Intelligent Prediction of Transmission Line Project Cost

Research ArticleIntelligent Prediction of Transmission Line Project Cost Basedon Least Squares Support Vector Machine Optimized by ParticleSwarm Optimization

Tao Yi12 Hao Zheng 12 Yu Tian12 and Jin-peng Liu 12

1School of Economics and Management North China Electric Power University Beijing 102206 China2Beijing Key Laboratory of New Energy and Low-Carbon Development North China Electric Power University Beijing 102206 China

Correspondence should be addressed to Hao Zheng 18811358655163com and Jin-peng Liu hbdlljp163com

Received 14 November 2018 Accepted 3 December 2018 Published 17 December 2018

Academic Editor Anna M Gil-Lafuente

Copyright copy 2018 Tao Yi et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to meet the demand of power supply the construction of transmission line projects is constantly advancing and the levelof cost control is constantly improving which puts forward higher requirements for the accuracy of cost prediction This paperproposes an intelligent cost predictionmodel based on least squares support vectormachine (LSSVM) optimized by particle swarmoptimization (PSO) Originally extracting natural technological and economic indexes from the perspective of cost compositionprincipal component analysis (PCA) is used to reduce the dimension of indexes AndPSO is innovatively introduced to optimize theparameters of LSSVMmodel to obtain the optimal parametersThe obtained principal component data are imported into empiricalparameter LSSVM prediction model and the optimized parameter PSO-LSSVM prediction model respectively for modeling andprediction and then comparing the prediction results to analyze the effect ofmodel optimizationThe results show that the absolutedeviation of the optimized parameter prediction model is less than 9 And the prediction accuracy of the optimized parameterprediction model is better than that of the empirical parameter model which can provide a reliable basis for investment decision-making of transmission line projects

1 Introduction

With the rapid economic development electricity demandhas also increased significantly so the pace of power trans-mission and transformation project construction is furtheraccelerated and the investment scale is further expandedHowever if the cost of power transmission and transforma-tion projects can not be effectively controlled the improve-ment of cost level will directly affect the economic benefitsand construction level of power grid projects The first taskto control the cost of transmission line project effectivelyis to determine project cost quickly and accurately Due tothe characteristics of large area span complex constructionenvironment many unpredictable factors and nonlinearityof transmission line project traditional forecasting methodsare no longer suitable Therefore in order to make reasonableinvestment decisions it is necessary to study the intelligentcost prediction model in depth to improve the speed andaccuracy of transmission line project cost prediction

In the traditional statistical analysis method multivariateregression analysis is used to predict the production cost byestablishing regression analysis model Elmousalami HH etal established a quadratic regression model and determinedthe key parameters of the model to establish a reliable con-ceptual cost estimation model for field canal improvementprojects (FCIP) [1] Zhang HB analyzed the cost and elementsthrough the regression analysis of the design parametersrevealed the influence degree of design parameters on thecost and elements of building structure and obtained theprediction model of the cost and elements of building struc-ture project [2] However the regression analysis method ispoor in the face of many uncertain factors and less sampledata The number of samples needed by time series analysismethod is relatively small but it can not fully considerthe accidental factors which are too numerous and difficultto estimate Moon S et al established an autoregressivefractionally integratedmoving average (ARFIMA) time seriesmodel with long memory characteristics [3] Moon T et al

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 5458696 11 pageshttpsdoiorg10115520185458696

2 Mathematical Problems in Engineering

established an interrupted time series forecasting model topredict the construction cost index (CCI) [4] And based onfuzzy logic Zhang R et al improved the prediction accuracyof time series [5]

With the development of artificial intelligence machinelearning and intelligent algorithms have gradually beenpopular for project cost prediction Juszczyk M introducedthe principal component analysis into the neural network topredict the cost of residential buildings in the design stage[6] Cheng MY et al used the artificial intelligence methodevolutionary fuzzy neural inference model (EFNIM) toimprove the accuracy of cost estimation [7] Sonmez Rproposed a neural network model with bootstrap predictionintervals for range estimation of construction costs [8] KimM et al proposed an approximate cost estimating modelfor irrigation-type river facility construction at the planningstage based on case-based reasoning (CBR) with GeneticAlgorithms (GA) [9] Kim S used hybrid analytic hierarchyprocess (AHP) and case-based reasoning (CBR) to studythe cost estimation model in the early stage of Koreanhighway project [10] Lesniak A et al believed that designaccording to the principle of sustainable development hasan impact on construction cost and proposed an approachto estimate the costs of sports field construction using thecase-based reasoning method [11] Rafiei MH et al proposeda cost estimation model including an unsupervised deepBoltzmann machine (DBM) learning approach and threelevel back propagation neural network (BPNN) [12] JuszczykM et al plotted the relationship between the total cost ofconstruction project and the cost prediction factors of thecharacteristics of the sports field and proposed a method forestimating the construction cost of the sports field based onthe neural network [13]

With the maturity of forecasting technology the researchon power engineering cost prediction is gradually deepenedWang FP combines the intelligent learning algorithmwith theactual situation of power transmission and transformationprojects and proposed a refinement method of control linefor power transmission and transformation project cost [14]Based on Chebyshev inequality Zhang GL et al established aprediction model of transmission and transformation projectcost which expanded the dimension of cost analysis [15]Wang X et al predicted the static investment of powertransmission and transformation project based on Bayesiannetwork gave the range of probabilistic interval estimationand provided a reasonable reference for project decision-making [16] Ling YP et al proposed a method to predictthe construction cost of transmission line based on BP neuralnetwork and established a predictionmodel of three-layer BPneural network [17] Lu Y et al proposed a decomposition-integration cost prediction model and selected differentforecasting models to predict different costs considering costcharacteristics [18]

