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Research ArticleWater Quality Modeling in Reservoirs Using Multivariate LinearRegression and Two Neural Network Models

Wei-Bo Chen1 and Wen-Cheng Liu23

1National Science and Technology Center for Disaster Reduction New Taipei City 23143 Taiwan2Department of Civil and Disaster Prevention Engineering National United University Miaoli 36063 Taiwan3Taiwan Typhoon and Flood Research Institute National Applied Research Laboratories Taipei 10093 Taiwan

Correspondence should be addressed to Wen-Cheng Liu wcliunuuedutw

Received 12 April 2015 Accepted 25 May 2015

Academic Editor Ozgur Kisi

Copyright copy 2015 W-B Chen and W-C Liu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In this study two artificial neural network models (ie a radial basis function neural network RBFN and an adaptive neurofuzzyinference system approach ANFIS) and a multilinear regression (MLR) model were developed to simulate the DO TP Chl a andSD in the Mingder Reservoir of central Taiwan The input variables of the neural network and the MLR models were determinedusing linear regression The performances were evaluated using the RBFN ANFIS and MLR models based on statistical errorsincluding the mean absolute error the root mean square error and the correlation coefficient computed from the measured andthe model-simulated DO TP Chl a and SD values The results indicate that the performance of the ANFIS model is superiorto those of the MLR and RBFN models The study results show that the neural network using the ANFIS model is suitable forsimulating the water quality variables with reasonable accuracy suggesting that the ANFIS model can be used as a valuable tool forreservoir management in Taiwan

1 Introduction

Water is an important resource for the survival and health ofhumans and ecosystems The quality of water is also crucialThe wording water quality can be used to address the con-dition in water column which included the characteristics ofphysical chemical and biological characteristics Assessingthe water quality variables is needed to develop best planningand management for water resources [1 2]

The definition of eutrophication is the nutrient enrich-ment which means the excessive phosphorus and nitrogenloads in lakes and reservoirs resulting in a serious problemThe natural or artificial enrichment of inland water bodiescan cause eutrophication with algal blooms to deteriorate thewater quality for human use and the decrease of dissolvedoxygen levels resulting in adverse effects on fisheries Theapplication of some modeling techniques to predict thebehavior of enriched water bodies allows for combatingadverse effects [3ndash5]

Due to the advanced computing capabilities two-di-mensionalthree-dimensional reservoir hydrodynamic and

water qualitymodels have been developed andwidely appliedto resolve water quality problems [6ndash9] Although determin-istic models have been adopted for modeling water qualitythese models require input data model parameters andextensive information to obtain results [10] Because a largenumber of factors affecting the water quality have compli-cated nonlinear relationships with the variables traditionaldeterministic models are not easy to handle

Because of the existing difficulties and challenges in thesimulating of water quality conditions using the hydrody-namic and water quality model relatively novel computa-tional approaches artificial neural networks (ANNs) whichhave found wide acceptance in many disciplines providean alternative method for understanding and managing thewater quality in reservoirs ANNs are well-suited for thisapplication because of their informative processing charac-teristics such as nonlinearity parallelism noise toleranceand learning and generalization capabilities [11 12]

One of the successful applications of artificial intelligencetechniques including knowledge-based systems genetic

Hindawi Publishing CorporationAdvances in Artificial Neural SystemsVolume 2015 Article ID 521721 12 pageshttpdxdoiorg1011552015521721

2 Advances in Artificial Neural Systems

27

26

25

24

23

22

21

Latit

ude (

∘ N)

117 118 119 120 121 122 123 124

Longitude (∘E)

Mainland China

East China Sea

Taiwan

Strai

t

Penghu Islands

South China Sea

Taiwan

Miaoli County

Pacific Ocean

Bashi Channel

Mingder Reservoir

Sampling station

720m

N

Figure 1 The Mingder Reservoir and water quality sampling stations

algorithms artificial neural networks and fuzzy inferencesystems has been simulating complex nonlinear systems [13]In particular artificial neural networks have been successfullyused as tools to simulate and predict water quality in waterbodies [14ndash18] The ANN model which is a black-box modeldoes not require knowledge of any of the parameters [19]ANNs have several advantages including learning abilitydealing with complex nonlinear data and parallel processingability Prediction with ANN can be performed by thenetwork learning experimentally generated data or usingvalidated models [20]

Recently Rankovic et al [21] developed a feed-forwardneural networkmodel to simulate the dissolved oxygen in theGruzaReservoir in Serbia Soltani et al [22] combined awaterquality simulation model and a hybrid genetic algorithmto determine the optimal operating polices for differentreservoir outlets The water quality simulation model isbased on an adaptive neural fuzzy inference system thatwas trained using the results of a numerical water qualitysimulationmodel Again Rankovic et al [15] used an adaptivenetwork-based fuzzy inference system model to simulate thedissolved oxygen in the Gruza Reservoir in Serbia However

evaluating the efficiency of multivariate linear regression andartificial neural network models to predict the water qualityparameters in reservoirs has not been reported

The main objective of this study is to establish a mul-tivariate linear regression (MLR) model and two artificialneural networkmodels including a radial basis function neu-ral network (RBFN) and an adaptive neurofuzzy inferencesystem (ANFIS) to simulate the dissolved oxygen (DO) thetotal phosphorus (TP) the chlorophyll a (Chl a) contentand the Secchi disk depth (SD) which are commonly usedas indicators of the eutrophication of reservoirs A furtheraim is to demonstrate the application of these models toidentify complex nonlinear relationships between the inputsand outputs in theMingder Reservoir TaiwanThe simulatedand measured DO TP Chl a and SD values were comparedusing the MLR RBFN and ANFIS models

2 Materials and Methods

21 Description of Study Area and Data Collection TheMingder Reservoir (Figure 1) is located in central TaiwanThe reservoir completed in 1970 has a total watershed area

Advances in Artificial Neural Systems 3

20132011200920082005200420022000199719951993

Year

30

35

40

45

50

55

60

65

70

CTSI

Eutrophic

Mesotrophic

Oligotrophic

Figure 2 Carlson trophic state index (CTSI) for the MingderReservoir

of 61 km2 and an effective storage volume of 165 times 108m3

and was built as a water supply source to Miaoli County forindustrial supply irrigation and flood control The dam siteof the Mingder Reservoir is located at the tributary of theHoulong River and is approximately 7 km fromMiaoli City

The Mingder Reservoir is an in-channel reservoir thatwas formed by the construction of an earth dam and has asurface area of 162 km2 Its water quality has been routinelymonitored over the past two decades once per season since1993 There are three water quality sampling stations in thereservoir

