Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems

doi:10.11949/j.issn.0438-1157.20150308

CIESC Journal ›› 2015, Vol. 66 ›› Issue (S1): 106-110.DOI: 10.11949/j.issn.0438-1157.20150308

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Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems

CUI Miao, DUAN Weiwei, GAO Xiaowei

State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning, China

Received:2015-03-11 Revised:2015-03-18 Online:2015-06-30 Published:2015-06-30
Supported by:
supported by the National Natural Science Foundation of China(51206014) and the Fundamental Research Funds for the Central Universities (DUT14LK03).

基于复变量求导法的共轭梯度法及其在热传导反问题边界条件辨识中的应用

崔苗, 端维伟, 高效伟

大连理工大学航空航天学院, 工业装备结构分析国家重点实验室, 辽宁大连 116024

通讯作者: 崔苗
基金资助:
国家自然科学基金项目(51206014);中央高校基本科研业务费项目(DUT14LK03)。

Abstract

Abstract:

The conventional conjugate gradient method is improved to utilize its advantage of high accuracy and fast convergence, and to avoid the complicated differentiating and derivation processes for solving nonlinear inverse heat conduction problems. In the present work, the complex-variable-differentiation method is introduced into the conventional conjugate gradient method, which is employed to precisely calculate the sensitivity coefficients. Transient nonlinear inverse heat conduction problems are solved, and then the boundary conditions are identified. Numerical examples are given to show the effectiveness and high accuracy. Compared with the conventional conjugate gradient method, the present algorithm has the advantage of easier implementation and higher accuracy.

Key words: conjugate gradient method, complex-variable-differentiation method, boundary condition, identification

摘要：

为了利用共轭梯度法的计算精度高和收敛速度快的优点, 避免传统共轭梯度法在求解非线性热传导反问题中的微分处理、复杂的推导过程等问题, 给出一种改进的共轭梯度法, 即将复变量求导法引入传统的共轭梯度法, 准确计算了各灵敏度系数, 进而对瞬态非线性热传导反问题进行求解, 并对边界条件进行辨识。算例验证了本文方法的有效性与精度。与传统共轭梯度法相比, 在处理非线性问题方面, 本文方法具有操作简单和精度高的优点。

关键词: 共轭梯度法, 复变量求导法, 边界条件, 辨识

CLC Number:

TK124

CUI Miao, DUAN Weiwei, GAO Xiaowei. Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems[J]. CIESC Journal, 2015, 66(S1): 106-110.

崔苗, 端维伟, 高效伟. 基于复变量求导法的共轭梯度法及其在热传导反问题边界条件辨识中的应用[J]. 化工学报, 2015, 66(S1): 106-110.

