Nonlinear bounded-error parameter estimation using interval computation

Luc Jaulin (1, 2, 3) , Eric Walter (4)

1 STIC - Département STIC [Brest]
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
3 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
4 L2S - Laboratoire des signaux et systèmes

This paper deals with the estimation of the parameters of a model from experimental data. The aim of the method presented is to characterize the set S of all values of the parameter vector that are acceptable in the sense that all errors between the experimental data and corresponding model outputs lie between known lower and upper bounds. This corresponds to what is known as bounded error estimation, or membership set estimation. Most of the methods available to give guaranteed estimates of S rely on the hypothesis that the model output is linear in its parameters, contrary to the method advocated here, which can deal with nonlinear model. This is made possible by the use of the tools of interval analysis, combined with a branch-and-bound algorithm. The purpose of the present paper is to show that the approach can be cast into the more general framework of granular computing.

Domaines: Sciences de l'ingénieur [physics]

Luc Jaulin, Eric Walter. Nonlinear bounded-error parameter estimation using interval computation. Witold Pedrycz. Granular Computing: An Emerging Paradigm, Physica Verlag Heidelberg, pp.397, 2001, Studies in Fuzziness and Soft Computing, Vol. 70, 978-3-7908-1387-6. ⟨hal-00845125⟩