Graph neural networks for dynamic modeling of roller bearings



Published Oct 26, 2023
Vinay Sharma Jens Ravesloot Cees Taal Olga Fink


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.

How to Cite

Sharma, V., Ravesloot, J., Taal, C., & Fink, O. . (2023). Graph neural networks for dynamic modeling of roller bearings . Annual Conference of the PHM Society, 15(1).
Abstract 212 | PDF Downloads 195



Graph neural Network, Bearing dynamics model, Deep learning, prognostics

Battaglia, Peter W., Jessica B. Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, et al. 2018. ‘Relational Inductive Biases, Deep Learning, and Graph Networks’. arXiv.

Gao, H., Zahr, M. J.,&Wang, J.-X. (2022). Physics-informed graph neural galerkin networks: A unified framework for solving pde-governed forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 390, 114502.

Greydanus, S., Dzamba, M., & Yosinski, J. (2019). Hamiltonian neural networks. Advances in neural information processing systems, 32.

Gupta, P. K. (Ed.). (1984). Advanced dynamics of rolling elements. Springer New York.

Haghighat, E., Raissi, M., Moure, A., Gomez, H., & Juanes, R. (2020). A deep learning framework for solution and discovery in solid mechanics. arXiv: 2003.02751.

Henkes, A., Wessels, H., & Mahnken, R. (2022). Physics-informed neural networks for continuum micromechanics. Computer Methods in Applied Mechanics and Engineering, 393, 114790.

Jagtap, A. D., Kharazmi, E., & Karniadakis, G. E. (2020). Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 365, 113028

Li, M., Chen, S., Zhao, Y., Zhang, Y., Wang, Y., & Tian, Q. (2020). Dynamic multiscale graph neural networks for 3d skeleton based human motion prediction. In Proceedings of the ieee/cvf conference on computer vision and pattern recognition (pp. 214–223).

Lundberg, G. (1939, sep). Elastische Ber¨uhrung zweier Halbr¨aume. Forschung auf dem Gebiete des Ingenieurwesens,10(5), 201–211. doi: 10.1007/bf02584950

Lutter, M., Listmann, K., & Peters, J. (2019). Deep lagrangian networks for end-to-end learning of energy based control for under-actuated systems. In 2019 ieee/rsj international conference on intelligent robots and systems (iros) (p. 7718–7725). IEEE Press.

Palmgren, A. (1959). Ball and roller bearing engineering. Philadelphia: SKF Industries Inc.

Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., & Battaglia, P. W. (2021). Learning mesh-based simulation with graph networks. In Proceedings of the international conference on learning representations.

Sanchez-Gonzalez, A., Godwin, J., Pfaff, T., Ying, R., Leskovec, J., & Battaglia, P. (2020). Learning to simulate complex physics with graph networks. In Proceedings of the International Conference on machine learning (p. 8459-8468).

Shlomi, J., Battaglia, P., & Vlimant, J.-R. (2020). Graph neural networks in particle physics. Machine Learning: Science and Technology, 2(2), 021001.

Yan, C., Vescovini, R., & Dozio, L. (2022). A framework based on physics-informed neural networks and extreme learning for the analysis of composite structures. Computers & Structures, 265, 106761.
Technical Research Papers

Most read articles by the same author(s)