Physics-informed neural networks for structural health monitoring: a case study for Kirchhoff–Love plates

Abstract

Physics-informed neural networks (PINNs), which are a recent development and incorporate physics-based knowledge into neural networks (NNs) in the form of constraints (e.g., displacement and force boundary conditions, governing equations) or loss function, offer promise for generating digital twins of physical systems and processes. Although recent advances in PINNs have begun to address the challenges of structural health monitoring (SHM), significant issues remain unresolved, particularly in modelling the governing physics through partial differential equations (PDEs) under temporally variable loading. This paper investigates potential solutions to these challenges. Specifically, the paper will examine the performance of PINNs that enforce a structure’s boundary conditions and utilises sensor data from a limited number of locations within it. Satisfaction of these boundary conditions, which can be expressed as derivatives of deflections and computed through automatic differentiation, is achieved through an additional term in the loss function. We also examine a PINN’s ability to predict deflections and internal forces for loads that have not been included in the training data sets. Three case studies are utilised to demonstrate and evaluate the proposed ideas. Case Study (1) assumes a constant uniformly distributed load (UDL) and analyses several setups of PINNs for four distinct simulated measurement cases obtained from a finite element model. In Case Study (2), the UDL is included as an input variable for the NNs. Results from these two case studies show that the modelling of the structure’s boundary conditions enables the PINNs to approximate the behaviour of the structure without requiring satisfaction of the governing PDEs across the whole domain of the plate. In Case Study (3), we explore the efficacy of PINNs in a setting resembling real-world conditions, wherein the simulated measurement data incorporates deviations from idealised boundary conditions and contains measurement noise. Results illustrate that PINNs can effectively