Abstract
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.
Highlights
Modelling and identification of linear time-varying (LTV) systems are usually treated by two approaches: the ARMA (Auto Regressive Moving Average) methods [1] and the state-space models, which are those preferred by authors to analyse complex systems
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
The idea of prediction of LTV systems is due to Kameyama [9], who tries to predict the future behaviour of a system looking at the rotation of the subspace generated by the columns of the observability matrix at two different time instants
Summary
Modelling and identification of LTV systems are usually treated by two approaches: the ARMA (Auto Regressive Moving Average) methods [1] and the state-space models, which are those preferred by authors to analyse complex systems. Their popularity is due to the recent increase of interest in subspace-based identification methods for state-space model realizations [2,3]. In [4,5,6] LTV systems are analyzed with a state-space model with time-varying matrices. Marchesiello et al / Prediction of modal parameters of linear time-varying systems
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