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Chaos phenomenon which exists widely in nature and society affects people's production and life. It has great important significance to find out the regularity of chaotic time series from a chaotic system. Since chaotic system has extremely complex dynamic characteristics and unpredictability, and chaotic time series prediction through traditional methods has low prediction precision, slow convergence speed and complex model structure, a prediction model about Hermite orthogonal basis neural network based on improved teaching-learning-based optimization algorithm is proposed. Firstly, according to the chaotic time series, autocorrelation method and Cao method are used to determine the best delay time and the minimum embedding dimension respectively, then a phase space is reconstructed to obtain the refactoring delay time vector. Secondly, on the basis of phase space reconstruction and best square approximation theory, combined with the neural network topology, a prediction model about Hermite orthogonal basis neural network with excitation functions based on the Hermite orthogonal basis functions is put forward. Thirdly, in order to optimize the parameters of the prediction model, an improved teaching-learning-based optimization algorithm is proposed, where a feedback stage is introduced at the end of the learning stage based on the teaching-learning-based optimization algorithm. Finally, the parameter optimization problem is transformed into a function optimization problem in the multidimensional space, then the improved teaching-learning-based optimization algorithm is used for parameter optimization of the prediction model so as to establish it and analyze it. Lorenz and Liu chaotic systems are taken as models respectively, then the chaotic time series which will be used as simulation object is produced by the fourth order Runge-Kutta method. The comparison experiments with other prediction models are conducted on single-step and multi-step prediction for the chaotic time series. The simulation results and numerical analysis show that compared with radial basis function neural network, echo state network, least square support vector machine prediction model and Hermite orthogonal basis neural network based on teaching-learning-based optimization algorithm, the proposed prediction model has the mean absolute error and root mean square error reduced significantly, has a decision coefficient close to 1, meanwhile, has a mean modeling time shortened greatly. So the proposed prediction model can improve the prediction precision, accelerate the convergence speed and simplify the model structure, thus the prediction model is effective and feasible, which makes it promoted and applied easily.
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Keywords:
- Hermite orthogonal basis neural network /
- improved teaching-learning-based optimization algorithm /
- chaotic time series /
- prediction
[1] Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese) [行鸿彦, 张强, 徐伟 2015 64 040506]
[2] Zhao Y P, Wang K K 2013 Acta Phys. Sin. 62 240509 (in Chinese) [赵永平, 王康康 2013 62 240509]
[3] L S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[4] Wang L, Zou F, Hei X, Yang D, Chen D, Jiang Q, Cao Z 2014 Neural Comput. Appl. 25 1407
[5] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[6] Lee S H, Chung K Y, Lim J S 2014 Pers. Ubiquit. Comput. 18 1315
