Research Article A Fuzzy Inference System for the Conjunctive Use of Surface and Subsurface Water

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1 Advances n Fuzzy Systems Volume 2013, Artcle ID , 10 pages Research Artcle A Fuzzy Inference System for the Conjunctve Use of Surface and Subsurface Water Lang-Cheng Chang, 1 Hone-Jay Chu, 2 and Y-Wen Chen 1 1 Department of Cvl Engneerng, Natonal Chao Tung Unversty, 1001 Ta Hsueh Road, Hsnchu 30050, Tawan 2 Department of Geomatcs, Natonal Cheng Kung Unversty, No. 1 Unversty Road, Tanan 701, Tawan Correspondence should be addressed to Hone-Jay Chu; honejaychu@gmal.com Receved 8 May 2013; Accepted 29 June 2013 Academc Edtor: Salvatore Sessa Copyrght 2013 Lang-Cheng Chang et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Ths study develops the water resources management model for conjunctve use of surface and subsurface water usng a fuzzy nference system (FIS). The study apples the FIS to allocate the demands of surface and subsurface water. Subsequently, water allocatons n the surface water system are smulated by usng lnear programmng technques, and the responses of subsurface water system wth respect to pumpng are forecasted by usng artfcal neural networks. The operatng rule for the water systems s that the more abundant water system supples more water. By usng the fuzzy rule, the FIS conjunctve use model easly ncorporates expert knowledge and operatonal polces nto water resources management. The result ndcates that the FIS model s more effectve and effcent when compared wth the decoupled conjunctve use and smulaton-optmzaton models. Furthermore, the FIS model s an alternatve way to obtan the conjunctve use polces between surface and subsurface water. 1. Introducton The objectve of the study s to develop a fuzzy rule-based method for the conjunctve use of surface and subsurface water systems. Zadeh [1] appled the fuzzy theory to mathematcally deal wth the mprecson and uncertanty. Fuzzy logc extends upon tradtonal Boolean logc and deals wth the mprecson n human experence [2]. The fuzzy nference system (FIS) s an artfcal ntellgence technque that combnes the fuzzy set, fuzzy logc, and fuzzy reasonng [1, 3 6]. The FIS utlzes lngustc varables, fuzzy rules, and fuzzy reasonng and provdes a tool for knowledge representaton based on degrees of membershp [7]. Durngthe past decade, the FIS applcaton ranged from runoff forecastng to surface water supply [3 6, 8, 9]. Shrestha et al. [3]developedaFISto determne a real-world reservor operaton. They constructed a fuzzy rule-based model to derve operaton rules for a multpurpose reservor. Ther research used reservor storages, estmated nflows, and demands as the premses and took reservor releases as the consequences. The fndng showed that the fuzzy-based structure was ordnary and tmesavng n computaton. Russell and Campbell [4] developed the FIS for a smplfed hydroelectrc reservor. The results also showed that fuzzy logc seemngly offered a way to mprove the exstng operatng practces, whch was relatvely easy to explan and understand when compared wth the complex optmzaton model. Pangrah and Mujumdar [5] used a FIS for a reservor operaton model. The study ncorporated expert knowledge for framng the fuzzy rule from an explct stochastc model. Russell and Campbell [4] appled the Adaptve-Network-Based FIS (ANFIS) to water resources management and used the genetc algorthm to search the optmal reservor operaton based on a gven nflow seres. They used FIS for determnng optmal water release accordng to reservor depth and nflow. However, prevous studes [3 5] mentoned that applyng fuzzy logc to reservor operaton could reman lmted to a sngle reservor system. Conjunctve use of surface and subsurface water s a challengngworkforwaterresourcesmanagement[10 14]. Conjunctve water management reduces the defcences by usng subsurface water to supplement scarce surface water supply durng the drought. The conjuncton use enhances the relablty of water supples by provdng ndependent sources. Başaǧaoǧlu and Marño [10] developed

