# Intelligent Evaluation Method of Engineering Cost Feasibility Model Based on Internet of Things

Authors: Liangqiong Chen; Hao Zhang; Fang Wang
Journal: Journal of Sensors
 (2022)

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## Abstract

In order to solve the problem of low accuracy of high-rise building cost evaluation, the author proposes an intelligent evaluation method of engineering cost feasibility model based on the Internet of Things. According to the overall investment composition of the construction project, this paper classifies the cost index, determines the overall cost correction coefficient, and uses the gray correlation analysis method to build the evaluation index system; according to the structure of BP neural network, the network error is calculated, and the error signals of output layer and hidden layer are defined by gradient descent method to obtain the network weight adjustment formula; finally, this paper uses the adaptive learning rate adjustment formula to set the network parameters, introduces the key parameters in the construction project to the input layer, and establishes the final cost evaluation model. Experimental results show that the error rate of this system is controlled within 10%, which meets the requirements of investment estimation.Conclusion. The proposed method can accurately and quickly evaluate the best solution for the cost of high-rise buildings with less information and has strong nonlinear information processing capabilities.


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## Body

## 1. Introduction

At present, the world is ushering in a period of great development and change in digital transformation. The new generation of information technology has accelerated to lead the breakthrough in technology application, bringing about major changes in industrial form, organizational management, social governance, and other aspects. The development of new generation technologies such as the Internet of Things has brought new impetus and new opportunities for the development of the digital economy. The Internet of Things technology presents the characteristics of integrated development, integrated innovation, large-scale application, and ecological acceleration, and hot technologies continue to emerge. The scale deployment of networks and platforms has been accelerated to lay a foundation for the comprehensive promotion of the Internet of Things.When we use the traditional construction project cost model to solve complex construction projects, there will be large data errors and many factors affecting the calculation results, resulting in inaccurate data, reduced credibility, and construction difficulties [1, 2]. Based on the above deficiencies, this paper improves the design of the traditional construction project cost model. The optimized construction cost model structure adopts multilevel calculation, which replaces the single-level calculation of the original construction cost model, reduces external influencing factors, and improves the reasonable configuration of internal levels, thereby, improving the accuracy of the construction cost model and reducing the calculation influencing factors. Improve the traditional construction cost model algorithm, add refined classification, reasonable quantitative classification, multidimensional theoretical calculation, and reasonable control of result errors for complex construction projects, so that each step of the calculation is close to the final settlement, thereby, the accuracy of data calculation is improved, the calculation efficiency is improved, and the error of data processing is reduced. Through simulation experiments of different dimensions, this paper verifies the investment estimate, design estimate, revised estimate, construction drawing estimate, and near completion final account before and after improvement [3, 4].BIM is a complete enterprise engineering information system model, which can integrate engineering information, processes, and human resources in all stages of the enterprise’s entire life cycle and apply it to the same model; it is convenient for the comprehensive management and operation of enterprises, projects, and engineering parties [5, 6]. This technology uses three-dimensional digital technology to accurately analyze and simulate the real situation and construction information of a large building and provides a coordinated and internally unified information model for the design and construction of the entire construction project. It realizes the integration of architectural design and construction and optimizes the communication and collaboration between various disciplines, which can greatly reduce the cost and production cost of the entire project and ensure the smooth progress of the entire project on time and quantity.


## 2. Literature Review

The project cost is an investment method for enterprises and the government, and the purpose is to obtain the maximum profit, so the cost must be strictly controlled during the construction process. In recent years, the progress of China’s market economy has promoted the rapid development of the construction industry, and the main body of construction investment has developed a trend of diversification [7, 8]. Under normal circumstances, the owner will do a basic preliminary assessment before investing, and accurate and rapid assessment of the project cost is the need for project bidding competition. In order to maximize profits in the process of investment and construction, we must comprehensively consider the investment cycle, amount, and other complex factors, firmly control the core elements of cost and realize scientific cost evaluation. Due to the late start of China’s engineering cost management, there is no complete theoretical knowledge system and lack of effective cost control, and the complex structure of high-rise buildings requires a long construction period. Therefore, seeking an efficient and practical cost assessment method has become the focus of scholars and industry professionals.At this stage, relevant scholars have proposed many cost assessment methods. For example, Zhan et al. and Jha et al. used WSR (Wuli-Shili-Renli, WSR for short) analytical model to evaluate the cost control of building seismic structures [9, 10]. First, they construct the hierarchical structure of price control and obtain multiple cost control schemes. Secondly, they use the QOS (quality of service) method to design the benefit control constraint equilibrium and select the best evaluation result. Finally, the simulation experiment proves that this method can effectively analyze the quality change characteristics of high-rise buildings and control the cost consumption better.Yang proposed a project cost management method based on BIM (representing building information model, Building information model, referred to as BIM) technology [11]. They analyzed the feasibility of introducing BIM technology in combination with the problems of the existing cost evaluation methods in China. They explored the basic principles and advantages of BIM and proposed corresponding application models for cost management of construction projects in different stages. Finally, the role of BIM technology is verified by a specific example.Although the above two methods play a certain role in cost control, they do not take into account the dynamics of prices and have strong subjectivity, resulting in low evaluation accuracy. Based on this, the author uses the BP (representing back propagation, back propagation, referred to as BP) neural network method to establish a high-rise building project cost evaluation model. This paper debugs the neural network model through the process of determining the neural network structure, calculating the network error, adjusting the weights, designing the network parameters, etc. and introduces the important parameters in the high-rise building project into it to build the final cost evaluation model. Simulation experiments show that the BP neural network method can solve the shortcomings of slow network convergence and easy to fall into the local minimum value, effectively improve the accuracy of cost evaluation in the early decision-making stage, and achieve rapid evaluation.


