实验7.随机系统模拟实验.zip_蒙特卡罗法_matlab_matlab例程

<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/6266f1544f8811599ec02a7b/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/6266f1544f8811599ec02a7b/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1<span class="ff2"> <span class="_ _0"> </span><span class="ff3 sc1 ls1">实验<span class="_ _1"> </span></span></span>7<span class="ff3 sc1">：<span class="ls1">随机系统模拟实验</span></span> </div><div class="t m0 x1 h3 y2 ff4 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h3 y3 ff4 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h4 y4 ff2 fs2 fc0 sc0 ls2 ws0">1.1<span class="ls0"> <span class="_ _2"></span><span class="ff5 sc1 ls1">实验题目<span class="_ _3"> </span></span>1<span class="ff5 sc1 ls1">：用蒙特卡罗法解定积分</span>. </span></div><div class="t m0 x2 h5 y5 ff3 fs1 fc0 sc1 ls0 ws0">请建立求解积<span class="_ _4"></span>分</div><div class="c x3 y6 w2 h6"><div class="t m1 x4 h7 y7 ff6 fs3 fc0 sc0 ls0 ws0"></div><div class="t m1 x5 h8 y8 ff6 fs4 fc0 sc0 ls0 ws0"></div><div class="t m1 x6 h9 y9 ff4 fs4 fc0 sc0 ls0 ws0">5</div><div class="t m1 x7 h9 y8 ff4 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m1 x8 h9 ya ff4 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m1 x9 ha yb ff7 fs5 fc0 sc0 ls3 ws0">dx<span class="_ _5"></span><span class="ls0">e<span class="_ _6"></span>x</span></div><div class="t m1 xa hb ya ff7 fs4 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xb hc y5 ff3 fs1 fc0 sc1 ls0 ws0">的蒙特卡罗模<span class="_ _4"></span>拟模型，并用<span class="_ _7"> </span><span class="ff1 sc0">MA<span class="_ _8"></span>TLAB<span class="_"> </span><span class="ff3 sc1">编程求解。</span> </span></div><div class="t m0 x1 h5 yc ff3 fs1 fc1 sc2 ls0 ws0">方法一：<span class="_ _9"></span>（平均值法）<span class="_ _8"></span><span class="fc0 sc1">利用积分中值<span class="_ _4"></span>定理</span></div><div class="c xc yd w3 hd"><div class="t m2 x8 he ye ff6 fs6 fc0 sc0 ls0 ws0"><span class="_"> </span><span class="_ _a"> </span><span class="_ _b"> </span></div><div class="t m3 xd hf yf ff7 fs7 fc0 sc0 ls0 ws0">a<span class="_ _c"></span>b<span class="_ _d"></span>f<span class="_ _e"></span><span class="ls4">dx<span class="_ _f"></span><span class="ls0">x<span class="_ _6"></span>f</span></span></div><div class="t m3 x6 h10 y10 ff7 fs8 fc0 sc0 ls0 ws0">b</div><div class="t m3 x5 h10 y11 ff7 fs8 fc0 sc0 ls0 ws0">a</div><div class="t m3 xe h11 yf ff6 fs7 fc0 sc0 ls0 ws0"><span class="_ _10"></span></div><div class="t m3 x4 h12 y12 ff6 fs9 fc0 sc0 ls0 ws0"></div><div class="t m3 xf h13 yf ff4 fs7 fc0 sc0 ls0 ws0">)<span class="_ _11"></span>(</div><div class="t m4 x10 h14 yf ff6 fsa fc0 sc0 ls0 ws0"></div></div><div class="t m0 x11 h5 yc ff3 fs1 fc0 sc1 ls0 ws0">；<span class="_ _8"></span>关键计算函数在</div><div class="t m0 x1 h5 y13 ff3 fs1 fc0 sc1 ls1 ws0">区间</div><div class="c x12 y14 w4 h15"><div class="t m5 x13 h16 y15 ff4 fsb fc0 sc0 ls0 ws0">]<span class="_ _12"></span>5<span class="_ _13"></span>,<span class="_ _13"></span>2<span class="_ _14"></span>[<span class="_ _4"></span><span class="ff6"></span></div></div><div class="t m0 x14 hc y13 ff3 fs1 fc0 sc1 ls0 ws0">上函数的均值<span class="_ _4"></span>。