Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes

Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon proce...

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Veröffentlicht in:Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-10
Hauptverfasser: Zhou, Guang-Dong, Li, Aiqun, Ding, You-Liang
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Ding, You-Liang
description Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.
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subjects Civil engineering
Closed form solutions
Decomposition
Density
Evolutionary
Exact solutions
Fourier transforms
Frequency distribution
Functions (mathematics)
Mathematical analysis
Methods
Power spectral density
Signal processing
Spectra
Stochastic models
Time dependence
Time domain analysis
Typhoons
Wavelet
Wavelet transforms
Wind
title Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes
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