Adaptive Bayesian support vector regression model for structural reliability analysis

In this paper, Bayesian support vector regression (SVR) model is developed for structural reliability analysis adaptively. Two SVR models, namely, least-square SVR and epsilon-SVR, are constructed under the Bayesian inference framework with a square loss function and a epsilon-insensitive square one respectively. In this framework, a Gaussian process prior is assigned to the regression function, and maximum posterior estimate results in a SVR problem. The proposed Bayesian SVR models provide point-wise probabilistic prediction while keeps the structural risk minimization principle, and it allows us to determine the optimal hyper-parameters by maximizing Bayesian model evidence. Two active learning algorithms are presented based on the Bayesian SVR models to estimate large and small failure probability of complex structure with limited model evaluations respectively. Four benchmark examples are employed to validate the performance of the presented method.

Automated summary

This paper proposes a structural reliability analysis method based on Bayesian support vector regression (SVR) model, which features point-wise probabilistic prediction while keeping the structural risk minimization principle. The method determines the optimal hyperparameters by maximizing Bayesian model evidence and presents two active learning algorithms based on the SVR model to estimate large and small failure probabilities of complex structures. Four benchmark examples are used to validate the performance of the proposed method.