Wave Physics Informed Dictionary Learning In One Dimension

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.