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Membership-set estimation using random scanning and principal component analysis

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  • 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
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    References listed on IDEAS

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    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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
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    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.

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