A local damage detection approach based on restoring force method

Abstract

Chain-like systems have been studied by many researchers for their simple structure and wide range of application. Previously, the damage in a chain-like system was detected by the reduction of the mass-normalized stiffness coefficient for certain elements as reported by Nayeri et al. (2008 [16]). However, some shortcomings exist in that approach and for overcoming them; an improved approach is derived and presented in this paper. In our improved approach, the mass normalized stiffness coefficients under two states (baseline state and potentially damaged state) are first estimated by a least square method, then these mass-stiffness coupled coefficients are decoupled to derive stiffness and mass relative change ratios for individual elements. These ratios are assembled in a vector, which is defined as damage indication vector (DIV). Each component in DIV is normalized individually to one to get multiple solutions. These solutions are averaged for estimating relative system changes, while abnormal solutions are discarded. The work of judging a solution as normal or abnormal is done by a cluster analysis algorithm. The most intriguing merit of this improved approach is that the relative stiffness and mass changes, which are coupled in the previous approach, can be separately identified. By this approach, the damage (single or multiple) extent and location can be correctly detected under operational conditions, meanwhile the proposed damage index has a clear physical meaning and is directly related to the stiffness reduction of corresponding structural elements. For illustrating the effectiveness and robustness of the improved approach, numerical simulation of a four floor building was carried out and experimental data from a structure tested at the Los Alamos National Laboratory was employed. Identified structural changes with both simulation and experimental data properly indicated the location and extent of actual structural damage, which validated the proposed approach.