improving dam seepage prediction using back-propagation

Research ArticleImproving Dam Seepage Prediction Using Back-PropagationNeural Network and Genetic Algorithm

Xuan Zhang Xudong Chen and Junjie Li

School of Water Conservancy Science and Engineering Zhengzhou University Zhengzhou 450001 China

Correspondence should be addressed to Xudong Chen chenxudongzzueducn

Received 20 September 2019 Revised 16 December 2019 Accepted 7 January 2020 Published 13 April 2020

Academic Editor Daniel Zaldivar

Copyright copy 2020 Xuan Zhang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Statistical model is a traditional safety diagnostic model for dam seepage It can hardly display the nonlinear relationship betweendam seepage and the load sets and has the disadvantage of poor extension prediction In this paper the theories of BackPropagation Neural Network (BPNN) combined with Genetic Algorithm (GA) are applied to the seepage prediction modelTaking a typical dam in China as an example the prediction results of BPNN-GA model and statistical model are compared withthe monitoring values e results show that the improved dam seepage model enhances the ability of nonlinear mapping andgeneralization and makes the seepage prediction more accurate and reasonable in the near future According to the establishedcriterion the safety state of the dam in flood season is evaluated

1 Introduction

Seepage can directly reflect the dam working state and plays animportant role in the dam safety monitoring Related statisticalstudies have shown that dam break caused by seepage accountsfor 30ndash40 of the total dam break [1] erefore developingor improving a reliable model timely analyzingthe damseepagemonitoring data and predicting its change trend are ofgreat significance to grasp the safety state of dam seepage

Faneli from Italy and Roeha from Portugal first applied thestatistical regression method to the field of dam safety mon-itoring Afterwards Fanarin and others combined the theory offinite element with the monitoring data-derived deterministicmodel and hybrid model [2] In recent years with the con-tinuous development of numerical simulation technologyscholars have introduced different prediction methods into thestudy of dam seepage analysis models [3ndash9] Artificial NeuralNetwork (ANN) is a research hotspot in the field of artificialintelligence since the 1980s For the water conservancy projectANN is a new and very important frontier research topic andthey have mature applications in many aspects includinghydrological simulating flood predicting safety monitoringand comprehensive evaluating [10ndash19] Dawson et al [10] usedthe Radial Basis Function Neural Network (RBFNN) to

simulate the local rainfall-runoff evolution of the Yangtze Riverin China which promoted its development in the field ofhydrological simulation Campolo et al [11] established a floodforecasting model based on the ANN and used real-time in-formation of a watershed to predict the water level evolutionJeong et al [12] used the ANNmethod to establish the rainfall-runoff model in order to predict the ensemble streamflowWang et al [13] used the improved ANN to predict thedisplacement of a concrete-faced rockfill dam which provideda new idea for monitoring dam displacement Mata [14]combined the ANNmodel with the comprehensive evaluationsystem and proposed the correspondingmethod for evaluatingthe dam working behaviour Zadhesh et al [15] adopted theANN to estimate the secondary permeability required for thegrouting quality assessment on the Cheraghvays damrsquosfoundation Unes et al [16] used the ANN to predict dailyreservoir levels of theMillers Ferry Dam on the Alabama Riverin the USA Li et al [17] applied the Back Propagation NeuralNetwork (BPNN) to analyze the relationship between thesediment-flushing efficiency of theree Gorges Reservoir andits influencing factors Shaw et al [18] successfully simulatedthe prediction ability of a high-fidelity hydrodynamic andwater quality model using the ANN Bui et al [19] proposed anovel hybrid artificial intelligent approach for modeling and

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 1404295 8 pageshttpsdoiorg10115520201404295

predicting of the horizontal displacement of hydropowerdams In the proposed model the neural fuzzy inferencesystem was used to create a regression model whereas particleswarm optimization was employed to search the best pa-rameters for the model

BPNN is a feedforwardmultilayer network using the errorbackpropagation training algorithm It can solve manycomplex nonlinear problems in practical engineering appli-cations GA is an evolutionary algorithm developed frombiology It is often used to find optimal solution In this paperwe combine the BPNN and GA to improve the dam seepageprediction model and illustrate it with a typical dam in ChinaOn this basis the seepage safety state of this dam is studied

2 Dam Seepage Statistical Model

Dam seepage monitoring variables are generally divided intotwo categories uplift pressure and leakage Taking the upliftpressure as an example it is mainly affected by factors in-cluding water pressure temperature and time-effect[2 20ndash25] which can be shown as

δ δH + δT + δθ (1)

where δ is the uplift pressure δH is the water pressurecomponent δT is the temperature component and δθ is thetime-effect component

(1) Water Pressure Component δH e change of reser-voir water levels has a great influence on the seepageof the dam and has a certain delay [2]e equivalentwater level can be calculated according to the methodin the literature [21ndash23] to express the delay effect ofseepage δH has a linear relationship with water levelso the water pressure component can be expressed as

δH a1Hlowast (2)

where Hlowast is the equivalent water level on themonitoring day and a1 is the regression coefficient

