基于单纯形寻优的响应面可靠性分析方法

Reliability analysis method of response surface based on simplex optimization

结构可靠度计算常采用经典的响应面法拟合隐式功能函数或高维功能函数,而对于强非线性功能函数的实际工程问题,尽管其能够计算出结构可靠度的结果,但此时多项式响应面的拟合精度不够,很容易造成不收敛的现象。为了解决上述问题,将响应面法与单纯形寻优的思路进行结合来探求一种有效的计算方法。本文利用单纯形算法对每次迭代的验算点进行优化;再以优化后的设计验算点为中心进行取样,利用响应面法循环迭代计算;最后,沿着真实响应面逐渐逼近最终的验算点。该方法能够解决高维非线性的隐式极限状态方程可靠度计算收敛性的问题,可以提高计算精度和计算效率,具有一定的工程适用性。

In the calculation of structural reliability,classical response surface method is used to fit implicit function or high-dimensional function.For actual engineering problems of strong nonlinear functions,though the result of structural reliability can be calculated,the fitting accuracy of polynomial response surface is not enough,which is easy to cause the non-convergence.In order to overcome the above problem,an effective method is to combine response surface method and simplex method.Therefore,the simplex algorithm is used to optimize the checking points of each iteration in this paper.Taking the optimized design checking point as the center for sampling,the response surface method was also used for iterative calculation.Finally,the final checking point is approximated by the real response surface.This method can solve the problem of the convergence of the reliability of the implicit limit state equation with high dimensional nonlinearity,it also improves the accuracy and efficiency.It’s appliable in engineering.