基于加权线性响应面法的支持向量机可靠性分析方法

针对估算非线性隐式极限状态函数的失效概率问题,提出了一种基于加权线性响应面法的支持向量机可靠性分析方法。首先采用加权线性响应面确定设计点,在线性响应面迭代的同时获得一定数量的样本,然后在这些样本和设计点附近补充抽取样本的基础上,采用具有良好小样本学习能力的支持向量机方法来训练样本,保证了在设计点周围获得更好的非线性极限状态函数的替代。这种方法既保证了对设计点的精确近似,又保证了对设计点附近非线性极限状态函数的良好近似,大大提高了失效概率的计算精度,为非线性隐式极限状态的可靠性分析提供了一种合理可行的方法。

A SUPPORT VECTOR MACHINE METHOD FOR RELIABILITY ANALYSIS BASED ON WEIGHTED LINEAR RESPONSE SURFACE

To estimate failure probability of nonlinear implicit limit state function, a support vector machine (SVM) method is presented in conjunction with weighted linear response surface method (WLRSM). The design point which is the most likely in failure region is determined exactly by the WLRSM at the first step of the presented method. Secondly, the experimental points selected by WLRSM and some additional samples located in the vicinity of the design point selected from complemental sampling strategy are used as the training samples for SVM, which possesses significant learning capacity at a small amount of information and generalization. Since the samples in the vicinity of the design point are selected as the training samples for SVM, a better surrogate of the nonlinear implicit limit state function around the design point can be constructed by the SVM, and the precision of the failure probability is improved for the nonlinear implicit limit state function. Examples are carried out to show the wide applicability and benefit of the presented method.