基于支持向量回归的响应面可靠度计算

 针对可靠度计算问题中极限状态函数比较复杂或为隐式的情况，提出了一种基于支持向量回归的响应面可靠度计算方法。该方法通过支持向量回归来拟合极限状态函数，所得函数偏导数计算简单，便于进一步采用常规的一次或二次可靠度方法进行求解。该方法首先用拉丁超立方抽样方法产生训练所需样本，通过支持向量回归构造极限状态函数的替代函数，然后用可靠度计算中比较常用的梯度优化法计算其可靠指标或失效概率。算例结果证明了本文方法的可靠性和有效性。

Response Surface Method for Reliability Computation Based on Support Vector Regression

On the complicated or implicit limit state functions in the reliability problems, a response surface method for reliability computation based on Support Vector Regression (SVR) is presented. A fit of the limit state function is constructed by this method. The partial derivatives of the fit could be easily computed and further be used to calculate the reliability through the ordinary first or second order reliability method. Firstly, the required training samples by Latin Hypercube sampling are generated in this paper. Secondly, the substituted function of the limit state function is obtained using the SVR. Thirdly, the reliability index and failure probability are calculated by the ordinary gradient optimization method. Results of the numerical examples justify the reliability and effectiveness of the proposed method, which provides a new approach for the reliability computation.