Carlson [23] proposed a trophic state index (CTSI)related to the diverse aspects of the trophic state found inmultiparameter indices The CTSI has the simplicity of asingle parameter index for the water quality assessment ofimpounded water bodies The CTSI has been adopted by theTaiwan Environmental Protection Administration (TEPA) todetermine eutrophication status It is calculated with threevariables the Secchi disk depth (SD) the total phosphorus(TP) and the chlorophyll a concentration (Chl-a) For thisreason these three water quality variables were predictedusing three approaches presented in this study

Figure 2 shows the CTSI values of the Mingder Reservoirfrom 1993 to 2013 A CTSI value above 50 indicates that thewater body is eutrophic as shown in Figure 2 for theMingderReservoir This figure shows that the reservoir is in a statusbetween mesotrophic and eutrophic Agricultural activitiesare the major sources of nutrients and provide excessivenutrient loads to the reservoir

The historical water quality data including the watertemperature pH electrical conductivity turbidity suspendedsolids total hardness total alkalinity Secchi disk depthdissolved oxygen chlorophyll a concentration total phos-phorus nitrate nitrogen and biochemical oxygen demandfrom 1993 to 2013 were collected from the TEPA andanalyzed A statistical summary of the water quality variablesis shown in Table 1

22 Adaptive Neurofuzzy Inference System (ANFIS) TheANFIS is a fuzzy Sugenomodel with multilayer feed-forwardnetwork which potentially captures the benefits of artificialneural networks and fuzzy logic approaches in a singleframework ANFIS provides easy learning and adaptation

since it is a framework of adaptive systems The Sugenosystem is themost commonly adapted fuzzymodel forANFISframework to deal with the complicated nonlinear problemsbecause of less computational time [24]

To easily understand the architecture of ANFIS weassume that the fuzzy inference system has two inputs 1199091 and1199092 and only one output 119910 Therefore two fuzzy if-then rulesbased on a first-order Sugeno fuzzymodel is provide as below[25]

Rule 1 if 1199091 is1198601 and 1199092 is 1198611 then 1199101 = 11990111199091+11990211199092+1199031Rule 2 if 1199091 is1198602 and 1199092 is1198612 then 1199102 = 11990121199091+11990221199092+1199032

where 119860119894and 119861

119894are the fuzzy sets and 119901

119894 119902119894 and 119903

119894are the

parameters that will be determined during the training andtesting processesThe architecture of ANFIS with two rules isshown in Figure 3 in which circles represent fixed nodes andsquares indicate adaptive nodes A brief introduction of theANFIS model follows

Layer 1 Each node 119894 in this fuzzy layer is an adaptive nodewith a node function

1198741119894 = 120583119860119894

(1199091) 119894 = 1 2

1198741119894 = 120583119861119894minus2

(1199092) 119894 = 3 4(1)

where 1199091 and 1199092 are the inputs to node 119894 119860119894and 119861

119894are the

linguistic labels and 120583119860119894and 120583

119861119894minus2are the membership func-

tions for the119860119894and119861

119894linguistic labels respectively Although

many membership functions such as the trapezoidal mem-bership function the Gaussian membership function theGaussian combination membership function the spline-based membership function and the sigmoidal membershipfunction can be used Chau [26] investigated the effect of dif-ferent membership functions on the performance of ANFISmodel and found that the differences are insignificant In thisstudy we adopted the generalized bell-shaped membershipfunction which is a commonly used function [26]

120583119860119894

=1

1 +1003816100381610038161003816(1199091 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

120583119861119894minus2

=1

1 +1003816100381610038161003816(1199092 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

(2)

where 119886119894 119887119894 and 119888

119894are the parameter sets The parameters in

this layer are the premise parameters

Layer 2 Each node in this layer is a fixed node which ismarked with circle and labeled with M in Figure 3 Theoutputs of this layer which are called the firing strengths(1198742119894) are the products of the corresponding degrees obtainedfrom Layer 1 (the input layer)

1198742119894 = 119908119894= 120583119860119894

(1199091) times 120583119861119894

(1199091) 119894 = 1 2 (3)

Layer 3 Every node in this layer is a circle node labeled 119873

(Figure 3) The third layer contains fixed nodes that calculate


Table 1 The statistic summary of the water quality variables in the Mingder Reservoir

Variables Minimum Maximum Mean St Dev C VWater temperature (∘C) 1370 3360 2346 518 022pH 528 950 811 067 008Electrical conductivity(120583mhocm 25∘C) 7800 44700 23474 5233 022

Turbidity (NTU) 087 75000 1364 5863 430Suspended solids (mgL) 148 43800 1049 3331 318Total hardness (mgL) 120 19000 9667 2270 023Total alkalinity (mgL) 2940 17400 9080 2240 025Secchi disk depth (m) 015 340 150 052 035Dissolved oxygen (mgL) 000 1480 768 315 041Chlorophyll a (120583gL) 010 5280 796 684 086Total phosphorus (120583gL) 300 19100 2201 1697 077Nitrate nitrogen (mgL) 001 190 012 021 169Biochemical oxygen demand(mgL) 069 5098 867 578 067

St Dev standard deviationC V coefficient of variation (St DevMean)

Input nodes Rule nodesAveragenodes

Consequentnodes Output nodes

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

A1

A2

B1

B2

M

M

N

N

w1

w1

sum

w1

w2

w1y

w2y

y

x1

x2

Figure 3 Architecture of the adaptive network-based fuzzy interface system (ANFIS)

the ratio of the firing strengths of the 119894th rule to the sum of allrulesrsquo firing strength

1198743119894 = 119908119894=

119908119894

1199081 + 1199082 119894 = 1 2 (4)

Layer 4 The nodes in this layer are adaptive and adjustableThe output of each node is the product of normalized firingstrength 119908

119894 from the third layer

1198744119894 = 119908119894119910119894= 119908119894(119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 2 (5)

where 119901119894 119902119894 and 119903

119894in this layer are consequent parameters

Layer 5 The single node computes the overall output bysumming all of the incoming signals

11987451 =

2sum

119894=1119908119894119910119894=

sum2119894=1 119908119894119910

1199081 + 1199082 (6)

The details and mathematical background for these algo-rithms can be found in Jang [24]