## 3. Methods

### 3.1. Construction of Evaluation Index System

#### 3.1.1. Composition of Total Investment in Construction Projects

As shown in Figure1, the cost of construction engineering refers to the combination of known construction content, scale and standards and other related requirements, all the costs that need to be spent in the process of completing all construction contents until delivery [12, 13]. It mainly includes investment in other fixed assets such as construction equipment purchase costs, installation costs, and preparation costs.Figure 1
The overall investment composition of construction projects.


#### 3.1.2. Classification of Cost Index

In different stages of construction, the manifestations of engineering cost are also different, for example, in the feasibility analysis stage, the performance behavior is investment estimation, the specific manifestation of each stage is shown in Figure2.Figure 2
The representation of project cost at different stages.The cost index is an indicator that reflects price changes in a fixed period of time, it can effectively reflect the trend and magnitude of cost changes, and at the same time objectively show the supply and demand relationship between the level of productivity and the construction market. Mainly divided into the following categories:(1) Individual indices, such as labor and materials,, by arranging the indices of different periods in chronological order to obtain the status of individual price changes and forecast the future development trend.(2)The price index of construction equipment and tools.(3) High-rise building installation cost index.(4) The cost index of a single project.


#### 3.1.3. Construction of Evaluation Index System Based on Grey Correlation

The author uses the grey relational analysis method to construct the evaluation index system; the core idea is to judge the density and proximity of the cost sequence curve by combining the characteristic index sequence curve of the construction project, the smaller the curve gap, the higher the correlation between the series. This method is simple in data processing and convenient in calculation, and is suitable for the selection of project cost evaluation indicators [14, 15].(1) Compare the Selection of the Matrix and the Reference Sequence. The comparison matrix is all the characteristic indexes that affect the project cost, suppose there are m sample projects and n index characteristics, therefore, the comparison matrix X is expressed as
(1)X=x11x12⋯x1nx21x22⋯x2n⋮⋮⋱⋮xm1xm2⋯xmn.When evaluating the cost, the unilateral cost is selected as the value of the reference sequence, and the correlation between different characteristic indicators and the unilateral cost is compared, the higher the degree of correlation, the closer the relationship between the eigenvalue and the unilateral cost. The formula for calculating this reference sequence value is(2)Xi0=X10,X20,⋯,Xm0.In formula (2), Xi0i=1,2,⋯,m represents the unilateral cost value.(2) Standardization of Index Values. In order to improve the evaluation accuracy and ensure the equivalence between the indicators, the linearization method is used to normalize the index values of different dimensions, and the expression is as follows:
(3)Xij=xijmaxxij.In formula (3), maxxij represents the maximum value of the k-th index in all projects.(3) Calculation of Correlation Coefficient. The correlation coefficient can reflect the correlation degree of different indicators in the comparison matrix X to the reference sequence X0 in the i-th sample. The gray correlation analysis method is used to calculate the correlation coefficient between the j-th index of the i-th project and the unilateral cost.
(4)ξij=minjminiXi0−Xij+ρmaxjmaxiXi0−XijXi0−Xij+ρmaxjmaxiXi0−Xij.In formula (4), ρ represents the resolution coefficient, and its value is 0.5, and its value will affect the difference between the correlation coefficients.(4) Correlation Degree Calculation. The grey correlation coefficient can only show the correlation degree of the indicators in a single sample, which is one-sided. Therefore, the author selects multiple samples and uses the mean method to determine the correlation of the j-th index.
(5)γj=1m∑i=1mξij.In formula (5), the obtained correlation degrees are sorted, the greater the correlation degree, the more consistent the change trend of the j-th index and the cost, that is, the higher the influence of Xj on X0. According to the rule of taking the larger one, the indicators with greater correlation are reserved.


### 3.2. Establishment of Cost Evaluation Model of BP Neural Network

#### 3.2.1. Features of BP Neural Network

BP neural network is a data processing system proposed on the basis of human brain organization and activity mechanism, so it can show many human brain characteristics.(1) Distributed Data Storage. The data storage method of BP neural network is quite different from traditional computer storage, the same data is not only stored in one place, but distributed in the connection structure between neural nodes.(2) Parallel Data Processing. In the neural network, any neural node can receive the transmission information, can combine the information for independent processing and operation, and send the calculation result to the next neural network for parallel data processing [16, 17].(3) Fault Tolerance of Information Processing. The structural characteristics of the neural network are mainly reflected in the huge structure and spatial distribution of storage, these two characteristics can make the neural network have better fault tolerance in the following two aspects: when some neural nodes are destroyed, it will not have a great impact on the network as a whole; for data input, if the data is incomplete or deformed, the neural network will repair the missing data according to some data.(4) Adaptability of Data Processing. Adaptive refers to changing its own characteristics according to environmental requirements. Mainly reflected in the following aspects:Self-Learning: during the training process, if the external environment changes, the network structure parameters can be automatically adjusted after a period of training.Self-Organization: when stimulated by the outside world, the connection parts between neural nodes can be adjusted according to certain learning rules, and the network can be reconstructed.


