Study of Spatial Distribution of Groundwater Quality Using LS-SVM, MLP, and Geostatistical Models

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1 LS-SVM MLP (// // ).. IDW.. EC. RSS. RMSE. MAE R RMSE R / RMSE.. / MAE / : Study of Spatal Dstrbuton of Groundwater Qualty Usng LS-SVM, MLP, and Geostatstcal Models A. Khashee Syuk M. Sarbaz (Receved Sep. 3, 03 Accepted Apr. 8, 04) Abstract Groundwater qualty control s of great mportance n (sem-)ard zones due to the water defct n these regons. Geostatstcal models are technques commonly developed for the nterpolaton and spatal predcton of groundwater qualty parameters. In ths study, IDW, Krgng, and CoKrgng methods were used n the geostatstcal, LS-SVM, and MLP models to predct the spatal dstrbuton of groundwater EC. The models were then compared n terms of ther effcency. For the purposes of ths study, data were collected from 0 wells n the Mashhad plan. Varograms were then drawn after normalzng the data for applcaton n the geostatstcal models. In the next stage, the lowest RSS value was used for selectng the one model that was sutable for fttng the expermental varogram whle cross-valdaton and RMSE were used to select the best method for nterpolaton. Comparson of the three models n queston was accomplshed by usng 5% of the observaton data and the statstcal parameters of RMSE, R, and MAE were determned. Results showed that the CoKrgng method outperformed ts Krgng counterpart n the geostatstc model for nterpolatng groundwater qualty. Fnally, the most accurate values for the qualty parameters (.e., R =0.93, RMSE=367.9, MAE=65.78( µ mos/ cm ) were obtaned wth the MLP model. Keyword: Varogram, Multlayered Perceptron (MLP), Least Squares Support Vector Machne (LS-SVM).. Assst. Prof. of Water Resources Engneerng, Brjand Unversty, Brjand (Correspondng Author) (+98 56) 5404 MSc n Deserts Management, Dept. of atural Resources, Tehran Unversty, Tehran () ( )

2 . LS-SVM LS-SVM..[]...[ ].[].. LS-SVM.[] MAPE RBF LS-SVM / RMSE / MAE /. / R OK AFIS. AFIS.[] OK A 5 Support Vector Machn (SVM) 6 Krgng [ ].[].[-].[] LM...[].[].[] Artfcal eural etwork (A) Radal Bass Functon (RBF) 3 Adaptve euro-fuzzy Inference System (AFIS) 4 Least Square Support Vector Machnes (LS-SVM) 94

3 MLP - : LS-SVM UTM LS-SVM MLP ( ) ( ).... ETP / MLP....[] 5 Statstcal Learnng Theory 6 Structure Rsk Mnmzaton.[] ph. A. -. BP..[ ].[]. a SAR EC.[]. LS-SVM.... Harran Back Propagaton (BP) 3 Levenberg Marquardt 4 Mult-Layer Perceptron (MLP) 95

4 - y R. T y(x) = w. ϕ(x) + b () T b W ϕ(x).. mn w,e,b j(w, e) T γ = w w + e () = y T = w ϕ(x ) + b + e () e γ..[]. SVM..[] SVM LS-SVM. - :. - LS-SVM.... n x R {x, y } = 96

5 X X X mn = Xmax X () mn norm + Xmax Xmn X. / / Xnorm..[] / /. EC EC.[].[] LS-SVM MLP. R.MBE RMSE () R = = = RMSE = ( P P )( O O ) ( P P ) ( O O ) 0.5 ( P O ) () = MBE = (O P ) () = MLP P O P O LS-SVM. O P -.. t L(w,b,e, α ) = j(w, e) α {w ϕ(x ) + b + e y } () = (KKT)-. α LS-SVM [] y(x) = α k(x, x ) + b = () [] LS-SVM - K(x, x j ) Mercer [],j=,..., () K(x, x j ) = ϕ(x ).ϕ(x j ) σ (γ) K(x,x ) j x x j = exp( ) () σ. ArcGIS 9.3 MLP. EC ArcGIS 9.3. MLP toolbox.[]. LS-SVM Overfttng MATLAB 97

