Generalized eigenvalue decomposition in time domain modal parameter identification

This paper is intended to point out the relationship among current time domain modal analysis methods by employing the generalized eigenvalue decomposition. Various well-known time domain modal analysis algorithms are reviewed. Ibrahim, Time Domain (ITD), Least Square Complex Exponent (LSCE) and Eigensystem Realization Algorithm (ERA) methods are chosen to do the comparison. Reformulation to these original forms show these three methods can all be attributed to a generalized eigenvalue problem with different matrix pairs. With this general format, we can see that Single-Input Multi-Output (SIMO) methods can easily be extended to Multi-Input Multi-Output (MIMO) case by taking advantage of the generalized Hankel matrix or generalized Toeplitz matrix. Copyright © 2006 by ASME