An Improved Multi-Taper S-Transform Method to Estimate Evolutionary Spectrum and Time-Varying Coherence of Nonstationary Processes

50 Pages Posted: 6 Mar 2023

See all articles by Yi-Ming Zhang

Yi-Ming Zhang

University of Cambridge

Zifeng Huang

Hong Kong Polytechnic University

Yong Xia

Hong Kong Polytechnic University

Abstract

Obtaining the accurate evolutionary spectrum and time-varying coherence of multivariate nonstationary processes is essential in engineering applications. However, estimating the time-varying coherence is challenging and has been rarely studied for a single realization of a nonstationary process. To address this issue, an improved multi-taper S-transform (MTST) method is developed to reduce the variance of the evolutionary spectrum and time-varying coherence estimates with a sufficient time-frequency resolution. This new method uses the different number of tapers (NoT) at each frequency to achieve the trade-off between the resolution and variance of the estimated spectrum and coherence. The nonstationary process defined by Wold-Cramer decomposition with a time-varying coherence is considered in this study. First, the analytical formulae of the bias and variance of the evolutionary spectrum of the improved MTST are deduced. The NoT is then analytically derived when time-frequency sine and Hermite tapers are adopted. Subsequently, an iterative procedure is proposed to determine the optimal NoT at each frequency without manual tuning. The proposed technique is finally applied to a nonstationary wind speed process and an earthquake ground motion with different spectral characteristics. Results demonstrate that the improved MTST technique outperforms Priestley’s method, the wavelet-based method, and the MTST method with fixed NoT by estimating a more accurate evolutionary spectrum and time-varying coherence.

Keywords: Multi-taper S-transform method, Nonstationary process, Evolutionary spectrum, Time-varying coherence

Suggested Citation

Zhang, Yi-Ming and Huang, Zifeng and Xia, Yong, An Improved Multi-Taper S-Transform Method to Estimate Evolutionary Spectrum and Time-Varying Coherence of Nonstationary Processes. Available at SSRN: https://ssrn.com/abstract=4379765 or http://dx.doi.org/10.2139/ssrn.4379765

Yi-Ming Zhang

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

Zifeng Huang

Hong Kong Polytechnic University ( email )

Hung Hom
Kowloon
Hong Kong

Yong Xia (Contact Author)

Hong Kong Polytechnic University ( email )

Hung Hom
Kowloon
Hong Kong

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