23 Radial Basis Function Neural Network (RBFN) A radialbasis function neural network (RBFN) contains a feed-forward structure including one input layer a single hiddenlayer and one output layer as shown in Figure 4The conceptof the RBFN is to establish a radial basis function (120601) and todetermine the relationship between the input and the outputusing curve-fitting approaches [27 28] A single output RBFNwith119898 hidden layer neurons can be described as

119910 =

119898

sum

119894=1120596119894120601119894(119909) (7)

where 119909 is the input vector 120596119894is the connecting weights

between the hidden layer and the output layer and 120601119894(119909)


x1

xn

sum y

1206011

1206012

120601m

1205961

1205962

120596m

Input layer Hidden layer Output layer

Figure 4 Architecture of the radial basis function neural network(RBFN)

is the output value of the neuron in the hidden layer aftertransfer by the radial basis function Many radial basisfunctions can be used in RBFN model The most commonradial function is theGaussian function [29]which is adoptedin the present study

120601119894(119909) = exp(minus

1003817100381710038171003817119909 minus 119888119894

1003817100381710038171003817

21205902 ) (8)

where 119888119894is center vector of the 119894th neuron in the hidden layer

120590 is defined as 120590 = 119889maxradic119899119888 119889max is the maximum distanceamong 119888

119894and 119899119888 is the number of the center vectors and

119909 minus 119888119894 denotes the Euclidean distance between 119909 and 119888

119894 The

approach used to determine 119899119888 is the orthogonal least squares(OLS) approach developed originally by Chen et al [30] andimproved by Ham and Kostanic [31] and Kecman [32] Thesimplest way to select RBFN centers is random method [33]However theOLS algorithmprovides an optimumnumber ofcenters (119899119888) in RBFN model from the training patterns [34]

24 Multilinear Regression Multilinear regression (MLR) isused to model the linear relationship between a dependentvariable and one or more independent variables MLR isbased on least squares the model is fit such that the sumof the squares of the differences between the observed andsimulated values is minimized [35] The model expresses thevalue of a predicted variable as a linear function of one ormore predictor variables

119910 = 1198870 + 11988711199091 + 11988721199092 + sdot sdot sdot + 119887119894119909119894 (9)

where 119909119894is the value of the 119894th predictor 1198870 is the regression

constant and 119887119894is the coefficient of the 119894th predictor

25 Indices of Simulation Performance Many statisticalindexes can be used to evaluate the performance of modelsThe most common indexes for evaluating the performanceof ANN models are the root mean square error (RMSE)and the correlation coefficient (119877) To strictly evaluate theperformance of MLR RBFNmodel and ANFISmodel three

criteria mean absolute error (MAE) RMSE and 119877 areemployed in this study These criteria can be defined by thefollowing equations

MAE =1119873

sum

119873

10038161003816100381610038161003816(119862119901)119873minus (119862119898)119873

10038161003816100381610038161003816

RMSE = radic1119873

sum

119873

[(119862119901)119873

minus (119862119898)119873]2

119877 =

sum119873[(119862119901)119873

minus 119862119901] [(119862119898)119873

minus 119862119898]

radicsum119873[(119862119901)119873

minus 119862119901]2

sum119873[(119862119898)119873

minus 119862119898]2

(10)

where119873 is the total number of data points 119862119901is a simulated

water quality variable 119862119898

is a measured water qualityvariable and 119862

119901and 119862

119898denote the average simulated and

measured water quality variables respectively

3 Results and Discussion

31 Selecting the Input Variables The selection of an appro-priate set of input variables for the MLR RBFN and ANFISmodels is important for predicting the water quality variablesin reservoirs [36] It is difficult to determine how many inputvariables and which input variables should be adopted in theMLR RBFN and ANFISmodelsThe straight and useful wayis to find the correlation coefficient between the individualdependent variables and water quality (DO TP Chl a andSD) A total of 389 data sets collected from 1993 to 2013 wereused for the analyses Table 2 shows the correlation coefficient(119877) between the individual dependent variables and DO TPChl a and SD respectively A correlation coefficient greaterthan 01 was set as the threshold for selecting the inputvariables It indicates that the most effective inputs to affectDO are the pH value chlorophyll a concentration watertemperature total phosphorus nitrate nitrogen and bio-chemical oxygen demand The most important water qualityvariables that affect the TP are the turbidity suspendedsolids pH value dissolved oxygen electrical conductivityand nitrate nitrogen It also illustrates that themost importantinput variables that affect Chl a and SD are respectivelythe six variables of the pH value dissolved oxygen watertemperature biochemical oxygen demand nitrate nitrogenand total hardness and the six variables of the suspendedsolids electrical conductivity turbidity total hardness totalalkalinity and total phosphorus

32 Water Quality Prediction Using the Multilinear RegressionModel The multilinear regression models were used topredict DO TP Chl a and SD The multilinear regressionmodels in (11) to (14) were obtained from the input waterquality variables

DO = 28083times pH+ 00887timesChl 119886 minus 0074

timesWTminus 00045timesTPminus 04928timesNO3

minus 00055timesBODminus 13851

(11)


Table 2 The correlation coefficient (119877) between individual dependent variable and DO TP Chl a and SD

Variables119877 value between

dependent variable andDO

119877 value betweendependent variable and

TP


Chl a

119877 value betweendependent variable

and SDWater temperature (WT) 02025 00861 03642 00571pH 06339 02401 04090 00765Electrical conductivity (EC) 00890 01769 00938 02164Turbidity (TB) 00715 03505 00003 02140Suspended solids (SS) 00812 03505 00094 02394Total hardness (TH) 00289 00145 01051 01989Total alkalinity (TA) 00250 00239 00488 01707Secchi disk depth (SD) 00062 00982 00916 mdashDissolved oxygen (DO) mdash 01917 03963 00062Chlorophyll a (Chl a) 03963 00453 mdash 00916Total phosphorus (TP) 01917 mdash 00453 01080Nitrate nitrogen (NO3) 01763 01740 01410 00978Biochemical oxygen demand (BOD) 01199 00507 01777 00528

TP = 0039timesTB+ 007times SSminus 44717times pH

minus 02463timesDOminus 00553timesEC+ 702402(12)

Chl 119886 = 11423times pH+ 05528timesDO+ 03228timesWT

+ 01079timesBODminus 17734timesNO3

minus 00103timesTHminus 128466

(13)

SD = minus 00119times SSminus 00025timesEC+ 00042timesTB

minus 00016timesTHminus 00010timesTAminus 00017

timesTP+ 24449

(14)

where BOD is the biochemical oxygen demand (mgL)EC is the electrical conductivity (120583mhocm 25∘C) NO

