کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1897102 1044490 2011 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On optimal reconstruction of constitutive relations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On optimal reconstruction of constitutive relations
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 240, Issue 16, 1 August 2011, Pages 1228–1244
نویسندگان
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