An efficient simulation method for vertically distributed stochastic wind velocity field based on approximate piecewise wind spectrum

Abstract

Stochastic wind velocity simulation based on the spectral representation method often requires considerable computation time due to the repetitive Cholesky decomposition of the power spectral density matrix. In this paper, a modified model is proposed for the Davenport coherence function and is used to improve the efficiency of the Cholesky decomposition based on an approximation technique where the target wind spectrum is reformulated as a piecewise function. Based on this new formulation where the major piece of the spectrum is regarded as a product of separate functions of frequency and height, vertically distributed wind velocity field can be efficiently generated through a closed-form expression of the Cholesky decomposition. When the target spectrum is not separable the Cholesky decomposition can still be avoided based on the proposed coherence function. In other words, the proposed simulation method does not require either the direct Cholesky decomposition or the eigenvector decomposition. Numerical investigations show that, more than 60% of computation time can be saved for the decomposition of the power spectral density matrix involved in the simulation of two hundred wind velocity processes and the entire simulation procedure is 3 times faster than the ordinary spectral representation method for the simulation of two hundred processes.