#### 3.2.2. Basic Structure of BP Neural Network

BP neural network belongs to a learning algorithm of forward multi-layer error back propagation. It has an input layer, an output layer and multiple hidden layers, the layers are fully interconnected, the nodes in the same layer are not connected to each other, each layer is composed of several neurons.Suppose that the BP neural network hasn input nodes, m output nodes, and the number of nodes is denoted as q. The input vector and output vector are X=x1,x2,⋯,xnT and Y=y1,y2,⋯,yn, respectively. The input vector and output vector of the hidden layer are denoted as S=s1,S2,⋯,sn and B=b1,b2,⋯,bq, respectively. The input and output vectors of the output layer are described as L=l1,l2,⋯,lm and C=c1,C2,⋯,Cm, respectively. The neurons in the input layer and the hidden layer are i and j, respectively, and the connection weight is Wij. The connection weight between the hidden layer and the output layer is Vjt, and the threshold of the neural node j in the hidden layer is θj.


#### 3.2.3. BP Neural Network Error Calculation

If the output of the BP neural network is quite different from the ideal output value, the ideal output value is the instance provided by the ideal output neural network by learning the training samples, adjust the connection weight coefficient according to certain rules, continuously improve its own performance, and finally achieve the most ideal state, this state is that when the input is given externally, it can make a relatively correct output, and the output value is the ideal output value. The expression of the error output result E is as follows:(6)E=12d−O2=12∑k=1ldk−ok2.In the formula,d represents the ideal state input value of BP neural network, O represents the ideal state output value of BP neural network, k represents the amount of sample data, l represents the number of hidden layer nodes, dk represents the actual state input value of the BP neural network, and ok represents the ideal state output value of the BP neural network.Expanding the above error to the hidden layer, we get(7)E=12∑k=1ldk−fnetk2.In the formula,fnetk represents the output constant value of the BP neural network.Formula (7) is further expanded to the input layer.
(8)E=12∑k=1ldk−f∑j=0mωjkfnetj2.In the formula,ωjj represents the number of output layer nodes.


#### 3.2.4. Weight Adjustment Based on Gradient Descent

According to the above formula, the adjustment of the network input error is the adjustment of the weightsWij and Vjt, so the weight adjustment can be performed by changing the error E. Using the gradient descent method to continuously reduce the network error, make sure that there is a proportional relationship between the amount of weight adjustment and the degree of error gradient descent.
(9)wij=−λ∂E∂wij,j=0,1,2,⋯,m;k=1,2,⋯,l,(10)vij=−λ∂E∂vij,j=0,1,2,⋯,n;j=1,2,⋯,l.In the formula, the negative sign represents gradient descent, andλ∈0,1 belongs to a proportional coefficient, which reflects the learning rate of the neural network during the training process. Therefore, it can be seen that the BP algorithm is a kind of σ learning rule.The above two formulas are not complete weight adjustment formulas, but only an expression of adjustment ideas. The derivation process of the adjustment formula will be described in detail below.It is assumed that in the derivation process of the weight adjustment formula, there are, respectively, for the output and input layers,i=0,1,2,⋯,n,j=1,2,⋯,m.For the output layer, formula (9) can be rewritten as
(11)Δwjk=−η∂E∂wjk=−η∂E∂netk∂netk∂wjk.Formula (10) can be written as
(12)Δvij=−η∂E∂vij=−η∂E∂netj∂netj∂vij.Define the error signals of the output layer and the hidden layer, respectively.(13)δko=−∂E∂netk,(14)δjy=−∂E∂net.Combining the above two formulas, we can get(15)Δwjk=ηδy.Therefore, it can be seen that only by calculating the error signalsδko and δjy, the inference of the weight adjustment amount can be realized.The expanded form of the signal errorδko in the output layer is
(16)δko=−∂E∂netk=−∂E∂ok∂ok∂netk=−∂E∂okf′netk.The expanded expression of the signal errorδjy in the hidden layer is
(17)δjy=−∂E∂netj=−∂E∂yi∂yj∂netj=−∂E∂yjf′net.Calculate the partial derivative of the error to the output layer and the hidden layer in the above two formulas.(18)∂E∂ok=−dk−ok,(19)∂E∂yj=−∑k=1ldk−okf′netkwjk.Bring the calculation results into formulas (15) and (16), and use formula f′x=fx1−fx to calculate
(20)δko=dk−okok1−ok,(21)δjy=∑k=1ldk−okf′netkwjkf′netj=∑k=1lδkowjkyj1−yj.Through formulas (20) and (21), the calculation formula of neural network algorithm weight adjustment can be obtained as
(22)Δwjk=ηδkoyi=ηdk−okok1−okyj,(23)Δvij=ηδjyxj=η∑k=1lδkowjkyj1−yjxi.


