Heating sources localization based on inverse heat conduction problem resolution

Beddiaf, Sara; Autrique, Laurent; Perez, Laetitia; Jolly, Jean-Claude

doi:10.3182/20120711-3-be-2027.00171

Cited by 2 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The effective numerical approaches, such as conjugate gradient method (CGM) and minimization algorithms based on CGM have been applied in [12][13][14]. The boundary element method and iterative algorithms are presented in [15,16].…”

Section: Introductionmentioning

confidence: 99%

Determination of Space and Time Dependent Function of Internal Heat Source in Heat Conductivity Equation

Diligenskaya

Mandra

2014

AMM

View full text Add to dashboard Cite

In the present work we propose the method for the solution inverse heat conduction problem that consists of the identification of unknown internal heat source function depending simultaneously on space and time variables. The source function can be represented as a separable variable. We consider an inverse problem of determining the heat source function based on temperature measurements.Inverse problem is formulated as an optimization problem, a variational formulation for solving the optimization problem is given. The estimation of internal heat source is investigated with the analytical method combined with the method for approximate modal definition of temperature state and source function. The temperature state and desired control input are represented in the form of finite expansion in terms of orthogonal system of eigenfunctions. The required eigencoefficients of temperature state can be determined using temperature measurements. Then eigencoefficients of heat source function can be defined sequentially.Some numerical examples are provided to show the efficiency of the proposed method.

show abstract

Section: Introductionmentioning

confidence: 99%

Determination of Space and Time Dependent Function of Internal Heat Source in Heat Conductivity Equation

Diligenskaya

Mandra

2014

AMM

View full text Add to dashboard Cite

show abstract

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

Beddiaf

Perez

Autrique

et al. 2013

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

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.

show abstract

Heating sources localization based on inverse heat conduction problem resolution

Cited by 2 publications

References 4 publications

Determination of Space and Time Dependent Function of Internal Heat Source in Heat Conductivity Equation

Determination of Space and Time Dependent Function of Internal Heat Source in Heat Conductivity Equation

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

Contact Info

Product

Resources

About