2 2 Advances n Fuzzy Systems a smulaton-optmzaton model of a hypothetcal rver basn to determne optmal operatng polces for jontly usng surface and subsurface water supples. The smulaton model was the response functon to ncorporate the transent hydraulc nteracton between stream and aqufer. The response functon coeffcents were derved from results of the numercal smulaton model. Peralta et al. [11] employed smulaton-optmzaton models to maxmze total annual allocaton of surface and subsurface water yeld. They used the models n attempt to satsfy temporally ncreasng water needs for alternatve future management scenaros. Phlbrck and Ktands [12] proposed the gradent dynamc programmng to solve the mnmal operatng cost problem by regardng surface and subsurface storages as state varables forrealzngthempactofconjunctveuse.nshkawa[15] developed a smulaton-optmzaton model for managng water resources for the cty of Santa Barbara n a fve-year plannng horzon. Moreover, subsurface water smulaton s lnked wth lnear programmng (LP). The model addressed the cost n water supply to meet demands and control seawater ntruson. Azaez [16] developed the model for the conjunctveuseofsurfaceandsubsurfacewaterwthanartfcal recharge and ntegrated opportunty costs for the unsatsfed demandonthelmtatonofthefnalsubsurfacewaterlevel. The problem was smplfed to be formulated as a convex program wth lnear constrants. Watkns and McKnney [14] appled decomposton algorthms to conjunctvely managed surface and subsurface water systems, wth reference to cost functons ncludng both dscrete and nonlnear terms. The complexty had manly arsen from ntegratng surface and subsurface water, that s, two reservors and a confned aqufer. Ther study ncorporated the subsurface water system nto the management model usng the response matrx approach. However, many studes appled the artfcal neural networks (ANNs) to model hydrology feld complexty [17 22] ncludng ranfall-runoff modelng [22, 23] and groundwater flow and transport [24]. The current work traned an ANN to predct the tme-varyng subsurface water level n response to management alternatves [18 21]. Coppola et al. [18] traned an ANN wth MODFLOW smulaton data to predct subsurface water levels at locatons under varous pumpng condtons. The ANN forecasted subsurface water levels at the next tme based on management alternatves ncludng control and state varables at the current tme. Utlzng fuzzy rules, the FIS provdes a tool to ncorporate human expert experence for modelng a conjunctve use of surface and subsurface water. The FIS obtaned allocated demand of ground and surface water n each stage smultaneously. Then, the smulator (.e., LP and ANN) determned the future state of system, such as reservor storages and hydraulc heads at the next tme. Moreover, the LP smulated theoperatonofsurfacewatersystem,andtheannpredcted hydraulc head varatons under tme-varyng pumpng. 2. Methods Fgure 1 llustrates the procedure of the FIS conjunctve use model. The FIS conjunctve use model comprses the control andsmulatonlevels.frstly,thefis,whchsnthecontrol level, determnes the assgned demand among surface and subsurface water each tme step. After determnng the assgned demands, the subsurface water submodel determnes the hydraulc head usng ANN[19], and the surface water allocaton submodel obtans the reservor supply and futurereservor storage usng LP [25, 26] Fuzzy Inference System (FIS). The FIS s composed of fve functonal blocks [5]: (1) arulebasecontannganumberof fuzzy f-then rules; (2) a relatonal database whch defnes membershp functons of the fuzzy set used n the fuzzy rules; (3) a fuzzfcaton nterface whch transforms crsp nputs nto degrees of match wth lngustc values; (4) a fuzzy reasonng whch performs nference operatons on the rules; n FIS applcatons, the max-mn and max product compostonal operators are used most commonly because of ther computatonal smplcty and effcency; and (5) a defuzzfcaton nterface whch transforms a combned output of fuzzy rules nto a crsp value [2, 10, 22]. The current study uses the centrod method to defuzzfy the aggregate fuzzy set, drectly computng the real valued output as a normalzed combnaton of membershp values. The study follows a typcal process n developng the fuzzy system; for example, (1) defne the lngustcs varables; (2) construct the fuzzy rule structures; (3) determne the fuzzy set parameters; (4) encode the fuzzy sets, fuzzy rules, and the procedures; and (5) evaluate and tune the system [2] (Fgure 2). In