Physics-Informed Machine Learning-Based Dynamic Parameter Identification of Gear Systems Using a Harmonic Complex-Spectrum Loss

Reliable vibration prediction for gear systems requires calibration of uncertain mesh and bearing parameters. Previous gear physics-informed machine learning (PIML) studies mainly estimated time-varying meshing stiffness (TVMS) or calibrated gearbox dynamics for fault diagnosis or response reconstruction. Yet identifying multiple key parameters from limited data remains challenging. This work develops a PIML-based dynamic parameter inversion method using limited housing-surface vibration acceleration measurements. A gear-shaft-bearing-housing system dynamic model is embedded directly in the optimization loop, and automatic differentiation provides gradients for updating selected parameters without training a separate response-prediction network. A weighted meshing harmonics complex-spectrum loss penalizes amplitude and phase differences, focusing calibration on mesh-related vibration. Numerical studies show that the method reconstructs time- and frequency-domain response features across speeds and initial estimates, and principal features remain discernible with 20% added noise. In experiments, with mesh and bearing stiffnesses fixed at theoretical values, the first two harmonics of static transmission error (STE), mesh damping, and bearing damping are identified from measurements at a single resonant speed of 3100 r/min. The calibrated model reproduces dominant harmonics at 2400 r/min and captures major resonance peaks across the tested speed range, providing a basis for identifying key dynamic parameters from limited vibration data.