CostIndexPredictionsforConstructionEngineeringBasedon...

Research ArticleCost Index Predictions for Construction Engineering Based onLSTM Neural Networks

Jiacheng Dong Yuan Chen and Gang Guan

School of Civil Engineering Zhengzhou University Zhengzhou 450001 China

Correspondence should be addressed to Yuan Chen chen_yuanzzueducn

Received 15 February 2020 Revised 26 August 2020 Accepted 4 September 2020 Published 24 September 2020

Academic Editor Reza Akhavian

Copyright copy 2020 JiachengDong 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

In recent years the cost index predictions of construction engineering projects are becoming important research topics inthe field of construction management Previous methods have limitations in reasonably reflecting the timeliness of en-gineering cost indexes +e recurrent neural network (RNN) belongs to a time series network and the purpose of timelinesstransfer calculation is achieved through the weight sharing of time steps +e long-term and short-term memory neuralnetwork (LSTM NN) solves the RNN limitations of the gradient vanishing and the inability to address long-term de-pendence under the premise of having the above advantages +e present study proposed a new framework based on LSTMso as to explore the applicability and optimization mechanism of the algorithm in the field of cost indexes prediction Asurvey was conducted in Shenzhen China where a total of 143 data samples were collected based on the index set for thecorresponding time interval from May 2007 to March 2019 A prediction framework based on the LSTM model which wastrained by using these collected data was established for the purpose of cost index predictions and test +e testing resultsshowed that the proposed LSTM framework had obvious advantages in prediction because of the ability of processing high-dimensional feature vectors and the capability of selectively recording historical information Compared with other ad-vanced cost prediction methods such as Support Vector Machine (SVM) this framework has advantages such as being ableto capture long-distance dependent information and can provide short-term predictions of engineering cost indexes botheffectively and accurately +is research extended current algorithm tools that can be used to forecast cost indexes andevaluated the optimization mechanism of the algorithm in order to improve the efficiency and accuracy of prediction whichhave not been explored in current research knowledge

1 Introduction

Due to unique industry characteristics construction projectsrequire a large amount of capital investment [1] Accuratecost predictions are essential for the effective implementa-tion of construction projects [2] +e cost indexes used inconstruction engineering projects are technical and eco-nomic indicators which reflect the impacts of market pricefluctuations on the construction costs of engineering factorsduring certain periods of time Construction engineeringcost indexes have been widely implemented in cost pre-dictions tender compilations and investment planning [3]In addition engineering cost indexes can be used to measurethe fluctuations in the construction costs and also providefoundations for the bidding quotations project predictions

and settlements in the cost management processes [4]+erefore the accurate cost predictions have major benefitsfor investment planning bidding and feasibility analysesduring the early stages of construction projects

+e research of engineering cost prediction has a longhistory +e initial prediction form must be based on acomplete design drawing which is unable to meet the re-quirements of the actual scenarios in terms of time andefficiency With the development of information technologycost prediction began to break away from the limitation ofdrawings and gradually a solution emerged to establish aninformation model based on various algorithms At presentthe cost prediction methods available based on informationtechnology can be divided into two branches constructioncost prediction and cost indexes prediction +e types of

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 6518147 14 pageshttpsdoiorg10115520206518147

construction cost prediction mainly include the predictionof bidding price [5] and market information price [6] +eprediction types of cost indexes mainly include the pre-diction of tender price index (TPI) [7] and EngineeringNews-Record (ENR) construction cost index (CCI) [8]Among them the construction cost prediction data mainlycomes from expert judgment or historical data of similarprojects [9] which lacks authority and persuasion Howeverthe data source of cost indexes prediction is generally adynamic release from authoritative institutions +e calcu-lation mode of construction cost is based on the engineeringcost indexes With reference to the concept of ComputerScience the cost indexes can be called the data provenance(lineage or pedigree) of construction cost By directly pro-cessing the data provenance the error and distortion of thedata during the processing can be avoided to a certain extent[10] Most of the current advanced research methods achieveprediction based on a certain regression analysis or as-suming some combination patterns to appear repeatedly[11] LSTM NN replaces the hidden layer neurons in theRNN with four logic units and establishes a long-time lagbetween input feedback and prevention of gradient ex-plosion +is structure type realizes the continuity of theinternal state error flow in the special memory unit enablesLSTM to capture the large dependence of the time stepdistance in the time series and has a strong approximationability for nonlinear and nonstationary time series whichwill improve the prediction efficiency and accuracy of se-quence data with temporal or spatial attributes

2 Literature Review

21 Cost PredictionMethods +emethods of cost predictionscan be divided into two categories causal analysis and timeseries analysis [12] With the development and advantages ofartificial intelligence machine learning algorithms have beenapplied in this field As determined by the available researchreports the causal method also known as causal analysis needsto specify the relationships between the predictive variables andthe dependent variables or between dependent variables andinterpretative variables [12] +erefore causal analysis pre-dictions are based on the interpretations of the relationshipsbetween the engineering cost indicators and other variableswhich can then be used to predict project cost indexes [13] Inthe present study previous related reports were reviewed inwhich causal methods had been successfully used to predicttender price indices (TPI) building prices and constructioncosts [8] Akintoye and Skitmore used OLSmultiple regressionanalysis to construct a contract price model and provided astructural explanation for the trend changes in the TPI throughthe structural equation model [14] Trost and Oberlenderobtained the ranking of the factors influencing the accuracy ofearly cost estimation through factor analysis and multipleregression analysis [15] Chen proposed a combinationmethodbased on transformed time series data multiple regressionanalysis YulendashWalker estimates and incomplete principalcomponent regression analysis to predict the company-levelcost flow within a certain range successfully [16]

Statistical methods are also known as black boxmethods or time series methods which can be divided intothe two categories of univariate andmultivariate time seriesanalyses [17] Wong et al utilized an autoregressive inte-grated moving average model (ARIMA) to predict the fivemain indicators of the Hong Kong labour market [18]Hwang proposed two dynamic univariate time seriesmodels to successfully predict ENR CCI [19] In contrastmultivariate time series analysis is based on multiplevariables +e advantage of this type of analysis is that onlyquantitative data can be used and objective predictions canbe made without additional subjective judgment processes+erefore multivariate time series analysis methods the-oretically have higher predictive abilities [20] Hwangcompared and analysed the prediction effects of autore-gressive moving average models (ARMA) and vectorautoregression (VAR) time series models on structural costindicators +e comparison results indicated that univar-iate and multivariate time series analysis methods each hadtheir own advantages resulting in the ARMA (5 5) havingslightly higher precision [20] Xu and Moon adopted acointegration equation to establish a cointegrated VARmodel in which the deviations between the cointegratingrelationships and the long-run stable relationships betweenthe variables were considered As a result the ENR CCI wassuccessfully predicted [12]

+e branch of machine learning which has been mostwidely used in the field of engineering cost prediction ismainly composed of neural networks support vector ma-chines (SVM) and k-nearest neighbour (KNN) algorithmsJuszczyk and Lesniak proposed a model based on the arti-ficial neural networks (ANN) which are involved in radialbasis functions (RBF) for the purpose of forecasting theindexes of site overhead costs It was found that the pre-diction models had achieved satisfactory results [21] Namet al proposed a hybrid model which combined artificialneural networks and wavelet transformation in its predic-tions of engineering cost index trends [22] In the studiesconducted by Cheng et al a hybrid method was proposedwhich was based on Least Squares support vector machines(LS-SVM) and differential evolution (DE) referred to asELSVM +e results of the aforementioned method indi-cated that it had the ability to successfully predict thefluctuations of ENR CCI [23] Wang and Ashuri adopted amodified KNN algorithm to establish prediction models Itwas found that although the models were better than thetime series models they still could not capture the feature ofjump in CCI +erefore this study believed that furtherexploration of more advanced nonlinear machine learningalgorithms was necessary [24]

