Reliability analysis of structures using stochastic response surface method and saddlepoint approximation
Reliability analysis of structures using stochastic response surface method and saddlepoint approximation
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DOI：
10.1007/s00158-016-1617-9
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发表时间：
2017-06
影响因子：
3.9
通讯作者：
Xianzhen Huang;Yang Liu;Yi-min Zhang;Xufang Zhang
中科院分区：
文献类型：
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作者：
Xianzhen Huang;Yang Liu;Yi-min Zhang;Xufang Zhang
随机响应面法（SRSM）是一种用于具有隐式或耗时极限状态函数的复杂结构系统可靠性分析的技术。响应面法的主要内容是样本点的收集、响应面的逼近和失效概率的估计。在本文中，样本点被选择接近最可能的破坏点和实际的极限状态面（LSS）。使用加权回归技术拟合响应曲面，该技术允许根据拟合点与LSS的距离对拟合点进行加权。解析地推导了响应面的累积量母函数。采用鞍点近似法（SPA）计算结构系统的失效概率。最后，通过四个算例，将该算法与传统的二次多项式随机响应曲面、基于Kriging的随机响应曲面和直接MCS进行了比较。
Stochastic response surface method (SRSM) is a technique used for reliability analysis of complex structural systems having implicit or time consuming limit state functions. The main aspects of the SRSM are the collection of sample points, the approximation of response surface and the estimation of the probability of failure. In this paper, sample points are selected close to the most probable point of failure and the actual limit state surface (LSS). The response surface is fitted using the weighted regression technique, which allows the fitting points to be weighted based on their distance from the LSS. The cumulant generating function (CGF) of the response surface is derived analytically. The saddlepoint approximation (SPA) method is utilized to compute the probability of failure of the structural system. Finally, four numerical examples compare the proposed algorithm with the traditional quadratic polynomial SRSM, Kriging based SRSM and direct MCS.