ths study, the operaton rule s the concept of water level ndex balance that the water system reachng the hghest levels at the current tme has a prorty for supply at the next tme [27, 28]. The FIS follows the followng rule; that s, the abundant water system supples more and the scarce water system supples less water. In the study, the premses of the fuzzy rule are surface and subsurface water states, and the consequence s the assgned demand of each well. The kth fuzzy rule n each tme step s gven as: f ( (V t + IF t ) s A k) and (h t s B k ), then (D t s C k ), where V t s the storage of the th reservor; IF t s the nflow of the th reservor; h t s the average subsurface water level n the observaton wells; D t s the assgned demand of each well n the subsurface water system; and A k,b k and, C k are lngustc values n the kth rule. The premses and consequences are assgned as the trangular membershp functons as n Fgure 3. Two nput varables are surface water state and subsurface water state, that s, average hydraulc head n the observatons. The fuzzy membershp functons of the nputs are dvded nto fve categores, that s, Low, Low Med., Medum, Hgh Med. and, Hgh. Trangular functons wth equal base wdths are the smplest possble, and these are often selected for practcal applcatons [4]. In the study, the surface water state ranges (1)

3 Advances n Fuzzy Systems 3 Surface water current states Subsurface water current states FIS Data base Rule base If (x s A) and (y s B), then (z s C) Fuzzfcaton Inference Defuzzfcaton FIS determnes the assgned demands of surface and subsurface water Smulators of surface and subsurface water LP for surface water smulaton ANN for subsurface water smulaton Update the system states Fgure 1: Flowchart of the FIS conjunctve use model. from 0 to m 3 and the average hydraulc head ranges from 70 to 94 m n the observaton wells. The output varable s the assgned demand of each well from subsurface water whch ranges from 0 to 0.3 cms and s dvded nto four categores n the membershp functon, that s, Low, Low Med., Medum, and Hgh. The FIS computes the weghts of each trggered rule, accumulatng weghts and outputs for each rule, and fnally computng the weghted output for each rule [6]. Moreover, fuzzy sets provde a means of translatng lngustc descrptors nto a usable numercal form [26]. Table 1 shows the fuzzy rules; for example, If surface water state s Low, andsubsurface water level s Hgh, then the assgned demand from subsurface water s Hgh. After the FIS determnes subsurface water demand, the surface water demand could be represented as D t =D t D t N p, (2) where D t s the whole water requrement n the tth tme step; D t s the surface water assgned demand n the tth tme step; and N P s the number of pumpng wells Surface Water Submodel. The surface water allocaton model s represented as subject to J t = mn [ c 1,j SH t X t j + (c 2, G t,k +c 3,Z t ) ], j [ ] V t+1 t=1 n;,k N S,j N D (3) =V t + IF t Xt OFt, N S, (4) V mn X mn,j V t V max, N S, (5) X t,j Xmax,j,,j Ω, (6) X t,j D t j, Ω,j N D, (7) where SH t j s the shortage n demand j at the tth tme step, SH t j = D t j Xt,j ; Xt,j means the supply from node n demand j at tme stept; andn D sthedemandnodeset;n

4 4 Advances n Fuzzy Systems Defne the lngustcs varables Construct fuzzy rule structures Number of fuzzy rules Number of fuzzy sets Shape of membershp functon (e.g. trangle, trapezod, etc.)... Table 1: Rule table for the operaton n conjunctve use operaton usng FIS wthn hgh usage of subsurface water. Surface water state Low Low Med. Medum Hgh Med. Hgh Subsurface water state Low Low Low Low Low Low Low Med. Hgh Hgh Low Low Low Medum Hgh Hgh Low Low Low Hgh Med. Hgh Hgh Low Low Low Hgh Hgh Hgh Low Low Low Determne fuzzy set parameters Vertex of trangle functon Base of trangle functon Encode the fuzzy sets, fuzzy rules, and the procedures Evaluate and tune the system Fgure 2: Procedure of developng the fuzzy system. the study, j=1. G t k s the dfference between water level ndex (WLI) of the reservors and k at the tth tme step [27, 28] and N S s the reservor storage node set; f =k,theng t k =0 otherwse. Z t s the rato of resdual volume to the capacty n reservor at the tth tme step: (V max V t )/Vmax ; c 1, c 2,andc 3 are the weght coeffcents appled to the