Numerical Data Fitting in Dynamical Systems

Transcription

1 Numerical Data Fitting in Dynamical Systems A Practical Introduction with Applications and Software by Klaus Schittkowski Department of Mathematics, University of Bayreuth, Bayreuth, Germany * * KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

2 Contents Preface xi 1. INTRODUCTION 1 2. MATHEMATICAL FOUNDATIONS 7 1 Optimality Criteria Notation Convexity and Constraint Qualification Necessary and Sufficient Optimality Criteria 10 2 Sequential Quadratic Programming Methods The Quadratic Programming Subproblem Line Search and Quasi-Newton Updates Convergence Systems of Nonlinear Equations 20 3 Least Squares Methods Optimality Conditions Gauss-Newton and Related Methods Solution of Least Squares Problems by SQP Methods Constrained Least Squares Optimization Alternative Norms 33 4 Numerical Solution of Ordinary Differential Equations Explicit Solution Methods Implicit Solution Methods Sensitivity Equations Internal Numerical Differentiation 46 5 Numerical Solution of Differential Algebraic Equations Algebraic Equations Index of a Differential Algebraic Equation Index Reduction and Drift Effect Projection Methods 55

3 V1U NUMERICAL DATA FITTING IN DYNAMICAL SYSTEMS 5.5 Consistent Initial Values Implicit Solution Methods 62 6 Numerical Solution of One-Dimensional Partial Differential Equations The General Time-Dependent Model Some Special Classes of Equations The Method of Lines Partial Differential Algebraic Equations Difference Formulae Polynomial Interpolation Upwind Formulae for Hyperbolic Equations Essentially Non-Oscillatory Schemes Systems of Hyperbolic Equations Sensitivity Equations Laplace Transforms Basic Properties Numerical Back-Transformation Automatic Differentiation Forward Mode Reverse Mode Statistical Interpretation of Results DATA FITTING MODELS Explicit Model Functions Laplace Transforms Steady State Equations Ordinary Differential Equations Standard Formulation Differential Algebraic Equations Switching Points Constraints Shooting Method Boundary Value Problems Variable Initial Times Partial Differential Equations Standard Formulation Partial Differential Algebraic Equations Flux Functions Coupled Ordinary Differential Algebraic Equations Integration Areas and Transition Conditions Switching Points 167

4 Contents ix 5.7 Constraints Optimal Control Problems NUMERICAL EXPERIMENTS Test Environment Numerical Pitfalls Local Solutions Slow Convergence Badly Scaled Data and Parameters Non-Identifiability of Models Errors in Experimental Data Inconsistent Constraints Non-Differentiable Model Functions Oscillating Model Functions Testing the Validity of Models Mass Balance and Steady State Analysis Statistical Analysis Constraints Performance Evaluation Comparing Least Squares Algorithms Individual Numerical Results CASESTUDIES Linear Pharmacokinetics Receptor-Ligand Binding Study Robot Design Multibody System of a Track Binary Distillation Column Acetylene Reactor Transdermal Application of Drugs Groundwater Flow Cooling a Hot Strip Mill Drying Maltodextrin in a Convection Oven Fluid Dynamics of Hydro Systems Hörn Radiators for Satellite Communication 278

5 X NUMERICAL DATA FITTING IN DYNAMICAL SYSTEMS Appendix A: Software Installation Hardware and Software Requirements System Setup Packing List 286 Appendix B: Test Examples Explicit Model Functions Laplace Transforms Steady State Equations Ordinary Differential Equations Differential Algebraic Equations Partial Differential Equations Partial Differential Algebraic Equations 331 Appendix C: The PCOMP Language 335 Appendix D: Generation of Fortran Code Model Equations Input of Explicit Model Functions Input of Laplace Transformations Input of Systems of Steady State Equations Input of Ordinary Differential Equations Input of Differential Algebraic Equations Input of Time-Dependent Partial Differential Equations Input of Partial Differential Algebraic Equations Execution of Generated Code 355 References 359 Index 387