Modeling and Optimization of Food and Bio-Processes

Gilles Trystram is Professor Emeritus at AgroParisTech and Managing Director of Genopole, France. His research areas include food and biotechnology processes, through their opimization, modeling and associated optimal control.Cristian Trelea is Professor at AgroParisTech, Université Paris-Saclay, France. His research areas include the dynamic modeling of physical, chemical and biological systems, for understanding phenomena, changing of scale and optimization and process control.

• General Introduction ixI.1. Why read this book? ixI.2. What is a model? xI.3. Why make models in process engineering? xiI.4. How to read this book? xivChapter 1. From Laws of Nature to Dynamic Models of Processes 11.1. General laws 11.2. Physical model: drying 21.2.1. Drying model at the scale of the individual grain or of the “thin layer” 31.3. Biological model: example of brewing fermentation 191.3.1. Alcoholic fermentation model 201.3.2. Aroma compounds production model 331.4. Conclusion on the writing models 37Chapter 2. Models and Their Parameters 412.1. Various quantities: constants and variables 412.2. How can parameters be found? A draft methodology 442.3. First set of plausible parameters 452.3.1. Example of thin layer drying 452.3.2. Example of brewing fermentation 552.4. A first simulation 632.4.1. Example of thin-layer drying of grains 632.4.2. Example of brewing fermentation 662.5. Which are the important parameters? A sensitivity analysis 692.5.1. Absolute sensitivity, relative sensitivity 692.5.2. Local sensitivity, global sensitivity 702.5.3. Linear scale, logarithmic scale 742.5.4. Example of the drying model 762.5.5. Example of brewing fermentation model 822.6. How to plan good dynamic experiments? 902.6.1. Example of a drying model 912.6.2. Example of brewing fermentation model 962.7. Conducting the experiments 1012.7.1. Example of the drying process 1012.7.2. Example of the fermentation process of brewing 1032.8. Data-based calibration of parameters 1062.8.1. A measure of the effective precision of the model 1082.8.2. A measure of the expected precision of the model 1092.8.3. Criterion for the calibration of the model 1102.8.4. Data for calibration and data for validation 1112.8.5. Example of the drying model 1122.8.6. Example of brewing fermentation 1232.9. In case things go wrong: classic pitfalls and traps 1472.9.1. Low-sensitivity parameters 1472.9.2. Strongly correlated parameters 1482.9.3. Very different orders of magnitude for the parameters 1492.9.4. Very high or very low order of magnitude for the calibration criterion 1512.9.5. Local optima during the optimization of parameters 1512.9.6. The optimized criterion does not reflect our real expectations 1542.10. Conclusion on the calibration of parameters 155Chapter 3. Dynamic Optimization of Processes Using Models 1573.1. Introduction 1573.2. Graphic optimization: construction of customized nomograms 1583.2.1. Example of the drying model 1593.2.2. Example of brewing fermentation model 1633.3. Multiobjective optimization: when the number of contradictory expectations and decision variables increases1653.3.1. How to compare solutions based on several criteria 1653.3.2. How to represent a dynamic optimization problem 1683.3.3. Example of the drying process 1713.3.4. Example of brewing fermentation process 1793.4. MCDM: when a single solution should be retained 1883.4.1. Human choice 1893.4.2. Automated choice 1903.4.3. Example of the drying process 1963.4.4. Example of brewing fermentation process 1973.5. Conclusion 201Chapter 4. Brief Overview of Several Numerical Methods 2034.1. Introduction 2034.2. Numerical resolution of differential equations 2044.2.1. Explicit schemes 2064.2.2. Implicit schemes 2064.2.3. Implicit form of differential equations 2074.2.4. Automatic management of the time step 2074.2.5. Precision of the solution 2084.2.6. Stiff equations 2094.2.7. Systems of algebraic-differential equations 2114.3. Numerical approximation of derivatives 2134.3.1. Unilateral finite differences 2144.3.2. Centered finite differences 2164.3.3. Polynomial approximation 2184.4. Numerical optimization 2204.4.1. A formalization of the optimization problem 2214.4.2. Several types of problems 2234.4.3. Several types of methods 2264.4.4. Important particular cases 2304.4.5. Several methods 2334.4.6. Optimization and models 2354.5. Estimation of confidence intervals for the parameters of the model 2384.5.1. Rapid estimation based on a local approximation 2394.5.2. Estimation based on random sampling 2414.5.3. What confidence is there in the confidence interval? 2444.5.4. Effect of a logarithmic transformation of parameters 2444.5.5. Accepting highly uncertain parameters 2454.6. Numerical libraries 2474.7. Conclusion 250General Conclusion 253C.1. What should be retained from this book? 253C.2. How to build a model 255C.3. How to keep a model alive 260C.4. How to go further 261References 263List of Authors 269Index 271