The Method of Separation: A Novel Approach for Accurate Estimation of Evolutionary Power Spectra

Abstract

One of the most widely used techniques for the simulation of Gaussian evolutionary random fields is the spectral representation method. Its key quantity is the power spectrum, which characterizes the random field in terms of frequency content and spatial evolution in a mean square sense. For the simulation of a random physical phenomenon, the power spectrum can be directly obtained from corresponding measured samples by means of estimation techniques. The present contribution starts with a short review of established power spectrum estimation techniques, which are based on the short-time Fourier, the harmonic wavelet and the Wigner–Ville transforms, and subsequently introduces a method for the estimation of separable random fields, called the method of separation. The characteristic drawbacks of the established methods, i.e. the limitation of simultaneous space–frequency localization or the appearance of negative spectral density, lead to poor estimation results, if the Fourier transform of the input samples consists of a narrow band of frequencies. The proposed method of separation, combining accurate spectrum resolution in space with an optimum localization in frequency, considerably improves the estimation accuracy in the presence of strong narrow-bandedness, which is illustrated by a practical example from stochastic imperfection modeling in structures.