Research for Parameter Estimation of Distributed Parameter Systems

分布参数系统的参数估计研究

基本信息

批准号：
59350021
负责人：
SUNAHARA Yoshifumi
金额：
$ 4.8万
依托单位：
Kyoto Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1984
资助国家：
日本
起止时间：
1984 至 1986
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-59350021/
关键词：
Distributed parameter system Stochastic distributed parameter system Partial differential equation Stochastic partial differential equation Functional space Parameter estimation Minimum variance estimate 最丈推定

项目摘要

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

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温度、压力等的扩散和/或分布的几个物理系统以及具有移动边界和存在条件的系统。从数学角度对所建立的模型进行唯一解的研究，从而建立了分布参数系统的建模。 2．参数估计理论数学公式的建立：已经建立了参数估计方法，用于估计数学系统模型和/或其边界条件中出现的未知参数，主要思想是引入最小方差估计和最大似然估计，并且在此合作期间。研究中，参数估计理论主要从集总参数系统发展到分布参数系统。参数估计算法的调整和发展：虽然参数估计的数值计算量如此庞大和复杂，但在本研究中，参数估计的数值计算量巨大且复杂。，通过引入有限元方法和边界元方法的研究，为参数估计数值计算方法的建立做出了巨大的贡献，并且对无限维系统用合适的有限维系统逼近时的计算精度问题进行了研究。 4. 参数估计算法在实际系统中的应用：本研究中开发的算法在遥感领域得到应用和测试，使用陆地卫星数据、太阳能收集系统、空间技术、的估计5．结论：如本格式所附的研究报告所示，本次合作研究在分布式参数系统的参数估计方面取得了巨大的成功。