Direct estimation of evolutionary power spectral density of nonstationary winds: A unified formulation

Abstract

Estimating the evolutionary power spectral density (EPSD) of non-stationary winds (e.g., tropical storms and downbursts) is necessary to predict the response of structures under such extreme winds. Following the review of the existing direct estimation methods of EPSD, this paper offers a two-step unified formulation, i.e., raw estimation and associated error reduction. The raw estimation is expressed in terms of a time-frequency transform with a general kernel function. It is shown that if the kernel function is described by a time-frequency analysis tool such as the short-time Fourier transform, the wavelet transform, and the S-transform, the generalized raw EPSD estimation becomes a particular case of the existing methods. The unified estimation method presented here can be viewed as a filter bank with adjustable time and frequency resolution. The analysis of error in the raw estimation is carried out on the bias and random errors accounting for the approximation in both the time and frequency domains. Various techniques for reducing such errors are then summarized and recast in the unified formulation, including series expansion, short-time window smoothing, and multi-tapering. Based on the unified perspective, a discussion and some prospects of EPSD estimating are provided.