22 Limitations of Traditional Prediction Methods and Ad-vantages of LSTM As discussed in previous literature re-view traditional prediction methods have their ownlimitations in predicting the construction cost index Forexample the causal methods require many explanatoryvariables to be predicted and cannot reflect the uncertainprice fluctuations [12] +e univariate time series methods

2 Advances in Civil Engineering

are only suitable for short-term predictions [11] and themultivariate time series methods are costly in terms of theiranalysis and prediction process [20] +e major drawback ofthe SVM and KNN algorithms is their high computationalburden [25 26] LSTM was originally proposed byHochreiter and Schmidhuber [27] which is an effectivenonlinear recurrent network LSTM has proven to be su-perior to most nonparametric prediction methods [28] +eadvantages of LSTM can be specifically analysed by com-paring with the limitations of other methods It has beenfound that RNNs have the problem of gradient vanishingand lacking of long-term memory ability [29] In the processof LSTM application in the field of cost prediction LSTMreplaces RNN neurons with memory cell states and controlsthe flow of information by adding an input gate forget gateand output gate +ese nonlinear summation units of LSTMuse the sigmoid function to calculate the memory state(previous network state) of the network as the input If theoutput result reaches the threshold then the output of thegate and the calculation result of the current layer are inputto the next layer by means of matrix multiplication If thethreshold is not reached then the output result is forgotten[30] +e weight of each layer of network and gate nodes willbe updated during each backpropagation training process+is structural form grants LSTM more sophisticatedtransition abilities for addressing gradients [31] therebycompensating for the limitations of RNNs Correspondinglyalthough LSTM has no advantage in dealing with highlynonlinear and long interval time series datasets [32] thetraining cost and duration of the LSTM model are generallylow and easy to control when the number of hidden layerneurons is set reasonably

3 Research Methodology

31 Research Questions and Methodology Consideration+is study poses two research questions how LSTMNN canbe applied to predict engineering cost indexes and howvarious factors can affect model performance includinginput features time series length and model structures

Applying LSTM NN in predictions of constructionengineering cost indexes and exploring the optimizationmechanism are mainly based on the followingconsiderations

(i) According to literature review and theoretical re-search analysis the structure type training cost andcalculation efficiency of LSTM NN are suitable forthe processing of cost indexes data However theperformance of LSTM NN in this field has not beenexplored in the previous research

(ii) +e feature selection of an LSTM neural networkmodel has a major influence on the prediction ac-curacy of the model However there is currently nostandard selection criterion for the selection of theparameters of such a model

32 Research Objectives and Research Methods +e aims ofthis research were to explore the various theories and

methods available for LSTM neural networks in the ac-curate predictions of construction engineering cost in-dexes and to evaluate the proposed modelrsquos predictionperformances +e first objective of this research is toinvestigate the research gaps in the field of cost predictionand the limitations of the current forecasting methods+e corresponding research methods are literature reviewand theoretical analysis methods +e second researchobjective is to determine a set of indicators suitable forthe prediction of Chinarsquos cost indexes +rough literaturereview and expert argumentation the content of theindicator set can reach a certain level of comprehen-siveness +e third research goal is to verify the appli-cability of the LSTM NN for which the case analysismethod can be used to objectively judge the predictiveperformance of the model +e final research goal is toexplore the optimization mechanism of the LSTM modelDifferent input features time series lengths and modelstructures are set by comparative analysis to improveprediction accuracy

4 Selection of the Prediction Indicators and theOriginal Data Collection

41 Selection and Adjustment of the Forecasting Indicators+e indicators selection criteria of this study benefit fromprevious research of Zhang [33] which analysed variousfactors affecting Taiwanrsquos engineering cost indexes +eindicators must reflect four aspects economy finance stockmarket and energy In addition the building materialsmarket is a new consideration+rough statistical analysis ofrelated studies and expert demonstrations six indicatorswere identified namely GDP [3 7 13 34] Floor SpaceStarted [3 13 19 20 34 35] Crude Oil Price[3 13 23 34 36] Prime loan rate [19 20 35 36] ConsumerPrice Index [3 7 12 13 19 20 23 34 36 37] and MoneySupply [3 7 13] Due to the fact that the price information ofmaterials has a great influence on the domestic cost indexesthe jury believes that the relevant indicators should be addedto the indicator set +en in order to evaluate the practi-cability of the proposed method eight experts in the field ofengineering and construction were interviewed includingtwo university professors two cost consulting experts twoengineering managers of construction units and twotechnicians of design units +e expertsrsquo review is dividedinto two rounds +e goal of the first round is to revise theinitial indicators and delete the individual indicators whichinvolves a level of correlation that is too low for our pur-poses +e second round is implemented through expertquestionnaire scoring and the opinion concentration (1113957Ei)and dispersion (σi) are calculated at the same timeWhen theindicator satisfies 1113957Ei le 1 or σi ge 3 it can be selected Sub-sequently 16 indicators were selected as the final index setas detailed in Table 1

42 Preparatory and Data Collection Processes +e originaldata used for the training of forecasting model in thisresearch were collected from several different data

Advances in Civil Engineering 3

resources including the CEIC database (httpsinsightsceicdatacom) National Data Network (httpdatastatsgovcn) Shenzhen Construction Cost Network (httpwwwszjsgovcn) and the Wide Timber Network(httpswwwgldjccom) Based on the established in-dicator set the data were collected from May 2007 toMarch 2019 totaling 143 months of datasets Eachmonthrsquos data attributes correspond to 16 indicators Atotal of 143 datasets which were collected from the variousdata sources were identified as appropriate for use in thefollowing model training and evaluation processes

Due to the fact that the original data only contained rawinformation which could potentially lead to problems re-lated to noise anomalous points missing information er-rors and frequency differences the data were preprocessedprior to being used for training the model Boxplot is amethod to describe data using five statistics in the dataminimum first quartile median third quartile and maxi-mum [38] +rough the boxplot method we found oneoutlier (cement price) Since the number of outliers has alittle impact on the total number of samples and would notreduce the effective information the method of deleting thedataset was used If there are a large number of outliers theymust be treated as missing values and the data must be filledin by means of average value or max likelihood Due to thedifferent dimensions and orders of magnitude min-max

standardization was adopted to perform a certain lineartransformation on the original data for the purpose ofmaking the processed data fall into the range of [0 1] +enfollowing the completion of the data preparatory processingthe characteristics of the dataset and the statistical resultswere determined as shown in Table 2

5 Development and Comparison of the LSTMNeural Networks

51 Model Creation and Performance Evaluations Based onnormal machining learning theories and pervious research[11 24 39] the division of training data and test datagenerally takes datasets of the last 5ndash10 time series as testsets Since this study uses five months as the prediction dataunit the training set and test set are divided in a 4 1 ratioie the first 80 of the data blocks was used as the trainingset with the remaining 20 used as the testing set +eaccuracy of each model was assessed according to its abilityto predict the engineering cost indexes based on the trainingdata +ree common statistical error measurement methodswere used to evaluate the accuracy and predictability resultsof the models namely mean square error (MSE) meanabsolute error (MAE) and mean absolute percentage error(MAPE) methods +eir equations are as follows

