A STOCHASTIC REALISATION ALGORITHM WITH APPLICATION TO MODAL PARAMETER ESTIMATION

This paper presents procedures that allow us to estimate the frequencies and damping coefficients of a vibrating system in time domain, from multioutput data only. The system is excited by a random force and a stochastic state space model is considered. Two algorithms are used to determine the transition matrix of the system which contains all modal information. The first algorithm uses a forward-innovation representation, and the transition matrix is connected to the controllability matrix of the system. The second algorithm uses a backward-innovation representation and the transition matrix is used to the observability matrix of the system. A numerical example is treated and compare these algorithms.