3.2. Validation of the calibration models
In order to see if the calibration models are able to predict the ethanol concentration during new process runs, each calibration model obtained from a cultivation run was validated with the data from the other two cultivations which have different initial concentrations. Fig. 7 (a) and Fig.7 (b) presents the predicted (using data from BC1 for the calibration model) as well as the off-line measurements of ethanol concentration as a function of time during BC2 and BC3 respectively. Fig. 7 (c) and Fig.7 (d) presents the predicted (using data from BC2 for the calibration model) as well as the off-line measurements of ethanol concentration as a function of time during BC1 and BC3 respectively. Fig. 7 (e) and Fig.7 (f) presents the predicted (using data from BC3 for the calibration model) as well as the off-line measurements of ethanol concentration as a function of time during BC1 and BC2 respectively.
Fig. 7 indicates that the predicted ethanol concentration using the MBC approach corresponds well with the off-line measurements during all cultivations. Furthermore, the ethanol production phase and ethanol consumption phase are clearly indicated by the predicted ethanol values without a significant time delay (in comparison with the off-line values). In S. cerevisiae batch cultivation, the metabolic shift of the yeast cells (shifting from ethanol production to ethanol consumption) is a critical point which indicates a significant change in its metabolism and can be observed using the gas sensor array. Ethanol prediction with the MBC approach was compared with the ethanol prediction using the CCM approach. For this reason RMSEP and SEP were calculated and the results are shown in Table 3.
Table. 3 reveals that, by using the MBC approach, the SEP of prediction is below 7 % in all cases besides when BC2 is used for calibration and the data set from BC1 is used for validation (SEP = 9.3 %). However, even though in the model-based calibration approach, during the calibration procedure of the chemometric model no off-line measurement were used, the prediction corresponds very well with the simulated values. Furthermore, in comparison with the predictions from using the classical calibration method, lower prediction errors are obtained.
The larger errors of prediction from the classical calibration method are because not so many off-line samples are used for calibration. Therefore, by increasing the number of off-line samples, more accurate predictions might be obtained. However this would be a time consuming and expensive approach.
When using the MBC approach, the percentage error highly depends on the kinetic parameters of the simulation model which are obtained from the optimization algorithm. If they are close to the real values, the process model will describe the process sufficiently accurate. Therefore, improving the optimization process can even lead to even lower percentage errors. Of course, the percentage errors also depend on how good the off-line samplings were performed and how accurate they are. However, the prediction error for ethanol concentrations are below 10 % in all three cultivations which is considered decent for a bioprocess especially when considering that no off-line values were used to achieve this result.