کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1897102 | 1044490 | 2011 | 17 صفحه PDF | دانلود رایگان |
In this investigation we develop and validate a computational method for reconstructing constitutive relations based on measurement data, applicable to problems arising in nonequilibrium thermodynamics and continuum mechanics. This parameter estimation problem is solved as PDE-constrained optimization using a gradient-based technique in the optimize-then-discretize framework. The principal challenge is that the control variable (i.e., the relation characterizing the constitutive property) is not a function of the independent variables in the problem, but of the state (dependent) variable. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. It relies on three main ingredients: a computationally friendly expression for the cost functional gradient, Sobolev gradients used in lieu of discontinuous L2L2 gradients, and a systematic technique for shifting the identifiability region. The performance of this approach is illustrated by the reconstruction of the temperature dependence of the thermal conductivity in a one-dimensional model problem.
► Computational method for reconstructing constitutive relations based on measurements.
► The parameter estimation problem is solved as a PDE-constrained optimization.
► Smooth constitutive relations reconstructed over a broad range of the state variable.
► Computational results for a 1D model problem.
Journal: Physica D: Nonlinear Phenomena - Volume 240, Issue 16, 1 August 2011, Pages 1228–1244