Table 1 Coding type and data sources of the index set

Indicator name Brief explanation Data source

Gross domesticproduct (GDP)

GDP refers to the final result of the production activities of all resident units ina country (or region) calculated in accordance with the national market pricein a certain period of time and is often recognized as the more accurate

indicator to measure the economic status of the country National Bureau of Statistics ofChinaConsumer price

index (CPI)CPI is a macroeconomic indicator that reflects changes in the price levels of

consumer goods and service items generally purchased by households

Money supply (MS)Money supply refers to the sum of cash and deposits in circulation at a certainpoint in time money supply is one of the main economic statistical indicators

compiled and published by the central banks of various countries

Floor space started(FSS)

Floor space started is the construction area of each house newly started in thereport period the commencement of the house shall be subject to the datewhen starting to break the ground and dig the trench (foundation treatment or

permanent pile driving) China entrepreneur InvestmentClubCrude oil price

(COP) Crude oil price is the first purchase price of a barrel of crude oil

Loan rate (LR)Loan rate is the interest rate charged to borrowers when banks and otherfinancial institutions issue loans this refers to the annual interest rate of the

Bank of Chinarsquos loans

Steel bar price (SBP) Glass price(GLP) +e information price is the publicly announced average

social price determined by the government costmanagement department based on the amount of various

typical engineering materials and social supply it isgenerally updated once a month

Material cost index is an index that reflects changes inmaterial cost prices in construction and installation

engineering

Shenzhen housing andConstruction Bureau Glodon

Company Limited

Concrete price (CP) Wood price(WP)

Cement price (CEP) Block price(BP)

Medium sand price(MSP)

Diesel price(DP)

Gravel price (GRP) Material costindex (MCI)

Shenzhenengineering costindex

Shenzhen engineering cost index is an indicator that reflects the degree ofimpact of price changes on engineering costs over a certain period of time


MSE 1N

1113944

N

t1[1113954Y(t) minus Y(t)]

2

MAE 1N

1113944

N

t1|1113954Y(t) minus Y(t)|

MAPE 1N

1113944

N

t1

|1113954Y(t) minus Y(t)|

Y(t)times 100

(1)

52 LSTM Neural Network Development

521 Data Input Due to the fact that cyclic calculationshave unique types the original data were required to besegmented by a time-step process and the input of each timestep was required to correspond to all of the index char-acteristics of a single time point In addition due to thepowerful synthesis ability of the LSTM at different timesteps the index feature information of multiple time pointscould be gradually extracted and synthesized within themovements of the time steps which allowed for theextracted feature vectors to be increasingly powerful in theirexpressions of the input data +erefore it was determinedthat during the data processing the data should be dividedinto blocks with each block containing the input indexcharacteristics of multiple time steps

+e data used in this study were divided into a set ofinput data representing every five-month period in order topredict the cost indexes of the following sixth month +emodel structure of the LSTM was organized by groups asshown in Figure 1 Each group contained five datasets eachof which included 16 indicators Meanwhile the dataset forthe first month of each group contained 17 indicators due tothe fact that the engineering cost index value of the firstmonth (T1) had been added to the dataset as a new feature+is was mainly due to the fact that the data for the firstmonth had been utilized to predict the cost index for the

second month +erefore there was no output value in thefirst month However there was an output value (T2prime)beginning from the second month and T2prime was the com-parison between the predicted value for the first month andthe actual value for the second month referred to as thecalculated residual +e values of engineering cost indexesfrom the second month to the fifth month (T2ndashT5) had beenplaced on the output end which was then compared with thepredicted values as the comparison data Due to the fact thatthe influence results were transmitted to the forecast of thenext month their input only included 16 indicators

522 Model Training During the process of developingdeep neural networks of LSTM a method of multilayeredLSTMwas applied for the structural combinations as shownin Figure 2 LSTMprime represents the given initial networkmodel [X1 X16 Y] represents 16 indicators and en-gineering cost index per month +e parameter learningprocesses for multiple LSTMs were conducted from theLSTM In order to match the actual application scenariosthe mode structure had specifically deployed an analysispattern in which every month had its own LSTM moduletrained using the data of the current month +e results areoutput after the multilayer structure training is completed+en the results of loss and gradient calculation are inputinto the multilayer LSTM structure and finally a cyclicnetwork is formed

MXNet is one of Amazonrsquos most powerful deep learningframeworks Currently distributed machine learning plat-forms that support time series prediction based on LSTMinclude MXNet PyTorch and Caffe2 Compared with otherdeep learning frameworks Mxnet has the advantages ofstrong readability ease of learning high parallel efficiencyand memory saving [40] It also supports multi-GPUtraining multiple language interfaces and multiple devices+ere are two main reasons for choosing MXNet as thedevelopment framework to be used in this study One is toensure the high efficiency of the model in the actual

Table 2 Statistics of the primary selection index set

Indicator name Mean Median Maximum Minimum Std DevShenzhen engineering cost index 136181 139260 177460 100000 22005Material cost index 112432 113110 134290 99520 7528Floor space started 10300070 10297610 22178700 2580100 4547512Crude oil price 572126 540860 948800 231870 188525Loan rate 5700 6000 7470 4350 0918Consumer price index 124960 127260 144080 100000 11624Money supply 92915 89557 173986 31671 43158Steel bar price 4225671 4250000 6050000 2400000 868063Concrete price 385115 360720 540920 314780 57445Cement price 491685 495000 630000 49000 68999Medium sand price 97531 95000 146000 54000 34170Gravel price 111252 120000 160000 60000 26289Glass price 38979 35000 52000 30000 7864Wood price 1169238 1200000 1499000 1000000 139684Block price 279203 290000 290000 233000 14054Diesel price 7325 7350 9360 5470 1110Gross domestic product 14125420 14035170 25269960 6015410 5116898


application scenario and another is to use the MXNetrsquosautomatic gradient function and the packaged optimizer Inpresent study two libraries in MXNet are used to build theentire LSTM model namely NDArray and Autograd +eformer is used to store and process data while the latter canautomatically derive the model parameters to achieve re-verse gradient propagation +e parameters needed formodel establishment based on MXNet include input gateforget gate output gate candidate memory cells weightparameters for the output layer and migration parameters+e weight parameters were randomly initialized to anormal distribution with a standard deviation of 001 and amean of 0+emigration parameters were all initialized to 0and gradients were created for all the network parameters+e network parameters were then connected to the networkstructure by an LSTM computing mode

+e LSTM model training process is shown in Figure 3In the internal structure of LSTM NN the calculationprocesses of the input gate forget gate output gate andcandidate memory cells consisted of the output of the input

layer and the last hidden state For example the 17 char-acteristic variables xt [f1 f2 f17] of the currentmonth and the valid information retained in the previousmonth +e calculations of the current memory cell werecontrolled by the output of both the input gate and the forgetgate+e forget gate controlled the reading of the cell state ofthe previous month and the input gate controlled the inflowof the current candidate cell state Finally the current hiddenstate was calculated by the output gate and the currentmemory cell and it had flowed into the next monthrsquos cal-culations along with the current cell state

+e loss function L2 was calculated by comparing thepredicted values calculated each month with the actualvalues placed in the output layer During the training phaseL2 was taken as the optimization goal and the L2 lossfunction was defined as follows

