寒区水库淡水冰导温系数的参数辨识与应用
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摘要
本文以淡水冰的热传导过程为背景，根据黑龙江红旗泡水库淡水冰的现场观测数据，利用分布参数系统的参数辨识方法，辨识得到了淡水冰的导温系数依赖于冰温的变化关系式，并使用该关系式模拟山西太原汾河二库淡水冰温度场的变化情况。本文所研究的内容是国家自然科学基金项目（No:40806075）的一部分。本文的主要研究结果概括如下：
1.本文利用在黑龙江红旗泡水库现场观测获得的气温、水库淡水冰表面总辐射、冰内的温度、冰的厚度、水库冰盖下水温等系列数据。依据分布参数系统的参数辨识方法，把实测数据每两天为一组，分为87组，将每组数据用线性函数和指数函数分别拟合导温系数，以寻求导温系数同温度的微小变化关系，最后归纳出整个温度区间上的导温系数函数。
2.在模拟2004年山西太原汾河二库淡水冰的温度场变化情况时，模型中的淡水冰导温系数分别使用经验性的常数和辨识得到的与冰温有关的导温系数关系式。然后，将两种导温系数模拟的冰温进行对比。结果表明：使用辨识得到的导温系数关系式模拟的冰温与实测冰温间的误差更小。从而说明辨识得到的导温系数关系式更符合实际情况。
With fresh ice heat-conduction as the background, based on the siteobservation data of fresh ice temperature in Hong Qipao Reservoir, we used theparameter identification of distributed parameter system, and get the relationalexpression that was between fresh ice thermal diffusivity and ice temperature. Weapplied this relational expression to simulate the situation of ice temperature inShanxi. The study in this paper is supported by the national natural sciencefoundation of China (40806075). The major academic achievements of this paperas follows:
We use the data of the temperature, total radiation in reservoir of ice surface,ice temperature, ice thickness and water temperature et cetera that we observed inHong Qipao Reservoir. Based on the parameter identification method of parametersystem,87groups of data can be got by two days a group. Used linear and indexfunction fitted thermal diffusivity, for finding relationship between thermaldiffusivity and ice temperature. Finally we summarized thermal diffusivityrelationship during temperature region.
2. We applied the relational expression that is empirical constant and thermaldiffusivity about ice temperature, when we simulate fresh ice temperature inShanxi in2004. Then compare to these two results. The results show that the icetemperature, which was simulating the given relational expression of thermaldiffusivity, is close to observing ice temperature.
1.本文利用在黑龙江红旗泡水库现场观测获得的气温、水库淡水冰表面总辐射、冰内的温度、冰的厚度、水库冰盖下水温等系列数据。依据分布参数系统的参数辨识方法，把实测数据每两天为一组，分为87组，将每组数据用线性函数和指数函数分别拟合导温系数，以寻求导温系数同温度的微小变化关系，最后归纳出整个温度区间上的导温系数函数。
2.在模拟2004年山西太原汾河二库淡水冰的温度场变化情况时，模型中的淡水冰导温系数分别使用经验性的常数和辨识得到的与冰温有关的导温系数关系式。然后，将两种导温系数模拟的冰温进行对比。结果表明：使用辨识得到的导温系数关系式模拟的冰温与实测冰温间的误差更小。从而说明辨识得到的导温系数关系式更符合实际情况。
With fresh ice heat-conduction as the background, based on the siteobservation data of fresh ice temperature in Hong Qipao Reservoir, we used theparameter identification of distributed parameter system, and get the relationalexpression that was between fresh ice thermal diffusivity and ice temperature. Weapplied this relational expression to simulate the situation of ice temperature inShanxi. The study in this paper is supported by the national natural sciencefoundation of China (40806075). The major academic achievements of this paperas follows:
We use the data of the temperature, total radiation in reservoir of ice surface,ice temperature, ice thickness and water temperature et cetera that we observed inHong Qipao Reservoir. Based on the parameter identification method of parametersystem,87groups of data can be got by two days a group. Used linear and indexfunction fitted thermal diffusivity, for finding relationship between thermaldiffusivity and ice temperature. Finally we summarized thermal diffusivityrelationship during temperature region.
2. We applied the relational expression that is empirical constant and thermaldiffusivity about ice temperature, when we simulate fresh ice temperature inShanxi in2004. Then compare to these two results. The results show that the icetemperature, which was simulating the given relational expression of thermaldiffusivity, is close to observing ice temperature.
