Modal analysis of random vibrating systems from multi-output data

A method for modal parameter identification of a random vibrating system from multi-output data only is presented. The method uses a multivariate state-space model and exploits shift properties of a block-Hankel matrix formed from the covariance matrices of output data. Since the number of modes excited is unknown, the model order is not known. Two methods for model order estimation are presented. They are based on tests that have a chi-square distribution. To illustrate the procedure for identifying the order, the parameters and spectrum of a noisy process, from output data only, and a numerical and an experimental mechanical system are studied.