Research for Parameter Estimation of Distributed Parameter Systems

1.随机分布参数系统的数学模型及其数学方面：已经建立了数学模型来描述几个物理系统的扩散和/或温度，压力等的分布以及具有移动边界的系统。并从数学的角度研究了所建立的模型存在唯一解的条件，建立了分布参数系统的模型.参数估计理论的数学公式的建立：已经建立了几种参数估计方法，用于估计出现在数学系统模型和/或其边界条件中的未知参数。主要思想是引入最小方差估计和最大似然估计，在这次合作研究中，参数估计理论从集中参数系统得到了广泛的发展， ...更多信息 分布式参数的一个。参数估计算法的调整与发展：虽然参数估计的数值计算是如此的庞大和复杂，但本研究通过引入有限元法和边界元法，为建立参数估计的数值计算方法做出了很大的贡献。此外，研究的计算精度，这是中心问题时，无限维系统的近似由适当的有限维的进行和贡献的数值算法的发展.参数估计算法在真实的系统中的应用：本研究开发的算法在LANDSAT数据遥感、太阳能收集系统、空间技术、气象场估计等领域进行了应用和测试.结论：如本格式所附研究报告所示，本合作研究在分布参数系统参数估计的系统研究方面取得了巨大成功。少

1. Mathematical Models of Stochastic Distributed Parameter Systems and Their Mathematical Aspects: Mathematical models have been established for describing several physical systems of diffusions and/or distributions of temperature, pressure, etc. as well as systems having moving boundaries. And conditions of the existence of unique solutions were studied for the established models from the mathematical point of view, and then the modelling of the distributed parameter systems has been established.2. Establishment of Mathematical Formulation of Parameter Estimation Theory: Several methods of the parameter estimation have been established for estimating unknown parameters appearing in the mathematical system models and/or in their boundary conditions. The main ideas were the introduction of the minimum variance estimate and the maximum likelihood one, and, during this Co-operative Research, the theory of parameter estimation was extensively developed from the lumped parameter systems to … More the distributed parameter ones.3. Adjustment and Development of Parameter Estimation Algorithms: Although the numerical computation for the parameter estimation is so massive and complicated, in this research, by introducing the finite element method and the boundary element method, a great contribution was made for establishing the method of numerical computation of parameter estimation. Also the investigation of the computational accuracy which is the central issue when the infinite-dimensional systems are approximated by suitable finite-dimensional ones was performed and contributed in the development of numerical algorithms.4. Application of Parameter Estimation Algorithms to Real Systems: Algorithms developed in this research were applied and tested in the field of remote-sensing using the LANDSAT data, solar energy collection system, space technology, estimation of meteorological field, and so on.5. Conclusion: As shown in the research report attached to this format, this Co-operative Research has achieved a great success in the systematic study of parameter estimation for the distributed parameter systems. Less