论文部分内容阅读
系统辨识是系统理论中的一个重要组成部分,为了准确地建立系统的数学模型,它是一个不可缺少的环节。 系统辨识是通过对系统输入、输出信号的数据处理,采用各种非线性规划方法确定系统特征值和特征向量,继之确定系统的各种真实分布参数。对比前后两次系统辨识的结果,可以用来“诊断”一个结构物(系统)的损坏及损坏部位。 系统辨识中的一个关键问题是非线性曲线拟合。由于结构物都是高阶系统,且各特征值分布比较密(或有疏有密),这时各种非线性规划法收敛速度很慢。本文提出所谓“假梯度”法,大大加速了目标函数在汉森矩阵(Hessian Matrix)特征值不相同情况下的收敛速度,计算准确,适用于任何高阶系统的参数辨识,为结构物的损坏及损坏部位的“诊断”提供了切实可行的途径。 本文是作者在美国马里兰大学机械系“系统辨识及其应用”研究小组的工作的一部分。
System identification is an important part of the system theory. In order to establish the mathematical model of the system accurately, it is an indispensable link. The system identification is through the data processing of the input and output signals of the system. Various nonlinear planning methods are used to determine the system eigenvalues and eigenvectors, and then the various real distribution parameters of the system are determined. The results of the two system identifications before and after comparison can be used to “diagnose” the damage and damage to a structure (system). A key issue in system identification is nonlinear curve fitting. Because the structures are all high-order systems, and the distribution of the eigenvalues is dense (or sparse and dense), the convergence speed of various nonlinear programming methods is very slow. In this paper, the so-called “pseudo-gradient” method is proposed, which greatly accelerates the convergence rate of the objective function when the eigenvalues of the Hessian matrix are not the same. The calculation is accurate and can be applied to the parameter identification of any high-order system and damage the structure. The “diagnosis” of the damaged area and its location provide a practical way. This article is part of the author’s work in the “System Identification and Applications” research group at the Department of Mechanical Engineering at the University of Maryland.