Graph neural networks for dynamic modeling of roller bearings

Machine learning has paved the way for the real-time monitoring of complex infrastructure and industrial systems. However, purely data-driven methods have not been able to learn the underlying dynamics and generalize them to operating conditions that have not been covered by the training datasets. Therefore, they have not been able to predict the long-term evolution of the system state of physical systems. Physics-informed neural networks (PINNs) have recently shown promising results in predicting the system state evolution over extended periods of time, owing to the loss terms derived from the underlying partial differential equations governing the dynamics of the systems. However, PINNs have limited generalization ability, i.e., a model trained on one type of boundary condition cannot generalize to other conditions. Moreover, the governing equations used for describing the dynamics of physical systems are an approximation of reality, which can lead to differences between the predictions and the actual roll-out of the trajectory. Recently, graph neural networks (GNNs) have been applied to predict the evolution of system dynamics. Due to the encoded inductive bias, they generalize well to systems with varying configurations and boundary conditions. Message-passing GNN comprises two parts that learn the interaction between nodes: an edge network that takes the translational invariant features between two nodes (for e.g., the distance vector) and generates a message, and a node network that takes the aggregated messages from all the neighboring nodes and produces a new node state. This process is repeated several times until the final node state is decoded as a required output. In the presented work, we propose to apply the framework of GNNs for predicting the dynamics of a rolling element bearing. The computational efficiency and generalizability of such a method enable the scalable use of a real-time digital twin to monitor the health state of a rotating machine. To this end, a GNN is used to mimic a dynamic spring-mass-damper model. Bearings consist of different interacting parts like the inner race, outer race, and multiple rolling elements. This interconnected and interacting architecture of a typical bearing is suitable to be modeled as a graph with nodes representing different components. We use the dynamic spring-mass-damper model to generate the training data for the GNN, where bearing components such as rolling elements, and inner and outer raceway are modeled as discrete masses. A Hertzian contact model is used to calculate the forces between these components. We evaluate the learning and generalization capabilities of the proposed GNN framework by testing bearing configurations different from the training configurations and comparing the performance to that of the spring-mass model.