[1]马家欣,许飞云,黄仁.一种线性/非线性自回归模型及其在建模和预测中的应用[J].东南大学学报(自然科学版),2013,43(3):509-514.[doi:10.3969/j.issn.1001-0505.2013.03.012]
 Ma Jiaxin,Xu Feiyun,Huang Ren.A linear and nonlinear auto-regressive model and its application in modeling and forecasting[J].Journal of Southeast University (Natural Science Edition),2013,43(3):509-514.[doi:10.3969/j.issn.1001-0505.2013.03.012]
点击复制

一种线性/非线性自回归模型及其在建模和预测中的应用()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
43
期数:
2013年第3期
页码:
509-514
栏目:
计算机科学与工程
出版日期:
2013-05-20

文章信息/Info

Title:
A linear and nonlinear auto-regressive model and its application in modeling and forecasting
作者:
马家欣许飞云黄仁
东南大学机械工程学院, 南京 211189
Author(s):
Ma Jiaxin Xu Feiyun Huang Ren
School of Mechanical Engineering, Southeast University, Nanjing 211189, China
关键词:
线性/非线性自回归模型 建模 预测
Keywords:
linear and nonlinear auto-regressive model modeling forecasting
分类号:
TP391
DOI:
10.3969/j.issn.1001-0505.2013.03.012
摘要:
为提高模型准确性,在经典时序建模策略的基础上,提出了一种带有外部输入的线性/非线性自回归模型,并应用Weierstrass逼近定理推导出其一般表达式(GNARX),该模型允许带有多个外部输入以实现复杂系统的建模和辨识.针对该模型结构给出了其最小二乘参数估计方法,并采用结合建模误差、预测误差及模型复杂度的修正信息准则(AIC)确定最优模型结构.最后,将该模型应用于仿真数据和振动位移采样电流数据的建模与预测.结果表明,GNARX模型的建模和预测精度均高于AR,GNAR,ARX模型及BP神经网络模型,表现出良好的线性/非线性建模和预测能力,及较好的通用性和实用价值.
Abstract:
To improve the model accuracy, a linear and nonlinear auto-regressive model with exogenous inputs is proposed based on classical time series modeling strategy. And, with the Weierstrass approximation theorem, the general expression for the linear and nonlinear auto-regressive model with exogenous inputs(GNARX)is deduced. As multiple exogenous inputs are allowable, this model can realize modeling and identification of complex systems. Furthermore, concerning the model structure, a least square parameter estimation method is presented. With modified information criterion(AIC)integrated with modeling error, forecasting error and model complexity, the optimal model is determined. Finally, this model is applied to the modeling and forecasting of simulation data and the current sampling data of vibration displacement. The results show that the modeling and forecasting accuracy of the GNARX model is higher than those of AR, GNAR, ARX models and BP neural network, indicating that the GNARX model has good linear and nonlinear modeling ability and forecasting ability with good universality and practical value.

参考文献/References:

[1] Box G E P, Jenkins G M, Reinsel G C. Time series analysis: forecasting and control [M]. 4th ed. Hoboken, USA: John Wiley & Sons Inc., 2008.
[2] Flores J J, Graff M, Rodriguez H. Evolutive design of ARMA and ANN models for time series forecasting [J]. Renewable Energy, 2012, 44: 225-230.
[3] Hansen P R, Huang Z, Shek H H.Realized GARCH: a joint model for returns and realized measures of volatility [J]. Journal of Applied Econometrics, 2012, 27(6): 877-906.
[4] 杨叔子,吴雅,轩建平.时间序列分析的工程应用:下册[M].2版.武汉:华中科技大学出版社,2007.
[5] 陈茹雯,黄仁,张志胜,等.基于数学模型的视觉测量系统图形畸变校正方法[J].机械工程学报,2009,45(7):243-248.
  Chen Ruwen, Huang Ren, Zhang Zhisheng, et al. Distortion correction method based on mathematic model inmachine vision measurement system[J]. Journal of Mechanical Engineering, 2009, 45(7): 243-248.(in Chinese)
[6] Huang Ren,Xu Feiyun,Chen Ruwen.General expression for linear and nonlinear time series models[J]. Frontiers of Mechanical Engineering in China, 2009, 4(1): 15-24.
[7] 陈茹雯,黄仁,史金飞,等.线性/非线性时间序列模型一般表达式及其工程应用[J].东南大学学报:自然科学版,2008,38(6):1077-1080.
  Chen Ruwen, Huang Ren, Shi Jinfei, et al. General expression for linear and nonlinear time series model and Its engineering application[J]. Journal of Southeast University: Natural Science Edition, 2008, 38(6): 1077-1080.(in Chinese)
[8] Muhannad Z, Yusoff Z M, Rahiman M H F, et al. Modeling of steam distillation pot with ARX model [C]//IEEE 8th International Colloquium on Signal Processing and Its Applications. Melaka, Malaysia, 2012: 194-198.
[9] Sanandaji B M, Vincent T L, Wakin M B,et al.Compressive system identification of LTI and LTV ARX models[C]//50th IEEE Conference on Decision and Control and European Control Conference. Orlando, FL, USA, 2011: 791-798.
[10] Raniman M H F, Taib M N, Salleh Y M. Black box modeling of steam distillation essential oil extraction system using ARMAX structure[C]//International Conference on Intelligent and Advanced Systems. Kuala Lumpur, Malaysia, 2007: 1059-1062.
[11] Stefanoiu D, Seraficeanu C, Culita J. Identification of MIMO-ARMAX models for glycemia and sodium ions tests through Particle Swarm Optimization[C]//IEEE International Conference on Control and Automation. Christchurch, New Zealand, 2009: 643-650.
[12] Giardina C R, Chirlian P M.Proof of Weierstrass approximation theorem using band-limited functions[J]. Proceedings of the IEEE, 1973, 61(4): 512.

