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

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

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.