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Full Description
Models have become an indispensable tool for scientists and engineers alike. For the scientist, a model makes it possible to quantitatively test hypotheses, understand phenomena, and, if necessary, revise them until a satisfactory agreement with experiments is reached. For the engineer, a technical object is nowadays designed, tested and optimized in simulation long before its physical birth. In all cases, modeling is an important gas pedal of research and engineering, and a tool for competitiveness in the modern world.
Modeling and Optimization of Food and Bio-Processes is aimed at anyone with a grounding in process, chemical or microbiological engineering, as well as students of these disciplines. Drawing on the authors' extensive teaching and research experience, this book is designed to teach engineers and scientists the main concepts and the right reflexes to adopt when embarking on the noble art of modeling.
Contents
General Introduction ix
I.1. Why read this book? ix
I.2. What is a model? x
I.3. Why make models in process engineering? xi
I.4. How to read this book? xiv
Chapter 1. From Laws of Nature to Dynamic Models of Processes 1
1.1. General laws 1
1.2. Physical model: drying 2
1.2.1. Drying model at the scale of the individual grain or of the "thin layer" 3
1.3. Biological model: example of brewing fermentation 19
1.3.1. Alcoholic fermentation model 20
1.3.2. Aroma compounds production model 33
1.4. Conclusion on the writing models 37
Chapter 2. Models and Their Parameters 41
2.1. Various quantities: constants and variables 41
2.2. How can parameters be found? A draft methodology 44
2.3. First set of plausible parameters 45
2.3.1. Example of thin layer drying 45
2.3.2. Example of brewing fermentation 55
2.4. A first simulation 63
2.4.1. Example of thin-layer drying of grains 63
2.4.2. Example of brewing fermentation 66
2.5. Which are the important parameters? A sensitivity analysis 69
2.5.1. Absolute sensitivity, relative sensitivity 69
2.5.2. Local sensitivity, global sensitivity 70
2.5.3. Linear scale, logarithmic scale 74
2.5.4. Example of the drying model 76
2.5.5. Example of brewing fermentation model 82
2.6. How to plan good dynamic experiments? 90
2.6.1. Example of a drying model 91
2.6.2. Example of brewing fermentation model 96
2.7. Conducting the experiments 101
2.7.1. Example of the drying process 101
2.7.2. Example of the fermentation process of brewing 103
2.8. Data-based calibration of parameters 106
2.8.1. A measure of the effective precision of the model 108
2.8.2. A measure of the expected precision of the model 109
2.8.3. Criterion for the calibration of the model 110
2.8.4. Data for calibration and data for validation 111
2.8.5. Example of the drying model 112
2.8.6. Example of brewing fermentation 123
2.9. In case things go wrong: classic pitfalls and traps 147
2.9.1. Low-sensitivity parameters 147
2.9.2. Strongly correlated parameters 148
2.9.3. Very different orders of magnitude for the parameters 149
2.9.4. Very high or very low order of magnitude for the calibration criterion 151
2.9.5. Local optima during the optimization of parameters 151
2.9.6. The optimized criterion does not reflect our real expectations 154
2.10. Conclusion on the calibration of parameters 155
Chapter 3. Dynamic Optimization of Processes Using Models 157
3.1. Introduction 157
3.2. Graphic optimization: construction of customized nomograms 158
3.2.1. Example of the drying model 159
3.2.2. Example of brewing fermentation model 163
3.3. Multiobjective optimization: when the number of contradictory expectations and decision variables increases
165
3.3.1. How to compare solutions based on several criteria 165
3.3.2. How to represent a dynamic optimization problem 168
3.3.3. Example of the drying process 171
3.3.4. Example of brewing fermentation process 179
3.4. MCDM: when a single solution should be retained 188
3.4.1. Human choice 189
3.4.2. Automated choice 190
3.4.3. Example of the drying process 196
3.4.4. Example of brewing fermentation process 197
3.5. Conclusion 201
Chapter 4. Brief Overview of Several Numerical Methods 203
4.1. Introduction 203
4.2. Numerical resolution of differential equations 204
4.2.1. Explicit schemes 206
4.2.2. Implicit schemes 206
4.2.3. Implicit form of differential equations 207
4.2.4. Automatic management of the time step 207
4.2.5. Precision of the solution 208
4.2.6. Stiff equations 209
4.2.7. Systems of algebraic-differential equations 211
4.3. Numerical approximation of derivatives 213
4.3.1. Unilateral finite differences 214
4.3.2. Centered finite differences 216
4.3.3. Polynomial approximation 218
4.4. Numerical optimization 220
4.4.1. A formalization of the optimization problem 221
4.4.2. Several types of problems 223
4.4.3. Several types of methods 226
4.4.4. Important particular cases 230
4.4.5. Several methods 233
4.4.6. Optimization and models 235
4.5. Estimation of confidence intervals for the parameters of the model 238
4.5.1. Rapid estimation based on a local approximation 239
4.5.2. Estimation based on random sampling 241
4.5.3. What confidence is there in the confidence interval? 244
4.5.4. Effect of a logarithmic transformation of parameters 244
4.5.5. Accepting highly uncertain parameters 245
4.6. Numerical libraries 247
4.7. Conclusion 250
General Conclusion 253
C.1. What should be retained from this book? 253
C.2. How to build a model 255
C.3. How to keep a model alive 260
C.4. How to go further 261
References 263
List of Authors 269
Index 271
