research on the prediction of the water demand of...

Research ArticleResearch on the Prediction of theWater Demand of ConstructionEngineering Based on the BP Neural Network

Hao Peng 1 Han Wu 2 and Junwu Wang 2

1School of Architectural Engineering Xinyang Vocational and Technical College Xinyang 464000 China2School of Civil Engineering and Architecture Wuhan University of Technology Wuhan 430070 China

Correspondence should be addressed to Han Wu wuhan20170620163com

Received 8 July 2020 Revised 15 August 2020 Accepted 13 September 2020 Published 1 November 2020

Academic Editor Tayfun Dede

Copyright copy 2020 Hao Peng 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

e scientific and effective prediction of the water consumption of construction engineering is of great significance to themanagement of construction costs To address the large water consumption and high uncertainty of water demand in projectconstruction a prediction model based on the back propagation (BP) neural network improved by particle swarm optimization(PSO) was proposed in the present work To reduce the complexity of redundant input variables this model determined the maininfluencing factors of water demand by grey relational analysis e BP neural network optimized by PSO was used to obtain thepredicted value of the output interval which effectively solved the shortcomings of the BP neural network model including itsslow convergence speed and easy to fall into local optimum problems In addition the water consumption interval data of theTaiyangchen Project located in Xinyang Henan Province China were simulated According to the results of the case study therewere four main factors that affected the construction water consumption of the Taiyangchen Project namely the intraday amountof pouring concrete the intraday weather the number of workers and the intraday amount of wood usede predicted data werebasically consistent with the actual data the relative error was less than 5 and the average error was only 266 However theerrors of the BP neural network model the BP neural network improved by genetic algorithm and the pluralistic return werelarger ree conventional error analysis tools in machine learning (the coefficient of determination the root mean squared errorand the mean absolute error) also highlight the feasibility and advancement of the proposed method

1 Introduction

e cost management of construction engineering is acomplex problem and different cost management strategiesshould be carried out according to the diverse characteristicsof construction materials [1] e cost management ofconstruction water has the following characteristics (1) eunit price of water is low and almost constanterefore theessence of cost analysis related to construction water is toanalyze the construction water demand (2) e totalamount of water used for construction is huge and ensuringthe stability of the water supply during construction istherefore of great significance to the smooth progress ofconstruction [2] In addition although the cost of con-struction water accounts for a small proportion of the totalcost of construction projects water plays a major role in the

construction process [3] e scientific and effective pre-diction of construction water consumption can not only beused to calculate the cost of construction water scientificallyand effectively but can also ensure the stability of the watersupply during construction as much as possible which isalso of great significance to the smooth progress ofconstruction

However the prediction of construction water con-sumption is complex Almost all construction operationsrequire water Operations such as on-site concrete con-struction and formwork construction are characterized byhigh water consumption Moreover construction engi-neering has complex stages and the water consumption indifferent construction stages is very different

e traditional methods for the prediction of industrialwater consumption include parametric statistics and

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8868817 11 pageshttpsdoiorg10115520208868817

deterministic models which have usually been incorporatedinto models for engineering calculation or physical analysisafter quantifying the factors that affect construction waterconsumption He and Tao [4] established a coupled greysystem and multivariate regression model to predict waterconsumption in Wuhan which was marked by a clearconcept and simple structure Via the power functionmodelthe linear function model the logarithmic function modeland the parabolic function model Zhang et al [5] fitted thecurves of water consumption in China in 2015 2020 and2030 e results showed that the correlation coefficient ofthe parabolic curve fitting was the largest the average ab-solute percentage error was the smallest and the fitting effectwas the best Buck et al [6] used a statistical samplingmethod to predict residential water consumption in Cal-ifornia Nevertheless these research methods were time-consuming and prone to predict errors because they as-sumed that the relationship between independent and de-pendent variables was a simple linear process Howeverregarding water consumption in construction engineeringthe interaction of various variables constitutes a large andcompound system with continuous and nonlinear changesA simplified model would affect the accuracy of the analysisresults thereby resulting in the prediction accuracy of waterconsumption in construction engineering being unable tomeet the needs of engineering practice and posing a sub-stantial threat to the smooth progress of engineering proj-ects In addition traditional water demand forecastingmethods need a large amount of complete statistical data toobtain consistent research results However hefty amountsof complete statistical data are difficult to obtain on con-struction sites

In recent years the emergence of artificial intelligencealgorithms such as artificial neural networks (ANNs) hasprovided new ideas for conducting the real-time predictionof the complex system of the water demand of constructionprojects [7] e ANN method has a good self-adaptivelearning ability and nonlinear mapping ability and is able tofully utilize the potential laws of input data thereby dem-onstrating significant advantages for the research andanalysis of complex systems with multifactor couplingWhen an ANN is applied to the water demand prediction ofbuilding engineering construction the model solves thenonlinear problem of water demand prediction by simu-lating the structural characteristics and action mechanism ofbiological neurons and uses the limited data measured in thefield instead of a large amount of complete statistical data topredict the water demand by using the data-driven methodAt present relevant scholars have carried out research onwater demand forecasting and have obtained rich researchresults

Donkor et al [8] summarized the research results relatedto urban water demand forecasting and pointed out thatscientific and effective forecasting variables are the key tosuccessfully forecasting urban water demand ey alsopointed out that the soft computing method yielded valuableresearch results in the short-term forecasting of water de-mand Piasecki et al [9] compared the ANN and themultiplelinear regression (MLR) method and a case study showed

that the ANNmethod was superior toMLR Zhang et al [10]used the main influencing factors of the predicted dailywater consumption as the input and the predicted dailywater consumption as the output after noise reduction Inthis work the multiscale chaotic genetic algorithm which ischaracterized by a strong global searching ability and fastsearching speed was utilized to optimize the parameters of aleast-squares support vector machine By using the ANNmethod Santos and Pereira [11] predicted the urban waterdemand of Satildeo Paulo Brazil e research indicated that theANN model could make accurate predictions with a largeamount of data and it was marked by the best performanceand a small error In addition Santos considered the in-fluences of weather variables on regional urban waterconsumption At present the application of artificial in-telligence prediction methods to water consumption pre-diction mainly includes the following two ideas amultiparameter prediction model and a time series-basedmodel Research on the prediction of drinking water de-mand in Portugal has shown that the univariate time seriesmodel based on historical data is useful and can be combinedwith other prediction methods to reduce errors [12] epreviously mentioned research has demonstrated that softcomputing algorithms such as ANNs can better deal withthe nonlinear problems in water resource demand man-agement erefore the complex and nonlinear mappingbetween the factors that affect water resource demand andconstruction water resource demand can be identified byANNs

