Restricted autoregressive models for synthetic generation of stationary homogeneous isotropic turbulence. A methodology based on multi-point spectrum fitting

Resumen

An approach to obtain autoregressive models for generating synthetic time series in a single point with a pre-defined von Kármán spectrum is presented. Statistical stationarity is assumed. Under the premise of the proposed approach a theoretical expression for the power spectral density of the autoregressive model is used to obtain the regression coefficients. This approach is proposed to avoid the aliasing effect which may appear when the autoregressive model is obtained to reproduce a given target autocovariance function. A genetic algorithm is used to achieve an optimal autoregressive model. This approach is compared to the approach proposed by Gallego-Castillo et al. where the autocovariance function of the von kármán model is employed as a target. The theoretical autoregressive spectrum obtained using the proposed approach is not affected by aliasing effect, however, it can also present overestimation of the spectrum values at high frequencies in certain circumstances explained in the present work. The proposed approach could facilitate the use of autoregressive models to generate synthetic wind velocity time series when the target statistical information is defined in the frequency domain, as it is the usual case with atmospheric turbulence models.