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Chaos phenomenon is one of the most important physical phenomena, which has significant effects on one's production and life. Therefore, it is indispensable to find out the regularity of chaotic time series from a chaotic system for weather forecasting, space missions, alarm systems, etc. Although various models and learning algorithms have been developed to predict chaotic time series, many traditional methods suffer drawbacks of high computational complexity, slow convergence speed, and low prediction accuracy, due to extremely complex dynamic characteristics of chaotic systems. In this paper, a brain-inspired prediction model, i.e., brain emotional learning (BEL) model combined with self-adaptive genetic algorithm (AGA) is proposed. The establishment of BEL model is inspired by the neurobiology research, which has been put forward by mimicking the high-speed emotional learning mechanism between amygdala and orbitofrontal cortex in mammalian brain, it has advantages of lowcomputational complexity and fast learning. The BEL model employs reward-based reinforcement learning to adjust the weights of amygdala and orbitofrontal cortex. However, the reward-based method is modelsensitive and hard to generalize to other issues. To improve the performance of BEL model, AGA-BEL is proposed for chaotic prediction, in which the AGA is employed for parameter optimization. Firstly, weights and biases of orbitofrontal cortex and amygdala in BEL model are distributed to chromosomal gene sequence for optimization. Secondly, fitness function is employed to adjust the weights of amygdale and orbitofrontal cortex by self-adaptive crossover and mutation operations Therefore, the parameter optimization problem is transformed into a function optimization problem in the search space. Finally, the best chromosome that represents the best combination of weights and biases for BEL model is chosen, which is used for chaotic prediction. Prediction experiments on the benchmark Lorenz chaotic time series and a real-world chaotic time series of geomagnetic activity Dst index are performed. The experimental results and numerical analysis show that the proposed AGA-BEL prediction model achieves lower mean absolute deviation, mean square error, mean absolute percentage error, and higher correlation coefficient than the original BEL, levenberg marquardt-back propagation (LM-BP) and multilayer perceptron-back propagation (MLP-BP). Meanwhile, the BEL-based models take less computational time than the traditional BP-based models. Therefore, the proposed AGA-BEL model possesses the advantages of fast learning and low computational complexity of BEL model as well as the global optimum solution of AGA. It is superior to other traditional methods in terms of prediction precision, execution speed, and stability, and it is suited for online prediction in fast-varying environments.
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Keywords:
- chaotic time series /
- prediction /
- brain emotional learning /
- self-adaptive genetic algorithm
[1] Lotfi E, Akbarzadeh T M R 2014 Neurocomputing 126 188
[2] Singh S, Gill J 2014 Int. J. Intell. Syst. Appl. 6 55
[3] Tian Z D, Gao X W, Shi T 2014 Acta Phys. Sin. 63 160508 (in Chinese)[田中大, 高宪文, 石彤. 2014 63 160508]
[4] Li D, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 787
[5] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[6] Wang X Y, Han M 2015 Acta Phys. Sin. 64 070504 (in Chinese)[王新迎, 韩敏 2015 64 070504]
[7] Han M, Xi J H, Xu S G 2004 IEEE Trans. Signal Process. 52 3409
