The Tail Distribution And First Passage Probability Estimate Of Random Seismic Responses Of Nonlinear Structures

Due to the randomness of the time?place and intensity of seismic activity,as well as randomness of material property?dimension and calculation model of structures,the seismic responses of structures must have significant uncertainties.On the other hand,structures are usually in the nonlinear state when they are subjected to an enormous earthquake.Therefore,estimation of the seismic responses of structures has to consider the related uncertainties and nonlinearity so that the resulting estimates are more tally with actual situation.The main aim of the seismic response estimate of nonlinear structures subjected to random earthquake loads is to evaluate the seismic reliability of the structures.The key issue of the problem is to estimate the first passage probability of the responses of the high thresholds.Some methods have been developed for solving the problem,such as the subset simulation method,tail equivalent linearization method,asymptotic sampling method and so on.However,the efficiency of the methods is too low to satisfy the requirement of the efficient estimate of random seismic responses of large scale structures.Thus,considering the randomness of ground motion acceleration and nonlinearity of the restoring force of structures,this paper makes in-depth study on the efficient estimate of random seismic responses of nonlinear structures subjected to random earthquake loads.The main research contents of the paper include:1.Models of the tails of the marginal distributions and joint distributions of nonlinear random responses of structures and the efficient estimate of the model parameters.2.The estimation method of the small first passage probabilities based on the well-known Rice crossing rates.3.The estimation method of small first passage probabilities based on the tail distributions of the extreme responses.4.Estimation of random seismic responses and small probabilities of failure of the nonlinear structures by using the proposed methods.The main contribution of this paper is to propose a parametric method for estimating random seismic responses of nonlinear structures based on the Shifted Generalized Lognormal Distribution(SGLD)and 2-level parameter estimation method.The analysis of the idealized systems and real structures demonstrate that the proposed method is very efficient in the estimate of random seismic responses and seismic reliabilities of nonlinear structures.This paper has reference value for seismic reliability estimate of large-scale nonlinear structures.