3is

the nitrate nitrogen (mgL) pH is the pH value SS is thesuspended solids (mgL) TA is the total alkalinity (mgL) TBis the turbidity (NTU) TH is the total hardness (mgL) andWT is the water temperature (∘C)

Equation (11) was used to predict the DO concentrationfor the training and testing phases 272 and 117 data sets wereused for training and testing the MLR model respectivelyTable 3 shows the performance evaluation using the MLRmodel for DO TP Chl a and SD The MAE RMSE and 119877

values for the DO training phase were 181mgL 233mgLand 067 and these values for the DO testing phase were181mgL 241mgL and 064 respectivelyTheMAE RMSEand 119877 values for the TP training phase were 982 120583gL1529 120583gL and 055 and these values for the TP testingphase were 999120583gL 1470 120583gL and 031 respectively TheMAE RMSE and 119877 values for the Chl a training phase were396 120583gL 585 120583gL and 050 and these values for the Chl 119886testing phase were 418 120583gL 592120583gL and 055 respectivelyTheMAE RMSE and119877 values for the SD training phase were034m 045m and 043 and these values for the SD testingphase were 037m 053m and 035 respectively

33 Water Quality Prediction Using the RBFN Model Dueto the poor performance using the multilinear regressionmodel the RBFN model was applied to predict the DO TPChl a and SD in the reservoir The same data sets adopted inthe multilinear regression model were used for training andtesting the RBFN model

Table 4 shows the performance evaluation for the DOTP Chl a and SD during the training and testing phasesThe MAE RMSE and 119877 values for the DO during thetraining phase were 149mgL 197mgL and 077 and thesevalues during the testing phase were 145mgL 196mgLand 079 respectively The MAE RMSE and 119877 values forthe TP during the training phase were 889 120583gL 1177 120583gLand 075 and these values during the testing phase were795 120583gL 991 120583gL and 073 respectively The MAE RMSEand 119877 values for Chl a during the training phase were309 120583gL 439 120583gL and 079 and these values during thetesting phasewere 286 120583gL 408120583gL and 075 respectivelyThe MAE RMSE and 119877 values for SD during the trainingphase were 029m 039m and 068 and these values duringthe testing phase were 023m 031m and 076 respectivelyThe performances for the DO TP Chl a and SD using theRBFN model were better than using the MLR model duringthe training and testing phases

Some specific parameters may cause significant changesin ANNmodel [37] In order to avoid overfitting or underfit-ting we repeated ANN model until the minimum of errorsoccurred Through the reiterative runs the sum of errorreduction ratio in RBFN model is set to 085 for providingthe best performances However the statistical errors for the119877 value were still lower than 08 using the RBFN modelwhich means that the RBFN model is not good enough forpredicting the water quality variables

34 Water Quality Prediction Using the ANFIS Model Analternative approach the ANFIS model was used to predictthe water quality variables The network was trained using


Table 3 Performance evaluation during the training and testing phases for multilinear regression model

Water quality variable Training phase Testing phaseMAE RMSE 119877 MAE RMSE 119877

DO 181mgL 233mgL 067 181mgL 241mgL 064TP 982 120583gL 1529 120583gL 055 999 120583gL 1470 120583gL 031Chlorophyll a 396 120583gL 585 120583gL 050 418120583gL 592 120583gL 055SD 034m 045m 043 037m 053m 036

Table 4 Performance evaluation during the training and testing phases for RBFN model


DO 149mgL 197mgL 077 145mgL 196mgL 079TP 889 120583gL 1177120583gL 075 795120583gL 991 120583gL 073Chl a 309 120583gL 439 120583gL 079 286 120583gL 408 120583gL 075SD 029m 039m 068 023m 031m 076

Table 5 Performance evaluation during the training and testing phases for ANFIS model


DO 130mgL 174mgL 085 092mgL 132mgL 088TP 645120583gL 992 120583gL 086 544 120583gL 742 120583gL 086Chl a 319 120583gL 467 120583gL 077 225 120583gL 305 120583gL 083SD 021m 031m 080 015m 024m 089

the training data set (ie 272 data sets) and then it wastested with the testing data set (ie 117 data sets) Figures5 and 6 show the comparison of the model-predicted DOand model-measured DO for the training and testing phasesand scatter plots respectively The error values represent-ing the predicted DO minus the measured DO are alsoshown in Figure 5 The MAE RMSE and 119877 values forthe training phase were 130mgL 174mgL and 085while these values for the testing phase were 092mgL132mgL and 088 respectively as shown in Table 5 Figures7 and 8 compare the model-predicted and model-measuredTP concentrations for the training and testing phases andscatter plots respectively The MAE RMSE and 119877 valuesfor the training phase were 645 120583gL 922120583gL and 086while these values for the testing phase were 544 120583gL742120583gL and 086 respectively Number of membershipfunctions of ANFIS model is specified as 2 to obtain the bestperformances

Figures 9 and 10 compare the model-predicted andmodel-measured chlorophyll 119886 concentrations for the train-ing and testing phases and scatter plots respectively TheMAE RMSE and 119877 values for the training phase were319 120583gL 467 120583gL and 077 and these values for the testingphase were 325 120583gL 305 120583gL and 083 respectively Theperformance evaluation for predicting the Chl 119886 concen-tration using the ANFIS model during the training phaseis slightly inferior to that using RBFN model but the per-formance evaluation for predicting the Chl 119886 concentrationusing the ANFIS model during testing phase is superior tothat using RBFNmodel (Table 4) This result may be the rea-son that the predicted Chl 119886 concentration using the ANFIS

model underestimated the high Chl 119886 concentration in theobservational data during the training phase

Figures 11 and 12 illustrate the comparison of the model-predicted and model-measured Secchi disk depth for thetraining and testing phases and scatter plots respectivelyThe MAE RMSE and 119877 values for the training phase were021m 031m and 080 while these values for the testingphase were 015m 024m and 089 respectively Overall theperformances of the DO TP Chl a and SD with the ANFISmodel are better than those with the multilinear regressionmodel and the RBFN model The performance evaluationswith ANFIS during the testing phase are superior to thoseduring the training phase A similar result is also found inRankovic et al [15]

Akkoyunlu et al [14] applied two ANN models andan MLR model to estimate the DO concentration in LakeIznik Turkey They found that the MLR model performedless accurately to predict the DO In the current study theMLR model not only is less accurate for predicting the DOconcentration but also does not simulate the TP Chl a or SDwell

