Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck
Keyword(s):  
Heat Conduction ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Regularization Methods ◽  
Inverse Heat Conduction ◽  
Random Errors ◽  
Internal Temperature ◽  
Inverse Heat Conduction Problems

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.

scholarly journals A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Arghand ◽  
Majid Amirfakhrian
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Meshless Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Linear Equations ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Radial Basis ◽  
The Stability

We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.

On Elliptic Inverse Heat Conduction Problems

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Initial Guess ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Robustness To Noise ◽  
Inverse Heat Conduction Problems ◽  
New Feature

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

scholarly journals FEATURES OF THE APPLICATION OF THE IQLAB PROGRAM FOR SOLVING THE INVERSE HEAT CONDUCTION PROBLEM FOR CHROMIUM-NICKEL CYLINDRICAL THERMOSONDES

2018 ◽  
Vol 40 (3) ◽  
pp. 91-96
Author(s):  
E.N. Zotov ◽  
A.A. Moskalenko ◽  
O.V. Razumtseva ◽  
L.N. Protsenko ◽  
V.V. Dobryvechir
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Computational Study ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Time Step ◽  
Correct Operation ◽  
Inverse Heat Conduction Problems ◽  
Variable Time Step

The paper presents an experimental-computational study of the results of using the IQLab program to solve inverse heat conduction problem and restore the surface temperature of cylindrical thermosondes from heat-resistant chromium-nickel alloys while cooling them in liquid media. The purpose of this paper is to verify the correct operation of the IQLab program when restoring the surface temperature of thermosondes with 1-3 thermocouples. The IQLab program is also designed to solve one-dimensional nonlinear direct lines and inverse heat conduction problems with constant initial and boundary conditions specified as a function of time in a tabular form with a constant and variable time step. A finite-difference method is used to solve the heat equation. Experiments were carried out on samples D = 10-50 mm in liquids with different cooling capacities such as aqueous solutions of  NaCl and Yukon-E polymer, rapeseed oil and I-20A mineral oil. For the calculation we used the readings of thermocouples installed at internal points of cylindrical thermosondes. The advantages of solving inverse heat conduction problems with the IQLab program include the possibility of restoring the surface temperature for cylindrical samples with a diameter of 10 mm to 50 mm with practical accuracy according to the indications of a single thermocouple located in the geometrical center of the thermosonde, which simplifies the manufacture of the probe. For larger dimensions with a diameter D ≥ 50 mm, it is necessary to install control intermediate thermocouples and perform additional tests. The solution of inverse heat conduction problems and restoration of the surface temperature of the sample makes it possible to calculate other important characteristics of the cooling process: the heat flux density and the heat transfer coefficient.

A Maximum Entropy Solution for a Two-Dimensional Inverse Heat Conduction Problem

2003 ◽  
Vol 125 (6) ◽  
pp. 1197-1205 ◽  
Author(s):  
Sun Kyoung Kim ◽  
Woo Il Lee
Keyword(s):  
Heat Conduction ◽  
Maximum Entropy ◽  
Optimization Problem ◽  
Entropy Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Measured Temperature ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems

A solution scheme based on the maximum entropy method (MEM) for the solution of two-dimensional inverse heat conduction problems is established. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. The proposed method converts the inverse problem to a nonlinear constrained optimization problem. The constraint of the optimization problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the numerical estimation of the maximum entropy solution. The characteristic feature of the proposed method is investigated with the sample numerical results. The presented results show considerable enhancement in resolution for stringent cases in comparison with a conventional method.

Sign in / Sign up

Export Citation Format

Share Document