基于SVM的结构可靠度分析响应面方法

SVM based on response surface method for structural reliability analysis

响应面法是解决隐式极限状态方程结构可靠度分析问题比较理想的方法,其关键问题是响应面函数的重构。根据响应面方法经验点集的小样本特点,利用支持向量机(SVM)对小样本数据良好的学习和泛化能力,用SVM重构结构响应面方程,建立了基于SVM的隐式极限状态方程结构可靠度分析的响应面方法。在此基础上,文中提出了改进SVM响应面方法,改进的方法充分利用每次有限元计算成果,大幅减少了有限元计算次数。算例表明本文方法具有很好的计算精度和计算效率。

Implicit performance functions are normally encountered in structural reliability analysis while the structural systems are complicated. Response surface method （RSM） is very good at copping with the issue with implicit performance functions for its satisfied accuracy and good efficiency. The key point of RSM is the reconstruction of the response surface. However, the amount of sample set used to reconstruct the response surface is small. According to the excellent learning ability and generalization of support vector machine （SVM） even with small samples, the response surface of structure is reconstructed by SVM, and then a new RSM for structural reliability analysis was proposed on SVM. The present results compared well with those calculated by the conventional quadratic polynomial method and artificial neural network method. Furthermore, an improved RSM is developed by SVM, which can get a new response surface and a new design point by adding the old design point to sample set in iterative process. So no any results of FEM calculation is abnegated and the amount of FEM calculations is reduced dramatically. It is proved by examples that the calculation efficiencies and accuracy can be increased by proposed methods.