Research ArticleA Hybrid Fuzzy Wavelet Neural Network Model withSelf-Adapted Fuzzy c-Means Clustering and Genetic Algorithm forWater Quality Prediction in Rivers

Mingzhi Huang ,1,2 Di Tian,2 Hongbin Liu,3 Chao Zhang,2 Xiaohui Yi,1 Jiannan Cai,4

Jujun Ruan ,5 Tao Zhang ,5 Shaofei Kong,6 and Guangguo Ying1

1Environmental Research Institute, Key Laboratory of Theoretical Chemistry of Environment Ministry of Education,South China Normal University, Guangzhou 510631, China2School of Geography and Planning, Guangdong Provincial Key Laboratory of Urbanization and Geo-Simulation,Sun Yat-sen University, Guangzhou 510275, China3Jiangsu Co-Innovation Center of Efficient Processing and Utilization of Forest Resources, Nanjing Forestry University,Nanjing 210037, China4Zhongshan Environmental Monitoring Station, Zhongshan 528400, China5School of Environmental Science and Engineering, Sun Yat-Sen University, Guangzhou 510275, China6Department of Atmospheric Sciences, School of Environmental Studies, China University of Geosciences (Wuhan),Wuhan 430074, China

Correspondence should be addressed to Mingzhi Huang; hmz2002xa@163.com, Jujun Ruan; ruanjujun@mail.sysu.edu.cn,and Tao Zhang; zhangt47@mail.sysu.edu.cn

Received 26 April 2018; Revised 18 July 2018; Accepted 13 August 2018; Published 12 December 2018

Academic Editor: Hassan Zargarzadeh

Copyright © 2018Mingzhi Huang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Water quality prediction is the basis of water environmental planning, evaluation, and management. In this work, a novelintelligent prediction model based on the fuzzy wavelet neural network (FWNN) including the neural network (NN), the fuzzylogic (FL), the wavelet transform (WT), and the genetic algorithm (GA) was proposed to simulate the nonlinearity of waterquality parameters and water quality predictions. A self-adapted fuzzy c-means clustering was used to determine the number offuzzy rules. A hybrid learning algorithm based on a genetic algorithm and gradient descent algorithm was employed to optimizethe network parameters. Comparisons were made between the proposed FWNN model and the fuzzy neural network (FNN),the wavelet neural network (WNN), and the neural network (ANN). The results indicate that the FWNN made effective use ofthe self-adaptability of NN, the uncertainty capacity of FL, and the partial analysis ability of WT, so it could handle thefluctuation and the nonseasonal time series data of water quality, while exhibiting higher estimation accuracy and betterrobustness and achieving better performances for predicting water quality with high determination coefficients R2 over 0.90. TheFWNN is feasible and reliable for simulating and predicting water quality in river.

1. Introduction

As environmental pollution becomes increasingly serious,water quality (WQ) has attracted extensive attention. Manycountries have put forward a variety of pollution preventionmeasures to improve WQ and to protect the ecological waterrequirements [1]. Online analytic instruments includeimportant information from the state of the river system, so

it can be utilized by operators to apply real-time managementstrategies and solve the problem of water pollution. However,due to the lack of suitable online analytic instrument (exist-ing lag and instability) [2] for measuring chemical oxygendemand (COD) and turbidity (TU), the effective monitoringand control for WQ especially are hampered in the riversystem. Hence, in order to overcome these problems, it isnecessary to develop a software sensor model to estimate

HindawiComplexityVolume 2018, Article ID 8241342, 11 pageshttps://doi.org/10.1155/2018/8241342

hard-to-measure variables from other online measurable var-iables. The modeling nonlinearity of WQ parameters andWQ prediction based on soft-measurement theory areimportant issues in water resource management and envi-ronmental engineering [3]. There are many mathematicalmodeling methods that have been used to forecast the long-term water demand [4, 5]. The traditional mathematicalmodeling technologies are restricted for applications ofactual large-scale complex changing processes. The mathe-matical models could be set up, but their models are complex,so it is difficult to handle the nonlinear characteristic of waterquality [6, 7].