Support vector machine (SVM) is based on the statisticallearning theory (SLT) established by Vapnik et al [19] It hasstrong generalization ability and outstanding performance insmall sample learning and nonlinear problems [20 21] andis suitable for transmission line project with many unpre-dictable factors and nonlinear characteristics Least square

support vector machine (LSSVM) is an improved algorithmof SVM which can effectively improve the efficiency ofmachine learning [22] The LSSVM has been successfullyapplied tomany forecasting problems ChengMY et al estab-lished the ELSVM hybrid forecasting model combined withdifferential evolutionmethod to optimize the core parametersof LSSVM and simulated the fluctuation of construction costindex (CCI) of construction project price change [23] CongYL et al proposed a traffic flow forecasting model based onLSSVM with two parameters automatically determined byFOA [24]

The fitting accuracy and generalization ability of LSSVMmainly depend on its two parametersrsquo selection (C and 1205902)Therefore it is very important to use appropriate heuristicalgorithm to determine parameter values General optimiza-tion algorithms show low calculation efficiency and pooraccuracy [25 26] and the particle swarm optimization (PSO)algorithm has faster convergence speed and higher accuracy[27] so this paper uses PSO to optimize the parameters ofLSSVM

This paper is organized as follows Section 2 brieflyintroduces PCA LSSVM and PSO Section 3 gives thescreening and calculation methods of the factors affectingthe cost Section 4 conducts an empirical study to verify theproposed model and Section 5 obtains the conclusion

2 Model Construction

This paper presents the proposal of an approach to theprediction of transmission line project cost which is based onLSSVM PCA is used to reduce the dimension of the originalindex to get the corresponding principal component as theinput index of the prediction model And PSO algorithm isused to automatically optimize the parameters of least squaressupport vector machine to obtain the optimal parametersThe process of model building is shown in Figure 1

As shown in Figure 1 the construction of the predictionmodel mainly includes the following four steps(1) Select the cost impact indexes and collect the originaldata of the impact indexes and cost(2) PCA is used to reduce the dimension of originaldata and output new samples Firstly the original data arestandardized to obtain standardized data then the correla-tion coefficient matrix and its eigenvalues and eigenvectorsare calculated based on the standardized data finally thevariance contribution rate of each principal component iscalculated and the first n principal components whosevariance contribution rate accumulates to the preset value areselected as the new sample output(3)Given the empirical parameters of the LSSVMmodelan empirical parameter prediction model is constructed(4) PSO is used to optimize the parameters of LSSVMFirstly the particle velocity and position are initialized andthe current particle fitness is calculated according to theparticle velocity and position The minimum fitness of thecurrent particle is selected as the individual extreme valueof the particle and the minimum global fitness particleis selected as the global extreme value Then update the

Mathematical Problems in Engineering 3

Principal component

PCA PSOOptimal parameters

C and σsup2

LSSVMPSO

Reduce dimensionality

Parameter optimization

Model training and prediction

N

Y

LSSVM

parameter

initialization

Particle velocity and position initialization

Calculating particle fitness M

SE(i)

Update Pbest (i)

Update G

best

Satisfy end condition

Return optimal

parameters

Prediction results

Precision analysis

Prediction results

Precision analysisd

Index selection

Index unitization and quantification

Project screening

Figure 1 Flowchart of transmission line engineering cost prediction model

particlersquos velocity and position and repeat the steps of calcu-lating the current particle fitness according to the particlersquosvelocity and position until the global optimal position isoutput when the iteration number reaches the maximumiteration number or the precision reaches the preset accuracythat is the parameters optimized for least squares supportvector machine Finally an optimized parameter predictionmodel is constructed according to the optimized parameters

21 Principal Component Analysis (PCA) The large numberof variables in transmission line project and the complexrelationship between them will significantly increase thecomplexity of the analysis problem Therefore this paperuses the principal component analysis method to reduce thedimension of variables so that the principal componentscan not only represent the main information of the originalvariables but also have no correlation with each other whichwill be helpful to the establishment of transmission lineproject cost predictionmodel and problem analysis Principalcomponent analysis (PCA) recombined the P indicators thathad a certain correlation into a new set of interrelatedcomprehensive indicators to replace the original indicatorsThe main calculation steps of PCA are as follows(1) Standardize the raw data

The original data are standardized according to thefollowing formula

119909lowastij = 119909ij minus xjradicvar (119909j) 119894 = 1 2 sdot sdot sdot 119899 119895 = 1 2 sdot sdot sdot 119901 (1)

where xj = (1119899)sum119899119894=1 119909119894119895 var(119909j) = (1(119899 minus 1))sum119899119894=1(119909119894119895 minus119909j)2 (119895 = 1 2 sdot sdot sdot 119901)(2) Calculate sample correlation coefficient matrix

Assuming that the original data is still expressed inX after standardization the correlation coefficients of thestandardized data are as follows

119877 =[[[[[[[[

11990311 11990312 sdot sdot sdot 1199031p11990321 11990322 sdot sdot sdot 1199032p 1199031199011 119903p2 sdot sdot sdot 119903pp

]]]]]]]](2)

where 119903119894119895 = cov(119909119894 119909119895)radicvar(1199091)radicvar(1199092) = sum119899119896=1(119909119896119894 minus119909119894)(119909119896119895 minus 119909119895)radicsum119899119896=1(119909119896119894 minus 119909119894)2radicsum119899119896=1(119909119896119895 minus 119909119895)2 119899 gt 1(3) Calculate the eigenvalues (1205821 1205822 sdot sdot sdot 120582119901) and corre-sponding eigenvectors 119886119894 = (119886i1 119886i2 sdot sdot sdot 119886ip) 119894 = 1 2 sdot sdot sdot 119901of the correlation coefficient matrix R(4) Select the important principal component and get theexpression of principal component

Through principal component analysis n principal com-ponents can be obtained However as the variance of eachprincipal component decreases the amount of informationcontained therein decreases accordingly Therefore in prac-tical analysis the first k principal components are usuallyselected according to the cumulative contribution rate ofeach principal component (the variance of one principalcomponent accounts for the proportion of the total variance)Generally the cumulative contribution rate of the first kprincipal components is required to be more than 85

