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<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/638b4bd6e53e5839a71c748d/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">3.1 <span class="_"> </span><span class="ff2 sc1">一次可靠度分析法</span></div><div class="t m0 x2 h4 y3 ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fc0 sc1">一次可靠度分析法<span class="_ _1"> </span></span><span class="ff1">(First Order Reliability </span></div><div class="t m0 x2 h4 y4 ff1 fs1 fc1 sc0 ls0 ws0">Method, FO<span class="_ _0"></span>RM)<span class="_"> </span><span class="ff2 sc2">计算结构构件可<span class="_ _0"></span>靠度的基本思路<span class="_ _0"></span>是：首先</span></div><div class="t m0 x2 h4 y5 ff2 fs1 fc1 sc2 ls0 ws0">将结构构件功能函数<span class="_ _1"> </span><span class="ff1 sc0">Z=g<span class="_ _0"></span>(X</span></div><div class="t m0 x3 h5 y6 ff1 fs2 fc1 sc0 ls0 ws0">l</div><div class="t m0 x4 h4 y5 ff2 fs1 fc1 sc0 ls0 ws0">，<span class="_ _2"> </span><span class="ff1">X</span></div><div class="t m0 x5 h5 y6 ff1 fs2 fc1 sc0 ls0 ws0">2</div><div class="t m0 x6 h4 y5 ff2 fs1 fc1 sc0 ls0 ws0">，<span class="sc2">…<span class="_ _3"></span><span class="sc0">，<span class="_ _2"> </span><span class="ff1">X</span></span></span></div><div class="t m0 x7 h5 y6 ff1 fs2 fc1 sc0 ls0 ws0">n</div><div class="t m0 x8 h4 y5 ff1 fs1 fc1 sc0 ls0 ws0">)<span class="_ _2"> </span><span class="ff2 sc2">展开成</span></div><div class="t m0 x2 h4 y7 ff1 fs1 fc1 sc0 ls0 ws0">Taylor<span class="_"> </span><span class="ff2 sc2">级数，忽略高<span class="_ _0"></span>阶项，仅保留线性<span class="_ _0"></span>项，再利用基本随</span></div><div class="t m0 x2 h4 y8 ff2 fs1 fc1 sc2 ls0 ws0">机变量<span class="_ _2"> </span><span class="ff1 sc0">X= (X</span></div><div class="t m0 x9 h5 y9 ff1 fs2 fc1 sc0 ls0 ws0">l</div><div class="t m0 xa h6 y8 ff1 fs1 fc1 sc0 ls0 ws0">, X</div><div class="t m0 xb h5 y9 ff1 fs2 fc1 sc0 ls0 ws0">2</div><div class="t m0 xc h6 y8 ff1 fs1 fc1 sc0 ls0 ws0">, …, X</div><div class="t m0 xd h5 y9 ff1 fs2 fc1 sc0 ls0 ws0">n</div><div class="t m0 xe h4 y8 ff1 fs1 fc1 sc0 ls0 ws0">)<span class="_"> </span><span class="ff2 sc2">的一阶矩、二阶矩求取<span class="_ _2"> </span></span>Z<span class="_"> </span><span class="ff2 sc2">的均值</span></div><div class="t m0 x2 h7 ya ff4 fs1 fc1 sc0 ls0 ws0">μ</div><div class="t m0 xf h5 yb ff1 fs2 fc1 sc0 ls0 ws0">z</div><div class="t m0 x10 h4 ya ff2 fs1 fc1 sc2 ls0 ws0">与标准差<span class="_ _2"> </span><span class="ff4 sc0">σ</span></div><div class="t m0 x11 h5 yb ff1 fs2 fc1 sc0 ls0 ws0">z</div><div class="t m0 x12 h4 ya ff2 fs1 fc1 sc2 ls0 ws0">，从而确定结构构<span class="_ _0"></span>件可靠指标。