# Research on Cost Forecasting Based on the BIM and Neural Network

Authors: Yan Wu; Xiaohua Wu; Jinqiang Fang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

In enterprise or project management, cost forecasting is an important factor affecting different stages of the project process, which requires effective control and management of cost forecasting. In this paper, BIM technology is introduced into the construction project, so that the project manager can master all the information of the building through this technology, which provides a good condition for the completion of cost accounting. In this paper, a cost prediction model based on a neural network is proposed, which uses a neural network prediction model, genetic algorithm prediction model, and GM (1, 1) prediction model. Through the same design company, the monthly cumulative cost of the construction and completion of the first, second, and third floors of the residential district is predicted. The results show that the error of the neural network model is small, while the error of the genetic algorithm and GM prediction model is large and unstable, which cannot provide more accurate and stable prediction, and has no better reference value. Therefore, we can see that the neural network prediction model has a good reference value, can provide accurate and stable prediction, and can help enterprises or project managers to make cost decisions.


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## Body

## 1. Introduction

In traditional project management, it is difficult to predict the cost, because people cannot grasp all the information of a building well. Therefore, it is very convenient to introduce BIM technology, which can store all the information of a building as an electronic database and then a use neural network to predict the cost, which can improve the prediction accuracy. In this paper, the following neural network and genetic algorithm are used to analyze the desired prediction target and then model for prediction, in which the target is the housing project cost. They are applied to the project planning stage, respectively, and their accuracy is compared [1]. Based on the structural cost data of Seoul from 1997 to 2000, three models are used to predict this. These three are the use of neural networks and genetic algorithms to determine the parameters and then further construction, and the other is to combine the two and then train and optimize the weights and then further model the goal. Finally, through the experimental data provided by a project in Jiangsu, it is concluded that the prediction accuracy of the last combined model is better, while the other two have certain errors. As we all know, cost estimation is very important for the follow-up development of a project and whether it can obtain better satisfaction [2]. In this paper, some problems about project cost are put forward, and a two-part method is put forward. The two parts are data collection and analysis of suggestions. For the second part, we ask the following questions: what kind of intelligent technology is used for this process, how to collect data, how to verify the results, and what are the factors for estimating the construction cost. Our main purpose is to find the best cost estimation result in the engineering project, so as to prevent the unacceptable extra amount in the construction process. When using BIM technology, we can intuitively see that the three-dimensional structure of the project is one dimension more than CAD technology and then get its useful information relatively quickly [3]. This technique can be used to calculate the reliability of engineering quantity take-off and cost improvement prediction in the early stage of the project. Through the above two advantages, the engineering cost which accords with AACE estimation accuracy can be calculated. The results show that the reliability of cost estimation can be further improved by determining the main equipment, internal main pipe, its shape, and minimum specification at the design stage. Construction projects are affected by the characteristics of owners, projects, and contracts, which will affect the actual construction time and cost [4]. In this paper, a cost prediction model is established, and the money data of a project in Jiangsu is used for experiment. The experimental results show that the increase in contract duration can reduce the prediction error of actual duration. Finally, according to the different customer departments, the selection mode of contractors, and the risk and uncertainty of project types, it shows that the model can be applied in cost prediction [5]. This paper mainly studies the green building certification system based on the BIM template. BIM creates and uses a unified and systematic computer information system, and it can be widely used in many places, such as design decision, preparation of advanced construction drawings, prediction of building performance, prediction of cost, and construction planning parameters. Its application may promote the improvement of a certification system. It has the advantage of providing a wide range of ways to take into account the diversity of users, managing information and ensuring its transparency and accessibility to all users, as well as collecting and analyzing performance information. People pay more and more attention to architecture, and they consider more and more influencing factors, among which environmental assessment is particularly important [6]. This paper studies the cost premium of green building through the neural network model which is generally considered to have excellent predictive ability and the introduction of LEED. Multivariate regression analysis is used to verify the prediction ability of the target model, and then, global sensitivity analysis is used to study the possible relationship between the output and input variables of the target model. Finally, it is found that the class of LEED is more susceptible to small changes of some factors and produces different effects. This paper studies the cost forecasting model using support vector regression [7]. SVR can deal with small samples well and can avoid the defects of the neural network such as falling into the local minimum and low accuracy. Finally, it is proven by experiments that the target model can be well applied to the cost prediction we want and it has high accuracy. In this paper, the neural network and PSO are combined to apply this method to software failure, and some reference opinions are given for prediction of some special cases in time. An artificial neural network classifies its software modules whether there is fault tendency and then uses PSO to reduce dimensions [8]. Experiments show that the proposed target method can establish the correlation between software metrics and module failure propensity, and the method is simple, does not need extra overhead, and can greatly reduce the workload and cost. In the case of sustainable engineering, maximizing fuel consumption is the expected result [9]. Therefore, a consumption model based on the artificial neural network is proposed here. The optimization goal of minimizing the travel distance is proposed. Five input nodes of the neural network model are used to represent the size of the engine, the distance between starting points, fuel type, speed, and passengers. By comparing the calculation results of the target model with other models, it shows that the cost estimation of this model can further optimize the target task and make the fuel consumption sufficient. Nonlinear characteristics will increase the difficulty of project cost prediction [10]. In this paper, some theorem is used to simplify the calculation, and a chaotic neural network is used to further improve the accuracy of the calculation. The model proposed in this paper is based on the theory of a nonlinear dynamic chaotic system and combines phase space reconstruction with the chaotic neural network. The experimental results show that the model has some advantages in short-term project investment estimation, and the prediction accuracy is further improved [11]. We know that low cost is very important in software engineering, so cost forecasting is really necessary. In this paper, we propose a low-cost reusability prediction model and find that the AGA-based artificial neural network as a classifier, combined with feature selection based on OO-SM, normalization, and T-test analysis, is superior to other existing technologies in accuracy and cost-effectiveness. Accurate cost prediction makes the software engineering community very concerned about the problem, and the key is to choose the most effective prediction model [12]. Model selection is generally based on prediction accuracy metrics and is a function of relative error to the model. We agree that the target model that can provide an optimal accuracy metric is the best and most accurate, and we do not need to test it. In this paper, we use statistics and other simulation tools to compare regression and stock price methods for cost prediction and use four known data sets to carry out experiments to verify the results. BIM technology has greatly changed the way people obtain and transmit information in traditional project management [13]. It can promote BIM through the analysis of all parties involved in construction projects. Therefore, it is proposed to establish multiple institutions to expand the application of BIM consultation, so that it can be well applied and everyone can get better convenience. The department puts forward the mode of combining BIM technology with energy-saving analysis to design energy-saving buildings in a certain way and makes use of the advantages of one dimension more than CAD to better serve everyone. Using the virtual building model established by the target model, the electronic database containing all the information of the building can automatically identify and respond to a large amount of information in the model by introducing this confidence into the energy-saving analysis tool, which can make the energy-saving building design get the results of energy efficiency quickly [14]. The neural network has the ability to study this aspect of the nonlinear dynamic system and give some opinions to lay the foundation for subsequent research [15]. The simulation results show that the proposed target model is feasible.


