Unified Hermite Polynomial Model and Its Application in Estimating Non-Gaussian Processes
Publication: Journal of Engineering Mechanics
Volume 145, Issue 3
Abstract
Non-Gaussian processes beset many aspects of structural engineering analysis. To estimate non-Gaussian processes, various third-order Hermite polynomial models have been proposed and widely applied. Different forms of expressions have been proposed for hardening and softening processes in existing Hermite polynomial models, which makes them inconvenient to implement. Furthermore, these models are either too simple to ensure accurate results or too complicated to implement conveniently. Thus, a unified third-order Hermite polynomial model that achieves a good balance between accuracy and convenience for both hardening and softening processes is proposed in this study. Explicit expressions for translations of the marginal distributions between the non-Gaussian and Gaussian processes using the proposed Hermite polynomial model are deduced, and the applicable ranges are provided. The accuracy of the proposed model is demonstrated by comparing the coefficients and estimated moments with those obtained from the moment-matching method. Furthermore, the application of the proposed model in evaluating first passage probability, analyzing fatigue damage, and estimating peak factors of non-Gaussian wind pressure coefficient histories is demonstrated with numerical and practical examples.
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Acknowledgments
This study was partially supported by the National Natural Science Foundation of China (Grant Nos. 51820105014, 51738001, U1434204, and 51421005), China Scholarship Council (Grant No. 201706370095), and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 1053320180507). All of the sources of support are gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 3 • March 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: May 16, 2018
Accepted: Sep 4, 2018
Published online: Jan 2, 2019
Published in print: Mar 1, 2019
Discussion open until: Jun 2, 2019
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