Reliability estimation through guided tail modeling using support vector machines

Abstract

Reliability estimation using classical tail modeling (CTM) is based on performing a relatively small number of limit-state evaluations through a sampling scheme and then fitting a tail model to the tail part of the data. However, the limit-state calculations that do not belong to the tail part are discarded, so majority of limit-state evaluations are wasted. Guided tail modeling (GTM), proposed earlier by the author, can provide a remedy through guidance of the limit-state function calculations towards the tail region. In the original GTM, the guidance is achieved through a procedure based on threshold estimation using univariate dimension reduction (UDR) and extended generalized lambda distribution (EGLD), and tail region approximation using UDR. This paper proposes a new GTM technique that utilizes support vector machines (SVM). In the proposed method, named GTM-SVM, the threshold estimation is still performed using UDR and EGLD, while the tail region approximation is based on SVM. The performance of GTM-SVM is tested with mathematical example problems as well as structural mechanics problems with varying number of variables. GTMSVM is found to be more accurate than both GTM and CTM for low-dimensional problems. For high-dimensional problems, on the other hand, the original GTM is found to be more accurate than GTM-SVM, which is superior to CTM. © 2012 by Erdem Acar.