Two major challenges associated with a vibration-based damage detection method using changes in natural frequencies are addressed: accurate modeling of structures and the development of a robust inverse algorithm to detect damage, which are defined as the forward and inverse problems, respectively. To resolve the forward problem, new physics-based finite element modeling techniques are developed for fillets in thin-walled beams and for bolted joints, so that complex structures can be accurately modeled with a reasonable model size. To resolve the inverse problem, a logistic function transformation is introduced to convert the constrained optimization problem to an unconstrained one, and a robust iterative algorithm using the Levenberg-Marquardt method is developed to accurately detect the locations and extent of damage. The new methodology can ensure global convergence of the iterative algorithm in solving under-determined system equations and deal with damage detection problems with relatively large modeling error and measurement noise. It is applied to various engineering structures including lightning masts, a space frame structure and one of its components, and a pipeline. The exact locations and extent of damage can be detected in the numerical simulation, and the locations and extent of damage can be successfully detected in experimental damage detection.
Structural damage analysis of explosive testing experimental bay using HEXDAM Modelling software
