基于小波算法的二阶线性定常分布参数系统的辨识

Wavelets Algorithm-based Identification of Linear Time-Invariant Second-Order Distributed Parameter System

本文基于正交函数逼近方法,借助于小波变换,并利用其运算矩阵及其运算性质,研究了分布参数系统的辨识问题。将Haar小波正交基应用于分布参数系统的辨识中,经正交小波逼近变换,将原偏微分描述的分布参数系统转化为代数矩阵方程,并且,考虑了初始条件和边界条件,获得了算法简单、计算方便、具有较高精度的辨识算法,简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法。仿真实例表明了本文所提出的算法的有效性。

In this paper, based on the orthogonal function approximation theory and with the help of the wavelets transform and their operational matrices, the identification problem of a class linear time-invariant second-order distributed parameter system is investigated. Haar wavelets and some operational matrices of Haar wavelets have been chosen to solve the presented problem. Because of these applications, time-invariant second-order distributed parameter system described by PDEs has been not only transformed into a LPS problem but also taking into account of initial conditions and boundary conditions. The proposed method has advantages of simple algorithm and less computation, simplifying the process of solution. Simulation example shows the presented method is an efficient algorithm for the parameters identification of linear time-invariant second-order distributed parameter system.