Structural damage localization using a modified sensitivity analysis

The scenario-based damage detection approaches mainly use the sensitivity equation which is basically derived based on the infinitesimal variation assumption. In this paper, a modified sensitivity equation is derived and implemented through a scenario-based scheme. Also, a new expression for the modal assurance criterion of the modified sensitivity analysis is presented. The objective is to localize damage using only natural frequencies in a traditional pseudo-inverse sense and a new modal assurance criterion. Compared to classic sensitivity approaches, the new one is based on structural modification theory and is applicable both to small- and large-scale stiffness changes. The efficiency of the new
sensitivity equation and the modal assurance indicator is evaluated and compared with the traditional sensitivity equations through an experimental case study of a T-shaped wooden beam with a saw cut of various lengths at the bottom. The vibration responses of the specimen are measured in the laboratory conditions and used as primary data in the operational modal analysis to calculate the frequency changes after damage. A finite element model of the specimen is built and updated, and the damage scenarios are induced by changing the stiffness and cross-section area reduction. The effect of the damage on the modal parameters, as well as the possibility of damage quantification is discussed. Also, the sensitivity
of the proposed approach to the damage severity and the required number of mode shapes is investigated. The results indicate that the damage detection approach based modal assurance criterion performs best in finding damage locations in symmetric damage scenario conditions.