Deep reconstruction of sparse elastic wavefield and graph-based damage detection for accelerated health monitoring of PZT ceramics

Structural health monitoring (SHM) of piezoelectric ceramics, particularly Lead Zirconate Titanate (PZT) substrates, requires accurate acquisition of elastic wave propagation to detect and localize damage. However, full-field wave acquisition is experimentally intensive and time-consuming. This study presents a sparse nonlinear reconstruction framework based on Coulomb coupling measurements that reduces acquisition complexity while maintaining diagnostic accuracy. Spatiotemporal wavefields are first acquired at a coarser temporal resolution from both healthy and damaged PZT specimens. For the healthy condition, the reduced data are used to compute a proper orthogonal decomposition (POD) basis, and QR pivoting identifies optimal sensing locations. The corresponding sparse measurements are then used to train a shallow decoder network (Q-SDN) for wavefield reconstruction. Rather than training a separate decoder for the damaged condition, transfer learning adapts the Q-SDN model to the damaged dataset. This refines the learned representation to accommodate damage-induced variations while leveraging knowledge from the healthy data. Transfer learning allows the model to retain prior knowledge and adapt to new conditions without full retraining. However, the QR-selected sensor locations optimal for the healthy state may not be ideal for capturing wave propagation in the damaged case. Despite this, maintaining the same sensor layout avoids experimental reconfiguration. These locations effectively act as random placements in the damaged state, leading to the QR-Random-SDN (Q-R-SDN) framework. The proposed method avoids reconfiguration and separate model training for each state. Reconstruction performance is compared with a linear QR/POD baseline. The Q-R-SDN shows improved accuracy in both healthy and damaged scenarios. The reconstructed wavefields are further analyzed using an unsupervised Graph Deviation Network (GDN) trained only on healthy data. Damage localization is performed using forecast-based deviation scores, followed by contrast enhancement and morphological filtering.