Jean-Claude Jolly

Simultaneous determination of time-varying strength and location of a heating source in a three-dimensional domain

In this article, identification of heating source location and time-dependent surface heat flux is investigated considering point temperature measurements on a boundary of the studied three-dimensional geometry. Such Inverse Heat Conduction Problems are ill-posed, since solution stability is not satisfied when observations are noisy/disturbed. We propose a robust algorithm for a simultaneous estimation of location and time-varying strength of a plane heat source. This iterative regularization method based on the conjugate gradient method is tested in several numerical configurations.

Parametric identification of a heating mobile source in a three-dimensional geometry

The resolution of an inverse problem of heat conduction in a three-dimensional plate using an iterative regularization method based on Alifanov’s iterative regularization method is investigated. Considering temperature observation on the upper face centre of a small thin steel plate, the time dependent strength of a plane heat source has to be identified. Two configurations are studied. For the first one, the heat source is fixed on the lower face centre. For the second one, the heat source is mobile and the trajectory is assumed to be known. For both situations, robustness of the approach is stated considering noisy measurements.

Heating Source Localization in a Reduced Time

Abstract Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

Search for Period-2 Cycles in a Class of Hybrid Dynamical Systems with Autonomous Switchings. Application to a Thermal Device

Abstract Our purpose is to complete the analysis of a class of hybrid dynamical systems with autonomous switchings generated by a hysteresis phenomenon. Because we yet have found limit period-1 cycles in paper (Quemard et al, 2005b) and because we deal with nonlinear equations systems, the question of the existence of more than one solution for them and so of the existence of cycles with more than one period is rather natural. Equations system for period-2 cycles is determined and a notion of stability is studied. A realistic application to a thermostat with anticipative resistance comes to illustrate theoretical results.

An inverse geometry problem for a one-dimensional heat equation: advances with complex temperatures

Abstract This paper presents an inverse problem in heat conduction, namely the determination of thicknesses of three materials of known heat capacities and thermal conductivities inside a rod of given length subjected to periodic heat flows from measurements of temperatures at both ends. The unknowns are, therefore, the positions of the two interior frontiers between the three materials. Classically, they can be obtained by minimizing the least-squares, non-linear criterion, between the measured and calculated temperatures. Nevertheless, we show that the global minimum providing the solution is close to three local minima that act as traps for a descent algorithm. After providing theoretical justification of the complex temperature method, a method based in this case on the periodicity of boundary fluxes, we suggest a new criterion allowing the global characterization or not of an a priori local minimizer to be tested. It is a criterion of topological nature based on the identification of a singularity.

Inverse geometry problem for a 1D heat equation: a globality criterion

Abstract The n unknown lengths of a composite rod or plate are determined by measuring the n complex temperatures at ends of the 1D heat conduction model associated. The usual identification method by local minimization of a quadratic criterion is supplemented here by introduction of an original globality criterion of the local minimizer previously obtained. This criterion also provides a test for the existence of the solution in an arbitrary region of the field of research. These results provide a positive conclusion to a survey for two unknowns conducted in an earlier work. They are illustrated by two simulations, one for two unknowns, the other one for four unknowns.