TD3-GraphMPC Model for Online Moisture Prediction in Infant Formula Powder Using Multi-Source Feature Fusion

Source abstract

Accurate online estimation of moisture in infant formula powder is required to support drying control, powder flowability, microbial stability, and packaging performance. This study proposes a TD3-GraphMPC soft sensor that integrates multi- source feature fusion with graph-structured dynamic prediction. Near-infrared spectral descriptors, inlet and outlet air conditions, powder temperature, chamber pressure, vibration-based flow indicators, and recipe-level composition variables are synchronized through residence-time compensation, weighted by a reliability gate, and represented as a heterogeneous process graph. A twin delayed deep deterministic policy gradient module learns bounded latent-state corrections for nonlinear drying behavior, while a model predictive consistency layer constrains short-horizon moisture evolution without applying exploratory actions to the plant. The model was evaluated on 3,840 production-inspired batch segments separated by parent batch into training, validation, and test sets. It achieved a test RMSE of 0.071 percentage points, an MAE of 0.053 percentage points, and an R² of 0.962. Relative to BiLSTM and a plain graph neural network, RMSE was reduced by 25.3% and 14.5%, respectively. Coverage within the +/-0.10 percentage-point tolerance band reached 93.6%, and the mean constraint violation rate was 1.8%. Under 30% spectral missingness, RMSE remained 0.094, compared with 0.114 for GNN-MPC and 0.148 for BiLSTM. These results indicate that graph-based sensor reasoning, cautious latent correction, and prediction-consistency constraints can improve robust moisture estimation, while prospective multi-line validation remains necessary before closed-loop deployment.