Approximate Method for Estimating Extreme Value Responses of Nonlinear Stochastic Dynamic Systems

Abstract

This paper proposes an approximate method for estimating the extreme value responses of nonlinear dynamic systems to random excitations. The method focuses on the mean zero responses with the unimodal and symmetrical distributions and uses, respectively, the generalized Gaussian distributions (GGDs) and the Nataf distribution to model the marginal distributions of the displacement and velocity responses and the joint distribution of them. By using an effective parameter estimation method and empirical formula, the parameters in the GGD models and Nataf model are estimated, respectively, from the response statistics obtained from stochastic simulation. Under the Poisson assumption of the upcrossing events of the response of interest, the extreme value estimate is obtained from the analysis of the first passage probabilities of the response. The proposed method is suitable for both hardening and softening responses and, moreover, has a high enough efficiency and accuracy for practical applications. Numerical examples demonstrate the efficiency, accuracy, and utility of the method in the extreme value response estimates.