Application of eigenvalue perturbation theory for detecting small structural damage using dynamic responses

Current methods for structural damage identification, such as genetic algorithms and artificial neural networks, are often implemented based on a few measured data and a large number of simulation data. The tremendous time-consuming computational work needed for calculating the response data to establish the dynamic model of damaged structures is an important issue for dynamic damage detection. In this paper through using the advanced modeling method of element stiffness matrix modification, the order of the global stiffness matrix can be kept invariable in establishing the model of intact and damaged structures. Then, eigenvalue perturbation theory is introduced to obtain the eigenvalues and eigenvectors of the damaged structure for reducing the computation load. Two artificial neural networks (ANN) are trained based on the response data simulated using finite element method (FEM) and perturbation theory enhanced finite element method (PFEM), respectively. The damage identification capability of these two ANN's are compared. Results show that the PFEM using the first order eigenvalue perturbation theory provides enough precision for detecting small structural damage and the computational requirement is greatly reduced. Typically, the eigensolution computational time for obtaining the train sample data using PFEM is only 1% of that using the traditional FEM.