Adaptive Low-Rank Spectral Sensing for Ultrasonic SHM

Ultrasonic-based Structural Health Monitoring (SHM) systems generate massive datasets that quickly exceed the capabilities of embedded/low power sensing systems. Additionally, in the case of distributed sensing with thousands of sensors, acquiring, storing, and transmitting the signals becomes a serious hurdle for traditional monitoring pipelines. Since SHM data is typically redundant, the problem can be alleviated through data reduction methods that filter irrelevant signal contributions in the sensors before they get transmitted or even recorded. Conventional Singular Value Decomposition (SVD)–based compression methods rely on fixed sub-spaces that fail to adapt to evolving environmental or operational conditions, leading to false alarms or missed detections of damage. To overcome these limitations, this work introduces a low-rank, frequency-domain subspace compression and adaptive update framework based on the Incremental SVD combined with Frequency Stretching applied to Direct Wave Interferometry (DWI) for damage detection and velocity change monitoring. A correlation-triggered mechanism is used to selectively update the baseline subspace only when Environmental and Operational Conditions (EOCs)/damage-induced variations exceed defined thresholds, forming a self-adjusting reference as a background task. This allows hardware-level switching between compressed sensing and full acquisition modes, ensuring efficient data reduction without loss of sensitivity. The proposed low-rank spectral subspace approach successfully distinguishes the damage-induced variations from environmental effects, where the measurement data is approximated with a small number of coefficients within an adaptive, low-dimensional subspace that is first learned from baseline reference data and continuously updated to retain structural information. This compressed form can be obtained directly in hardware through linear projections, enabling in-situ ("on-the-fly") spectral sensing data reduction before transmission or storage. As EOC variations or damage arise, the incremental SVD adaptively updates the baseline subspace representation without requiring full recomputation, ensuring stable performance over long-term monitoring. This framework enables robust SHM systems by integrating effective dimensionality reduction with adaptive performance under realistic environmental conditions.