In order to overcome the shortcomings of the traditionalmathematical modeling methods, intelligence techniques,such as the artificial neural network (ANN), the fuzzy logic(FL), and the wavelet transform (WT), were developed tomodel the nonlinearity of the WQ management process[8–13]. The neural network (NN) is capable of modelingthe complex relationships between the input and the outputparameters without requiring a detailed mechanistic descrip-tion of the phenomena [14], so it could be used to model theWQ management process. Faruk [15] used a backpropaga-tion neural network to predict the WQ using 108-monthWQ observational data, including water temperature, boron,and dissolved oxygen, in the Büyük Menderes River, Turkey.The results indicated that the model captures the nonlinearnature of the complex time series and produces moreaccurate predictions. Another continuous flow system per-formance was simulated using ANN by Ahmed [16] whodeveloped a feedforward NN model and a radial basis func-tion NN model to predict the dissolved oxygen from the bio-chemical oxygen demand (BOD) and the chemical oxygendemand (COD) in the Surma River. Although the ANN issuccessfully used for the modelingWQmanagement process,the ANN schemes still have a low convergence rate and alocal minimum [17].

To overcome the shortcomings of the ANN, varioustypes of novel integrated intelligent networks have beendeveloped, such as the FNNs [2, 18–20] and the waveletneural networks (WNNs) [21]. WNN is a new branch ofANN theory research that is constructed by taking thewavelet transform as the preprocessor of the ANN. Wavelettransform has a wide range of applications in the processingof complex systems due to its time-frequency localizationcharacteristics. The WNN is better than the traditionalANN in modeling precise and convergence rates and learn-ing memory ability and accuracy [22, 23]. On the basis ofthe various online input variables, an ensemble modelingapproach based on the wavelet analysis model was designedto forecast reservoir inflow [24]. A wavelet–linear geneticprogramming model was proposed to monitor sodium(Na+) concentration in rivers [25]. The WNN has difficultyin overcoming the subjectivity of selecting fuzzy rules byhuman, which is one of the characteristics of the FL. Gharibiet al. developed a WQ index based on the FL for WQ assess-ment, particularly for the analysis of human drinking water[26]. The results indicated that the method solves the uncer-tainty problem of the change of theWQ. AWQ index using afuzzy inference system has been successfully proposed, since

it has proven to be advantageous in addressing uncertaintyproblems [27].

A novel hybrid intelligent technique—fuzzy waveletneural network (FWNN)—is proposed by combining NN,FL, and WT. The FWNN makes effective use of the self-adaptability of NN, the uncertainty capacity of FL, and thepartial analysis ability of WT, so that the networks havebetter learning and higher speed and precision [28]. TheFWNN combines the time-frequency localization abilityof the wavelet, the fuzzy inference of the FL, and the edu-cation character of the ANN together, to improve its abil-ity to reach the global best results. The FWNN offers amuch more elegant and powerful way for the modelingprocess and simulation of the water management processthan the traditional modeling approaches.

In this study, a hybrid intelligent software sensor modelbased on the FWNN is developed for the real-time estimationof the WQ of the Pearl River, China. A self-adapted fuzzyc-means clustering was used to withdraw the system’scharacter and to optimize the network space. A hybridlearning algorithm was presented to further improve theneural network prediction capabilities. The FWNN modelwas developed to predict and estimate the WQ based onthe available historical data, such as COD, NH4

+-N, dissolvedoxygen (DO), electrical conductivity (EC), pH, water tem-perature (WT), and turbidity (TU), which could increasethe safety and improve the operational performance ofWQ management.