(2) Temperature Component δT e temperature com-ponent refers to the seepage change caused by thetemperature change of the dam concrete and foun-dation rock ermal expansion reduces cracks en-hances impermeability and then slows down seepageCooling shrinkage increases cracks reduces imper-meability and thus intensifies seepage e temper-ature of the dam body and foundation rock variesperiodically with atmospheric temperature which canbe expressed with a periodic function Consideringthe linear relationship between seepage and temper-ature the multiperiod harmonic is chosen as thefactor to represent the temperature component

δT 11139442

i1b1i sin

2πit

365+ b2i cos

2πit

3651113874 1113875 (3)

where t is the number of days from the initialmonitoring day to the monitoring day and b is theregression coefficient

(3) Time-Effect Component δθ e time-effect compo-nent is an irreversible component that develops in acertain direction over time It mainly reflects theinfluence of dam body material creep dam foun-dation rock creep rock mass joint crack and weakstructure on uplift pressure Its mechanism iscomplicated and the accurate expression is oftendifficult to derive [23] Typically the variation of thetime-effect component usually changes sharply at thebeginning and gradually turns stable during the laterperiod e general variation law of the time-effectcomponent can be expressed by the combination oftwo empirical formulas which can be expressed as

δθ c1θ + c2 ln θ (4)

where θ 001 t and c is the regression coefficientIn summary the statistical model of the uplift pressure

can be expressed as

δ 11139441

i0aiHlowast i

+ 11139442

i1b1i sin

2πit

365+ b2i cos

2πit

3651113874 1113875 + c1θ + c2 ln θ

(5)

3 Improved Dam Seepage Model Based onBPNN and GA

31 Back-Propagation Neural Network e Back Propaga-tion Neural Network (BPNN) was proposed by Rumelhartand McClelland in 1986 It is a multilayer feedforwardnetwork trained by the error backpropagation algorithm andis also the most widely used neural network model atpresent e BPNN consists of input layer hidden layer andoutput layer and each layer contains several neurons [26]e neurons in the same layer are not connected with eachother while the neurons in the adjacent layers are connectedwith each other as shown in Figure 1

Assuming the number of samples (xi yi) (i 1 2 n) isn the i is one of the samples xi is the input vector and yi isthe expected output vector of the BPNN Taking the node j atthem-level as the research object when sample i is input thenode j receives the output information of the previous layeras follows

Imji 1113944

n1

k1ωkj middot O

mminus1ki (6)

where k is a node in the upper layer n1 is the number ofnodes in this layer ωkj is the connection weight between thenode k and the node j and Oki is the output signal of thenode k

e output value of the node j after the action functioncan be expressed as

Omji f I

mji1113872 1113873 (7)

where f(x) is the function at the node j e sigmoidfunction is often used in practical applications e output

2 Mathematical Problems in Engineering

value of the sigmoid function is between (0 1) e form ofthe function is as follows

f(x) 1

1 + eminus x (8)

According to equations (6)ndash(8) the output value 1113954yi ofthe output layer can be obtained by calculating the outputlayer by layer

In the process of error backpropagation it is necessary todefine an objective function at is the sum of squares oferrors between the output value 1113954yji of the output layer andthe expected output value yji

Ei 12

1113944

l

j1yji minus 1113954yji1113872 1113873

2 (9)

where l is the number of nodes in the output layer of theBPNN In practical applications there is often only one nodein the output layer so the above expression can be expressed as

Ei 12

yi minus 1113954yi( 11138572 (10)

en the total error is

E 12n

1113944

n

i1Ei (11)

where n is the number of samplese process of error adjustment is equivalent to an

unconstrained optimization problem that is to minimize Eby adjusting the connection weights without any restriction

E(ω) min (12)

Repeat the above steps and constantly correct theweights of BPNN until the error meets the requirement

BPNN due to its ability to map complex nonlinear andunknown relationships is a preferred choice among researchersfor modeling unstructured problems and has been well appliedin many practical engineering problems However it also hassome shortcomings such as being affected by the initial valuesand easily falling into a local extremum [26ndash28] In this paperthe Genetic Algorithm (GA) is used to optimize the initialweights and thresholds of the BPNN so as to improve theconvergence speed of the BPNN and reduce the possibility ofthe BPNN algorithm falling into the local extremum

32 Optimizing BPNN by Genetic Algorithm Genetic Algo-rithm (GA) is a gradient-free global optimization and searchtechnique inspired by the evolutionary processes namelynatural selection and genetic variation It was first proposed byProfessor Holland of the United States in the 1970s It operatesdirectly on the structural object without restriction of deri-vation and function continuity It adopts the probabilisticoptimization method can automatically obtain and guide theoptimization search space adjusts the search directionadaptively and does not need to determine the rule Differentfrom the traditional optimization algorithm the GA allowssimultaneous search for optimal solutions in different direc-tions instead of starting from one direction [26] GA has nospecific requirements for the state of the objective functionand it has a good global search ability erefore GA can beused to optimize the connection weights and thresholds of theBPNN [26ndash29] and the flow chart is shown in Figure 2

