Modelling Local Geometric Geoid using Soft Computing and Classical Techniques: A Case Study of the University of Mines and Technology (UMaT) Local Geodetic Reference Network
Keywords:
Artificial Neural Networks, Geodetic Reference System, Geoid Modelling, Global Navigation Satellite System, Polynomial Regression Model
Abstract
Geoid determination for national heighting is one of the major research focuses in geodetic sciences. Many studies in the past and recent years have suggested various mathematical techniques for local geometric geoid modelling. This study considered an empirical evaluation of soft computing techniques such as Backpropagation Artificial Neural Network (BPANN), Multivariate Adaptive Regression Spline (MARS), Generalized Regression Neural Network (GRNN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and conventional methods such as Polynomial Regression Model (PRM), and Multiple Linear Regression (MLR). The motive is to apply and assess for the first time in our study area the working efficiency of the aforementioned techniques. Each model technique was assessed based on performance criteria indices such as mean error (ME), mean square error (MSE), minimum and maximum error value (rmin and rmax), correlation coefficient (R), coefficient of determination (R2) and standard deviation (SD). The statistical analysis of the results revealed that ANFIS, GRNN, MARS, BPANN, MLR and PRM, successfully estimate the geoid heights with a good precision for the study area. However, ANFIS outperforms BPANN, MARS, MLR, PRM, and GRNN in estimating a local geoid height. In terms of ME and SD, ANFIS achieved 0.0445 m and 0.0013m as compared to BPANN, MARS, MLR, PRM, and GRNN which achieved 0.1462 m, 0.0059 m, 0.1423 m, 0.0148 m, 0.3117 m, 0.0102 m, 0.1798 m, 0.0208 m, 0.0878 m and 0.0023, respectively. The main conclusion drawn from this study is that, the method of using soft computing is promising and can be adopted to solve some of the major problems related to height issues in Ghana.
References
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Gucek, M., Basic, T., 2009. Height Transformation Models from Ellipsoidal into the Normal Orthometric Height System for the Territory of the City of Zagreb. Studia Geophysica et Geodaetica 33, 17-38.
Hannan, S.A., Manza, R.R., Ramteke, R.J., 2010. Generalized Regression Neural Network and Radial Basis Function for Heart Disease Diagnosis. International Journal of Computer Applications 7 (13), 7-13.
Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feed forward networks are universal approximators. Neural Networks 2, 359-366.
Idri, A., Zakrani, A., Zahi, A., 2010. Design of Radial Basis Function Neural Networks for Software Effort Estimation. International Journal of Computer Science Issue 7 (4), 11-17.
Ismail, S., Shabri, A., Samsudin, R., 2012. A hybrid model of self-organizing maps and least square Support Vector Machine for River flow forecasting. Hydrological Earth System Science 16, 4417-4433.
Jang, J.R.S., 1993. ANFIS: Adaptive Network Based Fuzzy Inference System. IEEE Transactions on Systems, Man Cybernetics 23 (3), 665-685.
Kaloop, M.R., Rabah, M., Hu, J.W., Zaki, A., 2017. Using Advanced Soft Computing Techniques for Regional Shoreline Geoid Model Estimation and Evaluation. Marine Georesources & Geotechnology 36 (6), 688-697.
Kao, S.P., Ning, F.S., Chen, C.N., Chen, C.L., 2017. Using Particle Swarm Optimization to Establish a Local Geometric Geoid Model. Boletim de Ciências Geodésicas 23 (2), 327-337.
Kavzoglu, T., Saka, M.H., 2005. Modelling Local GPS/Levelling Geoid Undulations using Artificial Neural Networks. Journal of Geodesy 78 (9), 520-527.
Kiani, M., 2020. Local Geoid Height Approximation and Interpolation Using Moving Least Squares Approach. Geodesy and Geodynamics 11 (2), 120-126.
Kisi, O., Parmar, K.S., 2015. Application of Least Square Support Vector Machine and Multivariate Adaptive Regression Spline Models in Long Term Prediction of River Water Pollution. Journal of Hydrology 534, 104-112
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Ramouz, S., Afrasteh, Y., Reguzzoni, M., Safri, A., 2020. Assessment of Local Covariance Estimation Through Least Squares Collocation Over Iran. Advances in Geosciences, 50, 65-75.