2. Materials and Methods

2.1. Study Area. The Pearl River rises in the Yunnan Plateau,flows through the Guizhou, Guangxi, Guangdong, Hunan,and Jiangxi Provinces of China and through the northernpart of Vietnam, and finally pours into the South ChinaSea. The Pearl River, including the Xijiang, Beijiang, andDongjiang Rivers, is the third longest river in China, withan overall length of 2320 km and a river basin area of0.45× 106 km2. As the largest tributary of the Pearl River,the Xijiang River is “gold belt” with condensed resources inSouth China, which connects the coastal developed areas tothe Southwest of China. The accuracy and the efficiency ofthe developed prediction model were tested using observedwater quality data at the Hengsha station of the Xijiang Riverin Zhongshan City (China) (see Figure 1).

The Hengsha station with complete daily sampling wasselected. Six important WQ variables, COD, NH4

+-N, DO,EC, WT, pH, and TU, were analyzed. COD is one of the mostimportant parameters for the degree of water pollution. It iscommonly referred to as an important indicator of organicsubstances in water and is one of the most important param-eters in water monitoring. The TU is considered an integra-tive parameter and is an important index in water. TU isclosely related to other parameters associated with waterquality, such as the COD, or the concentrations of differentsubstances related to pollution (ammonium, sulphate, andnitrate). Due to the large effects of the other parameters,TU has become indicative of the comprehensive effect ofother parameters. TU is an integrative parameter. The COD

2 Complexity

and TU were selected as the prediction parameters. Therewere 340 samples collected from 2013 to 2014, of which 88percent (300 sets of data) were used to train the model forpredicting COD and TU level time series and 12 percent(40 sets of data) were used for model testing. DO, pH, EC,WT, and NH4

+-N were used as the input values.

2.2. Genetic Algorithm Evolving Fuzzy Wavelet NeuralNetwork (FWNN)

2.2.1. Structure of the Proposed FWNN. Figure 2 shows thebasic structure of the FWNN. It was divided into five layersas follows [29]:

(i) Layer 1 was the input layer, which was used to acceptthe present signal of the system. It consisted of theinfluencing factors (x1, x2,… , xn) where the outputswere used as the input into the second layer. In thiswork, the input parameters were DO, pH, EC, WT,and NH4

+-N; then, n = 5.(ii) Layer 2 was the fuzzy layer, where the input charac-

teristic variables were translated into fuzzy variables.In this work, the distribution of the WQ time serieswas close to a Gaussian function, so the membershipfunction was composed of the Gaussian function[29], which made the network weight values havedefinite knowledge meaning. The outputs of thelayer are shown below:

Fj xi = exp −xi − cij

2

2σ2ij,

 j = 1, 2,… , n, i = 1, 2,…m,

1

where i and j are the numbers of input variables andfuzzy linguistic terms, respectively, and cij and σij arethe center and the width parameters of the Gaussianfunction, respectively. A self-adapted fuzzy c-meansclustering was employed to determine the number ofclusters for the sample data and then to establish thenumber of rules (48 fuzzy rules). So, the number ofnodes was 48× 5 in this layer.

(iii) Layer 3 was termed the fuzzy rule layer, which wasused to realize the logical inference based on thefuzzy rule. Each node at layer 3 corresponded toone fuzzy logic rule according to the multiplication.So, there were 48 nodes in layer 3. In this layer, theoutputs were given as follows:

μ j x =n

j=1Fj xi , i = 1, 2,… ,m, 2

where n is the number of fuzzy rules.

(iv) Layer 4 was termed the wavelet layer. In thislayer, WNNs were utilized as the consequence ofthe network, where the wavelet function substitutedfor the effective function of the connotative layerand was used for data denoising transformation.The input in this layer was from the product ofthe output from layers 3 and 4. The output ofthe WNNs with the jth wavelet neuron wasrepresented as

woj =wjψj z ,

ψj z = 〠m

i=1

1aij

1 − z2ij ez2i j/2, 3

where zij = xi − bij /aij, in which aij and bij arethe dilation and the translation parameters ofthe wavelet network, respectively, and wj is theweight of the wavelet networks. The Mexicanhat wavelet was the second derivative of theGaussian function, which had excellent properties,particularly for the measurement of the instanta-neous amplitude and frequency of oscillating sig-nals. The Mexican hat wavelet was used as themother wavelet, and the number of decomposi-tion levels was the same as the number of fuzzylinguistic terms.