35 Discussion In general the neural network models pro-vide better performance than the MLR model in this studyThe MLR model is still a useful tool for simple and fastpredicting water quality although the predicted results byMLRmodel are of insufficient accuracy For instance Cheniniand Khemiri [38] adopted MLR approach to evaluate theground water quality in Maknassy Basin central TunisiaThoe and Lee [39] used MLR to forecast the daily waterquality of Hong Kong Beach


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820

ANFIS trainingMeasurementError

minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820

ANFIS testingMeasurementError

minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)

Figure 5 Comparison of predicted and measured dissolved oxygen using ANFIS model for the (a) training phase and (b) testing phase

R = 085MAE = 130mgLRMSE = 174mgL

AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)

Figure 6 Scatter plots of predicted and measured dissolved oxygen using ANFIS model for the (a) training phase and (b) testing phase

0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)

Figure 7 Comparison of predicted and measured total phosphorus using ANFIS model for the (a) training phase and (b) testing phase


R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200

Measured TP (120583gL)

0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)

Figure 8 Scatter plots of predicted and measured total phosphorus using ANFIS model for the (a) training phase and (b) testing phase

0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)

Figure 9 Comparison of predicted and measured chlorophyll a using ANFIS model for the (a) training phase and (b) testing phase

Chau [26] performed a benchmarking comparison forpredicting the river flow discharge using ANN and ANFISmodels His study indicated that the ANFIS model exhibitedbetter performance than ANN model but the performanceof these two models were very close Our study showed thatthe predictions of water quality using RBFN and ANFISmodels had significant differences It may be the reasonthat the characteristics of input data are different Chau [26]used antecedent flow data (ie 119876

119905 119876119905minus1

and 119876119905minus2

) as inputvector while input data with different independent variablesis adopted in the present study

4 Conclusions

ANN models (ie RBFN and ANFIS models) and an MLRmodel were developed to predict the DO TP Chl a and SD

in the reservoir The performances of the RBFN ANFIS andMLR models were evaluated using the mean absolute errorthe root mean square error and the correlation coefficientThe linear regression between the water quality variables(DO TP Chl a and SD) and the individual dependentvariables was used to select the major input variables for theRBFN ANFIS and MLR models

These models were then constructed to predict the DOTP Chl a and SD in theMingder Reservoir of central TaiwanThe water quality variables predicted using the MLR modeldid not yield good resultsThe correlation coefficient betweenthe predicted water quality variables and the measured datawas less than 08 using the RBFN model In general theANFIS model better predicts the water quality variables thanthe RBFNmodel doesThe ANNmodel including the RBFNand ANFIS model can preserve the nonlinear characteristics


R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)

Measured Chl a (120583gL)

(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)

Figure 10 Scatter plots of predicted and measured chlorophyll a using ANFIS model for the (a) training phase and (b) testing phase

0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)

Figure 11 Comparison of predicted and measured Secchi disk depth using ANFIS model for the (a) training phase and (b) testing phase

between the input and output variables which are superior toconventional statistical approaches (ie the MLR model) Inthe real world temporal and spatial distributions in obser-vational data do not exhibit simple regularities thereforethey are difficult to accurately predict It is necessary to usenonlinearmodels such as theANNmodel which are suitablefor complex nonlinear systemsThe proposed approach usingthe ANFIS model has yielded valuable information that canbe used by decision-makers for aiding reservoir water qualitymanagement

In the present study we focus on the prediction of waterquality instead of forecast In a future study different lead-time forecasts in the water quality can be developed to assistthe local authorities for water quality management The softcomputing techniques such as the combining fuzzy optimal

model with genetic programming [40 41] support vectormachine [42 43] and particle swarm optimization trainingalgorithm for a neural network [44] can also be develop toimprove the prediction of water quality in the reservoirs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The project under which this study was conducted is sup-ported by theNational ScienceCouncil (NSC) Taiwan under


0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)

Measured Secchi depth (m)

(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m

Measured Secchi depth (m)A

NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)

Figure 12 Scatter plots of predicted and measured Secchi disk depth using ANFIS model for the (a) training phase and (b) testing phase

Grant no NSC100-2625-M-239-001 The authors would liketo express their appreciation to the Environmental ProtectionAdministration Taiwan for providing the measured data

References

[1] W-C Liu W-B Chen and N Kimura ldquoImpact of phospho-rus load reduction on water quality in a stratified reservoir-eutrophication modeling studyrdquo Environmental Monitoring andAssessment vol 159 no 1ndash4 pp 393ndash406 2009

[2] A Najah A El-Shafie O A Karim and A H El-ShafieldquoPerformance of ANFIS versus MLP-NN dissolved oxygenprediction models in water quality monitoringrdquo EnvironmentalScience andPollutionResearch vol 21 no 3 pp 1658ndash1670 2014

[3] F Recknagel A Talib and D van der Molen ldquoPhytoplanktoncommunity dynamics of two adjacent Dutch lakes in responseto seasons and eutrophication control unravelled by non-supervised artificial neural networksrdquo Ecological Informaticsvol 1 no 3 pp 277ndash285 2006

[4] R O Strobl F Forte and L Pennetta ldquoApplication of artificialneural networks for classifying lake eutrophication statusrdquoLakes amp Reservoirs Research andManagement vol 12 no 1 pp15ndash25 2007

[5] A Afshar and M Saadatpour ldquoReservoir eutrophicationmodeling sensitivity analysis and assessment application tokarkheh reservoir Iranrdquo Environmental Engineering Sciencevol 26 no 7 pp 1227ndash1238 2009

[6] P Kudu A Debsarkar and S Mukherjee ldquoArtificial neuralnetworkmodeling for biological removal of organic carbon andnitrogen from slaughterhouse wastewater in a sequencing batchreactorrdquo Advances in Artificial Neural Systems vol 2013 ArticleID 268064 15 pages 2013

[7] G He H Fang S Bai X Liu M Chen and J Bai ldquoApplicationof a three-dimensional eutrophication model for the Beijing

Guanting Reservoir Chinardquo Ecological Modelling vol 222 no8 pp 1491ndash1501 2011

[8] C Lindim J L Pinho and JM PVieira ldquoAnalysis of spatial andtemporal patterns in a large reservoir using water quality andhydrodynamic modelingrdquo Ecological Modelling vol 222 no 14pp 2485ndash2494 2011

[9] C Zhang X Gao L Wang and Y Chen ldquoAnalysis of agri-cultural pollution by flood flow impact on water quality ina reservoir using a three-dimensional water quality modelrdquoJournal of Hydroinformatics vol 15 no 4 pp 1061ndash1072 2013

