Stochastic inverse heat conduction using a spectral approach

Velamur Asokan Badri Narayanan · Nicholas J. Zabaras

83 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Probabilistic and Robust Engineering Design Heat Transfer and Numerical Methods Numerical methods in inverse problems

Abstract

Abstract An adjoint‐based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill‐posed stochastic inverse problem is restated as a conditionally well‐posed L2 optimization problem. The gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field. The L2 optimization problem is solved using a conjugate‐gradient approach. Accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems. Copyright © 2004 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 1999Ingredients for a general purpose stochastic finite elements implementation 2001Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos 1988Response Variability Of Stochastic Finite Element Systems 1998Probabilistic characterization of transport in heterogeneous media 2002Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation

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