(v) Layer 5 was the output layer. In this layer, the totaloutput of the network y was as follows:

yk =∑n

j=1μj x woj∑n

j=1μj x4

In this work, theWQ indexes, COD, and TU were chosenas the outputs of the network.

The FWNN combines the time-frequency localizationability of the wavelet, the fuzzy inference, and the educationcharacter of the ANN together, where the ability to reachthe global best results was improved [30].

2.2.2. Training Algorithm to Optimize the Proposed FWNN.Anovel hybrid algorithm that combines the good property of

Figure 1: Map of the Guangzhou section of the Pearl River underconsideration.

3Complexity

the global search of the genetic algorithm (GA) and the goodproperty of the regional search of the gradient descent algo-rithm (GDA) was proposed to train the proposed FWNNand to optimize the network parameters. The center (cij)and the width (σij) parameters of the Gaussian functions,dilation (aij) and translation (bij) parameters of the wave-let functions, and the weight (wj) of the wavelet networkswere determined.

GA is a simple, but efficient, combinatorial optimizationalgorithm based on the principle of nature evolution [31].GDA determined that it easily fell into the local optimumand was sensitive to the initial values. The GA initializedthe network; then, the antecedent parameters and conse-quent parameters of the FWNN were simultaneously opti-mized with the GDA. In this work, an objective functionwas proposed to evaluate the minimum error (E) betweenthe desired values (yd L ) and the output values of theFWNN (yk), which is given as follows:

E = 12 〠

n

K=1ydk − yk

2 5

The output of the FWNN according to the s-th chromo-some with yk L was represented by the following equation:

ys L =∑n

j=1μsj xi L ⋅wosj

∑nj=1μ

sj xi L

=∑n

j=1wosj ⋅ iexp − xi L − csij

2/ σsij

2

∑nj=1 iexp − xi L − csij

2/ σsij

2

6

Here,

wosj =wsj ⋅ 〠

m

i=1asij

−1/21 −

xi L − bsijasij

2

exp −0 5xi L − bsij

asij

2

,7

Corresponding FWNN schematic architecture

Training ofthe MF

Learning ofthe rules

Learning ofdefuzzification

Rule base

Fuzzy systemgenerator

Geneticalgorithm

Pretreatmentfuzzy clustering

Fuzzifier Inference Defuzzifier

Waveletanalysis

Outputs

TranspirationAssimilationAllocation

LightTemperature

Relativehumidity

CO2

NutrientAge

Plant type

Wavelet transform

Inputs

wnn1

wnn2

wnn48

F1(x5)

F1(x1)

F1(x2)

F48(x2)

F48(x5)

F8(x1)

wo1

wo2

wo18

x1

R1

R2

R48

x2

x5

ro1

ro2

ro48

o

engine

.

.

. ...

.

.

...

...

.

Figure 2: Schematic structure of FWNN model.

4 Complexity

where i and j are the numbers of input variables and waveletneurons, respectively. The operation of the chromosome wasthe following real coding set:

Xns = csij σsij asij bsij ws

j , 8

where

csij = cs11 ⋯ csm1 ⋯ cs1n ⋯ csmn ,σsij = σs11 ⋯ σsm1 ⋯ σs

1n ⋯ σsmn ,asij = as11 ⋯ asm1 ⋯ as1n ⋯ asmn ,

bsij = bs11 ⋯ bsm1 ⋯ bs1n ⋯ bsmn ,ws

j = ws1 ⋯ws

n ,

9

where i and j are the numbers of input variables and fuzzylinguistic terms, respectively.

The initial parameters of the FWNN were optimizedthrough selection, crossover, and mutation. The initial popu-lation size N pop was 100, crossover rat Pc was 0.7, and theinterval of mutation Pm was 0.01.

2.2.3. Updating Parameters through the Gradient DescentAlgorithm. After the proposed FWNN was initialized byGA, the GDA was employed to update the parameters ofthe FWNN [29]. The center (cij) and the width (σij) parame-ters of the Gaussian functions, the dilation (aij) and transla-tion (bij) parameters of the wavelet functions, and theweight (wj) of the wavelet networks were adjusted accordingto the following function.

