Application of Least Squares Support Vector Machine for Regression to Reliability Analysis

In order to deal with the issue of huge computational cost very well in direct numerical simulation, the traditional response surface method (RSM) as a classical regression algorithm is used to approximate a functional relationship between the state variable and basic variables in reliability design. The algorithm has treated successfully some problems of implicit performance function in reliability analysis. However, its theoretical basis of empirical risk minimization narrows its range of applications for the regression model. In contrast to classical algorithms, the support vector machine for regression (SVR) based on structural risk minimization has the excellent abilities of small sample learning and generalization, and superiority over the traditional regression method. Nevertheless, SVR is time consuming and huge space demanding for the reliability analysis of large samples. This article introduces the least squares support vector machine for regression (LSSVR) into reliability analysis to overcome these shortcomings. Numerical results show that the reliability method based on the LSSVR has excellent accuracy and smaller computational cost than the reliability method based on support vector machine (SVM). Thus, it is valuable for the engineering application.