22 Least Squares Support Vector Machine Least squaressupport vector machine (LSSVM) as an improved algorithmof traditional standard support vector machine was firstproposed by Suykens and Vandewalle [22] LSSVM inherits aseries of excellent characteristics of SVM such as kernel func-tion structural risk minimization principle and small sample


size Based on regularization theory loss function in SVM isdefined as least squares loss function and equality constraintsare used instead of inequality constraints in standard SVMThrough the innovation of SVM objective function settingthe time consuming quadratic programming (QP) problemis transformed into the solving problem of linear equationswhich significantly reduces the complexity of the modelreduces the memory consumption in the training processand greatly improves the solving speed The following is abrief introduction to the mathematical model of least squaressupport vector machine

Given a set of sample vectors of n-dimensional input andone-dimensional output the sample under a single technicalscheme can be expressed as (1199091 1199101)(1199092 1199102) sdot sdot sdot (119909119897 119910119897) 119909119894 isin119877n 119910119894 isin 119877 119894 = 1 2 sdot sdot sdot 119897 The sample is mapped fromthe original space to the high-dimensional feature space bya nonlinear mapping 120593(119909119894) And the nonlinear estimationfunction is transformed into the linear estimation function119891(119909) = 120596 sdot 120593(119909) + 119887 in the high-dimensional feature spaceTheweight vector and the offset of the regression function areexpressed by 120596 and 119887 separately According to the structuralrisk minimization principle minimize 120596 and 119887 as follows

119877 = 12 1205962 + 119888119877119890119898119901 (3)

where 1205962 is used to control the complexity of the model 119888 isa regularization parameter to control the penalty degree of thesample exceeding the error119877119890119898119901 is the error control functionthat is the insensitive loss function 120576 LSSVM chooses thesquare of error 120585119894 as the loss function when optimizing thetarget so the optimization problem is as follows

min 12 1205962 + 119888 119897sum119894=1

1205852119894119904119905 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894 = 0

(119894 = 1 2 119897)(4)

where 120585119894 is the relaxation factor So in order to solve thisproblem the Lagrange function is established as follows

119871 (120596 119887 120585119894 120572) = 12 1205962 + 119888 119897sum119894=1

1205852119894minus 119897sum119894=1

120572119894 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894(5)

where 120572119894 (119894 = 1 2 sdot sdot sdot 119897) is Lagrange multiplier According tothe KKT optimization conditions the partial derivatives of 119871to120596 119887 120585119894 and 120572 are obtained respectively and they are equalto 0 The results are as follows

[0 119884119879119884 119885119885119879 + 119888minus1119868][119887120572] = [01] (6)

Then an arbitrary symmetric function satisfying Mercerrsquoscondition is introduced as the kernel function The param-eters of the kernel function determine the complexity of

the spatial distribution of the sample data and have agreat influence on the performance of the model 120572 and 119887are obtained by least square method Finally the decisionfunction of LSSVM regression analysis is obtained as follows

119891 (119909) = 119897sum119894=1

120572119894119870 (119909 119909119894) + 119887 (7)

23 Particle Swarm Optimization Algorithm Particle SwarmOptimization algorithm (PSO) is a global search algorithminitially inspired by the foraging behavior of birds and usedto solve the global optimal solution of optimization problems[28] The main idea of PSO algorithm is to initialize thelocation and velocity of a group of random particles andsearch for the optimal solution by iteration under certainconditions The best position of each particle in the searchprocess is defined as the individual extreme value 119875119887119890119904119905 andthe best position of the current population is defined as theglobal extreme value 119866119887119890119904119905 In each iteration the particleupdates its speed and position in the next iteration accordingto the change of the two

In a d-dimensional search space there are m parti-cles representing possible solutions to the problem 119883 =1198831 1198832 sdot sdot sdot 119883119898 where 119883119894 = 1199091198941 1199091198942 sdot sdot sdot 119909119894119889 representsthe position of the 119894 particle 119889 is the number of LSSVMparameters here 119889 = 2 Individual fitness is expressed by themean square error generated by each training set sample inLSSVM training and the fitness function is constructed asfollows

119872119878119864(119910119894) = 1119899119899sum119894=1

(119910119894 minus 119910119894)2119891 (119909) = 119872119878119864 (119909)

(8)

The velocity of particles in D dimensional space is definedas 119881119894 = V1198941 V1198942 sdot sdot sdot V119894119889 119875119894 = 1198751198941 1198751198942 sdot sdot sdot 119875119894119889 is thebest position 119875119887119890119904119905 (the minimum fitness) that the particlecan search for itself 119875119892 = 1198751198921 1198751198922 sdot sdot sdot 119875119892119889 is the bestposition 119866119887119890119904119905 for the entire population The velocity andposition update of the 119894 particle is determined according tothe following formula

V119905+1119894 = 120596V119905119894 + 1198881 rand ( ) (119875119905119894 minus 119883119905119894)+ 1198882 rand ( ) (119866119905119894 minus 119883119905119894)

119909119905+1119894 = 119909119905119894 + V119905+1119894

(9)

where 120596 is the weight factor of inertia 119905 is the number ofiterations 1198881 and 1198882 are acceleration factors representing thestep length of particle flying towards its optimal positionand overall optimal position rand( ) is a random numberuniformly distributed in the interval [0 1]

If the number of iterations reaches the maximum numberof iterations or the precision reaches the preset accuracythe iteration cycle will be withdrawn and the global optimalparameters will be returned PSO can be used to optimizekernel function parameters and penalty coefficient in LSSVM


Table 1 Influencing indexes of transmission line project cost

Index type Influencing indexes Number

Natural indexesTopography X1Geology X2

Thickness of ice and wind speed X3

Technical indexes

Single circuit length X4Conductor cross-section X5Conductor consumption X6

Tension ratio X7Number of towers X8

Tower material consumption X9Earthwork consumption X10

Foundation concrete consumption X11Foundation steel consumption X12

Economic indexesPrice of conductor X13

Price of tower material X14Price of foundation steel X15

model thus artificial exhaustion can be avoided and betterfitting effect can be obtained

