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).