Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Abstract

Abstract. Reliability assessment in the context of rare failure events still suffers from its computational cost despite some available methods widely accepted by researchers and engineers. Monte Carlo simulation methods even in their most efficient version such as subset simulation often require a large number of samples for an acceptable accuracy on the failure probability of interest. For low to moderately high dimensional problems and under the assumption of a rather smooth limit-state function, surrogate models a.k.a. metamodels or response surfaces represent interesting alternative solutions. This paper presents an adaptive method based on SVM surrogates used in regression. The SVM formulation hinges on the -insensitive loss function and a Gaussian RBF kernel. The key idea of the proposed method is to iteratively construct SVM surrogates which become more accurate as they get closer to the limit-state surface. Subset simulation is applied to the constructed SVM surrogates for assessing probabilities with respect to intermediate threshold values of the LSF and more importantly for generating new training points. The efficiency of the method is tested on several examples featuring various challenges: a parallel system, a highly curved limit-state surface at a single most probable failure point and a smooth high-dimensional limit-state surface with equal curvatures. The paper puts an emphasis on the key role of an optimal selection of SVM surrogate hyperparameters. This is achieved in the present work by minimizing an estimate of the leave-one-out error using the cross-entropy method.652

Comparative Study of Kriging and Support Vector Regression for Structural Engineering Applications

“…It should be noted here that a degenerate case of CMA-ES is the cross-entropy method for optimization which has been successfully used by Bourinet (2015) for the calibration of support vector machines classification's hyperparameters in high dimension. Here we consider directly CMA-ES in its general formulation as it has shown to be an efficient and robust search algorithm, especially for ill-posed problems (Hansen and Kern, 2004).…”