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

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 L2 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.