An innovative adaptive sparse response surface method for structural reliability analysis

Abstract

In the scope of infrastructure risk assessment, structural reliability analysis leads to a challenging problem in order to deal with conflicting objectives: accurate estimation of failure probabilities and computational efficiency. Since the application of classical reliability methods is limited and often leads to a prohibitive computational cost, metamodeling techniques (e.g. polynomial chaos, kriging, response surface methods (RSM), etc.) have been widely used. Nevertheless, existing RSM present limitations handling with highly non-linear limit states, large-scale problems and approximation error. To overcome these problems, this paper describes a cutting-edge response surface algorithm covering the following issues: (i) dimensionality reduction by a variable screening procedure; (ii) definition of a promising search domain; (iii) initial experimental design based on an optimized space-filling scheme; (iv) model selection according to a stepwise regression procedure; (v) model validation by a cross-validation approach; (vi) model fitting using a double weighted regression technique; (vii) sequential sampling scheme by exploring a defined region of interest; (viii) confidence interval of reliability estimates based on a bootstrapping technique. With the aim of proving its efficiency, a wide collection of six illustration examples, concerning both analytical and FE-based problems, was selected. By benchmarking obtained results with literature findings, proposed method not only outperforms existing RSM, but also provides a powerful alternative to the use of other metamodeling techniques.