At present the back propagation (BP) neural network isthemost commonly used neural network [13]When appliedto complex system analysis the traditional BP neural net-work might contain the following shortcomings (1) etraditional BP neural network is an optimization method oflocal search and it can easily fall into the local extremume weights can easily converge to local minima which leadsto the failure of network training [14] Furthermore the BPneural network is highly sensitive to initial network weightsWhen the network is initialized with different weights ittends to converge to different local minima [15] (2) estructure of the BP neural network can only be selected byexperience and there is no unified and complete theoreticalguidance for the selection of a BP neural network structureIf the selected network structure is too large the trainingefficiency will not be high and a fitting phenomenon mayoccur [16] resulting in low network performance and re-duced fault tolerance If the selection is too small thenetwork may not converge [17] Based on the precedinganalysis the traditional BP neural network should bestrengthened to develop a high-precision model

Similar to other metaheuristic algorithms such as thegenetic algorithm (GA) particle swarm optimization (PSO)is a population-based optimization tool that searches for theoptimal solution by updating generations PSO has noevolutionary operators such as crossover or mutationerefore the advantages of PSO are its very simple conceptlow calculation cost and few parameters that require ad-justment [18] In the fields of bottom hole pressure pre-diction ground vibration prediction [19] and asphaltene

2 Advances in Civil Engineering

precipitation prediction [20] PSO has been applied to op-timize the initial weights and thresholds of the BP neuralnetwork which results in higher accuracy

In addition most of the existing research results relatedto water demand forecasting have been aimed at large-scaleareas such as cities [11ndash14] To the best of the authorsrsquoknowledge research on the water demand forecasting forconstruction projects has not yet been reported

Hence in this paper a prediction model of the waterconsumption of construction projects was established basedon grey relational analysis and the BP neural network im-proved by PSO e main contributions of this paper are asfollows (1) Previous relevant research has primarily focusedon the water demand prediction of large-scale areas such ascities However the present study focused on the waterdemand prediction of construction projects in the con-struction stage and presented a detailed case analysis of theconstruction water of the Taiyangchen Project in XinyangCity Henan Province China is provided new insight forwater management in construction engineering (2) In thispaper the grey relational analysis method was adopted toidentify the key factors that affect the construction waterconsumption of building engineering and to reduce theinput variables of the BP model By setting the threshold ofthe grey relational degree it was determined that the keyfactors that affected the water consumption in theTaiyangchen Project were the intraday amount of pouringconcrete the intraday weather the number of workers andthe intraday amount of wood used (3) In view of theshortcomings of the BP neural network model such as itsslow convergence speed and easy to fall into local optimumPSO which is characterized by a fast convergence speed andeasy realization was adopted to optimize the initial weightsand thresholds of the BP neural network which effectivelysolved these problems Additionally the error analysis in thecase study demonstrated that the calculation results of theBP neural network improved by PSO achieved higher ac-curacy than the classical BP neural network model the BPneural network improved by GA and the pluralistic return

e remaining chapters of this paper are arranged asfollows Section 2 presents the materials andmethods and thefundamental factor identification method based on grey re-lational analysis and the BP neural network optimized by PSOare constructed in detail to build a water demand predictionmodel for construction projects Section 3 presents the resultsand discussion and makes a detailed case analysis of theconstruction water of the Taiyangchen Project in XinyangCity Henan Province China ree common error analysistools in machine learning are employed in this section tocompare the computational accuracy of different models andthe influence of the topological structure of the BP networkmodel on the calculation results is discussed Section 4presents the conclusion which summarizes the research re-sults of this paper and indicates future research directions

2 Materials and Methods

21 Identification of Key Factors Based on Grey RelationalAnalysis Grey system theory is a systematic scientific theory

put forward by Professor Deng Julong a famous Chinesescholar Grey relational analysis is a quantitative descriptionand comparison method of system development andchanging situations Its basic concept is tantamount to judgewhether factors are closely related by the geometric simi-larity of reference data columns and several comparison datacolumns which reflect the correlation degree betweencurves In the fields of risk assessment and prediction re-lational analysis can determine the weight of each influ-encing factor by comparing the compactness of each indexseries with the benchmark series [21]

e grey correlation method is in a position to analyzethe development trend of a system [22] is method canextract the factors that have great influences on the systemindex in a system with poor information and small samplesGrey relational analysis can overcome the problems of thecalculation amount being too large the samples not obeyinga certain probability distribution and the calculationshaving different quantitative and directional results

e steps for the use of grey relational analysis to find themain factors that affect water consumption in constructionprojects are reproduced below

Step 1 Raw data processingIn this paper the interval-valued processing method is

used to process the original data of construction water andits influencing factors [23]

Step 2 Calculate the grey correlation coefficiente degree of correlation can reflect the shape of the

sequence and the coefficient of the grey correlation of waterused for building engineering construction is

θmn ρΔnmax + Δnmin

ρΔnmax + Δmn(i) (1)

where Δnmax and Δnmin are the maximum and minimumvalues in the water consumption data series of constructionprojects respectively and ρ is a resolution function thefunction of which is to improve the significance of thedifference between correlation coefficients Generally asatisfactory resolution result can be obtained when the valueis 05 [24] Moreover m is the reference sequence n is thecomparison sequence s is the sequence length and Δmn(i) isthe absolute difference between the reference sequence m

and point i of the comparison sequence n

Step 3 Calculate the correlation degreee correlation degree calculation formula is as follows

[25]

λ xm yn( 1113857 1s

1113874 1113875 1113944

s

i1θmn(i) (2)

where s is the length of the reference sequence θmn(i) is thecorrelation coefficient between the reference sequencem andthe i value of the comparison sequence n and λ(xm yn) isthe correlation degree between the reference sequence m onthe x curve and the comparison sequence n on the y curve

Advances in Civil Engineering 3

Step 4 Rank analysis of correlation degreee correlation degree of each factor is sorted depending

on the numerical value and describes the relative changes ofthe reference sequence and comparison sequence Generallyif the correlation degree between two factors is large thechanges of construction water and the influencing factors areessentially the same [25 26]

22 Prediction Model of Water Demand Based on the BPNeural Network Optimized by PSO

221 Introduction of the BP Neural Network e BP neuralnetwork is an artificial neural network model with self-learning and self-adapting abilities and composes of twoparts namely the forward propagation of input data and thebackward propagation of the error value e standardneural network topology consists of input layer nodeshidden layer nodes and output layer nodes that are con-nected and the nodes in the same layer do not interact witheach other In this algorithm n samples X (x1 x2 xn)

are taken as the input nodes of the neural network and theexpected result Y (y1 y2 yn) is taken as the corre-sponding output node e error value can be obtained bycomparing the predicted result with the actual result and thefitness function is employed to measure whether the errorvalue is consistent For the calculation results that do notmeet the requirements the network will use the gradientdescent method to carry out error back propagation in theweight vector space for which the correction amount of eachweight of the hidden layer and the output layer [27] is shownin equation (3)e error reaches the expected value throughrepeated iteration thus completing the establishment of theBP neural network calculation model