3 Selection and Measurement of CostPrediction Indexes

31 Analysis of Factors Affecting Cost and Selection of IndexesThe transmission line project cost is composed of two partsontological project cost and other costs and other costs onlyaccount for about 20 of the project cost And more than60 of the other costs are concentrated on the constructionsite requisition and clearance fees while the constructionsite requisition and clearance fees are greatly affected by theregion which is not regular and difficult to accurately predictTherefore this paper only studies the ontological cost oftransmission line project and does not discuss the changes ofother costs Ontological project cost can be divided into sixparts foundation project cost tower project cost groundingproject cost erecting project cost annex project cost andauxiliary project cost And the voltage level has a greatimpact on the cost of transmission line project The costof transmission line project with different voltage levels hassignificant differences Therefore this paper only choosesone kind of transmission line project under voltage level foranalysis

The transmission line project consists of six unit projectsfoundation project tower project grounding project erect-ing project annex project and auxiliary project Thereforethis paper originally identifies the influencing factors of thecost from the perspective of the cost of the six unit projectsFirstly the influencing indexes of each ontological costmodule are determined separately and then the influencingindexes of overall cost are summarized The process ofidentifying indexes is shown in Figure 2

According to the impact indexes identified in Figure 2they can be classified into three categories natural techno-logical and economic indexes Among the technical indexes

because this paper studies the influence indexes of trans-mission line project cost under single voltage level andthe separated number of conductors matches with voltagelevel the influence factor of separated number of conductorsis eliminated Among the economic indexes the price ofearthwork and the price of concrete are relatively stablewhich have little impact on the cost of transmission lineprojects so they are also eliminated Therefore the indexesaffecting the transmission line project cost are shown inTable 1

32 Index Measurement Method

(1) Unitization of Gross Index In the analysis of the indexesaffecting the unit length cost of transmission line projectsome gross indexes can not be directly compared because ofthe different construction scale of the projects In order tobetter analyze the impact of these indexes it is necessary tounit some of the gross indexes as shown in Table 2

(2) Quantification of Qualitative Index In order to makesome qualitative indexes available for the input of predictionmodel it is necessary to quantify them according to thefactor level of each index If a project contains multiplelevels weighted average processing should be carried outproportionally The results of index quantification are shownin Table 3

4 Optimization Model Construction andExperiment Study

41 Project Samples and Data Statistics The original data of78 sets of 110 kV transmission lines in actual settlement ina certain area of China in 2017 are selected as samples Theinitial indexes of the model are obtained by quantitative andunit processing of the original data indicators as shown inTable 4


Ontologicalproject cost

Tower projectcost

Foundationproject cost

Erecting projectcost

Annex project cost

Groundingproject cost

Auxiliary projectcost

Topography

GeologyThickness of ice and

wind speed

Number of towersFoundation steel

consumption

Foundation concreteconsumption

Earthworkconsumption

Price offoundation steel

Price of concrete

Price of earthwork

Single circuit length

Conductorcross-section

Tension ratio

Tower materialconsumption

Price of towermaterial

Conductorconsumption

Price of conductor

Separated number ofconductor

Figure 2 Selection of influencing indexes of transmission line project cost

Table 2 Index unitization

Index Formula UnitUnit length cost Ontological cost Single circuit length 10kUSDkmUnit length tower Number of towers Single circuit length BasekmUnit tower material consumption Tower material consumption Number of towers tBaseUnit length conductor consumption Conductor material consumption Single circuit length tkmUnit foundation steel consumption Foundation steel consumption Number of towers tBaseUnit foundation concrete consumption Foundation concrete consumption Number of towers m3BaseUnit earthwork consumption Earthwork consumption Number of towers m3Base

In order to eliminate the interaction between indexesand reduce the number of indexes the principal componentanalysis (PCA) of the index data of the above 78 sampleprojects is carried out Each sample has 15 variables whichconstitutes a 78lowast15-order matrix

119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)

SPSS software was used for calculation and KMO suitabilitytest and Bartlett sphere test were performed for standardizeddata The results showed that KMO value was 0639 andBartlett spherical test value was 62287 which reached a sig-nificant level (p=0000 lt 0001) indicating that the data hadhigh efficiency and could be used for principal componentanalysis

On the basis of data standardization the influencingindexes of transmission line project cost are analyzed byprincipal component analysis The cumulative contributionof principal component is shown in Table 5 From the table

the cumulative contribution of variance of the first sevenprincipal components is 86530 which is more than 85That is to say the seven principal components can summarizemost of the information Therefore the first seven principalcomponents are selected as the input set of the transmissionline project cost prediction model

According to the component score coefficient matrixobtained by principal component analysis and the eigenval-ues of variables the principal component coefficient matrixis calculated as shown in Table 6

The principal components can be calculated by principalcomponent coefficient matrix and standardized variable dataTake the first principal component as an example

F1 = minus01297X1 minus 00510X2 minus 01686X3 minus 02460X4+ 02691X5 + 02278X6 + 03613X7minus 03620X8 + 03315X9 + 03593X10+ 02815X11 + 03215X12 + 01932X13+ 02157X14 minus 00153X15

(11)


Table 3 Index quantification

Topographiccoefficient

Flat Hill Rivernetwork Mire Mountain Alp Desert Steep

mountain -

1 2 3 4 5 6 7 8 -

Geologicalcoefficient

Frozen soil Ordinarysoil Hard soil Sand Puddle Mud puddle Drift sand

pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9

Thickness ofice and windspeedcoefficient

Ice-free⩽29 Ice-free31

Ice-free33

Ice-free35

Ice-free⩾37 Mild ice235

Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice

31Mild ice⩾33 Moderate ice

235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice

31Moderate ice⩾33 -

10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100

Evolutional generation range

Figure 3 Iterative process of parameter optimization Describe theminimumMSE for each iteration

42 Establishment and Training of Optimized ParameterModel Based on the principal component analysis of influ-encing indexes of transmission line project cost the calcu-lated seven principal components are used as input param-eters of the prediction model and the unit length cost oftransmission line project is used as expected output 60groups of sample data were selected as training samples toinput LSSVM empirical parameter model and PSO-LSSVMoptimization parameter model for model training

