Simulating Multivariate Multidimensional Homogenous Non-Gaussian Field Based on Unified Hermite Polynomial Model
Publication: Journal of Engineering Mechanics
Volume 149, Issue 7
Abstract
Reasonable simulation of stochastic fields is a key prerequisite for addressing stochastic mechanics problems with Monte Carlo simulation solver. This paper presents a novel method to simulate m-variate and n-dimensional () homogenous non-Gaussian fields according to the prescribed power spectral density matrix (PSDM) and first four moments. In the proposed method, the unified Hermite polynomial model (UHPM) is first extended to homogenous non-Gaussian fields. Then, based on the extended UHPM, a complete transformation model from the normalized non-Gaussian correlation function matrix (CFM) into the underlying Gaussian CFM with its applicable range is derived. In addition, two types of potential incompatibility of the transformation arising from the prescribed PSDM and first four moments are defined and neatly solved. Finally, a unified simulation framework for homogenous non-Gaussian fields is presented, where the fast Fourier transform technique can be embedded in both spectral representation method and Wiener-Khintchine transformation to speed up the simulation progress. Two numerical examples including the simulations of non-Gaussian wind fields and non-Gaussian fields of material properties are presented to demonstrate the effectiveness of the proposed method.
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Data Availability Statement
All data, models, and codes that support the findings of this study are available from the corresponding author upon reasonable request, including computer codes of all the numerical examples.
Acknowledgments
The study is partially supported by the National Natural Science Foundation of China (Grant Nos. 51820105014, 52108104, 51738001, and U19342171), China Scholarship Council (Grant No. 202006370005), and the 111 Project (Grant No. D21001). The support is gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Oct 1, 2022
Accepted: Mar 11, 2023
Published online: May 12, 2023
Published in print: Jul 1, 2023
Discussion open until: Oct 12, 2023
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