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

Guang-Dong Zhou,Ai-Qun Li,You-Liang Ding

doi:10.1155/2015/870420

Abstract

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.

Highlights

The wind-induced dynamic responses are important factors that must be taken into account during the design and assessment of long-span bridges, tall buildings, and other large-scale structures above ground or sea level with low stiffness and damping
The evolutionary power spectral density (EPSD) of nonstationary typhoon processes is deduced and constructed by closed-form representations of wavelets in time domain, which can break the restriction in the method proposed by Spanos and Failla that the analytical frequency-dependent wavelet functions are required
In [24], the time-dependent coefficients are determined at each time instant and the EPSD is constructed by wavelet functions in frequency domain

Summary

Introduction

The wind-induced dynamic responses are important factors that must be taken into account during the design and assessment of long-span bridges, tall buildings, and other large-scale structures above ground or sea level with low stiffness and damping. Iyama and Kuwamura have proposed a timedependent spectrum based on nonorthogonal wavelets under restrictive assumptions [23] In these studies, the computed time-dependent spectrum has been introduced in a somewhat heuristic manner as the local contribution to the mean-square value of the Fourier transform of the process and no rigorous treatment has been presented. The method developed by Spanos and Failla provides a desirable accuracy to estimate the EPSD of Priestley’s oscillatory processes and is effective in a large number of wavelet functions, including those which are not orthogonal in frequency domain. The EPSD of nonstationary typhoon processes is deduced and constructed by closed-form representations of wavelets in time domain, which can break the restriction in the method proposed by Spanos and Failla that the analytical frequency-dependent wavelet functions are required. The reliability of the proposed method is demonstrated by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes

Wavelet-Based Evolutionary Spectra Estimation

Numerical Example

Conclusions