shortage, surfacewater level ndex dfference, and resdual reservor volume rato, respectvely (c 1 =1, c 2 =10,andc 3 =1). X t denotes the release from reservor at tme stept; OF t denotes splls of reservorattmestept;andv t s the storage of the reservor. V mn and V max are mnmum and maxmum capacty of the reservor. X mn,j and X max,j are mnmum and maxmum dscharge of the ppe from node to j and Ω s the node set of the system network. The surface water demand consders hedgng rule at tme step t. Thehedgngrulesllustratedas follows: f V t jont V 2, then D t = D t, f V 2 >V t jont V 3, then D t =ω 1 D t f V t jont <V 3, then D t =ω 2 D t, where V t jont s the jont storage n all reservors; V 1 s the sum of maxmum storage (upper lmt) among the reservors; V 2 s (8) the sum of target storage (lower lmt) among the reservors; and V 3 s the sum of frm storage (crtcal lmt) among the reservors; ω 1 and ω 2 are the ratonng factors. In the study, ω 1 and ω 2 are 0.85 and Ths study uses the lnear programmng (LP) to smulate the surface water system n (3) (8). The formulaton s as follows. Equaton (3) specfes the objectve functon consstng of three subobjectves whch nclude the total shortage n each tme step, the dfference between the reservor water level, and the rato of the resdual water volume to the capacty of each reservor. Equatons (4) and(5) lst the mass balance equaton and the demand constrant of each reservor n each tme step. Equaton (6) specfes the capacty constrants for each reservor n each tme step. Equatons (7) and(8) specfy the constrants on the flow through the ppes and hedgng rule n each tme step. In the study, the model frst determnes the demand wth the hedgng rule (8), and then the LP determnes the flows n the system at t whle satsfyng the demand wth the hedgng rule Subsurface Water Submodel. The current study uses ANN to serve as the smulator for modelng nonlnear and tme-varyng groundwater flow. An ANN conssts of a number of neurons arranged n an nput layer, an output layer, and one hdden layer. The nputs are state vectors, whch are the set of hydraulc head (h t ) and the pumpng rate vector (P t ). The output s the hydraulc head vector at the next tme step (h t+1 ). The subsurface water model s llustrated as follows: h t+1 =f(h t,p t ), (9) P t D t, (10) where h t and h t+1 aresubsurfacewaterlevelvectorsattmet and t+1;p t s the supply vector offered from the pumpng well; and P t s the supply at the well n the tth tme step. Equaton (9) represents the subsurface water transent equaton wth the artfcal neural networks. Equaton (10) represents the demand-supply of constrant each well at tme t.pumpngrateofeachwellsassumedtobelessthanorequal to assgned demand wth the FIS n the study. The ANN was traned by the back-propagaton learnng algorthm [29] for subsurface water table predcton. The typcal processes of the ANN parameters dentfcaton such as the number of hdden layers and the neurons are lsted

5 Advances n Fuzzy Systems 5 n Negnevtsky [2]. Ths ANN conssts of a three-layer feedforward network and one hdden layer n whch the layer contans twenty neurons The Smulaton-Optmzaton Model. To compare the FIS wth the smulaton-optmzaton model, ths study further formulates the problem (1) (10) nto the sequental optmzaton problem. As prevously stated, ths nvestgaton ntegrates sequental optmzaton and smulaton models to solvetheproblemdefnedasfollows: J t = mn [ c 1,j SH t X t,p t j + (c 2, G t,k +c 3,Z t )+c 4SG t ], j [ ] subject to (4) (10), t=1 n;,k N S,j N D (11) where SG t represents the dfference between WLI of surface and subsurface water systems at tme step t and c 4 s the weght coeffcent appled to WLI dfference between surface and subsurface water systems (c 4 = 10). Inthemodel,the pumpng rates are frst obtaned by the heurstc optmzaton (.e., genetc algorthm (GA)). Then, the release of each reservor and next tme-step states are determned by (4) (10)usngtheLPandANN Case Study. Ths study performs numercal analyss on a water supply problem to verfy effectveness of the proposed methodology. The plannng horzon n the study s twenty years and each tme step s ten days. Fgure 4 shows the conjunctve use system ncludng two reservors and an aqufer. Reservors 1 and 2 contan a capacty of (m 3 ) and (m 3 ). Reservor operaton rules wll