F(ψω θ r) 1113944

N1

t11113944

M

s1yt(s) minus 1113954yt(s)1113858 1113859⎛⎝ ⎞⎠

minus (12)

(3)

where ψ is the error value in the BP neural network ω θ andr are the input layer hidden layer and output layer of theneural network respectively N1 and M are the weight andthreshold number of nodes respectively yt(s) is the ex-pected output of the neural network 1113954yt(s) is the actualoutput t is a node that needs to optimize the connectionweight and s is a node that needs to optimize the threshold

222 Optimization of the BP Neural Network by PSOPSO was first proposed by Eberhart and Kennedy in 1995[28] Its basic concept originated from the study of birdsrsquoforaging behavior and PSO was inspired by this biologicalpopulation behavior to solve the optimization problem InPSO each particle represents a solution of the problem andcorresponds to a fitness value Particle velocity determinesthe distance and direction of particle motion and is dy-namically adjusted by the motion of itself and other par-ticles thus realizing the optimization process of individualsin a solvable space

In the process of adopting PSO the error between thecapacity output and the expected capacity output obtained

by the forward learning of the BP neural network is firstinitialized by the PSO to determine the individual extre-mum and group extremum ie to find the weights andthresholds in the BP neural network e speed and po-sition are then updated as are the original individual ex-tremum and group extremum after calculating the fitnessFinally the obtained optimal neural network weights andthresholds are sent to the BP neural network for verification[29]

Supposing that the particle swarm X (X1 X2 Xn)

is composed of n particles and the dimension of the particlesis usually Q ere are n particles in the swarm each particleis Q-dimensional and the swarm composed of n particlessearches Q dimensions Every particle is expressed asXi (Xi1 Xi2 XiQ) which represents the position ofthe particle i in the Q-dimensional search space and also apotential solution to the problem According to the objectivefunction the fitness value corresponding to each particleposition Xi can be calculated [30] e velocity corre-sponding to each particle can be expressed asV (Vi1 Vi2 ViQ) and each particle should considertwo factors when searching

(1) e historical optimal value Pi Pi (Pi1

Pi2 PiQ) i 1 2 n(2) e optimal value Pg Pg (Pg1 Pg2 PgQ)

found by all particles It is worth noting that there isonly one Pg here

During each iteration particles update their own velocityand position via the individual extremum and global ex-tremum and the update formula of position velocity opti-mized by the PSO is as follows [31]

vk+1id ωv

kid + c1r p

kid minus x

kid1113872 1113873 + c2r p

kgd minus x

kid1113872 1113873

xk+1id x

kid + v

k+1id

(4)

where ω is the inertia weight d 1 2 D i 12 n k

is the current iteration number vid is the velocity of particlesc1 is the particle weight coefficient that tracks its own his-torical optimum value which represents the particlersquos owncognition and is called the acceleration factor c2 is theweight coefficient of the optimal value of the particletracking group which represents the cognition of particles tothe whole group knowledge and is called the accelerationfactor and r is a random number that is uniformly dis-tributed in the interval [0 1] In addition error analysisshould be carried out on the results

Based on the preceding analysis the calculation flowchart of the proposed model is presented in Figure 1

It can be observed in Figure 1 that via the analysis of thedata the historical data and several factors that have thegreatest influences on the water demand of building engi-neering construction are input into the neural networkAfter the neurons in each layer act on the influencing factorsthey generate the output e weights and thresholds of theneural network are optimized by PSO and the fitness value isobtained to determine the individual with the best fitnessAfter taking the output error as the objective function and


correcting the error to meet the requirements the trainedneural network can make predictions

3 Results and Discussion

31 Selection of Influencing Factors ere are many factorsthat affect water consumption in construction areas [32]such as the number of workers (R1) [33] the intradayamount of pouring concrete (R2) [34] the highest tem-perature (R3) [35] the intraday weather (R4) [35] the in-traday amount of wood used (R5) [34] and the intradayamount of steel used (R6) [34]

In this paper the data of the Taiyangchen Project in Mayand June 2019 were collected in units of days e data of thewater use of the Taiyangchen Project was processed by greyrelational analysis and the correlation coefficient and degreewere obtained By comparing the sizes the main factors thataffected the water use of the Taiyangchen Project weredetermined and then used as input layers and input into theneural network to predict the water use of the project

e daily water consumption of the Taiyangchen Projectin Xinyang City Henan Province China is the researchobject in this work e project consists of nine residentialbuildings with frame-shear wall structures all of which have18 floors above ground and 1 floor underground e heightof each building is 5290m and the total construction area ofeach building is 1344968m2

e quantification of the evaluation factors is an im-portant step in the selection and treatment of influencingfactors e number of workers (R1) the intraday amount ofpouring concrete (R2) the highest temperature (R3) the

intraday amount of wood used (R5) and the intradayamount of steel used (R6) were all determined by actual fieldinvestigation and statisticse score of the intraday weather(R4) is divided into four situations namely sunny (09)cloudy (06) light rain (03) and heavy rain (0)e values ofeach factor are presented in Table 1 Due to the limitations ofthe layout only some samples are reported in Table 1

e correlation coefficients of the influencing factorswere calculated by equations (1) and (2) and the calculationresults are shown in Table 2

It can be seen from Table 2 that the correlation degree ofthe influencing factors from the greatest to the least is asfollows the intraday amount of pouring concrete (R2)gt theintraday weather (R4)gt the number of workers (R1)gt theintraday amount of wood used (R5)gt the highest temper-ature (R3)gt the intraday amount of steel used (R6) isorder can be explained by the content and characteristics ofthe construction work Concrete pouring is a typical wetoperation that requires a lot of water e weather is anothersignificant factor that affects construction When it rainsmost of the work on the construction site will stop and theconstruction water consumption will decrease significantlye more workers there are the more water will be used forconstruction and living Timber for construction needs to bewatered and wetted to ensure that its moisture content isnear the optimum which also requires a large amount ofwater [36]

When the correlation degree is less than 06 the twosequences are considered to be independent and if thecorrelation degree is greater than 08 the two sequences havea good correlation A correlation value between 06 and 08 isbeneficial [35] In Table 2 the factors with a correlation degreegreater than 08 include the intraday amount of pouringconcrete (R2) the intraday weather (R4) the number ofworkers (R1) and the intraday amount of wood used (R5) andthese are therefore the key factors that affect the waterconsumption of building engineering construction

32 Result of Water Demand Forecasting In this work theconstruction water consumption of the Taiyangchen Projectin Xinyang City Henan Province China was taken as theresearch object and the data used were sourced from themonitoring data of the municipal pipe network waterconsumption of the Taiyangchen Project and the on-siteconstruction log