E = 12 yd t − y t 2 , 10

where yd t and y t were the desired values and the outputvalues of FWNN at time t, respectively. The parameter valuesof the FWNN were calculated by the following formulas:

wj t + 1 =wj t + η∂E∂wj

+ ξ wj t −wj t − 1 , 11

aij t + 1 = aij t + η∂E∂aij

+ ξ aij t − aij t − 1 , 12

bij t + 1 = bij t + η∂E∂bij

+ ξ bij t − bij t − 1 , 13

σij t + 1 = σij t + η∂E∂σij

+ ξ σij t − σij t − 1 , 14

cij t + 1 = cij t + η∂E∂cij

+ ξ cij t − cij t − 1 , 15

where η and ξ are the learning rate and the momentum factorof networks, respectively.

The values of derivatives in (11) and (15) were calculatedby the following formulas:

∂E∂wj

=y t − yd t ⋅ μj ⋅ ψ zj

∑nj=1μ j

,

∂E∂aij

=δ j 3 5z2ij − z4ij − 0 5 e−z

2i j/2

a3ij,

∂E∂bij

=δ j 3zij − z3ij e−z

2i j/2

a3ij,

∂E∂cij

=〠j

∂E∂y

∂y∂μj

∂μj

∂cij,

∂E∂σij

=〠j

∂E∂y

∂y∂μj

∂μj

∂σij,

∂E∂y

= y t − yd t ,

∂E∂μj

=woj − y

∑nj=1μj

,

∂E∂cij

=〠j

∂E∂y

∂y∂μj

∂μj

∂cij,

∂E∂cij

=μj xi

2 xi − cijσ2ij

, if i node is connected to rule node j,

0, otherwise,

∂E∂σij

=μj xi

2 xi − cijσ3ij

b,  if i node is connected to rule node j,

0, otherwise16

Here,

δj =y t − yd t ⋅ μj ⋅wj

∑nj=1μj

, i = 1,… ,m 17

2.3. Self-Adapted Fuzzy c-Means Clustering. In order to opti-mize the FWNN’s fuzzy rules automatically, a novel validityfunction, B K , was proposed to solve problems regardingthe partial optimization and to determine the cluster number[32]. The numerator and the denominator of the validityfunction represented the sum of the distances between classesand the sum of the intradistances of all the clusters. Highervalues for B K indicated better clustering results, and thebest cluster number was obtained when B K reached itsmaximum value. The validity function was given as follows:

B K =∑K

i=1∑nj=1u

mij vi − x 2/ K − 1

∑Ki=1∑

nj=1u

mij vi − x 2/ n − K

,

x = 1n〠K

i=1〠n

j=1umij xj,

18

5Complexity

where K and n are the classification number and the objectnumber in the calibration data. umij is the membership func-tion value, and m is the weight coefficient that representedthe fuzziness of the WQ classification. In which, ⋅ repre-sented the Euclidean distance measure.

The FCM clustering algorithm worked as an unsuper-vised classification method based on the minimization of acriterion function. The objective function was introducedbased on the minimum square sum of the weightedEuclidean distances dij. The objective function was definedas follows:

Jm U , V = 〠K

i=1〠n

j=1umij d

2ij, 19

〠K

i=1uij = 1, 1 ≤ j ≤ n, 20

where dij stands for the Euclidean distance between anobject and a cluster, which was defined by

dij = xj − vi , 21

where xj and vi are the observed value and the cluster cen-troid, respectively. · stands for the Euclidean distance mea-sure. For the individual objects, (20) was used for thecounting membership values. The membership functionvalue uij to the i

th cluster at the time k was defined as follows:

u kij = 1

∑cr=1 d k

ij /dkrj

2/ m−1 22

After computing the membership values for all the cali-bration objects, the cluster centers vi were provided by thefollowing equation:

v k+1i =

∑nj=1 u k

ij

mxj

∑nj=1 u k

ij

m 23

The minimization of (19) originated after providing theinitial values for the cluster centers. Equations (20)–(23) wererepeated successively in each iteration step.

