A Soft Sensor Model Based on RIME-TCN-BiGRU-Attention for Predicting Heavy Calcium Carbonate Particle Size Distribution

The online measurement of particle size distribution is significant to the particle size control of heavy calcium carbonate (HCC) powder. The soft sensor is an effective means to achieve online measurement. Currently, there is limited research on modeling soft sensor for particle size distribution in vertical roller mill (VRM) system. Moreover, the nonlinear, strong coupling, and time-delay characteristics of VRM system pose a major challenge to the realization of high-precision soft sensing for HCC particle size distribution. We propose a soft sensor model combining maximal information coefficient (MIC), temporal convolutional network (TCN), bidirectional gated recurrent unit (BiGRU), and attention mechanism. First, the data are preprocessed, the input features for modeling are selected using the maximum mutual information (MI) coefficient, and then, the dataset is reconstructed according to the time delay and time series features of the data. Second, for model development, we combine TCN, BiGRU, and attention mechanism, and the hybrid model can fully understand the complex coupling and delay relationship between input features and further use the RIME algorithm to optimize the key hyperparameters, improving the model performance. Finally, the model was trained and verified on the data collected on the VRM1100 and VRM1800 systems, and the soft-sensing accuracy ${R} ^{2}$ reached 0.9369 and 0.9492. The results show that compared with other models, the proposed RIME-TCN-BiGRU-Attention (TBiGA) performs well in predicting the accuracy of particle size distribution, which is more suitable for online measurement of particle size distribution of HCC.