非线性二维导热反问题的混沌-正则化混合解法
|
摘要
考虑热传导系数随温度变化 ,建立了非线性二维稳态导热反问题数值计算模型· 并把混沌优化方法和梯度正则化方法相结合 ,构成一种混沌_正则化混合算法求该计算模型的全局解· 以热传导系数随温度线性变化为例 ,由布置在结构边界上的观测点温度信息确定了结构材料热传导系数及其随温度变化规律· 结果表明混合算法计算结果与初值无关 ,具有很好的全局寻优性能 ,而且计算量远比经典遗传算法和单纯采用混沌优化方法小·
A numerical model of nonlinear two_dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature. Combining the chaos optimization algorithm with the gradient regularization method, a chaos_regularization hybrid algorithm was proposed to solve the established numerical model. The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature_dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
A numerical model of nonlinear two_dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature. Combining the chaos optimization algorithm with the gradient regularization method, a chaos_regularization hybrid algorithm was proposed to solve the established numerical model. The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature_dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
引文
[1] StolzGJ .Numericalsolutiontoaninverseproblemofheatconductionforsimpleshapes[J].Jour nalofHeatTransfer,1960,82C(1):20—26.
[2] 俞昌铭.计算热物性参数的导热反问题[J].工程热物理学报,1982,3(4):372—378.
[3] KohnR ,VogelinsM .Determiningconductivitybyboundarymeasurements[J].CommunicationsonPureandAppliedMathematics,1984,37(3):289—298.
[4] TervolaP .Amethodtodeterminethethermalconductivityfrommeasueredtemperatureprofiles[J].InternationalJournalofHeatandMassTransfer,1989,32(8):1425—1430.
[5] LinJY ,ChengTF .Numericalestimationofthermalconductivityfromboundarytemperaturemea surements[J].NumericalHeatTransfer,1997,32A(2):187—203.
[6] GarciaS ,GuynnJ ,ScottEP .UseofgeneticalgorithmsinthermalpropertyestimationPartⅡ:si multaneousestimationofthermalproperties[J].NumericalHeatTransfer,1998,33A(2):149—168.
[7] 白博峰,郭烈锦,陈学俊.最小二乘原理求解多维瞬态导热反问题[J].计算物理,1997,14(4_5):696—698.
[8] 王登刚,刘迎曦,李守巨.非线性二维稳态导热反问题的一种数值解法[J].西安交通大学学报,2000,34(11):49—52.
[9] 黄光远,刘小军.数学物理反问题[M].济南:山东科学技术出版社,1993,57—61.
[10] TikhonovAN ,ArseninVY .SolutionsofIll_PosedProblems[M].FritzJohnTransl.Washington:WinstonPress,1977.(Englishversion)
[11] 唐立民,张文飞,刘迎曦.微分方程反问题的梯度正则化方法[J].计算结构力学及其应用,1991,8(2):123—129.
[12] 刘迎曦,王登刚,张家良,等.材料物性参数识别的梯度正则化方法[J].计算力学学报,2000,17(1):69—75.
[13] 王登刚,刘迎曦,李守巨.二维稳态导热反问题的正则化解法[J].吉林大学自然科学学报,2000,(2):56—60.
[14] 王东生,曹磊.混沌、分形及其应用[M].合肥:中国科技大学出版社,1995,25—92.
[15] 李兵,蒋慰孙.混沌优化方法及其应用[J].控制理论与应用,1997,14(4):613—615.
[16] 孔祥谦.有限单元法在传热学中的应用(第二版)[M].北京:科学出版社,1986,148—150.
[17] 杨文采.地球物理反演和地震层析成象[M].北京:地质出版社,1989,117—119.
[2] 俞昌铭.计算热物性参数的导热反问题[J].工程热物理学报,1982,3(4):372—378.
[3] KohnR ,VogelinsM .Determiningconductivitybyboundarymeasurements[J].CommunicationsonPureandAppliedMathematics,1984,37(3):289—298.
[4] TervolaP .Amethodtodeterminethethermalconductivityfrommeasueredtemperatureprofiles[J].InternationalJournalofHeatandMassTransfer,1989,32(8):1425—1430.
[5] LinJY ,ChengTF .Numericalestimationofthermalconductivityfromboundarytemperaturemea surements[J].NumericalHeatTransfer,1997,32A(2):187—203.
[6] GarciaS ,GuynnJ ,ScottEP .UseofgeneticalgorithmsinthermalpropertyestimationPartⅡ:si multaneousestimationofthermalproperties[J].NumericalHeatTransfer,1998,33A(2):149—168.
[7] 白博峰,郭烈锦,陈学俊.最小二乘原理求解多维瞬态导热反问题[J].计算物理,1997,14(4_5):696—698.
[8] 王登刚,刘迎曦,李守巨.非线性二维稳态导热反问题的一种数值解法[J].西安交通大学学报,2000,34(11):49—52.
[9] 黄光远,刘小军.数学物理反问题[M].济南:山东科学技术出版社,1993,57—61.
[10] TikhonovAN ,ArseninVY .SolutionsofIll_PosedProblems[M].FritzJohnTransl.Washington:WinstonPress,1977.(Englishversion)
[11] 唐立民,张文飞,刘迎曦.微分方程反问题的梯度正则化方法[J].计算结构力学及其应用,1991,8(2):123—129.
[12] 刘迎曦,王登刚,张家良,等.材料物性参数识别的梯度正则化方法[J].计算力学学报,2000,17(1):69—75.
[13] 王登刚,刘迎曦,李守巨.二维稳态导热反问题的正则化解法[J].吉林大学自然科学学报,2000,(2):56—60.
[14] 王东生,曹磊.混沌、分形及其应用[M].合肥:中国科技大学出版社,1995,25—92.
[15] 李兵,蒋慰孙.混沌优化方法及其应用[J].控制理论与应用,1997,14(4):613—615.
[16] 孔祥谦.有限单元法在传热学中的应用(第二版)[M].北京:科学出版社,1986,148—150.
[17] 杨文采.地球物理反演和地震层析成象[M].北京:地质出版社,1989,117—119.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心