相似文献/References:

[1]王冬冬,达庆利.基于模糊Petri网的供应链诊断建模分析[J].东南大学学报(自然科学版),2006,36(4):662.[doi:10.3969/j.issn.1001-0505.2006.04.036]
 Wang Dongdong,Da Qingli.Analyzing and modeling of supply chain diagnosis based on fuzzy Petri net[J].Journal of Southeast University (Natural Science Edition),2006,36(3):662.[doi:10.3969/j.issn.1001-0505.2006.04.036]
[2]潘蕾,林中达,杨瑜文.燃气蒸汽联合循环燃料系统动力学建模的分析研究[J].东南大学学报(自然科学版),2005,35(1):40.[doi:10.3969/j.issn.1001-0505.2005.01.009]
 Pan Lei,Lin Zhongda,Yang Yuwen.Study on dynamical modeling of the fuel system in gas-stream combine cycle systems[J].Journal of Southeast University (Natural Science Edition),2005,35(3):40.[doi:10.3969/j.issn.1001-0505.2005.01.009]
[3]苏春,许超,孙庆鸿.基于扩展着色赋时Petri网的板材FMS建模及分析[J].东南大学学报(自然科学版),2000,30(2):89.[doi:10.3969/j.issn.1001-0505.2000.02.019]
 Su Chun,Xu Chao,Sun Qinghong.Modeling and Analysis of the Sheet Metal FMS Based on Extended Colored Timed Petri Nets[J].Journal of Southeast University (Natural Science Edition),2000,30(3):89.[doi:10.3969/j.issn.1001-0505.2000.02.019]
[4]沈卓炜,谢俊清,顾冠群.集成CORBA和UML的分布式应用开发[J].东南大学学报(自然科学版),2001,31(1):1.[doi:10.3969/j.issn.1001-0505.2001.01.001]
 Shen Zhuowei,Xie Junqing,Gu Guanqun.Integration of CORBA and UML in Distributed Application Development[J].Journal of Southeast University (Natural Science Edition),2001,31(3):1.[doi:10.3969/j.issn.1001-0505.2001.01.001]
[5]刘斌,宋卫卫,欧宗瑛,等.基于剔除拟合的股骨头修复建模[J].东南大学学报(自然科学版),2008,38(1):58.[doi:10.3969/j.issn.1001-0505.2008.01.012]
 Liu Bin,Song Weiwei,Ou Zongying,et al.Reparative modeling for femoral head based on eliminative fitting[J].Journal of Southeast University (Natural Science Edition),2008,38(3):58.[doi:10.3969/j.issn.1001-0505.2008.01.012]
[6]曹忻,盛昭瀚,徐南荣.非平稳时间序列的线性预测[J].东南大学学报(自然科学版),1989,19(6):86.[doi:10.3969/j.issn.1001-0505.1989.06.012]
 Cao Xin Sheng Zhaohan Xu Nanrong(College of Management).Linear Prediction of Nonstationary Time Series[J].Journal of Southeast University (Natural Science Edition),1989,19(3):86.[doi:10.3969/j.issn.1001-0505.1989.06.012]
[7]万德钧,黄仁,任兴明.陀螺随机漂移ARMA模型的建立[J].东南大学学报(自然科学版),1988,18(3):57.[doi:10.3969/j.issn.1001-0505.1988.03.008]
 Wan Dejun Huang Ren Ren Xingminq (Department of Automatic Control) Huang Rent Department of Mechanical Engineering of NIT Ren Xingming: 0 Research Institute,Nanjing.ARMA Modelling of Random Drift of Gyroscopes[J].Journal of Southeast University (Natural Science Edition),1988,18(3):57.[doi:10.3969/j.issn.1001-0505.1988.03.008]
[8]李大仰,林循泓.多维时序模型建模方法的探讨[J].东南大学学报(自然科学版),1988,18(5):118.[doi:10.3969/j.issn.1001-0505.1988.05.017]
 Li Dayang Lin Xunhong(Department of Mathematics and Mechanics).A New Approach for Modelling Multi-dimension Time Series Model[J].Journal of Southeast University (Natural Science Edition),1988,18(3):118.[doi:10.3969/j.issn.1001-0505.1988.05.017]
[9]张思,曹素云.系统“模态—物理模型”建模方法的研究[J].东南大学学报(自然科学版),1987,17(3):32.[doi:10.3969/j.issn.1001-0505.1987.03.004]
 Zhang Si Cao Suyun.On Modeling of“Modal-Physical Model”of Systems[J].Journal of Southeast University (Natural Science Edition),1987,17(3):32.[doi:10.3969/j.issn.1001-0505.1987.03.004]
[10]达庆利,何建敏.非平稳社会经济系统建模新方法及其应用[J].东南大学学报(自然科学版),1987,17(5):84.[doi:10.3969/j.issn.1001-0505.1987.05.010]
 Da Qingli He Jianmin (Research Institute of Automation).A New Method of Nonstationary Socio-economic System Modelling and Its Application[J].Journal of Southeast University (Natural Science Edition),1987,17(3):84.[doi:10.3969/j.issn.1001-0505.1987.05.010]

备注/Memo

备注/Memo:
作者简介: 马家欣(1988—),男,博士生;许飞云(联系人),男,博士,教授,博士生导师,fyxu@seu.edu.cn.
基金项目: 国家自然科学基金资助项目(51175079).
引文格式: 马家欣,许飞云,黄仁.一种线性/非线性自回归模型及其在建模和预测中的应用[J].东南大学学报:自然科学版,2013,43(3):509-514. [doi:10.3969/j.issn.1001-0505.2013.03.012]
更新日期/Last Update: 2013-05-20