On an iterative general-order perturbation method for multiple structural damage detection

A general order perturbation method involving multiple perturbation parameters is developed for eigenvalue problems with changes in the stiffness parameters. The perturbation solutions and eigenparameter sensitivities of all orders are derived explicitly. The perturbation method is used iteratively in conjunction with an optimization method to identify the stiffness parameters of structures. The generalized inverse method is used efficiently with the first order perturbations, and the gradient and quasi-Newton methods are used with the higher order perturbations. Numerical simulations on discrete and continuous structural systems demonstrated the robustness of the algorithm in detecting the locations and extent of small to large levels of damage. The effects of measurement noise and reduced measurements on the performance of the algorithm are evaluated.