Generalized Proper Complex Gaussian Ratio Distribution and Its Application to Statistical Inference for Frequency Response Functions
Publication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
The frequency response function governs many important processes. Defined as the quotients of the fast Fourier transform coefficients, frequency response functions can be modeled as ratio random variables in the complex domain. The circularly symmetric complex normal ratio distribution proposed previously is restricted to quantifying the uncertainties for the quotients of complex Gaussian random variables with zero mean. Such limitation motivates research to enlarge the group of probability distributions, allowing a wider scope of applicability. This study provides a theoretical proof for the closed-form of a generalized proper complex Gaussian ratio distribution using the principle of probability density transformation in tandem with an advanced integral technique. The equivalence between the distribution properties of complex ratio random variables and their counterparts in the real-valued domain is also proven. The generalized proper complex Gaussian ratio distribution is then used to infer the statistics of frequency response functions. Stochastic simulation and experimental study are used to demonstrate the goodness and efficiency of the proposed probabilistic model.
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Acknowledgments
The National Key Research and Development Plan (No. 2016YFE0113400) is highly appreciated. Financial support to complete this study was also provided in part by Natural Science Foundation of China (Nos. 51778203, 51408176, and 51778204) as well as the Fundamental Research Funds for the Central Universities under Award No. JZ2017HGTB0205. The authors would like to thank Long Yang, Shi-Ze Cao, and Peng-Peng Wang, postgraduates at Hefei University of Technology, for their kind help in the experimental test. Constructive comments from anonymous reviewers are also gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 9 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 26, 2016
Accepted: Mar 22, 2018
Published online: Jun 27, 2018
Published in print: Sep 1, 2018
Discussion open until: Nov 27, 2018
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