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.     

Experimental verification of space marching methods for solving inverse heat conduction problems

Two space marching methods for solving one-dimensional nonlinear inverse heat conduction problems developed earlier are validated using data obtained during emergency cooling simulation of PWR pressure vessels. The model of pressure vessel was preheated at 350 ^∘C and then cooled by injection of cold water at 20 ^∘C. Based on the vessel temperature histories measured at the distance of 50 mm from the inner surface and at the outside surface the transient temperature distribution in the pressure vessel was obtained. The comparison of the results obtained by both space marching methods with experimental data shows high accuracy of the space marching methods. Received on 3 May 1999     

A direct analytic approach for solving two-dimensional linear inverse heat conduction problems

A stable and accurate analytic approach is developed for solving two-dimensional inverse heat conduction problems where the front surface conditions are calculated from the knowledge of the time variation of the temperature at an interior point in the region. A combination of a splitting-up procedure and the least square technique is utilized for the solution of this inverse problem.The stability and accuracy of the present method of analysis are demonstrated by several numerical examples that provided a very strict test. The results illustrate that the method is: insensitive to measurement errors; remains stable for small time steps; and can accomodate, with high degree of accuracy, abrupt change with time in the unknown surface conditions.

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Eine direkte analytische Näherung zur Lösung zweidimensionaler, linear-inverser Wärmeleitungsprobleme

Zusammenfassung Es wurde ein stabiles und genaues analytisches Näherungsverfahren zur Lösung des zweidimensionalen, inversen Wärmeleitungsproblemes entwickelt, wobei die Randbedingungen an der vorderen Oberfläche aus der bekannten, zeitabhängigen Temperaturänderung an einem inneren Punkt in dem Bereich berechnet werden. Es wird eine Kombination einer Aufsplitt-Prozedur und einer Technik des kleinsten Fehlerquadrates benützt, um dieses inverse Problem zu lösen.Die Stabilität und Genauigkeit der vorliegenden Analysenmethode werden durch verschiedene numerische Beispiele demonstriert, die eine sehr strenge Prüfung gestatten. Die Ergebnisse zeigen, daß die Methode unempfindlich gegen Meßfehler ist, für kleine Zeitschritte stabil bleibt und sich mit hohem Auflösungsvermögen an plötzliche, zeitliche Änderungen unbekannter Oberflächenbedingungen anpassen kann.

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Nomenclature a, b lengths of the rectangular region - A ₀,A ₁,A ₂ functions defined by Eq. (6d, e, f) - G ₀,G ₁,₃,P ₀,P ₁,P ₁ p ₂,p ₃,P ₄,P ₅ functions defined in the Appendix - E least square error, Eq. (14) - f(t) actual unknown surface temperature - F (t) f(t)–T /T= modified unknown surface temT perature defined by Eq. (2) - R _t transient solution, Eq. (7) - S _j steady-state solution, Eq. (5) - t time variable, hr. - T temperature variable - T initial and environment temperature - U first-stage solution, Eq. (3) - V second-stage solution, Eq. (10) - x, y rectangular coordinate - y _i simulated experimental data (temperature readings) - Z _i the difference between the applied and computed surface temperature ati ^th time Greek letters thermal diffusivity, m²/h - _j's, _j's coefficients defined in Eq. (2) - _n, _m, _mn eigenvalues defined by Eqs. (6g), (8c, e), respectively - _mn eigenfunctions defined by Eq. (8b) - gq T–T/T, dimensionless temperature - t–_l, time variable, h - ₁ time at which abrupt change takes place in the applied surface temperature, h - standard deviation defined by Eq. (16)     

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     

Solution of non-linear inverse heat conduction problems using the method of lines

 Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first method presented in this study to higher dimensions inverse heat conduction problems is straightforward. Received on 3 May 1999     

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.     