引文
[1]王康宁,分布参数控制系统,北京:科学出版社,1986.
[2] J. L. Lions, E. Magenes, Non-homogeneous Boundary Value Problems and Applications,New York: Springer-Verlag,1972.
[3] K. N. Wang, Controllability and Observability for Distributed Parameter Control Systems,Acta Mathematica Scientia,1982,4(3),403-420.
[4]王康宁,分布参数控制系统的镇定问题,控制理论与应用,1984,1(2),11-21.
[5]李训经,姚允龙,分布参数系统的时间最优控制,中国科学,1980,23(7),619-627.
[6]王勇,分布参数系统辨识与最优控制及在地史模拟中的应用,大连:大连理工大学,2002.
[7]王康宁,最优控制的数学理论,北京:国防工业出版社,1995．
[8]茅泽育,吴剑疆,佘云童,河冰生消演变及其运动规律的研究进展,水力发电学报,2002,76(1),153-161.
[9] S. Beltaos, K. S. Davar, B. Pratte, A Primer on Hydraulics of Ice Covered River, Canada:Environmental Citizenship,1996.
[10]R. Pariset, H. Hausser, Formation and Evolution of Ice Covers on Rivers, Transactions ofthe Engineering Institute of Canada,1961,5(1),41-49.
[11]F. E. Parkinson, Water Temperature Observations during Break-up on the Liard-MackenzieRiver System, Proc., Workshop on Hydraulics of Ice-covered Rivers, Edmonton,1982.
[12]V. Matousek, Types of Ice Run and Conditions for Their Formation, IAHR Ice Symp,1984.
[13]U. Svensson, L. Billfalk, L. Hammar, A Mathematical Model of Border-ice FormationinRiver, Cold Regions Science and Technology,1989,16(2),179-189.
[14]S. Beltaos, Fracture and Breakup of River Ice Cover, Canadian Journal of CivilEngineering,1990,17(2),173-183.
[15]L. Hammar, T. H. Shen, Frazil Evolution in Channels, Journal of Hydraulic Res,1995,33(3),291-306.
[16]A. M. W. Lal, H. T. Shen, Mathematical Model for River Ice Processes, Journal ofHydraulic Engineering,1991,117(7),851-867.
[17]H. Shend, D. S. Wang, Under Cover Transport and Accumulation of Frazil Granules,Journal of Hydraulic Engrg,1995,120(2),184-194.
[18]S. F. Daly, Fracture of River Ice Cover by River Waves, Journal of Cold RegionsEngineering,1995,9(1),41-52.
[19]B. T. Smith, R. Ettema, Flow Resistance in Ice-covered Alluvial Channels, Journal ofHydraulic Engineering,1997,123(7),592-599.
[20]白乙拉,李志军,冯恩民,韩明,卢鹏,静水条件下淡水冰有效导温系数的优化辨识,计算力学学报,2007,24(2),187-191.
[21]霍耀东,陆君安,李汀芳,乔殿石,谢永刚,水库冰盖数值予报方法,武汉水利电力大学学报,1993,26(5),530-536.
[22]张学成,可素娟,潘启民,赵安林,黄河冰盖厚度演变数学模型,冰川冻土,2002,24(2),203-205.
[23]肖建民,金龙海,谢永刚,霍跃东,寒区水库冰盖形成与消融机理分析,水利学报.2004,35(6),80-85.
[24]李志军,孙万光,许士国,李青山,白炎,王昕,短期水文气象资料估算哈尔滨至同江冰厚度,水科学进展,2009,20(3),428-433.
[25]冯景山,白乙拉,李冰,寒区水库冰盖厚度增长数值模拟研究,渤海大学学报,2011,32(1),5-9.
[26]白乙拉,李志军,冯恩民,水库天然冰温度场数值模拟,黑龙江大学自然科学学报,2006,23(3),331-335.
[27]茅泽育,许昕,王爱民,张磊,岳光溪,开河期冰坝预测方法研究进展,水利水电科技进展,2007,27(3),76-94.
[28]可素娟,张学成,王玉明,封河预报数学模型研究,冰川冻土,2001,23(3),28-332.
[29]陆金甫,关治,偏微分方程数值解法,北京：清华大学出版社,2005.
[30]M. S. Bazaraa, D. Sherali, C. M. Shetty, Nonlinear Programming: Theory and Algorithms,New York: John Wiley and Sons Ltd,1993.
[31]唐焕文,秦学文,实用最优化方法,大连：大连理工大学出版社,2009.
