Physics-guided ODE neural network for high-fidelity gearbox dynamics modeling based on vibration measurements

High-fidelity dynamics modeling of gearboxes is the prerequisite for developing digital twins capable of elucidating failure behaviors under varying speed conditions. However, traditional approaches, such as finite element and lumped parameter models, often exhibit discrepancies from real-world measurements. This issue is particularly pronounced in complex systems, which limits their practical applicability. To overcome this limitation, we propose a novel physics-guided ordinary differential equation (ODE) neural network. This method integrates a neural network into the gearbox dynamics model to address model incompleteness, specifically the discrepancies between theoretical predictions and actual system behavior. Real acceleration measurements are utilized to calibrate both the neural network and the overall dynamics model, enabling the inference of unknown dynamic parameters without the need for prior determination. By aligning simulated responses with experimental data, the model captures system dynamics with high accuracy. The proposed physics-guided ODE neural network is fully differentiable with respect to both model incompleteness and undetermined dynamic parameters. The effectiveness of this high-fidelity modeling approach is demonstrated using an experimental two-stage gearbox system. Validation against experimental test rig data under varying rotational speeds and faulty conditions confirms the model capability to replicate real-world dynamic responses.