[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]
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一种线性/非线性自回归模型及其在建模和预测中的应用()
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《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.

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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