L2 12

1113944i

labeli minus predi

111386811138681113868111386811138681113868111386811138682 (2)

LSTMprime LSTM LSTM LSTM LSTM LSTM Output

[X1 X16 Y] [X1 X16 Y] [X1 X16 Y] [X1 X16 Y] [X1 X16 Y]

Gradientcalculation

Initial state

The loss functionquickly converges

to zero

Y

N

Figure 2 Training structure of the LSTM model

Cell

Cell

Cell

Cell

T1

T2

T5

T6prime

T5prime

T2prime

Input Output

The 1st month

The 2nd month

The 5th month

Pending month

17 indicators including the actual valueof the first month engineering cost index

The output value is the calculated residualThe actual value of the engineering cost

index is placed on the output

No output

16 indicators excluding the actual valueof the first month engineering cost index




Figure 1 LSTM model data input structure


A momentum method was used as the modelrsquos opti-mization algorithm By introducing the intermediate vari-ables the gradients in the irrelevant direction were cancelledboth positively and negatively which overcame the prob-lems of slow convergence or even nonconvergence caused bythe gradients swinging back and forth in the nondescendingdirection which had been encountered in the traditionalgradient descent methods +e updated parameter formulasfor each iteration of the momentummethod were as follows

υtlarrcυtminus1 + ηtgt

θtlarrθtminus1 minus υt(3)

where υt represents the current momentum ηt is the currentlearning rategt indicates the current gradient θt is the updatedparameter and c denotes the momentum parameter +eintermediate momentum υt needed to be initialized to υ0 whenusing the momentummethod optimizer After that the modelinitialization state data generator learning rate and learningrate attenuation mode could be set to perform the modelparameter training During the training stages the calculatedgradients were clipped to prevent gradient explosions duringthe process of backpropagation which would cause the modelto diverge +e gradients after clipping were as follows

min0

g 11113888 1113889g (4)

After the single batch gradient calculation was com-pleted the network parameters were updated by the mo-mentum method optimizer +e Stochastic GradientDescent Momentum (SGDM) was able to achieve fasterparameter updates and the model had displayed improvingconverging ability Finally the trained model parameterswere saved for future use during the prediction phase

In addition the detailed methods used in the trainingprocess included batch processing and flow training Withconsideration given to the performance levels of the com-puters used in this study the batch size of the training setwas established as 5 the batch size of the test set was 1 andthe learning rate was initialized to 01 after the in learning of200 epochs was completed +en in order to avoid themodel parameter values becoming too large this methodused a weight decay technique with a value of 5eminus 4 and agradient clipping parameter value of 01 which was able toachieve the effects of regularity for the L2 parameter +emodel total time step (num_steps) was set as 5 and a datablock consisted of datasets for every 5 months +e inputvalue for the single step was the feature number(FeatureNumber 17) which represented the 17 charac-teristic variables for the actual values of the engineering costindex+e output vector of each time step moving through asingle fully connected layer contained a single value(num_outputs 1) which indicated the only prediction ofthe engineering cost index for one month

Create LSTM modelparameters and gradients

LSTM internal networkstructure calculation

Calculate lossbased on L2

Training parametersbased on momentum

Update parameters

Epoch = 200

End of training

Data iterator

Provide data by batch

Set momentum initialvalue

Set the learning rateand attenuation mode

Initialize momentumparameters

Gradientclipping

Y

N

Figure 3 Training process of the LSTM model


523 Model Validation and Analysis Result After the de-velopment of the LSTM model the decreases in the outputfor the loss function with the number of learning iterationscould be used to determine the convergence and fittingeffects of the model As shown in Figure 4 the values of theloss function for the LSTM model had rapidly converged tonear zero as the number of learning iterations increasedduring the training process When the number of learningiterations reached 200 the value of loss function was ob-served to be almost zero which indicated that the model hadachieved a good convergence and could be used for thepredictions of the test sets

+e differences observed in the fitting effects between thepredicted and real values are displayed in Figure 5 +eseobserved differences indicated that the trend patterns of thetwo curves were almost same and that the LSTM model hadachieved improved prediction results

As can be seen in Figure 6 the error values of the LSTMprediction model were extremely small and it was slightlybiased around the value of 0 Negative error means that thepredicted value is lower than the actual value and thepositive errors are the opposite +e maximum error valuewas only minus203 and the minimum error value was deter-mined to be minus07 In addition the mean absolute error(MAE) of this studyrsquos 27 test sets was only 096 +ereforethe prediction effects had met the prediction requirements+e mean square error (MSE) and the mean absolute per-centage error (MAPE) were also selected to evaluate theprediction accuracy of the LSTM model +e calculationresults are detailed in Table 3 +e MAPE of this studyrsquosLSTM model was 071 and the prediction accuracy hadreached 9929 which was adequate to show the capacity ofthe LSTM neural networks to utilize the long-distance de-pendence information in the sequence data

53 Prediction Performance Comparison with SVM ModelFor comparing the performance of the proposed model thispaper selects the current advanced SVM algorithm as thecomparison object and trains the model based on the samedataset +e predicted results are shown in Figure 7 and theerror results are shown in Table 4

+rough comparison it is found that LSTM has ad-vantages in terms of both prediction accuracy and parameteradjustment+e accuracy of the SVMmodel is 9801 whilethat of the LSTMmodel is 9929 and the fitting effect of theLSTMmodel is better+e LSTMmodelrsquos fluctuation level ofthe absolute error and mean square error are smaller thanthat of the SVM model In addition the SVM model onlyinvolves two parameters the penalty term ldquoCrdquo and the kernelfunction difference coefficient ldquogammardquo However there isno universally accepted method for determining these +econventional approach is to take values based on experiencewithin a certain range then gradually narrow the range bycomparing the MSE after training to determine the strongerparameters Although LSTM involves many parameters andgenerally the input value output value and hidden layer theneuron number must be adjusted +e weights andthresholds are randomly assigned and the parameters are

200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200

Figure 4 Trend of the loss function of the LSTM training set

180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25

Figure 5 Prediction fitting of the LSTM model

20

15

10

05

00

ndash05

ndash10

ndash15

ndash20

0 5 10Number of test set

Test set errorMAE

Erro

r val

ue

15 20 25ndash25

Figure 6 Prediction error trend of the LSTM model


updated using SGDM Taking these aspects together theproposed prediction framework is shown to possess certaincompetitiveness

54 Framework Application Scenarios and Steps +e pro-posed framework can be applied in forecasting the short-term or long-term trend of macroeconomic situation thathas great influence to the cost and financial budget of aconstruction project in terms of the real practical scenariosincluding policy making of government departments theinvestment decision-making of real estate enterprises therationality of technical and economic indicators of designunit and the dispute settlement between the client and thegeneral contractor

Take the issue of contract risk between the client and thegeneral contractor as an example In the bidding stage thecontracting company usually gives harsh bidding conditionsfor the price adjustment of building materials which oftenmakes the construction units in a passive situation +eproposed framework can avoid the risk of the constructionparty to a certain extent +e specific steps are as followsFirstly the construction units can quickly establish atraining team within the validity period of the tender tocollect the indicators of the current period and previousyears and use it as the original training data Secondly theteammembers predict the monthly engineering cost indexesduring the construction phase based on the proposed modeland the construction period Finally judge the rationality of

the relevant requirements of the bidding documentsaccording to the change range of the cost indexes betweenthe completion period and the current period If the re-quirements are reasonable the construction units willnormally participate in the bidding Instead they can applyto negotiate with general contractor or abandon the bid tominimize their own risks In summary the proposedframework has practical value to assist bidding decisions

