Accurate estimation of evolutionary power spectra for strongly narrow-band random fields

One of the most widely used techniques for the simulation of non-homogeneous 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. The paper at hand proposes a method for the estimation of separable power spectra from a series of samples, which combines accurate spectrum resolution in space with an optimum localization in frequency. For non-separable power spectra, it can be complemented by a joint strategy, which is based on the partitioning of the space-frequency domain into several sub-spectra that have to be separable only within themselves. Characteristics and accuracy of the proposed method are demonstrated for analytical benchmark spectra, whose estimates are compared to corresponding results of established techniques based on the short-time Fourier, the harmonic wavelet and the Wigner–Ville transforms. It is then shown by a practical example from stochastic imperfection modeling in structures that in the presence of strong narrow-bandedness in frequency, the proposed method for separable random fields leads to a considerable improvement of estimation results in comparison to the established techniques.