根<span class="_ _0"></span>据功能</div><div class="t m0 x2 h4 yc ff2 fs1 fc1 sc2 ls0 ws0">函数线性化点的取法<span class="_ _0"></span>不同以及是否考虑<span class="_ _0"></span>基本随机变量的<span class="_ _0"></span>分</div><div class="t m0 x2 h4 yd ff2 fs1 fc1 sc2 ls0 ws0">布类型，一次可靠度<span class="_ _0"></span>分析法分为：<span class="_ _0"></span><span class="fc2 sc3">均<span class="_ _0"></span>值一次二阶矩法<span class="_ _1"> </span><span class="ff1 sc0">(<span class="_ _2"> </span></span>中</span></div><div class="t m0 x2 h4 ye ff2 fs1 fc2 sc3 ls0 ws0">心点法<span class="_ _2"> </span><span class="ff1 sc0">)<span class="_"> </span></span>，改进的一次二阶矩法<span class="_ _2"> </span><span class="ff1 sc0">(<span class="_"> </span></span>验算点法<span class="_ _2"> </span><span class="ff1 sc0">)<span class="_"> </span><span class="ff2">和<span class="_ _2"> </span></span>JC<span class="_ _2"> </span></span>法<span class="fc1 sc2">。</span></div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/638b4bd6e53e5839a71c748d/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">3.1 <span class="_"> </span><span class="ff2 sc1">一次可靠度分析法</span></div><div class="t m0 x2 h4 yf ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fc0 sc1">泰勒<span class="_ _2"> </span><span class="ff1 sc0">(Taylo<span class="_ _0"></span>r)<span class="_"> </span></span>中值定理<span class="_ _2"> </span><span class="ff1 sc0">(<span class="_ _2"> </span></span>一元<span class="_ _2"> </span><span class="ff1 sc0">):</span></span></div><div class="t m0 x2 h4 y10 ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 sc2">如果函数<span class="_ _2"> </span></span><span class="ff5">f<span class="ff1">(</span>x<span class="ff1">)<span class="_"> </span><span class="ff2 sc2">在含有<span class="_ _2"> </span></span></span>x</span></div><div class="t m0 x13 h5 y11 ff1 fs2 fc1 sc0 ls0 ws0">0</div><div class="t m0 x14 h4 y10 ff2 fs1 fc1 sc2 ls0 ws0">的某个开区间<span class="_ _1"> </span><span class="ff1 sc0">(a<span class="_ _2"> </span><span class="ff2">，<span class="_ _2"> </span></span>b)</span></div><div class="t m0 x2 h4 y12 ff2 fs1 fc1 sc2 ls0 ws0">内具有直到<span class="_ _2"> </span><span class="ff1 sc0">(n+<span class="_ _0"></span>1)<span class="_"> </span></span>阶导数，则当<span class="_ _2"> </span><span class="ff5 sc0">x<span class="_ _2"> </span><span class="ff2">在<span class="_ _2"> </span><span class="ff1">(a<span class="_"> </span></span>，<span class="_ _2"> </span><span class="ff1">b)<span class="_ _2"> </span></span></span></span>时， <span class="_ _2"> </span><span class="ff5 sc0">f<span class="ff1">(</span>x<span class="ff1">)<span class="_"> </span></span></span>可</div><div class="t m0 x2 h4 y13 ff2 fs1 fc1 sc2 ls0 ws0">表示为<span class="_ _2"> </span><span class="ff1 sc0">(<span class="ff5">x</span>- <span class="ff5">x</span></span></div><div class="t m0 x15 h5 y14 ff1 fs2 fc1 sc0 ls0 ws0">0</div><div class="t m0 x16 h4 y13 ff1 fs1 fc1 sc0 ls0 ws0">)<span class="_ _2"> </span><span class="ff2 sc2">的一个<span class="_ _2"> </span></span>n<span class="_"> </span><span class="ff2 sc2">次多项式与一个余项<span class="_ _2"> </span></span><span class="ff5">R</span></div><div class="t m0 x17 h5 y14 ff1 fs2 fc1 sc0 ls0 ws0">n</div><div class="t m0 x18 h4 y13 ff1 fs1 fc1 sc0 ls0 ws0">(<span