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

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。

In the engineering field we arc often faced with a problem that from test data is determined a non-linear curve which is strongly non-linear and not expressed by an analytical formula ,c. g. it is absolutely necessaryin aircraft flight test data analysis that from flight test data is determined a polar diagram (curve) which is a basic aerodynamic characteristic curve to calculate a flight performance. The above problem may be included in non-lincar curve identification. In this paper research on a non-linear maximum likelihood-optimization method for identifying the 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 a 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 (c. 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 identify above polar curve of an aircraft are presented.