3. Results and Discussion

3.1. Data Collection and Preprocessing. The data between2013 and 2014 was obtained from the China NationalEnvironmental Monitoring Centre and used to develop thesoftware sensor, as seen in Figure 3. The 340 samples werecollected from the Hengsha section of the Pearl River to formdaily composite samples for analysis. Among the total num-bers of data, the numbers for training and testing (predicting)were 300 and 40.

A database that contains system performance informa-tion is a prerequisite for the model development. Generally,it is developed by regularly collecting monitored parameters.The quality of the training database was critical for the modelto produce correct information about the system. The data-base should contain adequate and correct information inthe system for accurately describing the process. It remainscommon for a raw database to contain some redundant orconflicting data. Thus, it is necessary to pretreat the rawdatabase by removing redundancies and resolving conflictsin the data.

3.2. FWNN Development. In this study, the performance ofthe WQ software sensor system for forecasting the CODand the TU was simulated using the FWNN model. DO,pH, EC, WT, and NH4

+-N were the inputs of the models,and the output variables were COD and TU. Throughanalyzing the data set with the self-adapted fuzzy c-meansclustering, 48 fuzzy rule clusters were obtained. The self-adapted fuzzy c-means cluster algorithm that preprocessed

00

100

200

300

400

500

0

1

2

3

4

5

50 100

WTpHDOEC

TUNH+-NCOD

150 200

NH

+ -N, C

OD

(mg/

L)

4

WT(

0 C),p

H, E

C (𝜇

S/cm

), D

O (m

g/L)

, TU

(NTU

)

250 300 350

4

4

Figure 3: Variations of water quality parameters.

6 Complexity

the raw training data was required to prepare a concisedatabase and to serve as an actual training database. Thesoftware sensor system contained two FWNN models, theFWNNCOD and the FWNNTU, for predicting the CODand the TU. Each model had its own rule base, but they sharethe same input. The model was used for predicting the CODand the TU. The structure of the FWNN software sensorsystem is shown in Figure 2.

After the initial structure and the parameters of theFWNN model were determined, a hybrid learning algorithmthat integrated the GA and the GDA was applied to train andoptimize the network parameters. After the structure and theparameters of the FWNN were optimized by the GA, theGDA was employed to update the parameters of the network.

3.3. Simulation of the Hybrid FWNN Model. Two forecastingmodels based on the FWNN were implemented ontoMATLAB. The initial population size N pop was 100, thecrossover rat Pc was 0.7, the interval of mutation Pm was0.01, the maximum generation number was 200, the learningrate η was 0.01, and the momentum factor ξ was 0.5. Figure 4shows the training process of the FWNN (take FWNNCODfor example). Figure 3 shows that the hybrid algorithm hada rapid convergence ability and it rapidly met the target error.The centers and the widths of the membership functions ofthe fuzzification layer (cij and σij, respectively), the dilationand translation of the wavelet functions of the wavelet layer(aij and bij, respectively), and the weight of the wavelet

networks (wj) were decided, as shown in Table S1–S4(Supplementary Information).

As shown in Figures 5 and 6, the forecasting results of thesoftware sensor model based on the FWNN for testing data-sets were demonstrated. The observed values were consistentwith predictions made by the forecasting models. In order toevaluate the forecast accuracy of the proposed FWNNmodel,various performance indexes were used to assess the stabilityof the predicted values, which included the coefficient ofdetermination (R2), correlation coefficient (R), root meansquare errors (RMSE), mean square error (MSE), and meanabsolute percentage error (MAPE). As shown in Table 1,the performance indexes of the proposed FWNN modelswere acquired for testing datasets.

