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A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions
Wang-Ji Yan1; Meng-Yun Zhao2; Michael Beer3; Wei-Xin Ren4; Dimitrios Chronopoulos5
2020-04-29
Source PublicationMechanical Systems and Signal Processing
ISSN0888-3270
Volume145
Abstract

Complex-valued ratio distributions arises in many real applications such as statistical inference for frequency response functions (FRFs) and transmissibility functions (TFs) in structural health monitoring. As a sequel to our previous study, a unified scheme to solving complex ratio random variables is proposed in this study for the case when it is highly non-trivial or impossible to discover a closed-form solution such as the complex-valued t ratio distribution. Based on the probability transformation principle in the complex-valued domain, a unified formula is derived by reducing the concerned problem into multi-dimensional integrals, which can be solved by advanced numerical techniques. A fast sparse-grid quadrature (SGQ) scheme by constructing multivariate quadrature formulas using the combinations of tensor products of suitable one-dimensional formulas is utilized to improve the computational efficiency by avoiding the problem of curse of integral dimensionality. The unified methodology enables the efficient calculation of the probability density function (PDF) of a ratio random variable with its denominator and nominator specified by arbitrary probability distributions including Gaussian or non-Gaussian ratio random variables, correlated or independent random variables, bounded or unbounded ratio random variables. The unified scheme is applied to uncertainty quantification for raw FRFs and TFs without any post-processing such as averaging, smoothing and windowing, and the efficiency of the proposed scheme is verified by using the vibration test field data from a simply supported beam and from the Alamosa Canyon Bridge.

KeywordProbability Density Function Frequency Response Function Transmissibility Function Complex Ratio Distribution Sparse-grid Quadrature Rule Structural Health Monitoring
DOI10.1016/j.ymssp.2020.106886
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaEngineering
WOS SubjectEngineering, Mechanical
WOS IDWOS:000540834900005
PublisherACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 24-28 OVAL RD, LONDON NW1 7DX, ENGLAND
Scopus ID2-s2.0-85083890904
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Citation statistics
Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionTHE STATE KEY LABORATORY OF INTERNET OF THINGS FOR SMART CITY (UNIVERSITY OF MACAU)
Corresponding AuthorWang-Ji Yan; Wei-Xin Ren
Affiliation1.State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering,University of Macau,China
2.Department of Civil Engineering,Hefei University of Technology,Anhui,China
3.Institute for Risk and Reliability,Leibniz Universität Hannover,Germany
4.Depart of Civil Engineering,Shenzhen University,Shenzhen,China
5.Institute for Aerospace Technology & The Composites Group,The University of Nottingham,United Kingdom
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Wang-Ji Yan,Meng-Yun Zhao,Michael Beer,et al. A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions[J]. Mechanical Systems and Signal Processing,2020,145.
APA Wang-Ji Yan,Meng-Yun Zhao,Michael Beer,Wei-Xin Ren,&Dimitrios Chronopoulos.(2020).A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions.Mechanical Systems and Signal Processing,145.
MLA Wang-Ji Yan,et al."A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions".Mechanical Systems and Signal Processing 145(2020).
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