a multivariate calibration was performed using the sensor responses of all time
points of all 4 sensors resulting in 200 independent variables. For the unsmoothed
data, prediction errors of the validation data between 22.18% and 23.96% were
achieved (see row 1 of table 7). The prediction
errors of the validation data for the smoothed sensor signals are between 14.61%
and 34.85% (see row 2 of table 7). When
using the sensor signals of all 4 sensors no clear decision can be made if smoothing
is beneficial for the calibration. As the 200 input variables contain too much
redundant information for an optimal calibration, the parallel growing network
framework (50 networks per analyte) was applied to the calibration data of the
smoothed and the raw sensor signals. The importance of the different variables
is shown in figure 70 as frequency of selection.
For the raw signals the 2 Makrolon sensors of 160 nm and 80 nm dominate, whereas
the PUT sensor and the 120 nm Makrolon are by far less important. The variable
ranking of the smoothed signals looks similar with two differences: Although
the 160 nm and 80 nm sensors still dominate, the importance of the other two
sensors increased and the important time points of the 80 nm sensor shifted
from the end to the beginning of desorption. Compared with the 160 nm layer,
the 80 nm layer has gained importance after smoothing.
figure 70: Frequency of selection
of the different variables after the first step of the parallel growing network
step of the growing network framework stopped after the addition of 7 variables
for the raw sensor signals and after the addition of 10 variables for the smoothed
data. The variable selections for both data sets are similar and very astonishing.
For both data sets, only time points of the 80 nm and of the 160 nm Makrolon
layer are used. Additionally, only time points within the first 90 seconds of
sorption and within the first 75 seconds of desorption are used (instead of
240 seconds of sorption and 210 seconds of desorption) suggesting that faster
measurements are possible (see also discussion in section
10.3). Both, the predictions of the validation data and the predictions
of the calibration data are significantly better for the raw and the smoothed
data when compared with the calibrations using all time points of all sensors
(see row 3 and row 4 of table 7). The
quantification of methanol is better for the raw data, whereas the quantification
of ethanol and 1-propanol is better for the smoothed data whereby for this combination
of a thick and a thin layer no method can be generally preferred. The true-predicted
plots for the raw data are shown in figure 71.
figure 71: True-predicted plots
for the raw sensor signals of the array setup whereby only the sensor responses
of 2 sensors are evaluated.
to see the interactions of the thickness of layers and of smoothing, the sensor
responses of the single sensors are calibrated using unoptimized networks (50
input neurons, 5 hidden neurons and 1 output neuron). The predictions of these
single sensor calibrations for the raw and for the smoothed data are listed
in row 5 to row 12 of table 7. First of
all, the single sensor calibrations confirm the variable selection of the framework.
The 160 nm layer shows the best calibrations whereas the PUT sensor and the
120 nm Makrolon sensor show poor calibrations. From the chemical point of view,
the poor single sensor performance of the PUT sensor can be ascribed to the
immediate sensor response without any time-resolution possible whereas the poor
performance of the 120 nm Makrolon sensor cannot be explained.
of smoothing is quite interesting for the 3 Makrolon layers with a different
thickness. The 80 nm layer clearly benefits from the smoothing while the 160
nm layer shows worse calibration results if the smoothed sensor signals are
used instead of the raw sensor signals. The 120 nm layer with the medium thickness
shows no clear preference. The benefits of smoothing for thin layers can be
explained by the improvement of the signal to noise ratio overcompensating the
changes of the shapes of the sensor responses. On the other hand, the thick
layers with a rather good signal to noise ratio are mainly affected by the disadvantageous
changes of the shapes of the sensor signals without any real improvement of
the signal to noise ratio.
4 Sensors Raw
4 Sensors Smoothed
Raw (80 nm M2400)
Smoothed (80 nm
Raw (120 nm
Smoothed (120 nm
Raw (160 nm
Smoothed (160 nm
4 Sensors Static
4l Setup Framework
table 7: Relative RMSE for
different data analysis methods and for different setups.