be desgned to vary wth perods [30].Fgures5(a)and 5(b) are operaton rule curves for Reservors 1 and 2, respectvely. Full of water n reservors s assumed as the ntal condton. Fgure 6 shows both reservors nflows that reflect the hydrologcal dynamcs of Tawan. The nflow rato of drought season to wet season s 0.32 (Reservor 1) and 0.20 (Reservor 2). Moreover, the capacty factor (.e., effectve capacty/average annual flow) of Reservor 1 s 0.24 whle that of Reservor 2 s Fgure 7 demonstrates a hypothetcal homogeneous unconfned aqufer wth dmensons of 17 km by 17 km. The case contans fnte-dfference meshes along wthfvepumpngwells(redblocks)andfveobservaton wells (black blocks). The boundary condtons on the north and south sdes are no-flow boundares. The west and east constant-head boundares are 100 m and 80 m, respectvely. Aqufer propertes and smulaton parameters are shown n Table Results and Dscusson 3.1. Comparson of Decoupled and Coupled Conjunctve Use Operatons. Table 3 demonstrates the seres of models under the same water requrement amount, (m 3 /tenday). Case 1 consders decoupled operaton that surface Table 2: Aqufer propertes and smulaton parameters. Parameter Value Aqufer thckness (m) 110 Specfc yeld 0.2 Porosty 0.2 Horzontal hydraulc conductvty (m/s) Vertcal hydraulc conductvty (m/s) Smulaton tme step length (days) 10 Maxmum pumpng rate (cms) 0.3 Case number Table 3: Case abstract n the study. Descrpton 1 Decoupled conjunctve use operaton Conjunctve use operaton usng FIS wthn hgh usage 2 of subsurface water Conjunctve use operaton usng a 3 smulaton-optmzaton model Conjunctve use operaton usng FIS wthn low usage 4 of subsurface water water s suppled n advance, and subsurface water s then suppled. Case 2 consders the conjunctve use of surface and subsurface water smultaneously by usng FIS based on fuzzy rules (Table 1). Table 4 presents the water supply and shortage ndex (SI) [31, 32]whch,proposedbytheUSArmyCorpsof Engneers, could represent the severty of the long-term water shortage from surface and subsurface water. The result shows that the 10-day and annual SI of Case 2 are lower than those of Case 1. It mples that the FIS could mprove water shortage n the case study. Compared wth Case 1, Case 2 decreases the shortage by 26.23%, and the FIS makes a sgnfcant drop n defct rsk. Ths ndcates that the FIS conjunctve use of surface and subsurface water s more effcent. The FIS specfes how much water s suppled from surface and subsurface water to acheve system demand requrement. Accordng to the fuzzy rules, water s suppled from surface water n normal tme and from subsurface water durng the drought. Fgure 8 mples the relatonshp between subsurface water supply and shortage n decoupled and coupled conjunctve use models (Cases 1 and 2). Furthermore, subsurface water s suppled earler n coupled conjunctve use model (Case 2) than n the decoupled conjunctve use model (Case 1) durngthedrought.theresultndcatesthattmngofwater allocaton s sgnfcantly mportant. Consderng the FIS conjunctve operaton (Case 2), water supply from subsurface water n advance may reduce the mpact of shortage under a long-term operaton. Ponnambalam et al. [33] compared general operatng rules developed by both fuzzy rules and regresson-based rules. Ther results demonstrate that the FIS rules perform much better than the regresson rules for dealng wth uncertanty of nflows. Fuzzy sets provde a nonfrequentst approach to consderng uncertanty [34]. The FIS conjunctve use of surface and subsurface water can enhance the relablty of water supples by provdng

6 6 Advances n Fuzzy Systems Table 4: The shortage ndces and the supply of water system n the cases. Case day SI Annual SI Number of 10 days n shortage Surface water (10 4 m 3 10-day supply ) Annual supply Subsurface water (10 4 m 3 10-day supply ) Annual supply Low LowMed Medum HghMed Hgh Low Medum Hgh LowMed HghMed (10 6 m 3 ) (a) (m) (b) Low LowMed Medum Hgh (cms) (c) 0.3 Fgure 3: Fuzzy membershp functon for (a) nput 1: surface water state, (b) nput 2: subsurface water state, and (c) output: pumpng rate. Reservor 1 Max storage (m 3 ) Max storage (m 3 ) Reservor 2 Subsurface water system Requred demand (m 3 /ten-days) Max supply (m 3 /ten-days) Sea Fgure 4: Schematc dagram of water resources system.

