Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
How Accurate Can Instrumental Variable Models Become? Kapitel lesen Erstes Kapitel lesen

2012 | OriginalPaper | Buchkapitel

3. Identifiability, and Beyond

verfasst von : Eric Walter

Erschienen in: System Identification, Environmental Modelling, and Control System Design

Verlag: Springer London

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter is aimed at helping readers decide whether identifiability and the closely connected property of distinguishability are theoretically important and practically relevant for their research or teaching. If this is so, they will find here methods that can be used to test models for these properties. The chapter also shows that measures of identifiability can be maximized, provided that there are some degrees of freedom in the procedure for data collection. If the model of interest cannot be made identifiable, all may not be lost, as we shall see. A large part of the presentation is tutorial in nature, with academic examples worked out in detail.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Refined Instrumental Variable Methods for Hammerstein Box-Jenkins Models
Nächstes Kapitel Model Structure Identification and the Growth of Knowledge
Literatur
1.
Bellman, R., Aström, K.J.: On structural identifiability. Math. Biosci. 7, 329–339 (1970) CrossRef
2.
Bellu, G., Saccomani, M.P., Audoly, S., D’Angio, L.: DAISY: a new software tool to test global identifiability of biological and physiological systems. Comput. Methods Programs Biomed. 88, 52–61 (2007) CrossRef
3.
Berman, M., Schoenfeld, R.: Invariants in experimental data on linear kinetics and the formulation of models. J. Appl. Phys. 27(11), 1361–1370 (1956) CrossRef
4.
Berthier, F., Diard, J.P., Pronzato, L., Walter, E.: Identifiability and distinguishability concepts in electrochemistry. Automatica 32(7), 973–984 (1996) MathSciNetMATHCrossRef
5.
Berz, M., Makino, K.: Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliab. Comput. 4(4), 361–369 (1998) MathSciNetMATHCrossRef
6.
Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Computing representations for radicals of finitely generated differential ideals. Tech. Rep. IT306, LIFL (1997)
7.
Braems, I., Berthier, F., Jaulin, L., Kieffer, M., Walter, E.: Guaranteed estimation of electrochemical parameters by set inversion. J. Electroanal. Chem. 495(1), 1–9 (2001)
8.
Buchberger, B.: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleischungssystems. Aequ. Math. 4, 374–383 (1970) MathSciNetMATHCrossRef
9.
Chappell, M.J., Godfrey, K.R., Vajda, S.: Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. Math. Biosci. 102, 41–73 (1990) MATHCrossRef
10.
Chernoff, H.: Approaches in sequential design of experiments. In: Srivasta, J. (ed.) Survey of Statistical Design and Linear Models, pp. 67–90. North-Holland, Amsterdam (1975)
11.
D’Argenio, D.Z.: Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments. Math. Biosci. 99, 105–118 (1990) MathSciNetMATHCrossRef
12.
Fedorov, V.V.: Theory of Optimal Experiments. Academic Press, New York (1972)
13.
Fedorov, V.V., Atkinson, A.C.: The optimum design of experiments in the presence of uncontrolled variability and prior information. In: Dodge, Y., Fedorov, V.V., Wynn, H.P. (eds.) Optimal Design and Analysis of Experiments. North-Holland, Amsterdam (1988)
14.
15.
16.
Ford, I., Silvey, S.D.: A sequentially constructed design for estimating a nonlinear parametric function. Biometrika 67(2), 381–388 (1980) MathSciNetMATHCrossRef
17.
Glover, K., Willems, J.C.: Parametrizations of linear dynamical systems: canonical forms and identifiability. IEEE Trans. Autom. Control 19, 640–644 (1974) MathSciNetMATHCrossRef
18.
Godfrey, K.: Compartmental Models and Their Application. Academic Press, London (1983)
19.
Goodwin, G.C., Payne, R.: Dynamic System Identification: Experiment Design and Data Analysis. Academic Press, New York (1977) MATH
20.
Hansen, E.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (1992) MATH
21.
Happel, J., Walter, E., Lecourtier, Y.: Isotopic assessment of fundamental catalytic mechanisms by kinetic modeling. I&EC Fund. 25, 704–712 (1986) CrossRef
22.
Hoekens, J., Berz, M., Makino, K.: Efficient high-order methods for ODEs and DAEs. In: Corliss, G., Faure, C., Griewank, A. (eds.) Automatic Differentiation: From Simulation to Optimization, pp. 341–351. Springer, New York (2001)
23.
Jacquez, J.A.: Compartmental Analysis in Biology and Medicine. University of Michigan Press, Ann Arbor (1985)
24.
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001) MATH
25.
Jaulin, L., Walter, E.: Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica 29, 1053–1064 (1993) MathSciNetMATHCrossRef
26.
Kieffer, M., Walter, E.: Interval analysis for guaranteed nonlinear parameter and state estimation. Math. Comput. Model. Dyn. Syst. 11(2), 171–181 (2005) MathSciNetMATH
27.
