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According to the phase space reconstruction theory of nonlinear system, we propose a prediction method of support vector machine based on genetic algorithm. Using the improved autocorrelation method and Grassberger-Procaccia algorithm to determine the time delay and embedding dimension of chaotic signal, the phase space reconstruction is implemented. The penalty coefficient and the kernel function parameter of support vector machine are optimized by genetic algorithm. Combined with support vector machine, single-step prediction model of the chaotic sequence is set up, so we can detect the weak signal in chaos from the prediction error (including the transient signal and periodic signal). Lorenz attractor and the data from the McMaster IPIX radar sea clutter database are used in the simulation. The proposed method can effectively detect the weak target from chaotic signal. When the signal-to-noise ratio is -89.7704 dB in the chaotic noise background, by using the new method the root mean square error can be reduced by two orders of magnitude, reaching 0.00049521, while the conventional support vector machine can reach only 0.049 under the condition of -54.60 dB.
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Keywords:
- support vector machine /
- genetic algorithm /
- sea clutter /
- phase space reconstruction
[1] Zhang X D, Wang Z, Zhao P D 2008 Chin. Phys. Lett. 25 397
[2] Leung H, Haykin S 1990 Appl. Phys. Lett. 56 593
[3] Szajnowski W J 1976 Electron. Lett. 12 497
[4] Anastassopoulos V, Lampropulos G 1995 IEEE Trans. AES 31 52
[5] Conte E, Lops M, Ricci G 1994 IEE Proc. F 141 116
[6] Zhang X G 2000 Acta Autom. Sin. 26 32 (in Chinese) [张学工 2000 自动化学报 26 32]
[7] Cui W Z, Zhu C C, Bao W X, Liu J H 2005 Chin. Phys. 14 922
[8] Leung H, Lo T 1993 IEEE J. Oceanic Eng. 18 287
[9] Mukherjee S, Osuna E, Girosi F 1997 Workshop on Neural Networks for Signal Processing VII (Piscataway: IEEE Press) p511
[10] Haykin S, Bakker R, Currie B W 2002 Proc. IEEE 90 860
[11] Kenshi S, Yuko N, Shinichi A 2008 Chaos Solitons Fract. 38 1274
[12] Zhu J Y, Ren B, Zhang H X, Deng Z T 2002 Proceedings of the First International Conference on Machine Learning and Cybernetics Beijing, China, November 4, 5, 2002 p364
[13] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 物理学报 51 2459]
[14] Cui W Z, Zhu C C, Bao W X, Liu J H 2004 Acta Phys. Sin. 53 3303 (in Chinese) [崔万照, 朱长纯, 保文星, 刘君华 2004 物理学报 53 3303]
[15] You R Y, Chen Z, Xu S C, Wu B X 2004 Acta Phys. Sin. 53 2882 (in Chinese) [游荣义, 陈忠, 徐慎初, 吴伯僖 2004 物理学报 53 2882]
[16] Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) [叶美盈, 汪晓东, 张浩然 2005 物理学报 54 2568]
[17] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3773 (in Chinese) [行鸿彦, 徐伟 2007 物理学报 56 3773]
[18] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦, 金天力 2010 物理学报 59 140]
[19] Packard N H, Cratchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[20] Xing H Y, Cheng Y Y, Xu W 2012 Acta Phys. Sin. 61 100506 (in Chinese) [行鸿彦, 程艳艳, 徐伟 2012 物理学报 61 100506]
[21] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[22] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[23] Lo T, Leung H 1993 IEE Proc. F 140 243
[24] Aguirre L A 1995 Phys. Lett. A 203 88
[25] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[26] Wang Y N, Tan W 2003 Acta Phys. Sin. 52 2723 (in Chinese) [王耀南, 谭文 2003 物理学报 52 2723]
[27] Du J Y, Hou Y B 2007 J. Sci. Instrum. 28 555 (in Chinese) [杜京义, 侯媛彬 2007 仪器仪表学报 28 555]
[28] Wang F Y, Yuan G N, Xie Y J, Qiao X W 2009 Radar Sci. Technol. 7 53 (in Chinese) [王福友, 袁赣南, 谢燕军, 乔相伟 2009 雷达科学与技术 7 53]
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[1] Zhang X D, Wang Z, Zhao P D 2008 Chin. Phys. Lett. 25 397
[2] Leung H, Haykin S 1990 Appl. Phys. Lett. 56 593
[3] Szajnowski W J 1976 Electron. Lett. 12 497
[4] Anastassopoulos V, Lampropulos G 1995 IEEE Trans. AES 31 52
[5] Conte E, Lops M, Ricci G 1994 IEE Proc. F 141 116
[6] Zhang X G 2000 Acta Autom. Sin. 26 32 (in Chinese) [张学工 2000 自动化学报 26 32]
[7] Cui W Z, Zhu C C, Bao W X, Liu J H 2005 Chin. Phys. 14 922
[8] Leung H, Lo T 1993 IEEE J. Oceanic Eng. 18 287
[9] Mukherjee S, Osuna E, Girosi F 1997 Workshop on Neural Networks for Signal Processing VII (Piscataway: IEEE Press) p511
[10] Haykin S, Bakker R, Currie B W 2002 Proc. IEEE 90 860
[11] Kenshi S, Yuko N, Shinichi A 2008 Chaos Solitons Fract. 38 1274
[12] Zhu J Y, Ren B, Zhang H X, Deng Z T 2002 Proceedings of the First International Conference on Machine Learning and Cybernetics Beijing, China, November 4, 5, 2002 p364
[13] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 物理学报 51 2459]
[14] Cui W Z, Zhu C C, Bao W X, Liu J H 2004 Acta Phys. Sin. 53 3303 (in Chinese) [崔万照, 朱长纯, 保文星, 刘君华 2004 物理学报 53 3303]
[15] You R Y, Chen Z, Xu S C, Wu B X 2004 Acta Phys. Sin. 53 2882 (in Chinese) [游荣义, 陈忠, 徐慎初, 吴伯僖 2004 物理学报 53 2882]
[16] Ye M Y, Wang X D, Zhang H R 2005 Acta Phys. Sin. 54 2568 (in Chinese) [叶美盈, 汪晓东, 张浩然 2005 物理学报 54 2568]
[17] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3773 (in Chinese) [行鸿彦, 徐伟 2007 物理学报 56 3773]
[18] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦, 金天力 2010 物理学报 59 140]
[19] Packard N H, Cratchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[20] Xing H Y, Cheng Y Y, Xu W 2012 Acta Phys. Sin. 61 100506 (in Chinese) [行鸿彦, 程艳艳, 徐伟 2012 物理学报 61 100506]
[21] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[22] Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[23] Lo T, Leung H 1993 IEE Proc. F 140 243
[24] Aguirre L A 1995 Phys. Lett. A 203 88
[25] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[26] Wang Y N, Tan W 2003 Acta Phys. Sin. 52 2723 (in Chinese) [王耀南, 谭文 2003 物理学报 52 2723]
[27] Du J Y, Hou Y B 2007 J. Sci. Instrum. 28 555 (in Chinese) [杜京义, 侯媛彬 2007 仪器仪表学报 28 555]
[28] Wang F Y, Yuan G N, Xie Y J, Qiao X W 2009 Radar Sci. Technol. 7 53 (in Chinese) [王福友, 袁赣南, 谢燕军, 乔相伟 2009 雷达科学与技术 7 53]
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