Processes 2023 , 11 , 809
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Remark2. It is important to note that, in the LSTM-ANN-based controller, the past values of the outputs are fed in as input to the neural network along with the operating conditions (the cooking time, NaOH concentration, and temperature). Thus, during closed-loop operation, the outputs obtained from the multiscale model are fed into the surrogate LSTM-ANN model along with the other operating conditions in order to predict the future outputs of the process and obtain the optimal input profiles. An assumption here is that the measurements of the Kappa number and DP are available every 10 min from the multiscale model.
4. Results and Discussion 4.1. Multiscale Model
The multiscale model is used to predict the temporal evolution of wood chip properties as well as the spatiotemporal evolution of the kMC lattice at a temperature of 420 K and a NaOH concentration of 50 wt%. As shown in Figure 4, the orange, yellow, purple, and green sites represent lignin, cellulose, xylan, and galactoglucomman in the solid phase, respectively, while the blue sites represent the entrapped-liquor phase. As the solid components dissolve, the lignin and hemicellulose content in the chips fall significantly, and the entrapped-liquor content increases. The prediction trends of the Kappa number and cellulose DP are shown in Figure 5. The Kappa number is seen to gradually decrease from 165 to 113 as delignification occurs in the wood chips, while the cellulose DP shows a sharp drop at the beginning of the pulping process and then achieves the equilibrium around 1600. To verify the accuracy of the multiscale model, it was validated against data of three different wood species: Date Palm Rachis, Pinus Radiata, and Eucalyptus [61–63]. The model was run at 413 K with a cooking time of 120 min and a NaOH concentration of 12 wt%, and the results are shown inTable 2. It is seen that, for all three different wood species, the set-point values of the Kappa number and cellulose DP are similar to the values found in the literature [61–63], and the mean error is less than 10%. This suggests that the multiscale model is a valid virtual experiment for the batch pulp digester process, and can be used to generate data for varying operating conditions in order to train the LSTM-ANN model structure.
Figure4. Graphical illustration of the simulation lattice at t =0and t = 87.84 min.
Remark3. The results shown in Figure 5 are representative, and the trends of the Kappa number and DP for other input profiles follow a similar trend. It is assumed that the multiscale model remains effective under all these different operating conditions. 4.2. LSTM-ANN Model Through optimization of the network structure, the best structure was obtained with three hidden layers, each containing 40 nodes. A batch size of 16 and a dropout rate of 0.5
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