Inverse solution of process parameters in gear grinding using hierarchical bayesian physics informed neural network (HBPINN)

Accurate inverse solution of process parameters by surface roughness is crucial for precision gear grinding processes. When inversely solving process parameters, model parameters are typically obtained by fitting experimental data. However, model parameters exhibit complex correlations and uncertainties, posing significant challenges to the inverse solution of process parameters. To address these challenges, the study proposes a hierarchical Bayesian physics-informed neural network (HBPINN) for the inverse solution of gear-grinding process parameters. An innovative global-group-individual level hierarchical structure is constructed for model parameters. Correlation analysis among model parameters is conducted through group effects within a hierarchical Bayesian framework, followed by uncertainty analysis. Then, multivariate regression functions describing the relationship between process parameters and surface roughness are constructed to form the physics loss function. The regularization incorporates the Kullback-Leibler (KL) divergence of model parameters, integrating with the empirical loss function. Furthermore, datasets of different scales were established through Gaussian process regression (GPR) algorithms. Compared with Bayesian physics-informed neural network (BPINN), variational inference Bayesian physics-informed neural network (VI-BPINN), and physics-informed neural network (PINN), HBPINN demonstrates superior performance in terms of both efficiency and accuracy. With a training set size of 200, HBPINN reduced prediction time by 4-10 times and achieved an average R² of 0.9629. The model demonstrates excellent uncertainty quantification capabilities and robustness.