#### 3.2.5. Network Parameter Design

This paper mainly sets the learning rateη of BP neural network. The learning rate η can also be called the step size, and its value interval is usually a constant between [0, 1] in the standard learning algorithm, but in the process of evaluating the model construction, it is very difficult to determine a learning rate that works from start to finish [18, 19]. If η is too small, the number of model training will increase, and η needs to be increased during the training process; if η is too large, training oscillation may occur. There are many ways to adjust the learning rate, the ultimate purpose of these methods is to make the learning rate play an effective role in the entire training process, therefore, the more commonly used adaptive learning rate adjustment expression is selected.
(24)ηt+1=1.05tEt<Et−1,0.7ηtEt>1.04Et−1,ηt.In the process of neural network training, due to the continuous reduction of errors, the learning rate will increase, when the number of training times increases to a certain extent, the learning efficiency will be higher than 1. Therefore, when using the adaptive learning rate, we must increase the threshold value of the learning rate to obtain the best learning rate.


#### 3.2.6. Determination of BP Neural Network Evaluation Model

After the training of BP neural network is completed, we can input important project cost parameters into the learning network, and obtain the final unit cost price through evaluation. This method realizes the evaluation of numerical model based on historical data, which is easy to operate and has high accuracy. The BP neural network evaluation model is shown in Figure3.Figure 3
BP neural network evaluation model diagram.


### 3.3. Experimental Test

In order to prove the effectiveness of the cost evaluation model of high-rise building projects based on BP neural network, this paper selects 10 completed high-rise building projects in a certain place, and the sample data are all from the cost information network. This can ensure the regional uniformity of sample data, and the similarity between sample data is large, so the model accuracy will not be reduced. The obtained data was preprocessed in combination with the qualitative indicators and quantitative standards, and the index values of the sample data after screening are shown in Table1.Table 1
Engineering characteristic index values.
Serial numberConstruction areaLayersDoors and windowsEaves highStructure typeInstallation work1118254.1142220659.6143224287.6134119492.3225225389.5216223287.2147219174.8128118594.2339124284.11410225387.612


## 3.1. Construction of Evaluation Index System

### 3.1.1. Composition of Total Investment in Construction Projects

As shown in Figure1, the cost of construction engineering refers to the combination of known construction content, scale and standards and other related requirements, all the costs that need to be spent in the process of completing all construction contents until delivery [12, 13]. It mainly includes investment in other fixed assets such as construction equipment purchase costs, installation costs, and preparation costs.Figure 1
The overall investment composition of construction projects.


### 3.1.2. Classification of Cost Index

In different stages of construction, the manifestations of engineering cost are also different, for example, in the feasibility analysis stage, the performance behavior is investment estimation, the specific manifestation of each stage is shown in Figure2.Figure 2
The representation of project cost at different stages.The cost index is an indicator that reflects price changes in a fixed period of time, it can effectively reflect the trend and magnitude of cost changes, and at the same time objectively show the supply and demand relationship between the level of productivity and the construction market. Mainly divided into the following categories:(1) Individual indices, such as labor and materials,, by arranging the indices of different periods in chronological order to obtain the status of individual price changes and forecast the future development trend.(2)The price index of construction equipment and tools.(3) High-rise building installation cost index.(4) The cost index of a single project.


### 3.1.3. Construction of Evaluation Index System Based on Grey Correlation

The author uses the grey relational analysis method to construct the evaluation index system; the core idea is to judge the density and proximity of the cost sequence curve by combining the characteristic index sequence curve of the construction project, the smaller the curve gap, the higher the correlation between the series. This method is simple in data processing and convenient in calculation, and is suitable for the selection of project cost evaluation indicators [14, 15].(1) Compare the Selection of the Matrix and the Reference Sequence. The comparison matrix is all the characteristic indexes that affect the project cost, suppose there are m sample projects and n index characteristics, therefore, the comparison matrix X is expressed as
(1)X=x11x12⋯x1nx21x22⋯x2n⋮⋮⋱⋮xm1xm2⋯xmn.When evaluating the cost, the unilateral cost is selected as the value of the reference sequence, and the correlation between different characteristic indicators and the unilateral cost is compared, the higher the degree of correlation, the closer the relationship between the eigenvalue and the unilateral cost. The formula for calculating this reference sequence value is(2)Xi0=X10,X20,⋯,Xm0.In formula (2), Xi0i=1,2,⋯,m represents the unilateral cost value.(2) Standardization of Index Values. In order to improve the evaluation accuracy and ensure the equivalence between the indicators, the linearization method is used to normalize the index values of different dimensions, and the expression is as follows:
(3)Xij=xijmaxxij.In formula (3), maxxij represents the maximum value of the k-th index in all projects.(3) Calculation of Correlation Coefficient. The correlation coefficient can reflect the correlation degree of different indicators in the comparison matrix X to the reference sequence X0 in the i-th sample. The gray correlation analysis method is used to calculate the correlation coefficient between the j-th index of the i-th project and the unilateral cost.
(4)ξij=minjminiXi0−Xij+ρmaxjmaxiXi0−XijXi0−Xij+ρmaxjmaxiXi0−Xij.In formula (4), ρ represents the resolution coefficient, and its value is 0.5, and its value will affect the difference between the correlation coefficients.(4) Correlation Degree Calculation. The grey correlation coefficient can only show the correlation degree of the indicators in a single sample, which is one-sided. Therefore, the author selects multiple samples and uses the mean method to determine the correlation of the j-th index.
(5)γj=1m∑i=1mξij.In formula (5), the obtained correlation degrees are sorted, the greater the correlation degree, the more consistent the change trend of the j-th index and the cost, that is, the higher the influence of Xj on X0. According to the rule of taking the larger one, the indicators with greater correlation are reserved.


