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

Transcription

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 abbaskhashe@brjand.ac.r. MSc n Deserts Management, Dept. of atural Resources, Tehran Unversty, Tehran () ( ) - abbaskhashe@brjand.ac.r - 93

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

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