BPNN is based on gradient descent algorithm fortraining and weight adjustment Before training the BPNNrandomly initializes the connection weights and threshold ofeach layer to the values between interval [0 1] is methodof random initialization tends to slow down the convergencespeed of the BPNN and lead to local extremum problemwhile GA has strong global convergence but the ability oflocal refinement is deficient So we can combine GA withBPNN When the convergence speed of BPNN is slow theconnection weights and threshold of each layer in thenetwork can be used as the input information of GArough the genetic operator the optimal individual isobtained e optimal individual obtained by GA is decodedand assigned as the initial weights and thresholds of BPNNen BPNN is used for local optimization and the outputvalues with global optimal solution are obtained

From the point of view of BPNN based on GA themethod is to use GA to search the solution space of targetinformation en when the GA finds a better networkform it uses the BP algorithm to locate so as to find theoptimal solution of the problem e specific steps are asfollows [30ndash32]

(1) Initial Population Firstly the topological structure ofthe BPNN should be determined and then the lengthof individual should be determined according to thenetwork structure All weights and thresholds in thenetwork are real coded as a set of chromosomes X

X ω11ω12 ωmm θ1 θ2 θmφ11φ12 1113858

φmn μ1 μ2 μn1113859

(13)

where ω is the weight between the input layer and thehidden layer θ is the connection threshold betweeneach layer of the hidden layer φ is the weight be-tween the hidden layer and the output layer and μ isthe output layer threshold

(2) Fitness Function e reciprocal of the sum of theabsolute errors between the predicted output and the

Output layerHidden layerInput layer

hellip

hellip

x1

xi y

xn

Figure 1 Structure of a typical BPNN

Mathematical Problems in Engineering 3

expected output of the BPNN is taken as the fitnessfunction F

F 1

1113936Ni1

1113936mj1 yi

j minus oij1113872 1113873

21113969 (14)

where N is the number of training samples m is thedimension of the output variables yi

j is the targetvalue of the output node j of the BPNN when samplei acts and oi

j is the output value(3) Genetic Operations

(1) Selection Using the roulette method to select theoperator the probability of being selected is

pi Fi

1113936ci1 Fi

(15)

yik yikr + yjk(1 minus r)

yjk yjkr + yik(1 minus r)1113896 (16)

yij

yijr + yij minus ymax1113872 1113873r1 1 minuss

smax1113888 1113889 r2 ge 05

yijr + ymin minus yij1113872 1113873r1 1 minuss

smax1113888 1113889 r2 lt 05

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)

where c is the number of individuals in thepopulation

(2) Crossover Using the real number cross method thecross operation method of the ith and jth individualat the position k is as followswhere yik and yjk represent respectively the gene ofthe ith and jth individual at the position k and r is therandom number between (0 1)

(3) Mutation Selecting the jth gene of the ith individual(yij) for mutation operation the method is asfollowswhere ymax is the upper bound of yij ymin is thelower s is the current number of iterations smax isthe maximum number of iterations and r1 and r2are the random numbers between [0 1]

(4) Decodee weights and thresholds of GA output aretaken as the initial weights and thresholds of BPNNBPNN carries out forward propagation calculatesglobal error adjusts network parameters and repeatslearning training

Using GA to optimize the BPNN has a great probabilityto avoid the network falling into a local extremum and tospeed up the training of the network and the final con-nection weights will be more stable

33 Seepage Model Based on BPNN-GA e research objectof this paper is the dam seepage prediction model so theoutput variable is the predicted value of uplift pressure ofdam foundation in a certain period of time in the futureeprediction model is designed as a three-layer BPNNCombining the seepage theory with BPNN-GA in theimproved model the input variables are recorded as x

x Hlowast sin

2πt

365 cos

2πt

365 sin

4πt

365 cos

4πt

365 θ ln θ1113874 1113875

(18)

where the meaning of each letter is the same as equation (5)e output variable is the uplift pressure y and denote

the sample set as Qm

Qm x1 y1 x2 y2 xm ym1113864 1113865 (19)

where xi represents the input variables of the ith group andyi represents the corresponding uplift pressure monitoringvalue

e GA assigns the optimal initial weights to the BPNNthrough copying crossing and varying e BPNN uses thetraining set sample Qm for machine learning and the networkcontinuously adjusts the weights to achieve the set minimumerror so that the optimized BPNN can better predict the upliftpressure At this point if the test factors are input into thetrained model the model prediction value can be obtained

34 Evaluation Criterion of Dam Seepage State e BPNN-GAmodel is used to get the prediction value (δprime) of the upliftpressure at a certain time which can be compared with themonitoring value (δ) at that time According to the prob-ability and statistics theory the probability of |δ minus δprime| (theabsolute difference between the monitoring value and theprediction value) falling into (0 2S) is 955 and the

