Bouc-Wen-Baber-Noori model of hysteresis:Bouc-Wen-Baber-Noori磁滞模

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  • 2022-05-16 04:52
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该工具箱使用多目标优化进化算法(MOBEAs)计算Bouc–Wen–Baber–Noori滞后模型的参数。 该工具箱使用NSGA-II算法,这是一种精英非主导的排序EA。 该工具箱使用由Kalyanmoy Deb教授开发的原始NSGA-II算法,可以从以下网站下载:http://www.iitk.ac.in/kangal/codes.shtml Deb教授允许我使用和发布此工具箱。 有关工具箱的更多信息,请阅读文档和以下文件:-Kalyanmoy Deb,Sameer Agrawal,Amrit Pratap,T Meyarivan。 “一种快速,精英的多目标遗传算法:NSGA-II”。 IEEE进化计算期刊(IEEE-TEC)。 2002年6.第2页,第182-197页。 -Gilberto A. Ortiz,Diego A. Alvarez,Daniel Bedoya-Ruiz。 “使用多目标优化算法识别Bouc-Wen类型模型”。 计算机与结构。 卷114-115。 pp.121-132。 2013。
Bouc_Wen_Baber_Noori_model_of_hysteresis.zip
  • Bouc_Wen_Baber_Noori_model_of_hysteresis
  • input_data
  • 03_bouc_wen_baber_noori
  • bouc_wen_imperial.in
    3.3KB
  • displacement_mm_imperial.txt
    35KB
  • load_kN_el_centro.txt
    21.3KB
  • load_kN_simulation.txt
    7.5KB
  • bouc_wen_el_centro.in
    3.3KB
  • displacement_mm_simulation_40.txt
    14.9KB
  • displacement_mm_simulation.txt
    7.6KB
  • load_kN_simulation_40.txt
    14.9KB
  • bouc_wen_simulation_40.in
    3.3KB
  • displacement_mm_el_centro.txt
    23.7KB
  • load_kN_imperial.txt
    31.6KB
  • bouc_wen_simulation.in
    3.3KB
  • 02_with_degradation_no_pinching
  • bouc_wen_imperial.in
    2.7KB
  • displacement_mm_imperial.txt
    35KB
  • load_kN_el_centro.txt
    21.3KB
  • load_kN_simulation.txt
    7.5KB
  • bouc_wen_el_centro.in
    2.7KB
  • displacement_mm_simulation.txt
    7.6KB
  • displacement_mm_el_centro.txt
    23.8KB
  • load_kN_imperial.txt
    31.6KB
  • bouc_wen_simulation.in
    2.7KB
  • 01_without_degradation_nor_pinching
  • bouc_wen_imperial.in
    2KB
  • displacement_mm_imperial.txt
    35.2KB
  • load_kN_el_centro.txt
    21.3KB
  • load_kN_simulation.txt
    7.5KB
  • bouc_wen_el_centro.in
    2KB
  • displacement_mm_simulation.txt
    7.6KB
  • displacement_mm_el_centro.txt
    23.9KB
  • load_kN_imperial.txt
    31.6KB
  • bouc_wen_simulation.in
    2KB
  • Doc
  • Bouc_Wen_Baber_Noori_model_of_hysteresis.pdf
    320.2KB
  • decode.c
    1017B
  • eval.c
    1.4KB
  • crowddist.c
    3.5KB
  • tourselect.c
    1.9KB
  • rank.c
    2.6KB
  • problemdef.c
    6.5KB
  • Revision
    626B
  • crossover.c
    4.8KB
  • list.c
    1017B
  • sort.c
    2.6KB
  • rand.c
    2.1KB
  • mutation.c
    2.2KB
  • bouc.c
    16.3KB
  • allocate.c
    2.3KB
  • dominance.c
    1.9KB
  • report.c
    5KB
  • merge.c
    1.3KB
  • Makefile
    304B
  • Readme
    2.5KB
  • nsga2r.c
    53KB
  • auxiliary.c
    470B
  • display.c
    1.3KB
  • rand.h
    480B
  • Notice
    1.6KB
  • fillnds.c
    3.9KB
  • global.h
    6.8KB
  • initialize.c
    970B
内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/628167f73b39c07824f31256/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628167f73b39c07824f31256/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">T<span class="_ _0"></span>o<span class="_ _1"></span>olb<span class="_ _1"></span>o<span class="_ _2"></span>x<span class="_ _3"> </span>to<span class="_ _3"> </span>compute<span class="_ _3"> </span>the<span class="_ _3"> </span>parameters<span class="_ _3"> </span>of<span class="_ _3"> </span>the</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Bouc&#8211;W<span class="_ _0"></span>en&#8211;Bab<span class="_ _1"></span>er&#8211;No<span class="_ _1"></span>ori<span class="_ _3"> </span>mo<span class="_ _1"></span>del<span class="_ _3"> </span>of<span class="_ _3"> </span>h<span class="_ _2"></span>ysteresis</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">Gilb<span class="_ _1"></span>erto<span class="_ _4"> </span>Alejandro<span class="_ _4"> </span>Ortiz<span class="_ _5"> </span>Garc&#237;a</div><div class="t m0 x4 h4 y4 ff3 fs2 fc1 sc0 ls0 ws0">gialorga@gmail.com</div><div class="t m0 x5 h5 y5 ff4 fs2 fc0 sc0 ls0 ws0">Univ<span class="_ _6"></span>ersidad<span class="_ _7"> </span>Nacional<span class="_ _7"> </span>de<span class="_ _7"> </span>Colom<span class="_ _6"></span>bia.