<span class="ff1 sc0"> </span></div><div class="t m0 x1 hc y16 ff3 fs1 fc1 sc2 ls0 ws0">方法二：<span class="_ _15"></span>（利用几何概率<span class="_ _4"></span>建模）<span class="_ _4"></span><span class="ff1 sc0"> <span class="_"> </span></span>参考课件案例<span class="ff1 sc0">. </span></div><div class="t m0 x1 hc y17 ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 hc y18 ff3 fs1 fc1 sc2 ls0 ws0">提示：<span class="ff1 sc0"> </span></div><div class="t m0 x1 h17 y19 ff1 fs1 fc0 sc0 ls0 ws0">1<span class="ff2"> <span class="_ _16"> </span><span class="ff3 sc1 ls1">利用<span class="_ _17"> </span></span></span>MA<span class="_ _8"></span>TLAB<span class="_"> </span><span class="ff3 sc1">软件产生<span class="_ _4"></span></span>[a,b]<span class="ff3 sc1">上均匀分布的随机<span class="_ _4"></span>数的方法</span> </div><div class="t m0 x2 h17 y1a ff1 fs1 fc0 sc0 ls0 ws0">1.1<span class="ff2"> <span class="_ _18"> </span><span class="ff3 sc1">调用函数<span class="_ _7"> </span></span></span>rand<span class="ff3 sc1">：</span><span class="ls5"> </span>b+a*rand </div><div class="t m0 x2 h17 y1b ff1 fs1 fc0 sc0 ls0 ws0">1.2<span class="ff2"> <span class="_ _18"> </span><span class="ff3 sc1">调用函数<span class="_ _7"> </span></span></span>unifrnd<span class="ff3 sc1">：</span> <span class="_"> </span>unifrnd(a,b,1,1) <span class="_"> </span><span class="ff3 sc1">或</span> <span class="_"> </span>unifrnd(a,b) </div><div class="t m0 x1 h17 y1c ff1 fs1 fc0 sc0 ls0 ws0">2<span class="ff2"> <span class="_ _16"> </span><span class="ff3 sc1">积分<span class="_ _4"></span>中<span class="_ _4"></span>值<span class="_ _4"></span>定理<span class="_ _4"></span>公式<span class="_ _4"></span>中</span></span></div><div class="c x15 y1d w5 h15"><div class="t m6 x16 h16 y15 ff4 fsb fc0 sc0 ls0 ws0">)<span class="_ _11"></span>(</div><div class="t m7 x17 h18 y15 ff6 fsc fc0 sc0 ls0 ws0"></div><div class="t m6 x18 h19 y15 ff7 fsb fc0 sc0 ls0 ws0">f</div></div><div class="t m0 x19 h5 y1c ff3 fs1 fc0 sc1 ls0 ws0">可以<span class="_ _4"></span>通<span class="_ _4"></span>过<span class="_ _4"></span>如下<span class="_ _4"></span>方法<span class="_ _4"></span>取<span class="_ _4"></span>得：<span class="_ _4"></span>在</div><div class="c x1a y1d w5 h15"><div class="t m6 x16 h16 y15 ff4 fsb fc0 sc0 ls0 ws0">]<span class="_ _19"></span>,<span class="_ _1a"></span>[<span class="_ _1b"> </span><span class="ff7">b<span class="_ _6"></span>a</span></div></div><div class="t m0 x1b h5 y1c ff3 fs1 fc0 sc1 ls6 ws0">上均匀产生</div><div class="c x1c y1e w6 h1a"><div class="t m8 x4 h1b y1f ff7 fsd fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x1d h5 y1c ff3 fs1 fc0 sc1 ls0 ws0">个</div><div class="t m0 x2 h5 y20 ff3 fs1 fc0 sc1 ls0 ws0">点，这</div><div class="c x1e y21 w7 h1a"><div class="t m9 x4 h1b y1f ff7 fsd fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x1f h5 y20 ff3 fs1 fc0 sc1 ls0 ws0">个点函数值<span class="_ _4"></span>取平均作为</div><div class="c x20 y22 w5 h15"><div class="t m6 x16 h16 y15 ff4 fsb fc0 sc0 ls0 ws0">)<span class="_ _11"></span>(</div><div class="t m7 x17 h18 y15 ff6 fsc fc0 sc0 ls0 ws0"></div><div class="t m6 x18 h19 y15 ff7 fsb fc0 sc0 ls0 ws0">f</div></div><div class="t m0 x21 hc y20 ff3 fs1 fc0 sc1 ls0 ws0">的近似。