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Ph. D. ThesisPh. D. Thesis 9. Results – All Data Sets9. Results – All Data Sets 9.4. Quaternary Mixtures by the SPR Setup and the RIfS Array 9.4. Quaternary Mixtures by the SPR Setup and the RIfS Array 9.4.2. Results9.4.2. Results
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Ph. D. Thesis
  Abstract
  Table of Contents
  1. Introduction
  2. Theory – Fundamentals of the Multivariate Data Analysis
  3. Theory – Quantification of the Refrigerants R22 and R134a: Part I
  4. Experiments, Setups and Data Sets
  5. Results – Kinetic Measurements
  6. Results – Multivariate Calibrations
  7. Results – Genetic Algorithm Framework
  8. Results – Growing Neural Network Framework
  9. Results – All Data Sets
    9.1. Methanol and Ethanol by SPR
    9.2. Methanol, Ethanol and 1-Propanol by SPR
    9.3. Methanol, Ethanol and 1-Propanol by the RIfS Array and the 4l Setup
    9.4. Quaternary Mixtures by the SPR Setup and the RIfS Array
      9.4.1. Introduction
      9.4.2. Results
      9.4.3. Conclusions
    9.5. Quantification of the Refrigerants R22 and R134a in Mixtures: Part II
  10. Results – Various Aspects of the Frameworks and Measurements
  11. Summary and Outlook
  12. References
  13. Acknowledgements
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9.4.2.   Results

For all data sets, several calibrations using the corresponding calibration data set were performed, whereby the predictions of the external validation data are summarized in table 8. First of all, calibrations were performed using all time channels of the SPR setup and all smoothed time channels of the 3 sensors of the RIfS array setup (1st and 5th row of table 8). Then the same data sets were used for the parallel growing neural network framework (2nd and 6th row). It is obvious that for both setups the framework significantly improves the calibration of all analytes. The SPR setup performs better on the calibration of methanol and ethanol and the RIfS array with 3 sensors performs better on the calibration of 1-propanol and 1-butanol whereby the overall mean predictions of the RIfS array with 3 sensors are better. The predictions of the calibration and the validation data are shown in figure 73 for the SPR setup (the neural networks had been optimized by the framework). For both setups, the framework selected time points spread over all sensors and over the complete process of sorption and desorption. An interesting point is the restriction of the available time points to a certain shorter time interval, which would correspond to faster measurements. The restriction of the data analysis for the SPR measurements to 240 seconds (120 seconds of sorption and 120 seconds of desorption) instead of 930 seconds hardly had a negative impact on the calibration, whereas the restriction to 120 seconds of sorption significantly decreased the calibration performance. Decreasing the analysis time of the RIfS array from 3470 seconds to 640 seconds deteriorated the prediction performance less than decreasing the analysis time from 640 seconds to 236 seconds, which corresponds to the sorption process only. This means that for both setups the measurement time can be drastically reduced without too high an impact on the prediction performance. Yet, it is important to consider not only the sorption process but also the beginning of the desorption process. This is consistent with most variable selections by the frameworks in the previous sections (8.4.1, 9.1.2, 9.2.3, 9.2.4 and 9.3.2) with only variables selected directly after the beginning of exposure to analyte and directly after the end of exposure to analyte (see also discussion in section 10.3).

  

figure 73:  True-predicted plots of the SPR setup using the optimized networks and the time points of the complete measurement time.

The effect of smoothing the sensor signals of the RIfS array was investigated for the singles sensor responses of the two Makrolon layers. Similar to section 9.3.2, the thinner 95 nm layer benefited from the smoothing whereas the thicker 165 nm layer was adversely affected by smoothing. The single sensor predictions of the RIfS array are all worse than the single sensor predictions of the SPR setup even with nearly 4 times longer measurement times of the RIfS setup. As already discussed in section 9.3.1, the RIfS setup, which primarily detects changes of the thickness d of the sensitive layer [260], is more affected by Makrolon mainly changing the refractive index n when exposed to analyte, than the SPR setup, which mainly detects changes of the refractive index n. Nevertheless, the comparison with the static sensor evaluation (only the highest sensor signals of each sensor), which is an undetermined system with 3 sensors for 4 analytes and which consequently shows very high prediction errors, demonstrates the potential of the time-resolved measurements also for the RIfS principle with many possibilities for further developments (last row of table 8).

Method

Meth.

Eth.

Prop.

But.

Mean

SPR, unoptimized

9.6

11.0

16.4

19.0

14.0

SPR, optimized

5.8

6.5

10.2

16.0

9.6

SPR, optimized, <240 s

5.4

4.5

12.7

20.4

10.7

SPR, optimized, <120 s

13.5

12.2

15.8

20.9

15.6

RIfS, 95 + 165 + PUT, unopt., smoothed

15.1

13.6

12.9

12.1

13.4

RIfS, 95 + 165 + PUT, opt., smoothed

10.1

10.0

8.2

6.5

7.3

RIfS, 95 + 165 + PUT, opt., sm., < 640 s

9.9

10.0

9.7

7.2

9.2

RIfS, 95 + 165 + PUT, opt., sm., < 236 s

14.1

12.8

12.2

9.1

12.1

RIfS, 95 optimized, raw

12.6

11.7

14.2

20.3

14.7

RIfS, 95 optimized, smoothed

12.5

10.5

12.6

18.1

13.4

RIfS, 165 optimized, raw

19.6

17.6

13.9

15.5

16.7

RIfS, 165 optimized, smoothed

22.1

19.6

15.8

18.1

18.9

RIfS, 95 + 165 + PUT, 1 static time point

43.8

43.9

41.1

22.5

37.8

table 8:      Relative RMSE of the validation data in %  for the 4 analytes and the mean using different data analysis methods, different setups and different constraints of time points (95 = 95 nm Makrolon layer, 165 = 165 nm Makrolon layer, PUT = PUT layer; optimized = growing neural network framework, unoptimized = all time channels, smoothed  / raw sensor signals).

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