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Samui, P., 2013. Multivariate Adaptive Regression Spline (MARS) for prediction of Elastic Modulus of jointed Rock Mass. Geotechnical and Geological Engineering 31, 249-253.
Samui, P., Kim, D., 2012. Modelling of reservoir-induced earthquakes: a multivariate adaptive regression spline. Journal of Geophysics and Engineering 9, 494-497.
Sanlioglu, I., Maras, S.S., 2011. A Comparison with Orthometric Heights Obtained by Real Time Kinematics and by Local Geoid Model, Case Study in Adana. Geodesy and Mine Surveying Section, International Multidisciplinary Scientific GeoConference SGEM 2011, 2, 199-206.
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Tusat, E., 2011. A Comparison of Geoid Height Obtained with Adaptive Neural Fuzzy Inference Systems and Polynomial Coefficients Methods. International Journal of the Physical Sciences 6 (4), 789-795.
Tiryaki, B., 2008. Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks and regression trees. Engineering Geology 99, 51-60.
Veronez, M.R., De Souza, G.C., Matsuoka, T.M., Reinhardt, A., Da Silva, R.M., 2011. Regional Mapping of the Geoid using GNSS (GPS) Measurements and an Artificial Neural Network. Remote Sensing 3, 668-683.
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Yilmaz, M., Arslan, E., 2008. Effect of the Type of Membership Function on Geoid Height Modelling with Fuzzy Logic. Survey Review 40, 379-391.
Yonaba, H., Anctil, F., Fortin, V., 2010. Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Stream Flow Forecasting. Journal of Hydrologic Engineering 15 (4), 275-283.
Zaletnyik, P., Volgyesi, L., Kirchner, I., Palancz, B., 2007. Combination of GPS/Levelling and the Gravimetric Geoid by using the Thin Plate Spline Interpolation Technique Via Finite Element Method. Journal of Applied Geodesy 1, 233-239.
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Adoko, A.C., Jiao, Y.Y., Wu, L., Wang, H., Wang, Z.H., 2013. Predicting Tunnel Convergence using Multivariate Adaptive Regression Splines and Artificial Neural Network. Tunneling and Underground Space Technology, 38, 368-376.
Ahmadi, M.M.Y.B., Safari, A., Shahbazi, A., Foroughi, I., 2016. On the Comparison of Different Radial Basis Functions in Local Gravity Field Modelling using Levenberg-Marquardt Algorithm. European Geosciences Union General Assembly 2016, Vienna, Austria, 17-22 April 2016, 1-2.
Akcin, H., Celik, C.T., 2013. Performance of Artificial Neural Networks on Kriging Method in Modelling Local Geoid. Boletim De Ciencias Geodesicas 19 (1), 84-97.
Akyilmaz, O., Ozludemir, M.T., Ayan, T., Celik, R.N., 2009. Soft Computing Methods for Geoidal Height Transformation. Earth Planets Space 61, 825-833.
Al-Bayari, O., Al-Zoubi, A., 2007. Preliminary Study of the Gravimetric Local Geoid Model in Jordan: Case Study (GeoJordan Model). Annals of Geophysics 50 (3), 387-396.
Al-Krargy, E.M., Mohamed, H.F., Hosney, M.M., Dawod, G.M., 2017. A High-Precison Geoid for Water Resources Management: A Case Study in Menofia Governorate, Egypt. National Water Research Center (NWRC) Conference on: Research and Technology Development for Sustainable Water Resources Management, Cairo, Egypt, 1-13.
Chen, W., Hill, C., 2005. Evaluation Procedure for Coordinate Transformation. Journal of Surveying Engineering 43-49.
Craven, P., Wahba, G., 1979. Smoothing noisy data with spline function: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math 31, 317-403.
Dawod, G.M., Mohammed, H.F., Ismail, S.S., 2010. Evaluation and adaptation of the EGM2008 geopotential model along the Northern Nile Valley, Egypt: Case Study. Journal of Surveying 136, 36-40.
