Expected Uncertainty Reduction for Sequential Kriging-Based Reliability Analysis

Abstract

Several acquisition functions have been proposed to identify an optimal sequence of samples in sequential kriging-based reliability analysis. However, no single acquisition function provides better performance over the others in all cases. To address this problem, this paper proposes a new acquisition function, namely expected uncertainty reduction (EUR), that serves as a meta-criterion to select the best sample from a set of optimal samples, each identified from a large number of candidate samples according to the criterion of an acquisition function. EUR directly quantifies the expected reduction of the uncertainty in the prediction of limit-state function by adding an optimal sample. The uncertainty reduction is quantified by sampling over the kriging posterior. In the proposed EUR-based sequential sampling framework, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical case studies show that (1) EUR-based sequential sampling can perform as well as or outperform the single use of any acquisition function in the portfolio, and (2) the best-performing acquisition function may change from one problem to another or even from one iteration to the next within a problem.