A new adaptive multi-kernel relevance vector regression for structural reliability analysis

Surrogate models have been widely used in structural reliability analysis to improve the computational efficiency and the accuracy of failure probability. Recently, several multi-kernel relevance vector regression (MKRVR) models have been studied to evaluate the failure probability. However, existing multiple kernel functions for relevance vector regression models are fixed choices, which increases the number of calls to the limit state function (LSF) and leads to inaccurate results. To address the problem, this paper presents a new adaptive MKRVR model combined with Monte Carlo simulation (MCS). Firstly, a stepwise kernel selection strategy is developed to adaptively select better-performing kernel functions and eliminate redundant kernel functions for constructing the MKRVR model. Secondly, a new active learning function is proposed by considering the probability of mis-prediction and spatial locations of the existing sampling point to identify the new training sample points. Thirdly, a hybrid efficient stopping criterion is adopted to terminate the learning process automatically. Three benchmark examples and one practical engineering example are introduced to demonstrate the effectiveness of the proposed method. Results show that the proposed method can provide accurate failure probability by less number of calls to the LSF than existing fixed kernel-based methods.