On the Application of Physics-Informed Neural-Networks for Identification and State Estimation of Vibrating Structures

Structural health Monitoring (SHM) often draws from availability of vibration-based monitoring data for effectuating different downstream tasks. These involve target applications related to digital twinning/virtual sensing, damage/anomaly detection and reliable forward modeling. Most of these tasks can be classified under the main categories of system identification/equation discovery, i.e., inference of the system’s characteristics or model form, and response prediction. Often, these objectives are met using targeted methodological schemes, although certain methods can simultaneously achieve multiple of these goals. We here present physics-informed neural networks (PINNs) as a constrained learner for both system identification and response prediction, typically accomplished via equation solution discovery. In the former case, PINNs can be used to determine the parameters of the system’s governing equations. The advantage of PINNs in this context is the ease of implementation of varying boundary conditions, forcings, and governing equations. In the second case, PINNs can be employed for response estimation of vibrating systems, with the advantage of improved estimates in the case of sparse data, either for improved interpolation or for locations where measurements are unavailable. In this work, the PINN is applied to simulated vibrating structures in both contexts. The advantages are highlighted via assessment of the accuracy in prediction of the system’s response showcasing the simplicity of switching between motivations.