Dawod, G., 2008. Towards the redefinition of the Egyptian geoid: performance analysis of recent global geoid models and digital terrain models. Journal of Spatial Scienc, 53 (1), 31-42.
Darbeheshti, N., 2009. Modification of the Least-Squares Collocation Method for Non-Stationary Gravity Field Modelling. Publish PhD Dissertation, Department of Spatial Sciences, Curtin University of Technology, 1-169.
Devi, K.M., Karthikeyan, R., 2015. A Survey on Outlier Detection for Uncertain Meteorology Data, International Journal of Engineering Sciences & Research 4 (12), 203-208.
Doganalp, S., Selvi, H.Z., 2015. Local Geoid Determination in Strip Area Projects by using Polynomials, Least Squares Collocation and Radial Basis Functions. Measurement 73, 429-438.
Dudek, G., 2011. Generalized Regression Neural Network for Forecasting Time Series with Multiple Seasonal Cycles. Springer-Verlag Berlin Heidelberg 1, 1-8.
Durmaz, M., Karslioglu, M.O., Nohutcu, M., 2010. Regional VTEC modelling with multivariate adaptive regression splines. Advances in Space Research 46, 180-189.
Durmaz, M., Karslioglu, M O., 2011. Non-parametric regional VTEC modelling with Multivariate Adaptive Regression B-Splines. Advances in Space Research 48, 1523-1530.
Dreiseitl, S., Ohno-Machado, L., 2002. Logistic Regression and Artificial Neural Network Classification Models: A Methodology Review. Journal of Biomedicine International 35 (5-6), 352-359.
Eldessouki, M., Hassan, M., 2015. Adaptive Neuro-Fuzzy System for Quantitative Evaluation of Woven Fabrics’ Pilling Resistance. Experts Systems with Applications 42 (4), 2098-2113.
Erdogan, S., 2009. A Comparison of Interpolation Methods for Producing Digital Elevation Models at the Field Scale. Earth Surface Processes and Landforms 34, 366-376.
Erol, B., 2011. An Automated Height Transformation Using Precise Geoid Models. Journal of Scientific Research and Essays 6 (6), 1351-1363.
Erol, B., Celik, R.N., 2004. Precise Local Geoid Determination to make GPS Technique More Effective in Practical Applications of Geodesy. FIG Working Week 17 (3), 22-27.
Erol, B., Celik, R.N., 2005. Modelling Local GPS/Levelling Geoid with the Assessment of Inverse Distance Weighting and Geostatistical Kriging Methods. Athens, Greece, 1-5.
Erol, B., Erol, S., 2013. Learning-Based Computing Techniques in Geoid Modelling for Precise Height Transformation. Computers and Geosciences 52, 95-107.
Featherstone, W.E., Olliver, J.G., 2013. Assessment of EGM2008 over Britain using Vertical Deflections, and Problems with Historical Data. Survey Review 45 (352), 319-324.
Friedman, J.H., 1991. Multivariate adaptive regression splines. Annals Statistics 19, 1-67.
Fu, B., Liu, X., 2014. Application of artificial neural network in GPS height transformation. Applied Mechanics and Materials 501 (504), 2162-2165.
Ghilani, D.C., 2010. Adjustment Computations, Spatial Data Analysis. Fifth Edition, Wiley & Sons, INC. Hoboken, New Jersey, USA, 1-674.
Gucek, M., Basic, T., 2009. Height Transformation Models from Ellipsoidal into the Normal Orthometric Height System for the Territory of the City of Zagreb. Studia Geophysica et Geodaetica 33, 17-38.
Hannan, S.A., Manza, R.R., Ramteke, R.J., 2010. Generalized Regression Neural Network and Radial Basis Function for Heart Disease Diagnosis. International Journal of Computer Applications 7 (13), 7-13.
Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feed forward networks are universal approximators. Neural Networks 2, 359-366.
Idri, A., Zakrani, A., Zahi, A., 2010. Design of Radial Basis Function Neural Networks for Software Effort Estimation. International Journal of Computer Science Issue 7 (4), 11-17.
