An Improved Extreme Learning Machine Prediction Model for Ionospheric Total Electron Content

doi:10.11947/j.JGGS.2023.0101

Abstract

Abstract:

Earth’s ionosphere is an important medium for navigation, communication, and radio wave transmission. Total Electron Content (TEC) is a descriptive quantify for ionospheric research. However, the traditional empirical model could not fully consider the changes of TEC time series, the prediction accuracy level of TEC data performed not high. In this study, an improved Extreme Learning Machine (ELM) model is proposed for ionospheric TEC prediction. Improvements involved the use of Empirical Mode Decomposition (EMD) and a Fuzzy C-Means (FCM) clustering algorithm to pre-process data used as input to the ELM model. The proposed model fully uses the TEC data characteristics and expected to perform better prediction accuracy. TEC measurements provided by the Centre for Orbit Determination in Europe (CODE) were used to evaluate the performance of the improved ELM model in terms of prediction accuracy, applicable latitude, and the number of required training samples. Experimental results produced a Mean Relative Error (MRE) and a Root Mean Square Error (RMSE) of 8.5% and 1.39 TECU, respectively, outperforming the ELM algorithm (RMSE=2.33 TECU and MRE=17.1%). The improved ELM model exhibited particularly high prediction accuracy in mid-latitude regions, with a mean relative error of 7.6%. This value improved further as the number of available training data increased and when 20-doys data were trained, achieving a mean relative error of 4.9%. These results suggest the proposed model offers higher prediction accuracy than conventional algorithms.

Key words: ELM model; EMD; FCM; incentive function; ionospheric TEC prediction

Jianmin WANG,Jiapeng HUANG. An Improved Extreme Learning Machine Prediction Model for Ionospheric Total Electron Content[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(1): 1-10.

Figures/Tables 8

Tab.1

Various excitation functions"

Function name	Functional expression
Bent	f(x)= $x 2 + 1 - 1 2$ +x
PReLU	f(x)= $0, x < 0 α x, x ≥ 0$
SoftPlus	f(x)=ln(1+e^x)
ELU	f(x)= $0, x < 0 α (e x - 1), x ≥ 0$
Sinc	f(x)= $s i n (x) x, x = 0 1, x ≠ 0$
Gaussian	f(x)= $e - x 2$
Tanh	f(x)=2Sigmoid(2x)-1
Hardlim	f(x)= $1, x < 0 0, x = 0 1, x > 0$
Sine	f(x)=sin(x)
Sigmoid	f(x)= $1 1 + e - x$