## 2. Basic Overview

### 2.1. Cost Forecast

In order to maximize the benefits of the project or make the follow-up projects more smooth and further get a satisfactory effect for customers and investors, it is very important to introduce cost forecasting to guide the project and give everyone a general idea of money. Cost prediction is a scientific prediction of cost level and future trend according to the combination of various dynamic changes of production cost and various economic factors, combined with social market and employment prospects of enterprises, using existing technical methods. Commonly used forecasting methods are as follows.


#### 2.1.1. Time Series Method

This is mainly aimed at the sequence of numbers. Through some laws or quantitative relations reflected by the target sequence, we can imagine and extend it outward and give a possible result for the next step or future development. But obviously, the production cost is not only determined by the time factor, so this forecasting method is not so good for the cost prediction effect.


#### 2.1.2. Regression Analysis

This method is aimed at the function, through the establishment of its quantitative relationship and quantitative determination of its function, and then, use this equation to predict the target. Facts have proven that linear regression has a certain effect on cost prediction, and it has been widely used in heavy metal industry, logistics industry, and railway transportation industry.


#### 2.1.3. Neural Network Prediction Method

It is a neural operation model. The target has a strong learning function and can approximate a certain algorithm or function with any desired accuracy. It is widely used. The BP neural network is widely used in cost prediction of all walks of life.


### 2.2. Cost Accounting

There are two cost accounting methods:Traditional practice:(1)C=F+V,C=F+UX,whereC represents the total cost, F represents the fixed cost, V is the variable, U is the variable cost per unit, and X is the amount of output.Activity-based costing:(1)
Determination of the cost driver rateA cost driver is the factor of cost occurrence, and the calculation expression is as follows:(2)Costdriverrate=CostlibraryexpenseTotalcostdriversofcostpool.Or the formula expression is(3)rj=cjdj,j=1,2,⋯,n.(2)
Allocation of cost pool expensesThe manufacturing cost formula for each product is as follows:(4)OHj=∑j=1nrj⋅dij,i=1,2,⋯,m;j=1,2,⋯,n,wheredij represents the cost driver amount of cost pool j consumed by I products.
(3)
Calculation of total product costThe expression for calculatingTCi is as follows:
(5)TCi=DMi+DLi+OHi,i=1,2,⋯,m,whereDMi represents the direct material cost of product i, DLi represents the direct labor cost of product i, and OHi represents the manufacturing cost of product i.


### 2.3. Basic Technology of BIM

The full name of BIM is “building information modeling,” that is, building information model. This model contains all the identity information, functional requirements, and performance of different majors and is a real-time electronic database, which integrates all the information of design, construction, and management processes in the whole construction project into a building model. Its characteristics are as follows:(1)
It has one dimension more than CAD, relies on three-dimensional technology to show its advantages, and digitally expresses the three-dimensional sensory officers and various functions we want to get, so that we can get them well(2)
Compared with other technologies, it is perfect. It can talk about the data of different periods, and all kinds of information and favorable resources we want are connected with each other to provide convenient calculation and query functions(3)
Its data source is not diverse and messy, but “single-minded,” which can solve various problems and is more conducive to our cost accounting and prediction of a certain projectTable1 shows the differences between the two technologies.Table 1
Advantage table of BIM technology compared with CAD.
CAD technologyBIM technologyBasic elementPoint, line, and planeWalls, windows, doors, etc. have geometric characteristics, architectural physical characteristics, and functional characteristicsModify primitive position or sizeNeed to redrawJust change the propertiesCorrelation between different building locationsNoYesOverall modification of buildingsMultiple manual modifications are requiredIt only needs to be modified onceExpression of architectural informationElectronic paper drawingsVisual two-dimensional and three-dimensional drawingsWe can control the cost based on BIM technology. The flow chart of quota design based on BIM technology is shown in Figure1.Figure 1
Cost design process diagram using BIM technology.


## 2.1. Cost Forecast

In order to maximize the benefits of the project or make the follow-up projects more smooth and further get a satisfactory effect for customers and investors, it is very important to introduce cost forecasting to guide the project and give everyone a general idea of money. Cost prediction is a scientific prediction of cost level and future trend according to the combination of various dynamic changes of production cost and various economic factors, combined with social market and employment prospects of enterprises, using existing technical methods. Commonly used forecasting methods are as follows.


### 2.1.1. Time Series Method

This is mainly aimed at the sequence of numbers. Through some laws or quantitative relations reflected by the target sequence, we can imagine and extend it outward and give a possible result for the next step or future development. But obviously, the production cost is not only determined by the time factor, so this forecasting method is not so good for the cost prediction effect.


