Three-Variate Nonstationary Probabilistic Wind Field Modeling with Time-Varying Spatial Coherence via the NUFFT-Enhanced Stochastic Wave–Based Spectral Representation Method

Abstract

To conduct accurate reliability analysis of complex wind-sensitive structures, it is crucial to model three-variate (3V) nonstationary probabilistic turbulences considering two-point time-varying spatial coherence and single-point turbulence correlation. To this end, the nonuniform fast Fourier transform–enhanced (NUFFT-enhanced) stochastic wave–based spectral representation method (N-SWSRM) is upgraded in this study. A novel evolutionary wavenumber–frequency joint spectrum (EWFJS) matrix integrating the time-varying spatial coherence and turbulence coherence function is initially established. Three-dimensional proper orthogonal decomposition (3D-POD) is then introduced to facilitate the dimensionality reduction and decoupling of high-dimensional matrices, enabling the utilization of NUFFT in superposition of trigonometric series. The fusion of random functions and number-theoretic method (NTM) enables the proposed method to generate samples with explicit probabilistic information. Modeling of homogeneous and nonhomogeneous wind fields is employed as two numerical examples to analyze the method’s accuracy and computational efficiency. Results demonstrate that the established 3V turbulence exhibits a remarkable agreement with the targets in multiple statistical metrics, such as auto evolutionary power spectral density, thereby validating its accuracy. The time consumption primarily depends on the number of time segments of the modeling sample. More importantly, the time of less than 20 s to generate one single 3V sample indicates the high efficiency. In addition, the modeling samples can be used in the probability density evolution method (PDEM) from the probabilistic perspective.