[10] JM P Vieira J L S Pinho NDias D Schwanenberg andH FP van den Boogaard ldquoParameter estimation for eutrophicationmodels in reservoirsrdquoWater Science and Technology vol 68 no2 pp 319ndash327 2013

[11] C T Cheng K W Chau Y G Sun and J Y Lin ldquoLong-termprediction of discharges in Manwan Reservoir using artificialneural network modelsrdquo in Advances in Neural NetworksmdashISNN 2005 vol 3498 of Lecture Notes in Computer Science pp1040ndash1045 Springer Berlin Germany 2005

[12] W C Liu and C E Chung ldquoEnhancing the predicting accuracyof the water stage using a physical-basedmodel and an artificialneural network-genetic algorithm in a river systemrdquoWater vol6 no 6 pp 1642ndash1661 2014

[13] K-W Chau ldquoA review on integration of artificial intelligenceinto water quality modellingrdquoMarine Pollution Bulletin vol 52no 7 pp 726ndash733 2006

[14] A Akkoyunlu H Altun and H K Cigizoglu ldquoDepth-integrated estimation of dissolved oxygen in a lakerdquo Journal ofEnvironmental Engineering vol 137 no 10 pp 961ndash967 2011

[15] V Rankovic J Radulovic I Radojevic A Ostojic and LComic ldquoPrediction of dissolved oxygen in reservoirs usingadaptive network-based fuzzy inference systemrdquo Journal ofHydroinformatics vol 14 no 1 pp 167ndash179 2012

[16] H B Chu W X Lu and L Zhang ldquoApplication of artificialneural network in environmental water quality assessmentrdquo


Journal of Agricultural Science and Technology vol 15 no 2 pp343ndash356 2013

[17] O Kisi N Akbari M Sanatipour A Hashemi KTeimourzadeh and J Shiri ldquoModeling of dissolved oxygen inriver water using artificial intelligence techniquesrdquo Journal ofEnvironmental Informatics vol 22 no 2 pp 92ndash101 2013

[18] M Ay and O Kisi ldquoModelling of chemical oxygen demandby using ANNs ANFIS and k-means clustering techniquesrdquoJournal of Hydrology vol 511 pp 279ndash289 2014

[19] K P Singh A Basant A Malik and G Jain ldquoArtificial neuralnetwork modeling of the river water quality-A case studyrdquoEcological Modelling vol 220 no 6 pp 888ndash895 2009

[20] E Dogan B Sengorur and R Koklu ldquoModeling biologicaloxygen demand of the Melen River in Turkey using an artificialneural network techniquerdquo Journal of Environmental Manage-ment vol 90 no 2 pp 1229ndash1235 2009

[21] V Rankovic J Radulovic I Radojevic AOstojic andL ComicldquoNeural network modeling of dissolved oxygen in the Gruzareservoir Serbiardquo Ecological Modelling vol 221 no 8 pp 1239ndash1244 2010

[22] F Soltani R Kerachian and E Shirangi ldquoDeveloping operatingrules for reservoirs considering the water quality issues appli-cation of ANFIS-based surrogate modelsrdquo Expert Systems withApplications vol 37 no 9 pp 6639ndash6645 2010

[23] R E Carlson ldquoA trophic state index for lakesrdquo Limnology andOceanography vol 22 no 2 pp 361ndash369 1977

[24] J S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[25] T Takagi and M Sugeno ldquoFuzzy identification of systems andits applications to modeling and controlrdquo IEEE Transactions onSystems Man and Cybernetics vol 15 no 1 pp 116ndash132 1985

[26] K W Chau Modelling for Coastal Hydraulics and EngineeringSpon Press 2010

[27] J C Mason R K Price and A Temrsquome ldquoA neural networkmodel of rainfall-runoff using radial basis functionsrdquo Journalof Hydraulic Research vol 34 no 4 pp 537ndash548 1996

[28] Y B Dibike D P Solomatine and M B Abbott ldquoOn theencapsulation of numerical-hydraulic models in artificial neu-ral networkrdquo Journal of Hydraulic Research vol 37 no 2 pp147ndash161 1999

[29] M Verleysen and K Hlavackova ldquoLearning in RBF networksrdquoin Proceedings of the International Conference on Neural Net-work (ICNN rsquo96) pp 199ndash204 Washington DC USA June1996

[30] S Chen C F N Cowan and P M Grant ldquoOrthogonal leastsquares learning algorithm for radial basis function networksrdquoIEEETransactions onNeuralNetworks vol 2 no 2 pp 302ndash3091991

[31] F M Ham and I Kostanic Principles of Neurocomputing forScience and Engineering McGraw-Hill New York NY USA2001

[32] V Kecman Learning and Soft Computing Support VectorMachine Neural Networks and Fuzzy Logic Models MIT PressCambridge Mass USA 2001

[33] S Haykin Neural Networks A Comprehensive FoundationPrentice Hall Upper Saddle River NJ USA 2nd edition 1999

[34] M M Zirkohi M M Fateh and A Akbarzade ldquoDesign ofradial basis function network using adaptive particle swarmoptimization and orthogonal least squaresrdquo Journal of SoftwareEngineering and Applications vol 3 no 7 pp 704ndash708 2010

[35] SWeisbergApplied Linear Regression JohnWiley amp Sons NewYork NY USA 2nd edition 1985

[36] S Soyupak F Karaer H Gurbuz E Kivrak E Senturk andA Yazici ldquoA neural network-based approach for calculatingdissolved oxygen profiles in reservoirsrdquo Neural Computing ampApplications vol 12 no 3-4 pp 166ndash172 2003

[37] I V Tetko D J Livingstone and A I Luik ldquoNeural networkStudies 1 Comparison of overfitting and overtrainingrdquo Journalof Chemical Information and Computer Sciences vol 35 no 5pp 826ndash833 1995

[38] I Chenini and S Khemiri ldquoEvaluation of ground water qual-ity using multiple linear regression and structural equationmodelingrdquo International Journal of Environmental Science andTechnology vol 6 no 3 pp 509ndash519 2009

[39] W Thoe and J H W Lee ldquoDaily forecasting of Hong Kongbeach water quality by multiple linear regression modelsrdquoJournal of Environmental Engineering vol 140 no 2 Article ID04013007 2014

[40] O Kisi and T M Cengiz ldquoFuzzy genetic approach for esti-mating reference evapotranspiration of Turkey MediterraneanregionrdquoWater Resources Management vol 27 no 10 pp 3541ndash3553 2013

