Reliability analysis of structures by a three-stage sequential sampling based adaptive support vector regression model

Abstract

A three-stage adaptive support vector regression (SVR) based metamodel is built by sampling training data sequentially close to a limit state function (LSF). The approach alleviates the difficulty of scarcity of samples in the reduced space for reliability evaluation of a structure involving implicit LSF. Specifically, importance sampling is proposed to ensure a sufficient number of simulation points near the approximated failure plane. A design of experiment is initially constructed by a space-filling design over the entire domain. The optimum choices of the hyper-parameters of the SVR model are then determined by minimizing the generalized root mean square error (GRMSE). A subset of Monte Carlo simulation samples with magnitude of approximated LSF less than the noted GRMSE values are selected. Subsequently, the data points are added sequentially from the subset, based on the maximin criterion. Finally, the SVR model is iteratively updated to improve the reliability estimation by adding more data from the latest subset until convergence. An improved stopping condition is proposed to avoid false convergence. The effectiveness of the proposed approach along with estimation of very small probability of failure is elucidated through three numerical examples.