Ismail, S., Shabri, A., Samsudin, R., 2012. A hybrid model of self-organizing maps and least square Support Vector Machine for River flow forecasting. Hydrological Earth System Science 16, 4417-4433.
Jang, J.R.S., 1993. ANFIS: Adaptive Network Based Fuzzy Inference System. IEEE Transactions on Systems, Man Cybernetics 23 (3), 665-685.
Kaloop, M.R., Rabah, M., Hu, J.W., Zaki, A., 2017. Using Advanced Soft Computing Techniques for Regional Shoreline Geoid Model Estimation and Evaluation. Marine Georesources & Geotechnology 36 (6), 688-697.
Kao, S.P., Ning, F.S., Chen, C.N., Chen, C.L., 2017. Using Particle Swarm Optimization to Establish a Local Geometric Geoid Model. Boletim de Ciências Geodésicas 23 (2), 327-337.
Kavzoglu, T., Saka, M.H., 2005. Modelling Local GPS/Levelling Geoid Undulations using Artificial Neural Networks. Journal of Geodesy 78 (9), 520-527.
Kiani, M., 2020. Local Geoid Height Approximation and Interpolation Using Moving Least Squares Approach. Geodesy and Geodynamics 11 (2), 120-126.
Kisi, O., Parmar, K.S., 2015. Application of Least Square Support Vector Machine and Multivariate Adaptive Regression Spline Models in Long Term Prediction of River Water Pollution. Journal of Hydrology 534, 104-112
Kotsakis, C., Katsambalos, K., Ampatzidis, D., Gianniou, M., 2008. Evaluation of EGM2008 Using GPS and levelling Heights in Greece. Evaluation of EGM08 in Greece using GPS and leveling heights. Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation, June 23-27, 2008, Chania, Greece.
Kutoglu, H.S., 2006. Artificial Neural Networks versus Surface Polynomials for Determination of Local Geoid. 1st International Gravity Symposium, Istanbul, Turkey, 1-6.
Liu, S., Li, J., Wang, S., 2011. A hybrid GPS height conversion approach considering of neural network and topographic correction. International Conference on Computer Science and Network Technology, China, IEEE.
Mihalache, R.M., 2012. Coordinate Transformation for Integrating Map Information in the New geocentric European system using Artificial Neural Networks. GeoCAD, 1-9.
Mueller, V.A., Hemond, F.H., 2013. Extended artificial neural networks: in-corporation of a priori chemical knowledge enables use of ion selective electrodes for in-situ measurement of ions at environmental relevant levels. Talenta 117, 112-118.
Nohutcu, M., Karslioglu, M.O., Schmidt, M., 2010. B-Spline Modelling of VTEC over Turkey using GPS Observations. Journal of Atmospheric and Solar-Terrestrial Physics 72, 617-624.
Odera, P.A., Musyoka, S.M. Gachari, M.K., 2014. Practical Applications of the Geometric Geoid for Heightening over Nairobi Country and its Environs. Journal of Agriculture, Science and Technology 16 (2), 175-185.
Ophaug, V., Gerlach, C., 2017. On the Equivalence of Spherical Splines with Least-Squares Collocation and Stokes’s Formula for Regional Geoid Computation. Journal of Geodesy 91, 1367-1382.
Pavlis, K.N., Holmes, S.A., Kenyon, S.C., Factor, J.K., 2008. An Earth Gravitational Model to Degree 2160. EGU General Assembly 2008, Vienna, Austria, 1-5.
Pavlis, K.N., Holmes, S.A., Kenyon, S.C., Factor, J.K., 2012. The Development and Evaluation of the Earth Gravitational Model 2008 (EGM 2008). Journal of Geophysical Research, 117 (B16), 4406-4410.
Peprah, S.M., Yevenyo, Y.Y., Issaka, I., 2017. Performance Evaluation of the Earth Gravitational Model (EGM2008) A Case Study. South African Journal of Geomatics, 6(1), 47-72.
Pikridas, C., Fotiou, A, Katsougiannopoulos, S., Rossikopoulos, D., 2011. Estimation and evaluation of GPS geoid heights using an artificial neural network model. Appl Geomat 3, 183-187.
