Recurrent neural networks for process modelling

Neural networks as alternative tools have been extensively studied in process modelling because of their inherent capability to handle general nonlinear dynamic relationships between inputs and outputs. Many reviews of the applications of ANNs in modelling and control of biotechnological processes can be found in the literature [2,28,29,30,31,43]. Neural networks are able to extract underlying information from real processes in an efficient manner with normal availability of data. The main advantage of this data-driven approach is that modelling of complex bioprocesses can be achieved without a priori knowledge or detailed kinetic models of the processes [44,45,46,47,48,49].

RNN structures are more preferable than FNN structures for building bio-process models, because the topology of RNNs characterize a nonlinear dynamic feature [7,50,51,52,53,54,55,56]. The connections in RNNs include both feed-forward and feedback paths in which each input signal passes through the network more than once to generate an output. The storage of information covering the prediction horizon allow the network to learn complex temporal and spatial patterns. A RNN was employed to simulate a fed-batch fermentation of recombinant Escherichia coli subject to inflow disturbances [39]. The network that was trained with one kind of flow failure was used to predict the course of fermentation for other kinds of failures. It was found that the recurrent network was able to simulate the other two unseen processes with different inflow disturbances, and the prediction errors were smaller than those with FNNs for similar systems. Another comparison study was made by Acuna et al. [57]. Both static and recurrent (dynamic) network models were used for estimating biomass concentration during a batch culture. The dynamic model performed implicit corrective actions to perturbations, noisy measurements and errors in initial biomass concentrations. The results showed that the dynamic estimator was superior to the static estimator at the above aspects. Therefore, there is no doubt that the RNNs are more suitable than FNNs for the purpose of bioprocess modelling.

The prediction accuracy of the RNN models is heavily dependent on the structure being selected. The determination of the RNN structure includes the selection of the number of hidden neurons, the connection and the delays of feedback, and the input delays. It is problem specific and few general guidelines exist for the selection of the optimal nodal structure [28]. The above mentioned RNNs are structurally locally recurrent, globally feed-forward networks. These structures are rather limited in terms of including historical information [37], because the more feedback connections the RNNs have, the "dynamically richer" they are. A comparison between RNNs and augmented RNNs for modelling a fed-batch bioreactor was presented by Tian et al. [58]. The accuracy of long range prediction of secreted protein concentration was significantly improved by using the augmented RNN which contains two RNNs in series.

In this book, an extended RNN is adopted for modelling fed-batch fermentation of Saccharomyces cerevisiae. The difference between the extended RNN and the RNNs mentioned above is that, besides the output feedback, the activation feedbacks are also incorporated into the network, and tapped delay lines (TDLs) are used to handle the input and feedback delays. A dynamic model is built by cascading two such extended RNNs for predicting biomass concentration. The aim of building such a neural model is to predict biomass concentration based purely on the information of the feed rate. Therefore, the model can be used to maximize the final quantity of biomass at the end of reaction time by manipulating the feed rate profiles.

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