Table of Contents
1. Introduction
1.1. Outline
2. Theory – Fundamentals of the Multivariate Data Analysis
2.1. Overview of the Multivariate Quantitative Data Analysis
2.2. Experimental Design
2.3. Data Preprocessing
2.4. Data Splitting and Validation
2.4.1. Crossvalidation
2.4.2. Bootstrapping
2.4.3. Random Subsampling
2.4.4. Kennard Stones
2.4.5. Kohonen Neural Networks
2.4.6. Conclusions
2.5. Calibration of Linear Relationships
2.5.1. PLS
2.6. Calibration of Nonlinear Relationships
2.7. Neural Networks – Universal Calibration Tools
2.7.1. Principles of Neural Networks
2.7.2. Topology of Neural Networks
2.7.3. Training of Neural Networks
2.8. Too Much Information Deteriorates Calibration
2.8.1. Overfitting, Underfitting and Model Complexity
2.8.2. Neural Networks and the Complexity Problem
2.8.3. Brute Force Variable Selection
2.8.4. Variable Selection by Stepwise Algorithms
2.8.5. Variable Selection by Genetic Algorithms
2.8.6. Variable Selection by Simulated Annealing
2.8.7. Variable Compression by Principal Component Analysis
2.8.8. Topology Optimization by Pruning Algorithms
2.8.9. Topology Optimization by Genetic Algorithms
2.8.10. Topology Optimization by Growing Neural Network Algorithms
2.9. Measures of Error and Validation
3. Theory – Quantification of the Refrigerants R22 and R134a: Part I
3.1. Experimental
3.2. Single Analytes
3.3. Sensitivities
3.4. Calibrations of the Mixtures
3.5. Variable Selection by Brute Force
3.6. Conclusions
4. Experiments, Setups and Data Sets
4.1. The Sensor Principle
4.2. SPR Setup
4.3. RIfS Sensor Array
4.4. 4l Miniaturized RIfS Sensor
4.5. Data Sets
4.5.1. Refrigerants R22 and R134a
4.5.1.1. R22 and R134a by the SPR Setup
4.5.1.2. R22 and R134a by the RIfS Array and the 4l-Setup
4.5.2. Homologous Series of the Low Alcohols
4.5.2.1. Methanol and Ethanol by the SPR Setup
4.5.2.2. Methanol, Ethanol and Propanol by the SPR Setup
4.5.2.3. Methanol, Ethanol and Propanol by the RIfS Array and the 4l Setup
4.5.2.4. Quaternary Mixtures of Alcohols by the RIfS Array and the SPR Setup
5. Results – Kinetic Measurements
5.1. Static Sensor Measurements
5.2. Time-resolved Sensor Measurements
5.3. Makrolon – A Polymer for Time-resolved Measurements
5.3.1. General Properties of Makrolon
5.3.2. Time-resolved Measurements
5.3.3. Thickness of the Sensitive Layer
5.3.4. Influence of the Carrier Gas
5.4. Conclusions
6. Results – Multivariate Calibrations
6.1. PLS Calibration
6.1.1. Wald-Wolfowitz Runs Test
6.1.2. Durbin-Watson Statistics
6.1.3. Results of Statistical Tests
6.2. Box-Cox Transformation + PLS
6.3. INLR
6.4. QPLS
6.5. CART
6.6. Model Trees
6.7. MARS
6.8. Neural Networks
6.9. PCA-NN
6.10. Neural Networks and Pruning
6.11. Conclusions
7. Results – Genetic Algorithm Framework
7.1. Single Run Genetic Algorithm
7.2. Genetic Algorithm Framework - Theory
7.3. Genetic Algorithm Framework - Results
7.4. Genetic Algorithm Framework – Conclusions
8. Results – Growing Neural Network Framework
8.1. Modifications of the Growing Neural Network Algorithm
8.2. Application of the Growing Neural Networks
8.3. Growing Neural Network Algorithm Frameworks
8.4. Applications of the Growing Neural Network Frameworks
8.4.1. Parallel Framework
8.4.2. Loop-based Framework
8.5. Conclusions and Comparison of the Different Methods
9. Results – All Data Sets
9.1. Methanol and Ethanol by SPR
9.1.1. Single Analytes
9.1.2. Parallel Growing Neural Network Framework
9.1.3. Sensitivity Analysis
9.1.4. Brute Force Variable Selection
9.1.5. Conclusions
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
9.3.1. Signals and Data Preparation
9.3.2. Mixtures by the RIfS Array
9.3.3. Mixtures by the 4l Setup
9.3.4. Conclusions
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
10.1. Single or Multiple Analyte Rankings
10.2. Stopping Criteria for the Parallel Frameworks
10.3. Optimization of the Measurements
10.4. Robustness and Comparison with Martens' Uncertainty Test
11. Summary and Outlook
12. References
13. Acknowledgements
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Ph. D. Thesis