Inverse reconstruction of initial and boundary conditions of a heat transfer problem with accurate final state

• Published in: International journal of heat and mass transfer Vol. 54; no. 15; pp. 3749 - 3760
• Main Authors: Bourquin, Frédéric, Nassiopoulos, Alexandre
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2011; Elsevier
• Subjects: Adjoint method; Adjoints; Boundary conditions; Engineering Sciences; Exact sciences and technology; Flexibility; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Inverse problems; Inverse reconstruction; Mathematical models; Optimal control; Other; Physics; Real time; Reconstruction; Temperature assimilation; Vibration; Adjoint method; Temperature assimilation; Inverse problems; Optimal control; Temperature measurement; Reconstruction; Initial conditions; Digital simulation; Boundary conditions; Modelling; Data assimilation; Thermal conduction; CONTROLE; TEMPERATURE; METHODE NUMERIQUE; PROBLEME INVERSE
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2011.03.014

Temperature variations have strong effects on structure vibrations, urging the need for accurate real-time temperature identification. The work presented here deals with the reconstruction of the thermal field inside a structure, given pointwise temperature measurements. This is achieved by reconstructing both the initial and boundary conditions. The numerical procedure uses the adjoint method, which is unable, in its usual L 2 setting, to provide accurate results at the end of the observation period. This paper shows how the introduction of regularity assumptions yields an accurate and stable real-time temperature reconstruction while keeping the generality and flexibility of the usual adjoint method.