Simulation of Guided Waves for Structural Health Monitoring Using Physics-Informed Neural Networks

Abstract

Guided wave propagation is a valuable and reliable technique for structural health monitoring (SHM) of aerospace structures. Along with its higher sensitivity towards small damages, it offers advantages in traveling long distances with minimum attenuation. Simulation of guided wave propagation is essential to understand wave behavior, and calculating the dispersion relations forms an integral part of the procedure. Application of the current numerical techniques for complex media is highly involved and faces issues related to accuracy, stability, and computational resources. Development in the field of machine learning and graphical processing units (GPUs) leads to the implementation of a faster, automated, and scalable deep neural networks-based learning approach for such problems. Most of the implementation in the field is based on data collection and uses neural networks for nonlinear mapping from input space to target space. However, a large amount of prior information in the form of a governing differential equation is not utilized. In this paper, we have used Physics-Informed Neural Networks (PINNs), in which neural networks are utilized to solve governing partial differential equations. PINNs are implemented to obtain the solution of a one-dimensional wave equation with Dirichlet boundary conditions. The exact solutions and predicted responses match closely with lower mean square error in limited computational time. We have also conducted a detailed comparison of the effect of neural architecture on the mean square error and the training time. This study shows the merit of deep neural networks leveraging the available physical information to simulate the wave phenomenon for SHM efficiently.