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Mathematical Problems in Engineering
Volume 2014, Article ID 707969, 14 pages
Research Article

Damage Detection for Continuous Bridge Based on Static-Dynamic Condensation and Extended Kalman Filtering

Beijing Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China

Received 2 January 2014; Revised 3 April 2014; Accepted 7 April 2014; Published 30 April 2014

Academic Editor: Ying Lei

Copyright © 2014 Haoxiang He 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.


As an effective and classical method about physical parameter identification, extended Kalman filtering (EKF) algorithm is widely used in structural damage identification, but the equations and solutions for the structure with bending deformation are not established based on EKF. The degrees of freedom about rotation can be eliminated by the static condensation method, and the dynamic condensation method considering Rayleigh damping is proposed in order to establish the equivalent and simplified modal based on complex finite element model such as continuous girder bridge. According to the requirement of bridge inspection and health monitoring, the online and convenient damage detection method based on EKF is presented. The impact excitation can be generated only on one location by one hammer actuator, and the signal in free vibration is analyzed. The deficiency that the complex excitation information is needed based on the traditional method is overcome. As a numerical example, a three-span continuous girder bridge is simulated, and the corresponding stiffness, the damage location and degree, and the damping parameter are identified accurately. It is verified that the method is suitable for the dynamic signal with high noise-signal ratio; the convergence speed is fast and this method is feasible for application.