Poku-Gyamfi, Y., 2009. Establishment of GPS Reference Network in Ghana. Published MPhil Dissertation, Universitat Der Bundeswehr Munchen Werner Heisenberg-Weg 39, 85577, Germany, 1-218.
Ramouz, S., Afrasteh, Y., Reguzzoni, M., Safri, A., 2020. Assessment of Local Covariance Estimation Through Least Squares Collocation Over Iran. Advances in Geosciences, 50, 65-75.
Rummel, R., Sanso, F., 1993. Satellite Altimetry in Geodesy and Oceanography. Springer-Verlag, Berlin Heidelberg, 1-469.
Samui, P., 2013. Multivariate Adaptive Regression Spline (MARS) for prediction of Elastic Modulus of jointed Rock Mass. Geotechnical and Geological Engineering 31, 249-253.
Samui, P., Kim, D., 2012. Modelling of reservoir-induced earthquakes: a multivariate adaptive regression spline. Journal of Geophysics and Engineering 9, 494-497.
Sanlioglu, I., Maras, S.S., 2011. A Comparison with Orthometric Heights Obtained by Real Time Kinematics and by Local Geoid Model, Case Study in Adana. Geodesy and Mine Surveying Section, International Multidisciplinary Scientific GeoConference SGEM 2011, 2, 199-206.
Sheta, A.F., Ahmed, S.E.M., Faris, H., 2015. A Comparison between Regression, Artificial Neural Networks and Support Vector Machines for Predicting Stock Market Index. International Journal of Advanced Research in Artificial Intelligence 4 (7), 55-63.
Soycan, M., 2014. Improving EGM2008 by GPS and Levelling Data at Locale Scale. Bol. Cienc. Geod., Sec. Artigos, Curitiba, 20 (1), 3-18.
Specht, D., 1991. A General Regression Neural Network. IEEE Transactions on Neural Networks 2 (6), 568-576.
Srichandan, S., 2012. A New Approach of Software Effort Estimation using Radial Basis Function Neural Networks. ISSN (Print), 1 (1), 2319-2526.
Tusat, E., 2011. A Comparison of Geoid Height Obtained with Adaptive Neural Fuzzy Inference Systems and Polynomial Coefficients Methods. International Journal of the Physical Sciences 6 (4), 789-795.
Tiryaki, B., 2008. Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks and regression trees. Engineering Geology 99, 51-60.
Veronez, M.R., De Souza, G.C., Matsuoka, T.M., Reinhardt, A., Da Silva, R.M., 2011. Regional Mapping of the Geoid using GNSS (GPS) Measurements and an Artificial Neural Network. Remote Sensing 3, 668-683.
Wu, L., Tang, X., Zhang, S., 2012. The Application of Genetic Neural Network in the GPS Height Transformation. 2012 Fourth International Conference on Computational and Information Science, Beijing, China.
Yakubu, I., Dadzie, I., 2019. Modelling Uncertainties in Differential Global Positioning System Dataset. Journal of Geomatics. 13 (1), 16-23.
Yakubu, I., Ziggah, Y.Y., Peprah, M.S., 2018. Adjustment of DGPS Data using artificial intelligence and classical least square techniques. Journal of Geomatics 12 (1), 13-20.
Yilmaz, M., Turgut, B., Gullu, M., Yilmaz, I., 2017. Application of Artificial of Artificial Neural Networks to Height Transformation. Tehnicki Vjesnik 24 (2), 443-448.
Yilmaz, M., Arslan, E., 2008. Effect of the Type of Membership Function on Geoid Height Modelling with Fuzzy Logic. Survey Review 40, 379-391.
Yonaba, H., Anctil, F., Fortin, V., 2010. Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Stream Flow Forecasting. Journal of Hydrologic Engineering 15 (4), 275-283.
Zaletnyik, P., Volgyesi, L., Kirchner, I., Palancz, B., 2007. Combination of GPS/Levelling and the Gravimetric Geoid by using the Thin Plate Spline Interpolation Technique Via Finite Element Method. Journal of Applied Geodesy 1, 233-239.
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Published
2020-10-15
Section
Articles
Copyright (c) 2020 Michael Stanley Peprah, Bernard Kumi-Boateng
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