After the evaluation factor is quantified the difference ofits numerical dimension slows the convergence speed of thealgorithm and affects the accuracy of the model Because allindicators are benefit-based the data are normalized asfollows [37]

xlowastij

xij minus min xj1113872 1113873

max xj1113872 1113873 minus min xj1113872 1113873 (5)

where xlowastij indicates the value of the evaluation index afterstandardization max(xj) represents the maximum value ofindicator j and max(xj) represents the minimum value ofindicator j

Start

Input and preprocess the data of water demand of construction engineering

Input possible influencing factors of water demand

Determine the main factors affecting the water use in the

construction engineering in grey relational analysis

Determine the topological structure weight and threshold length of the BP neural network

Initialize parameters of the BPneural network

Initial population of neuron weight and threshold

Prediction results of water demand simulation

Meet terminal condition

Update weights and thresholds

Calculate error

Get the initial weight and threshold of the best neuron

Whether optimization

objectives are achieved

Calculate fitness of each population

End

Yes

Yes

No

No

Figure 1 Flow chart of the prediction model of water demand


According to grey relational analysis four main influ-encing factors of water demand in the construction intervalof building engineering were obtained e number of inputnodes is m 4 and the number of hidden layer nodes isn 2m + 1 9 so the structure of the BP neural network is4-9-1 [38] as illustrated in Figure 2 It is worth noting that avariety of BP neural network topologies were constructed inthis work and the calculation results are exhibited in Table 3

In the process of model formation using the BP neuralnetwork the available data should be divided into twogroups which respectively represent training and testingsets e data of the training set are used for training whilethe data of the testing set are used for checking the networkMany researchers choose data in the respective proportionsof 90 and 10 80 and 20 or 70 and 30 [39] In thisstudy the training set was data of the Taiyangchen Projectfrom May 1 to June 20 2018 including a total of 51 days ofdata e testing set was the data of the Taiyangchen Projectfrom June 21 to June 30 2018 including a total of 10 days ofdata e ratio of training set data to testing set data wastherefore 8361ndash1639

To achieve a better prediction effect the best parametersof the BP neural network and the PSOwere set including thefollowing the number of training iterations was 1000 thelearning rate was 01 and the training target was 0001 ecalculation parameters [40] of PSO included 1000 iterationsa population size of 50 the local learning factor c1 149445and the global learning factor c2 149445 e maximumerror of iteration termination was 000001

e convergence curve obtained after calculation ispresented in Figure 3 In a case analysis when the number ofiterations reaches about 500 the requirements are met Inthis study the population number and the maximumnumber of iterations were set to relatively large values toensure that the model could calculate more complexproblems Figure 3 shows the convergence curve after 1000iterations

Following the optimization calculation process of PSOthe error between the 498th iteration and 499th iteration was

greater than the minimum acceptable precision (000001)while the error between the 499th iteration and 500th it-eration was less than 000001 After that the errors of thecalculation results were all less than 000001 e calculationwas arrested at the 1000th iteration with a very small errorese findings indicate that the PSO found the optimalneural network weights and thresholds at the 500th iterationwhich is illustrated by both Figure 3 and Table 4 In additionit can be qualitatively judged from Figure 3 that the GA

Table 2 Correlation coefficients of influencing factors

Factor R1 R2 R3 R4 R5 R6

Correlation coefficient 08454 08927 05150 08589 08117 04625Mark Reserved Reserved Deleted Reserved Reserved Deleted

Correction of weight and threshold

R1

R2

R4

R5

Predictedquantity

Trainingquantity

Output layerHidden layer

hellip

Input layer

Figure 2 Topological structure diagram of the BP neural network

Table 3 Comparison of three error representations

Error representations R2 RMSE MAEBP 07921 7312692 454554PSO-BP 09959 960900 157467GA-BP 09853 1301673 203815Pluralistic return 03767 19381279 730130

Table 1 Numerical value of each factor and actual water consumption

No R1 R2 R3 R4 R5 R6 Actual water consumptionUnit mdash m3 degC mdash m3 t t1 May 228 31000 28 03 1300 7346 8361712 May 198 105000 24 06 5710 7267 12003633 May 219 120000 26 06 910 8307 14283504 May 255 73000 28 06 310 16573 567857⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮27 June 229 5000 36 03 3610 8441 75287328 June 200 15000 35 03 350 4468 75839429 June 215 78000 32 06 1830 3638 160137130 June 219 25000 32 03 490 10760 702361


converged between 700 and 800 generations e PSOconverged faster than GA is is an advantage of PSOcompared with GA

e prediction results obtained by using the proposedcalculationmodel are reported in Table 5 In addition the BPmodel the pluralistic return and the BP model improved byGA were also used to predict the results e parameters ofGA were set as follows population size was 100 endingevolution algebra was 1000 crossover probability was 05and mutation probability was 0001

In addition this paper used the standard calculationmethod which was commonly used in engineering practiceand multivariate linear return method to calculate thequantity used in the construction site

According to Chinese national standard (the Code forFire Protection Design of Buildings GB 50016-2014) thecalculation process of construction site water consumptionis as follows

(1) Water consumption for site operation

q1 K1 1113944Q1 middot N1

T1 middot t1113888 1113889 middot

K2

8 times 36001113874 1113875 (6)

where q1 (Ls) is the water consumption of con-struction site K1 is the unexpected constructionwater consumption coefficient Q1 (Ls) is the annualengineering quantity N1 is the construction waterquota (Lm3) T1 (days) is the annual effectiveworking day t (hours) is the number of working

shifts per day and K2 is the imbalance coefficient ofwater consumptionAccording to the field investigation K1 was 110 T1was 300 and t was 8 in this projecte calculated Q1and N1 were brought into equation (6) and the q1was 052 Ls

(2) Water for construction machinery

q2 K1 1113944 Q2 middot N2 middotK3

8 times 36001113874 1113875 (7)

where q2 is the water consumption of machinery K1is the unexpected construction water consumptioncoefficient Q2 is the same number of machinery N2is the water quota of construction machinery ma-chine-team and K3 is the water imbalance coeffi-cient of construction machineryAccording to field investigation K3 was 15According to the construction site statistics Q2 andN2 were taken into equation (8) and q2 (004 Ls)could be calculated

(3) Domestic water consumption on the constructionsite

q3 P1 middot N3 middot K4

t times 8 times 3600 (8)

where q3 is the domestic water consumption of theconstruction site P1 is the domestic water

Table 4 Precision level and calculation termination of PSO at the 1000th iteration

Iteration (n) Fitness (n minus 1) Fitness (n) Fitness (n) minus Fitness (n minus 1) Result498 1488344 1488344 0lt 000001 Continue499 1488344 1455848356 0032495395gt 00001 Continue500 1455848356 1455848356 0lt 00001 Continue1000 1455848 1455848 0lt 00001 Stop

