x 10

Fig. 5.9. Comparison of optimization results based on the mathematical model and RNN model.

5.6 Summary

Optimization of a fed-batch bioreactor using the cascade RNN model and the modified GA is investigated in this simulation study. The complex nonlinear relationship between manipulated feed rate and biomass product is represented by two neural blocks, in which outputs of one block are supplied into another neural block to provide meaningful information for biomass prediction. The results show that the error of prediction is less than 8%. The proposed model proves capable of capturing the dynamic nonlinear underlying phenomena contained in the training data set. The feasibility of the neural network model is further tested through the optimization procedure using the modified GA, which provides a mechanism to smooth feed rate profiles. The comparison of results of optimal feeding trajectories obtained based both on the mechanistic model and the neural network model have demonstrated that the cascade recurrent neural model is competent in finding the optimal feed rate profiles. The evolution of feed rate profiles through generations shows that the modified GA is able to generate a smooth profile, while the optimal-ity of the feed rates is still maintained. The final biomass quantity yields from the optimal feeding profile based on the neural network model reaches 99.8% of the "real" optimal value.

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