Model Based Parameter Estimation: Theory and Applications

Cover......Page 1
Model Based Parameter Estimation......Page 4
Parameter Estimation in Image Processing and Computer Vision......Page 6
Appendix 2: Proof of Proposition 2......Page 8
Contents......Page 10
1 Introduction......Page 12
2 Differential Equation Models......Page 13
3 Parameter Estimation Problems......Page 15
4 Parameterization of the DAE by Multiple Shooting......Page 16
5 Derivative Evaluation......Page 19
6 Generalized Gauß–Newton Method......Page 20
7 Local Convergence of Newton Type Methods......Page 22
7.1.1 Gauß–Newton and SQP Method......Page 25
7.1.2 Small and Large Residuals......Page 26
7.1.3 Statistical Perturbation of the Problem......Page 28
8 Optimum Experimental Design......Page 29
8.1 Multiple Experiment Parameter Estimation Problem......Page 30
8.2 Statistical Uncertainty of the Parameter Estimate......Page 33
8.3 The Experimental Design Optimization Problem......Page 35
8.4.2 Modification for Robust Experimental Design w.r.t. Parameter Uncertainty......Page 37
8.5 Methods for the Numerical Solution......Page 38
9 Summary......Page 39
References......Page 40
1 Introduction......Page 42
2 Basic Concept......Page 43
3 Adaptivity for Parameter Estimation in Stationary Problems......Page 45
3.1 Finite Element Discretization......Page 46
3.2 A Posteriori Error Estimators......Page 48
3.3 Estimation of Arrhenius Parameters for a Stationary Combustion Model......Page 50
4 Adaptivity for Parameter Estimation in Nonstationary Problems......Page 53
4.1.1 Temporal Discretization......Page 54
4.1.2 Spatial Discretization......Page 55
4.2 A Posteriori Error Estimators......Page 56
4.3 Estimation of Model Parameters for Propagation of Laminar Flames......Page 57
5 Adaptivity for Optimal Choice of Regularization Parameters......Page 61
References......Page 64
1 Introduction......Page 66
2 Robust Parameter Estimation Problem......Page 67
2.1 The Least Absolute Deviations Estimator......Page 69
2.2 Huber\'s M-Estimator......Page 71
3.1 Local Convergence of Gauss–Newton for Nonlinear Constrained l1 Norm Optimization......Page 74
3.2 Local Convergence of Gauss–Newton for Nonlinear Constrained Huber Optimization......Page 76
4.1 Line Search Strategies......Page 80
4.2 Numerical Solution of the Linearized Problem......Page 81
5.1 Parameter Estimation for a Chemical Reaction......Page 82
5.2 Parameter Estimation for the NF-κB Pathway......Page 84
6 Conclusion......Page 87
References......Page 96
1.1 Distributed Sensor Networks and Sensor Management......Page 99
1.3 Sensor Location for Parameter Estimation in DPSs......Page 101
1.4 Related Approaches......Page 102
1.5 Results in This Contribution......Page 105
1.6 Notation......Page 106
2 D-Optimal Sensor Activation Problem......Page 107
3.1 Key Idea......Page 111
3.2 Branching Rule and BB Algorithm......Page 113
4.1 Optimality Conditions......Page 115
4.3 Simplicial Decomposition......Page 117
4.4 Solution of the Restricted Master Problem......Page 119
5 Numerical Example......Page 122
6 Conclusions......Page 126
References......Page 130
1 Biological Question......Page 136
2.1 Quantitative Immunoblotting Data......Page 137
2.2 Live Cell Imaging......Page 138
2.3.1 Fluorescence Correlation Spectroscopy......Page 139
3.1 Ordinary Differential Equations Model......Page 140
3.2 Parameter Estimation......Page 143
3.3 Reaction Diffusion Model......Page 146
4 Results......Page 149
5 Perspectives......Page 150
References......Page 153
1 Modeling and Parameter Estimation in Systems Biology......Page 154
2 Bayesian Parameter Estimation in Biological Systems......Page 156
2.1 Importance......Page 157
2.2 Challenges......Page 158
3 Bayesian Experimental Design in Systems Biology......Page 161
4 Summary and Outlook......Page 163
References......Page 164
1 Introduction......Page 167
2 The FRAP Experiment......Page 168
3.1 Spot Bleaching......Page 170
3.2 Analysis on Raw Image Data......Page 172
4.1 Bleaching Duration and Initial Conditions......Page 173
4.2 Sample Geometry......Page 174
4.4 Model Choice and Parameter Identifiability......Page 175
References......Page 176
1 Introduction......Page 179
2.2 Model Formulation......Page 181
2.2.1 Susceptible Human Population H1s......Page 182
