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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. 

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.