基于REFOR算法的多输出非线性系统动态参数化建模方法研究

doi:10.3901/JME.2018.23.073

机械工程学报 ›› 2018, Vol. 54 ›› Issue (23): 73-81.doi: 10.3901/JME.2018.23.073

基于REFOR算法的多输出非线性系统动态参数化建模方法研究

罗忠^1,2, 刘昊鹏^1,2, 朱云鹏³, 王菲^1,2, 韩清凯⁴

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. 谢菲尔德大学自动控制与系统工程系谢菲尔德 S13JD 英国;
4. 大连理工大学机械工程学院大连 116023

收稿日期:2017-12-26 修回日期:2018-06-09 出版日期:2018-12-05 发布日期:2018-12-05
通讯作者: 罗忠(通信作者),男,1978年出生,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。发表论文70余篇。E-mail:zhluo@mail.neu.edu.cn
作者简介:刘昊鹏,男,1992年生,硕士。主要研究方向为机械动力学与模式识别。E-mail:1106881598@qq.com;朱云鹏,男,1991年生,博士。主要研究方向为机械动力学与非线性振动控制方法。E-mail:yzhu53@sheffield.ac.uk;王菲,女,1981年生,讲师。主要研究方向为机械动力学与控制方法研究。E-mail:feiwang@mail.neu.edu.cn;韩清凯,男,1969年生,教授,博士研究生导师。主要研究方向为机械动力学与振动。E-mail:hanqingkai@dlut.edu.cn
基金资助:
国家自然科学基金（11572082）、教育部基本科研业务费专项资金（N160312001，N150304004）及辽宁省高等学校优秀人才支持计划（LJQ2015038）资助项目。

Dynamic Parametrical Modeling Method of Nonlinear Systems with Multiple Outputs Based on REFOR Algorithm

LUO Zhong^1,2, LIU Haopeng^1,2, ZHU Yunpeng³, WANG Fei^1,2, HAN Qingkai⁴

1. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819;
2. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819;
3. Department of Automatic Control and System Engineering, University of Sheffield, Sheffield S13JD, UK;
4. School of Mechanical Engineering, Dalian University, Dalian 116023

Received:2017-12-26 Revised:2018-06-09 Online:2018-12-05 Published:2018-12-05

摘要/Abstract

摘要： 针对多输出非线性系统动态模型的辨识问题，提出一种新的非线性系统动态参数化建模方法，即冗余向前延拓正交（Redundant extended forward orthogonal regression，REFOR）算法。该算法旨在消除传统向前延拓正交（Extended forward orthogonal regression，EFOR）算法因遗漏某些重要模型项而造成所建模型精度较低的问题。首先，基于系统在各工况下辨识所得非线性有源自回归（Non-linear autoregressive with exogenous inputs，NARX）模型，利用REFOR算法统一各模型结构得到模型系数与设计参数间的函数关系，进而建立多输出非线性系统的动态参数化模型。其次，以四自由度非线性系统为例，说明了REFOR算法的优势及其在系统建模中的应用。最后，利用REFOR算法建立悬臂梁的动态参数化模型，并将REFOR预测输出与试验测得输出进行对比，试验结果表明，基于REFOR算法建立的非线性系统动态参数化模型，能准确预测系统的输出响应，为非线性系统建模方法的优化设计提供了理论基础。

关键词: REFOR算法, 动态参数化模型, 多输出, 非线性系统, 悬臂梁

Abstract: In allusion to the identification problem of nonlinear systems with multiple outputs, a new algorithm of nonlinear systems' dynamic parametrical modeling method, called the redundant extended forward orthogonal regression (REFOR) is proposed in this study, which aims to avoid the missing of some significant model terms when using extended forward orthogonal regression (EFOR) algorithm. Firstly, based on non-linear autoregressive with exogenous inputs (NARX) model, which correspond to different cases of parameter properties, a common-structured model is built via REFOR, and a functional relationship between the coefficients of unified model term and the design parameters is established. A dynamic parametrical model of nonlinear systems with multiple outputs is constructed as a consequence. Further, a 4th degree of freedom (4DOF) nonlinear system is taken as a case study to clarify the advantage of REFOR and its application in modeling. Finally, a dynamic parametrical model of cantilever beam is established via REFOR, and a contrast between REFOR's output and corresponding real measurement is given. The results indicate that the REFOR based dynamic parametrical model can accurately predict output response of nonlinear systems, which provide a theoretical basis for the optimal design of nonlinear systems' modeling methods.

Key words: cantilever beam, dynamic parametrical model, multiple outputs, nonlinear systems, REFOR algorithm

中图分类号:

TG156

罗忠, 刘昊鹏, 朱云鹏, 王菲, 韩清凯. 基于REFOR算法的多输出非线性系统动态参数化建模方法研究[J]. 机械工程学报, 2018, 54(23): 73-81.

LUO Zhong, LIU Haopeng, ZHU Yunpeng, WANG Fei, HAN Qingkai. Dynamic Parametrical Modeling Method of Nonlinear Systems with Multiple Outputs Based on REFOR Algorithm[J]. Journal of Mechanical Engineering, 2018, 54(23): 73-81.

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基于REFOR算法的多输出非线性系统动态参数化建模方法研究

Dynamic Parametrical Modeling Method of Nonlinear Systems with Multiple Outputs Based on REFOR Algorithm

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