Expressway Project Cost Estimation With a Convolutional Neural Network Model

With the development of the economy, the prediction of expressway project costs has gained increasing research attention. In this study, based on the convolution neural network (CNN) algorithm, the prediction of the expressway construction cost was analyzed with respect to the conceptual design stage. By summarizing the existing research results, 10 new factors related to the bridge and tunnel are creatively introduced into the cost-prediction index of the expressway conceptual design stage. In addition, the data structure of the expressway project cost prediction is defined and a CNN model is established. Finally, the project information of 415 expressways in China collected in this study is used to verify the research results. The results of the case analysis show that the 10 new indexes related to the bridge and tunnel can improve the prediction accuracy of the model. In addition, the CNN model is more suitable for solving the high-dimensional nonlinear problem of expressway cost prediction than the conventional artificial-neural-network and regression-analysis models, and it can improve the prediction accuracy. The findings of this study can be used to devise financial plans in the early stage of expressway construction and facilitate cost management at the conceptual design stage to help investors acquire project funds in advance.


I. INTRODUCTION
Socioeconomic development and the inclusion of other disciplines in the field of engineering project management [1] have resulted in increasing research attention on project funding over the entire life cycle of a project. For several years, persistent cost undervaluation has reflected a lack of scientific management in project costs across the industry [2]. Therefore, excellent project cost planning is essential to scientifically minimize capital risks [3] and reasonably manage limited funds [4], [5]; these are critical factors in the early stages of any project [6], [7]. Because of the uncertainties in the initial stages of a project, an accurate prediction of the project's ultimate cost is difficult [8], while focusing considerably on the improvement of cost-estimation accuracy in the design stage, i.e., before funding and other factors have been determined, is counterproductive. The gradual application of machine learning in the field of project management has allowed for The associate editor coordinating the review of this manuscript and approving it for publication was Xiaochun Cheng. the development of a data-driven model for efficient, simple, and accurate prediction of expressway project costs [9], with important theoretical and practical significance in this field of research.
Generally, machine learning can be classified as shallow learning and deep learning. Shallow learning methods, such as support vector machines, random forests, decision trees, and K-means methods, are not suitable for expressway costprediction problems, which usually involve many controlled factors; these method do no work well for high-dimensional nonlinear problems. In contrast, deep learning methods, such as artificial neural networks (ANNs) and convolutional neural networks (CNNs), have been widely used owing to the advantage of learning high-dimensional nonlinear models.
In recent decades, scholars have studied several project cost prediction problems, including highway cost forecasting. For example, Hegazy and Ayed [10] used a neural network (NN) to develop a model for predicting highway project costs. They considered 18 highway projects built in Newfoundland, Canada, and used the simplex method and a genetic algorithm to optimize the weights for computing project cost. Adeli and Wu [11] proposed a regularized NN that depended only on the training data and not on the NN structure, learning parameters, or the number of iterations required to train the system to compensate for the overfitting problem. Their approach considered the problem of noisy data for achieving improved prediction accuracy. They used the model to estimate the cost of a reinforced-concrete pavement project. Al-Tabtabai et al. [12] used an ANN to determine the functional relationship between changes in the construction cost of a typical highway and the parameters that caused these changes; they applied their model to the prediction of the percentage increase in the project cost.
Wilmot and Mei [13] summarized the influencing factors for the individual cost of 2827 highway projects in Louisiana from 1981 to 1995 and applied these factors to a NN model. They predicted that highway construction costs in Louisiana would double between 1998 and 2015. Sodikov [14] determined that estimating costs during the conceptual stage of a project was difficult because of the lack of preliminary information, lack of a database on road engineering costs, lack of appropriate cost-estimation methods, and other uncertain factors. Although conventional tools such as regression analysis (RA) have been applied to this uncertainty problem, statistical studies have shown no reduction in the cost-estimation errors. Sodikov [14] determined the method to solve the problem of missing data, analyzed the impact of different variables on the project costs, and proposed an ANN costestimation model for developing countries.
Anderson et al. [15] discussed the costs of highway projects and the method to estimate and manage them before the planning and construction stages to avoid cost increases. Chou and O'Connor [16] developed a web-based application called ''Preliminary Item-Level Cost Estimating System'' (PILCES), which uses the similarity between historical data stored in a database and input items to predict the cost of a highway project at the conceptual stage. Kim et al. [17] developed a two-stage approach for predicting the cost of a highway project. In the first stage, they used a case-based reasoning model to collect eight features that affected project costs and analyzed 92 cases. In the second stage, they built an estimation model based on quantity and unit costs, collected cost estimates for major projects, and validated their approach against 78 cases. Their approach allows the user to effectively control the cost within a particular budget for an efficient feasibility study and preliminary design.
