Abstract:
This study aimed to develop a digital-twin-based optimization method incorporating dual-source Pareto fusion for feed pelleting. The method addressed the dependence of process parameter settings on operator experience and the difficulty of balancing pellet quality and production efficiency under different feed formulation scenarios. A stacking ensemble prediction model was constructed using historical production data and was used as the digital twin evaluator. Newly collected field data were incorporated through daily rolling retraining to improve the evaluator's adaptability to changing production conditions. Steam pressure, feeder frequency, and conditioning temperature were selected as adjustable process parameters, whereas feed formulation, environmental conditions, and equipment and production status were treated as fixed scenario characteristics within each production batch. Tree-structured Parzen estimator-based multi-objective Bayesian optimization (TPE-MOBO) and the non-dominated sorting genetic algorithm II (NSGA-II) were employed to search for candidate operating conditions. Candidate Pareto solutions generated by the two algorithms were merged, deduplicated, screened against engineering constraints, and subjected to non-dominated sorting. The resulting archive was further processed through parameter discretization, evaluator-based verification, and multi-criteria decision-making to obtain executable operating recommendations. The optimization methods were compared under an equal total budget of 600 function evaluations, and field experiments were conducted to compare empirical operating conditions with selected optimized recommendations. Field forward validation using 11 production batches showed that daily rolling retraining improved the prediction performance for pellet hardness, pellet durability index (PDI), and productivity. The mean absolute percentage errors decreased from 2.40%, 3.48%, and 4.97% to 2.15%, 2.19%, and 4.45%, respectively. The root mean square errors for hardness, PDI, and productivity decreased from 1.143 to 0.919 N, from 2.963 to 1.805 percentage points, and from 0.994 to 0.955 t/h, respectively. The corresponding coefficients of determination increased from 0.400 to 0.612, from 0.725 to 0.898, and from 0.608 to 0.638. The improvement was most pronounced for PDI prediction. Under the equal evaluation budget, the dual-source fusion archives contained 14 and 43 Pareto solutions in production scenarios S1 and S2, respectively. Their spacing values were 0.054 and
0.0215, both lower than those of the corresponding individual algorithms, while the maximum spread values were 1.36 and 1.37. However, the hypervolume values of the fusion archives did not exceed those of both individual algorithms in either scenario. These results indicated that the principal contribution of fusion was not a consistent improvement in every optimization metric, but the integration of complementary non-dominated operating conditions and the provision of a more diverse set of quality–productivity trade-offs. Field comparison further demonstrated scenario-dependent effects. In S1, the productivity-priority recommendation increased measured productivity from 12.30 to 15.03 t/h, representing an increase of 22.2%, while PDI decreased from 72.69% to 68.43% and mean pellet hardness decreased from 28.75 to 26.21 N. In S2, the balanced-compromise recommendation increased productivity from 13.00 to 14.80 t/h, representing an increase of 13.8%; meanwhile, PDI increased from 71.32% to 74.84% and mean pellet hardness increased from 30.43 to 32.89 N. The results demonstrated that the productivity-priority strategy involved a quality–efficiency trade-off in S1, whereas the balanced-compromise strategy improved both productivity and PDI in S2. The proposed method integrated production performance prediction, dual-algorithm Pareto optimization, executable operating-condition selection, field validation, and daily model updating into a unified decision-support workflow. It provided a practical approach for selecting process parameters according to the requirements of different feed formulations. Further validation across a wider range of formulations, raw material batches, and equipment operating conditions was needed to determine the robustness and applicability of the recommended operating conditions.