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Ph. D. ThesisPh. D. Thesis 9. Results  All Data Sets9. Results All Data Sets 9.2. Methanol, Ethanol and 1-Propanol by SPR9.2. Methanol, Ethanol and 1-Propanol by SPR 9.2.2. Multivariate Calibrations of the Mixtures9.2.2. Multivariate Calibrations of the Mixtures
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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
      9.2.1. Single Analytes
      9.2.2. Multivariate Calibrations of the Mixtures
      9.2.3. Genetic Algorithm Framework
      9.2.4. Parallel Growing Neural Network Framework
      9.2.5. PCA-NN
      9.2.6. Conclusions
    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
    9.5. 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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9.2.2.   Multivariate Calibrations of the Mixtures

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.

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