Optimal Regularization Methods for Inverse Heat Transfer Problems

Volume 4 ◽  
2004 ◽  
Author(s):  
Kei Okamoto ◽  
Ben Q. Li
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Regularization Method ◽  
Cross Validation ◽  
Tikhonov Regularization Method ◽  
Inverse Algorithm ◽  
Marquardt Method ◽  
Inverse Heat Transfer ◽  
Regularization Parameters ◽  
Levenberg Marquardt

The Tikhonov regularization method has been used to find the unknown heat flux distribution along the boundary when the temperature measurements are known in the interior of a sample. Mathematically, the inverse problem is ill-posed, though physically correct, and prone to instability. This paper discusses the fundamental issues concerning the selection of optimal regularization parameters for inverse heat transfer calculations. Towards this end, a finite-element-based inverse algorithm is developed. Five different methods, that is, the maximum likelihood (ML), the ordinary cross-validation (OCV), the generalized cross-validation (GCV), the L-curve method, and the discrepancy principle, are evaluated for the purpose of determining optimal regularization parameters. An assessment of these methods is made using 1-D and 2-D inverse steady heat conduction problems where analytical solutions are available. The optimal regularization method is also compared with the Levenberg-Marquardt method for inverse heat transfer calculations. Results show that in general the Tikhonov regularization method is superior over the Levenberg-Marquardt method when the input data errors are noisy. With the appropriately determined regularization parameter, the inverse algorithm is applied to estimate the heat flux of spray cooling of a 3-D microelectronic component with an embedded heating source.

An Adaptive Parameter Choosing Approach for Regularization Model

2018 ◽  
Vol 32 (08) ◽  
pp. 1859013 ◽  
Author(s):  
Xiaowei Xu ◽  
Ting Bu
Keyword(s):  
Regularization Method ◽  
Numerical Experiments ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Estimation Algorithm ◽  
Tikhonov Regularization Method ◽  
Practical Applications ◽  
Adaptive Parameter ◽  
Regularization Parameters ◽  
Parameter Estimation Algorithm

The choice of regularization parameters is a troublesome issue for most regularization methods, e.g. Tikhonov regularization method, total variation (TV) method, etc. An appropriate parameter for a certain regularization approach can obtain fascinating results. However, general methods of choosing parameters, e.g. Generalized Cross Validation (GCV), cannot get more precise results in practical applications. In this paper, we consider exploiting the more appropriate regularization parameter within a possible range, and apply the estimated parameter to Tikhonov model. In the meanwhile, we obtain the optimal regularization parameter by the designed criterions and evaluate the recovered solution. Moreover, referred parameter intervals and designed criterions of this method are also presented in the paper. Numerical experiments demonstrate that our method outperforms GCV method evidently for image deblurring application. Especially, the parameter estimation algorithm can also be applied to many regularization models related to pattern recognition, artificial intelligence, computer vision, etc.

scholarly journals Wetting layer evolution and interfacial heat transfer in water-air spray cooling process of hot metallic surface

2021 ◽  
pp. 318-318
Author(s):  
Lidan Ning ◽  
Liping Zou ◽  
Zhichao Li ◽  
Huiping Li
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nucleate Boiling ◽  
Spray Cooling ◽  
Film Boiling ◽  
Metallic Surface ◽  
Interfacial Heat Transfer Coefficient ◽  
Interfacial Heat Transfer ◽  
Cooling Process ◽  
Inverse Heat Transfer

Spray cooling experiments on the hot metallic surfaces with different initial temperatures were performed. This paper adopts a self-developing program which is based on the inverse heat transfer algorithm to solve the interfacial heat transfer coefficient and heat flux. The temperature-dependent interfacial heat transfer mechanism of water-air spray cooling is explored according to the wetting layer evolution taken by a high-speed camera and the surface cooling curves attained by the inverse heat transfer algorithm. Film boiling, transition boiling, and nucleate boiling stages can be noticed during spray cooling process of hot metallic surface. When the cooled surface?s temperature drops to approximately 369?C - 424?C; the cooling process transfers into the transition boiling stage from the film boiling stage. The wetting regime begins to appear on the cooled surface, the interfacial heat transfer coefficient and heat flux begin to increase significantly. When the cooled surface?s temperature drops to approximately 217?C - 280?C, the cooling process transfers into the nucleate boiling stage. The cooled surface was covered by a liquid film, and the heat flux begins to decrease significantly.

Experimental Demonstration of Inverse Heat Transfer Methodologies for Turbine Applications

2019 ◽  
Author(s):  
David G. Cuadrado ◽  
Francisco Lozano ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Digital Filter ◽  
Heat Conduction Equation ◽  
Metal Temperature ◽  
Temperature Dependent ◽  
Sensitivity Coefficients ◽  
Inverse Heat Transfer ◽  
Transfer Method

Abstract Gas turbines operate at extreme temperatures and pressures, constraining the use of both optical measurement techniques as well as probes. A strategy to overcome this challenge consists of instrumenting the external part of the engine, with sensors located in a gentler environment, and use numerical inverse methodologies to retrieve the relevant quantities in the flowpath. An inverse heat transfer approach is a procedure used to retrieve the temperature, pressure or mass flow through the engine based on the external casing temperature data. This manuscript proposes an improved Digital Filter Inverse Heat Transfer Method, that consists of a linearization of the heat conduction equation using sensitivity coefficients. The sensitivity coefficient characterizes the change of temperature due to a change in the heat flux. The heat conduction equation contains a non-linearity due to the temperature-dependent thermal properties of the materials. In previous literature, this problem is solved via iterative procedures that however increase the computational effort. The novelty of the proposed strategy consists of the inclusion of a non-iterative procedure to solve the non-linearity features. This procedure consists of the computation of the sensitivity coefficients in function of temperature, together with an interpolation where the measured temperature is used to retrieve the sensitivity coefficients in each timestep. These temperature-dependent sensitivity coefficients, are then used to compute the heat flux by solving the linear system of equations of the Digital Filter Method. This methodology was validated in the Purdue Experimental Turbine Aerothermal Lab (PETAL) annular wind tunnel, a two minutes transient experiment with flow temperatures up to 450K. Infrared thermography is used to measure the temperature in the outer surface of the inlet casing of a high pressure turbine. Surface thermocouples measure the endwall metal temperature. The metal temperature maps from the IR thermography were used to retrieve the heat flux with the inverse method. The inverse heat transfer method results were validated against a direct computation of the heat flux obtained from temperature readings of surface thermocouples. The experimental validation was complemented with an uncertainty analysis of the inverse methodology: the Karhunen-Loeve Expansion. This technique allows the propagation of uncertainty through stochastic systems of differential equations. In this case, the uncertainty of the inner casing heat flux has been evaluated through the simulation of different samples of the uncertain temperature field of the outer casing.

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