Physics-Informed Filtering for Ultrasonic Guided Wave Structural Health Monitoring

This paper presents a methodology for physics-informed filtering, applied to ultrasonic guided waves. The physics-informed filters are derived by integrating physicsbased constraints into an optimization framework, where the cost function comprises of two components: a reconstruction error term and a regularization term. The reconstruction error term ensures the filtered data closely aligns with the original measurements while the regularization term enforces physical laws represented by a linear operator. We derive a general closed-form solution for these filters and then apply them with the two-dimensional Helmholtz equation. We apply these filters, using various parameters, to ultrasonic guided wave data collected by a laser Doppler vibrometer. We demonstrate the ability to characterize damage regions with thickness losses from the filtered data.