Efficient structural reliability analysis based on adaptive Bayesian support vector regression

To reduce the computational burden for structural reliability analysis involving complex numerical models, many adaptive algorithms based on surrogate models have been developed. Among the various surrogate models, the support vector machine for regression (SVR) which is derived from statistical learning theory has demonstrated superior performance to handle nonlinear problems and to avoid overfitting with excellent generalization. Therefore, to take the advantage of the desirable features of SVR, an Adaptive algorithm based on the Bayesian SVR model (ABSVR) is proposed in this study. In ABSVR, a new learning function is devised for the effective selection of informative sample points following the concept of the penalty function method in optimization. To improve the uniformity of sample points in the design of experiments (DoE), a distance constraint term is added to the learning function. Besides, an adaptive sampling region scheme is employed to filter out samples with weak probability density to further enhance the efficiency of the proposed algorithm. Moreover, a hybrid stopping criterion based on the error-based stopping criterion using the bootstrap confidence estimation is developed to terminate the active learning process to ensure that the learning algorithm stops at an appropriate stage. The proposed ABSVR is easy to implement since no embedded optimization algorithm nor iso-probabilistic transformation is required. The performance of ABSVR is evaluated using six numerical examples featuring different complexity, and the results demonstrate the superior performance of ABSVR for structural reliability analysis in terms of accuracy and efficiency.