Abstract
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.
Highlights
In civil engineering, the structures such as buildings and bridges will inevitably be damaged due to varied natural hazards and environmental effect
The damage detection methods mainly include four types: (1) methods based on modal parameters, such as the change of the frequencies, modal shapes, and transfer function, modal strain energy method (MSE), and flexibility matrix method (FM) [2]; (2) methods based on signal processing, such as wavelet analysis, wavelet packet analysis, and empirical mode decomposition (EMD) [3]; (3) methods based on intelligent computing and signal analysis, such as artificial neural network method, statistical pattern recognition, fuzzy theory, and genetic algorithm [2]; (4) methods on physical parameter identification, such as Kalman filter method and the generalized Tikhonov regularization method [4]
The results indicate that the unscented Kalman filter (UKF) can achieve better state estimation and parameter identification than the extended Kalman filtering (EKF)
Summary
The structures such as buildings and bridges will inevitably be damaged due to varied natural hazards and environmental effect. The limited amount of sensors in practice impede the application of MSE or FM It needs numerous hypothetical damage patterns for signal processing and intelligent computing, and these patterns are always simulated in complex finite element analysis. An algorithm based on sequential application of the extended Kalman estimator and least-squares estimation is proposed by Lei et al for the identification of structural parameters and unknown excitations [13,14,15,16]. (2) In addition, in order to realize the parameter identification with part of the output information, rotational response of the bending shear structure needs to be calculated with inverse algorithm, but the calculations are complex and the precision cannot fully meet the requirements. The imposition and acquisition of the vast excitations are effectively avoided, the identification accuracy is high, and the practicality and the convenience are evident
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