Efficient Method for Approximating the Joint Extreme Value Distribution of Multivariate Stationary Gaussian Processes
Publication: Journal of Engineering Mechanics
Volume 149, Issue 4
Abstract
The joint extreme value distribution (JEVD) of multivariate random processes is important for evaluating the system reliability of a structure subjected to random vibrations. There are very limited analytical approaches for predicting the JEVD, and these approaches are only computationally viable for problems up to three dimensions. This paper presents an efficient approximate method, which is not limited to low-dimensional problems, for estimating the JEVD of multivariate stationary Gaussian processes. The proposed method modifies an existing method by using the Gauss-Legendre quadrature to evaluate the extreme value correlation coefficients under the bivariate Poisson assumption. Then, the JEVD is approximated using the Nataf transformation. The effectiveness of the proposed method is demonstrated via two numerical examples. The first example concerns the airgap problem of an offshore structure subjected to random waves, in which the extreme wave elevations are evaluated at six locations, and failure is defined as threshold exceedance for any location. The second example is a random vibration problem comprising a three degrees-of-freedom system. Previous studies focused on series system reliability; here three system reliabilities are examined, including series, parallel, and hybrid systems. The proposed method solves the problems efficiently, and it is found to provide an accurate prediction of the JEVD by comparison with Monte Carlo simulation.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The study is partially supported by China Scholarship Council (Grant No. 202006370005). The anonymous reviewers are gratefully acknowledged for their constructive criticisms of the original version of the paper.
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© 2023 American Society of Civil Engineers.
History
Received: Jul 24, 2022
Accepted: Dec 13, 2022
Published online: Feb 6, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 6, 2023
ASCE Technical Topics:
- Continuum mechanics
- Correlation
- Design (by type)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Fluid mechanics
- Gaussian process
- Hydrologic engineering
- Joints
- Mathematics
- Motion (dynamics)
- Probability
- Random waves
- Solid mechanics
- Stationary processes
- Statistics
- Stochastic processes
- Structural design
- Structural engineering
- Structural members
- Structural reliability
- Structural systems
- System reliability
- Systems engineering
- Systems management
- Vibration
- Water and water resources
- Waves (fluid mechanics)
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