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

Abstract

2015)Parametric identification of a heating mobile source in a three-dimensional geometry, Inverse Problems in Science and Engineering, 23:1, 93-111,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. IntroductionFor several decades, resolution of inverse problems in thermal sciences is a key-goal in numerous engineering applications. Related literature is quite wide since applications deal with different geometries and configurations for many identification purposes like initial conditions [1], boundary exchange coefficient [2], thermal parameters[3] or heat source characterization. In this last framework, several applications are investigated in recent references: control of welding processes using nonintrusive observations [4,5]; prediction of the thermal effect of High Energy Laser (HEL) weapons, in order to predict the potential damage on a target [6] and estimation of temperature in human tissues submitted to a laser occurrence.[7] During the two past decades, several studies have been investigated from one-dimensional geometry [8] to two-dimensional geometries (see [9][10][11]). It is well known that such inverse problems are ill-posed. [12,13] Several approaches can be implemented to deal with parametric identification: singular value decomposition [13], Tikhonov regularization [14] and function specification.[15] The Alifanov's iterative regularization method has been successfully implemented in [16]. However, three-dimensional configurations are scarcely investigated due to important CPU time required for identification purposes (in [17][18][19][20][21][22] parametric identification in a thermal context is investigated). Nowadays, heat flux identification still remains a lively research topic (see recent references [23][24][25][26]).

A model‐based failure times identification for a system governed by a 2D parabolic partial differential equation

“…The stopping criterion is chosen according to the measurement noise on the observations $$\hat{T}_{i}(t)$$, temperatures measured at the sensors $$C_{i}$$. The whole identification method has been successfully implemented in [39–41].…”

Stabilization Using In-domain Actuator: A Numerical Method for a Non Linear Parabolic Partial Differential Equation

“…CGM is a descent method that solves the problem of parametric identification by stopping the minimization when a relevant threshold J stop is obtained. Such method has been developed for thermal applications in [14][15][16][17][18]. At each iteration k of the algorithm, three well-posed problems have to be solved:…”

“…In the framework of thermal properties identification, the iterative regularization method based on the CGM has been developed in [14]. In recent works, authors have proposed new developments for mobile heating source tracking in 2D and 3D geometries [15][16][17] and for quasi online identification of a temperature dependent characteristics in [18].…”

Unknown parameter identification of mobile heating source by using the sensitivity of sensor network

“…CGM is implemented to identify the unknown parameters [10] [11]. This algorithm requires iterative resolution of three well-posed problems: the direct problem (3) to calculate the cost-function J θ, I k and estimate the quality of the estimate I k at iteration k; the sensitivity problem to calculate the descent depth (in the descent direction); the adjoint problem to determine the gradient of the cost-function J θ, I and thus to define the next descent direction [12] [13].…”