Determine the structure of BPNN

Code

Initialize population

Calculate fitness

Whether thefitness meets therequirements

Whether theerror meets therequirements

Decode

Calculate the outputvalue of BPNN

Select

Vary

Cross

Y

N

Output result

Y

Adjust weightsN

Figure 2 Flow chart of BPNN-GA


probability of |δ minus δprime| falling into (0 3S) is 997 [33 34]where S is the standard deviation of the model

In this way the state of seepage can be evaluated [3 20]

(I) Normal |δ minus δprime||2S

(II) Basically normal 2Slt |δ minus δprime|le 3S and tendencyto change does not exist

(III) Abnormal 2Slt |δ minus δprime|le 3S and tendency tochange persists

(IV) Dangerous |δ minus δprime|gt 3S

4 Case Study

Cotton Beach hydropower station is located in YongdingCounty Fujian Province China e project is mainlybased on power generation with comprehensive benefitssuch as flood control navigation and aquaculture It be-longs to class I the layout of the hub is mainly composed ofthe main dam auxiliary dam the spillway the bottom holethe water delivery structure and the underground powerhouse e main dam is arranged in the main river bed ofthe river valley e dam crest elevation is 1790m themaximum dam height is 1130m and the dam crest lengthis 3085me normal water storage level of the reservoir is1730m the storage capacity is 1122 billion cubic metersand the check flood level is 1778m corresponding to atotal storage capacity of 2035 billion cubic meters emain dam is divided into six dam sections of which 1sim2are the left bank gravity dam sections 3sim4 are theoverflow dam sections and 5sim6 are the right bank gravitydam sections

e uplift pressure is one of the safety monitoringcontents of a gravity dam and its size directly affects thestability strength and engineering cost of the dam To thisend various engineering measures such as curtaingrouting dam foundation drainage or forced drainage areneeded to reduce uplift pressure in dam construction [35]Engineering practice shows that the geological conditionsof the dam section of the main river bed are complex andgreatly influenced by the environmental factors eseepage state in the overflow dam section should be paidmore attention due to the frequently overflow influence[20] erefore the measuring points UP9 and UP11 of theoverflow dam section are studied shown in Figure 3

Selecting the uplift pressure and monitoring data ofupstream water level temperature and time in the overflowsection of Cotton Beach dam from January 2006 to June2008 as training samples of BPNN-GA the model is carriedout e trained model is used to predict the uplift pressurein flood season (July 2008) e statistical model is used as acontrast model

e monitoring values and the prediction values of twomodels are shown in Figure 4 and Tables 1 and 2

It can be seen from Figure 4 that both the statisticalmodel and the BPNN-GA model have certain predictiveextension capability From the change trend the BPNN-GAmodel is more in line with the change of monitoring valuethan the statistical model

We also introduce the Mean Absolute Percentage Error(MAPE) Mean Square Error (MSE) and Mean AbsoluteError (MAE) to quantify the prediction effectiveness of thetwo models where a smaller parameter indicates a moreeffective model ey are expressed as follows

MAPE 1n

1113944

n

i1

Ai minus Fi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (20)

MSE

1n

1113944

n

i1Ai minus Fi( 1113857

2

11139741113972

(21)

MAE 1n

1113944

n

i1Ai minus Fi

11138681113868111386811138681113868111386811138681113868 (22)

where n is the number of samples Ai is the monitoringvalue and Fi is the prediction value e calculated pa-rameters are presented in Table 3

From Table 3 taking MAPE as an example it can be seenthat the prediction error of the statistical model is 018 and038 while that of the BPNN-GA model is only 008 and014eprediction accuracy of the BPNN-GAmodel is 180and 158 higher than that of the statistical model respectivelyis is mainly because the BPNN-GA model has strongernonlinear mapping and generalization ability which improvesthe prediction accuracy of the model e above results showthat the BPNN-GA model has better prediction ability

Since the prediction accuracy of BPNN-GA model ishigher than that of the statistical model the predictionvalues of the BPNN-GA model are used to evaluate theseepage safety state of Cotton Beach dam in flood seasone prediction values of uplift pressure from July 1 to 312008 of the two points are obtained by BPNN-GA eresults of the absolute difference |δ minus δprime| values are shown inFigure 5

From Figure 5 the absolute difference |δ minus δprime| values arerelatively small and stable on the whole illustrating theBPNN-GA model has a good prediction effect HoweverFigure 5(a) shows a slightly larger fluctuation on July 29eaffecting factors are analysed especially the water levelwhich is often considered to be the main factor e analysisresults show that the upstream water level dropped signif-icantly with a range of 06m on that day which has a certainimpact on data analysis When there are mutation data in thestationary time series the BPNN-GA model does not cap-ture its impact well which leads to the above error eaccuracy of the BPNN-GA model is slightly lower in cap-turing the mutation data but it can accurately predict thetrend of data change is is enough to meet the engineeringapplication needs