Tab.1

Fig.1

Tab.2

Fig.2

Tab.3

Tab.4

Tab.5

Tab.6

References 47

[1]	CANDER L R, HARALAMBOUS H. On the importance of total electron content enhancements during the extreme solar minimum[J]. Advances in Space Research, 2011, 47(2): 304-311. doi: 10.1016/j.asr.2010.08.026
[2]	CANDERL R. Re-visit of ionosphere storm morphology with TEC data in the current solar cycle[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2016, 138-139: 187-205. doi: 10.1016/j.jastp.2016.01.008
[3]	HABARULEMA J B, KATAMZI Z T, SIBANDA P, et al. Assessing ionospheric response during some strong storms in solar cycle 24 using various data sources[J]. Journal of Geophysical Research: Space Physics, 2017, 122(1): 1064-1082. doi: 10.1002/jgra.v122.1
[4]	NAVA B, COÏSSON P, RADICELLA S M. A new version of the NeQuick ionosphere electron density model[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2008, 70(15): 1856-1862. doi: 10.1016/j.jastp.2008.01.015
[5]	JAKOWSKI N, HOQUE M M, MAYER C. A new global TEC model for estimating transionospheric radio wave propagation errors[J]. Journal of Geodesy, 2011, 85(12): 965-974. doi: 10.1007/s00190-011-0455-1
[6]	TANG Jun. Studies on three-dimension ionospheric tomography using GNSS measurements and ionospheric disturbances[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(1): 117. DOI:10.11947/j.AGCS.2015.20130398. doi: 10.11947/j.AGCS.2015.20130398
[7]	ZHANG Xiaohong, REN Xiaodong, WU Fengbo, et al. Short-term TEC prediction of ionosphere based on ARIMA model[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(2): 118-124. DOI:10.13485/j.cnki.11-2089.2014.0018. doi: 10.13485/j.cnki.11-2089.2014.0018
[8]	WANG Jianmin, LI Yabo, MA Tianming, et al. Real time and fast algorithm for integer ambiguity of reference stations in large-scale network RTK[J]. Bulletin of Surveying and Mapping, 2017(10): 7-11. DOI: 10.13474/j.cnki.11-2246.2017.0307. doi: 10.13474/j.cnki.11-2246.2017.0307
[9]	DENG Zhongxin, LIU Ruiyuan, ZHEN Weimin, et al. Study on the ionospheric TEC storms over China[J]. Chinese Journal of Geophysics, 2012, 55(7): 2177-2184.
[10]	SHARMA G, RAY P, MOHANTY S, et al. Ionospheric TEC modelling for earthquakes precursors from GNSS data[J]. Quaternary International, 2017, 462: 65-74. doi: 10.1016/j.quaint.2017.05.007
[11]	CHERNOUSSA, SHAGIMURATOVII, IEVENKOIB, et al. Auroral perturbations as an indicator of ionosphere impact on navigation signals[J]. Russian Journal of Physical Chemistry B, 2018, 12(3):562-567. doi: 10.1134/S1990793118030065
[12]	MUKESHR, KARTHIKEYANV, SOMAP, et al. Cokriging based statistical approximation model for forecasting ionospheric VTEC during high solar activity and storm days[J]. Astrophysics and Space Science, 2019, 364(8):131.
[13]	LIU Xiandong, SONG Lijie, YANG Xiaohui, et al. Predicting shortdated ionospheric TEC based on wavelet neural network[J]. Hydrographic Surveying and Charting, 2010, 30(5): 49-51, 55.
[14]	AKHOONDZADEH M, DE SANTIS A, MARCHETTI D, et al. Anomalous seismo-LAI variations potentially associated with the 2017 M_W=7.3 Sarpol-e Zahab (Iran) earthquake from swarm satellites, GPS-TEC and climatological data[J]. Advances in Space Research, 2019, 64(1): 143-158. doi: 10.1016/j.asr.2019.03.020
[15]	YAN Xiangxiang, SHAN Xinjian, CAO Jinbin, et al. Preliminary study of the seimoionospheric perturbation before Tohoku-oki M_W 9.0 earthquake[J]. Progress in Geophysics, 2013, 28(1): 155-164.
[16]	ZHAO Chuanbao, ZHANG Baocheng, ODOLINSKI R, et al. Combined use of single-frequency data and global ionosphere maps to estimate BDS and Galileo satellite differential code biases[J]. Measurement Science and Technology, 2020, 31(1): 015002. doi: 10.1088/1361-6501/ab3d70
[17]	PEREZ R O. Using Tensor Flow-based neural network to estimate GNSS single frequency ionospheric delay[J]. Advances in Space Research, 2019, 63(5): 1607-1618. doi: 10.1016/j.asr.2018.11.011
[18]	JAKOBSEN J, KNUDSEN P, JENSEN A B O. Analysis of local ionospheric time varying characteristics with singular value decomposition[J]. Journal of Geodesy, 2010, 84(7): 449-456. doi: 10.1007/s00190-010-0378-2
[19]	AN Jiachun, NING Xinguo, WANG Zemin, et al. Antarctic ionospheric prediction based on spherical cap harmonic analysis and time series analysis[J]. Geomatics and Information Science of Wuhan University, 2015, 40(5): 677-681.
[20]	LIU Lilong, CHEN Jun, HUANG Liangke, et al. TEC forecast of short-term ionosphere based on wavelet-ARIMA[J]. Journal of Guilin University of Technology, 2016, 36(2): 294-299.
[21]	LU Chenlong, KUANG Cuilin, ZHANG Jinsheng, et al. Predicting ionosphere TEC with the combination of singular spectrum analysis and ARMA model[J]. Journal of Geodesy and Geodynamics, 2014, 34(6): 44-49.
[22]	TANG Jun, YAO Yibin, CHEN Peng, et al. Prediction models of ionospheric TEC improved by EMD method[J]. Geomatics and Information Science of Wuhan University, 2013, 38(4): 408-411, 444.
[23]	WANG Ruopeng, ZHOU Chen, DENG Zhongxin, et al. Predicting f_oF₂ in the China region using the neural networks improved by the genetic algorithm[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2013, 92: 7-17. doi: 10.1016/j.jastp.2012.09.010
