A tutorial on reproducing a predefined autocovariance function through AR models: application to stationary homogeneous isotropic turbulence

• DOI: 10.1007/s00477-021-02156-0
• Publication Date: 2021-12-24T05:02:26Z
• Authors: Cristobal Gallego...; Alvaro Cuerva-Tejero; Mohanad Elagamy; Oscar Lopez-Garcia; Sergio Avila-Sanchez
• Keywords: Autocovariance; Stationary process; Homogeneous isotropic turbulence

Abstract Sequential methods for synthetic realisation of random processes have a number advantages compared with spectral methods. In this article, the determination optimal autoregressive (AR) models reproducing predefined target autocovariance function process is addressed. To end, novel formulation problem developed. This linear and generalises well-known Yule-Walker (Y-W) equations recent approach based on restricted AR (Krenk-Møller approach, K-M). Two main features characterise introduced formulation: (i) flexibility in choice employed model determination, (ii) definition scheme. Both were exploited by genetic algorithm to obtain particular case generation homogeneous stationary isotropic turbulence time series. The obtained improved those Y-W K-M approaches same parsimony terms global fitting function. Implications reproduced spectra are also discussed. multivariate presented, highlighting causes behind some computational bottlenecks.