Simulation of Wide Sense Stationary Random Time Series With Specified Spectral Densities

Abstract

In this paper, an effective approach to the simulation of widesense stationary random timeseries, defined by its power spectral density (PSD) is presented. This approach is based on approximating the sample paths of target random process by finite series of sample functions of random processes, obtained as the outputs of suitably chosen set of secondorder linear filters to independent limited band Gaussian white noise inputs. Thus, the Gaussian distribution of simulated timeseries is obtained without applying the central limit theorem. Also, the Fourier spectra of the simulated sample paths are not discrete functions, as in the case of the multisine random timeseries representation used by most classical simulation methods. The method can be applied to any analytical or nonparametric representation of the specified PSD. The proposed approach is applied to simulation of road input sample paths, compatible with PSDs described by analytical forms that can or cannot be derived by linear shape filters. The method is validated by comparison of spectral response of a halfcar model to the input induced by a measured road profile with that obtained for the simulated road input. This input is derived from the nonparametric PSD, determined by thirdoctave filtering of the measured profile. The advantages of the proposed approach are highlighted by its comparison with a conventional method, based on the representation of simulated road input by a sum of harmonics with random phases.