## 3.1.1. Composition of Total Investment in Construction Projects

As shown in Figure1, the cost of construction engineering refers to the combination of known construction content, scale and standards and other related requirements, all the costs that need to be spent in the process of completing all construction contents until delivery [12, 13]. It mainly includes investment in other fixed assets such as construction equipment purchase costs, installation costs, and preparation costs.Figure 1
The overall investment composition of construction projects.


## 3.1.2. Classification of Cost Index

In different stages of construction, the manifestations of engineering cost are also different, for example, in the feasibility analysis stage, the performance behavior is investment estimation, the specific manifestation of each stage is shown in Figure2.Figure 2
The representation of project cost at different stages.The cost index is an indicator that reflects price changes in a fixed period of time, it can effectively reflect the trend and magnitude of cost changes, and at the same time objectively show the supply and demand relationship between the level of productivity and the construction market. Mainly divided into the following categories:(1) Individual indices, such as labor and materials,, by arranging the indices of different periods in chronological order to obtain the status of individual price changes and forecast the future development trend.(2)The price index of construction equipment and tools.(3) High-rise building installation cost index.(4) The cost index of a single project.


## 3.1.3. Construction of Evaluation Index System Based on Grey Correlation

The author uses the grey relational analysis method to construct the evaluation index system; the core idea is to judge the density and proximity of the cost sequence curve by combining the characteristic index sequence curve of the construction project, the smaller the curve gap, the higher the correlation between the series. This method is simple in data processing and convenient in calculation, and is suitable for the selection of project cost evaluation indicators [14, 15].(1) Compare the Selection of the Matrix and the Reference Sequence. The comparison matrix is all the characteristic indexes that affect the project cost, suppose there are m sample projects and n index characteristics, therefore, the comparison matrix X is expressed as
(1)X=x11x12⋯x1nx21x22⋯x2n⋮⋮⋱⋮xm1xm2⋯xmn.When evaluating the cost, the unilateral cost is selected as the value of the reference sequence, and the correlation between different characteristic indicators and the unilateral cost is compared, the higher the degree of correlation, the closer the relationship between the eigenvalue and the unilateral cost. The formula for calculating this reference sequence value is(2)Xi0=X10,X20,⋯,Xm0.In formula (2), Xi0i=1,2,⋯,m represents the unilateral cost value.(2) Standardization of Index Values. In order to improve the evaluation accuracy and ensure the equivalence between the indicators, the linearization method is used to normalize the index values of different dimensions, and the expression is as follows:
(3)Xij=xijmaxxij.In formula (3), maxxij represents the maximum value of the k-th index in all projects.(3) Calculation of Correlation Coefficient. The correlation coefficient can reflect the correlation degree of different indicators in the comparison matrix X to the reference sequence X0 in the i-th sample. The gray correlation analysis method is used to calculate the correlation coefficient between the j-th index of the i-th project and the unilateral cost.
(4)ξij=minjminiXi0−Xij+ρmaxjmaxiXi0−XijXi0−Xij+ρmaxjmaxiXi0−Xij.In formula (4), ρ represents the resolution coefficient, and its value is 0.5, and its value will affect the difference between the correlation coefficients.(4) Correlation Degree Calculation. The grey correlation coefficient can only show the correlation degree of the indicators in a single sample, which is one-sided. Therefore, the author selects multiple samples and uses the mean method to determine the correlation of the j-th index.
(5)γj=1m∑i=1mξij.In formula (5), the obtained correlation degrees are sorted, the greater the correlation degree, the more consistent the change trend of the j-th index and the cost, that is, the higher the influence of Xj on X0. According to the rule of taking the larger one, the indicators with greater correlation are reserved.


## 3.2. Establishment of Cost Evaluation Model of BP Neural Network

### 3.2.1. Features of BP Neural Network

BP neural network is a data processing system proposed on the basis of human brain organization and activity mechanism, so it can show many human brain characteristics.(1) Distributed Data Storage. The data storage method of BP neural network is quite different from traditional computer storage, the same data is not only stored in one place, but distributed in the connection structure between neural nodes.(2) Parallel Data Processing. In the neural network, any neural node can receive the transmission information, can combine the information for independent processing and operation, and send the calculation result to the next neural network for parallel data processing [16, 17].(3) Fault Tolerance of Information Processing. The structural characteristics of the neural network are mainly reflected in the huge structure and spatial distribution of storage, these two characteristics can make the neural network have better fault tolerance in the following two aspects: when some neural nodes are destroyed, it will not have a great impact on the network as a whole; for data input, if the data is incomplete or deformed, the neural network will repair the missing data according to some data.(4) Adaptability of Data Processing. Adaptive refers to changing its own characteristics according to environmental requirements. Mainly reflected in the following aspects:Self-Learning: during the training process, if the external environment changes, the network structure parameters can be automatically adjusted after a period of training.Self-Organization: when stimulated by the outside world, the connection parts between neural nodes can be adjusted according to certain learning rules, and the network can be reconstructed.


