The craft of designing mathematical models of dynamic objects offers a large number of methods to solve subproblems in the design, typically parameter estimation, order determination, validation, model reduc tion, analysis of identifiability, sensi tivi ty and accuracy. There is also a substantial amount of process identification software available. A typi cal 'identification package' consists of program modules that implement selections of solution methods, coordinated by supervising programs, communication, and presentation handling file administration, operator of results. It is to be run 'interactively', typically on a designer's 'work station' . However, it is generally not obvious how to do that. Using interactive identification packages necessarily leaves to the user to decide on quite a number of specifications, including which model structure to use, which subproblems to be solved in each particular case, and in what or der. The designer is faced with the task of setting up cases on the work station, based on apriori knowledge about the actual physical object, the experiment conditions, and the purpose of the identification. In doing so, he/she will have to cope with two basic difficulties: 1) The com puter will be unable to solve most of the tentative identification cases, so the latter will first have to be form11lated in a way the computer can handle, and, worse, 2) even in cases where the computer can actually produce a model, the latter will not necessarily be valid for the intended purpose.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
29
29 s/w Abbildungen
XII, 365 p. 29 illus.
Dateigröße
ISBN-13
978-3-642-48618-0 (9783642486180)
DOI
10.1007/978-3-642-48618-0
Schweitzer Klassifikation
1: Introduction.- 1.1 The terminology.- 1.2 The software.- 1.3 The purpose.- 1.4 The experiment facilities.- 1.5 The model structure.- 1.6 The philosophy.- 2: Randomness, probability, and likelihood.- 2.1 Bayes' idea.- 2.2 The information contents of an experiment.- 2.3 Covariation and causality.- 3: The experiment.- 3.1 An introductory example.- 3.2 Requirements for proper experimentation.- 3.4 Dynamic systems.- 3.5 Experiments on dynamic objects.- 4: The identification problem.- 4.1 Validation and falsification.- 4.2 Model structures, data descriptions, and purposive models.- 4.3 Fitting.- 4.4 Basic identification procedures.- 4.5 Conditions for Bayesian validation.- 4.6 The origin of 'pitfalls'.- 5: Modelling.- 5.1 Parametrization.- 5.2 The parameter map.- 5.3 Algorithmic models.- 5.4 The modelling of dynamic systems.- 5.5 Internal and external models.- 5.6 Implicit and explicit models.- 5.7 Finite-memory models.- 5.8 Classification of models by purpose.- 5.9 'Black-box' and 'grey-box' models.- 6: Large-sample theory.- 6.1 Equivalent dynamic models.- 6.2 Consistency.- 6.3 Identifiability.- 6.4 Falsification in the limit.- 6.5 Proper 'black-box' identification.- 6.6 A concluding example.- 7: Validation techniques.- 7.1 Validating parametric models.- 7.2 Large-sample techniques.- 7.3 Two 'pitfalls'.- 8: Falsification techniques.- 8.1 Statistical tests.- 8.2 Unconditional falsification.- 8.3 Conditional falsification of models.- 8.4 Conditional falsification of structures.- 8.5 The Likelihood-Ratio test.- 8.6 Efficiency vs safety.- 9: Structure identification.- 9.1 Using the biassed Likelihood.- 9.2 Sequential falsification.- 9.3 Philosophy revisited: Equivalence vs goodness.- 9.4 Designing the criterion: Description vs purpose.- 9.5 Defining theoptimal order: Accuracy vs complexity.- 9.6 Model structure selection.- 9.7 Terminology revisited.- 10: A unified design procedure.- 10.1 Summary of conditions for proper identification.- 10.2 Identification procedures.- 10.3 Procedure for modelling and identification.- References.- Glossary of notations.