[24]	LIU J Y, CHEN C H, CHEN Y I, et al. A statistical study of ionospheric earthquake precursors monitored by using equatorial ionization anomaly of GPS TEC in Taiwan during 2001—2007[J]. Journal of Asian Earth Sciences, 2010, 39(1-2): 76-80. doi: 10.1016/j.jseaes.2010.02.012
[25]	CESARONI C, SPOGLI L, ARAGON-ANGEL A, et al. Neural network based model for global total electron content forecasting[J]. Journal of Space Weather and Space Climate, 2020, 10(S335): 11. doi: 10.1051/swsc/2020013
[26]	ACHARYA R, ROY B, SIVARAMAN M R, et al. Prediction of ionospheric total electron content using adaptive neural network with in-situ learning algorithm[J]. Advances in Space Research, 2011, 47(1): 115-123. doi: 10.1016/j.asr.2010.08.016
[27]	WANG Jianmin, HUANG Jiapeng, LIU Ziran, et al. Improvement of prediction model for ionospheric TEC with adaptive Kalman filter[J]. Journal of Navigation and Positioning, 2018, 6(2): 121-127.
[28]	WANG Jianmin, HUANG Jiapeng, ZHU Huizhong, et al. Study of the ionosphere TEC forecasting method[J]. Science of Surveying and Mapping, 2016, 41(12): 47-52.
[29]	HUANG Z, LI Q B, YUAN H. Forecasting of ionospheric vertical TEC 1-h ahead using a genetic algorithm and neural network[J]. Advances in Space Research, 2015, 55(7): 1775-1783. doi: 10.1016/j.asr.2015.01.026
[30]	SABZEHEE F, FARZANEH S, SHARIFI M A, et al. TEC regional modeling and prediction using ANN method and single frequency receiver over IRAN[J]. Annals of Geophysics, 2018, 61(1): GM103.
[31]	TEBABAL A, RADICELLA S M, DAMTIE B, et al. Feed forward neural network based ionospheric model for the east African region[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2019, 191:105052. doi: 10.1016/j.jastp.2019.05.016
[32]	INYURT S, SEKERTEKIN A. Modeling and predicting seasonal ionospheric variations in Turkey using Artificial Neural Network (ANN)[J]. Astrophysics and Space Science, 2019, 364(4): 62. doi: 10.1007/s10509-019-3545-9
[33]	HUANG Guangbin, ZHOU Hongming, DING Xiaojian, et al. Extreme learning machine for regression and multiclass classification[J]. IEEE Transactions on Systems, Man,and Cybernetics, 2012, 42(2): 513-529.
[34]	LI Lin, JI Hongbing. Signal feature extraction based on an improved EMD method[J]. Measurement, 2009, 42(5): 796-803. doi: 10.1016/j.measurement.2009.01.001
[35]	WANG Tong, ZHANG Mingcai, YU Qihao, et al. Comparing the applications of EMD and EEMD on time-frequency analysis of seismic signal[J]. Journal of Applied Geophysics, 2012, 83: 29-34. doi: 10.1016/j.jappgeo.2012.05.002
[36]	SU Wenbin, LEI Zhufeng. Mold-level prediction based on long short-term memory model and multi-mode decomposition with mutual information entropy[J]. Advances in Mechanical Engineering, 2019, 11(12): 168.
[37]	JIN Xuebo, YANG Nianxiang, WANG Xiaoyi, et al. Hybrid deep learning predictor for smart agriculture sensing based on empirical mode decomposition and gated recurrent unit group model[J]. Sensors, 2020, 20(5): 1334. doi: 10.3390/s20051334
[38]	ZHANG Qian, ZHANG Jinjin. Short-term load forecasting method based on EWT and IDBSCAN[J]. Journal of Electrical Engineering & Technology, 2020, 15(2): 635-644.
[39]	CHEN Weijie, GIGER M L, BICK U. A fuzzy C-means-based approach for computerized segmentation of breast lesions in dynamic contrast-enhanced MR images[J]. Academic Radiology, 2006, 13(1): 63-72. pmid: 16399033
[40]	CHIN C S, JI Xi, WOO W L, et al. Modified multiple generalized regression neural network models using fuzzy C-means with principal component analysis for noise prediction of offshore platform[J]. Neural Computing and Applications, 2019, 34(4): 1127-1142.
[41]	KELOTRA A, PANDEY P. Stock market prediction using optimized deep-ConvLSTM model[J]. Big Data, 2020, 8(1): 5-24. doi: 10.1089/big.2018.0143
[42]	HATHAWAY R J, BEZDEK J C. Fuzzy C-means clustering of incomplete data[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 2001, 31(5): 735-744. doi: 10.1109/3477.956035
[43]	YU Jian, CHENG Qiansheng, HUANG Houkan. Analysis of the weighting exponent in the FCM[J]. IEEE Transactions on Systems, Man,and Cybernetics, Part B, 2004, 34(1): 634-639. doi: 10.1109/TSMCB.2003.810951
[44]	GHOSH S, KUMAR S. Comparative analysis of k-means and fuzzy C-means algorithms[J]. International Journal of Advanced Computer Science and Applications, 2013, 4(4): 35-39.
[45]	YIN Dongyang, SHENG Yifa, JIANG Mingjie, et al. Short-term wind speed forecasting using Elman neural network based on rough set theory and principal components analysis[J]. Power System Protection and Control, 2014, 42(11): 46-51.
[46]	SUN Zhenli, WANG Han, LAU W S, et al. Application of BW-ELM model on traffic sign recognition[J]. Neurocomputing, 2014, 128: 153-159. doi: 10.1016/j.neucom.2012.11.057
[47]	HUANG Guangbin, ZHU Qinyu, SIEW C K. Extreme learning machine: theory and applications[J]. Neurocomputing, 2006, 70(1-3): 489-501. doi: 10.1016/j.neucom.2005.12.126