50

45

40

35

30

25

20

15

10Fi

tnes

s

0 200 400 600 800 1000Number of iterations

PSO-BPGA-BP

Figure 3 e convergence curve of PSO and GA


consumption of the construction site N3 is the waterquota of the construction site K4 is the imbalancecoefficient of the construction site and t is thenumber of working shifts per dayAccording to the field investigation K4 was 13 and t

was 1 With equation (8) q3 was 208 Ls(4) Domestic water consumption in living quarters


24 times 3600 (9)

where q4 is the domestic water consumption in theliving area P2 is the number of residents in the livingarea N4 is the daily domestic water quota in theliving area and K5 is the unbalanced coefficient ofwater consumption in the living areaAfter field calculation P2 was 150 and K5 was 2Bringing complex N4 into equation (9) q4 was 08 Ls

(5) Total water consumption Q

Q q1 + q2 + q3 + q4 (10)

Bring q1 q2 q3 and q4 into equation (10) and the Q is344 Ls It is worth mentioning that the fire water was notconsidered in our calculation here because the fire water wasonly used in the fire

Considering that the daily construction time is 8 hoursthe water consumption calculated according to Chineseconstruction codes was 99072m3 Comparing the data inTables 1 and 5 the water consumption calculated by Chineseconstruction codes was often less than the actual waterdemand is situation would easily lead to water shortageand shutdown in the construction site which was one of theimportant backgrounds of the research work in this paperIn addition under the constraints of limited time andtimeliness of data collection it took a long time to investigatethe values of more than a dozen parameters by adoptingChinese national calculation standard which had the dis-advantage of low calculation efficiency

Using the return analysis function of Excel 2016 Soft-ware the expression of multivariate return was calculated asfollows

Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)

Bring the data of the test set into equation (11) and theprediction result is as shown in Table 5

33 Analysis and Discussion of Calculation Results Erroranalysis was conducted to verify the accuracy of this algo-rithm and the relative error value was obtained according tothe predicted and actual values e formula is as follows

E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

where E is the relative error cp is the predicted value and ca

is the true valueAccording to equation (12) the relative error value can

be calculated by the values present in Table 6 Comparedwith the actual water consumption the error of the calcu-lations of the proposed method was less than 5 and theaverage error was only 247 e average error of the GA-BP model was 406 and the maximum error was 836 Incontrast the error of the calculations of the BP model waslarger the maximum error was 4656 and the averageerror was 2239 e maximum error of the results cal-culated by multivariate return analysis was 7547 and theaverage error was 4161 is proves that the proposedmethod is effective and advanced in predicting the waterdemand of construction projects

e four calculation results of PSO-BP with the biggesterror appeared in the last four timesat was to say the firstsix predictions were very accurate and the last four pre-dictions had large errors

To better compare the prediction results of the twomethods and highlight the advantages of the proposed PSO-BP neural network model three common error analysistools in machine learning were used to compare severalalgorithms

Table 5 Prediction results of different models

Time Actual water consumption BP PSO-BP GA-BP Pluralistic return21 June 143037 139756 144650 144950 9672922 June 86032 60591 85748 88310 5544323 June 61036 70229 58146 63388 5717324 June 60413 87612 61522 55752 5166125 June 156054 136786 152854 161999 4630626 June 191000 231552 188837 187697 4685627 June 75287 61875 78622 77986 4855328 June 75839 72245 76390 74623 4207129 June 160137 140933 166854 171987 5511430 June 70236 102935 67301 65537 45015


e determination coefficient (R2) indicates the degreeof correlation between the measured value and the predictedvaluee closer R2 is to 1 the higher the correlation On thecontrary the closer R2 is to 0 the lower the correlation Aslisted in Table 3 the R2 values of the BP model the PSO-BPmodel the GA-PSO model and the pluralistic return werefound to be 07921 09959 09853 and 03767 respectivelythereby demonstrating that the PSO-BP model is better thanthe BP model the GA-BP model and the pluralistic returne root mean square error (RMSE) is an important stan-dard by which to measure the prediction results of machinelearning models e RMSE of the PSO-BP model was960900 which is notably less than the BP model the GA-BPmodel and the pluralistic return e mean absolute error(MAE) is the average of absolute errors which can betterreflect the actual situation of predicted value errors eRMSE of the PSO-BP model was 157467 which is notablyless than the BP model GA-PSO and pluralistic return ecomparative analysis of calculation errors indicates that thePSO-BP model achieved better prediction accuracy andoptimization performance is excellent calculation resultis also consistent with previous benchmark test results [41]

e number of hidden layers is another important factorthat affects the accuracy of the BP neural network [42]erefore the influences of the topological structures ofdifferent network models on the prediction results were alsoanalyzed [38]

Referring to the classical research results in related fields[43] the topological structures of six different networkmodels were designed and the related calculation results areshown in Table 7

It can be seen fromTable 3 that the calculation accuracy ofthe PSO-BP neural network model was significantly higherthan that of the BP model or GA-BP model when the samenetwork model topology was adopted Regardless of the to-pology of the network model the average error of the cal-culation results of the PSO-BP neural networkmodel was verysmall e calculation results demonstrate the effectivenessand advancement of the PSO-BP neural network model inforecasting the water demand of construction projects Inaddition overfitting or underfitting is a qualitative phe-nomenon that occurs in artificial neural network algorithmsand there is no tool with which to quantitatively describethem Referring to the details of previous research studies[41 44] it is believed that the prediction accuracy of the PSO-

BP neural network model is higher than the calculation ac-curacy of the BP neural network model which also dem-onstrates that the proposed model reduces the phenomenonof overfitting or underfitting After overfitting or underfittingthe prediction accuracy is often inadequate [45]

Regarding the PSO-BP neural network model with theincrease of the number of hidden layers the average errorwas considered to be further reduced ere are two hiddenlayers and the model with the 4-9-5-1 network structureachieved the highest calculation accuracy e accuracy ofcalculation with a hidden layer model was 247 which wasthe lowest in the PSO-BP neural network model and can alsomeet the needs of engineering practice [46]

is paper discussed the influence of the number ofinput variables on the calculation results e analysis hereadopted the calculation model of PSO-BP and the numberof hidden layer was 1e average error and maximum errorare shown in Table 8

When there were three input variables the calculationerror of the PSO-BP model was obviously larger than that offour input variables When the input variables were increasedto 5 or 6 the calculation accuracy was not significantly im-proved Considering the availability of construction site datathe field investigation time would increase significantly ifthere were 5 or 6 input variables erefore it could beconsidered that the four input variables obtained by greyrelational analysis in this paper were reasonable

4 Conclusions

e purpose of this research was to use the BP neuralnetwork to accurately predict the water consumption of


Time BP () PSO-BP () GA-BP () Pluralisticreturn ()

21 June 229 113 132 323822 June 2610 033 258 355523 June 1506 073 371 63324 June 4502 184 836 144925 June 1235 205 367 703326 June 2123 113 176 754727 June 1782 443 346 355128 June 2553 474 163 445329 June 1199 419 689 655830 June 4656 418 717 3591