### 2.1.2. Regression Analysis

This method is aimed at the function, through the establishment of its quantitative relationship and quantitative determination of its function, and then, use this equation to predict the target. Facts have proven that linear regression has a certain effect on cost prediction, and it has been widely used in heavy metal industry, logistics industry, and railway transportation industry.


### 2.1.3. Neural Network Prediction Method

It is a neural operation model. The target has a strong learning function and can approximate a certain algorithm or function with any desired accuracy. It is widely used. The BP neural network is widely used in cost prediction of all walks of life.


## 2.1.1. Time Series Method

This is mainly aimed at the sequence of numbers. Through some laws or quantitative relations reflected by the target sequence, we can imagine and extend it outward and give a possible result for the next step or future development. But obviously, the production cost is not only determined by the time factor, so this forecasting method is not so good for the cost prediction effect.


## 2.1.2. Regression Analysis

This method is aimed at the function, through the establishment of its quantitative relationship and quantitative determination of its function, and then, use this equation to predict the target. Facts have proven that linear regression has a certain effect on cost prediction, and it has been widely used in heavy metal industry, logistics industry, and railway transportation industry.


## 2.1.3. Neural Network Prediction Method

It is a neural operation model. The target has a strong learning function and can approximate a certain algorithm or function with any desired accuracy. It is widely used. The BP neural network is widely used in cost prediction of all walks of life.


## 2.2. Cost Accounting

There are two cost accounting methods:Traditional practice:(1)C=F+V,C=F+UX,whereC represents the total cost, F represents the fixed cost, V is the variable, U is the variable cost per unit, and X is the amount of output.Activity-based costing:(1)
Determination of the cost driver rateA cost driver is the factor of cost occurrence, and the calculation expression is as follows:(2)Costdriverrate=CostlibraryexpenseTotalcostdriversofcostpool.Or the formula expression is(3)rj=cjdj,j=1,2,⋯,n.(2)
Allocation of cost pool expensesThe manufacturing cost formula for each product is as follows:(4)OHj=∑j=1nrj⋅dij,i=1,2,⋯,m;j=1,2,⋯,n,wheredij represents the cost driver amount of cost pool j consumed by I products.
(3)
Calculation of total product costThe expression for calculatingTCi is as follows:
(5)TCi=DMi+DLi+OHi,i=1,2,⋯,m,whereDMi represents the direct material cost of product i, DLi represents the direct labor cost of product i, and OHi represents the manufacturing cost of product i.


## 2.3. Basic Technology of BIM

The full name of BIM is “building information modeling,” that is, building information model. This model contains all the identity information, functional requirements, and performance of different majors and is a real-time electronic database, which integrates all the information of design, construction, and management processes in the whole construction project into a building model. Its characteristics are as follows:(1)
It has one dimension more than CAD, relies on three-dimensional technology to show its advantages, and digitally expresses the three-dimensional sensory officers and various functions we want to get, so that we can get them well(2)
Compared with other technologies, it is perfect. It can talk about the data of different periods, and all kinds of information and favorable resources we want are connected with each other to provide convenient calculation and query functions(3)
Its data source is not diverse and messy, but “single-minded,” which can solve various problems and is more conducive to our cost accounting and prediction of a certain projectTable1 shows the differences between the two technologies.Table 1
Advantage table of BIM technology compared with CAD.
CAD technologyBIM technologyBasic elementPoint, line, and planeWalls, windows, doors, etc. have geometric characteristics, architectural physical characteristics, and functional characteristicsModify primitive position or sizeNeed to redrawJust change the propertiesCorrelation between different building locationsNoYesOverall modification of buildingsMultiple manual modifications are requiredIt only needs to be modified onceExpression of architectural informationElectronic paper drawingsVisual two-dimensional and three-dimensional drawingsWe can control the cost based on BIM technology. The flow chart of quota design based on BIM technology is shown in Figure1.Figure 1
Cost design process diagram using BIM technology.


## 3. Construction of the Prediction Model

### 3.1. Brief Introduction of the Neural Network

By simulating the way the neural system processes information, it combines with parallel computing to further improve the efficiency of computing. It is popular because of its self-learning and self-organizing ability. The neural network consists of the following three layers from outside to inside: output layer, hidden layer, and input layer. In the process of calculating and summarizing the parameters, the information needs to enter from the input and then pass through the hidden layer and finally to the output layer. In the learning process, when there is a large error between the output and the expected target output, the weight of the corresponding connection will be adjusted, and the error will become smaller and smaller through the continuous implementation of this process.What we study in this paper is the excellent degree of the neural network in cost estimation of enterprises or some engineering construction projects. The way its neurons are constructed is closely related to the learning algorithm.


#### 3.1.1. Transfer Function of the BP Neural Network

It mainly adopts a nonlinear transformation function-S function, which itself and its derivatives are continuous. The expression of unipolar S-type function is as follows:
(6)fx=11+e−x.The expression of the bipolarS-type function is as follows:
(7)fx=1−e−x1+e−x.


#### 3.1.2. Learning Algorithm of the BP Neural Network

When the actual result output is not equal to the expected output value, the data discrepancy between the two will be calculated and the output errorE will be defined as follows:
(8)E=12d−O2=12∑k=1ιdk−ok2.


