the%20CFD%20and%20Kriging%20method%20to%20an%20optimization%20of%20heat%20sink&author=K.%20W.%20Park&author=P.%20K.%20Oh&author=H.%20J.%20Lim&publication_year=2006" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B13"> <div class="referenceContent"> <p class="referenceText">s . n . Lophaven h·b·尼尔森j·桑德迦et al .,“鲦鱼MATLAB工具箱克里格,”科技。众议员imm - tr - 2002 - 12,丹麦技术大学,2002。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=DACE%20a%20MATLAB%20kriging%20toolbox&author=S.%20N.%20Lophaven&author=H.%20B.%20Neilson&author=J.%20Sondergaard&publication_year=2002" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B14"> <div class="referenceContent"> <p class="referenceText">s . Baluja“基于人口的增量学习:集成基于遗传搜索函数优化方法和竞争学习,“科技,众议员CMU_CS_95_163 Carnagie梅隆大学计算机科学学院匹兹堡,宾夕法尼亚州,美国,1994年。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Population-based%20incremental%20learning%3A%20a%20method%20for%20integrating%20genetic%20search%20based%20function%20optimization%20and%20competitive%20learning&author=S.%20Baluja&publication_year=1994" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B15"> <div class="referenceContent"> <p class="referenceText">Bureerat和k . Sriworamas“以人群为基础的多目标优化增量学习,”<我>软计算的进步</我>39卷,第232 - 223页,2007年。</p>视图: <a href="https://doi.org/10.1007/978-3-540-70706-6_21" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Population-based%20incremental%20learning%20for%20multiobjective%20optimisation&author=S.%20Bureerat&author=K.%20Sriworamas&publication_year=2007" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B16"> <div class="referenceContent"> <p class="referenceText">s . Bandyopadhyay s萨哈,Maulik, k . Deb”模拟annealing-based多目标优化算法:AMOSA”<我>IEEE进化计算</我>,12卷,不。3、269 - 283年,2008页。</p>视图: <a href="https://doi.org/10.1109/TEVC.2007.900837" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=A%20simulated%20annealing-based%20multiobjective%20optimization%20algorithm%3A%20AMOSA&author=S.%20Bandyopadhyay&author=S.%20Saha&author=U.%20Maulik&author=K.%20Deb&publication_year=2008" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B17"> <div class="referenceContent"> <p class="referenceText">y金”,一个全面的健身近似进化计算的调查中,“<我>软计算</我>9卷,3 - 12,2005页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=A%20comprehensive%20survey%20of%20fitness%20approximation%20in%20evolutionary%20computation&author=Y.%20Jin&publication_year=2005" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B18"> <div class="referenceContent"> <p class="referenceText">r . l .越来越r . n . Desmarais“使用曲面样条函数插值,”<我>杂志上的飞机</我>,9卷,不。2、189 - 191年,1972页。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Interpolation%20using%20surface%20splines&author=R.%20L.%20Harder&author=R.%20N.%20Desmarais&publication_year=1972" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B19"> <div class="referenceContent"> <p class="referenceText">m .淀粉和p·阿马托联系interpolation-optimization多准则优化策略问题,“<我>软计算</我>,9卷,不。1,54 - 65年,2005页。