[8] Su L Y 2010 Comput. Math. Appl. 59 737
[9] Su L Y, Li C L 2015 Discrete. Dyn. Nat. Soc. 2015 329487
[10] Tian Z D, Li S J, Wang Y H, Gao X W 2015 Acta Phys. Sin. 64 030506 (in Chinese)[田中大, 李树江, 王艳红, 高宪文 2015 64 030506]
[11] Mayer J D, Roberts R D, Barsade S G 2008 Annu. Rev. Psych. 59 507
[12] Ledoux J E 1991 Concepts Neurosci. 2 169
[13] Balkenius C, Morn J 2001 Cybern. Syst. 32 611
[14] Babaie T, Karimizandi L 2008 Soft. Comput. 12 857
[15] Abdi J, Moshiri B, Abdulhai B 2012 Eng. Appl. Arti. Intell. 25 1022
[16] Sharafi Y, Setayeshi S, Falahiazar A 2015 J. Math. Comput. Sci. 14 42
[17] Milad H S A, Farooq U, Hawary M, Asad M U 2016 IEEE Access 23 569
[18] Dorrah H T 2011 J. Adv. Res. 2 73
[19] Mei Y, Tan G Z, Liu Z T 2017 Algorithms 10 70
[20] Lotfi E, Akbarzadeh T M R 2016 Inf. Sci. 3 369
[21] Srinivas M, Patnaik L M 2002 IEEE Trans. Syst. M. Cyber. 24 656
[22] Guo Y Y 2013 M. S. Thesis (Harbin:Harbin Institute of Technology) (in Chinese)[郭圆圆 2013 硕士学位论文 (哈尔滨:哈尔滨工业大学)]
[23] Takens F 1981 Lecture Notes in Mathematics (Berlin:Springer-Verlag) p366
[24] Yang F 2012 Ph. D. Dissertation (Beijing:Beijing University of Posts and Telecommunications) (in Chinese)[杨飞 2012 博士学位论文(北京:北京邮电大学)]
[25] Lotfi E, Akbarzadeh T 2013 Cybernet. Syst. 44 402
[26] Amani J, Moeini R 2012 Sci. Iran. 19 242
[27] Li J, Feng J, Wang W 2016 Sci. Geog. Sin. 36 780
[28] Peng Y X, L J Y, Gu S J 2016 Chin. J. Space Sci. 36 866 (in Chinese)[彭宇翔, 吕建永, 顾赛菊 2016 空间科学学报 36 866]
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[1] Lotfi E, Akbarzadeh T M R 2014 Neurocomputing 126 188
[2] Singh S, Gill J 2014 Int. J. Intell. Syst. Appl. 6 55
[3] Tian Z D, Gao X W, Shi T 2014 Acta Phys. Sin. 63 160508 (in Chinese)[田中大, 高宪文, 石彤. 2014 63 160508]
[4] Li D, Han M, Wang J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 787
[5] Shi Z W, Han M 2007 IEEE Trans. Neural Netw. 18 359
[6] Wang X Y, Han M 2015 Acta Phys. Sin. 64 070504 (in Chinese)[王新迎, 韩敏 2015 64 070504]
[7] Han M, Xi J H, Xu S G 2004 IEEE Trans. Signal Process. 52 3409
[8] Su L Y 2010 Comput. Math. Appl. 59 737
[9] Su L Y, Li C L 2015 Discrete. Dyn. Nat. Soc. 2015 329487
[10] Tian Z D, Li S J, Wang Y H, Gao X W 2015 Acta Phys. Sin. 64 030506 (in Chinese)[田中大, 李树江, 王艳红, 高宪文 2015 64 030506]
[11] Mayer J D, Roberts R D, Barsade S G 2008 Annu. Rev. Psych. 59 507
[12] Ledoux J E 1991 Concepts Neurosci. 2 169
[13] Balkenius C, Morn J 2001 Cybern. Syst. 32 611
[14] Babaie T, Karimizandi L 2008 Soft. Comput. 12 857
[15] Abdi J, Moshiri B, Abdulhai B 2012 Eng. Appl. Arti. Intell. 25 1022
[16] Sharafi Y, Setayeshi S, Falahiazar A 2015 J. Math. Comput. Sci. 14 42
[17] Milad H S A, Farooq U, Hawary M, Asad M U 2016 IEEE Access 23 569
[18] Dorrah H T 2011 J. Adv. Res. 2 73
[19] Mei Y, Tan G Z, Liu Z T 2017 Algorithms 10 70
[20] Lotfi E, Akbarzadeh T M R 2016 Inf. Sci. 3 369
[21] Srinivas M, Patnaik L M 2002 IEEE Trans. Syst. M. Cyber. 24 656
[22] Guo Y Y 2013 M. S. Thesis (Harbin:Harbin Institute of Technology) (in Chinese)[郭圆圆 2013 硕士学位论文 (哈尔滨:哈尔滨工业大学)]
[23] Takens F 1981 Lecture Notes in Mathematics (Berlin:Springer-Verlag) p366
[24] Yang F 2012 Ph. D. Dissertation (Beijing:Beijing University of Posts and Telecommunications) (in Chinese)[杨飞 2012 博士学位论文(北京:北京邮电大学)]
[25] Lotfi E, Akbarzadeh T 2013 Cybernet. Syst. 44 402
[26] Amani J, Moeini R 2012 Sci. Iran. 19 242
[27] Li J, Feng J, Wang W 2016 Sci. Geog. Sin. 36 780
[28] Peng Y X, L J Y, Gu S J 2016 Chin. J. Space Sci. 36 866 (in Chinese)[彭宇翔, 吕建永, 顾赛菊 2016 空间科学学报 36 866]
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