基于正交匹配追踪算法的复杂系统动力学建模与分析

doi:10.3901/JME.2022.19.086

机械工程学报 ›› 2022, Vol. 58 ›› Issue (19): 86-94.doi: 10.3901/JME.2022.19.086

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基于正交匹配追踪算法的复杂系统动力学建模与分析

罗忠^1,2,3, 周广泽^1,2, 朱云鹏⁴, 高屹^1,2, 李雷^1,2

1. 东北大学机械工程与自动化学院沈阳 110819;
2. 东北大学航空动力装备振动及控制教育部重点实验室沈阳 110819;
3. 东北大学佛山研究生创新学院佛山 528312;
4. 谢菲尔德大学自动控制与系统工程系谢菲尔德S13JD英国

收稿日期:2022-02-07 修回日期:2022-06-10 出版日期:2022-10-05 发布日期:2023-01-05
通讯作者: 罗忠(通信作者)，男，1978年出生，博士，教授，博士研究生导师。主要研究方向为机械动力学与控制、模型试验理论与方法。E-mail：zhluo@mail.neu.edu.cn
作者简介:周广泽，男，1997年出生，硕士研究生。主要研究方向为基于数据驱动的复杂系统建模。E-mail：guangze988@163.com
基金资助:
国家科技重大专项(J2019-IV-0002-0069)、国家自然科学基金(11872148, U1908217)和广东省粤佛联合重点基金(2020B1515120015)资助项目。

Modelling and Analysis of Complex System Dynamics Based on Orthogonal Matching Pursuit Algorithm

LUO Zhong^1,2,3, ZHOU Guangze^1,2, ZHU Yunpeng⁴, GAO Yi^1,2, LI Lei^1,2

1. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819;
2. Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819;
3. Foshan Graduate School of Innovation, Northeastern University, Foshan 528312;
4. Department of Automatic Control and System Engineering, University of Sheffield, Sheffield UK S13JD

Received:2022-02-07 Revised:2022-06-10 Online:2022-10-05 Published:2023-01-05

摘要/Abstract

摘要： 针对非线性系统模型的辨识问题，通过引入正交匹配追踪(Orthogonal matching pursuit，OMP)算法实现快速非线性系统建模。该方法旨在解决非线性有源自回归(Nonlinear autoregressive with exogenous inputs，NARX)模型针对大型数据建模时效性差的问题。首先，说明了正交最小二乘(Orthogonal least squares，OLS)算法存在正交次数多、耗时长的问题，采用OMP算法可有效解决，通过与OLS算法对比正交差异性证明了OMP算法计算效率提升的理论基础，采用模型预报方法验证OMP算法所得NARX模型的动力学特性。其次，以单自由度非线性系统为例，说明了OMP算法系统建模的有效性。最后，利用OMP算法建立悬臂梁NARX模型，并分别将NARX模型预报输出与试验实测输出，NARX模型固有频率与悬臂梁实际固有频率进行对比。结果表明，与OLS算法相比，所提方法的建模效率平均提升了10倍，且模型可有效反应系统动力学特性。

关键词: 非线性系统, NARX模型, OLS算法, OMP算法, 差异性分析

Abstract: The problem of identifying non-linear system models is addressed by introducing the OMP (Orthogonal matching pursuit) algorithm for fast non-linear system modelling. The method aims to solve the problem of poor timeliness in modelling large data with NARX (Nonlinear autoregressive with exogenous inputs) models. Firstly, it is shown that the OLS (Orthogonal least squares) algorithm has the problem of many orthogonal times and time consuming, which can be effectively solved by using the OMP algorithm. The kinetic properties of the NARX model obtained by the OMP algorithm are verified using the model prediction method. Secondly, the effectiveness of the OMP algorithm system modelling is illustrated by taking a single degree of freedom non-linear system as an example. Finally, the NARX model of the cantilever beam is established using the OMP algorithm, and the NARX model prediction output is compared with the experimental measured output, the inherent frequency of the NARX model and the actual inherent frequency of the cantilever beam respectively. The results show that the modelling efficiency of the proposed method is on average 10 times higher than that of the OLS algorithm, and the model can effectively reflect the dynamics of the system.

Key words: nonlinear systems, NARX model, OLS algorithm, OMP algorithm, variance analysis

中图分类号:

TG156

罗忠, 周广泽, 朱云鹏, 高屹, 李雷. 基于正交匹配追踪算法的复杂系统动力学建模与分析[J]. 机械工程学报, 2022, 58(19): 86-94.

LUO Zhong, ZHOU Guangze, ZHU Yunpeng, GAO Yi, LI Lei. Modelling and Analysis of Complex System Dynamics Based on Orthogonal Matching Pursuit Algorithm[J]. Journal of Mechanical Engineering, 2022, 58(19): 86-94.

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基于正交匹配追踪算法的复杂系统动力学建模与分析

Modelling and Analysis of Complex System Dynamics Based on Orthogonal Matching Pursuit Algorithm

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