基于支持向量机的重要抽样方法

在结构可靠度分析中，对于非线性的隐式极限状态方程，与一次二阶矩方法相结合的传统响应面方法一般并不适用。支持向量机算法较好地解决了小样本的统计学习问题，为解决有限样本情况下结构极限状态功能函数的重构提供了有力的理论基础。基于回归支持向量机方法，采用有限的经验点重构结构极限状态方程，结合重要抽样方法计算非线性的隐式极限状态方程结构的可靠度。该方法相对传统响应面方法在结构计算工作不增加的条件下，可以获得高精度的解，能较有效地解决非线性的隐式极限状态方程的结构可靠分析问题。

Importance Sampling Method Based on SVM

The traditional response surface method in combination with first order second moment(FORM) approach isn't suitable for reliability analysis of structure with a non-linear implicit limit state equation.The support vector machine(SVM) method can deal with the problem of statistical learning of small samples,which provides a very good basic theory for the reconstruction of the limit state function.The structural reliability analysis is done with the importance sampling method by using SVM method and limited experimental samples to reconstruct the limit state performance function.In comparison with the traditional response surface method,the proposed approach in this paper can achieve a more accurate result without increasing the amount of structural calculation works and can deal with the problem of reliability analysis of structure with a non-linear implicit limit state equation effectively.