Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

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  • University of Liverpool
  • Tongji University
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Original languageEnglish
Article number110880
Number of pages32
JournalMechanical Systems and Signal Processing
Volume206
Early online date1 Nov 2023
Publication statusPublished - 1 Jan 2024

Abstract

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.

Keywords

    Harmonizable process, Loève spectrum, MTST method, Time-varying coherence, Wigner-Ville spectrum

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Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes. / Huang, Zifeng; Chen, Guan; Beer, Michael.
In: Mechanical Systems and Signal Processing, Vol. 206, 110880, 01.01.2024.

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abstract = "Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Lo{\`e}ve spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Lo{\`e}ve spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Lo{\`e}ve spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Lo{\`e}ve spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.",
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