Using
different data analysis methods introduced in chapter 6,
models were built using the calibration data set. Then the validation data were
predicted with the relative RMSE listed in table 6.
Method
Calibration Data
Validation Data
Meth.
Eth.
Prop.
Meth.
Eth.
Prop.
PLS
8.82
12.68
16.99
6.95
11.01
16.12
INLR
9.02
12.57
13.21
8.67
12.39
17.57
Neural Networks
2.83
6.25
7.41
4.33
8.65
12.58
GA Framework
3.24
6.91
7.84
3.58
6.20
7.60
Growing NN Framework
2.62
6.26
7.16
3.31
6.05
7.33
PCA-NN
2.42
6.39
7.31
3.63
8.68
13.36
table 6: Relative RMSE in
% for different calibration methods.
For the
calibration by the PLS, the optimum number of principal components was determined
by the minimum crossvalidation error with 4 principal components for methanol,
8 principal components for ethanol and 3 principal components for propanol.
The predictions of both, the calibration and the validation data are unacceptably
high. Similar to section 6.1, the calibration by the
PLS cannot deal with the nonlinearities of the data with systematic deviations
of the predictions. The INLR (see section 6.3) also showed
disappointing predictions of both data sets. Compared with the PLS, the systematic
deviations of the predictions were lower but the scattering was higher. In contrast,
the calibration by fully connected neural networks (6 hidden neurons and 3 output
neurons) was significantly better. Yet, the gap between the calibration and
validation data shows that there is still room for an optimization of the neural
networks to prevent an overfitting.
Ph. D. Thesis