Unsupervised Wave Physics-Informed Representation Learning for Guided Wavefield Reconstruction

Ultrasonic guided waves enable us to monitor large regions of a structure at one time. Characterizing damage through reflection-based and tomography-based analysis or by extracting information from wavefields measured across the structure is a complex dynamic-data driven applications system (DDDAS). As part of the measurement system, guided waves are often measured with in situ piezoelectric sensors or wavefield imaging systems, such as a scanning laser doppler vibrometer. Adding sensors onto a structure is costly in terms of components, wiring, and processing and adds to the complexity of the DDDAS while sampling points with a laser doppler vibrometer requires substantial time since each spatial location is often averaged to minimize perturbations introduced by dynamic data. To reduce this burden, several approaches have been proposed to reconstruct full wavefields from a small amount of data. Many of these techniques are based on compressive sensing theory, which assumes the data is sparse in some domain. Among the existing methods, sparse wavenumber analysis achieves excellent reconstruction accuracy with a small amount of data (often 50 to 100 measurements) but assumes a simple geometry (e.g., a large plate) and assumes knowledge of the transmitter location. This is insufficient in many practical scenarios since most structures have many sources of reflection. Many other compressive sensing methods reconstruct wavefields from Fourier bases. These methods are geometry agnostic but require much more data (often more than 1000 measurements). This paper demonstrates a new DDDAS approach based on unsupervised wave physics-informed representation learning. Our method enables learning full wavefield representations of guided wave datasets. Unlike most compressive sensing methodologies that utilize sparsity in some domain, the approach we developed in our lab is based on injecting wave physics into a low rank minimization algorithm. Unlike many other learning algorithms, including deep learning methods, our approach has global convergence guarantees and the low rank minimizer enables us to predict wavefield behavior in unmeasured regions of the structure. The algorithm can also enforce the wave equation across space, time, or both dimensions simultaneously. Injecting physics also provides the algorithm tolerance to data perturbations. We demonstrate the performance of our algorithm with experimental wavefield data from a 1m by 1m region of an aluminum plate with a half-thickness notch in its center.