Attal [18] used an NN to identify the parameters that affect the cost and duration of highway construction. Asmar et al. [19] developed a method similar to the program evaluation and review technique that decomposes the project work content at the conceptual stage and predicts the highway project cost by analyzing historical bidding data to determine the most likely cost. Elbeltagi et al. [20] established an ANN model to predict the highway project cost at the conceptual design stage. They identified 18 influencing factors, which were divided into three categories: project-specific, project participants, and environmental. Before using an NN model to predict data, the 18 factors were reduced to 11. The authors trained the model using the historical cost data of 67 projects in Libya. Further, they showed that their model could accurately predict the cost of Libyan highway projects at the conceptual stage and meet the requirement of an error less than 20% during the conceptual design phase. Swei et al. [21] proposed an RA-based cost-estimation method. The validity of their model was verified using 15 pavement bidding projects in five states of the United States. Tijanic et al. [22] established an ANN model for estimating road engineering costs and trained the model by using the road database of Croatia. The results showed that the NN is an effective method that can be used for cost predictions in the initial design stage.
In addition to predicting highway project costs, machine learning can be used for prediction in other fields such as meteorology, industry, agriculture, and other construction projects. Some researchers predicted the cost of residential projects using an NN model [23]- [26]. Rafiei and Adeli [27] used sensor collection techniques to propose a method for the global and local health assessment of structural systems. Chao and Skibniewski [28] applied the NN method to construction technology management. Hinton and Salakhutdinov [29] studied the conversion of high-dimensional data to low-dimensional data based on the use of an NN. Rafiei and Adeli [30] investigated NN-based feature extraction. Elfahham [31] forecasted the construction cost index by using NNs, linear regression, and autoregressive time series. Based on the early regularization method, Chandanshive and Kambekar [32] considered 78 construction projects in India as examples and used an ANN model to predict the early cost of the construction projects. The prediction results of the trained NN model showed that the model can well predict the cost of construction projects at the initial stage of construction. Abd et al. [33] determined 25 factors that affect the construction cost, employed them as input characteristic information, and used an ANN model to study the construction project cost in Iraq. A case analysis of the construction project cost proved the effectiveness of the ANN model in terms of cost prediction. Hashemi et al. [34] reviewed the cost of construction projects from 1985 to 2020 and concluded that, in almost all cases, the estimation and analyses of the factors affecting the costs of a project in the initial stage of the project is important, and ANN and RA are the most commonly used methods of project cost forecasting.
The continuous development of big-data technology in recent years has led to the gradual replacement of NN models with CNN models in an increasing number of applications. Cai et al. [35] used a recurrent NN (RNN) and a CNN to predict the load in commercial buildings. Chen et al. [36] used a CNN to model a tropical cyclone. They trained the model with satellite, infrared, brightness, temperature, and microwave rain rate data of 1097 tropical cyclones between 2003 and 2014 and used the data from 188 tropical cyclones from 2015 to 2016 to optimize the model. The results showed that their proposed model could improve the prediction accuracy. Yang et al. [37] proposed a dual-CNN model for predicting residual life. Their model took advantage of the powerful feature extraction capabilities of a CNN model; the model did not require the extraction of features to maximize the retention of useful information. Yang et al. [38] used a CNN to learn important features related to rice yields from low altitude remote-sensing images and established a model to predict grain yield. Delgado et al. [39] proposed a prediction analysis and modeling system and used a 2.75-million-point power-transmission-project dataset for conducting a case study. Three of the most popular costestimation models (linear regression, support vector regression, and ANNs) based on big data have been brought to fruition. Liu et al. [40] obtained the speed time series from GPS data, transformed the collected data into twodimensional data images, learned the traffic characteristics through a CNN model, and transformed the traffic incidentdetection problem into a classification problem. The effectiveness of the model was proved through experiments.
Based on the aforementioned literature review, four conclusions can be drawn.
• First, ANN and RA are the most commonly used methods of project cost forecasting, with machine learning being repeatedly applied for the cost prediction of engineering projects. Project cost prediction is closely related to the development of machine learning algorithms.
• Second, existing research on highway cost prediction has not fully considered factors that affect costs; for example, the influence of factors in terms of the type and scale of the bridge and tunnel projects have not been considered (see the data structure of Section III for a detailed discussion).
• Third, the NN models used to predict the cost of engineering projects have deficiencies such as overfitting, require excessive parameters, and involve complicated calculations. Although improved studies have been conducted, these limitations still remain to some extent.
• Fourth, CNN models provide obvious advantages over other machine learning approaches in terms of reducing overfitting, excessive parameters, and complicated calculation and have been widely used in the fields of meteorology, industry, agriculture, etc. However, research on their applicability to expressway cost prediction is still lacking.
Therefore, to overcome the shortcomings of existing studies on expressway project cost prediction, this study analyzed the problem based on the CNN-based machine learning algorithm by considering more comprehensive influencing factors. Factors that affect expressway project costs were systematically summarized and 10 factors related to the bridge and tunnel were introduced. A data structure was then constructed to establish the CNN model. In addition, two main prediction models (ANN and RA) applied in the field of engineering projects were introduced as comparative models to verify the effectiveness of the proposed CNN model based on the collected 415 expressway project data.

