Synthesis of multivariate random vibration systems: A two-stage least squares AR-MA model approach

A parametric time series model procedure for the synthesis of multivariate stationary time series random vibrations is shown. The vibrations are assumed to be the outputs of a regularly sampled, random noise excited, differential equation model of a vivration system. The procedure is a two-stage least squares method for realizing a multivariate disrcrete time mixed autoregressive-moving average (AR-MA) model from a given stationary process matrix covariance function. The synthesis procedure and the problem of the minimal representation of multivariate output systems and the overparameterization of AR-MA models are discussed and illustrated.