Abstract
The prediction of an accurate geodetic point velocity has great importance in geosciences. The purpose of this work is to explore the predictive capacity of three artificial neural network (ANN) models in predicting geodetic point velocities. First, the multi-layer perceptron neural network (MLPNN) model was developed with two hidden layers. The generalized regression neural network (GRNN) model was then applied for the first time. Afterwards, the radial basis function neural network (RBFNN) model was trained and tested with the same data. Latitude (\(\varphi\)) and longitude (λ) were utilized as inputs and the geodetic point velocities (\({V}_{X}\),\({V}_{Y}\),\({V}_{Z}\)) as outputs to the MLPNN, GRNN, and RBFNN models. The performances of all ANN models were evaluated using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (\({\text{R}}^{2}\)). The first investigation demonstrated that it was possible to predict the geodetic point velocities by using all the components as output parameters simultaneously. The other result is that all ANN models were able to predict the geodetic point velocity with satisfactory accuracy; however, the GRNN model provided better accuracy than the MLPNN and RBFNN models. For example, the RMSE and MAE values were 1.77–1.88 mm and 1.44–1.51 mm, respectively, for the GRNN model.
Similar content being viewed by others
References
Akhoondzadeh M (2014) Investigation of GPS-TEC measurements using ANN method indicating seismo-ionospheric anomalies around the time of the Chile (Mw= 8.2) earthquake of 01 April 2014. Adv Space Res 54(9):1768–1772. https://doi.org/10.1016/j.asr.2014.07.013
Aktuğ B, Parmaksız E, Kurt M, Lenk O, Kılıçoğlu A, Gürdal MA, Özdemir S (2013) Deformation of central anatolia: GPS implications. J Geodyn 67:78–96. https://doi.org/10.1016/j.jog.2012.05.008
Aktuğ B, Sezer S, Özdemir S, Lenk O, Kılıçoğlu A (2011) Türkiye ulusal temel GPS ağı güncel koordinat ve hızlarının hesaplanması. Harita Dergisi 145:1–14 ((in Turkish))
Bogusz J, Kłos A, Grzempowski P, Kontny B (2014) Modelling the velocity field in a regular grid in the area of Poland on the basis of the velocities of European permanent stations. Pure Appl Geophys 171(6):809–833. https://doi.org/10.1007/s00024-013-0645-2
Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355
Cakir L, Konakoglu B (2019) The impact of data normalization on 2D coordinate transformation using GRNN. Geod Vestnik 63(4):541–553. https://doi.org/10.15292/geodetski-vestnik.2019.04.541-553
Cakir L, Yilmaz N (2014) Polynomials, radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling. Measurement 57:148–153. https://doi.org/10.1016/j.measurement.2014.08.003
Cander LR (1998) Artificial neural network applications in ionospheric studies. Ann Geophys 41(5–6):757–766. https://doi.org/10.4401/ag-3817
Ching KE, Chen KH (2015) Tectonic effect for establishing a semi-dynamic datum in Southwest Taiwan. Earth Planets Space 67(1):207
Demir C, Açıkgöz M (2000) Türkiye ulusal temel GPS ağı noktalarındaki uzun peryotlu koordinat değişimlerinin (sküler hızların) kestirilmesi. Harita Dergisi, 1–19 (in Turkish)
Elshambaky HT, Kaloop MR, Hu JW (2018) A novel three-direction datum transformation of geodetic coordinates for Egypt using artificial neural network approach. Arab J Geosci 11(6):110. https://doi.org/10.1007/s12517-018-3441-6
Erol B, Erol S (2013) Learning-based computing techniques in geoid modeling for precise height transformation. Comput Geosci 52:95–107. https://doi.org/10.1016/j.cageo.2012.09.010
Farolfi G, Del Ventisette C (2016) Contemporary crustal velocity field in Alpine Mediterranean area of Italy from new geodetic data. GPS Solut 20(4):715–722. https://doi.org/10.1007/s10291-015-0481-1
