Error Analysis of Multivariate Wind Field Simulated by Interpolation-Enhanced Spectral Representation Method

Abstract

An interpolation-based technique can effectively reduce the computational demand involved in a traditional simulation of the multivariate wind field utilizing the spectral representation method (SRM). However, errors are introduced by interpolation and are propagated to simulated wind samples. This influences the statistics of the simulated samples, which may exhibit a departure from the target. In order to properly reduce these errors, closed-form expressions of the statistical errors introduced by interpolation are derived, including the apparent wave effect of wind. The closed-form solutions are verified by a numerical example. It is shown that the interpolation brings no additional error to the mean value of the simulated wind velocity, but the statistical errors in the cross power spectral density (CPSD) function depend on the interpolation of the decomposed CPSD matrix. Through a parametric analysis, the influence of factors related to the interpolation steps, involving interpolation functions and interpolation intervals, on the statistical errors are further investigated numerically. The results show that the Hermite interpolation is preferable, because it causes smaller statistical errors in the multivariate wind field. Reducing the interpolation interval may decrease statistical errors quickly when the interpolation intervals are rather large, as used in engineering applications.