II. RESEARCH METHODOLOGY
This study focused on developing a model for predicting the expressway cost at the conceptual design stage, which comprises 30% of the complete project design [19]. In the case of expressway projects, this involves the determination of corridors and basic engineering scales for bridges and tunnels. The proposed model was developed in five steps. First, a literature review was performed to obtain the factors influencing the expressway project cost. Second, these influencing factors were selected or newly introduced. Third, the characteristics of the influencing factors were reconstructed into a two-dimensional matrix and the CNN method was used to establish an expressway project cost-prediction model. The expressway project data were then collected. Finally, the CNN and ANN models by Elbeltagi et al. [20] were trained against historical data, and the prediction results were compared. The results were used to verify (1) the effectiveness of the 10 newly introduced indicators in improving the prediction accuracy of the model, (2) the advantages of the application and prediction accuracy of the CNN model over the conventional ANN and RA model, and (3) whether the CNN model proposed in this study meets the requirement [20] of providing a result with a prediction error of less than 20%.
The contributions of this article are two-fold: • First, 25 influencing factors for expressway project costs were systematically summarized, 10 of which are related to the bridge and tunnel and are innovatively introduced as influencing factors of the cost forecast at the conceptual design stage of the expressway.
• Second, the influencing factors were reconstructed to establish a CNN model for predicting the expressway project cost. To the best of the authors' knowledge, this is the first study to propose the application of a CNN model for predicting the cost of expressway projects.