Table 1 shows that R values of 0.9499 and 0.9678 for theCOD and the TU, respectively, were achieved by using theFWNN. The R2 values for the COD and the TU were0.9023 and 0.9366, respectively. MAPEs for the COD andthe TU were 19.2030 and 26.3203, respectively. The RMSEvalues were 0.3127 and 4.5452 for the COD and the TU,respectively, via the FWNN. These results showed that theproposed FWNN model achieved a satisfactory performancefor WQ prediction.

As seen in Table 1, the proposed FWNN model demon-strated a very satisfactory performance on the prediction ofthe WQ with high determination coefficient values (R2) ofabout 0.90 and 0.94 for COD and TU, respectively. The highvalue of the determination coefficient indicated that only

0 20 40 60 80 100 120 140 160 180 20020

40

60

80

100

Generation

Sum

-squ

ared

erro

r

(a)

0 20 40 60 80 100 120 140 160 180 200Generation

0.01

0.02

0.03

0.04

0.05

Fitness

(b)Su

m-s

quar

ed er

ror

0 500 1000 1500 2000 2500 30000.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Epoch

(c)

Figure 4: Training performance of FWNN based on hybrid GA-GDA algorithms.

7Complexity

Real valuesPredicted values

Training Testing

00

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

50 100 150Samples

COD

(mg/

L)

200 250 300 350

(a)

1009080706050Turbidity real values (NTU)

Turb

idity

pre

dict

ed v

alue

s by

FWN

N (N

TU)

4030201000

10

20

30

40

50

60

70

80

90

100

Predicted values by FWNNFitting

R = 0.9499R2 = 0.9023MAPE = 19.203RMSE = 0.3127MSE = 0.0978

(b)

Figure 5: FWNN performance of the estimation of water quality for COD.

0 50 100 150 200 250 300 3500

20

40

60

80

100

120

140

Samples

Turb

idity

(NTU

)

TestingTraining

Real valuesPredicted values

(a)

0

10

20

30

40

50

60

100

70

80

90

Turb

idity

(NTU

)

0 10 20 30 50 60 7040 80 90 100Samples

Predicted values by FWNNFitting

R = 0.9678R2 = 0.9366MAPE = 26.3203MSE = 4.5452

(b)

Figure 6: FWNN performance of the estimation of water quality for turbidity.

Table 1: Performances of FWNN, WNN, and NN in modeling water quality management.

Model (COD) Model (TU)FWNN FNN WNN NN FWNN FNN WNN NN

R 0.9499 0.8129 0.7733 0.5639 0.9678 0.8502 0.8332 0.6690

R2 0.9023 0.6608 0.598 0.318 0.9366 0.7228 0.6942 0.4476

MAPE 19.2030 26.2873 46.9316 34.0226 26.3203 29.6884 41.3267 66.0219

RMSE 0.3127 0.6035 0.6404 0.9198 4.5452 10.8572 11.9338 14.1188

MSE 0.0978 0.3643 0.4102 0.8461 20.6585 117.878 142.4146 199.3415

8 Complexity

10% and 6% of the total variations for COD and TU, respec-tively, were not explained by the proposed FWNN model.According to the high R for the COD and the TU, the pre-dicted values of the new model were closer to the measuredones. According to the values of other descriptive perfor-mance indexes (MAPE, RMSE, and MSE), the developedFWNN model showed a superior prediction performance.There was a small deviation produced by the developedFWNNmodel. Using theWQ prediction model, the unfavor-able influence of the river water function by a user’s waterdrainage was estimated. This was attributed to the severechanges of concentration of the COD and the TU in theZhongshan region.

3.4. Comparisons with FNN, WNN, and NN. The developedFWNN model were compared with the FNN, the WNN,and the NN models to demonstrate the correctness, the effi-ciency, and the advantages of the hybrid network. TheFWNN model had smaller RMSE (or MSE) and MAPE andhigher R2 and R values, as seen in Table 1. When the FWNNmodel was used for predicting the COD in rivers (examplebeing the COD), R, R2, MAPE, RMSE, and MSE values were0.9499, 0.9023, 19.203, 0.3127, and 0.0978, respectively.When the FNN, the WNN, and the NN models were usedto predict the COD in rivers, the R values were 0.8129,0.7733, and 0.5639, respectively. The R2 values were 0.6608,0.598, and 0.3180, respectively. The MAPE values were26.2873, 46.9316, and 34.0226, respectively. The RMSEvalues were 0.6025, 0.6404, and 0.9198, respectively. TheMSE values were 0.3643, 0.4102, and 0.8461, respectively.

