Error Analysis of Spatially Varying Seismic Ground Motion Simulation by Spectral Representation Method
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
This paper investigates statistical errors in the simulation of spatially varying seismic ground motions modeled by evolutionary Gaussian vector processes and simulated by the spectral representation method (SRM). Formulas are derived for both bias and random errors of the simulated evolutionary power spectral density (EPSD), time-varying correlation function, and standard deviation with respect to the target (idealized) ones. The closed-form error formulas for the EPSD are further simplified under specified conditions. It is shown that the simulated nonstationary characteristics are all unbiased, the closed-form random error formulas for the EPSD can reduce to those for stationary simulations, and the predicted random errors match those given by the ensemble average. By using the random error formulas, the factors influencing the random errors are investigated. The results show that the SRM implementation scheme involving both random amplitudes and phase angles would cause larger random errors, and increasing the number of samples and frequency intervals would reduce these errors. Closed-form error formulas are finally used to estimate errors in the simulation of spatially varying seismic ground motions for the Tsing Ma suspension bridge.
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Acknowledgments
The authors wish to acknowledge the financial support provided by the Research Grants Council of Hong Kong (PolyU 5304/11E), The Hong Kong Polytechnic University (PolyU 4-ZZCC), the National Natural Science Foundation of China (No. 51308244), Natural Science Foundation of Hubei Province in China (No. 2012FFB02605), and the U.S. National Science Foundation (CMMI 1462076). Any opinions and conclusions presented here do not necessarily represent the sponsors’ viewpoints.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 25, 2015
Accepted: Feb 10, 2017
Published online: Jun 8, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 8, 2017
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