</p>视图: <a href="https://doi.org/10.1007/s00500-003-0334-7" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</年代p一个n> <a href="https://scholar.google.com/scholar_lookup?title=Linked%20interpolation-optimization%20strategies%20for%20multicriteria%20optimization%20problems&author=M.%20Farina&author=P.%20Amato&publication_year=2005" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> <li class="ArticleReferences_articleReference__ouEuh" id="B20"> <div class="referenceContent"> <p class="referenceText">y s Ong p . b . Nair a·j·基恩和k . w . Wong“Surrogate-assisted进化优化框架高保真工程设计问题,”<我>知识整合在进化计算,研究模糊性和软计算</我>艾德,y,页307 - 332,施普林格,柏林,德国,2004年。</p>视图: <a href="https://scholar.google.com/scholar_lookup?title=Surrogate-assisted%20evolutionary%20optimization%20frameworks%20for%20high-fidelity%20engineering%20design%20problems&author=Y.%20S.%20Ong&author=P.%20B.%20Nair&author=A.%20J.%20Keane&author=K.%20W.%20Wong&publication_year=2004" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> </ol> </div> <h4 class="copyright-title" id="copyright">版权</h4> <div class="copyright-body"> 版权©2012 Siwadol Kanyakam和Sujin Bureerat。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</d我v> <div id="related-articles"></div> </div> </div> <div class="ant-col ThreeColumnLayout_rightColumn__b_MuL"> <div> <div> <div class="ArticleRightSection_articleRightSection__rG8Zh"> <div class="ArticleToolbar_articleToolbar__8fsAH"> <a 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d="M16.772,24H2.227A2.163,2.163,0,0,1,0,21.746V2.255A2.159,2.159,0,0,1,2.227,0H12.415L12.9.494h.03V.523L19,6.669V21.746A2.161,2.161,0,0,1,16.772,24ZM2.334,1A1.276,1.276,0,0,0,1,2.358V21.642A1.283,1.283,0,0,0,2.334,23H16.665A1.276,1.276,0,0,0,18,21.642V7.087l-.032-.033H14.215A2.131,2.131,0,0,1,12.02,4.832V1.005L12.015,1ZM13,2V4.745A1.192,1.192,0,0,0,14.261,6H17ZM4.012,20A1.032,1.032,0,0,1,3,18.923a2.505,2.505,0,0,1,.967-1.539,8.15,8.15,0,0,1,2.377-1.418c.344-.779.65-1.6.92-2.327l.008-.022.017-.046.009-.024c.2-.539.453-1.209.71-1.827a4.545,4.545,0,0,1-.372-3.862c.267-.569.6-.858.976-.858.556,0,.964.621,1.015,1.546a7.125,7.125,0,0,1-.681,3.143c.158.305.343.624.55.949a7.127,7.127,0,0,0,1.806,1.9,8.681,8.681,0,0,1,2.023-.279,4.23,4.23,0,0,1,1.468.238c.118.047,1.156.478,1.2,1.143a.688.688,0,0,1-.412.67,2.509,2.509,0,0,1-1.164.242,4.757,4.757,0,0,1-.671-.052,6.631,6.631,0,0,1-2.608-1.025c-.163.042-.323.086-.514.138l-.1.026-.15.041c-.235.067-.464.13-.679.185l-.292.076-.025.006-.019,0c-.794.205-1.615.418-2.4.705A14.033,14.033,0,0,1,6,18.437C5.832,18.7,4.941,20,4.012,20ZM6,17a6.865,6.865,0,0,0-1.287.871A1.927,1.927,0,0,0,4,18.831a.12.12,0,0,0,.041.1A.165.165,0,0,0,4.17,19c.327,0,.965-.631,1.356-1.219C5.671,17.564,5.83,17.3,6,17Zm7.044-2A4.632,4.632,0,0,0,12,15.131a4.76,4.76,0,0,0,1.675.792A2.906,2.906,0,0,0,14.32,16a1.629,1.629,0,0,0,.68-.13,2.672,2.672,0,0,0-.584-.528A2.752,2.752,0,0,0,13.045,15ZM8.166,13c-.177.449-.343.884-.481,1.25l-.01.025-.009.024-.007.02-.035.092-.032.085c-.156.409-.37.97-.59,1.5.6-.181,1.229-.341,1.733-.469l.031-.008.055-.014.028-.007.028-.007.307-.078c.191-.048.4-.105.674-.179l.03-.008.005,0,.036-.01.036-.01.01,0,.01,0,.016,0a8.291,8.291,0,0,1-1.566-1.767C8.341,13.285,8.264,13.16,8.166,13Zm.516-5a1.64,1.64,0,0,0-.34.365A2.425,2.425,0,0,0,8.437,11a4.012,4.012,0,0,0,.553-2.22A1.309,1.309,0,0,0,8.681,8Z" fill="currentColor"></path> </svg></span><span>PDF</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <a href="//www.newsama.com/journals/jam/2012/534783.ris" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Download Citation" tabindex="0" unselectable="on" data-testid="download-citation"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path d="M16 12H8C7.44772 12 7 12.4477 7 13C7 13.5523 7.44772 14 8 14H16C16.5523 14 17 13.5523 17 13C17 12.4477 16.5523 12 16 12Z" fill="currentColor"></path> <path d="M16 16H8C7.44772 16 7 16.4477 7 17C7 17.5523 7.44772 18 8 18H16C16.5523 18 17 17.5523 17 17C17 16.4477 16.5523 16 16 16Z" fill="currentColor"></path> <path d="M10 8H8C7.44772 8 7 8.44772 7 9C7 9.55228 7.44772 10 8 10H10C10.5523 10 11 9.55228 11 9C11 8.44772 10.5523 8 10 8Z" fill="currentColor"></path> <path d="M15 2C15 1.44772 14.5523 1 14 1C13.4477 1 13 1.44772 13 2V8C13 8.55228 13.4477 9 14 9H20C20.5523 9 21 8.55228 21 8C21 7.44772 20.5523 7 20 7H15V2Z" fill="currentColor"></path> <path fill-rule="evenodd" clip-rule="evenodd" d="M14.7071 1.29289C14.5196 1.10536 14.2652 1 14 1H6C4.34315 1 3 2.34315 3 4V20C3 21.6569 4.34315 23 6 23H18C19.6569 23 21 21.6569 21 20V8C21 7.73478 20.8946 7.48043 20.7071 7.29289L14.7071 1.29289ZM6 3H13.5858L19 8.41421V20C19 20.5523 18.5523 21 18 21H6C5.44772 21 5 20.5523 5 20V4C5 3.44772 5.44772 3 6 3Z" fill="currentColor"></path> </svg></span><span>下载引用</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span></a> <div class="ant-collapse ant-collapse-icon-position-end articleToolbarOtherFormats_otherFormatsCollapse__VHaOL"> <div class="ant-collapse-item"> <div class="ant-collapse-header" aria-expanded="false" aria-disabled="false" role="button" tabindex="0"> <div class="ant-collapse-expand-icon"> <span role="img" class="anticon ant-collapse-arrow"> <svg width="1em" height="1em" viewbox="0 0 32 32" fill="none"> <path fill-rule="evenodd" clip-rule="evenodd" d="M17.773 23.453l11.2-11.265a1.918 1.918 0 000-2.641 1.75 1.75 0 00-2.542 0l-9.929 10.101-9.933-10.1a1.75 1.75 0 00-2.542 0 1.919 1.919 0 000 2.64L15.23 23.453c.352.365.811.547 1.271.547.46 0 .92-.182 1.271-.547z" fill="currentColor"></path> </svg></span> </div> <span class="ant-collapse-header-text"><span><span role="img" class="anticon articleToolbarOtherFormats_atofDownloadIcon__YRM5T"> <svg width="1em" height="1em" viewbox="0 0 20 22"> <defs> <clippath> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </clippath> </defs> <g> <path fill-rule="evenodd" clip-rule="evenodd" d="M3,22a3,3,0,0,1-3-3V16a1,1,0,0,1,2,0v3a1,1,0,0,0,1,1H17a1,1,0,0,0,1-1V16a1,1,0,1,1,2,0v3a3,3,0,0,1-3,3Zm6.288-6.3-4-4a1,1,0,0,1,1.414-1.414L9,12.586V1a1,1,0,0,1,2,0V12.586l2.293-2.293a1,1,0,0,1,1.414,1.414l-4,4a1,1,0,0,1-1.423,0Z" fill="currentColor"></path> </g> </svg></span><span>下载其他格式</年代p一个n></span></span> </div> </div> </div> <a