An inverse heat conduction problem of estimating boundary fluxes in an irregular domain with conjugate gradient method

A Boundary Element Method (BEM)-based inverse algorithm utilizing the iterative regularization method, i.e. the Conjugate Gradient Method (CGM), is used to solve the Inverse Heat Conduction Problem (IHCP) of estimating the unknown transient boundary heat flux in a multi-dimensional domain with arbitrary geometry. Results show that the advantages of applying the CGM in the inverse calculations lie in that the major difficulties in (i) choosing a suitable quadratic norm, (ii) determining a proper regularization order and (iii) determining the optimal smoothing (or regularization) coefficient in the conventional Regularization Method (RM) are avoided. Received on 27 October 1997     

Determination of nonuniform heat flux density on boundary in inverse heat conduction problem

This paper develops reducing deviation method to solve inverse heat conduction problem with nonuniform heat flux density on boundary. When the thermocouple is placed a bit far from the boundary, there is no problem on non-convergence in this method. A calculation example is given.     

Numerical solutions for general inverse heat conduction problem

A family of numerical methods for determining the space-and time-variable heat transfer coefficient, based on experimentally acquired interior temperature-time data, is presented. Newton-type methods are utilized to compute simultaneously the unknown heat transfer coefficient components. To reduce the influence of random errors in the measurement data on the estimated heat transfer coefficients, the noisy data are smoothed using least squares approximation by cubic splines. Three test examples using experimental and random simulated data are used to illustrate the computation efficiency and generality of the present methods.     

A semi-numerical method for solving inverse heat conduction problems

A semi-numerical method is presented for solving the inverse heat conduction problems in homogeneous and composite bodies. The presented solution does not require both the initial temperature distribution in the body and the whole temperature-time history at the temperature sensor locations. Sample calculations confirm that this approach produces stable and accurate results for both exact and noisy data. The extension of the method presented to two or three dimensions is straightforward.     

Analytical solution of the overdetermined inverse heat conduction problem with an application to monitoring thermal stresses

The paper presents a technique for determining the transient temperature distribution, when input data as thermocouple responses are known at several interior locations. If the temperature field is known, then the thermal stresses can be calculated. The problem is overdetermined and is solved using a least squares method that minimizes the error between the computed and measured thermocouple temperatures. The present method incorporates the advantages of simplicity and accuracy of analytical solutions. Several numerical examples and measurements are presented as an indication of the accuracy of the presented method. Received on 10 January 1997     

变几何域传热的表面热流反演方法

变几何域的表面热流反演是一类特殊的热传导逆问题,在再入飞行器烧蚀型防热材料的表面热流反演中具有工程实用价值.本文首先对变几何域传热的正问题计算方法进行了校核验证,然后建立了求解变几何域表面热流反演问题的顺序函数法和共轭梯度法;给出了这两种反演方法的基本思想和算法推导,并针对典型算例进行了仿真.结果表明:两种反演方法都能计算出较好的反演结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性;反演算法能适应不同的几何域变化函数,但几何域变化量的测量误差在表面热流的反演结果中会有较为直接的反映.     

A space marching method for multidimensional transient inverse heat conduction problems

A new method for the solution of multidimensional heat conduction problems is formulated. The developed space marching method allows to determine quickly and exactly unsteady temperature distributions in the construction elements of irregular geometry. The method is especially appropriate for determining transient temperature distribution in thick-wall pressure components based on temperature measurements at the outer surface. Two examples are included to demonstrate the capabilities of the new approach. Received on 28 October 1998     

CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM

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Mixed boundary value problem of heat conduction for infinite slab

Summary An axisymmetric steady state heat conduction boundary value problem having mixed boundary conditions on both faces of an infinite slab, is reduced to a pair of Fredholm integral equations of the second kind. For large values of h, the slab thickness, a solution correct to O(h ^–6) is obtained by expanding the kernels in power series.Presently at Imperial College, London.     

A boundary value problem in extended thermodynamics - one-dimensional steady flows with heat conduction

Abstract. One-dimensional steady flows with heat conduction, treated by the 13-moment theory of extended thermodynamics are considered. The usual well-posed boundary conditions for the corresponding problems in the Navier-Stokes-Fourier (NSF) theory are insufficient to give unique solutions. In order to have unique physically sensible solutions, minimization of the deviation of iterative approximations from the exact solutions, proposed in [1], is used as a criterion. Moreover, the solutions are shown to be invariant with respect to change of consistent boundary conditions - a requirement abide by our physical intuition. In the problems of plane shearing flow and Couette flow, the minimization with respect to two uncontrollable parameters is involved. The examples are carried out numerically, and the results are compared with the classical results of NSF theory.Received: 16 August 2002, Accepted: 20 April 2003, Published online: 5 December 2003PACS: 83.20.Lr, 83.50.Ax Correspondence to: I-S. Liu Dedicated to Professor Ingo Müller on the occasion of his 65th birthday     

A finite difference method with non-uniform meshes for a non-linear heat conduction problem

Summary Iterative solutions of finite difference approximations with nonuniform meshes of the nonlinear heat conduction equation are presented. Results are obtained for the temperature distribution in the wall of a long hollow cylinder, separating two fluids with different temperatures. By introducing nonuniform meshes, the amount of numerical computations can be reduced considerably without loss of accuracy. The mesh points are distributed according to the variation of the third derivative of temperature curve obtained by a linear theory.