III. DATA STRUCTURE
The cost of an expressway project is closely related to its overall scale, structural characteristics, economic development, raw materials, labor costs, etc. Significant research has been conducted on exploring the influencing factors of engineering project costs [41], [42]. Herbsman [43] and Wilmot and Cheng [44] suggested that, in addition to labor, materials, equipment, and their inflation, the bidding volume impacted the cost of highway projects. Koehn et al. [45] discussed the influence of land price, interest rates, and government regulations on project bidding prices. Hegazy and Ayed [10] proposed 10 factors that affected the cost of a highway project and used these as inputs to an NN model: the project category, project scope, project implementation time, construction season, project location, project duration, project scale, project capacity, hydrological conditions, and geological conditions. Wilmot and Mei [13] proposed 11 factors that affected the cost of a highway project: the labor price, material price, equipment price, project bid quantity, contract terms, contract location, quarter of project implementation, annual bid scalar, change in bid quantity, change in project quantity, and change in specification standards. Elbeltagi et al. [20] summarized 18 factors that affected the cost of a highway project: the project type, construction detour, project location, construction year, project scope, project scale, project capacity, project duration, implementation season, geological type, capital status, transportation distance of materials and equipment, paving thickness, hydrological conditions, protection of public facilities, cost increase, project cooperation type, and contract interest. Rafiei and Adeli [30] proposed that the construction cost of a project was affected not only by the materials, labor, equipment and technology, project location, type, duration, and degree of material recycling but also by the fluctuations in economic variables such as the current assets, wholesale price index, and construction service level. These economic indicators may increase or decrease the cost but are difficult to characterize, and as such, are often ignored by conventional cost-prediction models.
Two types of problems could be formulated from the above discussion. First, some of the proposed factors, such as labor force, materials, machinery, paving thickness, hydrological conditions, and geological types, are difficult to accurately determine at the conceptual design stage of a project. In addition, a considerable amount of investment for determining these factors is considered impractical when the project implementation is uncertain. Second, most of the existing studies focused on factors related to project construction conditions and project scale, and the project-scale-related factors were often limited to mileage, capacity, number of lanes, etc. Existing studies ignore the two major categories of expressway bridge and tunnel scale, which have an important impact on the expressway cost. However, expressway construction projects are usually large-scale, and the terrain of the crossing area is complex and variable. Terrain and geological changes also have an impact on such bridge and tunnel projects.
Therefore, according to the systematization of the impact factors of the expressway project cost proposed by existing research, the data of China's expressway were used as a case study in this work, with the following influencing factors: content, overall scale, bridge scale, and tunnel size of the expressway project as well as economic development indicators for the starting year of the project. Among them, the content, overall scale, and economic indicators summarize the existing achievements, and these factors could easily be obtained during the early stages of expressway construction projects. The indicators of bridge scale and tunnel size are newly introduced among the 10 factors related to the bridge and tunnel and can be obtained at the conceptual design stage. In the second category (overall scale of the project), the authors considered the date of the project construction initiation as a factor, which enables the model to study the effect of the economic development level on expressway costs. In the case of the economic indicators, the current price was used for GDP and the expressway forecast value, so as to eliminate the influence of inflation factors and ensure the consistency of economic data forecasts. Fig. 1 shows the logical framework for collating the factors affecting the construction cost of an expressway. The cost of the project is summarized in Table 1. The reasons for the selection of the 25 factors are listed in Table 2. These factors serve as the basis for the subsequent model construction.

IV. CNN MODEL FOR EXPRESSWAY PROJECT-COST ESTIMATION A. INTRODUCTION TO THE CNN MODEL
The CNN is a deep learning model proposed by LeCun et al. [46]. Essentially, it is a multilayer perceptron, the main advantages of which are local connections and weight sharing. The CNN model not only reduces the number of weights but also makes the network easy to optimize. This helps to reduce model complexity and the risk of overfitting. The model generally includes a convolution layer, pooling layer, and fully connected layer, each of which is composed of many neurons. The shared weights are used to calculate the neurons, and the activation function is used as the input of the next layer for the nonlinear calculation output. The weights are obtained by training the dataset. The convolution layer extracts features, enhances the features of the original signal through the convolution operation, and reduces noise. The pooling layer compresses feature maps, extracts main features, and reduces dimensionality and overfitting [47], [48]. Considering these unique advantages, the CNN was used to establish the proposed expressway cost-prediction model with the following adjustments. Because the data features used in this study do not have high dimensions, the pooling layer was removed to avoid the deletion of necessary information. After feature extraction in the convolution layer, the fully connected layer is used at the end of the network to create the final nonlinear combination of features and predict the cost.

