IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v32y1990i5p535-543.html
   My bibliography  Save this article

Membership-set estimation using random scanning and principal component analysis

Author

Listed:
  • Keesman, Karel

Abstract

A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake.

Suggested Citation

  • Keesman, Karel, 1990. "Membership-set estimation using random scanning and principal component analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 535-543.
    • Handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:535-543
    DOI: 10.1016/0378-4754(90)90009-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475490900098
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(90)90009-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Clement, Thierry & Gentil, Sylviane, 1988. "Reformulation of parameter identification with unknown-but-bounded errors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(3), pages 257-270.
    2. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    3. Walter, E. & Piet-Lahanier, H. & Happel, J., 1986. "Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(6), pages 479-490.
    4. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
    5. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    6. Clement, Thierry & Gentil, Sylviane, 1990. "Recursive membership set estimation for output-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 505-513.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    2. Clement, Thierry & Gentil, Sylviane, 1990. "Recursive membership set estimation for output-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 505-513.
    3. Pronzato, Luc & Walter, Eric, 1990. "Experiment design for bounded-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 571-584.
    4. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
    5. Piet-Lahanier, Hélène & Veres, Sándor M. & Walter, Eric, 1992. "Comparison of methods for solving sets of linear inequalities in the bounded-error context," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(6), pages 515-524.
    6. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    7. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
    8. da Silva, Ivan N. & de Arruda, Lucia V.R. & do Amaral, Wagner C., 1999. "A novel approach to robust parameter estimation using neurofuzzy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 251-268.
    9. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    10. Piet-Lahanier, H. & Walter, E., 1990. "Characterization of non-connected parameter uncertainty regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 553-560.
    11. Norton, J.P. & Mo, S.H., 1990. "Parameter bounding for time-varying systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 527-534.
    12. Belforte, G. & Bona, B. & Cerone, V., 1990. "Identification, structure selection and validation of uncertain models with set-membership error description," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 561-569.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:535-543. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.