A system theory approach to multi-input multi-output modal parameters identification methods

In this paper, a new theory of multi-input multi-output (MIMO) modal parameters identification technique is developed from the view of system theory. In the first part of the paper, the necessity of the MIMO identification is introduced from controllability and observability theory. Then, by linear transformation of system state equations, a mathematical model which describes the relation between a vibration system's MIMO, is given; when the model parameters are estimated from the measurement of the vibration system's input and output, the modal parameters can be identified by means of reconstructing the system state equations. Formulae on the identification are also presented in the paper. This theory can serve as a unifying approach, as many well known identifying methods, such as the direct parameter model, polyreference, Ibrahim time domain method and Eigensystem realisation algorithm can be derived as special forms. These are presented in the last part of the paper, and the relationship among all these methods are shown.