2. 7. Calibration using off-line values
Ethanol concentration was also predicted by a classical calibration approach. The same chemometric model was used for this approach. The chemometric model was calibrated using the off-line ethanol concentrations.
For both calibration methods, data from all three cultivations were carried out separately for the calibration models (with each calibration method, three different calibration models were made). Each calibration model was evaluated individually with the data from the other two cultivations.
The calibration models were characterized by the root-mean-squared error of calibration (RMSEC), standard error of calibration with respect to the maximum ethanol concentration (SEC), root-mean-squared error of prediction (RMSEP) and standard error of prediction with respect to the maximum ethanol concentration (SEP).
The RMSEC describes how a model fits the calibration and RMSEP evaluates a calibration model versus a sample set from a new cultivation. They are calculated with the following equation:
\begin{equation} RMSEC\ or\ RMSEP=\ \sqrt{\sum_{i=1}^{N}{\ \frac{\left({\hat{Y}}_{i}-\ Y_{i}\right)^{2}}{N}}}\nonumber \\ \end{equation}
\({\hat{Y}}_{p}\) represents the calculated concentration during calibration (RMSEC) or prediction (RMSEP) and \(Y_{i}\) is the concentration determined by reference analysis (either simulated or off-line concentrations). N stands for the measurement count.
RMSEC and RMSEP provide an estimate of the prediction error in the same unit as the initial data (g/L), while SEC and SEP provide the prediction error with respect to the maximum ethanol concentration in the reference data in terms of percentage. SEC and SEP are calculated as follow:
\(\ SEC\ or\ SEP\ (\%)=\)\(\frac{\sqrt{\sum_{i=1}^{N}{\ \frac{\left({\hat{Y}}_{i}-\ Y_{i}\right)^{2}}{N}}}}{Y_{\max}}\)* 100 %
Where \({\hat{Y}}_{i}\) is the calculated concentration determined by the chemometric model and \(Y_{i}\) is the concentration determined by reference analysis (either simulated or off-line concentrations). N stands for the measurement count and \(Y_{\max}\) is the maximum ethanol concentration in the reference data.