基于LS-SVM的结构可靠度响应面分析方法

金伟良，袁雪霞 针对实际工程中常见的功能函数不能显式表达的可靠性分析问题，提出了一种基于最小二乘支持向量机（LS-SVM）的结构可靠度响应面分析方法.采用正交试验设计和有限元程序生成学习样本，并依据各随机变量的概率分布抽样得到检测样本;利用LS SVM的高度非线性映射能力，建立了结构响应量与随机变量之间的映射关系.进而结合Monte-Carlo原理，计算结构的失效概率.新方法可直接应用现有的有限元分析程序，对大型结构进行可靠性分析.通过典型工程结构的算例分析，结果表明该方法具有较好的效率和精度.

Response surface method based on LS-SVM for structural reliability analysis

Aiming at the reliability analysis problems with implicit performance functions,a response surface method based on least squares support vector machines(LS-SLM) was presented.Due to its high approximating capacity,LS-SVM was employed to approximate the implicit mapping between structural response variables and basic random variables.LS-SLM was learned by samples generated from orthographic design method and the finite element analysis(FEA) programs,then validated by selected samples according to their probabilistic distributions.The learned LS-SVM was integrated with Monte-Carlo method to calculate the response variables and then failure probability.The new method combined with the existing FEA programs such as ANSYS can be used to resolve the reliability problem in large complex structural engineering.The efficiency and accuracy of the proposed method were proved by structural reliability analysis of typical engineering examples.