Kieffer, M., Walter, E.: Guaranteed estimation of the parameters of nonlinear continuous-time models: contributions of interval analysis. Int. J. Adapt. Control Signal Process. 25(3), 191–207 (2011) MathSciNetMATHCrossRef
28.
Kolchin, E.: Differential Algebra and Algebraic Groups. Academic Press, San Diego (1973) MATH
29.
Koopmans, T.C., Reiersøl, O.: The identification of structural characteristics. Ann. Math. Stat. 21(2), 165–181 (1950) MATHCrossRef
30.
31.
Lohner, R.: Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems. In: Cash, J., Gladwell, I. (eds.) Computational Ordinary Differential Equations, pp. 425–435. Clarendon Press, Oxford (1992)
32.
Margaria, G., Riccomagno, E., Chappell, M.J., Wynn, H.P.: Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences. Math. Biosci. 174 (2001)
33.
Milanese, M., Norton, J., Piet-Lahanier, H., Walter, E. (eds.): Bounding Approaches to System Identification. Plenum, New York (1996) MATH
34.
Mitchell, T.J.: An algorithm for the construction of “D-optimal” experimental designs. Technometrics 16, 203–210 (1974) MathSciNetMATHCrossRef
35.
Moore, R.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979) MATH
36.
Müller, M.: Uber das Fundamentaltheorem in der Theory der gewöhlichen Differentielgleichungen. Math. Z. 26, 619–645 (1926) CrossRef
37.
Nedialkov, N.S., Jackson, K.R.: Methods for initial value problems for ordinary differential equations. In: Kulisch, U., Lohner, R., Facius, A. (eds.) Perspectives on Enclosure Methods, pp. 219–264. Springer, Vienna (2001) CrossRef
38.
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990) MATH
39.
Norton, J.: Special issue on bouded-error estimation: Issue 1. Int. J. Adapt. Control Signal Process. 8(1), 1–118 (1994) CrossRef
40.
Norton, J.: Special issue on bouded-error estimation: Issue 2. Int. J. Adapt. Control Signal Process. 9(1), 1–132 (1995) CrossRef
41.
Ollivier, F.: Le problème de l’identifiabilité structurelle globale: approche théorique, méthodes effectives et bornes de complexité. Ph.D. thesis, Ecole Polytechnique, Palaiseau (1990)
42.
43.
44.
Raissi, T., Ramdani, N., Candau, Y.: Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica 40(10), 1771–1777 (2004) MathSciNetMATHCrossRef
45.
Raksanyi, A., Lecourtier, Y., Walter, E., Venot, A.: Identifiability and distinguishability testing via computer algebra. Math. Biosci. 77(1–2), 245–266 (1985) MathSciNetMATHCrossRef
46.
Ritt, J.F.: Differential Algebra. American Mathematical Society, Providence (1950) MATH
47.
Shimizu, K., Aiyoshi, E.: Necessary conditions for min-max problems and algorithm by a relaxation procedure. IEEE Trans. Autom. Control 25, 62–66 (1980) MathSciNetMATHCrossRef
48.
Vajda, S., Rabitz, H.: State isomorphism approach to global identifiability of nonlinear systems. IEEE Trans. Autom. Control 34, 220–223 (1989) MathSciNetMATHCrossRef
49.
Venot, A., Walter, E., Lecourtier, Y., Raksanyi, A., Chauvelot-Moachon, L.: Structural identifiability of first-pass models. J. Pharmacokinet. Biopharm. 15, 179–189 (1987) CrossRef
50.
Walter, E.: Identification de paramètres en cinétique chimique non linéaire à l’aide du modèle de compartiments associé à un indicateur. Ph.D. thesis, Université Paris-Sud, Orsay (1975)
51.
52.
Walter, E. (ed.): Special issue on parameter identification with error bounds. Math. Comput. Simul. 32(5–6), 447–607 (1990) CrossRef
53.
Walter, E., Kieffer, M.: Interval analysis for guaranteed nonlinear parameter estimation. In: Proc. 13th IFAC Symposium on System Identification (SYSID), Rotterdam, pp. 259–270 (2003)
54.
Walter, E., Kieffer, M.: Guaranteed optimisation of the parameters of continuous-time knowledge-based models. In: Commault, C., Marchand, N. (eds.) Positive Systems, pp. 137–144. Springer, Heildelberg (2006) CrossRef
55.
Walter, E., Kieffer, M.: Guaranteed nonlinear parameter estimation in knowledge-based models. J. of Comput. and Applied Math. 199(2) (2007)
56.
57.
Walter, E., Lecourtier, Y.: Global approaches to identifiability testing for linear and nonlinear state space models. Math. Comput. Simul. 24, 472–482 (1982) MathSciNetMATHCrossRef
58.
Walter, E., Lecourtier, Y., Happel, J.: On the structural output distinguishability of parametric models, and its relation with structural identifiability. IEEE Trans. Autom. Control 29, 56–57 (1984) MATHCrossRef
59.
Walter, E., Lecourtier, Y., Happel, J., Kao, J.Y.: Identifiability and distinguishability of fundamental parameters in catalytic methanation. AIChE J. 32(8), 1360–1366 (1986) CrossRef
60.
Walter, E., Pronzato, L.: Identification of Parametric Models from Experimental Data. Springer, London (1997) MATH
61.
Zarrop, M.B.: Optimal Experiment Design for Dynamic System Identification. Springer, Heidelberg (1979) MATHCrossRef
Metadaten
Titel
Identifiability, and Beyond
verfasst von
Eric Walter
Copyright-Jahr
2012
Verlag
Springer London
Buch
System Identification, Environmental Modelling, and Control System Design

Print ISBN: 978-0-85729-973-4

Electronic ISBN: 978-0-85729-974-1

Copyright-Jahr: 2012

DOI
https://doi.org/10.1007/978-0-85729-974-1_3

Neuer Inhalt

    Bildnachweise