Detecting and locating damage information from waves reflected off damage is a common practice in non-destructive structural health monitoring systems. Yet, the transmitted ultrasonic guided waves are affected by the physical and material properties of the structure and are often complicated to model mathematically. This calls for data-driven approaches to model the behaviour of waves, where patterns in wave data due to damage can be learned and distinguished from non-damage data. Recent works have used a popular dictionary learning algorithm, K-SVD, to learn an overcomplete dictionary for waves propagating in a metal plate. However, the domain knowledge is not utilized. This may lead to fruitless results in the case where there are strong patterns in the data that are not of interest to the domain. In this work, instead of treating the K-SVD algorithm as a black box, we create a novel modification by enforcing domain knowledge. In particular, we look at how regularizing the K-SVD algorithm with the one-dimensional wave equation affects the dictionary learned in the simple case of vibrating string. By adding additional non-wave patterns (noise) to the data, we demonstrate that the “wave-informed K-SVD” does not learn patterns which do not obey the wave equation hence learning patterns from data and not the noise.
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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
- NSF-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
