基于加权响应面的支持向量回归机可靠性分析方法

SUPPORT VECTOR REGRESS METHOD FOR DETERMINATION OF FAILURE PROBABILITY ON THE BASIS OF WEIGHTED LINEAR RESPONSE SURFACE

针对非线性隐式功能函数的可靠性分析问题,提出一种基于加权线性响应面法的支持向量回归机可靠性分析方法。由于设计点周围区域对失效概率的贡献最大,所以所提方法首先采用加权线性响应面法确定设计点,然后在设计点周围进行补充抽样,把加权线性响应面法用到的样本及补充样本作为支持向量回归机的训练样本。通过有效的组合加权线性响应面法和支持向量回归机,所提方法在设计点周围获得更好的非线性隐式功能函数的近似,从而提高了非线性隐式功能函数失效概率的估计精度。算例表明该方法具有广泛的应用前景和一定的优越性。

For implicit nonlinear limit state function, a support vector regress method （SVRM） is presented in conjunction with weighted linear response surface method （WLRSM） to estimate failure probability. Since the region around design point makes significant contribution to failure probability, the WLRSM is employed to determine the design point at the first step of the presented method. Secondly, the implicit nonlinear limit state function in the vicinity of the design point is approximated by SVRM. The SVRM possesses significant learning capacity at a small amount of information and generalization. By appropriately selecting the training samples required by the SVRM at the important region for the failure probability, the SVRM can approximate the implicit nonlinear limit state function with high precision. In the presented method, the training samples for SVRM are composed of the experimental points from WLRSM and the additional samples selected from complementally sampling strategy. After integrating the WLRSM with the SVRM effectively, the better surrogate of the implicit nonlinear limit state function can be constructed by the SVR around the design point, and the precision of the failure probability, computed by Monte Carlo simulation method or advanced Monte Carlo simulation method such as importance sampiing, is improved for the implicit nonlinear limit state function. Examples are carried out to show the wide applicability and benefit of the presented method.