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

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, and 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, significant issues remain unresolved, particularly in modeling 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 enforcing boundary conditions and utilizing sensor data from a limited number of locations within it, demonstrated through three case studies. Case Study 1 assumes a constant uniformly distributed load (UDL) and analyzes 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 modeling of the structure’s boundary conditions enables the PINNs to approximate the behavior of the structure without requiring satisfaction of the 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 measurment data incorporate deviations from idealized boundary conditions and contain measurement noise. Results illustrate that PINNs can effectively capture the overall physics of the system while managing deviations from idealized assumptions and data noise.