href="//www.newsama.com/reprints/534783/confirm" class="ButtonGroup_buttonGroupWrapper__Rqhy0" role="button" type="ghost" aria-label="Order printed copies" tabindex="0" unselectable="on" target="_blank"><span class="ButtonGroup_leftGroup__FJAmS"><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M7.41667 1H18.6667C19.1269 1 19.5 1.44772 19.5 2V22C19.5 22.5523 19.1269 23 18.6667 23H7.41667C5.80584 23 4.5 21.433 4.5 19.5V4.5C4.5 2.567 5.80584 1 7.41667 1ZM6.16667 16.3368V4.5C6.16667 3.67157 6.72631 3 7.41667 3H17.8333V16H7.41667C6.96933 16 6.54552 16.1208 6.16667 16.3368ZM17.8333 18H7.41667C6.72631 18 6.16667 18.6716 6.16667 19.5C6.16667 20.3284 6.72631 21 7.41667 21H17.8333V18Z" fill="currentColor"></path> </svg></span><span>订单打印副本</年代p一个n></span><span role="img" class="anticon ButtonGroup_buttonGroupWrapperIcon__CFikg"> <svg width="1em" height="1em" viewbox="0 0 18 14"> <defs> <clippath id="a"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)"></path> </clippath> </defs> <g transform="translate(-3 -5)"> <path d="M10.293,13.707a1,1,0,0,1,0-1.414L14.586,8H1A1,1,0,0,1,1,6H14.586L10.293,1.707A1,1,0,0,1,11.707.293l6,6a1,1,0,0,1,.172.231h0l.01.019,0,.005.007.014.006.012,0,.008.008.018v0a1,1,0,0,1-.009.817l0,0L17.9,7.44l0,.009-.005.011-.007.013,0,.008-.008.015,0,.005-.01.016,0,0-.011.017,0,0-.012.018,0,0-.012.017,0,0L17.8,7.6l0,0-.011.014,0,.006-.01.012-.009.011-.006.007-.015.017h0l-.04.042-6,6a1,1,0,0,1-1.414,0Z" transform="translate(3 5)" fill="currentColor"></path> </g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</年代p一个n> <div class="articleToolbarStatistics_amount__vJIDp"> 908年</d我v> </div> <div> <span>下载</年代p一个n> <div class="articleToolbarStatistics_amount__vJIDp"> 872年</d我v> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</d我v> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2012/534783" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2012/534783&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 589 589"> <circle cx="420.944" cy="296.781" r="294.5" fill="#2daae1"></circle> <path d="M609.773 179.634c-13.891 6.164-28.811 10.331-44.498 12.204 16.01-9.587 28.275-24.779 34.066-42.86a154.78 154.78 0 0 1-49.209 18.801c-14.125-15.056-34.267-24.456-56.551-24.456-42.773 0-77.462 34.675-77.462 77.473 0 6.064.683 11.98 1.996 17.66-64.389-3.236-121.474-34.079-159.684-80.945-6.672 11.446-10.491 24.754-10.491 38.953 0 26.875 13.679 50.587 34.464 64.477a77.122 77.122 0 0 1-35.097-9.686v.979c0 37.54 26.701 68.842 62.145 75.961-6.511 1.784-13.344 2.716-20.413 2.716-4.998 0-9.847-.473-14.584-1.364 9.859 30.769 38.471 53.166 72.363 53.799-26.515 20.785-59.925 33.175-96.212 33.175-6.25 0-12.427-.373-18.491-1.104 34.291 21.988 75.006 34.824 118.759 34.824 142.496 0 220.428-118.052 220.428-220.428 0-3.361-.074-6.697-.236-10.021a157.855 157.855 0 0 0 38.707-40.158z" fill="#fff"></path> </svg></span></a></li> <li><a href="https://www.linkedin.com/shareArticle/?url=https://doi.org/10.1155/2012/534783" unselectable="on" 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