Table 7 Calculation results of topological structures of differentnetwork models

Model Number of hidden layers Number of hiddenlayer nodes

Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231

Table 8 Calculation results with different numbers of inputvariables

Input variables Average error () Maximum error ()r1 r2 r4 and r5 406 474r1 r2 and r4 743 1015r1 r2 and r5 955 1428r1 r4 and r5 890 1569r2 r4 and r5 705 1273r1 r2 r3 r4 and r5 367 421r1 r2 r3 r4 r5 and r6 331 396


construction projects First via the use of the data it wasfound that there are four factors that affect the waterconsumption in construction projects namely the intradayamount of pouring concrete the intraday weather thenumber of workers and the intraday amount of wood useden after taking these four key factors as the input layerand using the optimal neural network weights andthresholds obtained by PSO a predictive model of con-struction water consumption based on the neural networkmodel was constructed Finally a case study of the con-struction water consumption of the Taiyangchen Project inXinyang City Henan Province China revealed that com-pared with the actual water consumption the error calcu-lated by the proposed method was less than 5 and theaverage error was only 247 In addition the three com-mon error analysis tools used in machine learning (thecoefficient of determination the root mean squared errorand the mean absolute error) all highlighted that the cal-culation accuracy of the proposed method was significantlyhigher than the BP algorithm the GA-BP and the pluralisticreturn ere were two hidden layers in the PSO-BP neuralnetwork model and the model with the 4-9-5-1 networkstructure was found to have the highest calculation accuracye calculation accuracy of the model with a hidden layerand a network structure of 4-9-1 was 247 which can alsomeet the needs of engineering practice e model proposedin this paper can effectively predict the water consumptionof building engineering construction and determine ab-normal water in a timely manner to rationally dispatch thewater supply and ultimately achieve the purpose of savingwater In future research the sample set can be expandedthe learning effect of the model can be improved and a moreperfect predictionmodel of construction water consumptioncan be trained

Data Availability

e case analysis data used to support the findings of thisstudy are available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is study was supported by the Science and TechnologyProject of Wuhan Urban and Rural Construction BureauChina (201943)

References

[1] J-S Chou ldquoCost simulation in an item-based project in-volving construction engineering and managementrdquo Inter-national Journal of Project Management vol 29 no 6pp 706ndash717 2011

[2] I Ghalehkhondabi E Ardjmand W A Young et al ldquoWaterdemand forecasting review of soft computing methodsrdquo

Environmental Monitoring and Assessment vol 189 no 7Article ID 313 2017

[3] P W Jayawickrama and S Rajagopalan ldquoAlternative watersources in Earthwork constructionrdquo Transportation ResearchRecord vol 2004 pp 88ndash96 2007

[4] F He and T Tao ldquoAn improved coupling model of grey-system and multivariate linear regression for water con-sumption forecastingrdquo Polish Journal of EnvironmentalStudies vol 23 no 4 pp 1165ndash1174 2014

[5] X Zhang M Yue Y Yao and H Li ldquoRegional annual waterconsumption forecast modelrdquo Desalination and WaterTreatment vol 114 pp 51ndash60 2018

[6] S Buck M Auffhammer H Soldati et al ldquoForecastingresidential water consumption in California rethinkingmodel selectionrdquo Water Resources Research vol 56 no 12020

[7] X Wu V Kumar J Ghosh et al ldquoTop 10 algorithms in dataminingrdquo Knowledge and Information Systems vol 14 no 1pp 1ndash37 2008

[8] E A Donkor T A Mazzuchi R Soyer and J Alan RobersonldquoUrban water demand forecasting review of methods andmodelsrdquo Journal of Water Resources Planning and Manage-ment vol 140 no 2 pp 146ndash159 2014

[9] A Piasecki J Jurasz and B Kazmierczak ldquoForecasting dailywater consumption a case study in town Polandrdquo PeriodicaPolytechnica-Civil Engineering vol 62 no 3 pp 818ndash8242018

[10] W Zhang Q Yang M Kumar and Y Mao ldquoApplication ofimproved least squares support vector machine in the forecastof daily water consumptionrdquo Wireless Personal Communi-cations vol 102 no 4 pp 3589ndash3602 2018

[11] C C does Santos and A J Pereira ldquoWater demand fore-casting model for the metropolitan area of Satildeo Paulo BrazilrdquoWater Resources Management vol 28 no 13 pp 4401ndash44142014

[12] A Sardinha-Lourenccedilo A Andrade-Campos A Antunes andM S Oliveira ldquoIncreased performance in the short-termwater demand forecasting through the use of a paralleladaptive weighting strategyrdquo Journal of Hydrology vol 558pp 392ndash404 2018

[13] I A Basheer and M Hajmeer ldquoArtificial neural networksfundamentals computing design and applicationrdquo Journal ofMicrobiological Methods vol 43 no 1 pp 3ndash31 2000

[14] Z Zhao Q Xu and M Jia ldquoImproved shuffled frog leapingalgorithm-based BP neural network and its application inbearing early fault diagnosisrdquo Neural Computing and Ap-plications vol 27 no 2 pp 375ndash385 2016

[15] ZMa X Song RWan L Gao and D Jiang ldquoArtificial neuralnetwork modeling of the water quality in intensive Litope-naeus vannamei shrimp tanksrdquo Aquaculture vol 433pp 307ndash312 2014

[16] P Bansal S Gupta S Kumar et al ldquoMLP-LOA a meta-heuristic approach to design an optimal multilayer percep-tronrdquo Soft Computing vol 23 no 23 pp 12331ndash12345 2019

[17] S Yang X Zhu L Zhang L Wang and X Wang ldquoClassi-fication and prediction of Tibetan medical syndrome based onthe improved BP neural networkrdquo IEEE Access vol 8pp 31114ndash31125 2020

[18] D T Bui N D Hoang T D Pham et al ldquoA new intelligenceapproach based on GIS-based multivariate adaptive regres-sion splines and metaheuristic optimization for predictingflash flood susceptible areas at high-frequency tropical ty-phoon areardquo Journal of Hydrology vol 575 pp 314ndash3262019


[19] D J Armahani M Hajihassani E T Mohamad et alldquoBlasting-induced flyrock and ground vibration predictionthrough an expert artificial neural network based on particleswarm optimizationrdquo Arabian Journal of Geosciences vol 7no 12 pp 5383ndash5396 2014

[20] M A Ahmadi and S R Shadizadeh ldquoNew approach forprediction of asphaltene precipitation due to natural depletionby using evolutionary algorithm conceptrdquo Fuel vol 102pp 716ndash723 2012

[21] Z Zang Y Wang and Z X Wang ldquoA grey TOPSIS methodbased on weighted relational coefficientrdquo Journal of GreySystem vol 26 no 2 pp 112ndash123 2014

