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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 391815, 12 pages
Research Article

An Extended Time Series Algorithm for Modal Identification from Nonstationary Ambient Response Data Only

1Experimental Facility Division, National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
2Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan
3Instrumentation Development Division, National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan

Received 10 March 2014; Revised 17 June 2014; Accepted 26 June 2014; Published 17 July 2014

Academic Editor: Jaromir Horacek

Copyright © 2014 Chang-Sheng Lin et al. 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.


Modal Identification is considered from response data of structural systems under nonstationary ambient vibration. The conventional autoregressive moving average (ARMA) algorithm is applicable to perform modal identification, however, only for stationary-process vibration. The ergodicity postulate which has been conventionally employed for stationary processes is no longer valid in the case of nonstationary analysis. The objective of this paper is therefore to develop modal-identification techniques based on the nonstationary time series for linear systems subjected to nonstationary ambient excitation. Nonstationary ARMA model with time-varying parameters is considered because of its capability of resolving general nonstationary problems. The parameters of moving averaging (MA) model in the nonstationary time-series algorithm are treated as functions of time and may be represented by a linear combination of base functions and therefore can be used to solve the identification problem of time-varying parameters. Numerical simulations confirm the validity of the proposed modal-identification method from nonstationary ambient response data.