(1) LSSVM Empirical Parameter Model Training A standardLSSVM model is established and then input data into themodel for training Select the empirical parameters C=100and 1205902 = 04 as the basic parameters of the LSSVMprediction model the penalty factor and the kernel functionparameter And select radial basis function as the kernelfunction 119870(119909 119909119894)

119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)

(2) PSO-LSSVMOptimization Parameter Model TrainingThePSO-LSSVM model is used to forecast transmission line

7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150

Figure 4 Parameter optimization results based on PSO BestC=2768476 1205902 = 03412project cost The number of population is set at 30 theacceleration factor 1198881 is 15 and 1198882 is 17 the range of weightfactor of inertia 120596 is [04 095] the maximum number ofiterations is 300 the radial basis function is also chosen as thekernel function the range of penalty coefficient C is [0 300]and the range of kernel function parameter 1205902 is [0 200]

The iteration process of PSO is shown in Figure 3 and theresult of parameter optimization is shown in Figure 4 Thelowest point represents the optimal parameter combinationpoint The optimal parameters of LSSVM are optimized byPSO algorithm C=2768476 1205902 = 03412 and the minimumfitness is MSEmin=00188

43 Analysis of Prediction Results Theother 18 sets of data areselected as test sets to input the model trained above and thecost prediction analysis of transmission line project is carriedout to further verify the rationality of the prediction modelThe test samples are substituted into the empirical parametermodel and the optimization parameter model respectivelyand the simulation results show that the predicted value ofunit length cost is compared with the actual value as shownin Figure 5


Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519


Table 5 Total variance explained

Component Initial Eigenvalues Extraction Sum of Squared LoadingTotal of Variance Cumulative Total of Variance Cumulative

1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -

Table 6 The coefficient between the principal component and the canonical variables

F1 F2 F3 F4 F5 F6 F7X1 -01297 05014 03511 00871 -01248 -01359 00836X2 -00510 04369 04027 02805 02123 -02092 -00392X3 -01686 01471 -03002 02621 06817 01478 -00749X4 -02460 02493 02965 -02906 -01893 03707 00480X5 02691 02513 -03165 03022 -01994 00933 01723X6 02278 01963 -02009 04954 -03483 00453 01816X7 03613 -00397 00048 -00173 01011 -01750 -03387X8 -03620 00305 -00857 01595 02706 01497 01956X9 03315 -00967 01303 00478 00762 00971 04066X10 03593 00418 02828 -00941 00824 02517 -01884X11 02815 -01016 03283 -00001 03189 01754 04340X12 03215 -00581 00845 -00636 02444 -02249 00460X13 01932 03201 -02440 -02722 00494 06135 -01008X14 02157 04296 -01638 -02254 01187 -02493 -02922X15 -00153 02407 -03007 -05079 00611 -03495 05302

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE

LSSVMPSO-LSSVMError of LSSVMError of PSO-LSSVM

0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r

Figure 5 Comparison of prediction results of different models

As shown in Figure 5 the LSSVM empirical parametermodel predicts that the average absolute deviation ratebetween the cost and the real cost is 974 the PSO-LSSVM

optimized parametermodel predicts that the average absolutedeviation between the cost and the real cost is 673 Theprediction accuracy of the optimized parameter model ishigher than that of the empirical parameter model and itcan meet the accuracy requirement of project investmentdecision

Statistically the mean absolute percentage error (MAPE)and root mean square error (RMSE) are used to measure theaccuracy of the prediction model The calculation formulasare as follows

119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)


Table 7 Statistical error measures of prediction methods

Prediction models IndexesMAPE RMSE

LSSVM 974 155PSO-LSSVM 673 112

where 119910119894 represents the predicted value and 119910119894 representsthe actual value The MAPE values and RMSE values of theLSSVM model and the PSO-LSSVM model are calculatedrespectively as shown in Table 7

Table 7 shows that the MAPE of PSO-LSSVM is 3090higher than that of LSSVM which proves that the optimiza-tion parameter model can greatly improve the accuracy oftransmission line cost prediction model

5 Conclusions

This paper proposes an intelligent cost prediction modelbased on LSSVM optimized by PSO Firstly PCA is used toscreen and reduce the dimension of the transmission lineproject cost data and the principal components which canbasically describe the factors affecting the cost are obtainedas the input set of the prediction model Secondly theempirical parameters of LSSVM model which is maturein theory are given to determine the nonlinear mappingbetween transmission line project characteristics and costThen the parameters of the model are optimized by PSOto obtain the optimized parameters model and the model istrained Finally the trained model is used to predict the costof transmission line project And the accuracy of the modelis verified by comparing the cost predict value of empiricalparameter model optimized parameter model and actualvalue of cost

Cost control of transmission line projects directly affectsthe economic benefits of power grid projects so it is an urgentproblem to predict the cost with high accuracy in the earlystage of the project Although cost prediction models basedon various mathematical methods have been proposed inmany literatures they are difficult to apply to transmissionline project and the error is generally high For examplethe neural network model and the regression predictionmodel can not adapt to the characteristics of fewer samplesof transmission line engineering and the prediction modelbased on grey theory can not adapt to the characteristics ofmany influencing factors of transmission line engineeringso the error generated are rarely less than 10 The averageabsolute deviation rate of the PSO-LSSVM optimizationparameter model is 673 compared with the actual value ofthe cost and the accuracy of the PSO-LSSVM optimizationparameter model is improved greatly compared with otherprediction models

In summary the PSO-LSSVM cost prediction modelproposed in this paper can effectively improve the accuracyof transmission line project cost prediction This model hasstrong practical significance and good application effect intransmission line project cost prediction

Data Availability

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

Conflicts of Interest

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

Acknowledgments

This study is supported by theNationalNatural Science Foun-dation of China (NSFC) (71501071) Beijing Social ScienceFund (16YJC064) and the Fundamental Research Funds forthe Central Universities (2017MS059 and 2018ZD14)