Foresee FD, Hagan MT (1997) Gauss-Newton approximation to Bayesian learning. In: Proceedings of international conference on neural networks (ICNN'97), vol 3, pp 1930–1935. https://doi.org/10.1109/ICNN.1997.614194
Gülal E, Tiryakioğlu İ, Erdoğan S, Aykut NO, Baybura T, Akpinar B, Telli AK, Ata E, Gümüş K, Taktak F, Yilmaz İ, Öcalan T, Kalyoncuoğlu ÜY, Dolmaz MN, Elitok Ö, Erdoğan H, Soycan M (2013) Tectonic activity inferred from velocity field of GNSS measurements in southwest of Turkey. Acta Geod Geophys 48:109–121. https://doi.org/10.1007/s40328-012-0005-1
Gullu M (2010) Coordinate transformation by radial basis function neural network. Sci Res Essays 5:3141–3146
Güllü M, Yilmaz İ, Yilmaz M, Turgut B (2011) An alternative method for estimating densification point velocity based on back propagation artificial neural networks. Stud Geophys Geod 55(1):73–86. https://doi.org/10.1007/s11200-011-0005-6
Habarulema JB, McKinnell LA, Cilliers PJ (2007) Prediction of global positioning system total electron content using neural networks over South Africa. J Atmos Sol Terr Phys 69(15):1842–1850. https://doi.org/10.1016/j.jastp.2007.09.002
Hajian A, Ardestani EV, Lucas C (2011) Depth estimation of gravity anomalies using hopfield neural networks. J Earth Space Phys 37(2):1–9. https://doi.org/10.3997/2214-4609.20146872
Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall, p. 842
Hernandez-Pajares M, Juan JM, Sanz J (1997) Neural network modeling of the ionospheric electron content at global scale using GPS data. Radio Sci 32(3):1081–1089
Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366. https://doi.org/10.1016/0893-6080(89)90020-8
Hu W, Sha Y, Kuang S (2004) New method for transforming global positioning system height into normal height based on neural network. J Surv Eng 130(1):36–39. https://doi.org/10.1061/(ASCE)0733-9453(2004)130:1(36)
Huang Z, Yuan H (2014) Ionospheric single-station TEC short-term forecast using RBF neural network. Radio Sci 49(4):283–292. https://doi.org/10.1002/2013RS005247
Inyurt S, Sekertekin A (2019) Modeling and predicting seasonal ionospheric variations in Turkey using artificial neural network (ANN). Astrophys Space Sci 364:62. https://doi.org/10.1007/s10509-019-3545-9
Ito C, Takahashi H, Ohzono M (2019) Estimation of convergence boundary location and velocity between tectonic plates in northern Hokkaido inferred by GNSS velocity data. Earth Planets Space 71(1):86. https://doi.org/10.1186/s40623-019-1065-z
Kaloop MR, Hu JW (2015) Optimizing the de-noise neural network model for GPS time-series monitoring of structures. Sensors 15(9):24428–24444. https://doi.org/10.3390/s150924428
Kaloop MR, Rabah M, Hu JW, Zaki A (2018a) Using advanced soft computing techniques for regional shoreline geoid model estimation and evaluation. Mar Georesour Geotechnol 36(6):688–697. https://doi.org/10.1080/1064119X.2017.1370622
Kaloop MR, Yigit CO, Hu JW (2018b) Analysis of the dynamic behavior of structures using the high-rate GNSS-PPP method combined with a wavelet-neural model: numerical simulation and experimental tests. Adv Space Res 61(6):1512–1524. https://doi.org/10.1016/j.asr.2018.01.005
Kavzoglu T, Saka M (2005) Modelling local GPS/levelling geoid undulations using artificial neural networks. J Geod 78:520–527. https://doi.org/10.1007/s00190-004-0420-3
Kierulf HP, Ouassou M, Simpson MJR, Vestøl O (2013) A continuous velocity field for Norway. J Geod 87(4):337–349. https://doi.org/10.1007/s00190-012-0603-2
Kisi Ö (2008) Constructing neural network sediment estimation models using a data-driven algorithm. Math Comput Simul 79(1):94–103. https://doi.org/10.1016/j.matcom.2007.10.005