References 21

[1]	Frackowiak A, Wolfersdorf J V, Cialkowski M. Solution of the inverse heat conduction problem described by the Poisson equation for a cooled gas-turbine blade [J]. International Journal of Heat and Mass Transfer, 2011, 54(5/6): 1236-1243.
[2]	Liu Fungbao. A hybrid method for the inverse heat transfer of estimating fluid thermal conductivity and heat capacity [J]. International Journal of Thermal Sciences, 2011, 50(5): 718-724.
[3]	Yu Xiaochun, Bai Yuguang, Cui Miao, Gao Xiaowei. Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method [J]. Science China-Physics, Mechanics & Astronomy, 2013, 56(5): 966-973.
[4]	Cui Miao, Zhu Qianghua, Gao Xiaowei. A modified conjugate gradient method for transient nonlinear inverse heat conduction problems: a case study for identifying temperature-dependent thermal conductivities [J]. Journal of Heat Transfer-Transactions of the ASME, 2014, 136(9): 091301.
[5]	Monde Masanori, Kosaka Masataka, Mitsutake Yuichi. Simple measurement of thermal diffusivity and thermal conductivity using inverse solution for one-dimensional heat conduction [J]. International Journal of Heat and Mass Transfer, 2010, 53(23/24): 5343-5349.
[6]	Wang Guangjun, Zhu Lina, Chen Hong. A decentralized fuzzy inference method for solving the two-dimensional steady inverse heat conduction problem of estimating boundary condition [J]. International Journal of Heat and Mass Transfer, 2011, 54(13/14): 2782-2788.
[7]	Shi Hongchen(石宏臣), Zhang Xiaohuai(张晓怀), Sun Fengrui(孙丰瑞), Yang Li(杨立), Wang Weiqing(王为清). Inverse heat transfer algorithm for liqid-level detection of storage tank based on infrared imaging temperature measurement[J]. CIESC Journal(化工学报), 2012, 63(12): 3771-3775.
[8]	Lu Shuai, Heng Yi, Mhamdi Adel. A robust and fast algorithm for three-dimensional transient inverse heat conduction problems [J]. International Journal of Heat and Mass Transfer, 2012, 55(25/26): 7865-7872.
[9]	Liu Fungbao. Particle swarm optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux [J]. International Journal of Heat and Mass Transfer, 2012, 55(7/8): 2062-2068.
[10]	Khajehpour S, Hematiyan M R, Marin L. A domain decomposition method for the stable analysis of inverse nonlinear transient heat conduction problems [J]. International Journal of Heat and Mass Transfer, 2013, 58(1/2): 125-134.
[11]	Huang Shaojun(黄少君), Lu Mei(卢玫), Zhang Tao(张涛), Tao Liang(陶亮). An ant colony optimization algorithm suitable for searching heat source location in IHCP [J]. Journal of Engineering Thermophysics(工程热物理学报), 2013, 34(4): 694-697.
[12]	Movahedian B, Boroomand B. The solution of direct and inverse transient heat conduction problems with layered materials using exponential basis functions [J]. International Journal of Thermal Sciences, 2014, 77: 186-198.
[13]	Czel Balazs, Grof Gyula. Inverse identification of temperature- dependent thermal conductivity via genetic algorithm with cost function-based rearrangement of genes [J]. International Journal of Heat and Mass Transfer, 2012, 55(15/16): 4254-4263.
[14]	Pourgholi Reza, Dana Hassan, Tabasi Seyed Hashem. Solving an inverse heat conduction problem using genetic algorithm: sequential and multi-core parallelization approach [J]. Applied Mathematical Modelling, 2014, 38: 1948-1958.
[15]	Reddy B Konda, Balaji C. Bayesian estimation of heat flux and thermal diffusivity using liquid crystal thermography [J]. International Journal of Thermal Sciences, 2015, 87: 31-48.
[16]	Li Yanhao, Wang Guangjun, Chen Hong. Simultaneously estimation for surface heat fluxes of steel slab in a reheating furnace based on DMC predictive control [J]. Applied Thermal Engineering, 2015, doi: 10.1016/j.applthermaleng. 2015. 01. 069.
[17]	Zhou Jianhua, Zhang Yuwen, Chen J K, Feng Z C. Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object [J]. International Journal of Thermal Sciences, 2010, 49: 1669-1679.
[18]	Lin David T W, Yan Wei-Mon, Li Hung-Yi. Inverse problem of unsteady conjugated forced convection in parallel plate channels [J]. International Journal of Heat and Mass Transfer, 2008, 51(5/6): 993-1002.
[19]	Lü Shigui(吕事桂), Yang Li(杨立), Fan Chunli(范春利). Identification of irregular pipeline geometry boundary using infrared transient inspection based on finite element discretization [J]. CIESC Journal(化工学报), 2012, 63(12):3806-3811.
[20]	Cui Miao(崔苗), Gao Xiaowei(高效伟), Liu Yunfei(刘云飞). Inversion of temperature-dependent thermal conductivity based on transient inverse heat conduction problems [J]. Proceedings of the CSEE(中国电机工程学报), 2012, 32(14): 82-87.
[21]	Lyness N, Moler C B. Numerical differentiation of analytic functions [J]. SIAM Journal on Numerical Analysis, 1967, 4(2): 202-210.

Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems

基于复变量求导法的共轭梯度法及其在热传导反问题边界条件辨识中的应用

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