Damage Detection by the Topology Design Formulation Using Modal Parameters

The feasibility of using the topology design method for structural damage identification was investigated. For efficient damage identification in a structure, we used not only resonances but also anti-resonances as the damage identifying modal parameters and set up a formulation suitable for damage identification. The use of anti-resonances as well as resonances made it possible to identify damage location more effectively because changes in mode shapes due to any damage can be indirectly represented by the changes in anti-resonances. Point-frequency response functions were used to facilitate the extraction of the anti-resonances of a damaged structure. A finite element model of an undamaged structure was assumed to be given. Since considerably many resonances and antiresonances were used for damage identification, they were stated as constraint equations in the present formulation. An explicit penalty function designed to suppress intermediate design variables was used as the objective function because it may be otherwise difficult to obtain clear black-andwhite images at the end of the identification process. When damage extent is not severe, it may be difficult to identify the damage location only with a single-stage application of the present topology optimization-based method. To overcome this difficulty, a multi-stage damage location identification scheme, which reduces the number of candidate damaged elements over several topology optimization stages, was proposed. With the multi-stage technique, relatively small-sized damages were identified accurately as compared with a single-stage application. Through numerical examples, the identification performance improvement by the additional consideration of anti-resonances was demonstrated and the effectiveness of the multi-stage identification technique was also confirmed.