References

[1] H H ElMousalami A H Elyamany and A H IbrahimldquoPredicting Conceptual Cost for Field Canal ImprovementProjectsrdquo Journal of Construction Engineering andManagementvol 144 no 11 8 pages 2018

[2] H B Zhang ldquoResearch on Structural Cost Analysis atSchematic Design Stage using Multi-variant Regression Anal-ysisrdquo Engineering Cost Management vol 2 pp 49ndash52 2015

[3] S Moon S Chi and D Y Kim ldquoPredicting Construction CostIndex Using the Autoregressive Fractionally IntegratedMovingAverageModelrdquo Journal of Management in Engineering vol 34no 2 2018

[4] T Moon and D H Shin ldquoForecasting Construction CostIndex Using Interrupted Time-Seriesrdquo KSCE Journal of CivilEngineering vol 22 no 5 pp 1626ndash1633 2018

[5] R Zhang B Ashuri and Y Deng ldquoA novel method forforecasting time series based on fuzzy logic and visibility graphrdquoAdvances in Data Analysis and Classification ADAC vol 11 no4 pp 759ndash783 2017

[6] M Juszczyk ldquoApplication of PCA-based data compression inthe ANN-supported conceptual cost estimation of residentialbuildingsrdquo in Proceedings of the International Conference onNumerical Analysis and Applied Mathematics 2015 p 200007Rhodes Greece

[7] M-Y Cheng H-C Tsai andW-S Hsieh ldquoWeb-based concep-tual cost estimates for construction projects using EvolutionaryFuzzy Neural Inference Modelrdquo Automation in Constructionvol 18 no 2 pp 164ndash172 2009

[8] R Sonmez ldquoRange estimation of construction costs usingneural networks with bootstrap prediction intervalsrdquo ExpertSystems with Applications vol 38 no 8 pp 9913ndash9917 2011

[9] M Kim S Lee S Woo and D H Shin ldquoApproximate costestimating model for river facility construction based on case-based reasoning with genetic algorithmsrdquo KSCE Journal of CivilEngineering vol 16 no 3 pp 283ndash292 2012

[10] S Kim ldquoHybrid forecasting systembased on case-based reason-ing and analytic hierarchy process for cost estimationrdquo Journalof Civil Engineering and Management vol 19 no 1 pp 86ndash962013

[11] A Lesniak and K Zima ldquoCost Calculation of ConstructionProjects Including Sustainability Factors Using the Case BasedReasoning (CBR)Methodrdquo Sustainability vol 10 no 5 p 16082018


[12] M H Rafiei and H Adeli ldquoNovelMachine-LearningModel forEstimating Construction Costs Considering Economic Vari-ables and Indexesrdquo Journal of Construction Engineering andManagement vol 144 no 12 p 9 2018

[13] M Juszczyk A Lesniak and K Zima ldquoANN Based Approachfor Estimation of Construction Costs of Sports Fieldsrdquo Com-plexity vol 2018 Article ID 7952434 11 pages 2018

[14] F P Wang Subdividing Method and Applied Research ofPower Transmission and Transformation Project Cost ControlChongqing University China Chongqing 2015

[15] G L Zhang W N Wen and P D Li ldquoReasonable IntervalCalculationMethod for Power Transmission Project Cost Basedon Chebyshevrsquos Inequalityrdquo Electric Power Construction vol 35no 9 pp 118ndash122 2014

[16] X Wang P Y Geng and B B Yin ldquoBayesian Network BasedStatic Investment Forecast for Transmission and Transforma-tion Projectsrdquo China Power Enterprise Management vol 19 pp93ndash96 2015

[17] Y P Ling P F Yan and C Z Han ldquoBP Neural Network BasedCost Prediction Model for Transmission Projectsrdquo ElectricPower vol 45 no 10 pp 95ndash99 2012

[18] Y Lu D Niu J Qiu and W Liu ldquoPrediction Technology ofPower Transmission and Transformation Project Cost Basedon the Decomposition-Integrationrdquo Mathematical Problems inEngineering vol 2015 Article ID 651878 11 pages 2015

[19] V N Vapnik Statistical Learningeory JohnWiley NewYork1998

[20] C Aldrich and L Auret Statistical Learningeory and Kernel-based Methods Unsupervised Process Monitoring and FaultDiagnosis with Machine Learning Methods Springer LondonUK 2013

[21] L N Jiang Research on the Predict of the Construction CostBased on Support VectorMachine HebeiUniversity of Engineer-ing China Handan 2009

[22] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[23] M-Y Cheng N-D Hoang and Y-W Wu ldquoHybrid intelli-gence approach based on LS-SVM and differential evolutionfor construction cost index estimation a Taiwan case studyrdquoAutomation in Construction vol 35 pp 306ndash313 2013

[24] Y Cong J Wang and X Li ldquoTraffic flow forecasting by a leastsquares support vector machine with a fruit fly optimizationalgorithmrdquo Procedia Engineering vol 137 pp 59ndash68 2016

[25] Q Wu ldquoHybrid model based on wavelet support vectormachine and modified genetic algorithm penalizing Gaussiannoises for power load forecastsrdquo Expert Systems with Applica-tions vol 38 no 1 pp 379ndash385 2011

[26] F-C Yuan and C-H Lee ldquoUsing least square support vectorregression with genetic algorithm to forecast beta systematicriskrdquo Journal of Computational Science vol 11 pp 26ndash33 2015

[27] R G Gorjaei R Songolzadeh M Torkaman M Safari and GZargar ldquoA novel PSO-LSSVM model for predicting liquid rateof two phase flow through wellhead chokesrdquo Journal of NaturalGas Science and Engineering vol 24 pp 228ndash237 2015

[28] R C Eberhart and J Kennedy ldquoA new optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micromachine and Human Science pp 39ndash43 NagoyaJapan October 1995

Hindawiwwwhindawicom Volume 2018

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International Journal of


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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

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Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


established an interrupted time series forecasting model topredict the construction cost index (CCI) [4] And based onfuzzy logic Zhang R et al improved the prediction accuracyof time series [5]

