Time-frequency interpolation enhanced SWSRM for efficient simulation of time-varying coherent nonstationary nonhomogeneous wind fields

The precise and efficient simulation of nonstationary nonhomogeneous wind fields with intricate spatio-temporal characteristics is the premise of wind-resistant analysis and design for large-scale wind turbine structures. However, when generating nonstationary nonhomogeneous wind fields in two spatial dimensions with time-varying coherence function (TVCF) based on the stochastic wave spectral representation method (SWSRM), significant computational challenges persist. The construction, decomposition, and multifold summation operations of the high-dimensional evolutionary wavenumber-frequency joint spectrum (EWFJS) matrix, characterized by the coupling of frequency, time, wavenumber, and height, demand excessive memory allocation and exhibit inefficient computational performance. In this work, an innovative time-frequency interpolation (TFI) enhanced SWSRM is proposed. This methodology commences by constructing the EWFJS matrix exclusively at the well designed non-uniform time-frequency interpolation knots. Simultaneously, the hierarchical decomposition process, that is the proper orthogonal decomposition-based multivariate decoupling method (POD-MDM), is proposed to systematically decouple multiple variables in the high-dimensional EWFJS matrix. Subsequently, the tailored TFI scheme is developed to generate the surrogate model which accurately represents the EWFJS matrix. This approach not only diminishes computational memory usage through dimensionality reduction of EWFJS but also facilitates Fast Fourier Transform (FFT) implementation across time, frequency and wavenumber dimensions, thereby leading to substantial improvements in computational performance. Numerical examples in simulating nonstationary nonhomogeneous wind fields with TVCF of a wind turbine validate the accuracy and computational efficiency, given the comparison of the spectrum and computational time between the traditional SWSRM and the proposed TFI enhanced SWSRM.