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Shock and Vibration
Volume 17 (2010), Issue 4-5, Pages 483-490

Prediction of Modal Parameters of Linear Time-Varying Systems

S. Marchesiello, A. Bellino, and L. Garibaldi

Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received 18 June 2010; Accepted 18 June 2010

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many engineering structures, such as cranes, traffic-excited bridges, flexible mechanisms and robotic devices exhibit characteristics that vary with time and are referred to as time-varying or nonstationary. In particular, linear time-varying (LTV) systems have been often dealt with on a case-by-case basis. Many concepts and analytic methods of linear time-invariant (LTI) systems cannot be applied to LTV systems, as for example the conventional definition of modal parameters. In fact, LTV systems violate one of the assumptions of the conventional modal analysis, which is stationarity.

Subspace-based identification methods, proposed in the 1970s, have been attracting much attention due to their affinity to the modern control theory, which is based on the state space model. These methods are now successfully applied to many industrial cases and may be considered reference methods for identifying LTI systems.

In this paper the use of a subspace-based method for identifying LTV systems is discussed and applied to both numerical and experimental systems. More precisely a modified version of the SSI method, referred to here as ST-SSI (Short Time Stochastic Subspace Identification) is introduced as well as a method for predicting time-varying stochastic systems using the angle variation between the subspaces; the latter is able to predict the system parameter in the “near” future.