Novel Hermite Polynomial Model Based on Probability-Weighted Moments for Simulating Non-Gaussian Stochastic Processes
Publication: Journal of Engineering Mechanics
Volume 150, Issue 4
Abstract
The Hermite polynomial model based on the first-four central moments of non-Gaussian distribution is widely applied to simulate non-Gaussian stochastic processes due to its simplicity and efficiency. Although a variety of expressions have been developed to approximate the coefficients of the Hermite polynomial model, unsatisfactory accuracy and limited applicability could still be encountered. Compared to the central moments, probability-weighted moments possess abundant characteristics of probability distribution. In this paper, a new form of Hermite polynomial model is proposed based on probability-weighted moments for simulating non-Gaussian stochastic processes. The coefficients of the Hermite polynomial model can be conveniently determined via a linear system of equations, leading to a wide application range of the model. More importantly, the sample accuracy for simulating non-Gaussian processes can be significantly improved, and the incompatibility problem can be avoided to some extent by using the proposed model. In addition, a fast strategy for determining the Gaussian auto-correlation function is also suggested, which avoids the complicated manipulations of cubic equations of Gaussian and non-Gaussian auto-correlation functions. A classical example is investigated to demonstrate the better accuracy and applicability over conventional Hermite polynomial models for simulating non-Gaussian stochastic processes. Two engineering cases are also investigated to demonstrate practical applications of the proposed model.
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Data Availability Statement
All of the data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The National Natural Science Foundation of China (Nos. 52278178, 51978253), the Natural Science Foundation of Hunan Province (No. 2022JJ20012), the Science and Technology Innovation Program of Hunan Province (No. 2022RC1176), the Open Fund of State Key Laboratory of Disaster Reduction in Civil Engineering (No. SLDRCE21-04), and Fundamental Research Funds for the Central Universities (No. 531107040224) are gratefully appreciated for the financial support of this research.
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Journal of Engineering Mechanics
Volume 150 • Issue 4 • April 2024
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© 2024 American Society of Civil Engineers.
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Received: Dec 2, 2022
Accepted: Nov 16, 2023
Published online: Jan 31, 2024
Published in print: Apr 1, 2024
Discussion open until: Jun 30, 2024
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