Novel Ellipsoidal Heights Predictive Models Based on Artificial Intelligence Training Algorithms and Classical Regression Models Techniques: A Case Study in the Greater Kumasi Metropolitan Area Local Geodetic Reference Network, Kumasi, Ghana: A Case Study in the Greater Kumasi Metropolitan Area (GKMA) Local Geodetic Reference Network, Kumasi, Ghana

Yıl 2022, Cilt: 4 Sayı: 3, 493 - 515, 30.12.2022

Naa Lamkaı Daniel Asenso-gyambıbı Michael Stanley Peprah Edwin Kojo Larbı Benedict Asamoah Philip Okantey

Öz

The standard forward transformation for the direct conversion of curvilinear geodetic coordinates (φ, γ, Η) to its associated Cartesian coordinates (E, N, Z) has become a major challenge in most countries. This is due to the non-existence of the ellipsoidal height (h) in the modelling of their local geodetic reference network. Numerous studies in the past and recent years have suggested various mathematical techniques for predicting and estimating local ellipsoidal heights. Primary data used for the studies comprises of topographic data obtained from a survey in the Ghana urban water supply project in the Greater Kumasi Metropolitan Area (GKMA).This study considered an empirical evaluation of soft computing techniques such as Back Propagation Artificial Neural Network (BPANN), Generalized Regression Neural Network (GRNN), Radial Basis Function Artificial Neural Network (RBFANN) and conventional methods such as Polynomial Regression Model (PRM), Autoregressive Integrated Moving Average (ARIMA) and Least Square Regression (LSR). 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 statistical hypothesis (F, t) tests and performance criteria indices such as arithmetic mean error (AME), arithmetic mean square error (AMSE), minimum and maximum error value, and arithmetic standard deviation (ASD). The statistical analysis of the results revealed that, RBFANN, GRNN, BPANN, LSR, ARIMA and PRM, successfully estimated the ellipsoidal heights for the study area. However, the ANN models (RBFANN, BPANN, GRNN) outperforms the conventional models (LSR, PRM, ARIMA) in terms of accuracy and precision in estimating the local ellipsoidal heights. Also, statistical findings revealed that RBFANN produced more reliable results compared with the other methods. The main conclusion drawn from this study is that, the method of using soft computing is very much promising and can be adopted to solve some of the major problems related to height issues in Ghana. This study seeks to contribute to the existing knowledge on establishing a precise geodetic vertical datum in Ghana for national heightening purpose.

Anahtar Kelimeler

Artificial Intelligence, Geodetic Reference Network, Height systems, Performance Criteria Indices, Statistical Hypothesis, Regression Models

