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This work discusses an optimization framework to embed dictionary learning frameworks with the wave equation as a strategy for incorporating prior scientific knowledge into a machine learning algorithm. We modify dictionary learning to study ultrasonic guided wave-based defect detection for non-destructive structural health monitoring systems. Specifically, this work involves altering the popular-SVD algorithm for dictionary learning by enforcing prior knowledge about the ultrasonic guided wave problem through a physics-based regularization derived from the wave equation. We confer it the name “wave-informed K-SVD.” Training dictionary on data simulated from a fixed string added with noise using both K-SVD and wave-informed K-SVD, we show an improved physical consistency of columns of dictionary matrix with the known modal behavior of different one-dimensional wave simulations is observed.
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Wave Physics-Informed Matrix Factorizations
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc.), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it nearly satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality. Through this line of work we establish theoretical connections between wave-informed learning and filtering theory in signal processing. We further demonstrate the application of this work on modal analysis problems commonly arising in structural diagnostics and prognostics.
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- Award ID(s):
- 1747783
- PAR ID:
- 10488296
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Signal Processing
- Volume:
- 72
- ISSN:
- 1053-587X
- Page Range / eLocation ID:
- 535 to 548
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TSP.2023.3348948