class="ff5">x</span>)<span class="_"> </span><span class="ff2 sc2">之和：</span></div><div class="t m0 x19 h8 y15 ff6 fs3 fc1 sc0 ls0 ws0">'<span class="_ _4"></span>'</div><div class="t m0 x1a h8 y16 ff6 fs3 fc1 sc0 ls0 ws0">'<span class="_ _5"> </span>2</div><div class="t m0 x1b h8 y17 ff6 fs3 fc1 sc0 ls0 ws0">0</div><div class="t m0 x1c h8 y18 ff6 fs3 fc1 sc0 ls0 ws0">0<span class="_ _6"> </span>0<span class="_ _7"> </span>0<span class="_ _8"> </span>0</div><div class="t m0 x1d h8 y19 ff6 fs3 fc1 sc0 ls0 ws0">(<span class="_ _9"> </span>)</div><div class="t m0 x1e h8 y1a ff6 fs3 fc1 sc0 ls0 ws0">0</div><div class="t m0 x1f h8 y1b ff6 fs3 fc1 sc0 ls0 ws0">0</div><div class="t m0 x20 h8 y1c ff6 fs3 fc1 sc0 ls0 ws0">(<span class="_ _a"> </span>1)</div><div class="t m0 x21 h8 y1d ff6 fs3 fc1 sc0 ls0 ws0">1</div><div class="t m0 x22 h8 y1e ff6 fs3 fc1 sc0 ls0 ws0">0</div><div class="t m0 x23 h8 y1f ff6 fs3 fc1 sc0 ls0 ws0">0</div><div class="t m0 x13 h9 y20 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _b"> </span>)</div><div class="t m0 x24 h9 y21 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _c"> </span>)<span class="_ _d"> </span>(<span class="_ _b"> </span>)<span class="_ _e"> </span>(<span class="_ _b"> </span>)(<span class="_ _f"> </span>)<span class="_ _10"> </span>(<span class="_ _f"> </span>)</div><div class="t m0 x25 h9 y22 ff6 fs4 fc1 sc0 ls0 ws0">2<span class="_ _11"></span>!</div><div class="t m0 x26 h9 y23 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _b"> </span>)</div><div class="t m0 x27 h9 y24 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _f"> </span>)<span class="_ _12"> </span>(<span class="_ _c"> </span>)</div><div class="t m0 x12 h9 y25 ff6 fs4 fc1 sc0 ls0 ws0">!</div><div class="t m0 x28 h9 y26 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _13"> </span>)</div><div class="t m0 x29 h9 y27 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _c"> </span>)<span class="_ _14"> </span>(<span class="_ _f"> </span>)</div><div class="t m0 x2a h9 y28 ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _15"> </span>1<span class="_ _16"></span>)<span class="_ _11"></span>!</div><div class="t m0 x2b ha y19 ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x2c ha y29 ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x2d ha y1b ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x9 ha y1c ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x2e ha y1d ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x2f ha y1e ff7 fs3 fc1 sc0 ls0 ws0">n</div><div class="t m0 x30 hb y20 ff7 fs4 fc1 sc0 ls0 ws0">f<span class="_ _17"> </span>x</div><div class="t m0 x31 hb y21 ff7 fs4 fc1 sc0 ls0 ws0">f<span class="_ _18"> </span>x<span class="_ _19"> </span>f<span class="_ _18"> </span>x<span class="_ _1a"> </span>f<span class="_ _1b"> </span>x<span class="_ _1c"> </span>x<span class="_ _17"> </span>x<span class="_ _1d"> </span>x<span