In general all of the absolute difference |δ minus δprime| values liein the interval (0 2S) According to the criteria in Section34 it can be evaluated that the two points are in the normalseepage state indicating that the seepage control effect of theoverflow dam section is good Accordingly the samemethodcan be used to predict the seepage state of other points andanalyse the seepage control effect of other dam sections so


1 dam section

17900

10000

7600

6800

14000

2 dam section 3 dam section 4 dam section 5 dam section 6 dam section

UP9UP

Code name Instrument nameGraphic symbols

Pressure measuring tubeosmometer

UP11

Figure 3 Location of seepage monitoring points

Measured valueBPNN-GAStatistical model

950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)

Figure 4 e monitoring and prediction value process line of two points

Table 1 Comparison of prediction results of two models (UP9)

Date (yyyymd) Measured value(m)

Predictive value (m)Statistical model BPNN-GA

200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321


that the decision-makers can take corresponding counter-measures in special circumstances

5 Conclusions

In this paper the seepage monitoring model of the dam isstudied according to its own working characteristicsCombining the seepage theory with BPNN-GA an im-proved seepage model is established and applied to themonitoring and analysis of the uplift pressure of CottonBeach dam e results are shown as follows

(1) From the prediction results of the two pointscompared with the statistical model the BPNN-GAmodel has high prediction accuracy and can predictthe trend of data change better is shows that it isreasonable and feasible to apply the BPNN and GAtheory to improve the seepage prediction model

(2) Compared the prediction values of the improvedseepage prediction model with the monitoringvalues according to the established criteria of thedam seepage safety state the seepage safety state ofthe Cotton Beach dam in flood season is evaluatede results show that the seepage state of the twomeasuring points are normal and the seepage

control effect of the overflow dam section is goodis method can be extended to other points toobtain a comprehensive seepage safety state andseepage control treatment effect

Data Availability

e data used to support the findings of this study areavailable from the author upon request

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China under grant Nos 51609217 and51709239

References

[1] C Fang and Y Duan ldquoStatistical analysis of dam-break in-cidents and its cautionsrdquo Yangtze River vol 41 no 11pp 96ndash100 2010

Table 3 Evaluation parameters of the statistical model and BPNN-GA model for the two points

MAPE MSE MAE

UP9 Statistical model 00018 00392 01707BPNN-GA 00008 00202 00736


200871 200879 2008716 2008724 2008731

00

02

04

06

08

10

|δ ndash δprime|2S

Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)

Figure 5 Seepage safety assessment of two points By calculating the standard deviations of the two points are 029 and 034 respectively(a) UP9 (b) UP11


[2] Z Wu Safety Monitoring=eory amp its Application of HydraulicStructures Higher Education Press Beijing China 2003

[3] X Chen C Gu and H Chen ldquoEarly warning of dam seepagewith cooperation between principal component analysis andleast squares wavelet support vector machinerdquo FreseniusEnvironmental Bulletin vol 22 no 2 pp 500ndash507 2013

[4] C Liu H Jing and Y Cheng ldquoApplication of EMD-ARImodel in seepage forecasting of damrdquo Water Power vol 40no 7 pp 49ndash52 2014

[5] K Roushangar S Garekhani and F Alizadeh ldquoForecastingdaily seepage discharge of an earth dam using wavelet-mutualinformation-Gaussian process regression approachesrdquo Geo-technical and Geological Engineering vol 34 no 5pp 1313ndash1326 2016

[6] Y Xiang S-Y Fu K Zhu H Yuan and Z-Y Fang ldquoSeepagesafety monitoring model for an earth rock dam under in-fluence of high-impact typhoons based on particle swarmoptimization algorithmrdquo Water Science and Engineeringvol 10 no 1 pp 70ndash77 2017

[7] S-K Chen Q-D He and J-G Cao ldquoSeepage simulation ofhigh concrete-faced rockfill dams based on generalizedequivalent continuum modelrdquo Water Science and Engineer-ing vol 11 no 3 pp 250ndash257 2018

[8] P Li L Su and Y Jia ldquoBP-RBF neural network seepagemodelunder the influence of various factorsrdquo Yellow River vol 40no 4 pp 132ndash135 2018

[9] E Sharghi V Nourani N Behfar and G Tayfur ldquoData pre-postprocessing methods in AI-based modelling of seepage throughearthen damsrdquo Measurement vol 147 pp 1ndash13 2019

[10] C W Dawson C Harpham R L Wilby and Y ChenldquoEvaluation of artificial neural network techniques for flowforecasting in the river Yangtze Chinardquo Hydrology and EarthSystem Sciences vol 6 no 4 pp 619ndash626 2002

[11] M Campolo A Soldati and P Andreussi ldquoArtificial neuralnetwork approach to flood forecasting in the river arnordquoHydrological Sciences Journal vol 48 no 3 pp 381ndash398 2003

[12] D-I Jeong and Y-O Kim ldquoRainfall-runoff models using ar-tificial neural networks for ensemble streamflow predictionrdquoHydrological Processes vol 19 no 19 pp 3819ndash3835 2005