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Übersicht Es werden iterative Lösungen der nichtlinearen Wärmeleitungsgleichung mit Hilfe eines Differenzen-Verfahrens mit ungleicher Maschenweite abgeleitet. Die Temperaturverteilung im Inneren eines Zylindermantels, der zwei Flüssigkeiten verschiedener Temperatur voneinander trennt, wird berechnet. Durch Verwendung ungleicher Maschenweite kann der Rechenaufwand erheblich verringert werden, ohne da die Genauigkeit verloren geht. Die Maschenweite wird der 3. Ableitung der Temperaturkurve entsprechend gewählt, so wie sie sich aus der linearen Theorie ergibt.

     

水坝瞬态热传导分析中的拟初始条件边界元法

使用一种时域边界元方法对混凝土水坝进行瞬态热传导分析。在对时间积分进行离散计算时,采用一种拟初始条件法,即在时间步迭代计算的过程中,将之前计算结果对当前时间步的影响都视作当前时间步的初始条件。在所取时间步长较小的情况下,这种处理方法容易导致数值结果不稳定,即每一步的计算误差会累计放大,最终导致计算崩溃。本文提出一种虚拟时刻方法以缓解这类数值不稳定现象,在该方法中,时间步长首先放大至合适尺度,计算某个虚拟时刻(往往在真实计算时刻之后)的温度和流量分布,再通过插值方法换算出真实时刻的温度和流量分布。在虚拟时刻点上的温度和流量计算过程中,边界已知温度或流量由真实时刻的温度或流量进行外插得到。本文简单证明了该方法在温度和流量随时间呈线性变化情况下的正确性,最后给出了两个分析实例,验证了该方法的准确性和稳定性。     

Whole time domain solution of inverse heat conduction problem in multi-layer media

The unknown surface conditions in composite media is estimated by minimizing the nonlinear least squares error between the computed and measured temperatures over the whole time domain. This approach shown to be stable, efficient and accurate. The unknown surface conditions are assumed to have an abrupt change at unknown time. A sensitivity analysis is conducted to learn more insight into the nature of difficulties that can be encountered in the estimation of the parameters associated with the inverse problem. The stability and accuracy of the method is demonstrated by several numerical examples which provide very strict test conditions. Received on 7 March 1997     

基于数据驱动模型求解热传导反问题

热传导反问题求解在工程领域具有重要的应用价值.本文发展数据驱动模型识别了管道内壁几何形状和皮肤肿瘤生长参数等热传导反问题.在管道内壁几何形状识别问题中,首先采用随机生成模型结合有限元法求解热传导正问题,并采用有效导热系数转化的思想,建立机器学习模型,求解了测点温度与有效导热系数之间的抽象映射关系,进而实现管道内壁几何形...     

The inverse identification problem and its technical application

This paper presents an overview of a loading force identification technique. Load identification methods are based on the solution of the inverse identification problem. Many different approaches for linear systems have been developed in this area. For both linear and nonlinear systems, methods based on the minimization of assumed objective functions are formulated. The least square error between the simulated and measured system responses is mainly used as the objective function. The dynamic programming optimization method formulated by Bellman is commonly used for the minimization of the objective function to estimate the excitation forces. The inverse identification problem in most practical cases is ill-posed because not all the state variables or initial conditions are known. Ill-posed inverse identification problems can be solved using several techniques, the most useful of which are: the generalized cross-validation method, the dynamic programming technique and Tikhonov’s method. This article presents the theoretical background and main limits to the application of inverse identification methods. Numerical and experimental tests on a laboratory rig were made to verify the formulated procedures. The method is applied to the identification of wheel–rail contact forces during rail vehicle operation. The method can be applied for indirect measurements of contact forces in railway equipment testing.     

Identification of a moving boundary for a heat conduction problem in a multilayer medium

In this paper, we give a uniqueness theorem for the moving boundary of a heat problem in a composite medium. Through solving the Cauchy problem of heat equation in each subdomain, we finally find an approximation to the moving boundary for one-dimensional heat conduction problem in a multilayer medium. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique with the generalized cross-validation choice rule for a regularization parameter. Numerical experiments for five examples show that our proposed method is effective and stable.     

Immersed boundary conditions method for heat conduction problems in slots with time‐dependent geometry

A grid‐less, fully implicit, spectrally accurate algorithm for solving three‐dimensional, both stationary and time‐dependent, heat conduction problems in slots formed by either fixed or time‐dependent boundaries has been developed. The algorithm is based on the concept of immersed boundary conditions (IBC), where the physical domain is immersed within the computational domain and the boundary conditions take the form of internal constraints. The IBC method avoids the need to construct adaptive, time‐dependent grids resulting in the reduction of the required computational resources and, at the same time, maintaining accurate information about the location of the boundaries. The algorithm is spectrally accurate in space and capable of delivering first‐, second‐, third‐ and fourth‐order accuracy in time. Given a potentially large size of the resultant linear algebraic system, various methods that take advantage of the special structure of the coefficient matrix have been explored in search for an efficient solver, including a specialized direct solver as well as serial and parallel iterative solvers. The specialized direct solver has been found to be the most efficient from the viewpoints of the speed of the computations and the memory requirements. Copyright © 2010 John Wiley & Sons, Ltd.