55 Analysis and Optimization of the Prediction Accuracy ofthe LSTM Model +e aforementioned research resultsshowed that the proposed LSTM neural network model wassuitable in prediction applications of construction engi-neering cost indexes However during the process of cre-ating the LSTM model it was found that there was nostandard method available for sample selections parametersettings setup of time series lengths and the designing of themodel structure Generally speaking the setup of the modelwas in accordance with previous experience However it wasaccepted that the selection of the various samples and othermodel settings would potentially affect the prediction per-formance of the model +erefore it was necessary in thisstudy to discuss the mechanisms and optimization of theparameter selections andmodel settings for the developmentprocess of the LSTM model

551 Input Feature Analysis +ere are many factors whichmay potentially affect the predictions of construction project

Table 3 Prediction error and accuracy results of the LSTM model

Model Absolute maximum error Absolute minimum error MAE MSE MAPE Model accuracyLSTM 203 07 096 103 071 9929

180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number

SVM pre and true value

15 20 25

Figure 7 Prediction error trend of the SVM model

Table 4 Prediction error and accuracy results of the SVM model

Model Absolute maximum error Absolute minimum error MAE MSE MAPE () Model accuracySVM 723 074 283 1051 199 9801


cost indexes +ese factors can mainly be divided into fourcategories economic energy construction market and allindicators

In the present study in accordance with the afore-mentioned four groups of indicators the following fourmodels were established and a basic model of all the in-dicators was used as a comparison model in order to explorethe impacts of the input features on the engineering costindexes +e prediction results of the other three modelswere obtained by modifying the input sample dimensions ofthe base model +e mean square error and prediction ac-curacy of the model were then successfully calculated +eresults are shown in Table 5

+e absolute error values of the prediction results werecalculated according to the prediction results of the 27 testsets In order to compare the error values of the models andtheir stability the absolute error values of the predictions ofthe four models were determined as described in Figure 8

As previously illustrated in Table 5 the prediction ac-curacy of Model M1 had reached 9871 +erefore it wasalso confirmed to be appropriate to use the LSTM model ofthe economic indicators to predict the engineering costindexes In this studyrsquos comparison of Model M1 and ModelM12 it was observed that the LSTM model with energyindicators added was more effective However although theprediction accuracy had been improved the absolute errorfluctuations of Model M1 were found to be similar to thoseof Model M12 which indicated that the energy indicatorshad only increased the amount of training information andnot the amount of effective information+en by comparingModels M1 M12 and M123 it could be seen that theprediction accuracy of the LSTM model had graduallyimproved and the performance results of the model hadbecome increasingly more stable +ese findings indicatedthat when the dimension of input data was small appro-priately increasing the input features of the model couldpotentially improve the overall prediction accuracy of themodel

+is study then compared the four models in combi-nation with Table 5 and Figure 8 It was found that theprediction accuracy of Model M3 was almost the same asthat of Model M123 and the stability levels of the modelswere similar both of which were better than those of ModelM1 and Model M12 +erefore using this studyrsquos experi-mental results it was determined that the indicators relatedto the construction market had major impacts on the pre-dictions of the construction engineering cost indexes +enby comparing Model M12 with Model M123 it was foundthat the prediction accuracy of themodel had increased from9887 to 9929 which again showed that the indicatorsrelated to the construction market had major influences onthe predictions of the engineering cost indexes Further-more the results also indicated that the prediction accuracyof the model could be improved by the appropriate additionof effective input information In addition by outputting theloss values of the training set and test set it was observed thatthe loss functions of the four models had all decreasedrapidly with good convergence and no occurrences ofoverfitting

In summary among the three types of indicatorseconomic indicators energy indicators and constructionmarket indicators the construction market indicators werefound to have the most significant impacts on the pre-dictions of the engineering cost indexes and could be usedas effective information for the proposed model It wasobserved that when increasing or decreasing the dimen-sions of the input features the dimensions of the input datawere small appropriately increasing the effective infor-mation could potentially improve the prediction accuracyof the model However when the dimensions of the inputdata were larger the prediction accuracy of the modelcould not be greatly improved In such cases even re-dundancy of the input information may occur which couldpotentially reduce the accuracy of the model +erefore itwas determined in this study that the economic energyand construction market indicators should be used as theinput features for the proposed model which would im-prove the prediction accuracy of the LSTM model It wasalso believed that if the data collection was difficult theconstructionmarket indicators could be directly used as theinput features

56TimeSeries LengthAnalysis +e length of the time seriesmay also affect the prediction accuracy of a model +elength of a time series is usually obtained from the analysis ofspecific problems and there currently is no standard de-terminationmethod In the present study 16 indicators wereused as the input variables and the data were processed intotime series of lengths of 3 5 7 and 10 respectively+en themodel was established and trained +e results are shown inTable 6 Since the time series lengths of each model hadvaried it was necessary to redivide the training set and testset of each model +e test sets were extracted by a randomfunction in order to ensure that the prediction accuracy ofthe test sets also represented the prediction accuracy of themodel+en in accordance with the prediction results of the27 indicators of each model test set the absolute error valueswere calculated +e results are shown in Figure 9

As can be seen in Table 6 the prediction accuracy ofModel M123-d3 was lower than that of the other twomodels Meanwhile as shown in Figure 9 the absolute errorsof Model M123-d3rsquos predictions had fluctuated greatly andthe stability of the modelrsquos performance was obviously lowerthan that of the other three models In this studyrsquos com-parison results of Models M123-d5 and M123-d7 it wasfound that the accuracy levels had slightly decreased whichmay have been caused by the different test sets +e stabilitylevels of the aforementioned two models were also found tobe similar +en by comparing the three models with thetime series length of 5 7 and 10 it could be seen that theprediction accuracy results were close and the stability levelsof the modelsrsquo performances were also similar +at is to saywhen the time series lengths had increased the predictionaccuracy of the models had first improved and then almostremained unchanged Similarly the loss functions of thefour models still converged rapidly to 0 without anyoverfitting observed


It was observed in this study that when the time serieslength was excessively short and the effective informationprovided by the samples was insufficient the proposedLSTMmodel could not learn the transformation rules of thetraining samples which led to a low accuracy rate of themodel However because the further the data were takenfrom the predictive period the smaller the prediction im-pacts on the data of the prediction period would be theprediction accuracy of the model was not significantlyimproved when the time series length had been increasedMoreover the longer the time series was the more noise itwould contain which is not conducive to the accuratepredictions of the model In summary the time series lengthhas a certain influence on the prediction accuracy but thetraining cost is more sensitive to its change With the in-crease of time series length the improvement of training costis much higher than the prediction accuracy +erefore it isnecessary to select the appropriate time series length to

improve the application efficiency of the model In thepresent study it was observed that the M123-d5 and M123-d10 Models exhibited the highest prediction accuracy +eaccuracy rates of the twomodels were found to be analogousalthough the training duration of Model M123-d10 waslonger Subsequently the time series length was set as 5 inthis research in order to achieve an improved modelperformance

57 Analysis of the Model Structure For LSTM neural net-works the number of hidden layer neurons determines thestructure of the neural network model However there iscurrently no unified method which can be applied to de-termine the number of neurons in a hidden layer In thisstudy by comparing the prediction accuracy rates of themodel under the conditions of various numbers of neuronsin the hidden layer the most suitable number of neurons wasselected

