Modeling of the Earth’s rotation variations using a novel approach inspired by the brain emotional learning

Document Type : Research Article


1 Department of AI, Faculty of Computer Engineering, University of Isfahan, Isfahan, Iran

2 Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran

3 School of Continuing and Lifelong Education, National University of Singapore, Singapore


DT is a quantity that converts universal time (UT; defined by the Earth’s rotation) to terrestrial time (TT; independent of Earth’s rotation). The DT values during the time show the Earth’s rotation variations. Solar activities and the gravitational force of major solar system components are known as astronomical-based factors that can provide these variations. Recently, several models have been proposed to interpolate and forecast the DT values. Structurally, all mentioned methods have just used past DT values for modeling.
In this paper, we propose a novel approach for modeling DT based on the brain’s emotional learning with respect to astronomical-origin-based factors effective on the Earth’s rotation as the emotional input signals. This model, which employs memory units in the amygdala and orbitofrontal parts, can be named Memory-Based Brain Emotional Learning (MBBEL). MBBEL was run using the data from 1900 to 2000 and 2000 to 2019 as training and testing stages, respectively. After the modeling process, the mean absolute error (MSE) and maximum absolute error (MaxAE) of the train and test stages were 0.011, 0.051, 0.10, and 0.295, respectively. Comparing the MBBEL results against those of eight prior models revealed that MBBEL results considerably improved compared to those of the previous models.