<span class="_ _8"> </span>Sede<span class="_ _7"> </span>Manizales.</div><div class="t m0 x6 h3 y6 ff2 fs1 fc0 sc0 ls0 ws0">Diego<span class="_ _4"> </span>Andr&#233;s<span class="_ _5"> </span>&#193;lv<span class="_ _2"></span>arez<span class="_ _4"> </span>Mar&#237;n</div><div class="t m0 x7 h4 y7 ff3 fs2 fc1 sc0 ls0 ws0">daalvarez@unal.edu.co</div><div class="t m0 x5 h5 y8 ff4 fs2 fc0 sc0 ls0 ws0">Univ<span class="_ _6"></span>ersidad<span class="_ _7"> </span>Nacional<span class="_ _7"> </span>de<span class="_ _7"> </span>Colom<span class="_ _6"></span>bia.<span class="_ _8"> </span>Sede<span class="_ _7"> </span>Manizales.</div><div class="t m0 x8 h3 y9 ff2 fs1 fc0 sc0 ls0 ws0">No<span class="_ _2"></span>vem<span class="_ _2"></span>b<span class="_ _1"></span>er<span class="_ _4"> </span>20,<span class="_ _5"> </span>2012</div><div class="t m0 x9 h6 ya ff1 fs3 fc0 sc0 ls0 ws0">1<span class="_ _9"> </span>In<span class="_ _2"></span>tro<span class="_ _1"></span>duction</div><div class="t m1 x9 h7 yb ff4 fs4 fc0 sc0 ls0 ws0">The<span class="_ _4"> </span>Bouc&#8211;W<span class="_ _a"></span>en<span class="_ _4"> </span>model<span class="_ _4"> </span>of<span class="_ _4"> </span>h<span class="_ _2"></span>ysteresis<span class="_ _4"> </span>is<span class="_ _4"> </span>widely<span class="_ _4"> </span>used<span class="_ _7"> </span>in<span class="_ _4"> </span>the<span class="_ _4"> </span>areas<span class="_ _7"> </span>of<span class="_ _4"> </span>mechanical<span class="_ _7"> </span>and<span class="_ _4"> </span>structural</div><div class="t m2 x9 h7 yc ff4 fs4 fc0 sc0 ls0 ws0">engineering.<span class="_ _b"> </span>The<span class="_ _4"> </span>mo<span class="_ _c"></span>del<span class="_ _4"> </span>w<span class="_ _2"></span>as<span class="_ _4"> </span>prop<span class="_ _1"></span>osed<span class="_ _4"> </span>b<span class="_ _2"></span>y<span class="_ _4"> </span>Bouc<span class="_ _4"> </span>[</div><div class="t m0 xa h7 yc ff4 fs4 fc2 sc0 ls0 ws0">1</div><div class="t m2 xb h7 yc ff4 fs4 fc0 sc0 ls0 ws0">],<span class="_ _4"> </span>and<span class="_ _4"> </span>later<span class="_ _4"> </span>mo<span class="_ _c"></span>di&#64257;ed<span class="_ _4"> </span>b<span class="_ _2"></span>y<span class="_ _4"> </span>W<span class="_ _2"></span>en<span class="_ _7"> </span>[</div><div class="t m0 xc h7 yc ff4 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m2 xd h7 yc ff4 fs4 fc0 sc0 ls0 ws0">].<span class="_ _b"> </span>The<span class="_ _4"> </span>mo<span class="_ _c"></span>del</div><div class="t m0 x9 h7 yd ff4 fs4 fc0 sc0 ls0 ws0">is<span class="_ _4"> </span>giv<span class="_ _2"></span>en<span class="_ _4"> </span>by<span class="_ _7"> </span>the<span class="_ _4"> </span>following<span class="_ _7"> </span>expression:</div><div class="t m0 xe h7 ye ff5 fs4 fc0 sc0 ls0 ws0">m<span class="_ _1"></span><span class="ff6">&#168;<span class="_ _d"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="_ _e"> </span>+<span class="_ _e"> </span></span>c<span class="_ _f"> </span><span class="ff6">&#729;<span class="_ _10"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="_ _e"> </span>+<span class="_ _e"> </span></span>F<span class="_ _11"> </span><span class="ff6">[</span>x<span class="ff6">(</span>t<span class="ff6">)</span>,<span class="_ _f"> </span>z<span class="_ _c"></span><span class="ff6">(</span>t<span