Konakoglu B, Cakır L, Gökalp E (2016) 2D coordinates transformation using artificial neural networks. In: Geo advances 2016: ISPRS workshop on multi-dimensional and multi-scale spatial data modeling, At Mimar Sinan Fine Arts University/Istanbul, Volume XLII-2/W1: 3rd international geoadvances workshop. https://doi.org/10.5194/isprs-archives-XLII-2-W1-183-2016
Konakoğlu B, Gökalp E (2016) A Study on 2D similarity transformation using multilayer perceptron neural networks and a performance comparison with conventional and robust outlier detection methods. Acta Montan Slovaca 21(4):324–332
Kurt Aİ, Deniz R (2010) Deformasyon hızlarının iyileştirilmesinde sabit GPS istasyonları zaman serileri analizinden yararlanılması. Harita Dergisi 144:20–28 ((in Turkish))
Legates DR, McCabe GJ Jr (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241. https://doi.org/10.1029/1998WR900018
Lei Y, Zhao D, Cai H (2015) Prediction of length-of-day using extreme learning machine. Geod Geodyn 6(2):151–159. https://doi.org/10.1016/j.geog.2014.12.007
Li CK, Ching KE, Chen KH (2019) The ongoing modernization of the Taiwan semi-dynamic datum based on the surface horizontal deformation model using GNSS data from 2000 to 2016. J Geod 93(9):1543–1558. https://doi.org/10.1007/s00190-019-01267-5
Liao DC, Wang QJ, Zhou YH, Liao XH, Huang CL (2012) Long-term prediction of the earth orientation parameters by the artificial neural network technique. J Geodyn 62:87–92. https://doi.org/10.1016/j.jog.2011.12.004
Lin LS (2007) Application of a back-propagation artificial neural network to regional grid-based geoid model generation using GPS and leveling data. J Surv Eng 133(2):81–89. https://doi.org/10.1061/(ASCE)0733-9453(2007)133:2(81)
Lin LS, Wang YJ (2006) A study on cadastral coordinate transformation using artificial neural network. In: Proceedings of the 27th Asian conference on remote sensing, Ulaanbaatar, Mongolia.
MacKay DJ (1992) Bayesian interpolation. Neural Comput 4(3):415–447
Majdański M (2012) The structure of the crust in TESZ area by kriging interpolation. Acta Geophys 60(1):59–75. https://doi.org/10.2478/s11600-011-0058-5
Maruyama T (2008) Regional reference total electron content model over Japan based on neural network mapping techniques. Ann Geophys 25(12):2609–2614. https://doi.org/10.5194/angeo-25-2609-2007
McClusky S, Balassanian S, Barka A, Demir C, Ergintav S, Georgiev I, Gurkan O, Hamburger M, Hurst K, Kahle H, Kastens K, Kekelidze G, King R, Kotzev V, Lenk O, Mahmoud S, Mishin A, Nadariya M, Ouzounis A, Paradissis D, Peter Y, Prilepin M, Reilinger R, Sanli I, Seeger H, Teableb A, Toksöz MN, Veis G (2000) GPS constraints on crustal movements and deformations for plate dynamics. J Geophys Res 105:5695–5720. https://doi.org/10.1029/1999JB900351
McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133. https://doi.org/10.1007/BF02478259
Mosavi MR (2006) A practical approach for accurate positioning with L1 GPS receivers using neural networks. J Intell Fuzzy Syst 17(2):159–171
Müller MD, Geiger A, Kahle HG, Veis G, Billiris H, Paradissis D, Felekis S (2013) Velocity and deformation fields in the North Aegean domain, Greece, and implications for fault kinematics, derived from GPS data 1993–2009. Tectonophysics 597–598:34–49. https://doi.org/10.1016/j.tecto.2012.08.003
Park J, Sandberg IW (1991) Universal approximation using radial basis function networks. Neural Comput 3(2):246–257. https://doi.org/10.1162/neco.1991.3.2.246
Patterson DW (1996) Artificial neural networks theory and applications. Prentice Hall, Upper Saddle River, p 477
Pereira RAD, De Freitas SRC, Ferreira VG, Faggion PL, dos Santos DP, Luz RT, Tierra Criollo AR, Del Cogliano D (2012) Evaluation of a few interpolation techniques of gravity values in the border region of Brazil and Argentina. In: Geodesy for planet Earth. Springer, Berlin, pp 909–915