7 Advances n Fuzzy Systems 7 80.E E + 06 Storage (m 3 ) 60.E E E + 06 Storage (m 3 ) 40.E E E day Upper lmt Lower lmt Crtcal lmt (a) 00.E day Upper lmt Lower lmt Crtcal lmt (b) Fgure 5: The operaton rule curve of (a) Reservor 1 and (b) Reservor E klometers 20.E + 06 Inflow (m 3 ) 15.E E E E day 17 klometers h = 100 m A B C D E h=80m Reservor 1 Reservor 2 Fgure 6: Reservor nflows n surface water system. Drchlet B.C. No flow B.C. Drchlet B.C. ndependent sources. Surface and subsurface water systems contan dstnctly dfferent characterstcs; for example, surface water s rapd fluctuatons and subsurface water vares gradually. Consderng the fuzzy rules that abundant water system supples more water, the FIS s effcently applcable to the management of surface and subsurface water Comparson of FIS and Smulaton-Optmzaton Model. Ths study compares the FIS and smulaton-optmzaton models to verfy effectveness of the proposed FIS methodology for conjunctve use of surface and subsurface water. Smulaton-optmzaton approach s used n Case 3 for mnmzng the water shortage and balancng the usages between surface and subsurface water (11). In the smulatonoptmzatonmodel,thesurfaceandsubsurfacewatersmulaton models ncludng the LP and ANN are embedded n the genetc algorthm (GA) to determne the pumpng rate and water allocaton n each tme step sequentally. For the detals of GA refer to McKnney and Ln [35], Chen et al. [36], and Chang et al. [37]. The result reveals that 10-day and annual SI of the FIS and smulaton-optmzaton model (Cases 2 and 3) are smlar (Table 4). Both models can decrease the water shortage more than20%ncomparsoncase1.thsnformatonallowsthe (Red blocks mean pumpng well clusters and black blocks mean observaton wells) Fgure 7: Model of subsurface water system, observaton, and pumpng wells. (E+04m 3 ) day Case1 shortage Case2 shortage Case1 groundwater supply Case2 groundwater supply Fgure 8: Comparson of supply of subsurface water and shortage between Cases 1 and 2. decson makers to control water supply for a long term by the FIS. Smlar to the smulaton-optmzaton model, the fuzzy operatng rules specfy how water s managed throughout the system to acheve system demand requrement. Durng

8 8 Advances n Fuzzy Systems Table 5: Valdaton results n subsurface water ANN model. MSE (m 2 ) RMSE (m) AME (m) Obs Obs Obs Obs Obs Average hydraulc head (m) day Case 2 Case 4 Fgure 9: Comparson of average hydraulc heads n Case 2 and 4. the drought, subsurface water s used n advance, and surface water s saved. Water supply usng the FIS wll reduce the mpact of shortage. However, problem solvng requres hundreds to thousands of numercal smulaton runs for searchng water supply strateges n the GA approach. For example, the maxmum number of generatons s twenty, and the populaton sze for each generaton s ffty chromosomes. Therefore, 1000 searchng possbltes at most are needed n each tme step. The computaton s more effectve usng the FIS than the GA. However, the FIS approach obtans near-optmal solutons and saves consderable computatonal tme. The FIS provdes an alternatve way for conjunctve operatons that offer the good chances for water supply management [3 5]. The FIS s easy to apply and extend to a complex water system [3], utlzed n controllng humanstc systems n water resources management, and offers an alternatve way for conjunctve operaton Subsurface Water Table Smulaton by ANN and Control by FIS. The ANN nputs nclude the hydraulc heads n fve observaton wells and pumpng rates n fve pumpng wells at current tme, and the outputs are hydraulc heads n the observatons at next tme. The data are generated by the MODFLOW and sets of nput-output patterns are generated by a random pumpng rate between the mnmum and maxmum (from 0 to 0.3 cms). The MODFLOW, s a physcal fnte-dfference numercal flow model and a computer program developed by the US Geologcal Survey [38]. Moreover, a network tranng functon updates weght and bas values accordng to Levenberg-Marquardt optmzaton [39]. The transfer functons wth a hdden layer and the output layer are hyperbolc tangent. If the tranng stop crtera (.e., MSE = 10 7 ) are not met, the learnng algorthm contnues. Table 6: Rule table for the operaton n conjunctve use operaton usng FIS wthn low usage of subsurface water. Low Surface water state Low Med. Medum Hgh Med. Hgh Subsurface water state Low Low Low Low Low Low Low Med. Medum Medum Low Low Low Medum Medum Medum Low Low Low Hgh Med. Medum Medum Low Low Low Hgh Medum Medum Low Low Low The total avalable data has been dvded nto two sets, tranng and valdaton sets: 2,500 samples were used to tran the ANN, and 1,000 samples were used for valdaton. Table 5 presents the ANN valdaton results. Accuracy of the ANN model can be quantfed when compared wth MODFLOW. Comparng relatve errors