&nbsp;First passage probability assessment based on the first four moments of stationary non-Gaussian structural responses

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (1) : 128-135.

First passage probability assessment based on the first four moments of stationary non-Gaussian structural responses

ZHANG Longwen1, LU Zhaohui1,2, ZHAO Yangang1,2

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Abstract

An analytical procedure was developed for estimating the first passage probability of stationary non-Gaussian structural responses. In the procedure, based on the beforehand obtained first four moments of the stationary non-Gaussian structural responses, a stationary non-Gaussian response was mapped into stationary standard Gaussian processes by using the equivalent Gaussian fractile of translation model and the critical level. The equivalent Gaussian fractile of Winterstein’s polynomial (1994) and Ding and Chen model were used for softening and hardening non-Gaussian responses, respectively. Then, the Poisson model based on stationary non-Gaussian structural responses was established considering the effects of clumping and initial conditions on the up-crossing rate. The accuracy and efficiency of the modified method were demonstrated through the comparison study of numerical examples. The results show that the computational efficiency is greatly improved compared with the Monte-Carlo simulation, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian structural responses.

Key words

first passage probability / non-Gaussian structural responses / statistical moments / Winterstein (1994) model / Ding and Chen model

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ZHANG Longwen1, LU Zhaohui1,2, ZHAO Yangang1,2. First passage probability assessment based on the first four moments of stationary non-Gaussian structural responses[J]. Journal of Vibration and Shock, 2018, 37(1): 128-135

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