Physics-informed surrogate modeling for a damaged rotating shaft

In the online structural health monitoring framework, surrogate modeling aims to approximate the predictions of the underlying high-fidelity model to facilitate fast simulations. Generally, conventional machine learning techniques based on purely data-driven approaches often behave as black boxes, producing predictions that may lack physical consistency. In an effort to overcome these limitations, we proposed a neural network mapping constrained by the known physical relationships of an engineering model, which can be considered as a physics-informed inductive bias. This approach aims to enhance computational efficiency while reducing the required number of training examples. The physics-informed term guides the training process to yield predictions that exhibit greater physical consistency while maintaining high performance. We here propose a surrogate modeling approach relying on a Physics-Informed Neural Network (PINN) scheme, which is designed to enable robust and real-time monitoring of ballistic impact damage on a rotor shaft. At first, a high fidelity finite element model is developed to simulate the response of the rotor shaft under various operational conditions. As a first reduction step, substructuring is used to decrease the dimensionality of the system's matrices, thereby reducing the computational cost. For comparison and validation, an alternative model based on the Timoshenko beam theory is utilized. Both models examine the effects of impact-induced vibration loads due to ballistic occurrences. The PINN model receives the external load as input and predicts the system's response. The system matrices extracted from both models constitute the physics-informed term. This term is incorporated into the PINN architecture in order to steer the learning process towards more physically consistent and reliable predictions regarding the state and the response of the structure. The algorithm's performance is evaluated using response data derived from both models.