Reliability analysis based on active learning Kriging model for problems involving multimodally distributed random variables

A novel strategy, integrating the λ Mixture Model (λMM) and the Active Learning Kriging model (ALK), is proposed to cope with the problems involving multimodally distributed random variables. First, the λMMs are applied to represent the multimodal probability distributions of random variables, because of their excellent multimodal property. Next, the Rejection Sampling (RS) is adopted to draw the candidate points for the proposed AK-RS, which avoids calculating the inverse Cumulative Distribution Function (CDF) of complex λMM and ensures the independence between samples. Following, an advanced Errorbased Stopping Criterion (ESC) is introduced, to further improve the efficiency of the proposed approach. The study of three cases shows that, the AK-RS can superbly fit the Probability Density Functions (PDFs) of observations, while this method can dramatically enhance the computational efficiency and ensure the achievement of the target accuracy.