#### 3.1.3. Training Decomposition of the BP Neural Network

This process is mainly to continuously adjust the two parameters of the target to the values that are most suitable for the whole model, which can be divided into two important conduction calculation processes.(1) Forward transmission: this outputs the value layer by layer through the wave transmission mode:. The output layer calculation expression is as follows:
(9)Ij=∑i=1wijoj+θj.After initialization, the two parameters need to be randomly selected in the specified interval, and the value interval of each weight is−1,1. The offset is 0,1.
(10)oj=fIj=11+eIj.After the above values are calculated, the forward transmission part ends.(2) Reverse feedback: reverse layer by layer to adjust the weight and offset of the important parameters of the two neural networks:. For the output layer,
(11)Ej=Oj1−OjTj−Oj,whereEj represents the actual and expected discrepancy between the j-th node, Oj represents the output value completed by the j-th node, and Tj is responsible for recording all the output values, such as the problem of two-category classification, which stipulates that 01 represents category 1 and 10 represents category 2. If a record belongs to category 1, its T1=1,T2=0.The calculation formula of the second layer is summarized by accumulating one of the parameters as follows:(12)Ej=Oj1−Oj∑kEkWjk,whereWjk represents the weight value from the node j of the current layer to the node k of the next layer and Ek represents the error rate of the node k of the next layer.The rules for updating weights are as follows:(13)ΔWij=λEjOi,0≤λ≤1,Wij=Wij+ΔWij,whereλ represents the learning progress; the larger its value, the faster the training convergence process, but it is easier to fall into the local optimal solution. On the contrary, the smaller its value, the slower the convergence speed; it can approach the global optimal solution.After completing the above operation update, you need to update the bias parameter. Its update rules are as follows:(14)Δθj=λEj,θj=θj+Δθj.When the number of iterations reaches the maximum target set by us or the percentage calculated between the actual results and the predicted results reaches the prediction accuracy of the training set on the network, the training will be terminated.


### 3.2. Neural Network Model

The basic process of the BP neural network model mainly includes three parts: initial network creation, learning and training, and early warning. The algorithm flow chart is shown in Figure2.Figure 2
Algorithm flow chart of the BP neural network.


#### 3.2.1. Initial Network Creation

This process requires us to determine the specific number of nodes (n, l, and m) in each of the three layers from the inside out to combine.The input layer inputs the data of the middle layer asHj, and the hidden layer inputs Yk, and its calculation formula is as follows:
(15)Hj=x1w1j+x2w2j+⋯+xnwnj=∑i=1nxiwij;hj=f1Hj,Yk=h1w1k+h2w2k+⋯+hlwlk=∑j=1lhjwjk;yk=f2Yk,i=1,2,⋯,n;j=1,2,⋯,l;k=1,2,⋯,m,wherexi is the input data, wij is the connection weight input to the hidden layer, hj is the passed value, the weight from the hidden layer to the output layer is wjk, and yk represents the output value. f1 and f2 are the conversion functions of two layers outside the input layer. This conversion function generally uses the sigmoid function, which is a nonlinear function, including log and tan, which have the advantage of converting the values on −∞,+∞ to (0, 1) and (-1, 1), respectively.


#### 3.2.2. Carry Out Study and Training

Because the actual output is not completely consistent with the expected output, there are errors between them. Assume their error asE, and optimize it by using the mean square error minimization method, which is defined as follows:
(16)E=12∑k=1myk∗−yk2,whereyk∗ represents the desired output.Backpropagate the error, and you can get(17)E=12∑k=1myk∗−f2Yk2=12∑k=1myk∗−f2∑j=1lhjwjk2.By backpropagating to the input layer, you can get(18)E=12∑k=1myk∗−f2∑j=1lwjkf1Hj2=12∑k=1myk∗−f2∑j=1lwjkf1∑i=1nxiwij2.In this process, a certain parameter will change constantly, so we should constantly adjust it to make its error smaller and smaller. The method used in this process is a gradient descent algorithm, which can effectively reduce the error generated by parameters, and the following formula can be obtained:(19)Δwjk=−η∂E∂wjk=−η∂E∂Yk∂Yk∂wjk,j=1,2,⋯,l;k=1,2,⋯,m,Δwij=−η∂E∂wij=−η∂E∂Hj∂Hj∂wij,j=1,2,⋯,n;k=1,2,⋯,l,where the normal range of the learning rate is (0, 1) and the minus sign in the formula indicates that the gradient shows a downward trend, so thatδky=−∂E/∂Yk and δjh=−∂E/∂Hj; then, the expression of the adjustment amount of the weight value can be rewritten into the following form:
(20)Δwjk=ηδkyhj;Δwij=ηδjhxi.Therefore, the following results can be calculated:(21)δky=−∂E∂Yk=−∂E∂yk∂yk∂Yk=−∂E∂ykf2′Yk,δjh=−∂E∂Hj=−∂E∂hj∂hj∂Hj=−∂E∂Hjf2′Yk.The output layer can be obtained by the above formula:(22)∂E∂yk=−yk∗−yk.At the same time, the hidden layer formula can be obtained:(23)∂E∂hj=−∑k=1mym∗−ykf2′Ykwjk.Substituting formulas (22) and (23) and deriving the S function satisfy f′x=fx1−fx; the following formula can be obtained:
(24)δky=yk∗−ykyk1−yk,δjh=∑k=1myk∗−ykf2′Ykwjkhj1−hj.Therefore, the expression of weight change is obtained:(25)Δwjk=ηδkyhj=ηyk∗−ykyk1−ykhj,Δwij=ηδjhxi=η∑k=1mδkywjkhj1−hjxi.Finally, the final weight calculation expression is as follows:(26)wjkt+1=wjkt+Δwjk,wijt+1=wijt+Δwij.Finally, when the actual output meets the expected output, the training can be finished.


#### 3.2.3. Issue an Early Warning

After the above process is completed, the target data will be input for prediction, and the output results will be compared with the expected data to see if it has achieved better results and met the error requirements.In the aspect of recost, we need to deal with many factors affecting the target through the hidden layer, then get the output results, and then analyze and study this data with the expected cost data.


## 3.1. Brief Introduction of the Neural Network

By simulating the way the neural system processes information, it combines with parallel computing to further improve the efficiency of computing. It is popular because of its self-learning and self-organizing ability. The neural network consists of the following three layers from outside to inside: output layer, hidden layer, and input layer. In the process of calculating and summarizing the parameters, the information needs to enter from the input and then pass through the hidden layer and finally to the output layer. In the learning process, when there is a large error between the output and the expected target output, the weight of the corresponding connection will be adjusted, and the error will become smaller and smaller through the continuous implementation of this process.What we study in this paper is the excellent degree of the neural network in cost estimation of enterprises or some engineering construction projects. The way its neurons are constructed is closely related to the learning algorithm.