+erefore on the basis that all 16 indicators were used asthe input variables of the model and the time series lengthwas set as 5 the number of hidden layer neurons was set tothe value of 10 times between 10 and 150 +e modelrsquostraining and the prediction results were successfully ob-tained as shown in Table 7

It was observed in this study that when the number ofhidden layer neurons increased from 10 to 40 the meansquare errors of the modelrsquos predictions gradually decreased

Table 5 Effects of the input features on the modelrsquos accuracy

Model Dimension Category Indicators MSE Model accuracyM1 4 Economy LR CPI MS GDP 392 9871M3 10 Construction market MCI FSS SBP CP CEP MSP GRP GLP WP BP 127 9922M12 6 Economy+ energy MCI CPI MS GDP COP DP 316 9885M123 16 All All 103 9929

4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set

M1ndashabsolute errorM3ndashabsolute error


Figure 8 Predictions of the absolute error trends of the fourmodels with different input features

Table 6 Effects of the time series lengths on the accuracy rates ofthe models

Model Time serieslength

Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set

M123ndashd3ndashabsolute errorM123ndashd5ndashabsolute error


Figure 9 Predictions accuracy and absolute error trends of themodels with different time lengths


until reaching a minimum value In addition the predictionaccuracy rate of the model gradually increased until themaximum value was attained Furthermore as the number ofhidden layer neurons continued to increase the predictionaccuracy rate of the model did not improve and when thenumber of hidden layer neurons increased to approximately100 then the accuracy of the modelrsquos results tended tofluctuate It was determined in this study that too many or toofew hidden layer neurons would potentially reduce the pre-diction accuracy of the model For example if the number ofhidden layer neurons was too small then the underfitting ofthemodel led to increased prediction errorsMeanwhile if thenumber of hidden layer neurons was too great then theprediction accuracy of the model tended to not be improvedwhich had a tendency to lead to the occurrence of unstablephenomena and overfitting of the model

6 Conclusions

In this article we proposed a prediction model based on anLSTM neural network which is suitable for the short-termengineering cost indexes prediction or other cost data withtemporal or spatial properties +e proposed model will beapplied to the feasibility study stage or bidding stage of theproject It can provide accurate industry trends so that allengineering participants can evaluate the project risk in acomprehensive manner in advance which is helpful to for-mulate relevant response plans +is research makes signif-icant contributions in terms of new emerging tools and newAI algorithm for the traditional field of construction costindex prediction Firstly the new emerging tools are originallyapplied in this area after reviewing previous research resultsAlthough LSTMNN has been used in prediction problems inother application areas there is a lack of explorative researchto train the algorithm model by using specific constructiondate and evaluate the forecasting results for the theoreticallysuitability of cost index prediction Secondly the new AIalgorithm of LSTM NN has the ability to sort out the limi-tations of existing methods in cost index prediction Since

most of the traditional methods are not suitable for nonlinearfitting and have poor response to the timeliness of the dataLSTM NN has advantages in dealing with limitations of thegradient vanishing and the inability to address long-termdependence Upon analysing the experimental results of theLSTM model the following key findings are observed (1)Sixteen prediction indicators can comprehensively and timelyreflect the domestic economic energy and market condi-tions which meet the requirements of capturing the fluctu-ation trend of the engineering cost indexes (2) +e proposedLSTM model has good fitting effect and small predictionerror which fully demonstrates the ability of the algorithm toutilize long-distance dependent information in sequence data(3)+rough the optimizationmechanism in three aspects theexperience of model creation is successfully converted intoprinciple standards in which the optimization of the inputfeatures is the most critical (4) Compared with othermethods the LSTMmodel possesses significant advantages intraining cost time series process and short-term predictionaccuracy +is model can be used to deal with similar timeseries such as crowd or vehicle flow and stock pricesGenerally speaking it was confirmed in this study that theLSTM neural networks were applicable and effective in regardto predictions of construction cost indexes +e obtainedresearch findings of this study could potentially provide someguidance for subsequent researchers in selecting predictionalgorithms and model parameters However the proposedmethod framework still has some limitations such as thefollowing First the data required for the research weremainlytaken from four domestic databases and the authenticity ofthese historical data lacks verification Second the indexdetermination criteria used in this article lack authority anddifferent countries or organizations may involve variouscriteria Finally due to the limited amount of statistical dataavailable in China at present this study only validated theshort-term prediction performance of LSTM Based on theabove limitations our future work will focus on improvingthe structural layer of LSTM in order to compensate for itsdisadvantages in the long-term prediction process

Table 7 Effects of the modelrsquos structure on the accuracy results

Model Model structure Mean absolute error Mean square error Accuracy ()M123-h10 16-10-1 111 137 9918M123-h20 16-20-1 107 128 9921M123-h30 16-30-1 107 123 9921M123-h40 16-40-1 085 089 9934M123-h50 16-50-1 096 102 9929M123-h60 16-60-1 102 114 9924M123-h70 16-70-1 105 126 9921M123-h80 16-80-1 106 122 9921M123-h90 16-90-1 101 115 9927M123-h100 16-100-1 125 167 9911M123-h110 16-110-1 105 116 9924M123-h120 16-120-1 114 141 9917M123-h130 16-130-1 116 145 9915M123-h140 16-140-1 109 129 9920M123-h150 16-150-1 113 148 9918


Data Availability

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

Conflicts of Interest

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

References

[1] S-H Ji J Ahn H-S Lee and K Han ldquoCost estimationmodelusing modified parameters for construction projectsrdquo Ad-vances in Civil Engineering vol 10 p 2019 Article ID8290935 2019

[2] M G Meharie Z C Abiero Gariy R N N Mutuku andW J Mengesha ldquoAn effective approach to input variableselection for preliminary cost estimation of constructionprojectsrdquo Advances in Civil Engineering vol 2019 p 14Article ID 4092549 2019

[3] B Ashuri S M Shahandashti and J Lu ldquoEmpirical tests foridentifying leading indicators of ENR construction cost in-dexrdquo Construction Management and Economics vol 30no 11 pp 917ndash927 2012

[4] Y Elfahham ldquoEstimation and prediction of construction costindex using neural networks time series and regressionrdquoAlexandria Engineering Journal vol 58 no 2 2019

[5] B Wang and J Dai ldquoDiscussion on the prediction of engi-neering cost based on improved BP neural network algo-rithmrdquo Journal of Intelligent amp Fuzzy Systems vol 47 no 5pp 1ndash8 2019

[6] T Biqiu Z Sai and H Jia ldquoEstablishment of engineering costprediction system based on BIM and ELMrdquo ConstructionTechnology vol 17 2018

[7] J M WWong and S T Ng ldquoForecasting construction tenderprice index in Hong Kong using vector error correctionmodelrdquo Construction Management and Economics vol 28no 12 pp 1255ndash1268 2010

[8] B Ashuri and J Lu ldquoTime series analysis of ENR constructioncost indexrdquo Journal of Construction Engineering and Man-agement vol 136 no 11 pp 1227ndash1237 2010

[9] M Innocent J S Wasek and A Franz ldquoPredicting militaryconstruction project time outcomes using data analyticsrdquoEngineering Management Journal vol 30 no 4 pp 232ndash2462018

[10] S Islam ldquoProvenance lineage and workflowsrdquoMaster+esisBrown University Providence RI USA 2010

