基于边界元法和分散模糊推理算法的传热学
几何反问题
重庆大学硕士学位论文
（学术学位）
学生姓名：***
指导教师：王广军教授
专业：动力工程及工程热物理
学科门类：工学
重庆大学动力工程学院
二O一四年四月
4月英文Inver Geometry Problem Bad On Boundary Element Method and Decentralized Fuzzy Inference Method英国留学签证材料
A Thesis Submitted to Chongqing University
in Partial Fulfillment of the Requirement for the
Degree of Master of Engineering
镜子的英文By
Zhu Zhenyu
Supervisor: Prof. Wang Guangjun英语词组翻译
Major: Power Engineering and
Engineering Thermophysics
College of Power Engineering of
Chongqing University, Chongqing, China
April 2014
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摘要
根据传热对象的部分温度测量信息以及给定的边界条件，识别其未知边界形状，构成了传热学几何反问题。传热学几何反问题在无损检测、几何形状优化以及生物病灶检测等领域具有广阔的应用前景。目前，传热学几何反问题的主要研究方法为共轭梯度法(Conjugate Gradient Method，CGM)，Levenberg - Marquarat法(L-MM)、最速下降法(Steepest Descent Method，SDM)等基于梯度的优化方法。一方面，由于上述的优化方法属于局部搜索算法，容易陷入局部极值，其反演结果对几何形状的初始猜测值较为敏感；另一方面，由于传热学反问题是典型的不适定问题，采用基于梯度的优化方法研究传热学反问题时，反演结果对于温度测量信息的完整性以及测量误差有严重的依赖性，当温度测量信息不够完备或者存在较大的测量误差时，将会导致反演结果显著恶化。
vacal分散模糊推理算法(Decentralized Fuzzy Inference，DFI)是近年来提出的一种研究传热学反问题的反演算法，其推理过程具有良好的鲁棒性和容错能力，能够增强算法的抗不适定能力。本文借助边界元法(Boundary Element Method，BEM)和分散模糊推理算法(DFI)研究了二维传热系统的边界形状识别问题，主要研究内容包括以下四个方面：
①介绍了BEM的基本原理，并利用BEM建立了求解二维导热正问题的数值模型，验证了边界元法求解导热正问题的正确性，并对数值计算的网格无关性进行了验证。采用BEM求解导热正问题，克服了有
ahoy限元法等数值方法在求解传热学几何反问题过程中每次迭代都需对整个求解区域重新划分网格的缺点，降低了传热正问题的求解难度与计算量。compassionate
②针对二维平板导热问题和圆筒导热问题，利用BEM和CGM对边界未知几何形状进行了反演，并讨论了初始猜测值、测量点数目以及测量误差等对几何形状反演结果的影响，说明了利用CGM求解传热学几何反问题存在的主要问题。
③针对二维传热问题，建立了一种解决传热学几何反问题的分散模糊推理(DFI)反演系统，构造了一组模糊推理单元，根据温度测量值与其计算值的差值推理得到一组模糊推理分量，通过对模糊推理分量的综合加权，对边界几何形状的猜测值进行补偿并刷新。简述了利用分散式模糊推理反演系统进行边界形状反演的流程。
④利用BEM和DFI方法对二维平板导热系统和圆筒导热系统的未知边界形状进行了反演识别，验证了DFI方法的有效性，讨论了初始猜测值、测量点数目以及测量误差等因素对反演结果的影响，并与CGM的反演结果进行了对比。
数值试验结果表明：利用BEM求解导热正问题，只需要在每次迭代中对待反演的边界重新进行边界元离散，降低了传热学几何反问题的求解难度与计算量；对于所研究的二维导热系统，DFI方法能够有效地识别边界几何形状，与传统的CGM相比，DFI方法降低了对初始猜测值和温度测量点数目的依赖
程度，增强了反演结果对温度测量误差的抗干扰能力，具有更好的抗不适定性。
关键词：传热几何反问题，模糊推理，边界元法
ABSTRACT
Inver geometry problem of heat conduction is to estimate the unknown geometry boundary according to the information of temperature measurement and other boundary conditions of the rearch object. Inver geometry problem of heat conduction has broad application prospects in non-destructive testing, geometry optimization, biological lesion detection and other fields. Now, the main rearch methods of inver geometry problem of heat conduction are Conjugate Gradient Method (CGM), Levenberg-Marquarat method (L-MM) and Steepest Descent Method (SDM), which are the gradient-bad optimization methods. On the one hand, the gradient-bad optimization methods belong the local arch algorithm, which are easy to fall into local minima, and the inversion results are nsitive to the initial guess for the geometry; On the other hand, due to the inver problem of heat transfer is a typical ill-pod problem, the inversion results depend heavily on the completeness and accuracy of the temperature measurement information when using the gradient -bad optimization method to study inver heat transfer problem, if the temperature measurement information is incomplete or has errors, inversion results will deteriorate.
英语求职信
reroll
Decentralized Fuzzy Inference (DFI) method is an inversion algorithm for the inver heat transfer problem propod in recent years, which has good robustness and fault tolerance and can enhance ability of anti-ill-pod for the algorithm. The two-dimensional geometry boundary identification problem is studied bad on boundary element method (BEM) and decentralized fuzzy inference (DFI) in this paper, the main contents contain the following four aspects:
①The basic principles of BEM is introduced and a numerical model for solving two dimensional heat conduction problems is established bad on BEM. The correctness and grid–independent of results of the thermal positive problem bad on the BEM are verified. The shortcomings that each iteration requires redrawing the grid of the entire region are overcome when using BEM solve the thermal positive problem, the difficulty and the amount of calculation are reduced.
②The unknown boundary geometry are estimated bad on BEM and CGM for the two-dimensional flat and cylindrical thermal conduction problem. Then, the effects of the initial guess, the number of measurement points and measurement error on the inversion results are discusd, which show the main problems of CGM for the
