Application Of The Time Series Analysis To The Time Varying Modal Parameter Identification Of Vibrating Systems

Modal parameter identification of vibrating systems is one of the most important subjects in structural dynamics. Modal identification has significant roles at many aspects such as fault diagnosis, vibration and noise reduction, structural design, and state monitoring. The traditional identification methods have many limitations because that both the excitations and responses of systems are required to analyze the modal parameters. With the development of the identification technique, the methods, which only use the response signals of systems for identifying the modal parameters, are increasingly paid attention to and used widely. Among them, time series analysis is a kind of fairly efficient method, in which the modal parameters of structures are obtained by modeling parameter models of the response signals to be analyzed.First, the model type judgment methods of time series models, including AR, MA and ARMA models, are investigated as well as the criteria of order determination. Besides, various kinds of estimation methods of the AR and ARMA models and their features are introduced in detail. Corresponding simulation examples are analyzed. Good agreement between the computed and the theoretical values fully illustrates the validity of the introduced methods.Second, the application of the time series methods to the identificationof the time invariant modal parameters of vibrating systems is studied. The single variable ARMA model, the multivariate AR model and the Prony method are used to identify the modal parameters. The satisfied results are obtained through the simulated and practical examples.Finally, based on the identification theory of time invariant modal parameter, two new time varying modal parameter identification methods, i.e., the time varying multivariate AR model method and the time varying multivariate Prony method, are put forward. The new methods can identify the modal parameters of time varying vibrating systems with multi-output effectively. Through identifying the modal parameters of the simulated and practical time varying multiple degree of freedom systems, the identified results are identical to the theoretical ones. The feasibility and validity of the proposed methods are proved. The presented methods provide an effective analysis tool for the time varying parameters identification of multi-degree of freedom systems.