Use of S-transform and a new multi-taper S-transform for spectral and coherence estimates: With application to characterize and simulate multivariate non-Gaussian wind pressure coefficient

Abstract

Obtaining a long duration time series of wind pressure coefficient from wind tunnel tests may not be economically feasible for some projects, and simulated synthetic time series of wind pressure coefficient can be used. In this study, we propose a new multi-taper S-transform (ST), where the discrete prolate spheroidal sequences are used for tapering, and ST is applied to each tapered time series. The proposed multi-taper ST is simple and efficient. The simulation results indicate that the proposed transform provides an unbiased estimate of the power spectral density (PSD) function with small variability. It is also shown that the use of the temporally-averaged results from ST or the proposed multi-taper ST leads to an unbiased estimate of the coherence function. As an application, we use the obtained PSD and coherence, and marginal probability distribution function (PDF) from the time series of the wind pressure coefficient as the targets to simulate univariate and multivariate processes. For the simulation of the non-Gaussian processes, we use the iterative power and amplitude correction but include a digital filter to consider sample-to-sample variability in the PSD function. We show that the PSD and coherence functions and the marginal PDF from the samples match their targets.