Sparsity-based approaches for damage detection in plates

The data deluge in Structural Health Monitoring (SHM) and the need for automated online damage detection systems necessitates a move away from traditional model-based approaches. To that end, we propose sparsity-based algorithms for damage detection in plates. Instead of high-fidelity models, our proposed algorithms use dictionaries, consisting of response signals acquired directly from the system of interest, as the key feature to both detect and localize damages. We address the damage detection problem both when the damage is located on or off a grid of possible damage coordinates defined by the dictionary. This gives rise to two classes of problems, namely, on the grid and off the grid problems. In our sparsity-based on the grid damage detection (SDD-ON) platform, we solve a LASSO regression problem, where, the unknown vector is a pointer for existence of damage at the various locations defined on the grid used for dictionary construction. In our proposed off the grid damage detection (SDD-OFF) platform, we use a penalized regression algorithm to extend the dictionary of measured damage signals to points off-the-grid by linear interpolation. We evaluate the performance of both SDD frameworks, in detecting damages on plates, using finite element simulations as well as laboratory experiments involving a pitch-catch setup using a single actuator-sensor pair. Our results suggest that the proposed algorithms perform damage detection in plates efficiently. We obtain area under receiver operating characteristic (ROC) curves of 0.997 and 0.8314 for SDD-ON and SDD-OFF, respectively.