1) CONVOLUTION KERNEL SIZE
The convolution layer uses a convolution kernel to share the parameters of the same layer, thus greatly reducing the number of model parameters. The receptive field of the convolution kernel is used to extract the input features of the model. In this study, the authors selected the convolution kernel according to four aspects, the first being the improvement in the depth of model learning. Although a larger convolution kernel implies a larger receptive field, features must  be extracted in image learning. A 5 × 5 two-dimensional matrix was learned in this study, and the image dimension was considerably small. On using a larger convolution kernel, main feature information can be easily ignored and the depth of model learning can be reduced. Therefore, in this study, a small convolution kernel was selected for deep learning. The second aspect is to reduce computational complexity. Large convolution kernels require additional training parameters; this results in a sharp increase in the amount of computation and decreases computational performance. Third, the size of a convolution kernel must be greater than 1 to enhance the receptive field, and therefore, a 1 × 1 convolution kernel was not considered in this study. Fourth, 2 × 2, 3 × 3, and 4 × 4 convolution kernels were used for verification. After comparison of the operation of the parameters and the operation results, the input matrix used in this study was 5 × 5, and therefore, the use of a larger convolution kernel was not suitable. If a 2 × 2 convolution kernel is used, the number of parameters is reduced, computational performance could be improved, and learning depth of the model could be enhanced (see the case analysis of Section V for a detailed discussion). A convolution kernel is realized using a convolution operator and is formulated as where y is the output value of the convolution layer, X is the input feature information, W is the weight of the convolution layer, b is the bias of the convolution layer, and * is the convolution operation.

2) ACTIVATION FUNCTION SIZE
CNN usually uses the activation function of a nonlinear mapping as an excitation function at the output of the convolution layer, and it is modelled as

3) OPTIMIZER
The learning process of CNN involves the constant update of the weights and biases of an NN to minimize the value of the loss function. The smaller the loss function, the stronger is the learning ability of the NN corresponding to the parameters and the better is the prediction performance of the NN. In this study, the mean square error was used as the loss function, and it is formulated as follows: where y i and y i are the actual and predicted values, respectively. An optimizer is required to search for the optimal parameters. In this study, the optimizers of the CNN were compared (gradient descent, momentum, and Adam optimizers), and the Adam optimizer was selected. A detailed verification of the case analysis is presented in section V.

B. DEVELOPMENT OF EXPRESSWAY COST PREDICTION MODEL
The 25 selected factors were used to establish the data structure, which was reconstructed into a matrix to establish the CNN model.

1) DATA DEFINITION
The data structure for the expressway cost-prediction model is defined as follows, along with the classification of the influencing factors: where U is a category, and V i,j is the factor of a category. The 25 factors were placed into five categories depending on how they affect the expressway project cost. Each category contains five detailed indicators, as listed sequentially in Table 3.

3) CNN MODEL FOR EXPRESSWAY COST PREDICTION
For the proposed CNN model, the input is a 5 × 5 matrix, and the feature map has dimensions of 5 × 5 × 1 (Fig. 3). As this study involved relatively small data dimensions, the model structure was simplified by removing the pooling layer to avoid rounding out important feature information. The upper layer of the feature information comprises 2 × 2 convolution kernels. Each of the C1 convolution layer, C2 convolution layer, and FC4 fully connected layer uses 64 different convolution kernels. Finally, the model outputs the predicted expressway cost.

C. MODEL EVALUATION
The mean absolute percentage error (MAPE) represents the error degree of the model. The smaller the MAPE value, the smaller is the error and the higher is the accuracy. This value, as formulated in (4), represents the amount by which the predicted value deviates from the true value.
where p is the predicted value, and A is the actual value.

V. CASE ANALYSIS
To verify the validity of the proposed model, the CNN model was used to learn case data via Python, and the same case data were simulated using the ANN model adopted by Elbeltagi et al. [20] via MATLAB. The RA model was used to train historical data in the SPSS environment. A laptop running 64-bit Windows 10 with 8 GB of RAM and an Intel i7-8550u CPU was used for programming.

