UM
A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions
Yan,Wang Ji1; Zhao,Meng Yun2; Beer,Michael3; Ren,Wei Xin4; Chronopoulos,Dimitrios5
2020-11-01
Source PublicationMechanical Systems and Signal Processing
ISSN0888-3270
Volume145
AbstractComplex-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.
KeywordComplex ratio distribution Frequency response function Probability density function Sparse-grid quadrature rule Structural health monitoring Transmissibility function
DOI10.1016/j.ymssp.2020.106886
URLView the original
Language英语
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
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
Recommended Citation
GB/T 7714
Yan,Wang Ji,Zhao,Meng Yun,Beer,Michael,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 Yan,Wang Ji,Zhao,Meng Yun,Beer,Michael,Ren,Wei Xin,&Chronopoulos,Dimitrios.(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 Yan,Wang Ji,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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