[41] C T Cheng C P Ou and K W Chau ldquoCombining a fuzzyoptimalmodel with a genetic algorithm to solvemulti-objectiverainfall-runoff model calibrationrdquo Journal of Hydrology vol268 no 1ndash4 pp 72ndash86 2002

[42] J-Y Lin C-T Cheng and K-W Chau ldquoUsing support vectormachines for long-term discharge predictionrdquo HydrologicalSciences Journal vol 51 no 4 pp 599ndash612 2006

[43] H Tabari O Kisi A Ezani and P Hosseinzadeh Talaee ldquoSVMANFIS regression and climate based models for referenceevapotranspiration modeling using limited climatic data in asemi-arid highland environmentrdquo Journal of Hydrology vol444-445 pp 78ndash89 2012

[44] K W Chau ldquoParticle swarm optimization training algorithmfor ANNs in stage prediction of Shing Mun Riverrdquo Journal ofHydrology vol 329 no 3-4 pp 363ndash367 2006

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



27

26

25

24

23

22

21

Latit

ude (

∘ N)

117 118 119 120 121 122 123 124

Longitude (∘E)

Mainland China

East China Sea

Taiwan

Strai

t

Penghu Islands

South China Sea

Taiwan

Miaoli County

Pacific Ocean

Bashi Channel

Mingder Reservoir

Sampling station

720m

N

Figure 1 The Mingder Reservoir and water quality sampling stations

algorithms artificial neural networks and fuzzy inferencesystems has been simulating complex nonlinear systems [13]In particular artificial neural networks have been successfullyused as tools to simulate and predict water quality in waterbodies [14ndash18] The ANN model which is a black-box modeldoes not require knowledge of any of the parameters [19]ANNs have several advantages including learning abilitydealing with complex nonlinear data and parallel processingability Prediction with ANN can be performed by thenetwork learning experimentally generated data or usingvalidated models [20]

Recently Rankovic et al [21] developed a feed-forwardneural networkmodel to simulate the dissolved oxygen in theGruzaReservoir in Serbia Soltani et al [22] combined awaterquality simulation model and a hybrid genetic algorithmto determine the optimal operating polices for differentreservoir outlets The water quality simulation model isbased on an adaptive neural fuzzy inference system thatwas trained using the results of a numerical water qualitysimulationmodel Again Rankovic et al [15] used an adaptivenetwork-based fuzzy inference system model to simulate thedissolved oxygen in the Gruza Reservoir in Serbia However

evaluating the efficiency of multivariate linear regression andartificial neural network models to predict the water qualityparameters in reservoirs has not been reported

The main objective of this study is to establish a mul-tivariate linear regression (MLR) model and two artificialneural networkmodels including a radial basis function neu-ral network (RBFN) and an adaptive neurofuzzy inferencesystem (ANFIS) to simulate the dissolved oxygen (DO) thetotal phosphorus (TP) the chlorophyll a (Chl a) contentand the Secchi disk depth (SD) which are commonly usedas indicators of the eutrophication of reservoirs A furtheraim is to demonstrate the application of these models toidentify complex nonlinear relationships between the inputsand outputs in theMingder Reservoir TaiwanThe simulatedand measured DO TP Chl a and SD values were comparedusing the MLR RBFN and ANFIS models

2 Materials and Methods

21 Description of Study Area and Data Collection TheMingder Reservoir (Figure 1) is located in central TaiwanThe reservoir completed in 1970 has a total watershed area


20132011200920082005200420022000199719951993

Year

30

35

40

45

50

55

60

65

70

CTSI

Eutrophic

Mesotrophic

Oligotrophic












where 119860119894and 119861


119894 119902119894 and 119903

119894are the



1198741119894 = 120583119860119894

(1199091) 119894 = 1 2

1198741119894 = 120583119861119894minus2

(1199092) 119894 = 3 4(1)


119894are the






120583119860119894

=1

1 +1003816100381610038161003816(1199091 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

120583119861119894minus2

=1

1 +1003816100381610038161003816(1199092 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

(2)

where 119886119894 119887119894 and 119888




1198742119894 = 119908119894= 120583119860119894

(1199091) times 120583119861119894

(1199091) 119894 = 1 2 (3)











A1

A2

B1

B2

M

M

N

N

w1

w1

sum

w1

w2

w1y

w2y

y

x1

x2



1198743119894 = 119908119894=

119908119894

1199081 + 1199082 119894 = 1 2 (4)



1198744119894 = 119908119894119910119894= 119908119894(119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 2 (5)

where 119901119894 119902119894 and 119903



11987451 =

2sum

119894=1119908119894119910119894=

sum2119894=1 119908119894119910

1199081 + 1199082 (6)



119910 =

119898

sum

119894=1120596119894120601119894(119909) (7)




x1

xn

sum y

1206011

1206012

120601m

1205961

1205962

120596m




120601119894(119909) = exp(minus

1003817100381710038171003817119909 minus 119888119894

1003817100381710038171003817

21205902 ) (8)





119894 The



119910 = 1198870 + 11988711199091 + 11988721199092 + sdot sdot sdot + 119887119894119909119894 (9)





MAE =1119873

sum

119873

10038161003816100381610038161003816(119862119901)119873minus (119862119898)119873

10038161003816100381610038161003816

RMSE = radic1119873

sum

119873

[(119862119901)119873

minus (119862119898)119873]2

119877 =

sum119873[(119862119901)119873

minus 119862119901] [(119862119898)119873

minus 119862119898]

radicsum119873[(119862119901)119873

minus 119862119901]2

sum119873[(119862119898)119873

minus 119862119898]2

(10)




119901and 119862









(11)






TP


Chl a








(13)



timesTP+ 24449

(14)


3is

























0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




20132011200920082005200420022000199719951993

Year

30

35

40

45

50

55

60

65

70

CTSI

Eutrophic

Mesotrophic

Oligotrophic












where 119860119894and 119861


119894 119902119894 and 119903

119894are the



1198741119894 = 120583119860119894

(1199091) 119894 = 1 2

1198741119894 = 120583119861119894minus2

(1199092) 119894 = 3 4(1)


119894are the






120583119860119894

=1

1 +1003816100381610038161003816(1199091 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

120583119861119894minus2

=1

1 +1003816100381610038161003816(1199092 minus 119888

119894) 119886119894

1003816100381610038161003816

2119887119894

(2)

where 119886119894 119887119894 and 119888




1198742119894 = 119908119894= 120583119860119894

(1199091) times 120583119861119894

(1199091) 119894 = 1 2 (3)