[32]J. Launiainen, B Cheng, Modeling of Ice Thermodynamics in Natural Water Bodies, ColdRegions Science and Technology,1998,27(3),153-178.
[33]K. D. White, Review of Prediction Methods for Break Ice Jam, Canadian Journal of CivilEngineering,2003,30(1),1-12.
[34]茅泽育,吴剑疆,张磊,张瑞廷,天然河道冰塞演变发展的数值模拟,水科学进展,2003,14(6),700-705.
[35]李志军,杨宇,彭旭明,王国志,卢永超,黑龙江红旗泡水库冰生长过程现场观测数据分析,西安理工大学学报,2009,25(3),270-274.
[36]M. Sturm, J. Holmgren, M. Koenig, K. Morris, The Thermal Conductivity of SeasonalSnow, Journal of Glaciology,1997,43(143),26-41.
[37]P. H. Franses, G. Koop, R. Feistel, E. Hagen, A Gibbs Thermodynamic Potential of Sea Ice,Cold Regions Science and Technology,1998,28(2),83-142.
[38]U. Hammerschmidt, Thermal Transport Properties of Water and Ice from One SingleExperiment, International Journal of Thermophysics,2002,23(4),975-996.
[39]李荣华,偏微分方程数值解法,北京：高等教育出版社,2005.
[40]王索成,孟凡静,卢永超,红旗泡水库水质监测分析,黑龙江水利科技,2008,36(3),134-134.
[41]白乙拉,非光滑分布参数系统参数辨识及其应用,大连：大连理工大学,2006.
[42]Y. C. Yen, Review of Thermal Properties of Snow, Ice and Sea Ice, Hanover, NH, USA: U.S. Army, Corps of Engineers, Cold Regions Research and Engineering Laboratory,1981.
[43]N. V. Koubyshkin, K. E. Sazonov, Evaluation of Loads Due to Partial Freezing of SeawaterTrapped in Enclosed Cavities, Proceedings of17th International Symposium on Ice,2004.
[44]G. D. Ashton, River ice, Annual Review of Fluid Mechanics,1978,10(1),369-392.
[45]程斌,一维海冰热力模式的守恒型差分格式和数值模拟,海洋通报,1996,15(4),8-16.
[2] J. L. Lions, E. Magenes, Non-homogeneous Boundary Value Problems and Applications,New York: Springer-Verlag,1972.
[3] K. N. Wang, Controllability and Observability for Distributed Parameter Control Systems,Acta Mathematica Scientia,1982,4(3),403-420.
[4]王康宁,分布参数控制系统的镇定问题,控制理论与应用,1984,1(2),11-21.
[5]李训经,姚允龙,分布参数系统的时间最优控制,中国科学,1980,23(7),619-627.
[6]王勇,分布参数系统辨识与最优控制及在地史模拟中的应用,大连:大连理工大学,2002.
[7]王康宁,最优控制的数学理论,北京:国防工业出版社,1995．
[8]茅泽育,吴剑疆,佘云童,河冰生消演变及其运动规律的研究进展,水力发电学报,2002,76(1),153-161.
[9] S. Beltaos, K. S. Davar, B. Pratte, A Primer on Hydraulics of Ice Covered River, Canada:Environmental Citizenship,1996.
[10]R. Pariset, H. Hausser, Formation and Evolution of Ice Covers on Rivers, Transactions ofthe Engineering Institute of Canada,1961,5(1),41-49.
[11]F. E. Parkinson, Water Temperature Observations during Break-up on the Liard-MackenzieRiver System, Proc., Workshop on Hydraulics of Ice-covered Rivers, Edmonton,1982.
[12]V. Matousek, Types of Ice Run and Conditions for Their Formation, IAHR Ice Symp,1984.
[13]U. Svensson, L. Billfalk, L. Hammar, A Mathematical Model of Border-ice FormationinRiver, Cold Regions Science and Technology,1989,16(2),179-189.
[14]S. Beltaos, Fracture and Breakup of River Ice Cover, Canadian Journal of CivilEngineering,1990,17(2),173-183.
[15]L. Hammar, T. H. Shen, Frazil Evolution in Channels, Journal of Hydraulic Res,1995,33(3),291-306.
[16]A. M. W. Lal, H. T. Shen, Mathematical Model for River Ice Processes, Journal ofHydraulic Engineering,1991,117(7),851-867.
