An efficient reliability method combining adaptive global metamodel and probability density evolution method

Abstract An efficient reliability method, i.e., AGM-PDEM, is presented which combines the adaptive global metamodel (AGM) and the probability density evolution method (PDEM). The global metamodel is firstly constructed using an adaptive sampling technique and employed to represent the relationship between the equivalent extreme value (EEV) of responses and basic random variables of stochastic systems. The EEVs of representative point sets with enlarged size are approximated by the constructed surrogate model. Reliability of the stochastic systems then can be readily obtained by virtue of the PDEM. To demonstrate the accuracy and efficiency of the proposed method in metamodeling response surface and in assessing system reliability, the global metamodeling of three analytical functions with different nonlinear features, and the reliability analysis of an eight-story shear frame with different random parameters related to the performance level are addressed. A comparative study against the direct Monte Carlo simulation (MCS) with the established metamodel is carried out as well. Numerical results demonstrate that the adaptive sampling technique for global metamodeling is more superior by comparison with the one-stage sampling technique. The AGM-PDEM has a better applicability than the AGM-MCS in dealing with the problems of both moderate and small failure probabilities encountered in engineering structures. Furthermore, both the fidelity of global metamodel and the accuracy of the proposed reliability method can be guaranteed by specifying a moderate stopping condition in the adaptive sampling process. Therefore, the proposed AGM-PDEM exhibits a satisfactory accuracy and a high efficiency for the reliability assessment of structural systems in practice.

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