Resolution Of An Identification Problem ByCoupling Stochastic And DeterministicMethods

Abstract

This paper deals with the implementation of stochastic process coupling with classical minimization methods in order to solve an identification problem. A model for an industrial process (elastomer vulcanization) is proposed and then the minimization problems and methods are presented. The effect of random perturbations on these methods is studied. Numerical results are given. The interest of the coupling of stochastic and deterministic methods is shown. INTRODUCTION We are interested in a situation issued from thermal industry: the vulcanization. Gamier [1] has shown that, while the curing of some elastomers, an exothermical reaction can occur and damage the material. In order to avoid this destruction, a sharp control is essential and a fine modelling of the physical phenomena taking place during the industrial process is important. The identification of some of the elastomer's parameters must be performed by means of physical experiments (differential scanning calorimetry,...) or numerical methods using temperature measurements can be carried out. 1 A MODEL FOR THE INDUSTRIAL PROCESS In this section, we present a model for the curing of an elastomer. In the industrial process, the natural rubber is injected under pressure in a parallelepipedic cell heated by the top and the bottom (see figure la). Heat flux is supposed equal to 0 on the other faces. This 3-D geometry involved is simplified to 1-D (see figure Ib). Transactions on Engineering Sciences vol 5, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533