[13] WWang J Jin and Y Li ldquoPrediction of inflow atree GorgesDam in Yangtze river with wavelet network modelrdquo WaterResources Management vol 23 no 13 pp 2791ndash2803 2009

[14] J Mata ldquoInterpretation of concrete dam behaviour with ar-tificial neural network and multiple linear regression modelsrdquoEngineering Structures vol 33 no 3 pp 903ndash910 2011

[15] J Zadhesh F Rastegar F Sharifi H Amini andH M Nasirabad ldquoConsolidation grouting quality assessmentusing artificial neural network (ANN)rdquo Indian GeotechnicalJournal vol 45 no 2 pp 136ndash144 2015

[16] F Unes M Demirci and O Kisi ldquoPrediction of millers ferrydam reservoir level in USA using artificial neural networkrdquoPeriodica Polytechnica-Civil Engineering vol 59 no 3pp 309ndash318 2015

[17] X Li J Qiu Q Shang and F Li ldquoSimulation of reservoirsediment flushing of the three gorges reservoir using an ar-tificial neural networkrdquo Applied Sciences-Basel vol 6 no 5pp 1ndash11 2016

[18] A R Shaw H Smith Sawyer E J Le Boeuf M P McDonaldand B Hadjerioua ldquoHydropower optimization using artificialneural network surrogate models of a high-fidelity hydro-dynamics and water quality modelrdquo Water Resources Re-search vol 53 no 11 pp 9444ndash9461 2017

[19] K-T T Bui D Tien Bui J Zou C Van Doan and I RevhaugldquoA novel hybrid artificial intelligent approach based on neural

fuzzy inference model and particle swarm optimization forhorizontal displacement modeling of hydropower damrdquoNeural Computing and Applications vol 29 no 12pp 1495ndash1506 2018

[20] J Li X Chen C Gu and Z Huo ldquoSeepage comprehensiveevaluation of concrete dam based on grey cluster analysisrdquoWater vol 11 no 7 pp 1ndash16 2019

[21] J Qiu D Zheng and K Zhu ldquoSeepage monitoring modelsstudy of earth-rock dams influenced by rainstormsrdquo Math-ematical Problems in Engineering vol 2016 Article ID1656738 11 pages 2016

[22] Q Pang S Wang and Y Gu ldquoApplication of earth-rock damseepage water level model based on hysteresis effect functionrdquoJournal of Soil and Water Conservation vol 30 no 2pp 225ndash229 2016

[23] BWei M Gu H LiW Xiong and Z Xu ldquoModeling methodfor predicting seepage of RCC dams considering time-varyingand lag effectrdquo Structural Control amp Health Monitoringvol 25 no 2 pp 1ndash14 2018

[24] S-W Wang Y-L Xu C-S Gu and T-F Bao ldquoMonitoringmodels for base flow effect and daily variation of dam seepageelements considering time lag effectrdquo Water Science andEngineering vol 11 no 4 pp 344ndash354 2018

[25] X Cheng Q Li Z Zhou Z Luo M Liu and L Liu ldquoResearchon a seepage monitoring model of a high core rockfill dambased on machine learningrdquo Sensors vol 18 no 9 pp 1ndash142018

[26] W Sun and Y Xu ldquoFinancial security evaluation of theelectric power industry in China based on a back propagationneural network optimized by genetic algorithmrdquo Energyvol 101 pp 366ndash379 2016

[27] V Chandwani V Agrawal and R Nagar ldquoModeling slump ofready mix concrete using genetic algorithms assisted trainingof artificial neural networksrdquo Expert Systems with Applica-tions vol 42 no 2 pp 885ndash893 2015

[28] L Li Y Chen T Xu R Liu K Shi and C Huang ldquoSuper-resolution mapping of wetland inundation from remotesensing imagery based on integration of back-propagationneural network and genetic algorithmrdquo Remote Sensing ofEnvironment vol 164 pp 142ndash154 2015

[29] S Nasr M El-Shorbagy I El-Desoky Z Hendawy andA Mousa ldquoHybrid genetic algorithm for constrained non-linear optimization problemsrdquo British Journal of Mathematicsamp Computer Science vol 7 no 6 pp 466ndash480 2015

[30] T Gulati M Chakrabarti and A Singh ldquoComparative studyof response surface methodology artificial neural networkand genetic algorithms for optimization of soybean hydra-tionrdquo Food Technology Biotechnology vol 48 no 1pp 11ndash18 2010

[31] D Wang L Wang and G Zhang ldquoShort-term wind speedforecast model for wind farms based on genetic BP neuralnetworkrdquo Journal of Zhejiang University vol 46 no 5pp 837ndash841 2012

[32] S Li L Liu and Y Xie ldquoChaotic prediction for short-termtraffic flow of optimized BP neural network based on geneticalgorithmrdquo Control and Decision vol 26 no 10 pp 1581ndash1585 2011

[33] P Jiang J Zhao and JWei Error=eory and Data ProcessingNational Defence Industry Press Beijing China 2014

[34] A J Richard Probability And Statistics For Engineers Elec-tronics Industry Press Beijing China Ninth edition 2017