Grid point information		Year	Latitude	Training data/doy
Experimental group 1	Experiment 1	2008	(125°W, 87.5°N)	51—60
	Experiment 2	2011	(125°W, 45°N)	101—110
	Experiment 3	2014	(125°W, 22.5°N)	201—210
Experimental group 2	Experiment 4	2007	(125°W, 22.5°S)	31—35
	Experiment 5	2009	(125°W, 45°S)	151—155
	Experiment 6	2006	(125°W, 87.5°S)	351—355
Experimental group 3	Experiment 7	2017	(15°E, 45°N)	21—40
	Experiment 8	2017	(65°E, 45°N)	21—40
	Experiment 9	2017	(125°E, 22.5°S)	21—40

Experiment	RMSE/TECU	MRE/(%)	MAE/TECU	MSE/TECU	Excitation function	The number of hidden layers
1	0.566	14.0	0.435	0.320	ELU	21
2	1.408	7.4	1.071	1.983	Sig	10
3	1.198	3.3	0.875	1.434	Bent	7
4	5.992	15.4	3.598	35.905	ELU	2
5	1.023	13.2	0.868	1.046	SoftPlus	21
6	0.645	8	0.56	0.416	Gaussian	6
7	0.429	3.7	0.299	0.184	ELU	5
8	0.588	6.2	0.487	0.346	Bent	21
9	0.639	4.9	0.55	0.409	Tanh	23

Model name	RMSE /TECU	MRE /(%)	MAE /TECU	MSE /TECU
NAR	3.97	32.2	3.38	40.15
AR	3.49	26.7	2.93	22.51
GM(1,1)	5.02	40.9	4.35	38.62
ELM	2.33	17.1	1.77	8.73
Improved ELM	1.39	8.5	0.97	4.67

Sample latitude	RMSE /TECU	MRE /(%)	MAE /TECU	MSE /TECU
High	0.61	11.0	0.50	0.37
Mid	0.86	7.6	0.68	0.89
Low	2.61	7.9	1.67	12.58

Length /doys	RMSE /TECU	MRE /(%)	MAE /TECU	MSE /TECU
5	2.55	12.2	1.68	12.46
10	1.06	8.2	0.79	1.25
20	0.55	4.9	0.45	0.31