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Research Papers: Conduction

A Novel Methodology for Combined Parameter and Function Estimation Problems

[+] Author and Article Information
Hosein Molavi

Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iranhn.molavi@gmail.com

Ali Hakkaki-Fard

Department of Mechanical Engineering, McGill University Montreal, QC H3A 2T5, Canadaali.hakkaki-fard@mail.mcgill.ca

Ramin K. Rahmani

Department of Mechanical, Industrial, and Manufacturing Engineering, University of Toledo, Toledo, OH 43606rkhrahmani@yahoo.com

Anahita Ayasoufi

Department of Mechanical, Industrial, and Manufacturing Engineering, University of Toledo, Toledo, OH 43606aayasoufi@yahoo.com

Mehdi Molavi

Department of Mechanical Engineering, Azad University of Tehran, Tehran, Tehran 1777613651, Iran

Three test cases are studied in this paper. The thermal contact resistance is the unknown in the first one and values of thermal conductivity for two different materials are the unknowns in the second case. In the third one, the specific heat values for two different materials are the unknowns.

J. Heat Transfer 132(12), 121301 (Sep 17, 2010) (11 pages) doi:10.1115/1.4002283 History: Received March 04, 2009; Revised July 22, 2010; Published September 17, 2010; Online September 17, 2010

This article presents a novel methodology, which is highly efficient and simple to implement, for simultaneous retrieval of a complete set of thermal coefficients in combined parameter and function estimation problems. Moreover, the effect of correlated unknown variables on convergence performance is examined. The present methodology is a combination of two different classical methods: The conjugate gradient method with adjoint problem (CGMAP) and Box–Kanemasu method (BKM). The methodology uses the benefit of CGMAP in handling function estimation problems and BKM for parameter estimation problems. One of the unique features about the present method is that the correlation among the separate unknowns does not disrupt the convergence of the problem. Numerical experiments using measurement errors are performed to verify the efficiency of the proposed method in solving the combined parameter and function estimation problems. The results obtained by the present approach show that the combined procedure can efficiently and reliably estimate the values of the unknown thermal coefficients.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A flowchart of the combined parameter and function estimation strategy

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Figure 2

Problem geometry

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Figure 3

Schematic of grid spacing at contact interface

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Figure 4

The exact and estimated values of heat flux

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Figure 5

Reduction histories of the objective function for different level of measurements

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Figure 6

Normalized sensitivity coefficients for q(t) and R

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Figure 7

Study of the linear dependence between the scaled sensitivity coefficients of q(t) and R

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Figure 8

The exact and estimated values of heat flux

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Figure 9

Normalized sensitivity coefficients for q(t), kA, and kB

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Figure 10

Study of the linear dependence between the scaled sensitivity coefficients of q(t) and kA

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Figure 11

The exact and estimated values of heat flux

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Figure 12

Normalized sensitivity coefficients for q(t), CpA, and CpB

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Figure 13

Study of the linear dependence between the scaled sensitivity coefficients of q(t) and CpA

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