[11] G B Hua and T H Pin ldquoForecasting construction industrydemand price and productivity in Singapore the BoxJenkinsapproachrdquo Construction Management and Economics vol 18no 5 pp 607ndash618 2000

[12] J-w Xu and SMoon ldquoStochastic forecast of construction costindex using a cointegrated vector autoregression modelrdquoJournal of Management in Engineering vol 29 no 1pp 10ndash18 2011

[13] S M Shahandashti and B Ashuri ldquoForecasting engineeringnews-record construction cost index using multivariate timeseries modelsrdquo Journal of Construction Engineering andManagement vol 139 no 9 pp 1237ndash1243 2013

[14] A Akintoye and M Skitmore ldquoMacro models of UK con-struction contract pricesrdquo Civil Engineering and Environ-mental Systems vol 10 no 4 1993

[15] S M Trost and G D Oberlender ldquoPredicting accuracy ofearly cost estimates using factor Analysis and multivariateregressionrdquo Journal of Construction Engineering and Man-agement vol 129 no 2 pp 198ndash204 2003

[16] H L Chen ldquoDeveloping cost response models for company-level cost flow forecasting of project-based corporationsrdquoJournal of Management in Engineering vol 23 no 4 2007

[17] T Moon and D H Shin ldquoForecasting construction cost indexusing interrupted time-seriesrdquo KSCE Journal of Civil Engi-neering vol 22 no 5 pp 1626ndash1633 2018

[18] J M W Wong A P C Chan and Y H Chiang ldquoTime seriesforecasts of the construction labour market in Hong Kong theBox-Jenkins approachrdquo Construction Management and Eco-nomics vol 23 no 9 pp 979ndash991 2005

[19] S Hwang ldquoDynamic regression models for prediction ofconstruction costsrdquo Journal of Construction Engineering andManagement vol 135 no 5 pp 360ndash367 2009

[20] S Hwang ldquoTime series models for forecasting constructioncosts using time series indexesrdquo Journal of Construction En-gineering and Management vol 137 no 9 pp 656ndash662 2011

[21] M Juszczyk and A Lesniak ldquoSite overhead cost index pre-diction using RBF neural networksrdquo in Proceedings of the 3rdInternational Conference on Economics and Management(ICEM 2016) DEStech Transactions on Economics Businessand Management pp 381ndash386 Suzhou China 2016

[22] H Nam S H Han and H Kim ldquoTime series analysis ofconstruction cost index using wavelet transformation and aneural networkrdquo in Proceedings of the 24th InternationalSymposium on Automation amp Robotics in Construction(ISARC 2007) Chennai India September 2007

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

[24] J Wang and B Ashuri ldquoPredicting ENRrsquoS construction costindex using the modified K nearest neighbors (KNN) algo-rithmrdquo in Proceedings of the Construction Research CongressSan Juan Puerto Rico May 2016

[25] W-J Hwang and K-W Wen ldquoFast kNN classification al-gorithm based on partial distance searchrdquo Electronics Lettersvol 34 no 21 pp 2062-2063 1998

[26] H Wang and D Hu ldquoComparison of SVM and LS-SVM forregressionrdquo in Proceedings of the 2005 International Con-ference on Neural Networks and Brain October 2006

[27] S Hochreiter and J Schmidhuber ldquoLong short-term mem-oryrdquo Neural Computation vol 9 no 8 pp 1735ndash1780 1997

[28] Y Tian and P Li ldquoPredicting short-term traffic flow by longshort-termmemory recurrent neural networkrdquo in Proceedingsof the IEEE International Conference on Smart CitySocialcomSustaincom Chengdu China December 2016

[29] Y Bengio P Simard and P Frasconi ldquoLearning long-termdependencies with gradient descent is difficultrdquo IEEETransactions on Neural Networks vol 5 no 2 pp 157ndash1661994

[30] W Shihao Z Qinzheng Y Han L Qianmu and Q Yong ldquoAnetwork traffic prediction method based on LSTMrdquo ZteCommunications Shenzhen China 2019

[31] X Ran Z Shan Y Fang and C Lin ldquoAn LSTM-basedmethod with attention mechanism for travel time predictionrdquoSensors vol 19 no 4 p 861 2019

[32] M Langkvist L Karlsson and A Loutfi ldquoA review of un-supervised feature learning and deep learning for time-seriesmodelingrdquo Pattern Recognition Letters vol 42 2014


[33] Y Zhang ldquoForecasting the trend of construction cost indicesfor Taiwan employing support vector machinerdquo Masterrsquosthesis Chao Yang University of Technology Taichung Taiwan2007

[34] L Jian ldquoIs the information available from historical timeseries data on economic energy and construction marketvariables useful to explain variations in ENR construction costindexrdquo in Proceedings of the Construction Research CongressWest Lafayette Indiana May 2012

[35] T P Williams ldquoPredicting changes in construction cost in-dexes using neural networksrdquo Journal of Construction Engi-neering and Management vol 120 no 2 pp 306ndash320 1994

[36] M-T Cao M-Y Cheng and Y-W Wu ldquoHybrid compu-tational model for forecasting taiwan construction cost in-dexrdquo Journal of Construction Engineering and Managementvol 141 no 4 p 04014089 2015

[37] T Moon and D H Shin ldquoForecasting model of constructioncost index based on VECM with search queryrdquo KSCE Journalof Civil Engineering vol 22 no 8 pp 2726ndash2734 2018

[38] J W Tukey Exploratory Data Analysis Addition-WileyBostan MA USA 1997

[39] J Wang and B Ashuri ldquoPredicting ENR construction costindex using machine-learning algorithmsrdquo InternationalJournal of Construction Education and Research vol 13 no 1pp 47ndash63 2017

[40] T Chen L Mu L Yutian et al ldquoMXNet a flexible and ef-ficient machine learning library for heterogeneous distributedsystemsrdquo Journal of Computer Science httpsarxivorgabs151201274 2015


construction cost prediction mainly include the predictionof bidding price [5] and market information price [6] +eprediction types of cost indexes mainly include the pre-diction of tender price index (TPI) [7] and EngineeringNews-Record (ENR) construction cost index (CCI) [8]Among them the construction cost prediction data mainlycomes from expert judgment or historical data of similarprojects [9] which lacks authority and persuasion Howeverthe data source of cost indexes prediction is generally adynamic release from authoritative institutions +e calcu-lation mode of construction cost is based on the engineeringcost indexes With reference to the concept of ComputerScience the cost indexes can be called the data provenance(lineage or pedigree) of construction cost By directly pro-cessing the data provenance the error and distortion of thedata during the processing can be avoided to a certain extent[10] Most of the current advanced research methods achieveprediction based on a certain regression analysis or as-suming some combination patterns to appear repeatedly[11] LSTM NN replaces the hidden layer neurons in theRNN with four logic units and establishes a long-time lagbetween input feedback and prevention of gradient ex-plosion +is structure type realizes the continuity of theinternal state error flow in the special memory unit enablesLSTM to capture the large dependence of the time stepdistance in the time series and has a strong approximationability for nonlinear and nonstationary time series whichwill improve the prediction efficiency and accuracy of se-quence data with temporal or spatial attributes

