Abstract
We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of partial differential equations to the loss function. Our PINNs is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a trainable hyperparameter, which is optimized to achieve the best performance of the network. The adaptive activation function changes dynamically, involved in the optimization process. The usage of the adaptive activation function significantly improves the convergence, evidently observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.
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Acknowledgements
The work is supported by DARPA-AIRA Grant HR00111990025. This research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University. KS would like to acknowledge Dr. Helen Kershaw from CCV, Brown University for providing the help and feedback at various stages of the research especially for problems concerning to the computation.
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Appendices
Appendix A: Python Code Snippet of PCA Process
Appendix B: PCA Filtered Data Acquired at \(0^{\circ }\) and \(90^{\circ }\)
Filtering of wavefield data acquired at \(0^{\circ }\), using principle component analysis (PCA). PCA requires only the first 15 components to construct the original data by zeroing out the insignificant components
Filtering of the wavefield data acquired at \(90^{\circ }\), using principle component analysis (PCA). PCA requires only first 20 components to construct the original data by zeroing out the insignificant components
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Shukla, K., Di Leoni, P.C., Blackshire, J. et al. Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks. J Nondestruct Eval 39, 61 (2020). https://doi.org/10.1007/s10921-020-00705-1
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DOI: https://doi.org/10.1007/s10921-020-00705-1