RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis

Abstract

Owing to its time-consuming computation of complex structural responses, structural reliability analysis is still one of the challenging tasks. In this work, based on the FORM, the structural reliability analysis problem is transformed into a sequential surrogate constrained optimization problem. Subsequently, a reliability analysis method is developed that an adaptive radial basis function (RBF) metamodeling is adopted to approximate the performance function and the genetic algorithm (GA) is employed to solve the constrained optimization problem. The RBF is constructed on the initial design of experiments (DoE) generated by Latin hypercube sampling (LHS). Based on the metamodel, the GA is adopted to find the “potential” most probable point (MPP) by solving the constrained optimization problem, in which the distances between the found “potential” MPP to the existing DoE are dynamically controlled by a distance constraint. Then, the “potential” MPP is added to the DoE to refine the RBF. Finally, the Monte Carlo simulation (MCS) is employed to estimate the failure probability in terms of the metamodel. The above procedures are repeated until the failure probability converges. Five benchmark problems including small probability and high-dimensional situations are analyzed. The results illustrate the efficiency, accuracy, and robustness of the RBF-GA method.