### 3.1.1. Transfer Function of the BP Neural Network

It mainly adopts a nonlinear transformation function-S function, which itself and its derivatives are continuous. The expression of unipolar S-type function is as follows:
(6)fx=11+e−x.The expression of the bipolarS-type function is as follows:
(7)fx=1−e−x1+e−x.


### 3.1.2. Learning Algorithm of the BP Neural Network

When the actual result output is not equal to the expected output value, the data discrepancy between the two will be calculated and the output errorE will be defined as follows:
(8)E=12d−O2=12∑k=1ιdk−ok2.


### 3.1.3. Training Decomposition of the BP Neural Network

This process is mainly to continuously adjust the two parameters of the target to the values that are most suitable for the whole model, which can be divided into two important conduction calculation processes.(1) Forward transmission: this outputs the value layer by layer through the wave transmission mode:. The output layer calculation expression is as follows:
(9)Ij=∑i=1wijoj+θj.After initialization, the two parameters need to be randomly selected in the specified interval, and the value interval of each weight is−1,1. The offset is 0,1.
(10)oj=fIj=11+eIj.After the above values are calculated, the forward transmission part ends.(2) Reverse feedback: reverse layer by layer to adjust the weight and offset of the important parameters of the two neural networks:. For the output layer,
(11)Ej=Oj1−OjTj−Oj,whereEj represents the actual and expected discrepancy between the j-th node, Oj represents the output value completed by the j-th node, and Tj is responsible for recording all the output values, such as the problem of two-category classification, which stipulates that 01 represents category 1 and 10 represents category 2. If a record belongs to category 1, its T1=1,T2=0.The calculation formula of the second layer is summarized by accumulating one of the parameters as follows:(12)Ej=Oj1−Oj∑kEkWjk,whereWjk represents the weight value from the node j of the current layer to the node k of the next layer and Ek represents the error rate of the node k of the next layer.The rules for updating weights are as follows:(13)ΔWij=λEjOi,0≤λ≤1,Wij=Wij+ΔWij,whereλ represents the learning progress; the larger its value, the faster the training convergence process, but it is easier to fall into the local optimal solution. On the contrary, the smaller its value, the slower the convergence speed; it can approach the global optimal solution.After completing the above operation update, you need to update the bias parameter. Its update rules are as follows:(14)Δθj=λEj,θj=θj+Δθj.When the number of iterations reaches the maximum target set by us or the percentage calculated between the actual results and the predicted results reaches the prediction accuracy of the training set on the network, the training will be terminated.


## 3.1.1. Transfer Function of the BP Neural Network

It mainly adopts a nonlinear transformation function-S function, which itself and its derivatives are continuous. The expression of unipolar S-type function is as follows:
(6)fx=11+e−x.The expression of the bipolarS-type function is as follows:
(7)fx=1−e−x1+e−x.


## 3.1.2. Learning Algorithm of the BP Neural Network

When the actual result output is not equal to the expected output value, the data discrepancy between the two will be calculated and the output errorE will be defined as follows:
(8)E=12d−O2=12∑k=1ιdk−ok2.


## 3.1.3. Training Decomposition of the BP Neural Network

This process is mainly to continuously adjust the two parameters of the target to the values that are most suitable for the whole model, which can be divided into two important conduction calculation processes.(1) Forward transmission: this outputs the value layer by layer through the wave transmission mode:. The output layer calculation expression is as follows:
(9)Ij=∑i=1wijoj+θj.After initialization, the two parameters need to be randomly selected in the specified interval, and the value interval of each weight is−1,1. The offset is 0,1.
(10)oj=fIj=11+eIj.After the above values are calculated, the forward transmission part ends.(2) Reverse feedback: reverse layer by layer to adjust the weight and offset of the important parameters of the two neural networks:. For the output layer,
(11)Ej=Oj1−OjTj−Oj,whereEj represents the actual and expected discrepancy between the j-th node, Oj represents the output value completed by the j-th node, and Tj is responsible for recording all the output values, such as the problem of two-category classification, which stipulates that 01 represents category 1 and 10 represents category 2. If a record belongs to category 1, its T1=1,T2=0.The calculation formula of the second layer is summarized by accumulating one of the parameters as follows:(12)Ej=Oj1−Oj∑kEkWjk,whereWjk represents the weight value from the node j of the current layer to the node k of the next layer and Ek represents the error rate of the node k of the next layer.The rules for updating weights are as follows:(13)ΔWij=λEjOi,0≤λ≤1,Wij=Wij+ΔWij,whereλ represents the learning progress; the larger its value, the faster the training convergence process, but it is easier to fall into the local optimal solution. On the contrary, the smaller its value, the slower the convergence speed; it can approach the global optimal solution.After completing the above operation update, you need to update the bias parameter. Its update rules are as follows:(14)Δθj=λEj,θj=θj+Δθj.When the number of iterations reaches the maximum target set by us or the percentage calculated between the actual results and the predicted results reaches the prediction accuracy of the training set on the network, the training will be terminated.


## 3.2. Neural Network Model

The basic process of the BP neural network model mainly includes three parts: initial network creation, learning and training, and early warning. The algorithm flow chart is shown in Figure2.Figure 2
Algorithm flow chart of the BP neural network.


### 3.2.1. Initial Network Creation

This process requires us to determine the specific number of nodes (n, l, and m) in each of the three layers from the inside out to combine.The input layer inputs the data of the middle layer asHj, and the hidden layer inputs Yk, and its calculation formula is as follows:
(15)Hj=x1w1j+x2w2j+⋯+xnwnj=∑i=1nxiwij;hj=f1Hj,Yk=h1w1k+h2w2k+⋯+hlwlk=∑j=1lhjwjk;yk=f2Yk,i=1,2,⋯,n;j=1,2,⋯,l;k=1,2,⋯,m,wherexi is the input data, wij is the connection weight input to the hidden layer, hj is the passed value, the weight from the hidden layer to the output layer is wjk, and yk represents the output value. f1 and f2 are the conversion functions of two layers outside the input layer. This conversion function generally uses the sigmoid function, which is a nonlinear function, including log and tan, which have the advantage of converting the values on −∞,+∞ to (0, 1) and (-1, 1), respectively.


