Parameter Identification Of Non-smooth Distributed Parameter Systems And Its Application

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.