Interactive System Identification: Prospects and Pitfalls

ISBN-13: 9783642486203 / Angielski / Miękka / 2012 / 365 str.

Torsten Bohlin

Opis

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.

Spis treści

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.- 2.3.1 A theory for hidden variables.- 2.3.2 Probabilistic models.- 3: The experiment.- 3.1 An introductory example.- 3.2 Requirements for proper experimentation.- 3.2.1 Sufficient stimulation.- 3.2.2 Reproducibility.- 3.2.3 Separability.- 3.4 Dynamic systems.- 3.4.1 Large samples.- 3.5 Experiments on dynamic objects.- 3.5.1 Closed vs open loop.- 3.5.2 Cases of proper experiments.- 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.- 4.4.1 Two general algorithms.- 4.5 Conditions for Bayesian validation.- 4.6 The origin of ‘pitfalls’.- 4.6.1 The consequences of unvalidatability.- 4.6.2 Purposive models without validation.- 4.6.3 Sources of information for model design.- 5: Modelling.- 5.1 Parametrization.- 5.1.1 Integer parameters.- 5.1.2 The parameter distribution.- 5.2 The parameter map.- 5.3 Algorithmic models.- 5.4 The modelling of dynamic systems.- 5.4.1 Linear vs nonlinear models.- 5.5 Internal and external models.- 5.5.1 External models.- 5.5.2 Innovations.- 5.5.3 Internal models.- 5.5.4 Discrete-time vs continuous-time models.- 5.6 Implicit and explicit models.- 5.7 Finite-memory models.- 5.7.1 Internal stale-vector models.- 5.8 Classification of models by purpose.- 5.9 ‘Black-box’ and ‘grey-box’ models.- 5.9.1 The requirements of the control purpose.- 5.9.2 The ‘black-box’ approach.- 5.9.3 The approach of separating disturbances.- 5.9.4 The ‘grey-box’ approach.- 6: Large-sample theory.- 6.1 Equivalent dynamic models.- 6.2 Consistency.- 6.2.1 The structured approach.- 6.2.2 The unstructured approach.- 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.- 7.2.1 Approximations.- 7.2.2 Validating sufficient accuracy.- 7.3 Two ‘pitfalls’.- 8: Falsification techniques.- 8.1 Statistical tests.- 8.2 Unconditional falsification.- 8.2.1 Testing the parameter-free statistics.- 8.3 Conditional falsification of models.- 8.3.1 Asymptotic confidence regions.- 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.- 9.2.1 Sequence of conditional tests.- 9.2.2 Sequence of Likelihood-Ratio tests.- 9.2.3 Sequence of unconditional tests.- 9.3 Philosophy revisited: Equivalence vs goodness.- 9.4 Designing the criterion: Description vs purpose.- 9.5 Defining the optimal order: Accuracy vs complexity.- 9.5.1 Approximating the expected loss.- 9.5.2 Other ‘modern’ principles for determining complexity.- 9.5.3 The Bayesian approach.- 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.