Kaynakça

• Abeho, D.R., Hipkin, R., Tulu, B.B., 2014. Evaluation of EGM08 by means of GPS levelling Uganda. South African Journal of Geomatics 3 (3), 272–284.
• Acheamfour, L.B., Tetteh, J., 2014. 2010 Population and Housing Census, District Analytical Report, Kumasi Metropolitan. Ghana Statistical Service.
• 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 and Space 61, 825-833.
• Al-Krargy, E.M., Mohamed, H.F., Hosney, M.M., Dawod, G.M., 2017. A High-Precision 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.
• Annan, R.F., Ziggah, Y.Y., Ayer, J., Odutola, C.A., 2016. Accuracy Assessment of heights obtained from Total station and level instrument using Total Least Squares and Ordinary Least Squares Methods. Journal of Geomatics and Planning 3 (2), 87-92.
• Arthur, C.K., Temeng, V.A., Ziggah, Y.Y., 2019. Soft Computing – Based Techniques as a Predictive tool to Estimate Blast-Induced Ground Vibration. Journal of Sustainable Mining 18 (4), 287-296.
• Atayi, J., Kabo-bah, A. T., & Resources, N., 2018. Assessing the Impacts of Urbinization on the Climate of Kumasi. May 2020. https://doi.org/10.20944/preprints201809.0059.v1
• Ayer, J., Agyemang, A.B., Yeboah, F., Osei Jnr, E.M., Abebrese, S., Suleman, I., 2016. A Comparative Analysis of Extracted Heights from Topographic Maps and Measured Reduced Levels in Kumasi, Ghana. South African Journal of Geomatics 5 (3), 313-324.
• Bihter, E., 2011. An Automated Height Transformation Using Precise Geoid Models. Scientific Research and Essays 6 (6), 1351-1363.
• Box, G.E.P., Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control. Holden-Day, Boca Raton, Fla, USA.
• Cakir, L., Konakoglu, B., 2019. The Impact of Data Normalization on 2D Coordinate Transformation Using GRNN. Geodetski Vestnik 63 (4), 541-553.
• Chen, W., Hill, C., 2005. Evaluation Procedure for Coordinate Transformation. Journal of Surveying Engineering 131 (2), 43-49.
• Constantin-Octavian, A., 2006. 3D Affine coordinate transformations. Masters of Science Thesis in Geodesy No.3091 TRITA- GIT EX 06-004, School Architecture and the Built Environment,Royal,100 44 Stockholm, Sweden Institute of Technology (KTH), 7.
• Dawod, G.M., Al-krargy, E.M., Amer, H.A., 2022. Accuracy Assessment of Horizontal and Vertical Datum Transformations in Small-Areas GNSS Surveys in Egypt. Journal of Research in Environmental and Earth Sciences 8 (1), 19-28.
• Dudek, G., 2011. Generalized Regression Neural Network for Forecasting Time Series with Multiple Seasonal Cycles. Springer-Verlag Berlin Heidelberg, 1, 1-8.
• El-Rabbany, A., El-diasty, M., Raahemifar, K., 2015. Sequential Tidal Height Prediction Using Artificial Neural Network. October.
• 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., Celik, R.N., 2005. Modelling Local GPS/Levelling Geoid with the Assessment of Inverse Distance Weighting and Geostatistical Kriging Methods. Athens, Greece, 1-5.
• Falchi, U., Parente, C., Prezioso, G., 2018. Global Geoid Adjustment on Local Area for GIS Applications Using GNSS Permanent Station Coordinate. Geodesy and Cartography 44 (3), 80-88.
• Fu, B., Liu, X., 2014. Application of artificial neural network in GPS height transformation. Applied Mechanics and Materials 501 (504), 2162-2165.
• Fusami, A.A., Dodo, J., Ojigi, L., 2021. Modelling Orthometric Height from GPS-Derived Ellipsoidal Height. December 2019.
• 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 53, 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.
• Herbert, T., Ono, M.N., 2018. A Gravimetric Approach for the Determination of Orthometric Heights in Akure Environs, Ondo State, Nigeria. Journal of Environment and Earth Sciences 8 (8), 75-80.
• Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feed forward networks are universal approximators. Neural Networks 2 (5), 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 4 (7), 11-17.
• 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 Ciencias Geodesicas 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.
• Kim, T.K., 2015. T test as a parametric statistic. Korean Journal of Anesthesiology 68 (6), 541-546.
• Konakoglu, B., Cakır, L., Gokalp, E., 2016. 2D Coordinate Transformation Using Artificial Neural Networks 2d Coordinate Transformation Using Artificial Neural Network. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W1, 2016, 3rd International GeoAdvances Workshop, 16-17 October 2016, Istanbul, Turkey. https://doi.org/10.5194/isprs-archives-XLII-2-W1-183-2016.
• Konakoglu, B., Cakir, L., 2018. Generalized Regression Neural Network for Coordinate Transformation. International Symposium on Advancements in Information Sciences and Technologies (AIST), Montenegro, 5th 8th September 2018, 66-78.
• Kumar Singh, A., 2015. Topic : F-TEST and Analysis of Variance ( ANOVA ). University of Lucknow, IV, 1-9.
