State-space identification of vibrating systems from multi-output measurements

A 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 vibration system. The matrix block Hankel stochastic realisation method is used to determine the system matrices and modal parameters. The problem of the minimal representation is discussed and a new test for determining the number of states in the model is derived. This test is based in the estimation of the coefficients in a particular column of the observability matrix and has a chi(2) distribution. A numerical example illustrates the procedure for identifying the order, parameters and spectrum of a noisy process. (C) 1998 Academic Press.