class="_ _17"> </span>x</div><div class="t m0 x32 hb y23 ff7 fs4 fc1 sc0 ls0 ws0">f<span class="_ _1e"> </span>x</div><div class="t m0 x33 hb y24 ff7 fs4 fc1 sc0 ls0 ws0">x<span class="_ _17"> </span>x<span class="_ _1f"> </span>R<span class="_ _20"> </span>x</div><div class="t m0 x34 hb y25 ff7 fs4 fc1 sc0 ls0 ws0">n</div><div class="t m0 x35 hb y26 ff7 fs4 fc1 sc0 ls0 ws0">f</div><div class="t m0 x36 hb y27 ff7 fs4 fc1 sc0 ls0 ws0">R<span class="_ _20"> </span>x<span class="_ _21"> </span>x<span class="_ _17"> </span>x</div><div class="t m0 x20 hb y28 ff7 fs4 fc1 sc0 ls0 ws0">n</div><div class="t m0 x37 hb y2a ff7 fs4 fc1 sc0 ls0 ws0">x<span class="_ _22"> </span>x</div><div class="t m1 x38 hc y26 ff8 fs5 fc1 sc0 ls0 ws0"></div><div class="t m1 x39 hc y2a ff8 fs5 fc1 sc0 ls0 ws0"></div><div class="t m0 x34 hd y1c ff8 fs3 fc1 sc0 ls0 ws0"></div><div class="t m0 x3a hd y1d ff8 fs3 fc1 sc0 ls0 ws0"></div><div class="t m0 x3b he y21 ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _23"> </span><span class="_ _24"> </span><span class="_ _25"> </span><span class="_ _26"> </span><span class="_ _27"> </span><span class="_ _28"> </span></div><div class="t m0 x3c he y24 ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _29"> </span></div><div class="t m0 x3d he y27 ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _14"> </span></div><div class="t m0 x3e he y28 ff8 fs4 fc1 sc0 ls0 ws0"></div><div class="t m0 x3f he y21 ff8 fs4 fc1 sc0 ls0 ws0"></div><div class="t m0 x40 hf y2a ff9 fs4 fc1 sc0 ls0 ws0">是<span class="_ _2a"> </span>与<span class="_ _2b"> </span>之间某个值</div><div class="t m0 x41 h10 y2b ff2 fs6 fc2 sc3 ls0 ws0">一元函数</div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/638b4bd6e53e5839a71c748d/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">3.1 <span class="_"> </span><span class="ff2 sc1">一次可靠度分析法</span></div><div class="t m0 x2 h4 yf ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fc0 sc1">泰勒公式<span class="_ _2"> </span><span class="ff1 sc0">(<span class="_"> </span></span>二元<span class="_ _2"> </span><span class="ff1 sc0">):</span></span></div><div class="t m0 x2 h4 y10 ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2">设<span class="_ _2"> </span><span class="ff1">z=<span class="ff5">f</span>(<span class="ff5">x,y</span>)<span class="_"> </span></span><span class="sc2">在点<span class="_ _2"> </span></span><span class="ff1">(<span class="ff5">x</span></span></span></div><div class="t m0 x42 h5 y11 ff1 fs2 fc1 sc0 ls0 ws0">0</div><div class="t m0 x43 h6 y10 ff1 fs1 fc1 sc0 ls0 ws0">,<span class="ff5">y</span></div><div class="t m0 x44 h5 y11 ff1 fs2 fc1 sc0 ls0 ws0">0</div><div class="t m0 x45 h4 y10 ff1 fs1 fc1 sc0 ls0 ws0">)<span class="_ _2"> </span><span class="ff2 sc2">的某一邻域内连续且有</span></div><div class="t m0 x2 h4 y12 ff2 fs1 fc1 sc2 ls0 ws0">直到<span class="_ _2"> </span><span class="ff1 sc0">(n+1)<span