• Kumi-Boateng, B., Peprah, M.S., 2020. 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. International Journal of Earth Sciences Knowledge and Applications 2, 166-177.
• Kumi-Boateng, B., Ziggah, Y.Y., 2017. Horizontal coordinate transformation using artificial neural network technology- A case study of Ghana geodetic reference network. 11(1), 1–11.
• Kwak, S.G., Kim, J.H. 2017. Central limit theorem: the cornerstone of modern statistics. Korean Journal of Anesthesiology 70 (2), 144-156.
• Lee, J.M., Min, K.S., Min, W.K., Park, H., 2020. A Study on the Actively Capture of Road Construction Information Using Spatial Analysis. Journal of the Korean Society of Cadastre 36 (2), 149-159.
• 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. https://doi.org/10.1109/ICCSNT.2011.6182386.
• Massey, A., Miller, S.J., 2004. Tests of Hypotheses Using Statistics. Mathematics Department Brown University Providence, RI 02912, 1-32.
• Mihalache, R.M., 2012. Coordinate Transformation for Integrating Map Information in the New geocentric European system using Artificial Neural Networks. GeoCAD, 1-9.
• Miller, S.J., 2006. Methods of Least Squares, Statistics Theory. Cornell University, USA, 3, 1-2.
• 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 (15), 112-118.
• Oduro, C., Kafui, O., Peprah, C., 2014. Analyzing Growth Patterns of Greater Kumasi Metropolitan Area Using GIS and Multiple Regression Techniques Analyzing Growth Patterns of Greater Kumasi Metropolitan Area Using GIS and Multiple Regression Techniques. Journal of Sustainable Development 7 (5), 13-31. https://doi.org/10.5539/jsd.v7n5p13.
• 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 (6), 1-16. https://doi.org/10.1007/s00190-017-1030-1.
• Osei-Nuamah, I., Appiah-Adjei, E.K., 2017. Hydrogeological Evaluation Of Geological Formations In Ashanti Region , Ghana. Journal of Science and Technology 37 (1), 34-50.
• Peprah, M.S., Kumi, S.A., 2017. Appraisal of Methods for Estimating Orthometric Heights – A Case Study in a Mine. Journal of Geoscience and Geomatics 5 (3), 96-108.
• Peprah, M.S., Mensah, I.O., 2017. Performance Evaluation of the Ordinary Least Square ( OLS ) and Total Least Performance Evaluation of the Ordinary Least Square ( OLS ) and Total Least Square ( TLS ) in Adjusting Field Data : An Empirical Study on a DGPS Data. South African Journal of Geomatics 6 (1), 73-89.
• Pikridas, C., Fotiou, A., Katsougiannopoulos, S., Rossikopoulos, D., 2011. Estimation and evaluation of GPS geoid heights using an artificial neural network model. Applied Geomatics 3, 183-187. https://doi.org/10.1007/s12518-011-0052-2.
• Poku-Gyamfi, Y., 2009. Establishment of GPS Reference Network in Ghana. MPhil Dissertation. Universitat Der Bundeswehr Munchen Werner Heisenberg-Weg 39, 85577, Germany, 1-218.
• Schaffrin, B., 2006. A note on Constrained Total Least Square estimation. Linear Algebra and Its Application, 417, 245-258.
• Specht, D., 1991. A General Regression Neural Network. IEEE Transactions on Neural Networks 6 (2), 568–576.
• Srichandan, S., 2012. A New Approach of Software Effort Estimation using Radial Basis Function Neural Networks. International Journal on Advanced Computer Theory and Engineering ISSN (Print) 1 (1), 113-120.
• Sureiman, O., Mangera, C.M., 2020. F ‑ Test of Overall Significance in Regression Analysis Simplified. Journal of the Practice of Cardiovascular Sciences 6 (2), 116-122. https://doi.org/10.4103/jpcs.jpcs.
• 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.
• Ugoni, A., Walker, B.F., 2014. The t TEST An introduction. Comsic Review 4 (2), 37-40.
• Veronez, M.R., 2011. Regional Mapping of the Geoid Using GNSS ( GPS ) Measurements and an Artificial Neural Network. Remote Sensing 668–683. https://doi.org/10.3390/rs3040668.
• 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 (4), 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 Neural Networks to Height Transformation. Tehnicki Vjesnik 24 (2), 443-448.
• 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.
• Yusof, F., Kane, I.L., Yusof, Z., 2013. Hybrid of ARIMA-GARCH Modelling in Rainfall Time Series. Journal Teknologi 63 (2), 27-34.
• 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, 223-239.
• Ziggah, Y.Y., Youjian, H., Laari, P.B., Hui, Z., 2017. Novel Approach To Improve Geocentric Translation Model Performance Using Artificial Neural Network. Boletim de Ciências Geodésicas 23 (1), 213-233.
• Ziggah, Y.Y., Tierra, A., Youjian, H., Konate, A.A., Hui, Z., 2015. Performance Evaluation of Artificial Neural Networks for Planimetric Coordinate Transformation-A Case Study, Ghana. Arabian Journal of Geoscience, 9, 698–714.
• Ziggah, Y.Y., Yakubu, I., Kumi-Boateng, B., 2016. Analysis of Methods for Ellipsoidal Height Estimation – The Case of a Local Geodetic Reference Network. Ghana Mining Journal 16 (2), 1-9. https://doi.org/10.4314/gm.v16i2.1.