Main Subjects

[1]  C. Audoin, B. Guinot, and others, “The measurement of time,” Time, Freq. At. Clock, New York, 2001.
[2]  J. O. Dickey, “Earth rotation variations from hours to centuries,” Highlights Astron., vol. 10, pp. 17–44, 1995.
[3]  W. Schlüter, A. Böer, R. Dassing, H. Hase, P. Sperber, and R. Kilger, “TIGO-Transportable Integrated Geodetic Observatory, status of the project,” Proc. Dyn. Solid Earth, Pasadena, 1995.
[4] R. A. Del Rio, “The influence of global warming in Earth rotation speed,” in Annales Geophysicae, 1999, vol. 17, no. 6, pp. 806–811.
[5] R. A. Del Rio, D. Gambis, and D. A. Salstein, “Interannual signals in length of day and atmospheric angular momentum,” in Annales Geophysicae, 2000, vol. 18, no. 3, pp. 347–364.
[6]  R. Del Rio, D. Gambis, D. Salstein, P. Nelson, and A. Dai, “Solar activity and earth rotation variability,” J. Geodyn., vol. 36, pp. 423–443, 2003.
[7] R. G. Currie, “Detection of the 11-yr sunspot cycle signal in Earth rotation,” Geophys. J. Int., vol. 61, no. 1, pp. 131–140, 1980.
[8] H. Spencer Jones, “The rotation of the earth, and the secular accelerations of the sun, moon and planets,” Mon. Not. R. Astron. Soc., vol. 99, p. 541, 1939.
[9] A. R. Hakimi and S. Setayeshi, “A novel approach to delta-T from 1620 to 2010,” Mon. Not. R. Astron. Soc., vol. 417, no. 4, pp. 2714–2720, 2011, doi: 10.1111/j.1365-2966.2011.19435.x.
[10] J. Meeus and L. Simons, “Polynomial approximations to Delta T, 1620 (2000 AD,” J. Br. Astron. Assoc., vol. 110, 2000.
[11] F.-R. Stephenson and L. V Morrison, “Long-term changes in the rotation of the Earth: 700 BC to AD 1980,” Phil. Trans. R. Soc. Lond. A, vol. 313, no. 1524, pp. 47–70, 1984.
[12] J. M. Steele, “Predictions of eclipse times recorded in Chinese history,” J. Hist. Astron., vol. 29, no. 3, pp. 275–285, 1998.
[13] F.-R. Stephenson, “Book Review: Historical eclipses and Earth’s rotation/Cambridge U Press, 1997,” J. Br. Astron. Assoc., vol. 107, p. 220, 1997.
[14] F.-R. Stephenson and J. T. Baylis, “Early Chinese observations of occultations of planets by the Moon,” J. Hist. Astron., vol. 43, no. 4, pp. 455–477, 2012.
[15]  F.-R. Stephenson and L. J. Fatoohi, “Accuracy of solar eclipse observations made by Jesuit astronomers in China,” J. Hist. Astron., vol. 26, no. 3, pp. 227–236, 1995.
[16] F.-R. Stephenson and L. J. Fatoohi, “The Babylonian unit of time,” J. Hist. Astron., vol. 25, no. 2, pp. 99–110, 1994.
[17] F.-R. Stephenson and M. A. Houlden, Atlas of Historical Eclipse Maps: East Asia 1500 BC-AD 1900. Cambridge University Press, 1986.
[18]  D. F. Crouse, “An Overview of Major Terrestrial, Celestial, and Temporal Coordinate Systems for Target Tracking,” 2016.
[19] D. Gambis and B. Luzum, “Earth rotation monitoring, UT1 determination and prediction,” Metrologia, vol. 48, no. 4, p. S165, 2011.
[20] J. Meeus, “The effect of Delta T on astronomical calculations,” J. Br. Astron. Assoc., vol. 108, pp. 154–156, 1998.
[21] O. Montenbruck and T. Pfleger, Astronomy on the personal computer. Springer, 2013.
[22] S. Islam, M. Sadiq, and M. S. Qureshi, “ASSESSING POLYNOMIAL APPROXIMATION FOR ∆T,” J. Basic Appl. Sci., vol. 4, no. 1, pp. 1–4, 2008.
[23]  F. Espenak and J. Meeus, “Five Millennium Catalog of Solar Eclipses:-1999 to+ 3000 (2000 BCE to 3000 CE)-Revised,” 2009.
[24]    M. Khalid, M. Sultana, and F. Zaidi, “Delta: Polynomial Approximation of Time Period 1620--2013,” J. Astrophys., vol. 2014, 2014.
[25] A. Hakimi, S. A. Monadjemi, and S. Setayeshi, “An introduction of a reward-based time-series forecasting model and its application in predicting the dynamic and complicated behavior of the Earth rotation (Delta-T values)[Formula presented],” Appl. Soft Comput., vol. 113, 2021, doi: 10.1016/j.asoc.2021.107920.
[26] A. M. Yazdani, A. Mahmoudi, M. A. Movahed, P. Ghanooni, S. Mahmoudzadeh, and S. Buyamin, “Intelligent Speed Control of Hybrid Stepper Motor Considering Model Uncertainty Using Brain Emotional Learning,” Can. J. Electr. Comput. Eng., vol. 41, no. 2, pp. 95–104, 2018.
[27]  M. Roshanaei, E. Vahedi, and C. Lucas, “Adaptive antenna applications by brain emotional learning based on intelligent controller,” IET microwaves, antennas Propag., vol. 4, no. 12, pp. 2247–2255, 2010.
[28] W. Fang, F. Chao, C.-M. Lin, L. Yang, C. Shang, and C. Zhou, “An Improved Fuzzy Brain Emotional Learning Model Network Controller for Humanoid Robots,” Front. Neurorobot., 2019.
[29]  S. H. Fakhrmoosavy, S. Setayeshi, and A. Sharifi, “A modified brain emotional learning model for earthquake magnitude and fear prediction,” Eng. Comput., vol. 34, no. 2, pp. 261–276, 2018.
[30] E. Lotfi, O. Khazaei, and F. Khazaei, “Competitive brain emotional learning,” Neural Process. Lett., vol. 47, no. 2, pp. 745–764, 2018.
[31] Q. Wu et al., “Self-Organizing Brain Emotional Learning Controller Network for Intelligent Control System of Mobile Robots,” IEEE Access, vol. 6, pp. 59096–59108, 2018.
[32] S. Motamed, S. Setayeshi, and A. Rabiee, “Speech emotion recognition based on brain and mind emotional learning model,” J. Integr. Neurosci., no. Preprint, pp. 1–15, 2018.
[33] M. Moradi Zirkohi, “An Efficient Optimal Fractional Emotional Intelligent Controller for an AVR System in Power Systems,” J. AI Data Min., vol. 7, no. 1, pp. 191–200, 2019.
[34] R. Ayanzadeh, A. S. Z. Mousavi, and S. Setayeshi, “Fossil fuel consumption prediction using emotional learning in Amygdala,” in 2011 19th Iranian Conference on Electrical Engineering, 2011, pp. 1–6.
[35] Z. Farhoudi, S. Setayeshi, and A. Rabiee, “Using learning automata in brain emotional learning for speech emotion recognition,” Int. J. Speech Technol., vol. 20, no. 3, pp. 553–562, 2017.
[36]  S. H. Fakhrmoosavy, S. Setayeshi, and A. Sharifi, “An intelligent method for generating artificial earthquake records based on hybrid PSO--parallel brain emotional learning inspired model,” Eng. Comput., vol. 34, no. 3, pp. 449–463, 2018.
[37] J. Zhao, C.-M. Lin, and F. Chao, “Wavelet Fuzzy Brain Emotional Learning Control System Design for MIMO Uncertain Nonlinear Systems,” Front. Neurosci., vol. 12, 2018.
[38] R. Adhikari and R. K. Agrawal, “An introductory study on time series modeling and forecasting,” arXiv Prepr. arXiv1302.6613, 2013.
[39] H. Schwenk and Y. Bengio, “Boosting neural networks,” Neural Comput., vol. 12, no. 8, pp. 1869–1887, 2000.
[40] R. Meir and G. Rätsch, “An introduction to boosting and leveraging,” in Advanced lectures on machine learning, Springer, 2003, pp. 118–183.
[41] M. G. Orozco-Del-Castillo, J. C. Ortiz-Alemán, C. Couder-Castañeda, J. J. Hernández-Gómez, and A. Solís-Santomé, High solar activity predictions through an artificial neural network, vol. 28, no. 6. 2017. doi: 10.1142/S0129183117500759.
[42] H. Iijima, H. Hotta, S. Imada, K. Kusano, and D. Shiota, “Improvement of solar-cycle prediction: Plateau of solar axial dipole moment,” Astron. Astrophys., vol. 607, p. L2, 2017.
[43] G. A. Krasinskii, E. I. Saramonova, M. L. Sveshnikov, and E. S. Sveshnikova, “Universal time, lunar tidal deceleration and relativistic effects from observations of transits, eclipses and occultations in the XYIII-XX centuries,” Astron. Astrophys., vol. 145, pp. 90–96, 1985.
[44] M.-F. Loutre, “Earth history: Sediments to planetary motion,” Nature, vol. 409, no. 6823, p. 991, 2001.
[45] S. Chandrasekhar, Newton’s Principia for the common reader. Oxford University Press, 2003.