<span class="_ _4"></span><span class="ff1 sc0"> </span></div><div class="t m0 x1 hc y23 ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 hc y24 ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 hc y25 ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h4 y26 ff2 fs2 fc0 sc0 ls2 ws0">1.2<span class="ls0"> <span class="_ _2"></span><span class="ff5 sc1 ls1">实验题目<span class="_ _3"> </span></span>2<span class="ff5 sc1 ls1">：电子管的寿命</span> </span></div><div class="t m0 x2 hc y27 ff3 fs1 fc0 sc1 ls0 ws0">安装有四只型<span class="_ _4"></span>号规格完全相同<span class="_ _4"></span>的电子管，<span class="_ _1c"></span>已知电子管寿命为<span class="_ _7"> </span><span class="ff1 sc0">1000<span class="ls7">--</span>2000<span class="_"> </span></span><span class="ls1">小时</span></div><div class="t m0 x1 hc y28 ff3 fs1 fc0 sc1 ls0 ws0">之间的均匀分<span class="_ _4"></span>布。<span class="ff1 sc0"> </span></div><div class="t m0 x2 h5 y29 ff3 fs1 fc0 sc1 ls0 ws0">当电子管损坏<span class="_ _4"></span>时有两种维修方<span class="_ _4"></span>案，<span class="_ _1d"></span>一是每次更换损坏<span class="_ _4"></span>的那一只；<span class="_ _1d"></span>二是当其中</div><div class="t m0 x1 hc y2a ff3 fs1 fc0 sc1 ls0 ws0">一只损坏时四<span class="_ _4"></span>只同时更换。<span class="_ _4"></span><span class="ff1 sc0"> </span></div><div class="t m0 x12 hc y2b ff3 fs1 fc0 sc1 ls0 ws0">已知更换时间<span class="_ _4"></span>为换一只时需<span class="_ _7"> </span><span class="ff1 sc0">1<span class="_"> </span></span>小时，<span class="_ _1d"></span><span class="ff1 sc0">4<span class="_"> </span><span class="ff3 sc1">只同时换为<span class="_ _7"> </span></span>2<span class="_"> </span><span class="ff3 sc1">小时。<span class="_ _1d"></span>更换时机器<span class="_ _4"></span>因停</span></span></div><div class="t m0 x1 hc y2c ff3 fs1 fc0 sc1 ls0 ws0">止运转每小时<span class="_ _4"></span>的损失为<span class="_ _0"> </span><span class="ff1 sc0">20<span class="_ _0"> </span></span>元<span class="_ _4"></span>，又每只电子管<span class="_ _4"></span>价格<span class="_ _0"> </span><span class="ff1 sc0">10<span class="_ _0"> </span></span>元，试用模拟<span class="_ _4"></span>方法决定哪</div><div class="t m0 x1 hc y2d ff3 fs1 fc0 sc1 ls0 ws0">一个方案经济<span class="_ _4"></span>合理？<span class="ff1 sc0"> </span></div><div class="t m0 x1 hc y2e ff1 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 hc y2f ff3 fs1 fc1 sc2 ls0 ws0">实验提示：<span class="ff1 sc0"> </span></div><div class="t m0 x1 h17 y30 ff1 fs1 fc0 sc0 ls0 ws0">1.<span class="ff2"> <span class="_ _1"> </span><span class="ff3 sc1">产生均<span class="_ _4"></span>匀分布随机数数，<span class="_ _4"></span>使用<span class="_ _17"> </span></span></span>u<span class="_ _4"></span>nifrnd </div><div class="t m0 x1 h17 y31 ff1 fs1 fc0 sc0 ls0 ws0">2.<span class="ff2"> <span class="_ _1"> </span><span class="ff3 sc1">先设计<span class="_ _4"></span>模拟算法再模拟<span class="_ _4"></span></span></span>. </div><div class="t m0 x1 hc y32 ff1 fs1 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div> </body> </html>