Vibrational NDT with Under-sampled Data through Physics-informed Neural Networks

The vibrational response of solid materials and structural components is substantially governed by their mechanical and geometrical properties. Low-frequency vibrations and modal frequencies are sensitive to global geometrical deviations, while high-frequency vibrations and traveling waves interact with small defects and localized irregularities that are comparable to the wavelength. As such, vibrational techniques have shown great performance in multiscale non-destructive testing (NDT) of products. Typically, the test piece is subjected to a vibrational excitation (e.g. using a surface mounted transducer) and its response is measured at a set of measurement points on the surface, for further evaluation and signal processing. Extracting quantitative information about material properties and further characterization of internal defects, requires vibrational response of the surface to be sampled at a sufficiently high spatial frequency according to the Nyquist theorem. Advent of advanced measurement techniques e.g. scanning laser Doppler vibrometry has enabled capturing the high-resolution vibrational response of the surface over a fine measurement grid. However, long measurement time and high storage requirements are the limiting factors to be tackled. Physics-informed neural networks (PINNs) have been recently shown to be a great choice for efficient inversion of physical problems and discovery of hidden physics from limited labeled data. Hence, we propose the application of PINNs in quantitative vibrational NDT with spatial under-sampling. To this end, PINN is formulated based on the elastic wave equation in solid materials and is trained using the vibrational response of an aluminum plate on the top surface, obtained from finite element simulation and manipulated with virtual noise. Performance of PINNs in simultaneously (i) inferring the elastic constants, (ii) high- resolution reconstruction of surface’s response and (iii) reconstruction of internal vibration fields, from under-sampled surface response at different excitation frequencies is demonstrated. Furthermore, the potential of technique for reconstruction of internal defects is investigated.