3.2. Calibration models
For the model based-based calibration approach (MBC), the proposed method in section 2.6 was applied to the sensor data gathered from the headspace gas analysis of the bioreactor during each cultivation process separately. The evaluation of the predicted ethanol concentrations from the gas sensor array was compared with the simulated ethanol concentrations. The sum of squared differences was calculated and minimized by the particle swarm optimization method. With this approach, the parameters of the chemometric models (\(p_{0}\), \(p_{1}\) and\(p_{2}\)) as well as the growth rates of the simulation model (\(\mu_{G0}\) and \(\mu_{E0}\)) were obtained.
For the classical calibration method (CCM), the off-line ethanol concentrations (measured from the off-line samples taken during the cultivation) were fitted to the response of the gas sensor array and the sum of squared differences was minimized. The predicted values for the specific growth rates on glucose and ethanol (obtained from the MBC approach) as well as the parameters of the PCR model using both calibration approaches are presented in Table.1.
The data in Table 1. reveals that, there is no significant difference between the growth parameters (\(\mu_{G0}\) and \(\mu_{E0}\)) from cultivations with different initial conditions. This shows that the yeast cells have regulatory mechanisms to be able to balance the cellular activity in different conditions. Furthermore, the values for\(\mu_{G0}\) and \(\mu_{E0}\) that were obtained by fitting the theoretical process model directly to the off-line data of the same cultivations were \(0.15\ h^{-1}\) and\(\ 0.074\ h^{-1}\), respectively, therefore the parameter estimation method can be considered reliable.
As a method of assessing the fit of the calibration models to the data, the correlation plots were prepared (Fig. 6). In Fig. 6 the predicted versus simulated ethanol concentrations using the MBC approach for all three cultivations (BC1 - BC3) as well as the predicted versus off-line measured ethanol concentrations using the CCM approach for all three cultivations (BC1 - BC3) are presented.
The root-mean-square error of calibration (RMSEC) and standard error of calibration (SEC) was chosen as the numerical tool for the accuracy assessment of the calibration models. The values are given in Table 2.
The results if Table 2 indicates that the most suitable calibration method for the determination of the ethanol concentration is the MBC approach (RMSEC is below 3.5 % in all 3 cultivations). This was to be expected due to the difference in the number of data used during calibration, because for the CCM approach just 13 samples were collected and analyzed off-line. However, with a relatively small number of training data, the CCM approach is also a reliable method for the determination of ethanol concentration (RMSEC is below 5.5 % in all 3 cultivations).