Evaluation of the Probability Distribution of the Extreme Value of the Response of Nonlinear Structures Subjected to Fully Nonstationary Stochastic Seismic Excitations
Publication: Journal of Engineering Mechanics
Volume 146, Issue 2
Abstract
A two-step methodology is presented for evaluating the extreme value distribution (EVD) of the response of random nonlinear structures under fully nonstationary stochastic seismic excitations. The fully nonstationary stochastic seismic excitations are modeled by the spectral representation method (SRM) based on the evolutionary power spectral density. In this regard, the randomness in both structural properties and external excitations is considered, whereby a problem involving a high-dimensional random-variate space needs to be tackled. In the proposed methodology, the probability density evolution method (PDEM) is first employed, where Latin hypercube simulation (LHS) is incorporated, to provide an estimated solution of the EVD of the response with efficiency. Then, a highly flexible distribution model named the shifted generalized lognormal distribution (SGLD) model is fitted, where the estimated solution is served as the original data. The parameters in SGLD model are then specified, and the entire range of accurate EVD of the response can be recovered accordingly. A numerical example involving a nonlinear random structure exhibiting hysteretic behavior under stochastic seismic ground motions is used to illustrate the implementation of the proposed methodology and assess its accuracy and efficiency, especially for the tail distribution. Some features of the EVD of the dynamic response are also discussed.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The research described in this paper is financially supported by the National Natural Science Foundation of China (Nos. 51978253 and 51608186), the Natural Science Foundation of Hunan Province (No. 2017JJ3016), and the Fundamental Research Funds for the Central Universities of China (No. 531107040110). The support is gratefully acknowledged. The reviewers are also highly acknowledged for constructive comments to improve the original manuscript.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jun 20, 2017
Accepted: Jun 24, 2019
Published online: Dec 7, 2019
Published in print: Feb 1, 2020
Discussion open until: May 7, 2020
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