TY - JOUR

T1 - A unified scheme to solving arbitrary complex-valued ratio distribution with application to statistical inference for raw frequency response functions and transmissibility functions

AU - Yan, Wang-Ji

AU - Zhao, Meng-Yun

AU - Beer, Michael

AU - Ren, Wei-Xin

AU - Chronopoulos, Dimitrios

N1 - Funding information: Financial support to complete this study was provided in part by Natural Science Foundation of China (No. 51778203 and 51778204), the Science and Technology Development Fund, Macau SAR (File no. SKL-IOTSC-2018-2020), the National Key Research and Development Program of China (No. 2019YFB2102702) and Shenzhen Science and Technology Program (No. KQTD20180412181337494). Furthermore, the authors would thank Los Alamos National Laboratory for providing the data from the various vibration tests performed on the Alamosa Canyon Bridge to the public. The authors would like to thank Shi-Ze Cao and Long Yang, postgraduates at Hefei University of Technology, for their kind help in preparing for the specimen and conducting the experiment.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Complex ratio distribution

KW - Frequency response function

KW - Probability density function

KW - Sparse-grid quadrature rule

KW - Structural health monitoring

KW - Transmissibility function

UR - http://www.scopus.com/inward/record.url?scp=85083890904&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.106886

DO - 10.1016/j.ymssp.2020.106886

M3 - Article

AN - SCOPUS:85083890904

VL - 145

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 106886

ER -