Kriging-based reliability analysis considering predictive uncertainty reduction

Over the past decade, several acquisition functions have been proposed for kriging-based reliability analysis. Each of these acquisition functions can be used to identify an optimal sequence of samples to be included in the kriging model. However, no single acquisition function provides better performance over the others in all cases. Further, the best-performing acquisition function can change at different iterations over the sequential sampling process. 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 does not rely on the local utility measure derived based on the kriging posterior of a performance function as most existing acquisition functions do. Instead, 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 process, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Each of these samples is optimal with respect to the selection criterion of the corresponding acquisition function. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical and one practical 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.