### 3.2.2. Basic Structure of BP Neural Network

BP neural network belongs to a learning algorithm of forward multi-layer error back propagation. It has an input layer, an output layer and multiple hidden layers, the layers are fully interconnected, the nodes in the same layer are not connected to each other, each layer is composed of several neurons.Suppose that the BP neural network hasn input nodes, m output nodes, and the number of nodes is denoted as q. The input vector and output vector are X=x1,x2,⋯,xnT and Y=y1,y2,⋯,yn, respectively. The input vector and output vector of the hidden layer are denoted as S=s1,S2,⋯,sn and B=b1,b2,⋯,bq, respectively. The input and output vectors of the output layer are described as L=l1,l2,⋯,lm and C=c1,C2,⋯,Cm, respectively. The neurons in the input layer and the hidden layer are i and j, respectively, and the connection weight is Wij. The connection weight between the hidden layer and the output layer is Vjt, and the threshold of the neural node j in the hidden layer is θj.


### 3.2.3. BP Neural Network Error Calculation

If the output of the BP neural network is quite different from the ideal output value, the ideal output value is the instance provided by the ideal output neural network by learning the training samples, adjust the connection weight coefficient according to certain rules, continuously improve its own performance, and finally achieve the most ideal state, this state is that when the input is given externally, it can make a relatively correct output, and the output value is the ideal output value. The expression of the error output result E is as follows:(6)E=12d−O2=12∑k=1ldk−ok2.In the formula,d represents the ideal state input value of BP neural network, O represents the ideal state output value of BP neural network, k represents the amount of sample data, l represents the number of hidden layer nodes, dk represents the actual state input value of the BP neural network, and ok represents the ideal state output value of the BP neural network.Expanding the above error to the hidden layer, we get(7)E=12∑k=1ldk−fnetk2.In the formula,fnetk represents the output constant value of the BP neural network.Formula (7) is further expanded to the input layer.
(8)E=12∑k=1ldk−f∑j=0mωjkfnetj2.In the formula,ωjj represents the number of output layer nodes.


### 3.2.4. Weight Adjustment Based on Gradient Descent

According to the above formula, the adjustment of the network input error is the adjustment of the weightsWij and Vjt, so the weight adjustment can be performed by changing the error E. Using the gradient descent method to continuously reduce the network error, make sure that there is a proportional relationship between the amount of weight adjustment and the degree of error gradient descent.
(9)wij=−λ∂E∂wij,j=0,1,2,⋯,m;k=1,2,⋯,l,(10)vij=−λ∂E∂vij,j=0,1,2,⋯,n;j=1,2,⋯,l.In the formula, the negative sign represents gradient descent, andλ∈0,1 belongs to a proportional coefficient, which reflects the learning rate of the neural network during the training process. Therefore, it can be seen that the BP algorithm is a kind of σ learning rule.The above two formulas are not complete weight adjustment formulas, but only an expression of adjustment ideas. The derivation process of the adjustment formula will be described in detail below.It is assumed that in the derivation process of the weight adjustment formula, there are, respectively, for the output and input layers,i=0,1,2,⋯,n,j=1,2,⋯,m.For the output layer, formula (9) can be rewritten as
(11)Δwjk=−η∂E∂wjk=−η∂E∂netk∂netk∂wjk.Formula (10) can be written as
(12)Δvij=−η∂E∂vij=−η∂E∂netj∂netj∂vij.Define the error signals of the output layer and the hidden layer, respectively.(13)δko=−∂E∂netk,(14)δjy=−∂E∂net.Combining the above two formulas, we can get(15)Δwjk=ηδy.Therefore, it can be seen that only by calculating the error signalsδko and δjy, the inference of the weight adjustment amount can be realized.The expanded form of the signal errorδko in the output layer is
(16)δko=−∂E∂netk=−∂E∂ok∂ok∂netk=−∂E∂okf′netk.The expanded expression of the signal errorδjy in the hidden layer is
(17)δjy=−∂E∂netj=−∂E∂yi∂yj∂netj=−∂E∂yjf′net.Calculate the partial derivative of the error to the output layer and the hidden layer in the above two formulas.(18)∂E∂ok=−dk−ok,(19)∂E∂yj=−∑k=1ldk−okf′netkwjk.Bring the calculation results into formulas (15) and (16), and use formula f′x=fx1−fx to calculate
(20)δko=dk−okok1−ok,(21)δjy=∑k=1ldk−okf′netkwjkf′netj=∑k=1lδkowjkyj1−yj.Through formulas (20) and (21), the calculation formula of neural network algorithm weight adjustment can be obtained as
(22)Δwjk=ηδkoyi=ηdk−okok1−okyj,(23)Δvij=ηδjyxj=η∑k=1lδkowjkyj1−yjxi.