Poyraz F, Hastaoğlu KO, Koçbulut F, Tiryakioğlu I, Tatar O, Demirel M, Duman H, Aydin C, Ciğer AF, Gursoy O, Turk T, Sigirci R (2019) Determination of the block movements in the eastern section of the Gediz Graben (Turkey) from GNSS measurements. J Geodyn 123:38–48. https://doi.org/10.1016/j.jog.2018.11.001
Reitermanová Z (2010) Data splitting. In: Safránková J, Pavlu J (eds) In: WDS 2010 proceedings of contributed papers, part I: mathematics and computer sciences. Matfyzpress, Prague, pp 31–36
Schuh H, Ulrich M, Egger D, Müller J, Schwegmann W (2002) Prediction of Earth orientation parameters by artificial neural networks. J Geod 76(5):247–258. https://doi.org/10.1007/s00190-001-0242-5
Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(6):568–576. https://doi.org/10.1109/72.97934
Stopar B, Ambrožič T, Kuhar M, Turk G (2006) GPS-derived geoid using artificial neural network and least squares collocation. Surv Rev 38(300):513–524. https://doi.org/10.1179/sre.2006.38.300.513
Tebabal A, Radicella SM, Nigussie M, Damtie B, Nava B, Yizengaw E (2018) Local TEC modelling and forecasting using neural networks. J Atmos Sol Terr Phys 172:143–151. https://doi.org/10.1016/j.jastp.2018.03.004
Tierra A, Dalazoana R, De Freitas S (2008) Using an artificial neural network to improve the transformation of coordinates between classical geodetic reference frames. Comput Geosci 34(3):181–189. https://doi.org/10.1016/j.cageo.2007.03.011
Tierra A, Romero R (2014) Planes coordinates transformation between PSAD56 to SIRGAS using a multilayer artificial neural network. Geod Cartogr 63(2):199–209. https://doi.org/10.2478/geocart-2014-0014
Tierra AR, De Freitas SRC (2005) Artificial neural network: a powerful tool for predicting gravity anomaly from sparse data. In Gravity, geoid and space missions. Springer, Berlin, pp 208–213
Veronez MR, De Souza GC, Matsuoka TM, Reinhardt A, Da Silva RM (2011) Regional mapping of the geoid using GNSS (GPS) measurements and an artificial neural network. Remote Sens 3:668–683. https://doi.org/10.3390/rs3040668
Wang Q, Liao D, Zhou Y (2008) Real-time rapid prediction of variations of Earth’s rotational rate. Chin Sci Bull 53(7):969–973. https://doi.org/10.1007/s11434-008-0047-5
Yilmaz M, Gullu M (2014) A comparative study for the estimation of geodetic point velocity by artificial neural networks. J Earth Syst Sci 123(4):791–808. https://doi.org/10.1007/s12040-014-0411-6
Zaletnyik P (2004) Coordinate transformation with neural networks and with polynomials in Hungary. In: International symposium on modern technologies, education and professional practice in geodesy and related fields, Sofia, Bulgaria, pp 471–479
Ziggah YY, Youjian H, Tierra A, Konaté AA, Hui Z (2016a) Performance evaluation of artificial neural networks for planimetric coordinate transformation—a case study, Ghana. Arab J Geosci 9:698–714. https://doi.org/10.1007/s12517-016-2729-7
Ziggah YY, Youjian H, Tierra AR, Laari PB (2019) Coordinate transformation between global and local data based on artificial neural network with K-fold cross-validation in Ghana. Earth Sci Res J 23(1):67–77. https://doi.org/10.15446/esrj.v23n1.63860
Ziggah YY, Youjian H, Xianyu Yu, Basommi LP (2016b) Capability of artificial neural network for forward conversion of geodetic coordinates (ϕ, λ, h) to cartesian coordinates (X, Y, Z). Math Geosci 48:687–721. https://doi.org/10.1007/s11004-016-9638-x
Acknowledgements
The author would like to thank anonymous reviewers for their valuable comments which helped to improve this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Konakoglu, B. Prediction of geodetic point velocity using MLPNN, GRNN, and RBFNN models: a comparative study. Acta Geod Geophys 56, 271–291 (2021). https://doi.org/10.1007/s40328-021-00336-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40328-021-00336-6