A1

A2

B1

B2

M

M

N

N

w1

w1

sum

w1

w2

w1y

w2y

y

x1

x2



1198743119894 = 119908119894=

119908119894

1199081 + 1199082 119894 = 1 2 (4)



1198744119894 = 119908119894119910119894= 119908119894(119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 2 (5)

where 119901119894 119902119894 and 119903



11987451 =

2sum

119894=1119908119894119910119894=

sum2119894=1 119908119894119910

1199081 + 1199082 (6)



119910 =

119898

sum

119894=1120596119894120601119894(119909) (7)




x1

xn

sum y

1206011

1206012

120601m

1205961

1205962

120596m




120601119894(119909) = exp(minus

1003817100381710038171003817119909 minus 119888119894

1003817100381710038171003817

21205902 ) (8)





119894 The



119910 = 1198870 + 11988711199091 + 11988721199092 + sdot sdot sdot + 119887119894119909119894 (9)





MAE =1119873

sum

119873

10038161003816100381610038161003816(119862119901)119873minus (119862119898)119873

10038161003816100381610038161003816

RMSE = radic1119873

sum

119873

[(119862119901)119873

minus (119862119898)119873]2

119877 =

sum119873[(119862119901)119873

minus 119862119901] [(119862119898)119873

minus 119862119898]

radicsum119873[(119862119901)119873

minus 119862119901]2

sum119873[(119862119898)119873

minus 119862119898]2

(10)




119901and 119862









(11)






TP


Chl a








(13)



timesTP+ 24449

(14)


3is

























0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











A1

A2

B1

B2

M

M

N

N

w1

w1

sum

w1

w2

w1y

w2y

y

x1

x2



1198743119894 = 119908119894=

119908119894

1199081 + 1199082 119894 = 1 2 (4)



1198744119894 = 119908119894119910119894= 119908119894(119901119894119909+ 119902119894119910+ 119903119894) 119894 = 1 2 (5)

where 119901119894 119902119894 and 119903



11987451 =

2sum

119894=1119908119894119910119894=

sum2119894=1 119908119894119910

1199081 + 1199082 (6)



119910 =

119898

sum

119894=1120596119894120601119894(119909) (7)




x1

xn

sum y

1206011

1206012

120601m

1205961

1205962

120596m




120601119894(119909) = exp(minus

1003817100381710038171003817119909 minus 119888119894

1003817100381710038171003817

21205902 ) (8)





119894 The



119910 = 1198870 + 11988711199091 + 11988721199092 + sdot sdot sdot + 119887119894119909119894 (9)





MAE =1119873

sum

119873

10038161003816100381610038161003816(119862119901)119873minus (119862119898)119873

10038161003816100381610038161003816

RMSE = radic1119873

sum

119873

[(119862119901)119873

minus (119862119898)119873]2

119877 =

sum119873[(119862119901)119873

minus 119862119901] [(119862119898)119873

minus 119862119898]

radicsum119873[(119862119901)119873

minus 119862119901]2

sum119873[(119862119898)119873

minus 119862119898]2

(10)




119901and 119862









(11)






TP


Chl a








(13)



timesTP+ 24449

(14)


3is

























0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




x1

xn

sum y

1206011

1206012

120601m

1205961

1205962

120596m




120601119894(119909) = exp(minus

1003817100381710038171003817119909 minus 119888119894

1003817100381710038171003817

21205902 ) (8)





119894 The



119910 = 1198870 + 11988711199091 + 11988721199092 + sdot sdot sdot + 119887119894119909119894 (9)





MAE =1119873

sum

119873

10038161003816100381610038161003816(119862119901)119873minus (119862119898)119873

10038161003816100381610038161003816

RMSE = radic1119873

sum

119873

[(119862119901)119873

minus (119862119898)119873]2

119877 =

sum119873[(119862119901)119873

minus 119862119901] [(119862119898)119873

minus 119862119898]

radicsum119873[(119862119901)119873

minus 119862119901]2

sum119873[(119862119898)119873

minus 119862119898]2

(10)




119901and 119862









(11)






TP


Chl a








(13)



timesTP+ 24449

(14)


3is

























0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








TP


Chl a








(13)



timesTP+ 24449

(14)


3is

























0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




















0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

(a)

Sample number

02468

101214161820


minus606

Diss

olve

d ox

ygen

(mg

L)Er

ror

(mg

L)

0 10 20 30 40 50 60 70 80 90 100 110

(b)



AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(a)


AN

FIS

pred

icte

d D

O (m

gL)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Measured DO (mgL)

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number

020406080

100120140160180200


minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

(a)

Sample number

200

406080

100120140160180200

MeasurementError

minus800

80

Erro

r( 120583

gL)

Tota

l pho

spho

rus

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




R = 086MAE = 645120583gLRMSE = 922 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200A

NFI

S pr

edic

ted

TP (120583

gL)

(a)

R = 086MAE = 544120583gLRMSE = 742 120583gL

0 20 40 60 80 100 120 140 160 180 200


0

20

40

60

80

100

120

140

160

180

200

AN

FIS

pred

icte

d TP

(120583g

L)(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

(a)

Sample number

MeasurementError

Erro

r( 120583

gL)

60

50

40

30

20

10

0

300

minus30

Chlo

roph

ylla

(120583g

L)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)



119905 119876119905minus1

and 119876119905minus2


4 Conclusions





R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




R = 077MAE = 319 120583gLRMSE = 467120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60A

NFI

S pr

edic

ted

Chl-a

(120583g

L)


(a)

R = 083MAE = 225 120583gLRMSE = 305120583gL

0 10 20 30 40 50 60

0

10

20

30

40

50

60

AN

FIS

pred

icte

d Ch

l-a(120583

gL)


(b)


0 20 40 60 80 100 120 140 160 180 200 220 240 260

Sample number


0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

(a)

Sample number

MeasurementError

0

1

2

3

4

5

Secc

hi d

epth

(m)

20

minus2Erro

r (m

)

0 10 20 30 40 50 60 70 80 90 100 110

ANFIS testing

(b)







Acknowledgments



0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 1 2 3 4 50

1

2

3

4

5

R = 080MAE = 021 mRMSE = 031m

AN

FIS

pred

icte

d Se

cchi

dep

th (m

)


(a)

0 1 2 3 4 50

1

2

3

4

5

R = 089MAE = 015 mRMSE = 024m


NFI

S pr

edic

ted

Secc

hi d

epth

(m)

(b)



References























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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