### 3.2.5. Network Parameter Design

This paper mainly sets the learning rateη of BP neural network. The learning rate η can also be called the step size, and its value interval is usually a constant between [0, 1] in the standard learning algorithm, but in the process of evaluating the model construction, it is very difficult to determine a learning rate that works from start to finish [18, 19]. If η is too small, the number of model training will increase, and η needs to be increased during the training process; if η is too large, training oscillation may occur. There are many ways to adjust the learning rate, the ultimate purpose of these methods is to make the learning rate play an effective role in the entire training process, therefore, the more commonly used adaptive learning rate adjustment expression is selected.
(24)ηt+1=1.05tEt<Et−1,0.7ηtEt>1.04Et−1,ηt.In the process of neural network training, due to the continuous reduction of errors, the learning rate will increase, when the number of training times increases to a certain extent, the learning efficiency will be higher than 1. Therefore, when using the adaptive learning rate, we must increase the threshold value of the learning rate to obtain the best learning rate.


### 3.2.6. Determination of BP Neural Network Evaluation Model

After the training of BP neural network is completed, we can input important project cost parameters into the learning network, and obtain the final unit cost price through evaluation. This method realizes the evaluation of numerical model based on historical data, which is easy to operate and has high accuracy. The BP neural network evaluation model is shown in Figure3.Figure 3
BP neural network evaluation model diagram.


## 3.2.1. Features of BP Neural Network

BP neural network is a data processing system proposed on the basis of human brain organization and activity mechanism, so it can show many human brain characteristics.(1) Distributed Data Storage. The data storage method of BP neural network is quite different from traditional computer storage, the same data is not only stored in one place, but distributed in the connection structure between neural nodes.(2) Parallel Data Processing. In the neural network, any neural node can receive the transmission information, can combine the information for independent processing and operation, and send the calculation result to the next neural network for parallel data processing [16, 17].(3) Fault Tolerance of Information Processing. The structural characteristics of the neural network are mainly reflected in the huge structure and spatial distribution of storage, these two characteristics can make the neural network have better fault tolerance in the following two aspects: when some neural nodes are destroyed, it will not have a great impact on the network as a whole; for data input, if the data is incomplete or deformed, the neural network will repair the missing data according to some data.(4) Adaptability of Data Processing. Adaptive refers to changing its own characteristics according to environmental requirements. Mainly reflected in the following aspects:Self-Learning: during the training process, if the external environment changes, the network structure parameters can be automatically adjusted after a period of training.Self-Organization: when stimulated by the outside world, the connection parts between neural nodes can be adjusted according to certain learning rules, and the network can be reconstructed.


## 3.2.2. Basic Structure of BP Neural Network

BP neural network belongs to a learning algorithm of forward multi-layer error back propagation. It has an input layer, an output layer and multiple hidden layers, the layers are fully interconnected, the nodes in the same layer are not connected to each other, each layer is composed of several neurons.Suppose that the BP neural network hasn input nodes, m output nodes, and the number of nodes is denoted as q. The input vector and output vector are X=x1,x2,⋯,xnT and Y=y1,y2,⋯,yn, respectively. The input vector and output vector of the hidden layer are denoted as S=s1,S2,⋯,sn and B=b1,b2,⋯,bq, respectively. The input and output vectors of the output layer are described as L=l1,l2,⋯,lm and C=c1,C2,⋯,Cm, respectively. The neurons in the input layer and the hidden layer are i and j, respectively, and the connection weight is Wij. The connection weight between the hidden layer and the output layer is Vjt, and the threshold of the neural node j in the hidden layer is θj.


## 3.2.3. BP Neural Network Error Calculation

If the output of the BP neural network is quite different from the ideal output value, the ideal output value is the instance provided by the ideal output neural network by learning the training samples, adjust the connection weight coefficient according to certain rules, continuously improve its own performance, and finally achieve the most ideal state, this state is that when the input is given externally, it can make a relatively correct output, and the output value is the ideal output value. The expression of the error output result E is as follows:(6)E=12d−O2=12∑k=1ldk−ok2.In the formula,d represents the ideal state input value of BP neural network, O represents the ideal state output value of BP neural network, k represents the amount of sample data, l represents the number of hidden layer nodes, dk represents the actual state input value of the BP neural network, and ok represents the ideal state output value of the BP neural network.Expanding the above error to the hidden layer, we get(7)E=12∑k=1ldk−fnetk2.In the formula,fnetk represents the output constant value of the BP neural network.Formula (7) is further expanded to the input layer.
(8)E=12∑k=1ldk−f∑j=0mωjkfnetj2.In the formula,ωjj represents the number of output layer nodes.