6 . RMSE, R, AME.[] MLP Y X MLP3 AME RMSE. Y X / /. MLP3.[] EC... MLP -- MLP..[] MLP. () () () µmos/cm - (Cl) - (X) - (Y) ( ) ( ) (meq/lt) (mmos/cm) EC X Y

7 / / /..[]. /..[]...( )...[].[] MAE RMSE. MLP - X - Y- CL X-Y (MLP3) (MLP) LS-SVM -- LS-SVM. Lnsearch Grdsearch Smplex. RBF LS-SVM. γ.. LS-SVM3. Smplex RMSE./ R / Smplex LS-SVM.. b a Y=a+bx. Cokrgng - MAE RMSE R smplex RBF LS-SVM smplex *RBF LS-SVM smplex Polynomal LS-SVM smplex **Polynomal LS-SVM smplex ***Lnear LS-SVM smplex Lnear LS-SVM lnsearch Lnear LS-SVM grdsearch RBF LS-SVM3 *** ** * 99

8 () () () () () () -.( Y X ) LS-SVM 3 LS-SVM MLP3 MLP (Y) (X) - RMSS RMSE Lag sze

9 - RMSS RMSE Lag sze MLP LS-SVM - MAE(µmos/cm) RMSE(µmos/cm) R MLP MLP COKRIGIG LS-SVM KRIGIG LS-SVM3.[]..[] MLP LS-SVM MLP.( ) Y X. LS-SVM. Y X LS-SVM.. MLP -- LS-SVM.. LS-SVM MLP3. CL Y X MLP3. LS-SVM3. RBF RBF.. LS-SVM LS-SVM MLP - 0

10 MLP.. - X. Y.. LS-SVM -. Izad, S.A., Davar, K., Alzadeh, A., and Ghahraman, B. (007). Usng artfcal neural network to predct the water table. J. of Irrgaton and Dranage,, Khashe-Suk, A., Kouchakzadeh, M., and Ghahraman, B., (03). Comparson of artfcal neural network models, AFIS and regresson estmaton of shallow aqufer n shapur. J. of Irrgaton and Dranage,, (In Persan) 3. Saman,., Gohar-Moghadam, M., and Safav, A.A. (007). A smple neural network model for the determnaton of aqufer parameters. J. of Hydrology, 340, ayak, P., Satyaj Rao, Y.R., and Sudheer, K. P. (006). Groundwater level forecastng n a shallow aqufer usng artfcal neural network approach. J. of Water Resources Management, () Marsly, G.D., and Ahmed, S. (987). Applcaton of krgng technques n groundwater hydrology. J. of the Geologcal Socety of Inda, 9(), Sreekanth, P.D., Geethanjal,.D., Sreedev, P.D., Shakeel, A., and Steyl, G. (009). Applcaton of artfcal neural networks n the feld of geohydrology. Insttute of Groundwater Studes Faculty of atural and Agrcultural Scences, Unversty of the Free State. 7. Ahmad-Zadeh, K. (009). Modelng daly reference evapotranspraton by usng neural-fuzzy nference system. MSc Thess, Dranage and Irrgaton, Faculty of Agrculture, Tarbat Modarres Unversty, Tehran. 8. Khashe-Suk, A., Kouchakzadeh, M., and Ghahraman, B. (0). Predctng dryland wheat yeld from meteorologcal data usng expert system n Khorasan provnce, I.R. Iran. J. of Agrcultural Scence and Technology, 3, (In Persan) 9. Affand, A., and Watanabe, K. (007). Daly groundwater level fluctuaton forecastng usng soft computng technque. J. of ature and Scence, 5(), Mer-Araby, M., and akhae, A. (008). Predcton of groundwater level fluctuatons smokng usng artfcal neural networks. Proceedngs of the Twelfth Symposum of Geologcal Socety of Iran, South Ol Company, Ahvaz. (In Persan). Mohtasham, M., Dehghan, A., Akbarpour, A., Meftah holgh, and Etebar, B. (00). Predcton table usng Artfcal eural etwork (Case Study: Plan smokng). J. of Irrgaton and Dranage, (4), -9. (In Persan). Ks, O. (0). Least squares support vector machne for modelng daly reference evapotranspraton. Irrg. Sc., 3(4), Sef, A., and Rah-Madvar, H. (0). Input varable selecton n expert systems based on hybrd gamma test-least square support vector machne AFIS and A models. Provsonal chapter. Intech, do: 0.577/ Asefa, T.W., Kemblowsk, M., Urroz, G., Mckee, M., and Khall, A. (004). Support vectors machnes (SVM) for montorng network desgn. J. of Groundwater, 43(3),