[35] K R Dhawan S Burele and K Bagwan ldquoCurtain grouting atool used for stopping the seepage from an existing damrdquoIndian Geotechnical Journal vol 49 no 5 pp 552ndash565 2019


predicting of the horizontal displacement of hydropowerdams In the proposed model the neural fuzzy inferencesystem was used to create a regression model whereas particleswarm optimization was employed to search the best pa-rameters for the model

BPNN is a feedforwardmultilayer network using the errorbackpropagation training algorithm It can solve manycomplex nonlinear problems in practical engineering appli-cations GA is an evolutionary algorithm developed frombiology It is often used to find optimal solution In this paperwe combine the BPNN and GA to improve the dam seepageprediction model and illustrate it with a typical dam in ChinaOn this basis the seepage safety state of this dam is studied

2 Dam Seepage Statistical Model

Dam seepage monitoring variables are generally divided intotwo categories uplift pressure and leakage Taking the upliftpressure as an example it is mainly affected by factors in-cluding water pressure temperature and time-effect[2 20ndash25] which can be shown as

δ δH + δT + δθ (1)

where δ is the uplift pressure δH is the water pressurecomponent δT is the temperature component and δθ is thetime-effect component

(1) Water Pressure Component δH e change of reser-voir water levels has a great influence on the seepageof the dam and has a certain delay [2]e equivalentwater level can be calculated according to the methodin the literature [21ndash23] to express the delay effect ofseepage δH has a linear relationship with water levelso the water pressure component can be expressed as

δH a1Hlowast (2)

where Hlowast is the equivalent water level on themonitoring day and a1 is the regression coefficient

(2) Temperature Component δT e temperature com-ponent refers to the seepage change caused by thetemperature change of the dam concrete and foun-dation rock ermal expansion reduces cracks en-hances impermeability and then slows down seepageCooling shrinkage increases cracks reduces imper-meability and thus intensifies seepage e temper-ature of the dam body and foundation rock variesperiodically with atmospheric temperature which canbe expressed with a periodic function Consideringthe linear relationship between seepage and temper-ature the multiperiod harmonic is chosen as thefactor to represent the temperature component

δT 11139442

i1b1i sin

2πit

365+ b2i cos

2πit

3651113874 1113875 (3)

where t is the number of days from the initialmonitoring day to the monitoring day and b is theregression coefficient

(3) Time-Effect Component δθ e time-effect compo-nent is an irreversible component that develops in acertain direction over time It mainly reflects theinfluence of dam body material creep dam foun-dation rock creep rock mass joint crack and weakstructure on uplift pressure Its mechanism iscomplicated and the accurate expression is oftendifficult to derive [23] Typically the variation of thetime-effect component usually changes sharply at thebeginning and gradually turns stable during the laterperiod e general variation law of the time-effectcomponent can be expressed by the combination oftwo empirical formulas which can be expressed as

δθ c1θ + c2 ln θ (4)

where θ 001 t and c is the regression coefficientIn summary the statistical model of the uplift pressure

can be expressed as

δ 11139441

i0aiHlowast i

+ 11139442

i1b1i sin

2πit

365+ b2i cos

2πit

3651113874 1113875 + c1θ + c2 ln θ

(5)

3 Improved Dam Seepage Model Based onBPNN and GA

31 Back-Propagation Neural Network e Back Propaga-tion Neural Network (BPNN) was proposed by Rumelhartand McClelland in 1986 It is a multilayer feedforwardnetwork trained by the error backpropagation algorithm andis also the most widely used neural network model atpresent e BPNN consists of input layer hidden layer andoutput layer and each layer contains several neurons [26]e neurons in the same layer are not connected with eachother while the neurons in the adjacent layers are connectedwith each other as shown in Figure 1

Assuming the number of samples (xi yi) (i 1 2 n) isn the i is one of the samples xi is the input vector and yi isthe expected output vector of the BPNN Taking the node j atthem-level as the research object when sample i is input thenode j receives the output information of the previous layeras follows

Imji 1113944

n1

k1ωkj middot O

mminus1ki (6)

where k is a node in the upper layer n1 is the number ofnodes in this layer ωkj is the connection weight between thenode k and the node j and Oki is the output signal of thenode k

e output value of the node j after the action functioncan be expressed as

Omji f I

mji1113872 1113873 (7)

where f(x) is the function at the node j e sigmoidfunction is often used in practical applications e output



f(x) 1

1 + eminus x (8)



Ei 12

1113944

l

j1yji minus 1113954yji1113872 1113873

2 (9)


Ei 12

yi minus 1113954yi( 11138572 (10)


E 12n

1113944

n

i1Ei (11)



E(ω) min (12)







