Evolutionary Spectra Estimation of Field Measurement Typhoon Processes Using Wavelets

Abstract

This paper presents a wavelet-based method for estimating evolutionary power spectral density (EPSD) of nonstationary stochastic oscillatory processes and its application to field measured typhoon processes. The EPSD, which is deduced in a closed form based on the definition of the EPSD and the algorithm of the continuous wavelet transform, can be formulated as a sum of squared moduli of the wavelet functions in time domain modulated by frequency-dependent coefficients that relate to the squared values of wavelet coefficients and two wavelet functions with different time shifts. A parametric study is conducted to examine the efficacy of the wavelet-based estimation method and the accuracy of different wavelets. The results indicate that all of the estimated EPSDs have acceptable accuracy in engineering application and the Morlet transform can provide desirable estimations in both time and frequency domains. Finally, the proposed method is adopted to investigate the time-frequency characteristics of the Typhoon Matsa measured in bridge site. The nonstationary energy distribution and stationary frequency component during the whole process are found. The work in this paper may promote an improved understanding of the nonstationary features of typhoon winds.