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Mathematical Problems in Engineering
Volume 2014, Article ID 568637, 15 pages
Research Article

Numerical and Experimental Investigation on Parameter Identification of Time-Varying Dynamical System Using Hilbert Transform and Empirical Mode Decomposition

1Department of Building Engineering, State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
2Department of Civil Engineering, KU Leuven, 3000 Leuven, Belgium

Received 21 November 2013; Accepted 3 February 2014; Published 7 April 2014

Academic Editor: Hua-Peng Chen

Copyright © 2014 Jun Chen and Guanyu Zhao. 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.


This paper proposes an approach to identifying time-varying structural modal parameters using the Hilbert transform and empirical mode decomposition. Definition of instantaneous frequency and instantaneous damping ratio based on Hilbert transform for single-degree-of-freedom (SDOF) system is first introduced. The following is the definition of Hilbert damping spectrum from which the time-varying damping ratio of multi-degree-of-freedom (MDOF) system can be calculated. Identification procedures for both instantaneous frequency and damping ratios based on their definition are then introduced. Applicability of the proposed identification algorithm has been validated through several numerical examples. The instantaneous frequency and damping ratios of SDOF system under free vibration and under sinusoidal and white noise excitation have been identified. The proposed method is also applied to MDOF system with slow and sudden changing structural parameters. The results demonstrate that when the system modal parameters are slowly changing, the instantaneous frequency could be easily and well identified with satisfied accuracy for all cases. However, the instantaneous damping ratio could be extracted only when the system is lightly damped. The damping results are better for free vibration situation than for the forced vibration cases. It is also shown that the suggested method can easily track the abrupt change of system modal parameter under free vibration. The proposed method is then applied to a 12-story short-lag shear wall structure model tested on a shaking table. The instantaneous dynamic properties of the structure were identified and were then introduced as known parameters into a finite element model. Comparisons with the numerical results using constant structural parameters demonstrate that the calculated structural responses using the identified time-varying parameters are much closer to the experimental results.