class="_"> </span></span>阶导数，有：</div><div class="t m0 x46 h8 y2c ff6 fs3 fc1 sc0 ls0 ws0">0<span class="_ _2c"> </span>0<span class="_ _2d"> </span>0<span class="_ _2e"> </span>0<span class="_ _2c"> </span>0<span class="_ _2f"> </span>0<span class="_ _30"> </span>0<span class="_ _2c"> </span>0</div><div class="t m2 x47 hb y2d ff6 fs4 fc1 sc0 ls0 ws0">(<span class="_ _31"> </span>,<span class="_ _32"> </span>)<span class="_ _d"> </span>(<span class="_ _33"> </span>,<span class="_ _34"> </span>)<span class="_ _35"> </span>[(<span class="_ _f"> </span>)<span class="_ _36"> </span>(<span class="_ _33"> </span>,<span class="_ _34"> </span>)<span class="_ _b"> </span>(<span class="_ _37"> </span>)<span class="_ _38"> </span>(<span class="_ _33"> </span>,<span class="_ _34"> </span>)]<span class="_ _39"></span><span class="ff7">f<span class="_ _18"> </span>x<span class="_ _3a"> </span>y<span class="_ _19"> </span>f<span class="_ _18"> </span>x<span class="_ _3b"> </span>y<span class="_ _f"> </span>x<span class="_ _17"> </span>x<span class="_ _3c"> </span>f<span class="_ _18"> </span>x<span class="_ _3b"> </span>y<span class="_ _38"> </span>y<span class="_ _2c"> </span>y<span class="_ _f"> </span>f<span class="_ _3d"> </span>x<span class="_ _3b"> </span>y</span></div><div class="t m2 x48 hb y2e ff7 fs4 fc1 sc0 ls0 ws0">x<span class="_ _3e"> </span>y</div><div class="t m2 x49 he y2f ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _3f"> </span></div><div class="t m2 x4a he y2d ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _40"> </span><span class="_ _41"> </span><span class="_ _42"> </span><span class="_ _43"> </span><span class="_ _44"> </span></div><div class="t m2 x4b he y2e ff8 fs4 fc1 sc0 ls0 ws0"><span class="_ _45"> </span></div><div class="t m2 x4c he y2d ff8 fs4 fc1 sc0 ls0 ws0"></div><div class="t m0 x4d h10 y30 ff2 fs6 fc2 sc3 ls0 ws0">一次可靠度分析常取前面</div><div class="t m0 x4d h10 y31 ff2 fs6 fc2 sc3 ls0 ws0">两项。即线性项。</div><div class="t m0 x4d h10 y32 ff2 fs6 fc2 sc3 ls0 ws0">可以推广至有<span class="_ _46"> </span><span class="ff1 sc0">n<span class="_"> </span></span>元情况</div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/638b4bd6e53e5839a71c748d/bg4.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4e h11 y33 ff1 fs6 fc3 sc0 ls0 ws0"> <span class="fs7">2.2.1 <span class="_ _1"> </span><span class="ff2 sc4">均值一次二阶矩法</span></span></div><div class="t m0 x1 h3 y34 ff1 fs0 fc1 sc0 ls0 ws0">2.2 <span class="_"> </span><span class="ff2 fc0 sc1">一次可靠度分析法</span></div><div class="t m0 x2f h10 y35 ff1 fs6 fc0 sc0 ls0 ws0">1 <span class="_"> </span><span class="ff2 sc1">、均值一次二阶矩法<span class="_ _46"> </span></span>(<span class="_ _46"> </span><span class="ff2 sc1">中心点法<span class="_ _47"> </span></span>)<span class="fc1"> </span></div><div class="t m0 x2f h12 y36 ff1 fs6 fc1 sc0 ls0 ws0"><span class="fc4 sc0"> </span><span class="fc4 sc0"> </span></div><div class="t m0 x4f h10 y37 ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fs6 sc2">当功能函数包含有多个相互独立的<span class="fc0 sc1">正态随机变量</span></span><span class="fs6"> </span></div><div class="t m0 x4f h12 y38 ff1 fs6 fc1 sc0 ls0 ws0">X= (X</div><div class="t m0 x50 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">l</div><div class="t m0 x2f h12 y38 ff1 fs6 fc1 sc0 ls0 ws0">, X</div><div class="t m0 x51 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">2</div><div class="t m0 x52 h12 y38 ff1 fs6 fc1 sc0 ls0 ws0">, …, X</div><div class="t m0 x34 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">n</div><div class="t m0 x53 h10 y38 ff1 fs6 fc1 sc0 ls0 ws0">)<span class="_"> </span><span class="ff2 sc2">，状态函数为：<span class="_ _47"> </span></span>Z=g(X</div><div class="t m0 x54 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">l</div><div class="t m0 x55 h10 y38 ff2 fs6 fc1 sc0 ls0 ws0">，<span class="_ _46"> </span><span class="ff1">X</span></div><div class="t m0 x56 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">2</div><div class="t m0 x57 h10 y38 ff2 fs6 fc1 sc0 ls0 ws0">，<span class="sc2">…<span class="_ _48"></span><span class="sc0">，<span class="_ _46"> </span><span class="ff1">X</span></span></span></div><div class="t m0 x58 h13 y39 ff1 fs8 fc1 sc0 ls0 ws0">n</div><div class="t m0 x59 h10 y38 ff1 fs6 fc1 sc0 ls0 ws0">)<span class="_"> </span><span class="ff2 sc2">。</span></div><div class="t m0 x5a h10 y3a ff2 fs6 fc0 sc1 ls0 ws0">随机变量</div><div class="t m0 x5a h10 y3b ff2 fs6 fc0 sc1 ls0 ws0">标准差与</div><div class="t m0 x5a h10 y3c ff2 fs6 fc0 sc1 ls0 ws0">其函数标</div><div class="t m0 x5a h10 y3d ff2 fs6 fc0 sc1 ls0 ws0">准差的近</div><div class="t m0 x5a h10 y3e ff2 fs6 fc0 sc1 ls0 ws0">似表达。</div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>
<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/638b4bd6e53e5839a71c748d/bg5.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4e h11 y33 ff1 fs6 fc3 sc0 ls0 ws0"> 3<span class="fs7">.1.1 <span class="_ _1"> </span><span class="ff2 sc4">均值一次二阶矩<span class="_ _4"></span>法</span></span></div><div class="t m0 x1 h3 y34 ff1 fs0 fc1 sc0 ls0 ws0">3.1 <span class="_"> </span><span class="ff2 fc0 sc1">一次可靠度分析法</span></div><div class="t m0 x2f h10 y35 ff1 fs6 fc0 sc0 ls0 ws0">1 <span class="_"> </span><span class="ff2 sc1">、均值一次二阶矩法<span class="_ _47"> </span></span>(<span class="_"> </span><span class="ff2 sc1">中心点法<span class="_ _47"> </span></span>)<span class="fc1"> </span></div><div class="t m0 x2f h12 y36 ff1 fs6 fc1 sc0 ls0 ws0"><span class="fc4 sc0"> </span><span class="fc4 sc0"> </span></div><div class="t m0 x4f h10 y37 ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fs6 sc2">计算步骤：</span></div><div class="t m0 x4f h10 y3f ff3 fs1 fc1 sc0 ls0 ws0"> <span class="_ _0"></span> <span class="_ _1"> </span><span class="ff2 fs6 sc2">当功能函数包含有多个相互独立的<span class="fc0 sc1">正态随机变量</span></span><span class="fs6"> </span></div><div