An adaptive GPR-EKF framework for uncertainty-calibrated cutting-force prediction

Targeting cutting-force prediction under nonstationary disturbances and multisource uncertainties, we propose a closed-loop, four-level adaptive GPR-EKF hybrid that combines probabilistic learning, recursive state correction, and out-of-loop adaptation. GPR provides a nonlinear prior, the EKF performs recursive correction, and residual-gain scaling together with mini-batch retraining mitigate transient disturbances and track slow drift. Validation across G1-G3 machining conditions demonstrates strong predictive performance, with NMAE of 3.0-3.8% and R²> 0.969. Uncertainty calibration is likewise improved: PICP exceeds 96%, average interval width is reduced by 24-25%, and interval variance is decreased by 49-60%. Ablation studies indicate that residual-gain scaling and mini-batch retraining contribute 1.8 and 2.4%-point reductions in NMAE, respectively, while EKF effectively suppresses short-term error spikes under high-frequency disturbances, highlighting enhanced robustness. Overall, the framework provides an interpretable, adaptive, and computationally feasible closed-loop solution for process monitoring and real-time adaptive compensation in intelligent manufacturing.