Identifying radial internal clearance from nonlinear rolling-bearing dynamics using a physics-informed approach

Abstract Rolling-element bearings exhibit strongly nonlinear dynamic behaviour due to radial internal clearance, intermittent Hertzian contact, eccentricity, damping, and raceway imperfections. This study addresses the inverse identification of radial internal clearance in a nonlinear 2-DOF rolling-bearing system governed by intermittent contact. A physics-informed neural formulation is employed to reconstruct the two-dimensional bearing response and simultaneously estimate the unknown clearance by embedding the governing equations of motion directly into the training loss. A SIREN architecture with sinusoidal activation functions is used to represent the oscillatory displacement response and its time derivatives. The framework is assessed using limited and noisy displacement observations generated from 4th-order Runge–Kutta solutions for different clearance values and operating conditions, with noise levels of $$1\%$$ 1 % , $$5\%$$ 5 % , and $$10\%$$ 10 % . The method accurately reconstructs both transient and steady-state responses. The clearance-normalized vector reconstruction error ranges from $$0.085\%$$ 0.085 % to $$0.162\%$$ 0.162 % , while the maximum relative error in radial internal clearance identification remains below $$0.012\%$$ 0.012 % . No systematic deterioration in reconstruction or identification accuracy is observed with increasing noise under the considered conditions. These results establish a physics-informed computational framework for identifying radial internal clearance from nonlinear bearing dynamics. Although the present validation is based on model-generated observations, the formulation provides a basis for subsequent assessment using experimental bearing data.