### 3.2.2. Carry Out Study and Training

Because the actual output is not completely consistent with the expected output, there are errors between them. Assume their error asE, and optimize it by using the mean square error minimization method, which is defined as follows:
(16)E=12∑k=1myk∗−yk2,whereyk∗ represents the desired output.Backpropagate the error, and you can get(17)E=12∑k=1myk∗−f2Yk2=12∑k=1myk∗−f2∑j=1lhjwjk2.By backpropagating to the input layer, you can get(18)E=12∑k=1myk∗−f2∑j=1lwjkf1Hj2=12∑k=1myk∗−f2∑j=1lwjkf1∑i=1nxiwij2.In this process, a certain parameter will change constantly, so we should constantly adjust it to make its error smaller and smaller. The method used in this process is a gradient descent algorithm, which can effectively reduce the error generated by parameters, and the following formula can be obtained:(19)Δwjk=−η∂E∂wjk=−η∂E∂Yk∂Yk∂wjk,j=1,2,⋯,l;k=1,2,⋯,m,Δwij=−η∂E∂wij=−η∂E∂Hj∂Hj∂wij,j=1,2,⋯,n;k=1,2,⋯,l,where the normal range of the learning rate is (0, 1) and the minus sign in the formula indicates that the gradient shows a downward trend, so thatδky=−∂E/∂Yk and δjh=−∂E/∂Hj; then, the expression of the adjustment amount of the weight value can be rewritten into the following form:
(20)Δwjk=ηδkyhj;Δwij=ηδjhxi.Therefore, the following results can be calculated:(21)δky=−∂E∂Yk=−∂E∂yk∂yk∂Yk=−∂E∂ykf2′Yk,δjh=−∂E∂Hj=−∂E∂hj∂hj∂Hj=−∂E∂Hjf2′Yk.The output layer can be obtained by the above formula:(22)∂E∂yk=−yk∗−yk.At the same time, the hidden layer formula can be obtained:(23)∂E∂hj=−∑k=1mym∗−ykf2′Ykwjk.Substituting formulas (22) and (23) and deriving the S function satisfy f′x=fx1−fx; the following formula can be obtained:
(24)δky=yk∗−ykyk1−yk,δjh=∑k=1myk∗−ykf2′Ykwjkhj1−hj.Therefore, the expression of weight change is obtained:(25)Δwjk=ηδkyhj=ηyk∗−ykyk1−ykhj,Δwij=ηδjhxi=η∑k=1mδkywjkhj1−hjxi.Finally, the final weight calculation expression is as follows:(26)wjkt+1=wjkt+Δwjk,wijt+1=wijt+Δwij.Finally, when the actual output meets the expected output, the training can be finished.


### 3.2.3. Issue an Early Warning

After the above process is completed, the target data will be input for prediction, and the output results will be compared with the expected data to see if it has achieved better results and met the error requirements.In the aspect of recost, we need to deal with many factors affecting the target through the hidden layer, then get the output results, and then analyze and study this data with the expected cost data.


## 3.2.1. Initial Network Creation

This process requires us to determine the specific number of nodes (n, l, and m) in each of the three layers from the inside out to combine.The input layer inputs the data of the middle layer asHj, and the hidden layer inputs Yk, and its calculation formula is as follows:
(15)Hj=x1w1j+x2w2j+⋯+xnwnj=∑i=1nxiwij;hj=f1Hj,Yk=h1w1k+h2w2k+⋯+hlwlk=∑j=1lhjwjk;yk=f2Yk,i=1,2,⋯,n;j=1,2,⋯,l;k=1,2,⋯,m,wherexi is the input data, wij is the connection weight input to the hidden layer, hj is the passed value, the weight from the hidden layer to the output layer is wjk, and yk represents the output value. f1 and f2 are the conversion functions of two layers outside the input layer. This conversion function generally uses the sigmoid function, which is a nonlinear function, including log and tan, which have the advantage of converting the values on −∞,+∞ to (0, 1) and (-1, 1), respectively.


## 3.2.2. Carry Out Study and Training

Because the actual output is not completely consistent with the expected output, there are errors between them. Assume their error asE, and optimize it by using the mean square error minimization method, which is defined as follows:
(16)E=12∑k=1myk∗−yk2,whereyk∗ represents the desired output.Backpropagate the error, and you can get(17)E=12∑k=1myk∗−f2Yk2=12∑k=1myk∗−f2∑j=1lhjwjk2.By backpropagating to the input layer, you can get(18)E=12∑k=1myk∗−f2∑j=1lwjkf1Hj2=12∑k=1myk∗−f2∑j=1lwjkf1∑i=1nxiwij2.In this process, a certain parameter will change constantly, so we should constantly adjust it to make its error smaller and smaller. The method used in this process is a gradient descent algorithm, which can effectively reduce the error generated by parameters, and the following formula can be obtained:(19)Δwjk=−η∂E∂wjk=−η∂E∂Yk∂Yk∂wjk,j=1,2,⋯,l;k=1,2,⋯,m,Δwij=−η∂E∂wij=−η∂E∂Hj∂Hj∂wij,j=1,2,⋯,n;k=1,2,⋯,l,where the normal range of the learning rate is (0, 1) and the minus sign in the formula indicates that the gradient shows a downward trend, so thatδky=−∂E/∂Yk and δjh=−∂E/∂Hj; then, the expression of the adjustment amount of the weight value can be rewritten into the following form:
(20)Δwjk=ηδkyhj;Δwij=ηδjhxi.Therefore, the following results can be calculated:(21)δky=−∂E∂Yk=−∂E∂yk∂yk∂Yk=−∂E∂ykf2′Yk,δjh=−∂E∂Hj=−∂E∂hj∂hj∂Hj=−∂E∂Hjf2′Yk.The output layer can be obtained by the above formula:(22)∂E∂yk=−yk∗−yk.At the same time, the hidden layer formula can be obtained:(23)∂E∂hj=−∑k=1mym∗−ykf2′Ykwjk.Substituting formulas (22) and (23) and deriving the S function satisfy f′x=fx1−fx; the following formula can be obtained:
(24)δky=yk∗−ykyk1−yk,δjh=∑k=1myk∗−ykf2′Ykwjkhj1−hj.Therefore, the expression of weight change is obtained:(25)Δwjk=ηδkyhj=ηyk∗−ykyk1−ykhj,Δwij=ηδjhxi=η∑k=1mδkywjkhj1−hjxi.Finally, the final weight calculation expression is as follows:(26)wjkt+1=wjkt+Δwjk,wijt+1=wijt+Δwij.Finally, when the actual output meets the expected output, the training can be finished.


