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Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory

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  • Walter, E.
  • Piet-Lahanier, H.
  • Happel, J.

Abstract

A new methodology for estimating parameters that are not structurally globally identifiable is presented. The set of all the models which have exactly the same input–output behavior is first generated. The influence of the measurement noise and structural error is then taken into account by assuming that upper and lower bounds of the acceptable output error are available. The set of all the models compatible with this hypothesis is characterized, and ranges for the possible values of the estimated parameters are provided. An example is treated involving two real–life model structures used to describe the behavior of an isotopic tracer in a reactor producing methane from carbon monoxide and hydrogen.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:28:y:1986:i:6:p:479-490
    DOI: 10.1016/0378-4754(86)90043-1
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    References listed on IDEAS

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    1. Walter, Eric & Lecourtier, Yves, 1982. "Global approaches to identifiability testing for linear and nonlinear state space models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(6), pages 472-482.
    2. Bekey, George A. & Masri, Sami F., 1983. "Random search techniques for optimization of nonlinear systems with many parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(3), pages 210-213.
    3. Pronzato, Luc & Walter, Eric & Venot, Alain & Lebruchec, Jean-Francois, 1984. "A general-purpose global optimizer: Implimentation and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(5), pages 412-422.
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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.
    2. 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.
    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. 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.

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