2.2.2 Infected Human Population H1i......Page 183
2.2.5 Infected Vector Population H2i......Page 184
2.2.7 Resistant Parasite Population Pr......Page 185
3.2 Parameter Values......Page 187
3.3 Setup of Parameter Estimation Problem and Simulation Problem......Page 188
3.4 Result of Parameter Estimation......Page 190
3.5 Result of Simulation with Controllable Parameters......Page 192
3.5.2 Drug Regimens with Different Half-Lives......Page 193
3.5.3 Different Treatment Policies: Combined Control of α and d......Page 195
4 Conclusions......Page 196
4.2 Summary......Page 197
References......Page 198
1 Introduction......Page 199
2.1 Assumptions......Page 202
2.3 A Special Case......Page 203
2.3.1 Signal Feedback......Page 204
4 Simulation of Stem Cell Transplantation......Page 206
4.1 Comparison of Simulations to Clinical Data......Page 207
4.2 Application to Large Patient Groups......Page 208
4.3 Application to Clinical Scenarios......Page 210
5 Discussion......Page 211
References......Page 213
2 Description of Simplified Combustion Systems......Page 216
3 Mathematical Modeling of Homogeneous Combustion System......Page 217
4 Sensitivity Analysis and Mechanism Reduction......Page 220
5 Mechacut, a Practical Tool for Simplifying Reaction Mechanisms......Page 223
6 Parameter Estimation for Combustion Chemistry as an Optimization Problem......Page 225
References......Page 232
1 Background......Page 235
2 Fundamentals......Page 236
2.1 Heterogeneous Reaction Mechanisms......Page 237
2.2 Homogeneous Reactions......Page 239
2.3 Coupling of Chemistry and Mass and Heat Transport......Page 240
2.4 Monolithic Catalysts......Page 241
2.6 Mathematical Optimization of Reactor Conditions and  Catalyst Loading......Page 242
3.1 Synthesis Gas from Natural Gas by High-Temperature Catalysis......Page 243
3.2 Olefin Production by High-Temperature Oxidative Dehydrogenation of Alkanes......Page 244
3.2.1 Formulation of an Optimal Control Problem......Page 246
3.3 Hydrogen Production from Logistic Fuels by High-Temperature Catalysis......Page 248
4 Model Parameters......Page 251
References......Page 254
1 Introduction......Page 260
2.1 Continuity Equations......Page 261
2.2 Approximations to the Continuity Equations......Page 262
2.3 Boundary Conditions......Page 263
3 Experimental Setup......Page 265
4.1 Numerical Methods......Page 266
4.3 Initial and Boundary Values......Page 267
5.1 Intuitive Versus Optimal Design of Experiments......Page 268
5.3 Validation of the Model......Page 270
6 Summary and Outlook......Page 273
References......Page 274
1 Introduction......Page 275
2 Model......Page 277
2.1 Boundary Conditions......Page 278
2.3 Bulk Diffusion......Page 279
2.5 Charge Transfer......Page 280
2.8 Other Boundary Conditions......Page 281
3.1 Weak Formulation......Page 282
3.3 Approximation of the RVE......Page 283
4.1 Calibration of the Reduced Model......Page 284
4.2 Least-Squares Problem......Page 286
4.3 Confidence Regions......Page 287
5 Numerical Results......Page 288
6 Conclusion......Page 291
References......Page 292
1 Introduction......Page 294
2 The Modeling Cycle......Page 296
3.1 Classic Laboratory Measurements......Page 297
3.3 Remote Sensing Techniques......Page 298
3.4 Virtual Experiments: Direct Numerical Simulation in Fluid Dynamics......Page 299
4 Parameter Estimation from Experimental Data......Page 300
5.1 Setup and Basic Concept......Page 303
5.3 Modeling......Page 305
5.5 Formulating the Parameter Estimation Problem......Page 309
5.6 Results of the Parameter Estimation......Page 310
5.7 Optimal Experimental Design as Extension of the Modeling Cycle......Page 311
6 Summary......Page 312
References......Page 313
1 Introduction......Page 317
2.1 Optimization of Filter Kernels......Page 318
2.2 Optical Flow Estimation......Page 319
2.2.1 Global, Variational Methods for Optical Flow Estimation......Page 320
2.3 Confidence and Situation Measures for Optical Flows......Page 321
2.4 Image Restoration......Page 322
2.5 Optical Flow Reconstruction......Page 324
2.6 Motion Segmentation......Page 325
2.7 Joint Estimation of Optical Flow, Segmentation and  Denoising......Page 327
3.1 Key Modeling Decisions......Page 329
3.3 Object Detection in Cluttered Scenes......Page 332
References......Page 334