An active-learning reliability method based on support vector regression and cross validation

Abstract

To reduce the high computational cost of the probability density evolution method (PDEM) for structural reliability analysis, an active-learning reliability method that combines the support vector regression (SVR) and the PDEM is proposed, which is abbreviated as the ASVR-PDEM. First, the empirical probability distribution of the SVR is proposed based on the leave-one-out cross-validation (LOOCV) strategy. On this basis, two different learning functions are proposed according to the concept of the PDEM-oriented expected improvement function, which accommodate to any type of metamodels in essence. Then, the pseudo-interpolation replacement is devised to avoid the prediction error of the SVR at the representative points in the region of interest and, thus, maintains the precision of failure probability. Moreover, the influences of four key ingredients on the proposed method are investigated, namely the type of metamodels, the form of learning functions, the deployment of the pseudo-interpolation replacement and the training scheme in the LOOCV strategy. Three numerical examples are investigated to show the feasibility of the ASVR-PDEM. Comparisons are made against several conventional reliability methods. The results highlight the superiority of the ASVR-PDEM in terms of computational accuracy, efficiency and computational time, especially in the case of the time-consuming dynamic reliability problems.