X ω11ω12 ωmm θ1 θ2 θmφ11φ12 1113858

φmn μ1 μ2 μn1113859

(13)




hellip

hellip

x1

xi y

xn




F 1

1113936Ni1

1113936mj1 yi

j minus oij1113872 1113873

21113969 (14)





pi Fi

1113936ci1 Fi

(15)



yij


smax1113888 1113889 r2 ge 05


smax1113888 1113889 r2 lt 05

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)







x Hlowast sin

2πt

365 cos

2πt

365 sin

4πt

365 cos

4πt

365 θ ln θ1113874 1113875

(18)



Qm x1 y1 x2 y2 xm ym1113864 1113865 (19)





Code


Calculate fitness



Decode


Select

Vary

Cross

Y

N

Output result

Y

Adjust weightsN









4 Case Study







MAPE 1n

1113944

n

i1

Ai minus Fi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (20)

MSE

1n

1113944

n


2

11139741113972

(21)

MAE 1n

1113944

n

i1Ai minus Fi

11138681113868111386811138681113868111386811138681113868 (22)







1 dam section

17900

10000

7600

6800

14000


UP9UP



UP11



950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)





200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321



5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)








































f(x) 1

1 + eminus x (8)



Ei 12

1113944

l

j1yji minus 1113954yji1113872 1113873

2 (9)


Ei 12

yi minus 1113954yi( 11138572 (10)


E 12n

1113944

n

i1Ei (11)



E(ω) min (12)







X ω11ω12 ωmm θ1 θ2 θmφ11φ12 1113858

φmn μ1 μ2 μn1113859

(13)




hellip

hellip

x1

xi y

xn




F 1

1113936Ni1

1113936mj1 yi

j minus oij1113872 1113873

21113969 (14)





pi Fi

1113936ci1 Fi

(15)



yij


smax1113888 1113889 r2 ge 05


smax1113888 1113889 r2 lt 05

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)







x Hlowast sin

2πt

365 cos

2πt

365 sin

4πt

365 cos

4πt

365 θ ln θ1113874 1113875

(18)



Qm x1 y1 x2 y2 xm ym1113864 1113865 (19)





Code


Calculate fitness



Decode


Select

Vary

Cross

Y

N

Output result

Y

Adjust weightsN









4 Case Study







MAPE 1n

1113944

n

i1

Ai minus Fi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (20)

MSE

1n

1113944

n


2

11139741113972

(21)

MAE 1n

1113944

n

i1Ai minus Fi

11138681113868111386811138681113868111386811138681113868 (22)







1 dam section

17900

10000

7600

6800

14000


UP9UP



UP11



950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)





200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321



5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)








































F 1

1113936Ni1

1113936mj1 yi

j minus oij1113872 1113873

21113969 (14)





pi Fi

1113936ci1 Fi

(15)



yij


smax1113888 1113889 r2 ge 05


smax1113888 1113889 r2 lt 05

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)







x Hlowast sin

2πt

365 cos

2πt

365 sin

4πt

365 cos

4πt

365 θ ln θ1113874 1113875

(18)



Qm x1 y1 x2 y2 xm ym1113864 1113865 (19)





Code


Calculate fitness



Decode


Select

Vary

Cross

Y

N

Output result

Y

Adjust weightsN









4 Case Study







MAPE 1n

1113944

n

i1

Ai minus Fi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (20)

MSE

1n

1113944

n


2

11139741113972

(21)

MAE 1n

1113944

n

i1Ai minus Fi

11138681113868111386811138681113868111386811138681113868 (22)







1 dam section

17900

10000

7600

6800

14000


UP9UP



UP11



950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)





200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321



5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)













































4 Case Study







MAPE 1n

1113944

n

i1

Ai minus Fi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (20)

MSE

1n

1113944

n


2

11139741113972

(21)

MAE 1n

1113944

n

i1Ai minus Fi

11138681113868111386811138681113868111386811138681113868 (22)







1 dam section

17900

10000

7600

6800

14000


UP9UP



UP11



950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)





200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321



5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)







































1 dam section

17900

10000

7600

6800

14000


UP9UP



UP11



950

955

960

965

970

Tube

wat

er le

vel (

m)

200879 2008716 2008724 2008731200871Date (yyyymd)

(a)

Date (yyyymd)


200871 200879 2008716 2008724 2008731

11200

11250

11300

11350

11400

Tube

wat

er le

vel (

m)

(b)





200871 9661 9642 9647200872 9662 9638 9650200873 9667 9637 9652200874 9645 9634 9642200875 9652 9631 9649

2008728 9607 9624 96122008729 9557 9614 95102008730 9571 9624 95732008731 9606 9647 9599




200871 11350 11292 11343200872 11330 11285 11327200873 11326 11283 11323200874 11314 11278 11309200875 11303 11273 11297

2008728 11240 11248 112362008729 11202 11230 112092008730 11237 11245 112462008731 11312 11281 11321



5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)








































5 Conclusions





Data Availability




Acknowledgments


References



MAPE MSE MAE



200871 200879 2008716 2008724 2008731

00

02

04

06

08

10


Date (yyyymd)

(a)

00

02

04

06

08

10


Date (yyyymd)200871 200879 2008716 2008724 2008731

(b)







































improving dam seepage prediction using back-propagation

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