Model-based damage detection using constraint forces at measurements

The number of measurement nodes of a finite element model for damage detection is fewer than the model order. Thus, measurement data should be expanded or the system order should be reduced for evaluating the structural performance. A local damage in the model leads to stiffness deterioration at the corresponding element and variations in the responses of the adjacent elements, including the damaged elements. The response difference between two intact and damage-expected states can be approximately predicted by the constraint forces acting at the measurement nodes. The damage at the element represents the abrupt change in the constraint forces. This work proposes static and dynamic methods to detect damages based on the constraint forces acting on the measurement nodes. It is shown that the damage can be explicitly detected by the constraint forces that satisfy each constraint or measurements separating the given constraints rather than the entire constraint set. The validity of the proposed method is illustrated in two numerical applications of static and dynamic systems, and the effect of external noise is also investigated.