A synergistic deep learning framework integrating GWO-VMD and dual-channel TCN-GRU for cobalt ion concentration prediction in zinc hydrometallurgical purification

Accurate prediction of cobalt ion concentration is important for maintaining electrolyte purity and process stability in zinc hydrometallurgical purification. However, conventional laboratory analysis is time-consuming and difficult to support timely process adjustment. This work proposes a GWO-VMD-TCN-GRU framework for one-step-ahead prediction of cobalt ion concentration in the second-stage purification process. GWO is used to optimize VMD parameters and decompose the non-stationary concentration series into trend and detail components, while the TCN-GRU network captures local fluctuations and temporal dependencies. Experiments were conducted using 720 hourly samples collected over 30 consecutive days. The final selected model, evaluated on the fixed chronological test set, achieved RMSE, MAE, R², and KGE values of 0.1349, 0.1095, 0.9922, and 0.9710, respectively. Compared with representative statistical, machine learning, and deep learning baseline models evaluated under the same fixed chronological testing protocol, the proposed GWO-VMD-TCN-GRU model reduced RMSE by 75.3% to 94.5% and MAE by 73.1% to 94.3%. Five-fold time-series validation was further conducted to evaluate temporal generalization across chronological folds, with average R 2 and KGE values of 0.9824 and 0.9582, respectively. A SHAP-based interpretability analysis showed that lagged trend features contributed most to the prediction, while detail features provided supplementary information for short-term fluctuation tracking. Finally, a prototype software platform was developed to integrate offline model development, online prediction, three-stage purification visualization, zinc powder dosage recording, alarm information, and monitoring record export. Overall, the proposed framework demonstrates reliable short-term forecasting performance for cobalt ion concentration and provides predictive and early-warning information for purification monitoring and operator assessment of zinc powder addition.