引用本文:邓建华.辨识非线性曲线的非线性极大似然—优化法[J].控制理论与应用,1991,8(4):407~413.[点击复制]
Deng Jianhua.Non-Linear Maximum Likelihood -Optimization Method for Identifying Non-Linear Curve[J].Control Theory and Technology,1991,8(4):407~413.[点击复制]
辨识非线性曲线的非线性极大似然—优化法
Non-Linear Maximum Likelihood -Optimization Method for Identifying Non-Linear Curve
摘要点击 827  全文点击 376  投稿时间：1990-03-23  修订日期：1991-03-25
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DOI编号  
  1991,8(4):407-413
中文关键词  非线性曲线辨识  极大似然法  优化法  样条函数  飞行器极曲线
英文关键词  non-linear curve identification  maximum likelihood method  optimization method  spline function  polar curve of an aircraft
基金项目  
作者单位
邓建华 西北工业大学飞机系 
中文摘要
      工程上经常碰到非线性曲线辨识问题。本文探讨一种非线性极大似然—优化法并结合三次样条函数拟配法，形成统一的逐次逼近的直接辨识非线性曲线的非线性辨识方法。该法兼有极大似然法的唯一性、很好的收敛性和优化法直接处理非线性系统的能力，辨识出的样条函数曲线能无限地光滑地逼近非线性曲线。
英文摘要
      In the engineering field we are often faced with a problem that from test date is determined a non-linear curve which is strongly non-linear and not expressed by an analytical formula, e.g. it is absolutely necessary in aircraft flight test data analysis that from flight test data is determined a polar diagram (curve) which is a basic aerodynamic characteristics curve to calculate a flight performance. The above problem may be included in non-linear curve identification. In this paper research on a non-linear maximum likelihood-optimization method for identifying non-linear curve is presented. A general idea of this method is: first the non-linear curve is approached by a suitable function system (e.g. a cubical spline-polynomial); secondly the non-linear curve identification is transformed into a normal parameter identification; thirdly a criterion of a maximum likelihood function is built; finally is established a unified successive iterate procedure that criterion of the maximum likelihood function is driven into an extreme using an optimization method. This method has a uniqueness and a good astringency of the maximum likelihood method and a capability of solving a non-linear problem by the optimization method. An identified function curve (e.g. a cubical spline function curve) can approach the non-linear curve unlimitedly smoothly. In this paper a fundamental principle of this method and its application to identity above polar curve of an aircraft are presented.