class="ff6">);<span class="_ _f"> </span></span>t<span class="ff6">]<span class="_ _7"> </span>=<span class="_ _12"> </span></span>f<span class="_ _13"></span><span class="ff6">(</span>t<span class="ff6">)</span>,</span></span></span></span></div><div class="t m3 x9 h7 yf ff4 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x2 h7 yf ff5 fs4 fc0 sc0 ls0 ws0">m</div><div class="t m3 xf h7 yf ff4 fs4 fc0 sc0 ls0 ws0">is<span class="_ _5"> </span>the<span class="_ _5"> </span>mass<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _8"> </span>system,</div><div class="t m0 x10 h7 yf ff5 fs4 fc0 sc0 ls0 ws0">c</div><div class="t m3 x11 h7 yf ff4 fs4 fc0 sc0 ls0 ws0">is<span class="_ _5"> </span>the<span class="_ _5"> </span>viscous<span class="_ _5"> </span>linear<span class="_ _5"> </span>damping<span class="_ _8"> </span>co<span class="_ _c"></span>e&#64259;cien<span class="_ _2"></span>t,</div><div class="t m0 x12 h7 yf ff5 fs4 fc0 sc0 ls0 ws0">x</div><div class="t m3 x13 h7 yf ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x14 h7 yf ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x15 h7 yf ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _5"> </span><span class="ff4">is<span class="_ _5"> </span>the</span></div><div class="t m3 x9 h7 y10 ff4 fs4 fc0 sc0 ls0 ws0">displacemen<span class="_ _6"></span>t,</div><div class="t m0 x16 h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">F</div><div class="t m3 x17 h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">[</div><div class="t m0 x18 h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">x</div><div class="t m3 x19 h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x1a h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x1b h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">)</div><div class="t m0 x1c h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">,<span class="_ _f"> </span>z</div><div class="t m3 x1d h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x1e h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x1f h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">);</div><div class="t m0 x20 h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x21 h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">]<span class="_ _4"> </span><span class="ff4">is<span class="_ _5"> </span>the<span class="_ _4"> </span>restoring<span class="_ _5"> </span>force,<span class="_ _4"> </span>and</span></div><div class="t m0 x22 h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">f</div><div class="t m3 x23 h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x24 h7 y10 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x25 h7 y10 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _4"> </span><span class="ff4">is<span class="_ _5"> </span>the<span class="_ _4"> </span>external<span class="_ _5"> </span>excitation.<span class="_"> </span>The</span></div><div class="t m3 x9 h7 y11 ff4 fs4 fc0 sc0 ls0 ws0">o<span class="_ _6"></span>v<span class="_ _2"></span>erdots<span class="_ _5"> </span>in<span class="_ _4"> </span>the</div><div class="t m0 x26 h7 y11 ff5 fs4 fc0 sc0 ls0 ws0">x</div><div class="t m3 x27 h7 y11 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x19 h7 y11 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x28 h7 y11 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _4"> </span><span class="ff4">v<span class="_ _2"></span>ariable<span class="_ _4"> </span>represents<span class="_ _7"> </span>the<span class="_ _5"> </span>deriv<span class="_ _2"></span>ativ<span class="_ _2"></span>e<span class="_ _4"> </span>with<span class="_ _4"> </span>resp<span class="_ _c"></span>ect<span class="_ _5"> </span>to<span class="_ _4"> </span>time,<span class="_ _4"> </span>hence</span></div><div class="t m0 x29 h7 y11 ff6 fs4 fc0 sc0 ls0 ws0">&#729;<span class="_ _10"></span><span class="ff5">x</span></div><div class="t m3 x2a h7 y11 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x2b h7 y11 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x2c h7 y11 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _4"> </span><span class="ff4">and</span></div><div class="t m0 x2d h7 y12 ff6 fs4 fc0 sc0 ls0 ws0">&#168;<span class="_ _d"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="_ _7"> </span><span class="ff4">represent<span class="_ _7"> </span>the<span class="_ _4"> </span>velocity<span class="_ _7"> </span>and<span class="_ _4"> </span>the<span class="_ _4"> </span>acceleration<span class="_ _4"> </span>resp<span class="_ _c"></span>ectiv<span class="_ _6"></span>ely<span class="_ _a"></span>.</span></span></span></div><div class="t m4 x2e h7 y13 ff4 fs4 fc0 sc0 ls0 ws0">A<span class="_ _2"></span>ccording<span class="_ _4"> </span>to<span class="_ _4"> </span>the<span class="_ _4"> </span>Bouc&#8211;W<span class="_ _a"></span>en<span class="_ _4"> </span>mo<span class="_ _c"></span>del,<span class="_ _4"> </span>the<span class="_ _7"> </span>restoring<span class="_ _4"> </span>force<span class="_ _4"> </span>is<span class="_ _4"> </span>giv<span class="_ _2"></span>en<span class="_ _4"> </span>by<span class="_ _7"> </span>the<span class="_ _4"> </span>follo<span class="_ _6"></span>wing<span class="_ _4"> </span>expression:</div><div class="t m0 x20 h7 y14 ff5 fs4 fc0 sc0 ls0 ws0">F<span class="_ _11"> </span><span class="ff6">[</span>x<span class="ff6">(</span>t<span class="ff6">)</span>,<span class="_ _f"> </span>z<span class="_ _c"></span><span class="ff6">(</span>t<span class="ff6">);<span class="_ _f"> </span></span>t<span class="ff6">]<span class="_ _7"> </span>=<span class="_ _12"> </span></span>&#945;k<span class="_ _c"></span>x<span class="ff6">(</span>t<span class="ff6">)<span class="_ _e"> </span>+<span class="_ _e"> </span>(1<span class="_ _e"> </span><span class="ff7">&#8722;<span class="_ _e"> </span></span></span>&#945;<span class="ff6">)</span>k<span class="_ _c"></span>z<span class="_ _1"></span><span class="ff6">(</span>t<span class="ff6">)</span>,</div><div class="t m3 x9 h7 y15 ff4 fs4 fc0 sc0 ls0 ws0">where</div><div class="t m0 x2f h7 y15 ff5 fs4 fc0 sc0 ls0 ws0">&#945;k<span class="_ _c"></span>x</div><div class="t m3 x30 h7 y15 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x31 h7 y15 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x32 h7 y15 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _14"> </span><span class="ff4">represen<span class="_ _6"></span>ts<span class="_ _14"> </span>the<span class="_ _14"> </span><span class="ff8">elastic<span class="_ _14"> </span>c<span class="_ _2"></span>omp<span class="_ _2"></span>onent<span class="_ _15"> </span><span class="ff4">(instan<span class="_ _6"></span>taneous<span class="_ _14"> </span>resp<span class="_ _c"></span>onse)<span class="_ _14"> </span>and<span class="_ _14"> </span>the<span class="_ _14"> </span>second</span></span></span></div><div class="t m3 x9 h7 y16 ff4 fs4 fc0 sc0 ls0 ws0">expression:<span class="_ _16"> </span><span class="ff6">(1</span></div><div class="t m0 x33 h7 y16 ff7 fs4 fc0 sc0 ls0 ws0">&#8722;<span class="_ _7"> </span><span class="ff5">&#945;</span></div><div class="t m3 x28 h7 y16 ff6 fs4 fc0 sc0 ls0 ws0">)</div><div class="t m0 x1b h7 y16 ff5 fs4 fc0 sc0 ls0 ws0">k<span class="_ _c"></span>z</div><div class="t m3 x5 h7 y16 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x34 h7 y16 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m3 x35 h7 y16 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _8"> </span><span