Foreword vii
Prologue: Challenges for the Third Millennium ix
1 Introduction 1
1.1 Industrial Batch Processes 1
1.2 Types of Sensors 3
1.3 Batch Process Modeling 5
1.3.1 Knowledge-based Models 5
1.3.2 Data-driven Models 6
1.3.3 Hybrid Models 7
1.4 Bilinear Modeling Cycle for Batch Process Monitoring 7
2 Data-driven Models Based on Latent Variables 13
2.1 Compression 13
2.2 Principal Component Analysis 18
2.2.1 Data Preprocessing 21
2.2.2 Selection of the Number of Principal Components 26
2.2.3 Parameters Stability 30
2.3 Regression 33
2.4 Regression Models Based on Latent Variables 35
2.4.1 Principal Component Regression 35
2.4.2 Partial Least Squares 36
2.4.3 Data Preprocessing 38
2.4.4 Selection of the Number of Latent Variables 41
2.4.5 PLS Versus Other Regression Models 42
2.5 Multivariate Exploratory Data Analysis 43
2.6 Missing Data 46
2.6.1 Model Exploitation 47
2.6.2 Model Building 52
2.6.3 Final Reflections About Missing Data Imputation and MSPC 52
3 Batch Data Equalization 55
3.1 Introduction 55
3.2 Challenges in Batch Equalization 56
3.3 Equalization of Variables Within a Batch 59
3.3.1 Discarding Intermediate Values 62
3.3.2 Estimating Missing Values 64
3.3.2.1 Comparison of Equalization Methods Based on Latent Variable Models 70
3.3.3 Rearranging Data 71
3.4 Multirate System 74
4 Batch Synchronization 79
4.1 Introduction 79
4.2 Synchronization Approaches 81
4.2.1 Indicator Variable 83
4.2.2 Time Linear Expanding/Compressing 87
4.2.2.1 Observation (OWU) Level and TLEC Synchronization Approach 89
4.2.3 Dynamic Time Warping 90
4.2.3.1 Warping Function Constraints 92
4.2.3.2 The DTW Algorithm 94
4.2.3.3 Optimization Problem 95
4.2.3.4 End-of-batch DTW Synchronization for Batch Process Monitoring 97
4.2.3.5 On the Use of Warping Information 100
4.2.4 Relaxed Greedy Time Warping 105
4.2.4.1 Enhanced Global Constraints 107
4.2.4.2 Cross-validation for the Estimation of the RGTW Parameters 110
4.2.5 Multisynchro 114
4.2.5.1 Asynchronism Detection 115
4.2.5.2 Specific Batch Synchronization 117
4.2.5.3 Iterative Batch Synchronization and Anomaly Detection Procedure 120
4.3 Effects of Synchronization on the Correlation Structure 129
5 Batch Data Preprocessing 141
5.1 Batch Preprocessing Operations 141
5.2 Mean Centering 143
5.3 Scaling 144
6 Three-way to Two-way Transformation 149
6.1 Introduction 149
6.2 Single-model Approach 150
6.2.1 Batch-wise Unfolding 150
6.2.2 Variable-wise Unfolding 156
6.2.3 Batch Dynamic Unfolding 160
6.3 K-models Approach 162
6.3.1 Hierarchical-model Approach 168
6.4 Multiphase Approach 171
6.4.1 Phases in Batch-wise Data 172
6.4.2 Phases in Variable-wise Data 175
6.4.3 Phases in Batch Dynamic Data 177
6.5 Conclusion 178
7 Batch Process Data Analysis and Statistical Monitoring 181
7.1 Introduction 181
7.2 Historical Batch Data Analysis 181
7.3 Batch Multivariate Statistical Process Control 186
7.3.1 Phase I 186
7.3.2 Phase II 187
7.3.2.1 Post-batch Process Monitoring 187
7.3.2.2 Real-time Process Monitoring 188
7.4 Practical Issues 190
List of Acronyms 197
Bibliography 199
Index 211
