A novel sensitivity-based method for damage detection of structures under unknown periodic excitations

This paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response. The method is capable of identifying the damage parameters without finding the input excitations. We first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition. Roughly speaking, the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering this novel geometrical viewpoint, an equation called kernel parallelization equation (KPE) is derived for damage detection under unknown periodic excitations and a sensitivity-based algorithm for solving KPE is proposed accordingly. The method is evaluated via three case studies under periodic excitations, which confirm the efficiency of the proposed method.