class="ff4">is<span class="_ _b"> </span>the<span class="_ _8"> </span><span class="ff8">hyster<span class="_ _2"></span>etic<span class="_ _b"> </span>c<span class="_ _2"></span>omp<span class="_ _2"></span>onent<span class="_"> </span><span class="ff4">(whic<span class="_ _2"></span>h<span class="_ _b"> </span>depends<span class="_ _b"> </span>on<span class="_ _8"> </span>the<span class="_ _b"> </span>past<span class="_ _8"> </span>history</span></span></span></div><div class="t m3 x9 h7 y17 ff4 fs4 fc0 sc0 ls0 ws0">of<span class="_ _8"> </span>stresses<span class="_ _8"> </span>and<span class="_ _8"> </span>strains),</div><div class="t m0 x36 h7 y17 ff5 fs4 fc0 sc0 ls0 ws0">k</div><div class="t m3 x21 h7 y17 ff4 fs4 fc0 sc0 ls0 ws0">is<span class="_ _8"> </span>the<span class="_ _8"> </span>sti&#64256;ness<span class="_ _8"> </span>of<span class="_ _8"> </span>the<span class="_ _b"> </span>system,</div><div class="t m0 x37 h7 y17 ff5 fs4 fc0 sc0 ls0 ws0">&#945;</div><div class="t m3 x38 h7 y17 ff4 fs4 fc0 sc0 ls0 ws0">is<span class="_ _8"> </span>a<span class="_ _8"> </span>relation<span class="_ _8"> </span>b<span class="_ _c"></span>etw<span class="_ _2"></span>een<span class="_ _8"> </span>the<span class="_ _b"> </span>&#64257;nal</div><div class="t m5 x9 h7 y18 ff4 fs4 fc0 sc0 ls0 ws0">sti&#64256;ness<span class="_ _4"> </span>and<span class="_ _7"> </span>initial<span class="_ _4"> </span>sti&#64256;ness<span class="_ _4"> </span>(<span class="ff6">0</span></div><div class="t m0 x39 h7 y18 ff7 fs4 fc0 sc0 ls0 ws0">&#8804;<span class="_ _12"> </span><span class="ff5">&#945;<span class="_ _7"> </span></span>&#8804;</div><div class="t m5 x3a h7 y18 ff6 fs4 fc0 sc0 ls0 ws0">1<span class="ff4">),<span class="_ _4"> </span>and</span></div><div class="t m0 x3b h7 y18 ff5 fs4 fc0 sc0 ls0 ws0">z</div><div class="t m5 x3c h7 y18 ff6 fs4 fc0 sc0 ls0 ws0">(</div><div class="t m0 x3d h7 y18 ff5 fs4 fc0 sc0 ls0 ws0">t</div><div class="t m5 xb h7 y18 ff6 fs4 fc0 sc0 ls0 ws0">)<span class="_ _4"> </span><span class="ff4">is<span class="_ _7"> </span>the<span class="_ _4"> </span>hysteretic<span class="_ _7"> </span>displacement<span class="_ _7"> </span>(a<span class="_ _4"> </span>&#64257;ctitious</span></div><div class="t m6 x9 h7 y19 ff4 fs4 fc0 sc0 ls0 ws0">displacemen<span class="_ _2"></span>t)<span class="_ _4"> </span>which<span class="_ _7"> </span>is<span class="_ _4"> </span>given<span class="_ _7"> </span>by<span class="_ _4"> </span>the<span class="_ _7"> </span>next<span class="_ _4"> </span>di&#64256;erential<span class="_ _7"> </span>equation<span class="_ _4"> </span>with<span class="_ _4"> </span>initial<span class="_ _4"> </span>condition</div><div class="t m0 x3e h7 y19 ff5 fs4 fc0 sc0 ls0 ws0">z</div><div class="t m6 x15 h7 y19 ff6 fs4 fc0 sc0 ls0 ws0">(0)<span class="_ _12"> </span>=<span class="_ _7"> </span>0<span class="ff4">:</span></div><div class="t m0 x3f h7 y1a ff6 fs4 fc0 sc0 ls0 ws0">&#729;<span class="_ _10"></span><span class="ff5">z<span class="_ _c"></span><span class="ff6">(</span>t<span class="ff6">)<span class="_ _7"> </span>=<span class="_ _12"> </span></span>A<span class="_ _f"> </span><span class="ff6">&#729;<span class="_ _10"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="_ _e"> </span><span class="ff7">&#8722;<span class="_ _e"> </span></span>(</span>&#946;<span class="_ _1"></span><span class="ff7">|<span class="_ _f"> </span><span class="ff6">&#729;<span class="_ _10"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="ff7">||</span></span>z<span class="_ _1"></span><span class="ff6">(</span>t<span class="ff6">)<span class="ff7">|</span></span></span></span></span></span></span></span></div><div