【作者】 白乙拉；

【导师】 冯恩民； 李志军；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2006， 博士

【摘要】 本文以夏季北极海冰、天然河冰以及油浸风冷三相变压器的热传导问题为背景,依据原型实测温度数据,分别建立了各温度场相应的热传导方程和初边值条件及其分布参数系统参数辨识模型,在实现参数辨识的基础上,对给定的温度场进行了数值模拟。对上述参数辨识问题的研究,是国家自然科学基金资助项目(10471014,40233032)的一部分,这项研究不仅可推动一类非线性抛物型(高阶导数项系数依赖于状态变量)分布参数系统参数辨识问题的研究,还可推动对天然冰导温系数等热力学参数的优化辨识研究。另外,本文依据实验室冰样拖曳运动试验数据,研究了冰样与水流之间摩拖曳系数和形拖曳系数的优化辨识方法。本文研究的内容与取得的主要结果概括如下: 1、针对夏季北极雪/冰层内的热量传递问题,建立了描述雪/冰相变过程中的焓度、比焓和导焓系数的概念、焓度热传导方程与定解条件以及焓度与温度之间的转换关系,构造了以焓扩散系数为参量的分布参数系统参数辨识模型及优化算法。焓度热传导方程是一类高阶导数项系数依赖于状态变量的非光滑非线性抛物方程,证明了该方程初边值问题弱解的存在唯一性和解对控制参数的连续依赖性;应用Polak提出的不可微函数的优化理论和方法,分析得到了系统及其解的一些性质,证明了该参数辨识问题最优解的存在性及一阶最优性条件。根据中国第二次北极科学考察现场采集的雪/冰温度数据进行了数值模拟,数值模拟结果与实测温度吻合良好。 2、构造了以天然河冰导温系数为参量的非光滑分布参数系统参数辨识模型与优化算法,针对该参数辨识问题给出了其最优解的存在性及一阶最优性条件。利用天然河冰垂直剖面温度实测数据,辨识了天然冰(-0.19～-14.02℃)导温系数随温度的变化关系。特别对高温冰层进行了多组次有效辨识,获取了-0.19～-2.12℃天然冰的导温系数,反映出当冰温低于-0.76℃时,天然冰导温系数与温度的关系符合前人报道的结果;当温度处于相变区间(0～-0.76℃)时,导温系数随温度呈现强非线性关系,并给出了该非线性关系的数学表达式。 3、丛龙飞等在国内首次全面考虑大型油浸风冷变压器的流场、绕组和铁芯诸介质的温升计算问题,根据变压器温度场计算区域分片光滑的特点,建立了一个直角坐标系和两个柱坐标系下的分片光滑的温度场方程,并给出边界条件和各界面之间的穿透性条件,构造了以变压器油流速分布函数为参量的分布参数系统参数辨识模型,构成了多区域耦合的高度非光滑分布参数系统参数辨识问题。本文证明了该非光滑抛物系统弱解的存在唯一性、解对控制参数的连续依赖性;参数辨识问题最优解的存在性与最优性条件。更多还原

【Abstract】 With the background of the temperature fields of Arctic sea ice in summer, natural river ice and the oil-immersed wind-cooled three-phrase transformer, on the basis of the observed data, this dissertation establishes heat conduction equations with initial boundary conditions and distributed parameter identification models respectively. Then, the numerical simulation is performed. The study of the parameter identification problems, which is supported by the National Natural Science Foundation of China （Grant No. 10471014 and 40233032）, can promote not only the study of parameter identification problems for a class of nonlinear parabolic （coefficients of higher derivative terms depend on state variants） distributed parameter systems, but also the study of optimization and parameter identification for the thermodynamics parameters of natural ice （i.e. sea ice and river ice）. In addition, according to the data of current-ice drag experiments, the dissertation studies the optimization identification methods of the skin drag coefficients and the form drag coefficients between the ice samples and water current.The main contributions are as follows:1. For the heat transfer problems of the Arctic snow/ice layer in summer, the dissertation presents the definition of degree of enthalpy, specific enthalpy and enthalpy conduction, ceofficient, a heat conduction equation of enthalpy and the initial boundary conditions, and the transformation relationship of the enthalpy and temperature. The parameter identification model of distributed parameter systems of diffusion coefficients of enthalpy and optimistic algorithm are established. The heat conduction equation of degree of enthalpy is a non-smooth nonlinear parabolic equation which coefficients of higher derivative terms depend on degree of enthalpy. For the above parameter identification problems of distributed parameter systems, the dissertation proves the existence and uniqueness of weak solutions of the non-smooth parabolic equation and the continued dependence of solutions on control parameters. Some important properties of the system and its solutions are considered by using the optimization theory and methods of non-differentiable function of Polak, and the existence of optimal solutions and first-order optimality conditions are given. Based on the snow/ice temperature data presented by the Second China Arctic Research Expedition, numerical simulation results tally with the observed temperature.2. A parameter identification model of non-smooth distributed parameter systems about coefficients of thermal diffusivity of natural river ice and optimistic algorithm are established, the existence of optimal solution and first-order optimality conditions are presented for the parameter identification problems. On the basis of the vertical temperature profile data of natural river ice, the relationship between the thermal diffusivity of natural river ice （₀.19^-14.02°C） and the ice temperature is identified. Especially a lot of effective identifications are performed for the ice layer of higher temperature, thermal diffusivity of the natural ice between -0.19 and -2.12°C is obtained, which shows that when the ice temperature lowers than -0.76°C, the relationship between thermal diffusivity of river ice and temperature corresponds with the previous;when the temperature is in phase-change range（0—0.76’>C）,the relationship of thermal diffusivity and ice temperature is nonlinear, and for this relationship, the nonlinear mathematical equations are given.3. Cong Longfei et al. have first considered computation problems of temperature rise of flow field, coil and iron core in the oil-immersed wind-cooled three-phrase transformer. Based on the piece-smooth characteristic of the computation range of transformer temperature field, [60] established piece-smooth temperature equations of a rectangular coordinate system and two cylindrical coordinate systems, boundary conditions and penetrability conditions among the interfaces, and formulated the parameter identification model of distributed parameter systems of distributed function of flow velocity of transformer oil, which constituted a multi-domain coupled parameter identification problem of non-smooth distributed parameter system. The dissertation proves the existence and uniqueness of the weak solutions of non-smooth parabolic system, the continuous dependence of solutions on the control variables, the existence of optimal solution of optimal control problem and optimality conditions.4. Drag movement experiments are performed to obtain movement data of ice samples by using a wave-current tank in laboratory for freshwater ice samples. Current-ice drag coefficient is divided into skin drag coefficient and form drag coefficient. Two roughness indexes - profile bearing length rate and deviation of the profile are introduced. By analyzing the relationships of coefficients and indexes, it is found that skin drag coefficient is direct proportion to profile bearing length rate of ice sample bottom, and form drag coefficient increases nonlinearly with the change of sum of average length/draft ratio and root-mean-square deviation of the bottom profile. These relationships uniform the skin drag coefficients of ice floe and iceberg.更多还原