The NN model was unable to extract the nonstationarityfrom the data set. The NN model demonstrated theirweakness to extract the nonlinearity when the length of thetraining data set was the same. This showed that the NNmodel had a limited capability to extract the nonstationarityfrom the data sets. The performances of the WNN and theFNN models were better than that of the NN model. Thiswas because the wavelet transformation decomposed compo-nents of time series data extracted different time-varyingcomponents, which could be representative of the sum ofthe subprocesses associated with the original time series dataset. These different components facilitated the ability of theNN model that used the WTs and the fuzzy inferences toextract nonlinearity and nonstationarity, making its perfor-mance superior to the NN model developed using raw datasets. The performance of the FWNN model, which includedthe NN, the FL, theWT, and the GA, was found to be the bestcompared to those of the remaining models.

The FWNN model achieved better performances thanthe FNN, the WNN, and the NN models, which illustratedthat the FWNN model for predicting the WQ was moreaccurate than the FNN, the WNN, and the NN models.The results clearly indicated that the FWNN model had ahigh ability to extract the dynamic behavior and the complexinterrelationships from various WQ variables. The results ofthis study suggested that the FWNNmodel had a high abilityto extract the dynamic changes of the water resourcemanagement system.

Considering the high level of complexity in WQmanage-ment, there was a large quantity of variable informationspread in the dataset and the wide concentration ranges, suchas good prediction performance of the FWNN model for theparameters. The FWNN was a good choice for modeling theWQ management. The simulated models, based on theFWNN model, can be effectively applied to WQ manage-ment in order to cope with water quality variations. Theresults indicated that after hybrid learning, the proposedFWNN could perform better in the WQ management pro-cess than the FNN, theWNN, and the NN.With the environ-mental standards maintained, the FWNN model couldeffectively achieve both environmental and economic objec-tives of the WQ management in real time.

4. Conclusion

TheWQ prediction is an important means for understandingwater pollution tendencies. This study presented a WQmodel based on FWNN for estimating for the WQ data sets.The performance of the FWNN model was compared to theperformances of the three different models: the traditionalANN, the WNN, and the FNN models. The proposed WQprediction model, based on the FWNN, produced betterperformance than the other threemodels. The descriptive per-formance indexes proposed by the FWNN model indicatedthat the FWNN could handle the severely fluctuating timeseries data of the better WQ accuracy. The proposed hybridapproach provided an effective and useful tool for modelingthe WQ time series, which enables engineers to monitorvarious WQ parameters for improving WQmanagement.

Data Availability

The data used to support the findings of this study have notbeen made available because the authors are asked to sign aconfidentiality agreement with the Chinese governmentwhich provides the basis of the data.

Conflicts of Interest

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

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (nos. 51208206 and 51210013),Guangdong Province Natural Science Foundation (no.2016A030306033), Guangdong Provincial Science and Tech-nology Plan Project Foundation (no. 2014A020216007),Technological Innovation Young Talents of Guangdong Spe-cial Support Plan (no. 2014TQ01Z530), Pearl River NovaProgram of Guangzhou (no. 201506010058), and Fundamen-tal Research Funds for the Central Universities (no.310829161005). The authors are thankful to the anonymousreviewers for their insightful comments and suggestions.

9Complexity

Supplementary Materials

(1) The parameters of FWNNTU were determined: the cen-ter and the width parameters of the membership functions(cij and σij, respectively), the dilation and the translationparameters of the wavelet functions (aij and bij, respectively),and the weight of the wavelet networks (wj) were drawn, asshown in Table S1–S4. (2) The main code of the hybridalgorithm was added. (Supplementary Materials)

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