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。     

多宗量瞬态热传导反演识别

引入Bregman距离加权函数,建立了多宗量瞬态热传导反演的一种求解模式.时域上采用精细算法,分别建立了便于敏度分析的有限元正/反演模型,应用同伦算法进行反问题求解,对导热系数和边界条件等宗量进行有效的组合识别.对信息误差和计算效率作了探讨,并给出了相应的数值验证.     

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。     

时域自适应算法求解移动荷载下梁的多宗量反问题

通过一种时域自适应算法,建立了求解变速移动荷载下梁的多宗量反问题的数值模型,可同时识别移动荷载和梁的物性参数.正问题采用时域自适应算法和FEM建模,并可由此方便地推导敏度公式;在反问题求解中采用Levenberg-Marquardt法,计算表明该方法具有较好的抗不适定性.通过两个算例,对所提算法进行了数值验证,并探讨了噪声和测点的变化对反演结果的影响,结果令人满意.     

三维非稳态热传导逆问题反演算法研究

利用表面温度测量来反演热传导方程中的热源项是一类典型的热传导逆问题,在采用有限体积法对三维非稳态热传导问题进行数值求解的基础上,将该热传导逆问题转化为优化问题,建立了伴随方程法和共轭梯度法这两类反演算法. 采用这两类算法对一个典型算例的计算结果表明:建立的两类反演算法是有效的,具有较好的抗噪性能. 此外,对反演算法中计算收敛准则的选取进行了较深入的分析,结果表明,由于热传导逆问题的不适定性,优化过程中目标函数值越小并不意味着反演结果与真值更为接近,可以通过设定合适的收敛准则来模拟正则化项的作用,克服不适定性的影响.      

带源参数的二维热传导反问题的无网格方法

利用无网格有限点法求解带源参数的二维热传导反问题，推导了相应的离散方程. 与 其它基于网格的方法相比，有限点法采用移动最小二乘法构造形函数，只需要节点信息，不 需要划分网格，用配点法离散控制方程，可以直接施加边界条件，不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.     

面载荷识别的TSVD正则化方法

线性系统的响应可以表示为单位脉冲响应函数与动态载荷的卷积分,经离散后得到载荷识别反问题。引入TSVD正则化方法处理反问题的不适定性,对不同噪声的实测响应进行了面载荷的反演求解,并对识别精度做出了分析。算例表明,TSVD正则化方法对响应误差的适应性强,识别精度高。     

松散堆积体工程边坡变形机理分析及支护对策研究

利用表面温度测量来反演热传导方程中的热源项是一类典型的热传导逆问题,在采用有 限体积法对三维非稳态热传导问题进行数值求解的基础上,将该热传导逆问题转化为优化问 题,建立了伴随方程法和共轭梯度法这两类反演算法. 采用这两类算法对一个典型算例的计 算结果表明：建立的两类反演算法是有效的,具有较好的抗噪性能. 此外,对反演算法 中计算收敛准则的选取进行了较深入的分析,结果表明,由于热传导逆问题的不适定性,优 化过程中目标函数值越小并不意味着反演结果与真值更为接近,可以通过设定合适的收敛准 则来模拟正则化项的作用,克服不适定性的影响.     

自由-自由运行体系动态载荷反演问题研究

对自由-自由运行体系动态载荷识别问题进行深入研究,将自由-自由运行体系振动积分方程时域离散化,建立了体系动态载荷反演的力学模型。在动态载荷反演模型求解过程中,由于结构矩阵的病态特性以及测量噪声的影响,常规最小二乘法往往失效;通过对载荷反演模型进行奇异值分解,指出该病态问题的本质,并提出相应的正则化求解方法。数值仿真表明了本文方法能够得到满足工程要求的稳定近似解。本文研究对于实际飞行器运行过程所受动载荷评估具有一定的意义。     

基于同伦技术的偶应力反问题求解

引入Bregman距离构造同伦函数,建立偶应力反问题的一种求解模式,可以对偶应力理论相关参数进行识别.利用有限元技术,建立了偶应力正/反问题数值求解模型,该模型不仅考虑了非均质的影响,而且也便于反问题的敏度分析.文中给出了相关的数值算例,并对信息误差和不同的函数形式计算结果做了初步探讨,得到满意的结果.数值算例表明该模...     

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…     

Retrieving the heat transfer coefficient for jet impingement from transient temperature measurements

Algorithm of retrieving the heat transfer coefficient (HTC) from transient temperature measurements is presented. The unknown distributions of two types of boundary conditions: the temperature and heat flux are parameterized using a small number of user defined functions. The solutions of the direct heat conduction problems with known boundary temperature and flux are expressed as a superposition of auxiliary temperature fields multiplied by unknown parameters. Inverse problem is formulated as a least squares fit of calculated and measured temperatures and is cast in a form of a sum of two objective functions. The first results originates from an inverse problem for retrieving the boundary temperature the second comes from the inverse problem for reproducing the boundary heat flux. The final form of the objective function is obtained by enforcing constant in time value of the heat transfer coefficient. This approach leads to substantial regularization of the results, when compared with the standard technique, where HTC is calculated from separately reconstructed temperature and heat flux on the boundary. The validation of the numerical procedure is carried out by reconstructing a known distribution of the HTC using simulated measurements laden by stochastic error. The proposed approach is also used to reconstruct the distribution of the HTC in a physical experiment of heating a cylindrical sample using an impinging jet.     

Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method

The Non-uniform rational B-spline(NURBS)enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper.The scaled boundary finite element method is a semi-analytical technique,which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction.In this method,only the boundary is discretized in the finite element sense leading to a reduction of the spatial dimension by one with no fundamental solution required.Nevertheless,in case of the complex geometry,a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often unavoidable in the conventional finite element approach,which leads to huge computational efforts and loss of accuracy.NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape.In the proposed methodology,the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions,while the straight part of the boundary is discretized by the conventional Lagrange shape functions.Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analysis and the solution is obtained using the modified precise integration method.The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion.Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method.The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.     

基于遗传算法的混凝土三维非稳态温度场反分析

大体积混凝土结构施工期间的合理温度控制问题非常重要，而精确进行温度计算所需的一些材料参数往往不易直接测得，需要根据一些易测得的量进行反求。本文基于三维瞬态温度场有限元求解理论与反问题理论，建立了混凝土三维瞬态温度场反问题求解数值模型。运用遗传算法寻求非线性反演问题全局最优解，只需要若干点温度实测值便可实现混凝土多个热学参数如绝热温升、导温、导热系数及热交换系鼓等的同时反演，算例对本文反演方法的反演精度及数值稳定性给出了满意的证明。     

Estimation of aerodynamic heat transfer in free flight at Mach number up to 4.7

Heat and Mass Transfer - A one-dimensional inverse transient heat conduction problem with a radiation boundary condition is analysed using implicit finite difference approximation. An iterative...