Efficient simulation of non-stationary non-homogeneous wind field: Fusion of multi-dimensional interpolation and NUFFT

Abstract

The stochastic wave approach is a new realization of the spectral representation method and has been widely used for the simulation of stationary non-homogeneous or non-stationary homogeneous wind fields. However, it inevitably creates many unnecessary simulation points due to the invoking of the Fast Fourier Transform (FFT) and suffers from low efficiency in non-stationary non-homogeneous scenarios due to the incapability to accelerate the summation of trigonometric functions. In this study, an efficient approach is developed for the simulation of non-stationary non-homogeneous wind field. Central to this approach is a multi-dimensional interpolation used to decouple the evolutionary spectra accompanied by the application of non-uniform FFT (NUFFT) to expedite the simulation. A surrogate model that accurately approximates the 3D evolutionary spectrum related to height, frequency, and time is established by the 3D reduced Hermite interpolation, which enables a successful separation of the frequency components. Then, the NUFFT is applied to speed up the summation of trigonometric functions over wavenumbers with a well-designed non-uniformly distributed sampling points, which effectively reduces the segments used in the Fourier transform. Since there is no required mapping between the wavenumbers and the locations of simulation points in NUFFT, a significant number of unnecessary simulation points in the FFT scenario is avoided. Moreover, the wind samples at different locations can be obtained by directly altering the query points of NUFFT, thus the efficiency of the enhanced approach is almost independent of the number of simulation points. The numerical example in simulating the non-stationary non-homogeneous wind field of a long-span cable-stayed bridge demonstrates the efficiency of the developed approach and validates the effectiveness of the simulated wind samples in view of evolutionary spectrum and coherence function.