## 3.2.3. Issue an Early Warning

After the above process is completed, the target data will be input for prediction, and the output results will be compared with the expected data to see if it has achieved better results and met the error requirements.In the aspect of recost, we need to deal with many factors affecting the target through the hidden layer, then get the output results, and then analyze and study this data with the expected cost data.


## 4. Simulation Experiment

### 4.1. Data Preprocessing

We experimented on the cost of a real estate project. A residential district is a 12-storey building, in which 1#, 2#, and 3# buildings are designed by the same design company, which starts and completes the engineering work at the same time. Table2 is a statistical table of the accumulated investment amount of the three projects from the beginning to the end of the whole work (all the units in the following forms are $100,000).Table 2
Statistical table of accumulated investment amount of 3 projects in the whole work.
ProjectMonth123456Accumulated cost1#12.818.721.625.829.7432.62#12.818.721.625.829.7432.63#9.212.719.926.9730.234.8The statistical data of accumulated investment in the whole work of the three projects are shown in Table2.We use the neural network model, genetic algorithm model, and GM (1, 1) prediction model to model and fit the above summarized data, and the specific results are as follows (Tables3–5).Table 3
Forecast results of the cumulative cost prediction model of 1# building in a residential district.
Month123456Actual value12.818.721.625.829.7432.6Neural network prediction12. 7818.221.326.92933Genetic algorithm prediction1420.122.625.728.631.4GM (1,1) prediction11.319.420.724.728.1630.9Table 4
Forecast results of the cumulative cost prediction model of 2# building in a residential district.
Month123456Actual value12.821.928.930.834.533.7Neural network prediction13.5122.829.1313333Genetic algorithm prediction14.324.443032.33032GM (1,1) prediction10.123.631.125.53430.88Table 5
Forecast results of the cumulative cost prediction model of 3# building in a residential district.
Month123456Actual value9.212.719.926.9730.234.8Neural network prediction9.5513212730.2935Genetic algorithm prediction1014.7620.928.9932.834.1GM (1,1) prediction8.9213.719.22829.332The prediction results of the cumulative cost prediction model of building 1# in a residential district are shown in Table3.The prediction results of the cumulative cost prediction model of building 2# in a residential district are shown in Table4.The prediction results of the cumulative cost prediction model of building 3# in a residential district are shown in Table5.


### 4.2. Comparison of Experimental Results

We draw the fitting effect of the three prediction models into a line chart, which is shown in Figures3–5, so that we can compare the effects of the three prediction models more clearly.Figure 3
Comparison of prediction results of three prediction models for 1# building in a residential district.Figure 4
Comparison of prediction results of three prediction models for 2# building in a residential district.Figure 5
Comparison of prediction results of three prediction models for building 3 in a residential district.From Figure3, we can see that the fitting effect of the neural network prediction model is better than that of the genetic algorithm prediction model and GM (1, 1) prediction model, while the prediction result of the genetic algorithm is generally higher, while that of the GM prediction model is unstable, which is higher and lower than the actual value. Neither of these two models is more accurate and stable than the neural network prediction model. Therefore, it can be seen that the neural network model has certain advantages.From Figure4, we can see that the neural network prediction model has relatively large errors except May, and the predicted values of other months are basically consistent with the actual values. On the whole, the neural network prediction model is obviously better, followed by the genetic algorithm model and finally the GM (1, 1) prediction model.It can be seen from Figure5 that the values predicted by the neural network in six months are almost completely consistent with the actual values, but both genetic algorithm and GM prediction have large error values, and their two algorithms have large error fluctuations, while the neural network has relatively small and stable errors.Through the above three diagrams, we can conclude that the cost prediction model of the neural network proposed by us has a good fitting effect, which can be applied to the real estate industry effectively and provides a good value consideration for the design stage of the project.


### 4.3. Comparison of Algorithm Performance

We mainly show it in the form of graphs through recall rate,F1 value, and accuracy rate, which is convenient for us to better observe the rules and find the advantages and disadvantages of their respective algorithms.The comparison of the recall rates of the three algorithms is shown in Figure6.Figure 6
Comparison of recall rates of three algorithms.From Figure6, we can see that the recall rate of each algorithm is not stable, and there is a general situation of one high and one low. By comparing each point, we find that the recall rate of the neural network is higher than that of the other two algorithms as a whole, which means that our proposed algorithm can have better prediction ability.The accuracy rates of the three algorithms are shown in Figure7.Figure 7
Comparison of accuracy rates of three algorithms.Through Figure7, we can also find that the accuracy rate is not stable for each algorithm. Similarly, we also analyze each point and find that the accuracy rate of the neural network is higher, followed by the genetic algorithm, and the worse one is GM prediction.TheF1 values of the three algorithms are compared in Figure 8.Figure 8
Comparison ofF1 values of three algorithms.From Figure8, we can clearly see that the performance of the neural network is the best, followed by the genetic algorithm and finally GM prediction. Once again, the neural network is relatively affirmed.Through the above performance comparison, we can be surer that the neural network model we proposed has a certain degree of excellence, which can carry out a good experiment on cost prediction and provide some help to project managers and enterprises.


