中文摘要：

经典的响应面方法作为回归方法来模拟可靠性设计中的状态变量和基本变量之间的函数关系,用以解决直接数值模拟方法计算量大的问题。这类算法已经成功解决了一些隐式功能函数的可靠性分析问题,但它依据的'经验风险最小'原则影响了它的使用范围。基于'结构风险最小化'的支持向量回归机方法具有良好的小样本学习性能和泛化能立,比传统的回归方法具有优越性。但支持向量回归机方法对大样本的可靠性问题在时间和空间上开销巨大。为了克服这一不足,本文将最小二乘支持向量回归机引入到可靠性分析中。算例结果表明:基于最小二乘支持向量回归机的可靠性方法计算得到结果精度较高,在计算耗时上远小于支持向量回归机的可靠性方法,因此在工程应用上具有一定价值。

英文摘要：

In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design. The algorithm has treated successfully some problems of implicit performance function in reliability analysis. However, its theoretical basis of empirical risk minimization narrows its range of applications for...