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本文分析了传统支持向量机预测算法产生的误差特性，发现产生的预测误差不同于噪声，具有较强的规律性，单一的预测模型遗漏了许多混沌序列中的确定性分量. 经过误差补偿后，残差的冗余信息减少，随机性增强. 在此基础上，本文提出一种基于迭代误差补偿的最小二乘支持向量机预测算法，能够通过多模型联合预测更加有效地逼近混沌系统的映射函数，在预测精度上取得了大幅度的提升. 此外，算法通过留一交叉验证法的方法能够在预测前自动优化模型参数组合，克服了现有算法无法仅利用先验信息优化预测模型参数的缺陷. 对MackeyGlass和Lorenz混沌时间序列进行了仿真实验，实验结果优于相关文献记载方法的预测性能，在性能指标上好于现有算法一个数量级.This paper analyzes the error characteristic of traditional support vector machine prediction algorithm, where the error series are smooth and regular. This is because a single prediction model is incapable of fitting chaotic system mapping function and omitting some deterministic component. On this basis, a prediction algorithm that consists of an iterative error correction and a least square support vector machine (LSSVM) is proposed. The algorithm creats multiple predictive models via the method of iterative error correction to approximate the chaotic system mapping function and obtain significant improvements of predictive performance. In addition, the optimal parameters of the prediction model are automatically obtained from the pattern search algorithm which is simple and effective. Experiment conducted on Lorenz time series and MackeyGlass time series indicates that the proposed algorithm has a much better performance than that recorded in the literature.
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Keywords:
- chaos time series prediction /
- least square support vector machine /
- iterative error correction /
- parameter composite optimization
[1] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 61 100501]
[2] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 62 120510]
[3] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 61 080506]
[4] Lei Z, Fengchun T, Shouqiong L, Lijun D, Xiongwei P, Xin Y 2013 Sensors and Actuators B: Chemical 182 71
[5] Rohitash C, Mengjie Z 2012 Neurocomputing 86 116
[6] Cheng-Jian L, Cheng-Hung C, Chin-Teng L 2009 IEEE Trans. Sys. Tem. Man Cyber. 39 55
[7] Ma Q L, Zheng Q L, Peng H, Tan J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[8] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[9] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[10] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
[11] Zhang W Z, Long W, Jiao J J 2012 Acta Phys. Sin. 61 220506 (in Chinese) [张文专, 龙文, 焦建军 2012 61 220506]
[12] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[13] Arash M, Majid A 2013 IEEE Trans. Neural Netw. 24 207
[14] Yu Y H, Song J D 2012 Acta Phys. Sin. 61 170516 (in Chinese) [于艳华, 宋俊德 2012 61 170516]
[15] Vapnik V N, 1999 The Nature of Statistical Learning Theory (2nd Ed.) (New York, Springer) pp183-190
[16] Sapankevych N I, Sankar R 2009 IEEE Comput. Intell. Mag. 4 24
[17] Cai C Z, Fei J F, Wen Y F, Zhu X J, Xiao T T 2009 Acta Phys. Sin. 58 S008 (in Chinese) [蔡从中, 裴军芳, 温玉锋, 朱星键, 肖婷婷 2009 58S008]
[18] Ligang Z, Kin K L, Lean Y 2009 Soft Comput. 13 149
[19] Chen M H, Ceckbum B, Reitich F 2005 J. Sci. Comput. 22 205
[20] Mirmomeni M, Lucas C, Araabi B N, Moshiri B, Bidar M R 2011 IET Signal Process. 5 515
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[1] Chen D Y, Liu Y, Ma X Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义 2012 61 100501]
[2] Han M, Xu M L 2013 Acta Phys. Sin. 62 120510 (in Chinese) [韩敏, 许美玲 2013 62 120510]
[3] Song T, Li H 2012 Acta Phys. Sin. 61 080506 (in Chinese) [宋彤, 李菡 2012 61 080506]
[4] Lei Z, Fengchun T, Shouqiong L, Lijun D, Xiongwei P, Xin Y 2013 Sensors and Actuators B: Chemical 182 71
[5] Rohitash C, Mengjie Z 2012 Neurocomputing 86 116
[6] Cheng-Jian L, Cheng-Hung C, Chin-Teng L 2009 IEEE Trans. Sys. Tem. Man Cyber. 39 55
[7] Ma Q L, Zheng Q L, Peng H, Tan J W 2009 Acta Phys. Sin. 58 1410 (in Chinese) [马千里, 郑启伦, 彭宏, 覃姜维 2009 58 1410]
[8] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[9] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[10] Chatzis S P, Demiris Y 2011 IEEE Trans. Neural Netw. 22 1435
[11] Zhang W Z, Long W, Jiao J J 2012 Acta Phys. Sin. 61 220506 (in Chinese) [张文专, 龙文, 焦建军 2012 61 220506]
[12] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[13] Arash M, Majid A 2013 IEEE Trans. Neural Netw. 24 207
[14] Yu Y H, Song J D 2012 Acta Phys. Sin. 61 170516 (in Chinese) [于艳华, 宋俊德 2012 61 170516]
[15] Vapnik V N, 1999 The Nature of Statistical Learning Theory (2nd Ed.) (New York, Springer) pp183-190
[16] Sapankevych N I, Sankar R 2009 IEEE Comput. Intell. Mag. 4 24
[17] Cai C Z, Fei J F, Wen Y F, Zhu X J, Xiao T T 2009 Acta Phys. Sin. 58 S008 (in Chinese) [蔡从中, 裴军芳, 温玉锋, 朱星键, 肖婷婷 2009 58S008]
[18] Ligang Z, Kin K L, Lean Y 2009 Soft Comput. 13 149
[19] Chen M H, Ceckbum B, Reitich F 2005 J. Sci. Comput. 22 205
[20] Mirmomeni M, Lucas C, Araabi B N, Moshiri B, Bidar M R 2011 IET Signal Process. 5 515
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