识别含热源瞬态热传导问题的热扩散系数

周焕林; 严俊; 余波; 陈豪龙

doi:10.21656/1000-0887.380199

识别含热源瞬态热传导问题的热扩散系数

doi: 10.21656/1000-0887.380199

¹合肥工业大学土木与水利工程学院, 合肥 230009;²中铁四局集团钢结构建筑有限公司, 合肥 230088

基金项目: 国家自然科学基金(11672098;11502063)

详细信息

作者简介:
周焕林(1973—)，男，教授，博士生导师(通讯作者. E-mail: zhouhl@hfut.edu.cn).

中图分类号: TK124
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出版历程
- 收稿日期: 2017-07-19
- 修回日期: 2017-12-18
- 刊出日期: 2018-02-15

Identification of Thermal Diffusion Coefficients for Transient Heat Conduction Problems With Heat Sources

¹School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China;²Steel Structure Construction Co. Ltd., China Tiesiju Civil Engineering Group, Hefei 230088, P.R.China

Funds: The National Natural Science Foundation of China(11672098;11502063)

摘要

摘要: 针对含有热源的瞬态热传导反问题，引入一个变换将含热源热传导问题转换为无热源热传导问题，采用改进布谷鸟算法反演热扩散系数.正问题由边界元法求解.将热扩散系数作为优化变量，以计算温度和测量温度之间的接近程度为目标函数，通过改进布谷鸟算法极小化目标函数来优化估计热扩散系数.比较共轭梯度法、布谷鸟算法和改进布谷鸟算法的反演结果.与共轭梯度法相比，改进布谷鸟算法对迭代初值不敏感；与布谷鸟算法相比，改进布谷鸟算法收敛速度更快.算例讨论了测点数量、鸟巢数量、测量误差对计算结果的影响.增加测点数量，反演结果精度降低；增加鸟巢数量，迭代次数减少；随着测量误差的增大，结果精度降低.数值算例验证了改进布谷鸟算法反演热扩散系数的准确性和有效性.
- 热传导 /
- 反问题 /
- 热扩散系数 /
- 改进布谷鸟算法 /
- 边界元法
Abstract: An improved cuckoo search (ICS) algorithm was developed to identify the thermal diffusion coefficients for inverse transient heat conduction problems with heat sources. The heat conduction problem with heat source was transformed into one without heat source. The direct problem was solved with the boundary element method. The thermal diffusion coefficient was treated as the optimization variable, and the difference between the calculated temperature and the measured temperature was taken as the objective function. The thermal diffusion coefficient was optimized through minimization of the objective function with the ICS algorithm. Comparison between the results of the conjugate gradient method (CGM), the cuckoo search (CS) algorithm and the ICS algorithm indicates that the ICS algorithm is less sensitive to iterative initialization than the CGM, and the ICS algorithm has higher efficient convergence than the CS algorithm. The numerical examples were devoted to the influences of the measured point number, the nest number and the measured noise. The result accuracy decreases with the measured point number, and the iteration number decreases with the nest number. Moreover, the higher the measured noise goes, the lower the result accuracy will be. The results show that the ICS algorithm is accurate and efficient for the identification of thermal diffusion coefficients.
- heat conduction /
- inverse problem /
- thermal diffusion coefficient /
- improved cuckoo search algorithm /
- boundary element method

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