With the development of artificial intelligence machinelearning and intelligent algorithms have gradually beenpopular for project cost prediction Juszczyk M introducedthe principal component analysis into the neural network topredict the cost of residential buildings in the design stage[6] Cheng MY et al used the artificial intelligence methodevolutionary fuzzy neural inference model (EFNIM) toimprove the accuracy of cost estimation [7] Sonmez Rproposed a neural network model with bootstrap predictionintervals for range estimation of construction costs [8] KimM et al proposed an approximate cost estimating modelfor irrigation-type river facility construction at the planningstage based on case-based reasoning (CBR) with GeneticAlgorithms (GA) [9] Kim S used hybrid analytic hierarchyprocess (AHP) and case-based reasoning (CBR) to studythe cost estimation model in the early stage of Koreanhighway project [10] Lesniak A et al believed that designaccording to the principle of sustainable development hasan impact on construction cost and proposed an approachto estimate the costs of sports field construction using thecase-based reasoning method [11] Rafiei MH et al proposeda cost estimation model including an unsupervised deepBoltzmann machine (DBM) learning approach and threelevel back propagation neural network (BPNN) [12] JuszczykM et al plotted the relationship between the total cost ofconstruction project and the cost prediction factors of thecharacteristics of the sports field and proposed a method forestimating the construction cost of the sports field based onthe neural network [13]

With the maturity of forecasting technology the researchon power engineering cost prediction is gradually deepenedWang FP combines the intelligent learning algorithmwith theactual situation of power transmission and transformationprojects and proposed a refinement method of control linefor power transmission and transformation project cost [14]Based on Chebyshev inequality Zhang GL et al established aprediction model of transmission and transformation projectcost which expanded the dimension of cost analysis [15]Wang X et al predicted the static investment of powertransmission and transformation project based on Bayesiannetwork gave the range of probabilistic interval estimationand provided a reasonable reference for project decision-making [16] Ling YP et al proposed a method to predictthe construction cost of transmission line based on BP neuralnetwork and established a predictionmodel of three-layer BPneural network [17] Lu Y et al proposed a decomposition-integration cost prediction model and selected differentforecasting models to predict different costs considering costcharacteristics [18]

Support vector machine (SVM) is based on the statisticallearning theory (SLT) established by Vapnik et al [19] It hasstrong generalization ability and outstanding performance insmall sample learning and nonlinear problems [20 21] andis suitable for transmission line project with many unpre-dictable factors and nonlinear characteristics Least square

support vector machine (LSSVM) is an improved algorithmof SVM which can effectively improve the efficiency ofmachine learning [22] The LSSVM has been successfullyapplied tomany forecasting problems ChengMY et al estab-lished the ELSVM hybrid forecasting model combined withdifferential evolutionmethod to optimize the core parametersof LSSVM and simulated the fluctuation of construction costindex (CCI) of construction project price change [23] CongYL et al proposed a traffic flow forecasting model based onLSSVM with two parameters automatically determined byFOA [24]

The fitting accuracy and generalization ability of LSSVMmainly depend on its two parametersrsquo selection (C and 1205902)Therefore it is very important to use appropriate heuristicalgorithm to determine parameter values General optimiza-tion algorithms show low calculation efficiency and pooraccuracy [25 26] and the particle swarm optimization (PSO)algorithm has faster convergence speed and higher accuracy[27] so this paper uses PSO to optimize the parameters ofLSSVM

This paper is organized as follows Section 2 brieflyintroduces PCA LSSVM and PSO Section 3 gives thescreening and calculation methods of the factors affectingthe cost Section 4 conducts an empirical study to verify theproposed model and Section 5 obtains the conclusion

2 Model Construction

This paper presents the proposal of an approach to theprediction of transmission line project cost which is based onLSSVM PCA is used to reduce the dimension of the originalindex to get the corresponding principal component as theinput index of the prediction model And PSO algorithm isused to automatically optimize the parameters of least squaressupport vector machine to obtain the optimal parametersThe process of model building is shown in Figure 1

As shown in Figure 1 the construction of the predictionmodel mainly includes the following four steps(1) Select the cost impact indexes and collect the originaldata of the impact indexes and cost(2) PCA is used to reduce the dimension of originaldata and output new samples Firstly the original data arestandardized to obtain standardized data then the correla-tion coefficient matrix and its eigenvalues and eigenvectorsare calculated based on the standardized data finally thevariance contribution rate of each principal component iscalculated and the first n principal components whosevariance contribution rate accumulates to the preset value areselected as the new sample output(3)Given the empirical parameters of the LSSVMmodelan empirical parameter prediction model is constructed(4) PSO is used to optimize the parameters of LSSVMFirstly the particle velocity and position are initialized andthe current particle fitness is calculated according to theparticle velocity and position The minimum fitness of thecurrent particle is selected as the individual extreme valueof the particle and the minimum global fitness particleis selected as the global extreme value Then update the


Principal component


C and σsup2

LSSVMPSO




N

Y

LSSVM

parameter

initialization



SE(i)

Update Pbest (i)

Update G

best


Return optimal

parameters

Prediction results

Precision analysis

Prediction results

Precision analysisd

Index selection


Project screening








119877 =[[[[[[[[


]]]]]]]](2)







119877 = 12 1205962 + 119888119877119890119898119901 (3)


min 12 1205962 + 119888 119897sum119894=1

1205852119894119904119905 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894 = 0

(119894 = 1 2 119897)(4)


119871 (120596 119887 120585119894 120572) = 12 1205962 + 119888 119897sum119894=1

1205852119894minus 119897sum119894=1

120572119894 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894(5)


[0 119884119879119884 119885119885119879 + 119888minus1119868][119887120572] = [01] (6)



119891 (119909) = 119897sum119894=1

120572119894119870 (119909 119909119894) + 119887 (7)



119872119878119864(119910119894) = 1119899119899sum119894=1

(119910119894 minus 119910119894)2119891 (119909) = 119872119878119864 (119909)

(8)



