Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software

ISBN-13: 9781475760507 / Angielski / Miękka / 2013 / 396 str.

Klaus Schittkowski

Opis

Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Spis treści

Preface. 1: Introduction. 2. Mathematical Foundations. 1. Optimality Criteria. 2. Sequential Quadratic Programming Methods. 3. Least Squares Methods. 4. Numerical Solution of Ordinary Differential Equations. 5. Numerical Solution of Differential Algebraic Equations. 6. Numerical Solution of One-Dimensional Partial Differential Equations. 7. Laplace Transforms. 8. Automatic Differentiation. 9. Statistical Interpretation of Results. 3: Data Fitting Models. 1. Explicit Model Functions. 2. Laplace Transforms. 3. Steady State Equations. 4.Ordinary Differential Equations. 5. Partial Differential Equations. 6. Optimal Control Problems. 4: Numerical Experiments. 1. Test Environment. 2. Numerical Pitfalls. 3. Testing the Validity of Models. 4. Performance Evaluation. 5: Case Studies. 1. Linear Pharmacokinetics. 2. Receptor-Ligand Binder Study. 3. Robot Design. 4. Multibody System of a Truck. 5. Binary Distillation Column. 6. Acetylene Reactor. 7. Transdermal Application of Drugs. 8. Groundwater Flow. 9. Cooling a Hot Strip Mill. 10. Drying Maltodextrin in a Convection Oven. 11. Fluid Dynamics of Hydro Systems. Appendix A: Software Installation. 1. Hardware and Software Requirements. 2. System Setup. 3. Packing List. Appendix B: Test Examples. 1. Explicit Model Functions. 2. Laplace Transforms. 3. Steady State Equations. 4. Ordinary Differential Equations. 5. Differential Algebraic Equations. 6. Partial Differential Equations. 7. Partial Differential Algebraic Equations. Appendix C: The PCOMP Language. Appendix D: Generation of Fortran Code. 1. Model Equations. 2. Execution of Generated Code. References. Index.