class="t m0 x4f h12 y40 ff1 fs6 fc1 sc0 ls0 ws0">X= (X</div><div class="t m0 x50 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">l</div><div class="t m0 x2f h12 y40 ff1 fs6 fc1 sc0 ls0 ws0">, X</div><div class="t m0 x51 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">2</div><div class="t m0 x52 h12 y40 ff1 fs6 fc1 sc0 ls0 ws0">, …, X</div><div class="t m0 x34 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">n</div><div class="t m0 x53 h10 y40 ff1 fs6 fc1 sc0 ls0 ws0">)<span class="_"> </span><span class="ff2 sc2">，状态函数为：<span class="_ _47"> </span></span>Z=g(X</div><div class="t m0 x54 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">l</div><div class="t m0 x55 h10 y40 ff2 fs6 fc1 sc0 ls0 ws0">，<span class="_ _46"> </span><span class="ff1">X</span></div><div class="t m0 x56 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">2</div><div class="t m0 x57 h10 y40 ff2 fs6 fc1 sc0 ls0 ws0">，<span class="sc2">…<span class="_ _48"></span><span class="sc0">，<span class="_ _46"> </span><span class="ff1">X</span></span></span></div><div class="t m0 x58 h13 y41 ff1 fs8 fc1 sc0 ls0 ws0">n</div><div class="t m0 x59 h10 y40 ff1 fs6 fc1 sc0 ls0 ws0">)<span class="_"> </span><span class="ff2 sc2">。</span></div><div class="t m0 x4f h10 y42 ff1 fs6 fc1 sc0 ls0 ws0"> (1)<span class="_"> </span><span class="ff2 sc2">用各随机变量的均<span class="_ _49"></span>值代入功能函数，得出功能函数的均</span></div><div class="t m0 x4f h10 y43 ff2 fs6 fc1 sc0 ls0 ws0">值<span class="_ _46"> </span><span class="ff1">μ</span></div><div class="t m0 x5b h13 y44 ff1 fs8 fc1 sc0 ls0 ws0">Z</div><div class="t m0 x5c h10 y43 ff2 fs6 fc1 sc2 ls0 ws0">；</div><div class="t m0 x4f h10 y45 ff1 fs6 fc1 sc0 ls0 ws0"> (2)<span class="_"> </span><span class="ff2 sc2">求功能函数</span></div><div class="t m0 x4f h10 y46 ff2 fs6 fc1 sc2 ls0 ws0"> <span class="_ _47"> </span>的标准<span class="fc4 sc0">差</span><span class="_ _46"> </span><span class="ff4 sc0"><span class="fc4 sc0">σ</span></span></div><div class="t m0 x22 h13 y47 ff1 fs8 fc1 sc0 ls0 ws0"><span class="fc4 sc0">Z</span></div><div class="t m0 x2c h10 y46 ff2 fs6 fc1 sc2 ls0 ws0"><span class="fc4 sc0">；</span></div><div class="t m0 x4f h10 y48 ff1 fs6 fc1 sc0 ls0 ws0"> (3)<span class="_"> </span><span class="ff2">求<span class="_ _47"> </span><span class="ff9 sc2">β<span class="_ _4a"> </span></span>和<span class="_ _46"> </span></span>P</div><div class="t m0 x5d h13 y49 ff1 fs8 fc1 sc0 ls0 ws0">f</div><div class="t m0 x28 h10 y48 ff2 fs6 fc1 sc2 ls0 ws0">。</div><div class="t m0 x5e h10 y4a ff2 fs6 fc3 sc4 ls0 ws0">将随机</div><div class="t m0 x5e h10 y4b ff2 fs6 fc3 sc4 ls0 ws0">变量的</div><div class="t m0 x5e h10 y4c ff2 fs6 fc3 sc4 ls0 ws0">均值代</div><div class="t m0 x5e h10 y4d ff2 fs6 fc3 sc4 ls0 ws0">入<span class="fc1 sc2"> </span></div><div class="t m0 x5e h10 y4e ff2 fs6 fc1 sc2 ls0 ws0"> </div></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>