class="t m0 xb h8 y1b ff9 fs5 fc0 sc0 ls0 ws0">n<span class="ffa">&#8722;<span class="ffb">1</span></span></div><div class="t m0 x40 h7 y1a ff5 fs4 fc0 sc0 ls0 ws0">z<span class="_ _c"></span><span class="ff6">(</span>t<span class="ff6">)<span class="_ _e"> </span>+<span class="_ _e"> </span></span>&#947;<span class="_ _12"> </span><span class="ff6">&#729;<span class="_ _10"></span><span class="ff5">x<span class="ff6">(</span>t<span class="ff6">)<span class="ff7">|</span></span>z<span class="_ _c"></span><span class="ff6">(</span>t<span class="ff6">)<span class="ff7">|</span></span></span></span></div><div class="t m0 x41 h8 y1b ff9 fs5 fc0 sc0 ls0 ws0">n</div><div class="t m0 x42 h7 y1a ff6 fs4 fc0 sc0 ls0 ws0">)<span class="ff5">,</span></div><div class="t m0 x9 h7 y1c ff4 fs4 fc0 sc0 ls0 ws0">where<span class="_ _4"> </span>the<span class="_ _4"> </span>parameters<span class="_ _7"> </span><span class="ff5">A</span>,<span class="_ _4"> </span><span class="ff5">&#946;<span class="_ _1"></span></span>,<span class="_ _4"> </span><span class="ff5">&#947;<span class="_ _8"> </span></span>and<span class="_ _4"> </span><span class="ff5">n<span class="_ _7"> </span></span>control<span class="_ _4"> </span>the<span class="_ _7"> </span>hysteresis<span class="_ _7"> </span>shap<span class="_ _c"></span>e.</div><div class="t m3 x2e h7 y1d ff4 fs4 fc0 sc0 ls0 ws0">Later,<span class="_ _5"> </span>in<span class="_ _4"> </span>1985,<span class="_ _5"> </span>Bab<span class="_ _c"></span>er<span class="_ _5"> </span>and<span class="_ _5"> </span>Noori<span class="_ _5"> </span>[</div><div class="t m0 x43 h7 y1d ff4 fs4 fc2 sc0 ls0 ws0">3</div><div class="t m3 x11 h7 y1d ff4 fs4 fc0 sc0 ls0 ws0">]<span class="_ _5"> </span>modi&#64257;ed<span class="_ _5"> </span>the<span class="_ _4"> </span>mo<span class="_ _1"></span>del,<span class="_ _5"> </span>and<span class="_ _4"> </span>prop<span class="_ _c"></span>osed<span class="_ _5"> </span>the<span class="_ _5"> </span>inclusion<span class="_ _4"> </span>of</div><div class="t m3 x9 h7 y1e ff4 fs4 fc0 sc0 ls0 ws0">parameters,<span class="_ _5"> </span>whic<span class="_ _2"></span>h<span class="_ _5"> </span>enhance<span class="_ _5"> </span>the<span class="_ _4"> </span>capacity<span class="_ _4"> </span>of<span class="_ _5"> </span>the<span class="_ _4"> </span>mo<span class="_ _c"></span>del<span class="_ _5"> </span>to<span class="_ _5"> </span>represen<span class="_ _2"></span>t<span class="_ _5"> </span>h<span class="_ _2"></span>ysteretic<span class="_ _5"> </span>shap<span class="_ _c"></span>es.<span class="_ _15"> </span>This</div><div class="t m7 x9 h7 y1f ff4 fs4 fc0 sc0 ls0 ws0">mo<span class="_ _c"></span>di&#64257;cation<span class="_ _4"> </span>of<span class="_ _7"> </span>the<span class="_ _4"> </span>mo<span class="_ _c"></span>del<span class="_ _4"> </span>is<span class="_ _4"> </span>kno<span class="_ _2"></span>wn<span class="_ _4"> </span>as<span class="_ _4"> </span>the:<span class="_ _b"> </span><span class="ff8">Bouc&#8211;W<span class="_ _a"></span>en&#8211;Bab<span class="_ _2"></span>er&#8211;No<span class="_ _2"></span>ori<span class="_ _8"> </span><span class="ff4">hysteresis<span class="_ _7"> </span>mo<span class="_ _c"></span>del.<span class="_ _b"> </span>Suc<span class="_ _6"></span>h</span></span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m8"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m8"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m8"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m8"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m8"></div></a></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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