A. DATA PREPARATION AND ANALYSIS
The case analysis was performed using information on 415 expressway projects collected through the credit information management system of the China expressway construction market (https://glxy.mot.gov.cn/). Data on expressway projects from 2005-2018 were collected, covering 31 provinces and direct municipalities. The relationship between each feature and the predicted value is shown in Fig. 4, depicting the relationship between the expressway project cost and each feature (described in Table 1) arranged from left to right and from top to bottom. The figure shows that most of the features have no obvious linear relationship with the predicted values, and the wide coverage of the case data allows for the easy development of a discrete distribution.

B. DATA NORMALIZATION
To make the data comparable, each feature value, depicted as in (5), was normalized using (6).
where X i represents the sample value of feature i, and m represents the number of samples. After normalization, X is obtained as follows: where X min and X max are the minimum and maximum values of a feature, respectively.

C. CASE STUDY 1: COMPARISON BETWEEN RA, ANN, CNN MODELS
To illustrate the superiority of the CNN model over the conventional RA and ANN models, the same proportion of training and test datasets were used in random sampling for the same case data; the RA, ANN, and CNN models were used to forecast the cost of highway projects. Moreover, three simulation studies were performed.

1) PREDICTION USING THE RA MODEL
First, the most commonly used RA model, i.e., the multiple linear RA (MLRA), was evaluated. MLRA refers to the linear regression model with multiple explanatory variables; this is used to reveal the linear relationship between the explained variables and other multiple explanatory variables. The mathematical model of MLRA is given as VOLUME 8, 2020 where p is the number of explanatory variables, y is the explained variable, x i is the explanatory variable, and e is a random term.
To extract the main features as explanatory variables of the regression model, the Pearson product-moment correlation coefficient was used to calculate the correlation among all variables. The explanatory variables of the regression model were selected according to the correlation strength. The Pearson product-moment correlation coefficient is calculated as follows: The Pearson product-moment correlation coefficient is shown in Fig. 5, where the variables could not be presented because of space restrictions. The variables from left to right and from top to bottom are as follows: province; mileage; administrative level; speed; traffic capacity; nature of construction; duration in months; starting date of the project; bridge and tunnel ratio; sources of funds; lengths of the small, medium, large, and super bridges; number of culverts; lengths of the short, medium, long, and super-long tunnels; number of tunnels; investment in fixed assets; CPI; PPI; benchmark lending rates; and GDP.
Generally, the strong and weak relations among the variables represented by the Pearson product-moment correlation coefficient are divided as shown in Table 4.
Because this dataset is relatively discrete, six variables (mileage, length of the super bridge, lengths of the short, medium, and long tunnels, and number of tunnels) with  correlation coefficients ≥0.4 were utilized as explanatory variables. After multiple regression using the SPSS software, three variables were determined to have insignificant correlation and were removed from the regression equation. The remaining three variables (mileage, length of the super bridge, and number of tunnels) were used as explanatory variables for the multiple regression. The regression equation and coefficient correlation were significant, and the correlation parameters are listed in Tables V-VII.  The regression model was obtained from the data in Table 7.
The regression model was used to predict the test data, shown in Fig. 6(a); the MAPE was 29.26%, and the evaluation parameters of the RA model are listed in Table 8 (RA ).

