Modal parameter identification by an iterative approach and by the state space model

Abstract

The problem of estimating a spectral representation of exponentially decaying signals from a set of sampled data is of considerable interest in several applications such as in vibration analysis of mechanical systems. In this paper we present a nonparametric and a parametric method for modal parameter identification of vibrating systems when only output data is available. The nonparametric method uses an iterative adaptive algorithm based in the formation of a two dimensional grid mesh, both in frequency and damping domains. We formulate the identification problem as an optimization problem where the signal energy is obtained from each frequency grid point and damping grid point. The modal parameters are then obtained by minimizing the signal energy from all grid points other than the grid point which contains the modal parameters of the system. The parametric approach uses the state space model and properties of the controllability matrix to obtain the state transition matrix which contains all modal information. We discuss and illustrate the benefits of the proposed algorithms using a numerical and two experimental tests and we conclude that the nonparametric approach is very time consuming when a large number of samples is considered and does not outperform the parametric approach.