基于Kriging模型与重要性抽样的可靠性灵敏度分析

Reliability sensitivity analysis based on Kriging model and importance sampling

针对因无法获得功能函数的梯度信息而不能使用解析方法的情形,提出了进行可靠性灵敏度分析的高效的仿真方法,首先基于Kriging模型和重要性抽样去计算失效概率,然后通过记分函数(score function)方法求出失效概率对各个参数的偏导数。在计算失效概率时采用反问题(inversion problems)中的不确定性逐步减少(stepwise uncertainty reduction)准则来更新功能函数的Kriging模型,继而在重要性抽样的框架下将失效概率表示成一个"增大"的失效概率与修正项的乘积;而记分函数方法只是对前面抽样方法的一个简单后处理,不需要计算额外的功能函数值.对所提方法使用算例验证表明:当功能函数为昂贵的计算模型或对系统(非单个构件)进行灵敏度分析时,该方法具有较高的计算效率和精度。

Due to the lack of the gradient information, the reliability sensitivity analysis can＇t be im- plemented in an analytical manner. Therefore the paper proposed a simulation-based sensitivity method. It is suggested to compute the failure probability by the combination of Kriging model and importance sampling at first, and then the estimator of failure probability is differentiated through the score function approach. The combination of Kriging and importance sampling resorts to the construction of an accurate Kriging surrogate of the limit state function through stepwise uncertainty reduction （SUR） criterion which is commonly used in inversion problems, and score function approach enables the estimation of the gradi- ent of the failure probability without any additional evaluation to the limit state function. The numerical examples illustrate that the proposed method is efficient and precise, especially when the performance function involves the output of an expensive-to-evaluate computational model or the analysis of a system （not a component） is considered.