Efficient simulation of fully non-stationary random wind field based on reduced 2D hermite interpolation

Abstract

The spectral representation method (SRM) has been widely used to simulate stationary or non-stationary wind fields for engineering structures. Although several attempts have been made to realize the invoking of Fast Fourier Transform (FFT), the SRM is still very inefficient to simulate the fully non-stationary wind field with a time-varying coherence due to the extremely time-consuming Cholesky decompositions and large memory requirement. In this paper, a reduced 2D Hermite interpolation-enhanced approach is developed to further improve the efficiency of SRM in simulating fully non-stationary wind fields. Central to this approach is the interpolation procedure which requires Cholesky decompositions and storage of cross power spectral density matrix (CEPSD) elements only at interpolation knots. Thus the computational costs of Cholesky decompositions and memory requirement are dramatically decreased. The number of Cholesky decompositions is then fixed with no relation to the segments of frequency and duration of wind samples, which eliminates the Cholesky decomposition as a cause that affects the simulation efficiency. Meanwhile, each element in the decomposed CEPSD matrix is decoupled into products of time- and frequency-dependent functions by the reduced 2D Hermite interpolation, so the FFT can be used to expedite the summation of trigonometric terms. Apart from using FFT, another merit of the proposed approach is that an accelerated FFT algorithm can be incorporated to further improve the simulation efficiency based on the specific decoupled expression of frequency-dependent functions. The parametric analysis shows that the proposed approach is very efficient in comparison with the existing method using proper orthogonal decomposition (POD), and it provides a desired level of simulation accuracy when appropriate interpolation interval is selected. The case study in simulating the fully non-stationary wind field of a long-span cable-stayed bridge demonstrates the effectiveness of the proposed approach with verifications on both evolutionary power spectra and correlation functions.