One-class support vector machine based schemes for structural reliability assessment under imbalanced sample conditions

Abstract

Structural reliability analysis is the key approach to assess uncertainties so that to increase the safety of engineering structures. Quantifying the failure probability (FP) is central to direct the result of the reliability assessment. In aerospace and military fields, normal samples collected from a structure are easily available, however, failure samples are extremely limited. Such imbalanced samples circumstance may lead to a large approximate bias of the failure probability. The critical problem in structural reliability analysis is how to use a smaller number of samples to get more precise failure probabilities. Although the Monte Carlo simulation (MCS) is the recognized benchmark, the high computational cost of calling limit state function has forced people to seek alternative ways. On the other hand, the surrogate model method, such as the adaptive Kriging model (abbreviated as AK-MCS), has been proposed to reduce the computational burden. To evaluate small failure probability, however, the number of the candidate points must be large for a convergent solution. To this end, this paper constructs a security domain identified model (SDIM) based on the one-class support vector machine (SVM) and imbalanced data. Different types of misjudged samples and approximate errors of the trained SDIM are analyzed. Two schemes are proposed accordingly to reduce the tested estimate error of the failure probability. Comparing with MCS and AK-MCS, the numerical and engineering examples demonstrate the accuracy and efficiency of the proposed method under different scenarios.