[22] Z X Wang ldquoCorrelation analysis of sequences with intervalgrey numbers based on the kernel and greyness degreerdquoKybernetes vol 42 no 1-2 pp 309ndash317 2013

[23] G Deng J Qiu G Liu and K Lv ldquoEnvironmental stress levelevaluation approach based on physical model and intervalgrey association degreerdquo Chinese Journal of Aeronauticsvol 26 no 2 pp 456ndash462 2013

[24] N M Xie and S F Liu ldquoResearch on evaluations of severalgrey relational models adapt to grey relational axiomsrdquoJournal of Systems Engineering and Electronics vol 20 no 2pp 304ndash309 2009

[25] B Zhu L Yuan and S Ye ldquoExamining the multi-timescalesof European carbon market with grey relational analysis andempirical mode decompositionrdquo Physica A Statistical Me-chanics and its Applications vol 517 pp 392ndash399 2019

[26] K Zhang Y Chen and L F Wu ldquoGrey spectrum analysis ofair quality index and housing price in Handanrdquo Complexityvol 2019 Article ID 8710138 2019

[27] S M Huang ldquoProduction capacity prediction based on neuralnetwork technology in an efficient economic and manage-ment environment of oil fieldrdquo Fresenius EnvironmentalBulletin vol 29 no 4 pp 2442ndash2449 2020

[28] C A C Coello G T Pulido and M S Lechuga ldquoHandlingmultiple objectives with particle swarm optimizationrdquo IEEETransactions on Evolutionary Computation vol 8 no 3pp 256ndash279 2004

[29] C Hou X Yu Y Cao C Lai and Y Cao ldquoPrediction ofsynchronous closing time of permanent magnetic actuator forvacuum circuit breaker based on PSO-BPrdquo IEEE Transactionson Dielectrics and Electrical Insulation vol 24 no 6pp 3321ndash3326 2017

[30] Z H Zhan J Zhang Y Li et al ldquoAdaptive particle swarmoptimizationrdquo IEEE Transactions on Systems Man and Cy-bernetics Part B-Cybernetics vol 39 no 6 pp 1362ndash13812009

[31] F vandenBergh and A P Engelbrecht ldquoA cooperative ap-proach to particle swarm optimizationrdquo IEEE Transactions onEvolutionary Computation vol 8 no 3 pp 225ndash239 2004

[32] A Piasecki J Jurasz and W Marszelewski ldquoApplication ofmultilayer perceptron artificial neural networks to mid-termwater consumption forecasting - a case studyrdquo OchronaSrodowiska vol 38 no 2 pp 17ndash22 2016

[33] M E Banihabib and P Mousavi-Mirkalaei ldquoExtended linearand non-linear auto-regressive models for forecasting theurban water consumption of a fast-growing city in an aridregionrdquo Sustainable Cities and Society vol 48 Article ID101585 2019

[34] M Y Han G Q Chen J Meng X D Wu A Alsaedi andB Ahmad ldquoVirtual water accounting for a building con-struction engineering project with nine sub-projects a case inE-town Beijingrdquo Journal of Cleaner Production vol 112pp 4691ndash4700 2016

[35] L N Yang W Z Li and X Liu ldquoOn campus interval waterdemand prediction based on grey genetic BP neural networkrdquoJournal of Water Resources and Water Engineering vol 30no 3 pp 133ndash138 2019

[36] R Walker S Pavıa and M Dalton ldquoMeasurement ofmoisture content in solid brick walls using timber dowelrdquoMaterials and Structures vol 49 no 7 pp 2549ndash2561 2016

[37] D Liu J P Feng H Li et al ldquoSpatiotemporal variationanalysis of regional flood disaster resilience capability using animproved projection pursuit model based on the wind-drivenoptimization algorithmrdquo Journal of Cleaner Productionvol 241 Article ID 118406 2019

[38] W Cheng M Zhou J J Ye et al ldquoPSO-BPmodeling researchon fee rate measurement of construction project safe con-struction costrdquo China Safety Science Journal vol 26 no 5pp 146ndash151 2016

[39] G Zhang B Eddy Patuwo and M Y Hu ldquoForecasting withartificial neural networksrdquo International Journal of Fore-casting vol 14 no 1 pp 35ndash62 1998

[40] I C Trelea ldquoe particle swarm optimization algorithmconvergence analysis and parameter selectionrdquo InformationProcessing Letters vol 85 no 6 pp 317ndash325 2003

[41] H H Li Y D Lu C Zheng et al ldquoGroundwater levelprediction for the arid oasis of Northwest China based on theartificial Bee Colony algorithm and a back-propagation neuralnetwork with double hidden layersrdquo Water vol 11 no 4Article ID 860 2019

[42] A Kaveh and H Servati ldquoDesign of double layer grids usingbackpropagation neural networksrdquo Computers amp Structuresvol 79 no 17 pp 1561ndash1568 2001

[43] K M Neaupane and S H Achet ldquoUse of back propagationneural network for landslide monitoring a case study in thehigher Himalayardquo Engineering Geology vol 74 no 3-4pp 213ndash226 2004

[44] Q Shen W-m Shi X-p Yang and B-x Ye ldquoParticle swarmalgorithm trained neural network for QSAR studies of in-hibitors of platelet-derived growth factor receptor phos-phorylationrdquo European Journal of Pharmaceutical Sciencesvol 28 no 5 pp 369ndash376 2006

[45] X F Yan ldquoHybrid artificial neural network based on BP-PLSRand its application in development of soft sensorsrdquo Chemo-metrics and Intelligent Laboratory Systems vol 103 no 2pp 152ndash159 2010

[46] F Y Jiang Y L Zhao S Dong et al ldquoPrediction of submarinepipeline damage based on genetic algorithmrdquo Transactions ofOceanology and Limnology vol 3 pp 52ndash59 2019


deterministic models which have usually been incorporatedinto models for engineering calculation or physical analysisafter quantifying the factors that affect construction waterconsumption He and Tao [4] established a coupled greysystem and multivariate regression model to predict waterconsumption in Wuhan which was marked by a clearconcept and simple structure Via the power functionmodelthe linear function model the logarithmic function modeland the parabolic function model Zhang et al [5] fitted thecurves of water consumption in China in 2015 2020 and2030 e results showed that the correlation coefficient ofthe parabolic curve fitting was the largest the average ab-solute percentage error was the smallest and the fitting effectwas the best Buck et al [6] used a statistical samplingmethod to predict residential water consumption in Cal-ifornia Nevertheless these research methods were time-consuming and prone to predict errors because they as-sumed that the relationship between independent and de-pendent variables was a simple linear process Howeverregarding water consumption in construction engineeringthe interaction of various variables constitutes a large andcompound system with continuous and nonlinear changesA simplified model would affect the accuracy of the analysisresults thereby resulting in the prediction accuracy of waterconsumption in construction engineering being unable tomeet the needs of engineering practice and posing a sub-stantial threat to the smooth progress of engineering proj-ects In addition traditional water demand forecastingmethods need a large amount of complete statistical data toobtain consistent research results However hefty amountsof complete statistical data are difficult to obtain on con-struction sites