2) PREDICTION USING THE ANN MODEL
Elbeltagi et al. [20] developed an ANN-based prediction model, in which all the transfer functions of the hidden and output layers used Tansig, while Traimlm was used as the training function; the model was trained using MATLAB. VOLUME 8, 2020  Their results showed that the model had good applicability to the cost prediction of 67 highway projects in Libya. In the current study, we used the collected data to reproduce the ANN model in [20], with Tansig as the activation function and the Levenberg Marquardt algorithm as the optimizer. From the input data, 90% of the 415 case data were randomly extracted as the learning set, and the remaining 10% was used as the test set. There is no criterion for feature selection and the selection of the number of hidden-layer neurons in ANN-based models. However, the selection of these parameters has a significant influence on the prediction accuracy. To overcome these defects and ensure that the ANN model [20] achieves the best prediction result, two improvements were made in this study. First, the rationality of the ANN model in feature selection was ensured by calculating the distance correlation coefficients between the 25 features and the predicted values (as shown in Table 9 ). According to the correlation of the distance coefficient, 6-25 features were selected as input neurons in descending order. Second, as there was no clear optimal number of neurons in each NN layer [20], the number of  neurons in the first hidden-layer is used to select the average input of the first hidden layer and the output of the first hidden neurons [49]. In addition, the number of neurons in the second hidden-layer is used to select a sequence of numbers between 6 and 50 with equal intervals of 2; for example, 6, 8, 10, 12, 14, 16, 18, 20, . . . , 50. Lastly, the user executed each ANN several times, and the ANN structure with the smallest error rate was selected as the MAPE value of each structure (as shown in Fig. 7). Fig. 7 shows the various network structures corresponding to the first 6 and 25 input neurons of the distance correlation coefficients, arranged from left to right and from top to bottom, respectively. The ANN structure is labeled above each subgraph (''input neuron''-''first hidden layer neuron''-''second hidden layer neuron''-''output neuron''). For example, the first row, first column, first structure for 6-4-x-1 represents the first six distance correlation coefficients as input neurons; first hidden-layer neuron (4); second hidden-layer neuron (x), which is a sequence with VOLUME 8, 2020 equal intervals of 2 between 6 and 50; and the output-layer neuron (1). The longitudinal axis represents the MAPE value corresponding to each ANN structure, and the horizontal axis represents the number of neurons in the second hidden layer, X . The ANN-predicted MAPE for input neuron 22, with the first hidden layer as 12 and the second hidden layer 12, is 22.84%, which is optimal. The characteristics of the model input information are listed in Table 10, and the operation result parameters of ANN (with bridge and tunnel factors) are listed in Table 8. In addition, the prediction results are shown in Fig. 6(b).
In this study, the input information of an NN was divided into five categories. Among the 25 factors, the optimal input information of the 22-12-12-1 ANN model in Fig. 7

3) PREDICTION USING THE CNN MODEL a: LEARNING RATE
For implementing the proposed CNN model, 90% of the case data were randomly selected as the training set, and 10% were selected for the test set. Fig. 8 shows that the model was sensitive to changes in the training and test datasets at a learning rate of 0.001, and the difference between errors of the training and test datasets converged after 620 iterations. Therefore, the learning rate of the model was set to 0.001.   Fig. 10(b)]. The operation parameters of the three convolution kernels are shown in Table 11. The experimental results show that the 2 × 2 convolution kernel can reduce the number of parameters, improve the computational performance, enhance the depth of model learning, and improve the prediction accuracy.

c: OPTIMIZER
Three optimizers, i.e., the gradient descent, momentum, and Adam optimizers, were used to run the model. The loss function value of the test data is shown in Fig. 9. As the value of the loss function obtained using the Adam optimizer was the smallest, the Adam optimizer was used in this study.  Therefore, the CNN model was selected with a learning rate of 0.001, 620 iterations, and the Adam optimizer. The results of the CNN (with bridge and tunnel factors) are shown in Fig. 6(c), and the parameters are listed in Table 8.
As Fig. 6 and Table 8 shown, the prediction error (17%) of the CNN-based model presented in this study is lower than those of the ANN (22.84%) model and the RA model (29.26%). In addition, the 20% error requirement at the conceptual design stage [20], [50] was satisfied, which demonstrated the advantages of the input features and the CNN model proposed herein. Second, under the same input conditions, the CNN model has more iterations than the ANN model, showing its superiority over the ANN model in terms of learning ability. Moreover, the CNN model reduces the overfitting problem in machine learning owing to its advantage of high-dimensional learning.

