Parameter estimation in nonlinear dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Stichting Mathematisch Centrum
1998
|
| Schriftenreihe: | CWI Tract
124 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 176 S. graph. Darst. |
| ISBN: | 9061964822 |
Internformat
MARC
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| 100 | 1 | |a Stortelder, Walter J. H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Parameter estimation in nonlinear dynamical systems |c W. J. H. Stortelder |
| 264 | 1 | |a Amsterdam |b Stichting Mathematisch Centrum |c 1998 | |
| 300 | |a VI, 176 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804133007891628032 |
|---|---|
| adam_text | Contents
Contents i
Nomenclature v
1 Introduction and Outline 1
1.1 Mathematical formulation 4
1.2 Fitness criterion 5
1.3 Variational equations 5
1.4 Numerical solution of the model equations 7
1.5 Minimisation 8
1.6 Statistical background 9
1.7 Parameter constraints 12
1.8 A case study from biochemistry 13
1.9 A case study from population dynamics 14
1.10 Concluding remarks 16
Appendix l.A 16
Appendix l.B 16
Appendix l.C 17
2 Parameter Estimation by Total Least Squares 21
2.1 Introduction 21
2.2 Mathematical description of TLS 22
2.3 Statistical background 25
2.4 Total least squares with parameter constraints 26
2.5 Conclusions 28
3 Maximum Likelihood Estimators 29
3.1 Introduction 29
3.2 Least squares criterion 29
3.3 Weighted least squares criterion 31
3.3.1 A priori known weights 31
3.3.2 Unknown weights 31
3.4 Numerical computation (independent case) 35
3.5 Dependent measurement errors 37
3.6 Numerical computation (dependent case) 39
3.7 MLE and total least squares 41
ii Contents
3.7.1 A priori known weights 41
3.7.2 Unknown weights (TLS) 42
3.7.3 Independent measurement errors 42
3.7.4 Dependent measurement errors 43
3.8 L optimisation and Laplace distribution 44
3.9 Conclusions 45
4 Nonlinear Regression, Bias and Curvature 47
4.1 Overview of the chapter 47
4.2 Linear Regression 48
4.3 Biased estimators 50
4.3.1 Analytic result 50
4.3.2 Monte Carlo 52
4.3.3 Bias measure of Box 53
4.4 Curvature measures 54
4.5 Investigation of levelsets 62
4.6 Parameter constraints and redundancy 63
4.7 Concluding remarks 64
5 Optimal Experiment Design 67
5.1 Introduction 67
5.2 Problem formulation 67
5.3 Parameter state variable dependence 69
5.4 OED and improved confidence regions 72
5.4.1 Design criteria 72
5.4.2 Repeated design 73
5.4.3 Sequential design 75
5.5 OED and model discrimination 78
5.6 OED and nonlinearity 79
5.7 Concluding remarks 79
6 Case Studies 81
6.1 Production of resins 81
6.1.1 Introduction 81
6.1.2 Reaction mechanism 82
6.1.3 Experiments performed 83
6.1.4 Model equations 84
6.1.5 Treatment of the melamine concentrations 85
6.1.6 Parameter estimation 86
6.1.7 Reparametrisation and results 86
6.1.8 Conclusions 91
6.2 Modelling of blood coagulation 94
6.2.1 Introduction 94
6.2.2 Experimental data 95
6.2.3 Reaction mechanism 96
Contents iii
6.2.4 Model equations 98
6.2.5 Parameter estimation and model validation 100
6.2.6 Results 102
6.2.7 Conclusions 103
6.3 Production by plant cells in suspension 106
6.3.1 Introduction 106
6.3.2 Materials and methods 107
6.3.3 Model development 108
6.3.4 Experimental results and final model confirmation ... Ill
6.3.5 Conclusions 116
6.4 ZLA kinetics 119
6.4.1 Description of the chemical reactions 119
6.4.2 Problem description of ZLA kinetics 120
6.4.3 Parameter estimation results for ZLA kinetics 121
6.4.4 Conclusions and remarks for further research 123
6.5 Water penetration in an aramide yarn 124
6.5.1 Introduction to the problem 124
6.5.2 Proposed models 124
6.5.3 Numerical implementation 126
6.5.4 Model discrimination and parameter estimation 126
6.5.5 Conclusions 128
6.6 Macroeconomic time series 130
6.6.1 Introduction 130
6.6.2 Derivation of candidate models 130
6.6.3 Comparison of prediction results 132
6.6.4 Concluding remarks 133
6.7 The DOW problem 134
6.7.1 Introduction 134
6.7.2 Description of the problem 134
6.7.3 Data 136
6.7.4 Results 136
6.7.5 More general model equations 140
6.7.6 Concluding remarks 142
Appendix 6.A 145
Appendix 6.B 149
7 Software Design and Implementation 151
7.1 Introduction 151
7.2 Design principles of the application splds 152
7.3 Structure of the software 154
7.4 Themodelfile 155
7.5 The datafile 160
7.6 Algebraic Engine 162
7.7 Filter 163
iv Contents
7.8 Numerical engine 163
7.9 Graphical user interface (GUI) 164
7.10 Database manager 165
7.11 Concluding remarks 166
Bibliography 167
Index 173
|
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| id | DE-604.BV019637425 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:52Z |
| institution | BVB |
| isbn | 9061964822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012966381 |
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| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | VI, 176 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Stichting Mathematisch Centrum |
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| series | CWI Tract |
| series2 | CWI Tract |
| spelling | Stortelder, Walter J. H. Verfasser aut Parameter estimation in nonlinear dynamical systems W. J. H. Stortelder Amsterdam Stichting Mathematisch Centrum 1998 VI, 176 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CWI Tract 124 CWI Tract 124 (DE-604)BV001902011 124 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012966381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stortelder, Walter J. H. Parameter estimation in nonlinear dynamical systems CWI Tract |
| title | Parameter estimation in nonlinear dynamical systems |
| title_auth | Parameter estimation in nonlinear dynamical systems |
| title_exact_search | Parameter estimation in nonlinear dynamical systems |
| title_full | Parameter estimation in nonlinear dynamical systems W. J. H. Stortelder |
| title_fullStr | Parameter estimation in nonlinear dynamical systems W. J. H. Stortelder |
| title_full_unstemmed | Parameter estimation in nonlinear dynamical systems W. J. H. Stortelder |
| title_short | Parameter estimation in nonlinear dynamical systems |
| title_sort | parameter estimation in nonlinear dynamical systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012966381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT stortelderwalterjh parameterestimationinnonlineardynamicalsystems |