MODAL PARAMETER ESTIMATION USING THE STATE SPACE METHOD

Abstract

In modal parameter identification, the damped complex exponential response methods extract modal parameters using free decay responses. Although there are several different complex exponential methods, they are based on the Prony method. The Prony method has some limitations, such as poor robustness to noise, computational burden and the unstable nature of root solver routines. Recent developments in signal processing indicate that model-based eigendecomposition methods are very viable alternatives. In this paper one of the model-based eigendecomposition methods, the state space method, is first introduced. The state space method makes use of the singular value decomposition (SVD) to form a well-conditioned data matrix and obtains the modal parameters through the eigendecomposition of the data matrix. The paper then focuses on an analytical derivation of the SVD of the data matrix in order to present a theoretical base for the method. A simulation is used to illustrate important properties of the SVD and performance of the state space method. Finally, more applications of the SVD of the data matrix are explored and the proposed applications are demonstrated by modal testing example. It is shown that the state space method provides an elegant and robust tool for extracting modal parameters. The SVD of the data matrix offers significant information about the system order and mode participation of a free response.