reveals that, among the table, Observaton 1 s the lowest error n the estmaton. Results demonstrate that relatve error wth respect to average subsurface water level s 1.3% or less. After the valdaton, the ANN smulates the subsurface water level wth tme behnd the FIS operatng. Accordngly, the ANN obtans better results, and the computng tme of the ANN model s about1/53ofatradtonalmodflow.thsresultrevealsthat the ANN predcts hydraulc heads effcently at the selected control locatons under varable pumpng but condensed surrogate for subsurface water flow model n nterestng cells [18, 21]. Results show the ANN approach has a great potental to predct subsurface water level because t permts developng complex and nonlnear models. Fgure 9 shows tme-varyng hydraulc heads n the two FIS cases (Cases 2 and 4) under varous pumpng strateges. The fuzzy rules for hgh and low usages n Cases 2 and 4 are represented n Tables 1 and 6. Overall, the average hydraulc heads vary wth dry-wet cycles. In Cases 2 and 4, a fuzzy rule-based system determnes the pumpng rate consderng hydraulc head constrant mplctly. Moreover, the FIS wll decde to pump a large volume of subsurface water n Case 2 and pump a small volume of subsurface water n Case 4; therefore the hydraulc head n Case 4 s hgher than that n Case 2. Approprate subsurface water usage makes water resources sustanable. Moreover, subsurface water overdraft causes land subsdence problems n many places; therefore preventng the consequences of aqufer explotaton s essental [40, 41]. Results show that the mnmum hydraulc head ncase2saround73mandthatncase4saround81m (Fgure 9), representng that hydraulc head s under control usng the FIS. As a result, fuzzy rules consder hydraulc head constrants mplctly for envronmental conservaton. Accordngly, the FIS s the ntellgent control model based on the fuzzy rule and controls humanstc systems n water resources management. In the FIS approach, the rules wth the expert experence can satsfy demand and envronmental conservaton adaptvely. The FIS offers the ablty for the adaptve management so that the system follows the fuzzy

9 Advances n Fuzzy Systems 9 rule and adapts the supply water based on the states of the system. Thus, the managers can adjust the fuzzy operaton strategy to satsfy the water demand and envronmental conservaton. 4. Conclusons Ths study appled a fuzzy nference system (FIS) for the conjunctve use of surface and subsurface water. The FIS determnes operatng polces between surface and subsurface water based on the current states. The approach wth the expert knowledge could obtan effcent and near-optmal solutons when compared to the smulaton-optmzaton approach.afterassgnngthedemandofsurfaceandsubsurfacewater,theannandlpsmulatethesurfaceandsubsurface water states. Results show that the FIS enhances relablty of water supply and provdes a decson for utlzng two water sources. To mnmze the mpacts of consequental shortages, the FIS follows the operaton rules n whch abundant water system supples more, but scarce water system supples less. The FIS mproves shortage performance because the FIS supples subsurface water early and retans surface water durng dry season. The FIS controls the supply between surface and subsurface water and reduces the mpact of overpumpng of subsurface water. Therefore, the FIS s best utlzed n controllng humanstc systems whose behavor s nfluenced by expert knowledge for water resources management. Drecton for future studes could consder an autotunng technology and a neural learnng technology or parameter optmzaton approaches further acqurng the rule from expert knowledge [42]. Acknowledgments TheauthorswouldlketothankC.W.Huang,P.C.Chen, edtors, revewers, and the anonymous helpers for ther contrbutons to ths study. In addton, the authors also thank Water Resources Agency, Department of Land Admnstraton, Mnstry of Interor and Natonal Scence Councl, Tawan, for fnancally supportng ths research. References [1] L. A. Zadeh, Fuzzy sets, Informaton and Control, vol. 8, no. 3, pp , [2] M. 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11 Journal of Advances n Industral Engneerng Multmeda The Scentfc World Journal Appled Computatonal Intellgence and Soft Computng Internatonal Journal of Dstrbuted Sensor Networks Advances n Fuzzy Systems Modellng & Smulaton n Engneerng Submt your manuscrpts at Journal of Computer Networks and Communcatons Advances n Artfcal Intellgence Internatonal Journal of Bomedcal Imagng Advances n Artfcal Neural Systems Internatonal Journal of Computer Engneerng Computer Games Technology Advances n Advances n Software Engneerng Internatonal Journal of Reconfgurable Computng Robotcs Computatonal Intellgence and Neuroscence Advances n Human-Computer Interacton Journal of Journal of Electrcal and Computer Engneerng