Prediction results and discussion

Based on the simulation results obtained in Section 4.2, the network topology was optimized to the structure of 13-6-1 with zero input delay, one activation feedback delay and four output feedback delays. The 13 inputs to the input layer consisted of current states of feed rate, DO, volume, six activation feedbacks and four output feedbacks. This network structure was considered as a starting point for the experimental investigation.

Figure 4.10 shows the on-line biomass prediction when applying the neural softsensor to the unseen experimental data of stair-shape feed flow (see Figure 4.9). The prediction starts from an arbitrary initial point. As can be seen from the figure, the softsensor is able to converge within a very short time and can predict the trend of the growth of biomass. However, the MSE between the estimated values and the actual values of biomass is 0.3580. It is a little higher than 0.35, which has been previously reported in the literature by using Knowledge Based Modular networks [99]. As can be seen in the plot, a fluctuation appears in the prediction trajectory. The RMSP error is 11.7%. The network topology chosen for this prediction is exactly the same as the one used for the simulation given in Figure 4.5. As discussed in the simulation study, the main reason for the fluctuation could be that the historical input values are not presented to the network. Furthermore, under realistic conditions, errors in the biomass measurement, the effects of sampling, bias in the noise characteristics, noisy training data and batch to batch variations may have a significant affect on the estimation accuracy [73].

Soft sensor's output Error bars Sample means

200 250 300 Time (minutes)

Fig. 4.10. On-line biomass concentration prediction in a fed-batch baker's yeast fermentation process. The network input delays: 0; output feedback delays: 1, 2, 3, 4; activation feedback delay: 1.

For the neural softsensor to overcome the output fluctuation, historic input values are required so that a smooth prediction, which is closer to the reality of biomass growth, can be achieved. Figure 4.11 shows the prediction result using a modified neural model in which two input delays have been incorporated through TDLs. In order to distinguish the effects caused by activation feedback delays and input delays, the activation feedback delays have been set to be zero. It is obvious that the fluctuation has been reduced significantly. However, the error is slightly higher than that in Figure 4.10 (RMSP error is 12.1%). In particular, the errors on the prediction at both ends, the beginning and the final period of the fermentation, are still large.

In order to improve the predictive ability on both ends of fermentation, an approach that was used in the study is to connect activation feedback to the network input through TDLs. After such modification, one can see from Figure 4.12 that a smooth prediction has been gained on both the initial phase and ending phase. The prediction RMSP error between the measured values and the estimated values is further decreased to 10.3%. Figure 4.10 to Figure 4.12 show a gradual improvement is achieved.

Time (minutes)

Fig. 4.11. On-line biomass concentration prediction in a fed-batch baker's yeast fermentation process. The network input delays: 1, 2; output feedback delays: 1, 2, 3, 4; activation feedback delay: 0.

Time (minutes)

Fig. 4.11. On-line biomass concentration prediction in a fed-batch baker's yeast fermentation process. The network input delays: 1, 2; output feedback delays: 1, 2, 3, 4; activation feedback delay: 0.

Time (minutes)

Fig. 4.12. On-line biomass concentration prediction in a fed-batch baker's yeast fermentation process. The network input delays: 1, 2; output feedback delays: 1, 2, 3, 4; activation feedback delay: 1.

Time (minutes)

Fig. 4.12. On-line biomass concentration prediction in a fed-batch baker's yeast fermentation process. The network input delays: 1, 2; output feedback delays: 1, 2, 3, 4; activation feedback delay: 1.

For a comparison, the RMSP error and MSEs of the biomass predictions using three different topologies are listed in Table 4.1. The experimental results show that the highest predictive ability is obtained from the neural soft-sensor with two input delays, four output feedback delays and one activation feedback delay.

Table 4.1. Prediction errors using three different RNN topologies.

RNN topology_MSE_RMSP error(%)

0/1/4 0.3580 11.7 2/0/4 0.3159 12.1 2/1/4_0.3107_10.3_

4.4 Conclusions

This work assesses the suitability of using RNNs for on-line biomass estimation in fed-batch fermentation processes. The proposed neural network sensor only requires the DO, feed rate and volume to be measured. Based on a simulated model, the neural network topology is selected. Simulations show that the neural network is able to predict the biomass concentrations within 3% of the true values. This prediction ability is further investigated by applying it to a laboratory fermentor. The experimental results show that the lowest RMSP error is 10.3%. From the results obtained in both simulation and real processes, it can be concluded that RNNs are powerful tools for on-line biomass estimation in fed-batch fermentation processes.

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