The generalized flexibility matrix method for structural damage detection with incomplete mode shape data

Achieving complete data of measured mode shapes is costly during the process of structural dynamic test. This results in a challenge for the damage detection. This paper concentrates on structural damage detection problem with incomplete mode shape data. An efficient method to deal with this problem is proposed. The generalized flexibility matrix (GFM) is employed. By introducing a few new variables and partitioning the involved matrices, a nonnegative linear least square model is derived. Most of the variables in the model are the damage extents of structural elements. Our method does not involve mode shape expansion or reduction technique. Three numerical examples show that the performance of the proposed method is superior to that of the GFM method combining with mode shape expansion, it is almost the same as that of the GFM approach with complete mode shapes data.