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结构可靠性分析的支持向量机方法
引用本文:李洪双,吕震宙,岳珠峰.结构可靠性分析的支持向量机方法[J].应用数学和力学,2006,27(10):1135-1143.
作者姓名:李洪双  吕震宙  岳珠峰
作者单位:西北工业大学,航空学院,西安,710072
基金项目:国家自然科学基金;航天基金;国家新世纪优秀人才支持计划项目
摘    要:针对结构可靠性分析中功能函数不能显式表达的问题,将支持向量机方法引入到结构可靠性分析中,支持向量机是一种实现了结构风险最小化原则的分类技术,它具有出色的小样本学习性能和良好的泛化性能,因此提出了两种基于支持向量机的结构可靠性分析方法,与传统的响应面法和神经网络法相比,支持向量机可靠性分析方法的显著特点是在小样本下高精度地逼近函数,并且可以避免维数灾难,算例结果也充分表明支持向量机方法可以在抽样范围内很好地逼近真实的功能函数,减少隐式功能函数分析(通常是有限元分析)的次数,具有一定的工程实用价值。

关 键 词:结构可靠性  隐式功能函数  支持向量机
文章编号:1000-0887(2006)10-1135-09
收稿时间:2005-12-26
修稿时间:2006-07-09

Support Vector Machine for Structural Reliability Analysis
LI Hong-shuang,L Zhen-zhou,YUE Zhu-feng.Support Vector Machine for Structural Reliability Analysis[J].Applied Mathematics and Mechanics,2006,27(10):1135-1143.
Authors:LI Hong-shuang  L Zhen-zhou  YUE Zhu-feng
Institution:LI Hong-shuang,L(U) Zhen-zhou,YUE Zhu-feng
Abstract:Support vector machine(SVM) was introduced to analyze the reliability of the implicit performance function,which is difficult to implement by the classical methods such as the first order reliability method(FORM) and the Monte Carlo simulation(MCS).As a classification method where the underlying structural risk minimization inference rule is employed,SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data.Hence,two approaches,i.e.SVM-based FORM and SVM-based MCS,were presented for the structural reliability analysis of the implicit limit state function.Compared to the conventional response surface method(RSM) and the artificial neural network(ANN),which are widely used to replace the implicit state function for alleviating the computation cost,the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the "curse of dimensionality".The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis(usually finite element analysis),and the computational precision can satisfy the engineering requirement,which are demonstrated by illustrations.
Keywords:structural reliability  implicit performance function  sapport vector machine
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