function?AFOSMJC（NE）
%AFOSM法+JC法（Rackwitz-Fiessler方法）
%適用范圍：隨機變量為任意分布，變量間獨立
%特點：保證等價前后失效概率具有較高的近似精度，特征點取MPP點
%缺點：設計點迭代可能不收斂，可能陷入局部最優，可使用遺傳算法計算設計點
%輸入參數：NE?-?極限狀態函數索引，整數
????global?Prob
????tic
????if?nargin<1?NE?=?0;?end?????????????????????????????????%如果未定義方程索引，默認使用索引0
????%1.定義符號變量
????syms?x1??x2??x3??x4??x5??x6?x7??x8??x9??xa??xb??xc??xd??xe??xf??xg;
????X=[?x1??x2??x3??x4??x5??x6?x7??x8??x9??xa??xb??xc??xd??xe??xf??xg?];
????XX=[‘x1‘;??‘x2‘;??‘x3‘??;‘x4‘?;?‘x5‘;??‘x6‘?;‘x7‘;??‘x8‘;??‘x9‘;??‘xa‘;??‘xb‘;??‘xc‘;??‘xd‘;??‘xe‘;??‘xf‘;?‘xg‘];

????%2.獲得方程相關公式、變量數目、變量分布、變量參數
????Prob?=?FunDist（?NE?）;

????%3.獲得相應參數
????gFun=Prob.Fung;?????????????????????????????????????????%用符號變量表示極限狀態函數
????for?i=1:Prob.Nx???
????????[muX（i:）sigmaX（i:）]=RandomVariableStat（Probi）;
????end;?
????
????%4.推導偏導函數，符號變量賦值
????for?i=1:Prob.Nx
????????dgFun（i:）=diff（gFunX（i））;?????????????????????????%求極限狀態函數偏導數表達式
????	eval（[XX（i:）?‘=muX（i:）;‘]）;???????????????????????%為符號變量賦值?-?變量均值
????end;
????
????%5.計算功能函數值及導數值
????gValue=eval（gFun）;??????????????????????????????????????%求解極限狀態函數在均值點處函數值
????for?i=1:Prob.Nx????????????????????????????????????????
????????dgValue（i:）=eval（subs（dgFun（i）））;??????????????????%求解極限狀態函數在均值點處導數值
????end;

????%6.迭代求解MPP點
????x=muX;
????x0=repmat（epslength（muX）1）;
????IteratingStep=0;
????while?norm（x-x0）/norm（x0）?>?1e-6
????????IteratingStep=IteratingStep+1;
????????x0=x;
????????%6.1符號變量賦值
????????for?i=1:Prob.Nx
????????????eval（[XX（i:）?‘=x（i）;‘]）;???????????????????????%為符號變量賦值?-?xi迭代值
????????end;
????????%6.2計算功能函數值及導數值
????????gValue=eval（gFun）;
????????dgValue=eval（subs（dgFun））;??????????????????????????%求在xi點的偏導數值dg/dxi|xi
????????%%%%%%%%%%%%%%%%%%%%
????????%6.3?JC法對非正態分布變量進行轉換處理
????????[muXsigmaX]=JCMethod（Prob?x）;
????????%%%%%%%%%%%%%%%%%%%%
????????%6.4計算加權標準差
????????gs=dgValue.*sigmaX;
????????%如果gs值為零，需要偏移當前點位置，重新計算
????????if（norm（gs））?==?0
????????????x=x+0.1;
????????????continue;
????????end
????????%6.5計算靈敏度系數
????????alphaX=-gs/norm（gs）;
????????%6.6計算可靠度指標
????????beta=（gValue+dgValue.‘*（muX-x））/norm（gs）;
????????%6.7計算新的x向量值
????????x=muX+sigmaX.*alphaX*beta;
????end
????
????%7.求解函數值及失效概率
????MPP=eval（subs（x））;???????????????????????????????????????%求解基本變量x的值
????Pf=normcdf（-beta）;???????????????????????????????????????%失效概率
????
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????fprintf（‘××××××AFOSMJC?失效模式可靠性分析結果××××××\n‘）;?
????fprintf（‘設計點迭代步數：????%d\n‘IteratingStep）;?
????fprintf（‘設計點坐標：‘）;
????for?i=1:Prob.Nx
????????fprintf（‘????????%10.8f‘MPP（i））;
????end????
????fprintf（‘\n‘）;?
????fprintf（‘設計點g值：?????????g（x）=%10.10f\n‘gValue）;
????fprintf（‘可靠度指標：????????β=%10.10f\n‘beta）;
????fprintf（‘失效概率：??????????Pf=%10.10f\n‘Pf）;
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????toc
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