Hybrid grey-box digital twin and the Bees Algorithm optimization for batch chocolate conching: industrial-scale calibration and validation under hold-window robustness

Abstract

This paper develops a digital-twin workflow for batch chocolate conching by integrating a hybrid grey-box dynamic model with the Bees Algorithm (BA) to synthesize constraint-satisfying operating policies and additive schedules. The modelling contribution is a compact, equation-driven representation that couples (i) event-driven phase progression (dry–plastic–liquid), (ii) temperature–mixing–aeration accelerated moisture and volatile stripping, and (iii) structure-governed Herschel–Bulkley rheology via an interpretable closure linking a latent coating/dispersion index to yield stress and consistency evolution. The optimization contribution is a band-constrained formulation that enforces industrial rheology bands together with strict limits on residual moisture/volatiles and caps on maximum temperature and specific energy, while enabling early-stop termination once feasibility is sustained over a discharge-relevant hold window. Industrial-scale experiments were conducted on an instrumented 2.5-t conche at MEMAK using three batches, with two batches used for parameter calibration and one batch retained for independent cross-validation. Measured temperature and power/energy trajectories, together with discrete rheology, moisture, and volatile-marker measurements, were used to estimate uncertain model parameters and to provide a preliminary assessment of predictive performance under the investigated formulation and operating conditions. Simulation–experiment agreement was quantified using trajectory-level error metrics and discharge-relevant hold-window comparisons. The optimized policy achieved η_ref = 3.229 Pa·s within the prescribed 3–5 Pa·s range and τ_y = 7.165 Pa within the 7–9 Pa range, while satisfying moisture, volatile, temperature, and specific-energy constraints and enabling early termination at 451.7 min. Given the limited three-batch dataset, these results should be interpreted as preliminary industrial-scale calibration and cross-validation rather than definitive evidence of plant-wide robustness.