D. CASE STUDY 2: COMPARISON BETWEEN THE USE OF 25 AND 15 FACTORS
To verify the effectiveness of the 10 proposed factors related to the bridge and tunnel for improving the accuracy of model prediction, the CNN model was applied without the bridge and tunnel factors for a comparison with the simulations obtained in the first case study. To this end, 90% and 10% of the case data were randomly selected as the training and test sets, respectively. A result with an error rate of 23. 78%  TABLE 11. Comparison of operating parameters of 2 × 2, 3 × 3, and 4 × 4 convolutional kernels. was obtained after 450 iterations at a learning rate of 0.001. The parameters used in this CNN (without bridge and tunnel factors) are listed in Table 8, and the test results are shown in Fig. 11(a). Compared with the 17% error rate obtained using the 25-factor CNN model, the 15-factor CNN model achieves an error rate of 23.78%, which is relatively similar to that of the ANN model (22.84%). To verify the superiority of the CNN model under the same condition, the ANN model was executed again without the bridge and tunnel factors, and an error rate of 40.62% was obtained. The parameters of this ANN (without bridge and tunnel factors) are listed in Table 8, and the test results are depicted in Fig. 11(b). The results prove the superiority of the CNN model over the ANN model. Moreover, the significant difference in the prediction results of the ANN model, caused by the removal of the bridge and tunnel factors, further highlights the effectiveness of the new factors in terms of improving the prediction accuracy of the CNN model. Table 8 shows that, under the same input conditions, the CNN model completes more iterations than the ANN model, thus confirming the superior learning ability of the CNN model. Moreover, although the ANN model has the advantage of a small number of training parameters for learning low-dimensional nonlinear problems, its prediction accuracy is considerably less than that of the CNN model. Furthermore, the CNN model offers the advantage of a small number of training parameters in high-dimensional nonlinear problems, and its accuracy is better than that of the ANN model, indicating that the CNN model is more suitable for high-dimensional nonlinear problems.

VI. CONCLUSION
In terms of project management, researchers have devoted increasing efforts toward the early prediction of highway project costs. At present, most of the cost-prediction methods are based on the ANN and RA models. However, these models suffer from a few disadvantages, such as over fitting, excessive parameters, and complex calculations.
Based on existing research results pertaining to factors influencing the cost of a highway project, 15 factors with high importance that are easy to obtain at the conceptual design stage were selected as the research object. Additionally, compared with previous studies, 10 innovative factors related to the bridge and tunnel were proposed; these have an important impact on the expressway project cost and can be obtained at the conceptual design stage. By reconstructing the characteristics of the influencing factors, the CNN model for expressway cost prediction was constructed. To the best of the authors' knowledge, this is the first study to demonstrate the application of a CNN model in expressway project cost prediction. Based on the data of 415 expressway projects collected in this study, the mainstream cost prediction models (ANN and RA) used in the field of construction engineering management were introduced for comparison. The case analysis results showed that the 10 new indexes related to the bridge and tunnel factors can improve the prediction accuracy of the model. A comparison of the CNN model with the conventional ANN and RA models showed that the CNN model is more suitable for highway cost prediction, which is a high-dimensional nonlinear problem, and it can improve the prediction accuracy.
This study can be used to devise financial plans in the early stage of expressway construction and to manage cost at the conceptual design stage, so as to enable investors to acquire project funds in advance. The 10 newly proposed factors related to the bridge and tunnel allow for a more comprehensive and multi-perspective analysis of the cost-influencing factors at the conceptual design stage of an expressway project. The information of 415 expressways collected in this study can also be used as a reference for conducting similar research in the future.
Although the influencing factors of the project cost include the starting date of the project, investment in fixed assets, CPI, PPI, benchmark lending rates, GDP, and other factors related to time series, the CNN model only studies the relationship between these index values and the highway project cost; it does not learn the characteristics of data from the perspective of overall time series. In the future, researchers can combine the advantages of the RNN-based machine learning model that learns time series with those of the CNN model.