Semi‐supervised structural linear/nonlinear damage detection and characterization using sparse identification

As a useful class of techniques for structural health monitoring, vibration-based structural damage detection has been intensively studied in civil engineering community for decades. Structural damage is commonly assumed to be linear stiffness reduction, which cannot represent nonlinear damage from the real world, such as plastic deformation, cracks, and joint looseness. Novelty detection-based and supervised classification-based methods have been used for nonlinear damage detection, but direct physical interpretation of the damage cannot be accessed. To address this limitation, the major scope of this work is to detect and physically characterize linear/nonlinear-type structural damage in a semi-supervised way. The proposed method first uses previously proposed sparse identification to establish a baseline (undamaged) model. Then, damage is considered as a variation of restoring forces in the structural system. It can be further treated as a pseudoforce along with the external disturbance force applied to the structural system. Thus, the damaged system is transformed into an equivalent linear system and nonlinear restoring force. By comparing the corresponding outputs from the prediction of baseline model and newly measured data, a variation of mass-normalized restoring (pseudo) force is identified, which can be used for further damage characterization. An illustrative example and three experimental tests are introduced in this work to verify the effectiveness of the proposed method.