Comparisons and improvements concerning the accuracy and robustness of inverse heat conduction algorithms

Abstract

This article describes a detailed investigation concerning the accuracy and robustness of several algorithms for solving the inverse heat conduction problem (IHCP). A variety of existing methods are classified into three categories: the direct inverse solutions, the observer-based solutions, and the optimization type solutions. The typical methods in each category are briefly analyzed and reviewed, i.e., whole domain regularization, optimal solution, and singular value decomposition (SVD) in the direct inverse category; sequential estimation in the observer-based category; and conjugate gradient functional optimization in the optimization category. An algorithm calibration procedure is used to ensure the best performance with each method. A detailed uncertainty analysis including systematic uncertainties and auto-correlations is described and used to calculate the uncertainty due to system parameters and temperature measurements. Accuracy and robustness indices are suggested to evaluate the performance of each method considered. Finally, a zero-phase, low-pass filter post-processing technique is proposed to improve the robustness in performance of the methods with weak accuracy or robustness. Several simulation results show comparisons of the concerned algorithm in terms of accuracy and robustness, and the effect of the proposed post-processing technique.

Keywords:

• Ill-posed
• Inverse heat conduction
• Robustness
• Zero-phase filter
• Conjugate gradient
• Observer
• Uncertainty
• Singular value decomposition
• AMS 2000 Mathematics Subject Classifications: IHCP: Inverse Heat Conduction Problems
• BM: Blum Marquardt Method
• SVD: Singular Value Decomposition
• CGM: Conjugate Gradient Method
• FD: Finite Difference
• FE: Finite Element
• FCV: Finite Control Volume
• FFT: Fast Fourier Transform

Acknowledgments

Suggestions from Dr. Bin Zhang are greatly appreciated. The authors would like to thank the Cast Metals Coalition (CMC) and the USDOE for their support during this investigation.

Nomenclature

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