In recent years the emergence of artificial intelligencealgorithms such as artificial neural networks (ANNs) hasprovided new ideas for conducting the real-time predictionof the complex system of the water demand of constructionprojects [7] e ANN method has a good self-adaptivelearning ability and nonlinear mapping ability and is able tofully utilize the potential laws of input data thereby dem-onstrating significant advantages for the research andanalysis of complex systems with multifactor couplingWhen an ANN is applied to the water demand prediction ofbuilding engineering construction the model solves thenonlinear problem of water demand prediction by simu-lating the structural characteristics and action mechanism ofbiological neurons and uses the limited data measured in thefield instead of a large amount of complete statistical data topredict the water demand by using the data-driven methodAt present relevant scholars have carried out research onwater demand forecasting and have obtained rich researchresults

Donkor et al [8] summarized the research results relatedto urban water demand forecasting and pointed out thatscientific and effective forecasting variables are the key tosuccessfully forecasting urban water demand ey alsopointed out that the soft computing method yielded valuableresearch results in the short-term forecasting of water de-mand Piasecki et al [9] compared the ANN and themultiplelinear regression (MLR) method and a case study showed

that the ANNmethod was superior toMLR Zhang et al [10]used the main influencing factors of the predicted dailywater consumption as the input and the predicted dailywater consumption as the output after noise reduction Inthis work the multiscale chaotic genetic algorithm which ischaracterized by a strong global searching ability and fastsearching speed was utilized to optimize the parameters of aleast-squares support vector machine By using the ANNmethod Santos and Pereira [11] predicted the urban waterdemand of Satildeo Paulo Brazil e research indicated that theANN model could make accurate predictions with a largeamount of data and it was marked by the best performanceand a small error In addition Santos considered the in-fluences of weather variables on regional urban waterconsumption At present the application of artificial in-telligence prediction methods to water consumption pre-diction mainly includes the following two ideas amultiparameter prediction model and a time series-basedmodel Research on the prediction of drinking water de-mand in Portugal has shown that the univariate time seriesmodel based on historical data is useful and can be combinedwith other prediction methods to reduce errors [12] epreviously mentioned research has demonstrated that softcomputing algorithms such as ANNs can better deal withthe nonlinear problems in water resource demand man-agement erefore the complex and nonlinear mappingbetween the factors that affect water resource demand andconstruction water resource demand can be identified byANNs

At present the back propagation (BP) neural network isthemost commonly used neural network [13]When appliedto complex system analysis the traditional BP neural net-work might contain the following shortcomings (1) etraditional BP neural network is an optimization method oflocal search and it can easily fall into the local extremume weights can easily converge to local minima which leadsto the failure of network training [14] Furthermore the BPneural network is highly sensitive to initial network weightsWhen the network is initialized with different weights ittends to converge to different local minima [15] (2) estructure of the BP neural network can only be selected byexperience and there is no unified and complete theoreticalguidance for the selection of a BP neural network structureIf the selected network structure is too large the trainingefficiency will not be high and a fitting phenomenon mayoccur [16] resulting in low network performance and re-duced fault tolerance If the selection is too small thenetwork may not converge [17] Based on the precedinganalysis the traditional BP neural network should bestrengthened to develop a high-precision model

Similar to other metaheuristic algorithms such as thegenetic algorithm (GA) particle swarm optimization (PSO)is a population-based optimization tool that searches for theoptimal solution by updating generations PSO has noevolutionary operators such as crossover or mutationerefore the advantages of PSO are its very simple conceptlow calculation cost and few parameters that require ad-justment [18] In the fields of bottom hole pressure pre-diction ground vibration prediction [19] and asphaltene




















[25]

λ xm yn( 1113857 1s

1113874 1113875 1113944

s

i1θmn(i) (2)








F(ψω θ r) 1113944

N1

t11113944

M

s1yt(s) minus 1113954yt(s)1113858 1113859⎛⎝ ⎞⎠

minus (12)

(3)











vk+1id ωv

kid + c1r p

kid minus x

kid1113872 1113873 + c2r p

kgd minus x

kid1113872 1113873

xk+1id x

kid + v

k+1id

(4)


















xlowastij




Start











Calculate error





End

Yes

Yes

No

No













R1

R2

R4

R5

Predictedquantity

Trainingquantity


hellip

Input layer














K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References




































































[25]

λ xm yn( 1113857 1s

1113874 1113875 1113944

s

i1θmn(i) (2)








F(ψω θ r) 1113944

N1

t11113944

M

s1yt(s) minus 1113954yt(s)1113858 1113859⎛⎝ ⎞⎠

minus (12)

(3)











vk+1id ωv

kid + c1r p

kid minus x

kid1113872 1113873 + c2r p

kgd minus x

kid1113872 1113873

xk+1id x

kid + v

k+1id

(4)


















xlowastij




Start











Calculate error





End

Yes

Yes

No

No













R1

R2

R4

R5

Predictedquantity

Trainingquantity


hellip

Input layer














K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References























































F(ψω θ r) 1113944

N1

t11113944

M

s1yt(s) minus 1113954yt(s)1113858 1113859⎛⎝ ⎞⎠

minus (12)

(3)











vk+1id ωv

kid + c1r p

kid minus x

kid1113872 1113873 + c2r p

kgd minus x

kid1113872 1113873

xk+1id x

kid + v

k+1id

(4)


















xlowastij




Start











Calculate error





End

Yes

Yes

No

No













R1

R2

R4

R5

Predictedquantity

Trainingquantity


hellip

Input layer














K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References






























































xlowastij




Start











Calculate error





End

Yes

Yes

No

No













R1

R2

R4

R5

Predictedquantity

Trainingquantity


hellip

Input layer














K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References




























































R1

R2

R4

R5

Predictedquantity

Trainingquantity


hellip

Input layer














K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References

























































K2

8 times 36001113874 1113875 (6)





8 times 36001113874 1113875 (7)








50

45

40

35

30

25

20

15

10Fi

tnes

s


PSO-BPGA-BP






24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References





















































24 times 3600 (9)



Q q1 + q2 + q3 + q4 (10)




Q 2111739 + 08247r1 + 01152r2 + 722757r4 + 16083r5

(11)



E cp minus ca

11138681113868111386811138681113868

11138681113868111386811138681113868

ca

(12)

















4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References


























































4 Conclusions







Averageerror

BP1 9 11662 9-5 17372 9-7 953

GA-BP1 9 4062 9-5 3652 9-7 237

PSO-BP

1 9 2472 9-5 1382 9-7 231





Data Availability




Acknowledgments


References



















































Data Availability




Acknowledgments


References


















































research on the prediction of the water demand of...

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