this chapter, several multivariate calibration methods were used for the
quantification of the refrigerants R22 and R134a in mixtures measured by a
single sensor SPR setup. It was demonstrated that the combination of the
time-resolved measurement approach with a multivariate data analysis allows
the quantification of 2 analytes using only 1 single sensor.
most common multivariate calibration method, PLS, was not capable of dealing
with the nonlinear relationship between the sensor signals and the
concentrations of the analytes resulting in unacceptably high prediction errors
and systematical biases. Thus, different well-known methods for linearizing the
data or for introducing nonlinearities into linear models were used. In principle,
these methods successfully compensated the nonlinearities in the data structure.
Yet, compared with the standard deviations of the sensor signals with 0.2% for
R22 and 1.3% for R134a, which were calculated for 60 seconds exposure to
analyte of different concentrations using reproduced measurements, the overall quality
of predictions seems to be improvable.
of uniform fully connected neural networks showed the best results with respect
to generalization ability. In contrast to the methods mentioned before, the
neural networks make no assumption of the type of relationship between the input
and the response variables (linear, quadratic...) and thus can approximate the
relationship between the time-resolved sensor responses and the concentrations
of the analytes quite well, for which no model exists at the moment. A significant
drawback, which can also be seen in table 2,
is the overfitting of the neural networks, which is observable as gap between
the prediction errors of the calibration data and of the validation data. In
contrast to all other methods mentioned before, the neural networks perform
no variable selection or compression of the input information resulting in a
high number of adjustable parameters and consequently running into the danger
of overfitting. Therefore, neural networks combined with a principal component
analysis were used for the compression of the input variables and two pruning
algorithms were applied for thinning out the network structure. Whereas the
pruning algorithms showed unstable and worse results, the combination of the
PCA with neural networks demonstrated that in principle smaller neural network
could calibrate the relationships at least as well as the non-optimized networks.
As the PCA-NN is a very simple method to reduce the neural network size, a more
sophisticated variable selection method is expected to show even better results.
Thus, in the next chapter genetic algorithms are combined
with neural networks to perform a variable selection and thus to reduce the
PCA - NN
MAG-Pruning - NN
OBS-Pruning - NN
table 2: Comparison of the
rel. RMSE of the calibration and validation data in %. Additionally the degrees
of nonlinearity and overfitting of the predictions are listed.