[7] Zhao N, Yu F R, Sun H, Yin H, Wang G 2015 Wirel. Netw. 21 1227
[8] Li S, Zhang C, Shi M 2015 J. Shanghai Jiaotong Univ. (Sci.) 20 224
[9] Zhao L, Shui P, Jiang F, Qiu H, Ren S, Li Y, Zhang Y 2014 Earth Sci. Inform. 7 59
[10] Bansal A, Chen T, Zhong S 2011 Neural Comput. Appl. 20 143
[11] Yu X, Wang B, Batbayar B, Wang L, Man Z 2011 J. Global Optim. 51 271
[12] Li P H, Chai Y, Xiong Q Y 2013 Acta Autom. Sin. 39 1511 (in Chinese) [李鹏华, 柴毅, 熊庆宇 2013 自动化学报 39 1511]
[13] Han M, Xu M L, Wang X Y 2014 Chin. J. Comput. 37 2268 (in Chinese) [韩敏, 许美玲, 王新迎 2014 计算机学报 37 2268]
[14] Kohli A K, Rai A 2013 Circ. Syst. Signal Pr. 32 223
[15] Aiyer B G, Kim D, Karingattikkal N, Samui P, Rao P R 2014 KSCE J. Civ. Eng. 18 1753
[16] Han M, Wang X Y 2013 Control Theory Appl. 30 1467 (in Chinese) [韩敏, 王新迎 2013 控制理论与应用 30 1467]
[17] Lazzús J A 2011 Chin. Phys. Lett. 28 110504
[18] Pandey A, Thapa K B, Prasad R, Singh K P 2012 J. Indian Soc. Remote 40 709
[19] Hosseini E S, Esmaeelzadeh V, Eslami M 2015 Wireless Pers. Commun. 80 1579
[20] Sardashti A, Daniali H M, Varedi S M 2013 Meccanica 48 1681
[21] Zhang S, Zhang Y, Zhu J 2015 J. Mech. Sci. Technol. 29 605
[22] Pawar P J, Rao R V 2013 Int. J. Adv. Manuf. Tech. 67 1955
[23] Liao X X, Luo Q 2010 Sci. Sin. Technol. 40 1086 (in Chinese) [廖晓昕, 罗琦 2010 中国科学:信息科学 40 1086]
[24] Huang Y 2014 Acta Phys. Sin. 63 080505 (in Chinese) [黄沄 2014 63 080505]
[25] Wang Z L 2010 Nonlinear Dynam. 59 455
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[1] Xing H Y, Zhang Q, Xu W 2015 Acta Phys. Sin. 64 040506 (in Chinese) [行鸿彦, 张强, 徐伟 2015 64 040506]
[2] Zhao Y P, Wang K K 2013 Acta Phys. Sin. 62 240509 (in Chinese) [赵永平, 王康康 2013 62 240509]
[3] L S X, Wang Z S, Hu Z H, Feng J C 2014 Chin. Phys. B 23 010506
[4] Wang L, Zou F, Hei X, Yang D, Chen D, Jiang Q, Cao Z 2014 Neural Comput. Appl. 25 1407
[5] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[6] Lee S H, Chung K Y, Lim J S 2014 Pers. Ubiquit. Comput. 18 1315
[7] Zhao N, Yu F R, Sun H, Yin H, Wang G 2015 Wirel. Netw. 21 1227
[8] Li S, Zhang C, Shi M 2015 J. Shanghai Jiaotong Univ. (Sci.) 20 224
[9] Zhao L, Shui P, Jiang F, Qiu H, Ren S, Li Y, Zhang Y 2014 Earth Sci. Inform. 7 59
[10] Bansal A, Chen T, Zhong S 2011 Neural Comput. Appl. 20 143
[11] Yu X, Wang B, Batbayar B, Wang L, Man Z 2011 J. Global Optim. 51 271
[12] Li P H, Chai Y, Xiong Q Y 2013 Acta Autom. Sin. 39 1511 (in Chinese) [李鹏华, 柴毅, 熊庆宇 2013 自动化学报 39 1511]
[13] Han M, Xu M L, Wang X Y 2014 Chin. J. Comput. 37 2268 (in Chinese) [韩敏, 许美玲, 王新迎 2014 计算机学报 37 2268]
[14] Kohli A K, Rai A 2013 Circ. Syst. Signal Pr. 32 223
[15] Aiyer B G, Kim D, Karingattikkal N, Samui P, Rao P R 2014 KSCE J. Civ. Eng. 18 1753
[16] Han M, Wang X Y 2013 Control Theory Appl. 30 1467 (in Chinese) [韩敏, 王新迎 2013 控制理论与应用 30 1467]
[17] Lazzús J A 2011 Chin. Phys. Lett. 28 110504
[18] Pandey A, Thapa K B, Prasad R, Singh K P 2012 J. Indian Soc. Remote 40 709
[19] Hosseini E S, Esmaeelzadeh V, Eslami M 2015 Wireless Pers. Commun. 80 1579
[20] Sardashti A, Daniali H M, Varedi S M 2013 Meccanica 48 1681
[21] Zhang S, Zhang Y, Zhu J 2015 J. Mech. Sci. Technol. 29 605
[22] Pawar P J, Rao R V 2013 Int. J. Adv. Manuf. Tech. 67 1955
[23] Liao X X, Luo Q 2010 Sci. Sin. Technol. 40 1086 (in Chinese) [廖晓昕, 罗琦 2010 中国科学:信息科学 40 1086]
[24] Huang Y 2014 Acta Phys. Sin. 63 080505 (in Chinese) [黄沄 2014 63 080505]
[25] Wang Z L 2010 Nonlinear Dynam. 59 455
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