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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 870420, 10 pages
Research Article

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

1College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
2China Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing 210096, China

Received 14 August 2014; Accepted 9 October 2014

Academic Editor: Ting-Hua Yi

Copyright © 2015 Guang-Dong Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.