Network simulation method for solving phase-change heat transfer problems with variable thermal properties

 The transient heat conduction equation in a finite slab undergoing phase change (two-phase problem of melting and solidification), with isothermal, adiabatic or convective boundary conduction is studied by the network simulation method; solid phase conductivity and specific heat are assumed to be dependent on temperature. Ablation, as a particular case, is also analysed. A network model is established for a cell and boundary conditions are added to complete the whole network model. No restrictions exist, as to the kinds of linear and non-linear boundary conditions, Stefan number values or the initial conditions (when hypotheses concern of the Stefan problem, numerical and exact solutions are compared for a large interval of Stefan numbers; simulation values show good agreement). Movement of the solid–liquid boundary and thermal fields are determined in all cases. Received on 10 May 2000 / Published online: 29 November 2001     

二阶非定常热传导反问题的多宗量辨识

引入Bregman距离构造同伦函数,建立了二阶非定常多宗量热传导反问题的一种求解模式,可对导热系数和边界条件等宗量进行识别。时域上采用精细算法,建立了便于敏度分析的有限元正/反演模型,对各宗量进行有效的组合识别。对信息测量误差和初值选取作了初步探讨,数值验证取得了满意的结果。     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

瞬态热传导问题的加权最小二乘无网格法

加权最小二乘无网格法是一种基于节点信息的纯无网格法,该方法使用最小二乘法建立系统的变分原理,通过移动最小二乘法构造近似函数,控制方程在节点处的残量使用最小二乘法予以消除,边界条件通过罚函数法引入。本文推导了瞬态热传导问题的加权最小二乘无网格计算格式,编制了相应的计算程序,算例结果表明,该方法具有精度高、前后处理简单的优点,是一种高效的的新型无网格法。     

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suit- able for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.     

PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

The complex variable boundary element method for solving sandwich plate problems

The objective of this paper is to develop a new complex variable boundary element method for sandwich plates of Reissner's type and Hoff's type. The general solution of Helmhotz equation in complex field is given. Based on the Vekua's complex integral representation of the analytic function, the new boundary integral equations are formulated. The density function in the integral equation is determined directly by boundary element method. Some standard examples are presented, and the results of numerical solutions are accurate everywhere in the plate. The approach presented is only applicable for bounded simply connected regions. The project is supported by the National Science Foundation of China.     

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.     

基于物理信息神经网络的功能梯度材料稳态/瞬态热传导分析

采用物理信息神经网络PINN(Physics-informed Neural Networks)求解稳态和瞬态功能梯度材料(FGMs)热传导问题。该方法利用控制方程、边界及初始条件的残差构造损失函数,在无任何响应数据的情况下得到了更具泛化能力的神经网络模型,同时避免了传统数值方法在求解计算力学问题时所需的微分、积分公式推导以及繁重的建模和划分网格等前处理工作。本文探究了PINN及其域分解的扩展物理信息神经网络XPINN(eXtended Physics-informed Neural Networks)在求解稳态和瞬态FGMs热传导问题时的适用性,讨论了网络结构对预测结果的影响。研究结果表明,PINN/XPINN在解决几何复杂的稳态和瞬态FGMs热传导问题时仍具有较高的可靠性和简洁的求解流程,同时,为极端环境下求解复杂多场耦合和夹杂等问题提供了新思路。     

正交各向异性稳态热传导问题的ICVEFG方法

论文将改进的复变量无单元Galerkin方法(Improved Complex Variable Element-free Galerkin method,ICVEFG)应用于求解正交各向异性介质中的稳态热传导问题,提出了正交各向异性稳态热传导问题的ICVEFG方法.采用罚函数法引入本质边界条件,推导了正交各向异性介质中的稳态热传导问题的Galerkin积分弱形式.采用改进的复变量移动最小二乘近似(Improved Complex Variable Moving least-squares approximation,ICVMLS)建立二维温度场问题的逼近函数,推导了相应的计算公式.编制了计算程序,对三个正交各向异性介质中的热传导问题进行了分析,说明了论文方法的有效性.