2 Literature Review

21 Cost PredictionMethods +emethods of cost predictionscan be divided into two categories causal analysis and timeseries analysis [12] With the development and advantages ofartificial intelligence machine learning algorithms have beenapplied in this field As determined by the available researchreports the causal method also known as causal analysis needsto specify the relationships between the predictive variables andthe dependent variables or between dependent variables andinterpretative variables [12] +erefore causal analysis pre-dictions are based on the interpretations of the relationshipsbetween the engineering cost indicators and other variableswhich can then be used to predict project cost indexes [13] Inthe present study previous related reports were reviewed inwhich causal methods had been successfully used to predicttender price indices (TPI) building prices and constructioncosts [8] Akintoye and Skitmore used OLSmultiple regressionanalysis to construct a contract price model and provided astructural explanation for the trend changes in the TPI throughthe structural equation model [14] Trost and Oberlenderobtained the ranking of the factors influencing the accuracy ofearly cost estimation through factor analysis and multipleregression analysis [15] Chen proposed a combinationmethodbased on transformed time series data multiple regressionanalysis YulendashWalker estimates and incomplete principalcomponent regression analysis to predict the company-levelcost flow within a certain range successfully [16]

Statistical methods are also known as black boxmethods or time series methods which can be divided intothe two categories of univariate andmultivariate time seriesanalyses [17] Wong et al utilized an autoregressive inte-grated moving average model (ARIMA) to predict the fivemain indicators of the Hong Kong labour market [18]Hwang proposed two dynamic univariate time seriesmodels to successfully predict ENR CCI [19] In contrastmultivariate time series analysis is based on multiplevariables +e advantage of this type of analysis is that onlyquantitative data can be used and objective predictions canbe made without additional subjective judgment processes+erefore multivariate time series analysis methods the-oretically have higher predictive abilities [20] Hwangcompared and analysed the prediction effects of autore-gressive moving average models (ARMA) and vectorautoregression (VAR) time series models on structural costindicators +e comparison results indicated that univar-iate and multivariate time series analysis methods each hadtheir own advantages resulting in the ARMA (5 5) havingslightly higher precision [20] Xu and Moon adopted acointegration equation to establish a cointegrated VARmodel in which the deviations between the cointegratingrelationships and the long-run stable relationships betweenthe variables were considered As a result the ENR CCI wassuccessfully predicted [12]

+e branch of machine learning which has been mostwidely used in the field of engineering cost prediction ismainly composed of neural networks support vector ma-chines (SVM) and k-nearest neighbour (KNN) algorithmsJuszczyk and Lesniak proposed a model based on the arti-ficial neural networks (ANN) which are involved in radialbasis functions (RBF) for the purpose of forecasting theindexes of site overhead costs It was found that the pre-diction models had achieved satisfactory results [21] Namet al proposed a hybrid model which combined artificialneural networks and wavelet transformation in its predic-tions of engineering cost index trends [22] In the studiesconducted by Cheng et al a hybrid method was proposedwhich was based on Least Squares support vector machines(LS-SVM) and differential evolution (DE) referred to asELSVM +e results of the aforementioned method indi-cated that it had the ability to successfully predict thefluctuations of ENR CCI [23] Wang and Ashuri adopted amodified KNN algorithm to establish prediction models Itwas found that although the models were better than thetime series models they still could not capture the feature ofjump in CCI +erefore this study believed that furtherexploration of more advanced nonlinear machine learningalgorithms was necessary [24]

22 Limitations of Traditional Prediction Methods and Ad-vantages of LSTM As discussed in previous literature re-view traditional prediction methods have their ownlimitations in predicting the construction cost index Forexample the causal methods require many explanatoryvariables to be predicted and cannot reflect the uncertainprice fluctuations [12] +e univariate time series methods






































engineering


Company Limited




Diesel price(DP)





MSE 1N

1113944

N

t1[1113954Y(t) minus Y(t)]

2

MAE 1N

1113944

N

t1|1113954Y(t) minus Y(t)|

MAPE 1N

1113944

N

t1

|1113954Y(t) minus Y(t)|

Y(t)times 100

(1)














L2 12

1113944i

labeli minus predi

111386811138681113868111386811138681113868111386811138682 (2)



Gradientcalculation

Initial state


to zero

Y

N


Cell

Cell

Cell

Cell

T1

T2

T5

T6prime

T5prime

T2prime

Input Output

The 1st month

The 2nd month

The 5th month

Pending month




No output











min0

g 11113888 1113889g (4)







Update parameters

Epoch = 200

End of training

Data iterator





Gradientclipping

Y

N








200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References















































































engineering


Company Limited




Diesel price(DP)





MSE 1N

1113944

N

t1[1113954Y(t) minus Y(t)]

2

MAE 1N

1113944

N

t1|1113954Y(t) minus Y(t)|

MAPE 1N

1113944

N

t1

|1113954Y(t) minus Y(t)|

Y(t)times 100

(1)














L2 12

1113944i

labeli minus predi

111386811138681113868111386811138681113868111386811138682 (2)



Gradientcalculation

Initial state


to zero

Y

N


Cell

Cell

Cell

Cell

T1

T2

T5

T6prime

T5prime

T2prime

Input Output

The 1st month

The 2nd month

The 5th month

Pending month




No output











min0

g 11113888 1113889g (4)







Update parameters

Epoch = 200

End of training

Data iterator





Gradientclipping

Y

N








200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References











































MSE 1N

1113944

N

t1[1113954Y(t) minus Y(t)]

2

MAE 1N

1113944

N

t1|1113954Y(t) minus Y(t)|

MAPE 1N

1113944

N

t1

|1113954Y(t) minus Y(t)|

Y(t)times 100

(1)














L2 12

1113944i

labeli minus predi

111386811138681113868111386811138681113868111386811138682 (2)



Gradientcalculation

Initial state


to zero

Y

N


Cell

Cell

Cell

Cell

T1

T2

T5

T6prime

T5prime

T2prime

Input Output

The 1st month

The 2nd month

The 5th month

Pending month




No output











min0

g 11113888 1113889g (4)







Update parameters

Epoch = 200

End of training

Data iterator





Gradientclipping

Y

N








200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References















































L2 12

1113944i

labeli minus predi

111386811138681113868111386811138681113868111386811138682 (2)



Gradientcalculation

Initial state


to zero

Y

N


Cell

Cell

Cell

Cell

T1

T2

T5

T6prime

T5prime

T2prime

Input Output

The 1st month

The 2nd month

The 5th month

Pending month




No output











min0

g 11113888 1113889g (4)







Update parameters

Epoch = 200

End of training

Data iterator





Gradientclipping

Y

N








200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References















































min0

g 11113888 1113889g (4)







Update parameters

Epoch = 200

End of training

Data iterator





Gradientclipping

Y

N








200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References
















































200

150

100Loss

val

ue

50

0

0 25 50 75 100Epoch

LSTM loss

125 150 175 200


180

170

160

150

140

Valu

e

130

120

110

100

0 5

PredictTrue

10Number

LSTM pre and true

15 20 25


20

15

10

05

00

ndash05

ndash10

ndash15

ndash20


Test set errorMAE

Erro

r val

ue

15 20 25ndash25











180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References



















































180

170

160

150

140

Valu

e

130

120

110

1000 5

PredictTrue

10Number


15 20 25





















4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References



























































4

5

6

3

2

Abso

lute

erro

r

1

00 5 10 15 20 25

Number of test set






Mean squareerror

Model accuracy()

M123-d3 3 227 9895M123-d5 5 103 9929M123-d7 7 110 9922M123-d10 10 088 9933

25

20

15

Abso

lute

erro

r

10

050 5 10 15 20 25

Number of test set






6 Conclusions






Data Availability




References












































6 Conclusions






Data Availability




References











































Data Availability




References











































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