A new active-learning function for adaptive Polynomial-Chaos Kriging probability density evolution method

A new active-learning function is developed to integrate Polynomial-Chaos Kriging with probability density evolution method. First, the relative importance of each representative point to the probability of failure is separately measured, thereby the region of interest is defined for the probability density evolution method, which covers the representative points exerting vital contributions to the probability of failure. Then, a new learning function called the probability density evolution method-oriented information entropy is readily devised based on the information theory, and the stopping condition is defined by specifying a threshold for the learning function values. Two examples are studied to show the efficacy of the adaptive Polynomial-Chaos Kriging probability density evolution method, and the recommended values of two key parameters associated with this new learning function are provided. Moreover, comprehensive comparisons are conducted against several existing reliability methods. The results highlight the advantage of the proposed active-learning function for structural reliability analysis in terms of both computational accuracy and efficiency.