A general failure-pursuing sampling framework for surrogate-based reliability analysis

Design of experiment and active learning strategy are vital for the surrogate-based reliability analysis. However, the existing sampling and modeling methods usually ignore some useful information that can guide the choice of training samples, or heavily rely on the characteristics of surrogates. These lead to the inefficiency of sampling strategies or limit the application respectively. Therefore, this work proposes a failure-pursuing sampling framework, which is able to adopt various surrogate models or active learning strategies. In each iteration, it organically and sequentially takes into account the joint probability density function of random variables, the individual information at candidate points and the improvement of the accuracy of predicted failure probability. To measure the probability of the improvement, a global predicted failure probability error is proposed based on the real-time reliability analysis result. Furthermore, Voronoi diagram is applied to partition the sampling region into some local cells for keeping the uniformity of the training samples. Besides, a model-free response-distance function is developed and combined with the framework to avoid relying on the characteristics of surrogates, such as the statistical information provided by Kriging. Finally, four examples are investigated to demonstrate the applicability, stability and generality of the proposed method.