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.