[1]黄仁,许飞云,陈茹雯,等.基于逼近理论的线性/非线性建模[J].东南大学学报(自然科学版),2018,48(1):30-37.[doi:10.3969/j.issn.1001-0505.2018.01.006]
 Huang Ren,Xu Feiyun,Chen Ruwen,et al.Linear and nonlinear modeling based on approximation theory[J].Journal of Southeast University (Natural Science Edition),2018,48(1):30-37.[doi:10.3969/j.issn.1001-0505.2018.01.006]
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基于逼近理论的线性/非线性建模()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
48
期数:
2018年第1期
页码:
30-37
栏目:
计算机科学与工程
出版日期:
2018-01-20

文章信息/Info

Title:
Linear and nonlinear modeling based on approximation theory
作者:
黄仁许飞云陈茹雯马家欣
东南大学机械工程学院, 南京 211189
Author(s):
Huang Ren Xu Feiyun Chen Ruwen Ma Jiaxin
School of Mechanical Engineering, Southeast University, Nanjing 211189, China
关键词:
Weierstrass逼近定理 系统辨识 DIC准则 线性/非线性建模
Keywords:
Weierstrass approximation theory system identification direct information criterion(DIC) linear and nonlinear modeling
分类号:
TP391
DOI:
10.3969/j.issn.1001-0505.2018.01.006
摘要:
针对ARMA模型(包括AR、MA模型)不适用于非线性、非平稳系统的问题,分析了Weierstrass逼近定理,并指出了其工程应用的可行性.在传统系统辨识的基础上,对照典型的输入/输出模型,针对不同的输入形式提出了3种不同的模型表达式,由数据可以直接计算模型参数,而无需用模拟方法先求传递函数,这对工程应用具有十分重要的意义.然后,针对模型定阶,分析了传统AIC准则存在的问题,提出了DIC准则.DIC准则不仅适用于线性/非线性建模,也可用于随机过程的建模.最后,将GNPAX模型应用于钢板冲击信号的建模.结果表明,通过模型参数的变化,GNPAX模型能准确识别钢板的结构损伤,识别精度高于AR,GNPA和ARX模型.
Abstract:
To solve the problem that ARMA models(including AR and MA models)are not suitable for nonlinear and nonstationary systems, the Weierstrass approximation theory is analyzed and the feasibility of engineering application is indicated. On the basis of the traditional system identification, compared with the typical input-output model, three different model expressions are proposed for three different input forms. With no need for transfer function calculated by simulations, model parameters are directly figured out with data, which is of great importance for engineering application. Further, for model order determination, the problem of Akaike information criterion(AIC)is pointed out, and the direct information criterion(DIC)is proposed. Then, its suitability for linear and nonlinear modeling and feasibility for stochastic process modeling are illustrated. Finally, a GNPAX model for linear and nonlinear modeling is used for signal modeling of the steel plate. The results show that with the change of model parameters, the structural damage of the steel plate is exactly recognized, and the recognition accuracy of GNPAX model is higher than those of AR, GNPA, ARX models.

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备注/Memo

备注/Memo:
收稿日期: 2017-08-10.
作者简介: 黄仁(1928—),男,教授,rhuangcn@126.com.
基金项目: 国家自然科学基金资助项目(51575101).
引用本文: 黄仁,许飞云,陈茹雯,等.基于逼近理论的线性/非线性建模[J].东南大学学报(自然科学版),2018,48(1):30-37. DOI:10.3969/j.issn.1001-0505.2018.01.006.
更新日期/Last Update: 2018-01-20