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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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K-SVD based Periodicity Dictionary Learning
It has recently been shown that periodicity in discrete-time data can be analyzed using Ramanujan sums and associated dictionaries. This paper explores the role of dictionary learning methods in the context of period estimation and periodic signal representation using dictionaries. It is shown that a wellknown dictionary learning algorithm, namely K-SVD, is able to learn Ramanujan and Farey periodicity dictionaries from the noisy, sparse coefficient data generated from them without imposing any periodicity structure in the learning stage. This similarity between the learned dictionary and the underlying original periodicity dictionary reaffirms the power of the KSVD in predicting the right dictionary from data without explicit application-specific constraints. The paper also examines how the choice of different parameter values affect the similarity of the learned dictionary to the underlying dictionary. Two versions of K-SVD along with different initializations are analyzed for their effect on representation and denoising error for the data.
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- Award ID(s):
- 1712633
- PAR ID:
- 10275652
- Date Published:
- Journal Name:
- Proc. Asil. Conf. Sig., Sys., and Comp
- Page Range / eLocation ID:
- 1333 to 1337
- 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
- Conference Paper:
- https://doi.org/10.1109/IEEECONF51394.2020.9443567