11 5. Asefa, T.W., Kemblowsk, M., Urroz, G., Mckee, M., and Khall, A. (005). Support vectors-based groundwater head observaton networks desgn. J. of Water Resources Research, 40(), do: 09/004 WR ESMI-Khan, M., Safavd, H., and Yazdanpour, M. (00). Integrated management of surface water and groundwater methods usng support vector machne and genetc algorthms. The Ffth atonal Congress on Cvl Engneerng, Mashhad, Iran. 7. Rezae, E. (03). Desgn pezometrc well groundwater wthdrawals usng support vector machne. MSc Thess Department of Water Resources and Water Engneerng, Unversty of Brjand, Brjand. 8. Kholgh, M., and Hossen, S.M. (009). Comparson of groundwater level estmaton usng neuro-fuzzy and ordnary krgng. J. of Envron. Model. Assess., 4, Sahnkaya, E., Muhsn,., and Ozkaya, B. (008). eural network predcton of ntrate n groundwater of Harran Plan, Turkey M. Irfan Yeslnacar. J. of Envron. Geol., 56, Ahmad, S.H., and Sedghamz, A. (007). Geostatstcal analyss of spatal and temporal varatons of groundwater level. J. of Envron. Mont. Assess., 9, Taghzadeh, M., Zarean Jahrom, M., Mahmod, Sh., and Hedar, A. (008). Spatal dstrbuton of groundwater qualty wth geostatstcs (Case study: Yazd-Ardakan plan). World Appled Scences Journal, 4(), Safar, M. (00). Determnaton of water fltraton usng geostatstcal etwork. MSc Thess, Faculty of Agrculture, Tarbat Modarres Unversty, Tehran, Iran. (In Persan) 3. Rezae, M., Davatgar,., Tajdar, K., and Abolpour, B. (00). Investgaton the spatal varablty of some mportant groundwater qualty factors n Gulan, Iran. J. of Water and Sol, 4(5), (In Persan). 4. Vapnc, V.. (998). Statstcal learnng theory, Wley, ew York. 5. Crstann,., and Shawe-Taylor, J. (000). An ntroducton to support vector machnes, Cambrdge Unversty Press, UK. 6. Vandewalle, J., and Suykens, J.A.K. (999). Least squares support vector machne classers. J. of eural Processng Letters, 9(3), Mellt, A., Mass Pavan, A., and Benghanem, M. (03). Least squares support vector machne for shortterm predcton of meteorologcal tme seres. J. of Theor. Appl. Clmatol.,, Saf, A. (00). Development of an expert system to predct daly reference evapotranspraton by usng Support Vector Machne (SVM) and compare ts results wth AFIS, A and expermental methods. MSc Thess Irrgaton and Dranage Engneerng, Faculty of Agrculture, Tarbat Modarres Unversty, Tehran. (In Persan) 9. Kardan Moghaddam, H., and Khashe-Suk, A. (03). Zonng n the water scences by geostatstcs, Astan Qods Press, Mashhad. (In Persan) 30. Gundogdu, K.S., and Guney, I. (007). Spatal analyses of groundwater levels usng unversal krgng. J. of Earth System Scence, 6(), Coulbaly, P. Anctl, F., and Bobee, B. (999) Provson hydrologque par reseaux de neurons artfcals. Can. J. Cvl Eng., 6(3), Dagostno, V., Greene, E.A., Passarella, G., and Vurro, M. (998). Spatal and temporal study of ntrate concentraton n groundwater by means of co regonalzaton. J. of Envronmental Geology, 36, Mouser, J.M., and Rzzo, D.M. (000). Evaluaton of geostatstcs for combned hydrochemstry and mcrobal communty fngerprntng at a waste dsposal ste. <<ascelbrary. Org/do/pdf/0.06/40737 (004) 06>> (Apr. 04) 34. Khashe-Suk, A., and Sarbaz, M. (04). Evaluaton of AFIS, A, and geostatstcal models to spatal dstrbuton of groundwater qualty (case study: Mashhad plan n Iran). Saud Socety for Geoscences. Do: 0.007/s

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