## 4.1. Data Preprocessing

We experimented on the cost of a real estate project. A residential district is a 12-storey building, in which 1#, 2#, and 3# buildings are designed by the same design company, which starts and completes the engineering work at the same time. Table2 is a statistical table of the accumulated investment amount of the three projects from the beginning to the end of the whole work (all the units in the following forms are $100,000).Table 2
Statistical table of accumulated investment amount of 3 projects in the whole work.
ProjectMonth123456Accumulated cost1#12.818.721.625.829.7432.62#12.818.721.625.829.7432.63#9.212.719.926.9730.234.8The statistical data of accumulated investment in the whole work of the three projects are shown in Table2.We use the neural network model, genetic algorithm model, and GM (1, 1) prediction model to model and fit the above summarized data, and the specific results are as follows (Tables3–5).Table 3
Forecast results of the cumulative cost prediction model of 1# building in a residential district.
Month123456Actual value12.818.721.625.829.7432.6Neural network prediction12. 7818.221.326.92933Genetic algorithm prediction1420.122.625.728.631.4GM (1,1) prediction11.319.420.724.728.1630.9Table 4
Forecast results of the cumulative cost prediction model of 2# building in a residential district.
Month123456Actual value12.821.928.930.834.533.7Neural network prediction13.5122.829.1313333Genetic algorithm prediction14.324.443032.33032GM (1,1) prediction10.123.631.125.53430.88Table 5
Forecast results of the cumulative cost prediction model of 3# building in a residential district.
Month123456Actual value9.212.719.926.9730.234.8Neural network prediction9.5513212730.2935Genetic algorithm prediction1014.7620.928.9932.834.1GM (1,1) prediction8.9213.719.22829.332The prediction results of the cumulative cost prediction model of building 1# in a residential district are shown in Table3.The prediction results of the cumulative cost prediction model of building 2# in a residential district are shown in Table4.The prediction results of the cumulative cost prediction model of building 3# in a residential district are shown in Table5.


## 4.2. Comparison of Experimental Results

We draw the fitting effect of the three prediction models into a line chart, which is shown in Figures3–5, so that we can compare the effects of the three prediction models more clearly.Figure 3
Comparison of prediction results of three prediction models for 1# building in a residential district.Figure 4
Comparison of prediction results of three prediction models for 2# building in a residential district.Figure 5
Comparison of prediction results of three prediction models for building 3 in a residential district.From Figure3, we can see that the fitting effect of the neural network prediction model is better than that of the genetic algorithm prediction model and GM (1, 1) prediction model, while the prediction result of the genetic algorithm is generally higher, while that of the GM prediction model is unstable, which is higher and lower than the actual value. Neither of these two models is more accurate and stable than the neural network prediction model. Therefore, it can be seen that the neural network model has certain advantages.From Figure4, we can see that the neural network prediction model has relatively large errors except May, and the predicted values of other months are basically consistent with the actual values. On the whole, the neural network prediction model is obviously better, followed by the genetic algorithm model and finally the GM (1, 1) prediction model.It can be seen from Figure5 that the values predicted by the neural network in six months are almost completely consistent with the actual values, but both genetic algorithm and GM prediction have large error values, and their two algorithms have large error fluctuations, while the neural network has relatively small and stable errors.Through the above three diagrams, we can conclude that the cost prediction model of the neural network proposed by us has a good fitting effect, which can be applied to the real estate industry effectively and provides a good value consideration for the design stage of the project.


## 4.3. Comparison of Algorithm Performance

We mainly show it in the form of graphs through recall rate,F1 value, and accuracy rate, which is convenient for us to better observe the rules and find the advantages and disadvantages of their respective algorithms.The comparison of the recall rates of the three algorithms is shown in Figure6.Figure 6
Comparison of recall rates of three algorithms.From Figure6, we can see that the recall rate of each algorithm is not stable, and there is a general situation of one high and one low. By comparing each point, we find that the recall rate of the neural network is higher than that of the other two algorithms as a whole, which means that our proposed algorithm can have better prediction ability.The accuracy rates of the three algorithms are shown in Figure7.Figure 7
Comparison of accuracy rates of three algorithms.Through Figure7, we can also find that the accuracy rate is not stable for each algorithm. Similarly, we also analyze each point and find that the accuracy rate of the neural network is higher, followed by the genetic algorithm, and the worse one is GM prediction.TheF1 values of the three algorithms are compared in Figure 8.Figure 8
Comparison ofF1 values of three algorithms.From Figure8, we can clearly see that the performance of the neural network is the best, followed by the genetic algorithm and finally GM prediction. Once again, the neural network is relatively affirmed.Through the above performance comparison, we can be surer that the neural network model we proposed has a certain degree of excellence, which can carry out a good experiment on cost prediction and provide some help to project managers and enterprises.


## 5. Conclusion

In this paper, the neural network, genetic algorithm, and GM prediction model are used to predict the design and decoration cost of a three-storey building in a residential district. Through the comparison between the actual data and the prediction results, it is found that the prediction results of the neural network are obviously better than those of the other two algorithms. Experiments show that the neural network is superior to other algorithms in the accuracy of project cost prediction. Then, the performance indexes of the three prediction algorithms are compared, and the overall performance of the neural network is superior to that of other algorithms in terms of recall, accuracy, andF1 value. Therefore, the neural network model proposed in this paper can be well applied to cost prediction. In the future, it is necessary to further improve the efficiency of the algorithm by introducing the multiobjective optimization method and the neural network model for joint analysis. Big data technology is introduced to improve the execution time and reduce the complexity of the algorithm, and relatively good cost control is analyzed through different data sets.



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*Source: 4659881-2022-03-31.xml*