[17]H. Shend, D. S. Wang, Under Cover Transport and Accumulation of Frazil Granules,Journal of Hydraulic Engrg,1995,120(2),184-194.
[18]S. F. Daly, Fracture of River Ice Cover by River Waves, Journal of Cold RegionsEngineering,1995,9(1),41-52.
[19]B. T. Smith, R. Ettema, Flow Resistance in Ice-covered Alluvial Channels, Journal ofHydraulic Engineering,1997,123(7),592-599.
[20]白乙拉,李志军,冯恩民,韩明,卢鹏,静水条件下淡水冰有效导温系数的优化辨识,计算力学学报,2007,24(2),187-191.
[21]霍耀东,陆君安,李汀芳,乔殿石,谢永刚,水库冰盖数值予报方法,武汉水利电力大学学报,1993,26(5),530-536.
[22]张学成,可素娟,潘启民,赵安林,黄河冰盖厚度演变数学模型,冰川冻土,2002,24(2),203-205.
[23]肖建民,金龙海,谢永刚,霍跃东,寒区水库冰盖形成与消融机理分析,水利学报.2004,35(6),80-85.
[24]李志军,孙万光,许士国,李青山,白炎,王昕,短期水文气象资料估算哈尔滨至同江冰厚度,水科学进展,2009,20(3),428-433.
[25]冯景山,白乙拉,李冰,寒区水库冰盖厚度增长数值模拟研究,渤海大学学报,2011,32(1),5-9.
[26]白乙拉,李志军,冯恩民,水库天然冰温度场数值模拟,黑龙江大学自然科学学报,2006,23(3),331-335.
[27]茅泽育,许昕,王爱民,张磊,岳光溪,开河期冰坝预测方法研究进展,水利水电科技进展,2007,27(3),76-94.
[28]可素娟,张学成,王玉明,封河预报数学模型研究,冰川冻土,2001,23(3),28-332.
[29]陆金甫,关治,偏微分方程数值解法,北京：清华大学出版社,2005.
[30]M. S. Bazaraa, D. Sherali, C. M. Shetty, Nonlinear Programming: Theory and Algorithms,New York: John Wiley and Sons Ltd,1993.
[31]唐焕文,秦学文,实用最优化方法,大连：大连理工大学出版社,2009.
[32]J. Launiainen, B Cheng, Modeling of Ice Thermodynamics in Natural Water Bodies, ColdRegions Science and Technology,1998,27(3),153-178.
[33]K. D. White, Review of Prediction Methods for Break Ice Jam, Canadian Journal of CivilEngineering,2003,30(1),1-12.
[34]茅泽育,吴剑疆,张磊,张瑞廷,天然河道冰塞演变发展的数值模拟,水科学进展,2003,14(6),700-705.
[35]李志军,杨宇,彭旭明,王国志,卢永超,黑龙江红旗泡水库冰生长过程现场观测数据分析,西安理工大学学报,2009,25(3),270-274.
[36]M. Sturm, J. Holmgren, M. Koenig, K. Morris, The Thermal Conductivity of SeasonalSnow, Journal of Glaciology,1997,43(143),26-41.
[37]P. H. Franses, G. Koop, R. Feistel, E. Hagen, A Gibbs Thermodynamic Potential of Sea Ice,Cold Regions Science and Technology,1998,28(2),83-142.
[38]U. Hammerschmidt, Thermal Transport Properties of Water and Ice from One SingleExperiment, International Journal of Thermophysics,2002,23(4),975-996.
[39]李荣华,偏微分方程数值解法,北京：高等教育出版社,2005.
[40]王索成,孟凡静,卢永超,红旗泡水库水质监测分析,黑龙江水利科技,2008,36(3),134-134.
[41]白乙拉,非光滑分布参数系统参数辨识及其应用,大连：大连理工大学,2006.
[42]Y. C. Yen, Review of Thermal Properties of Snow, Ice and Sea Ice, Hanover, NH, USA: U.S. Army, Corps of Engineers, Cold Regions Research and Engineering Laboratory,1981.
[43]N. V. Koubyshkin, K. E. Sazonov, Evaluation of Loads Due to Partial Freezing of SeawaterTrapped in Enclosed Cavities, Proceedings of17th International Symposium on Ice,2004.
[44]G. D. Ashton, River ice, Annual Review of Fluid Mechanics,1978,10(1),369-392.
[45]程斌,一维海冰热力模式的守恒型差分格式和数值模拟,海洋通报,1996,15(4),8-16.