Digital twin-driven multi-objective optimization of milling parameters under small-sample conditions

To address the high experimental cost, insufficient parameter-space coverage, and multi-objective trade-off difficulties in milling parameter optimization under small-sample conditions, this study proposes a digital twin-driven multi-objective optimization method for milling parameters. An end-milling process is considered, with spindle speed, feed rate, axial depth of cut, and radial depth of cut selected as input parameters. A unified virtual evaluation interface is constructed to rapidly evaluate machining time, cutting force, and the probability of satisfying surface quality constraints. To improve parameter-space coverage, a diffusion-inspired noise-perturbation augmentation method is used to generate supplementary samples, which are further filtered using parameter bounds and cutting-force physical consistency constraints. A Gaussian process regression model is then established as a surface roughness threshold classification model, transforming surface quality evaluation into a probabilistic constraint satisfaction problem. Based on the virtual evaluation model, Bayesian optimization and a multi-objective genetic algorithm are combined to search for Pareto non-dominated solutions. The case study shows that the proposed method can generate a relatively continuous set of trade-off solutions among machining time, cutting force, and surface quality feasibility, providing alternative parameter combinations for different machining preferences. The optimization results are further integrated into a digital twin visualization system for interactive comparison and decision support. The recommended parameter combinations still require further validation through physical machining experiments.