119909119905+1119894 = 119909119905119894 + V119905+1119894

(9)








Technical indexes




















Tower projectcost



Annex project cost



Topography


wind speed


consumption




Price of concrete

Price of earthwork



Tension ratio




Price of conductor






119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)







(11)





mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018









Principal component


C and σsup2

LSSVMPSO




N

Y

LSSVM

parameter

initialization



SE(i)

Update Pbest (i)

Update G

best


Return optimal

parameters

Prediction results

Precision analysis

Prediction results

Precision analysisd

Index selection


Project screening








119877 =[[[[[[[[


]]]]]]]](2)







119877 = 12 1205962 + 119888119877119890119898119901 (3)


min 12 1205962 + 119888 119897sum119894=1

1205852119894119904119905 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894 = 0

(119894 = 1 2 119897)(4)


119871 (120596 119887 120585119894 120572) = 12 1205962 + 119888 119897sum119894=1

1205852119894minus 119897sum119894=1

120572119894 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894(5)


[0 119884119879119884 119885119885119879 + 119888minus1119868][119887120572] = [01] (6)



119891 (119909) = 119897sum119894=1

120572119894119870 (119909 119909119894) + 119887 (7)



119872119878119864(119910119894) = 1119899119899sum119894=1

(119910119894 minus 119910119894)2119891 (119909) = 119872119878119864 (119909)

(8)



119909119905+1119894 = 119909119905119894 + V119905+1119894

(9)








Technical indexes




















Tower projectcost



Annex project cost



Topography


wind speed


consumption




Price of concrete

Price of earthwork



Tension ratio




Price of conductor






119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)







(11)





mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018











119877 = 12 1205962 + 119888119877119890119898119901 (3)


min 12 1205962 + 119888 119897sum119894=1

1205852119894119904119905 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894 = 0

(119894 = 1 2 119897)(4)


119871 (120596 119887 120585119894 120572) = 12 1205962 + 119888 119897sum119894=1

1205852119894minus 119897sum119894=1

120572119894 119910119894 [120596119879 sdot 120593 (119909119894) + 119887] minus 1 + 120585119894(5)


[0 119884119879119884 119885119885119879 + 119888minus1119868][119887120572] = [01] (6)



119891 (119909) = 119897sum119894=1

120572119894119870 (119909 119909119894) + 119887 (7)



119872119878119864(119910119894) = 1119899119899sum119894=1

(119910119894 minus 119910119894)2119891 (119909) = 119872119878119864 (119909)

(8)



119909119905+1119894 = 119909119905119894 + V119905+1119894

(9)








Technical indexes




















Tower projectcost



Annex project cost



Topography


wind speed


consumption




Price of concrete

Price of earthwork



Tension ratio




Price of conductor






119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)







(11)





mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018













Technical indexes




















Tower projectcost



Annex project cost



Topography


wind speed


consumption




Price of concrete

Price of earthwork



Tension ratio




Price of conductor






119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)







(11)





mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018










Tower projectcost



Annex project cost



Topography


wind speed


consumption




Price of concrete

Price of earthwork



Tension ratio




Price of conductor






119883 =1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381611990911 sdot sdot sdot 119909115 d

119909781 sdot sdot sdot 1199097815

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816(10)







(11)





mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018












mountain -

1 2 3 4 5 6 7 8 -



pitRock

blastingRock

artificial1 2 3 4 5 6 7 8 9



Ice-free33

Ice-free35


Mild ice25

Mild ice27

Mild ice29

1 2 3 4 5 6 7 8 9Mild ice


235Moderate ice

25Moderate ice

27Moderate ice

29Moderate ice


10 11 12 13 14 15 16 17 -

03

025

02

015

01

005

MSE

0 20 40 60 80 100





119870(119909 119909119894) = exp(minus1003817100381710038171003817119909 minus 1199091198941003817100381710038171003817221205902 ) (12)


7

6

5

4

3

2

1

0

MSE

200150

10050

0

200300

150250

100500

2

C

150





Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018









Table4Orig

inaldataof

transm

issionlin

eprojectcost

Sample

X1X2

X3X4

X5X6

X7X8

X9X10

X11

X12

X13

X14

X15

Unitlengthcost

(10kUSD

km)

1098

398

656

2048

18498

227

018

315

422

5772

1278

087

123

060

043

694

210

0453

528

1130

24000

302

045

177

1011

15311

2175

177

132

067

025

826

315

3385

448

2218

2399

8278

039

151

915

11954

2274

212

130

066

045

542

410

0400

446

1329

24000

294

027

226

2155

10833

4144

182

120

061

028

880

510

0200

450

2000

24000

290

023

235

807

8124

3052

071

132

058

056

1059

610

0256

473

879

24000

301

038

182

699

6485

1677

123

129

062

011

554

710

0434

381

2176

24000

294

045

193

744

16112

3339

200

129

065

037

650

815

0355

700

7172

18500

230

019

337

392

6096

1309

072

125

062

032

634

78098

283

798

2795

2399

8288

014

284

476

5178

1221

051

128

060

031

519




1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018











1 5103 34019 34019 5103 34019 340192 2093 13954 47973 2093 13954 479733 1936 12906 60880 1936 12906 608804 1434 9557 70437 1434 9557 704375 0941 6272 76709 0941 6272 767096 0807 5378 82087 0807 5378 820877 0667 4443 86530 0667 4443 865308 0541 3607 90137 - - -9 0388 2588 92725 - - -10 0348 2319 95044 - - -11 0253 1688 96732 - - -12 0212 1415 98146 - - -13 0116 0775 98921 - - -14 0103 0687 99608 - - -15 0059 0392 100000 - - -



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ACTUAL VALUE


0

2

4

6

8

10

12

Uni

t len

gth

cost

(10k

USD

km

)

2

4

6

8

10

12

14

Erro

r





119872119860119875119864 = 1119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119910119894 minus 11991011989411991011989410038161003816100381610038161003816100381610038161003816 (13)

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (14)







5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018














5 Conclusions




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018

































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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Intelligent Prediction of Transmission Line Project Cost