## 3.2.4. Weight Adjustment Based on Gradient Descent

According to the above formula, the adjustment of the network input error is the adjustment of the weightsWij and Vjt, so the weight adjustment can be performed by changing the error E. Using the gradient descent method to continuously reduce the network error, make sure that there is a proportional relationship between the amount of weight adjustment and the degree of error gradient descent.
(9)wij=−λ∂E∂wij,j=0,1,2,⋯,m;k=1,2,⋯,l,(10)vij=−λ∂E∂vij,j=0,1,2,⋯,n;j=1,2,⋯,l.In the formula, the negative sign represents gradient descent, andλ∈0,1 belongs to a proportional coefficient, which reflects the learning rate of the neural network during the training process. Therefore, it can be seen that the BP algorithm is a kind of σ learning rule.The above two formulas are not complete weight adjustment formulas, but only an expression of adjustment ideas. The derivation process of the adjustment formula will be described in detail below.It is assumed that in the derivation process of the weight adjustment formula, there are, respectively, for the output and input layers,i=0,1,2,⋯,n,j=1,2,⋯,m.For the output layer, formula (9) can be rewritten as
(11)Δwjk=−η∂E∂wjk=−η∂E∂netk∂netk∂wjk.Formula (10) can be written as
(12)Δvij=−η∂E∂vij=−η∂E∂netj∂netj∂vij.Define the error signals of the output layer and the hidden layer, respectively.(13)δko=−∂E∂netk,(14)δjy=−∂E∂net.Combining the above two formulas, we can get(15)Δwjk=ηδy.Therefore, it can be seen that only by calculating the error signalsδko and δjy, the inference of the weight adjustment amount can be realized.The expanded form of the signal errorδko in the output layer is
(16)δko=−∂E∂netk=−∂E∂ok∂ok∂netk=−∂E∂okf′netk.The expanded expression of the signal errorδjy in the hidden layer is
(17)δjy=−∂E∂netj=−∂E∂yi∂yj∂netj=−∂E∂yjf′net.Calculate the partial derivative of the error to the output layer and the hidden layer in the above two formulas.(18)∂E∂ok=−dk−ok,(19)∂E∂yj=−∑k=1ldk−okf′netkwjk.Bring the calculation results into formulas (15) and (16), and use formula f′x=fx1−fx to calculate
(20)δko=dk−okok1−ok,(21)δjy=∑k=1ldk−okf′netkwjkf′netj=∑k=1lδkowjkyj1−yj.Through formulas (20) and (21), the calculation formula of neural network algorithm weight adjustment can be obtained as
(22)Δwjk=ηδkoyi=ηdk−okok1−okyj,(23)Δvij=ηδjyxj=η∑k=1lδkowjkyj1−yjxi.


## 3.2.5. Network Parameter Design

This paper mainly sets the learning rateη of BP neural network. The learning rate η can also be called the step size, and its value interval is usually a constant between [0, 1] in the standard learning algorithm, but in the process of evaluating the model construction, it is very difficult to determine a learning rate that works from start to finish [18, 19]. If η is too small, the number of model training will increase, and η needs to be increased during the training process; if η is too large, training oscillation may occur. There are many ways to adjust the learning rate, the ultimate purpose of these methods is to make the learning rate play an effective role in the entire training process, therefore, the more commonly used adaptive learning rate adjustment expression is selected.
(24)ηt+1=1.05tEt<Et−1,0.7ηtEt>1.04Et−1,ηt.In the process of neural network training, due to the continuous reduction of errors, the learning rate will increase, when the number of training times increases to a certain extent, the learning efficiency will be higher than 1. Therefore, when using the adaptive learning rate, we must increase the threshold value of the learning rate to obtain the best learning rate.


## 3.2.6. Determination of BP Neural Network Evaluation Model

After the training of BP neural network is completed, we can input important project cost parameters into the learning network, and obtain the final unit cost price through evaluation. This method realizes the evaluation of numerical model based on historical data, which is easy to operate and has high accuracy. The BP neural network evaluation model is shown in Figure3.Figure 3
BP neural network evaluation model diagram.


## 3.3. Experimental Test

In order to prove the effectiveness of the cost evaluation model of high-rise building projects based on BP neural network, this paper selects 10 completed high-rise building projects in a certain place, and the sample data are all from the cost information network. This can ensure the regional uniformity of sample data, and the similarity between sample data is large, so the model accuracy will not be reduced. The obtained data was preprocessed in combination with the qualitative indicators and quantitative standards, and the index values of the sample data after screening are shown in Table1.Table 1
Engineering characteristic index values.
Serial numberConstruction areaLayersDoors and windowsEaves highStructure typeInstallation work1118254.1142220659.6143224287.6134119492.3225225389.5216223287.2147219174.8128118594.2339124284.11410225387.612


## 4. Results and Discussion

According to the neural network evaluation model established by the author, simulation experiments are carried out on the basis of Matlab 2016b software. The simulation results are compared with the use of WSR analysis model to control the cost of building seismic structure, the project cost management methods based on BIM technology are compared, and the comparison results are shown in Table2.Table 2
Model evaluation results of different methods.
MethodActual value (yuan/㎡)Predictive value(yuan/㎡)Difference(yuan/㎡)Error rate%The cost control method of building seismic structure using WSR analysis model1525.21835.231016.9Project cost management method based on BIM technology1541.31848.2306.916.7Method1428.61521.893.26.1From the results in Table2, it can be seen that the evaluation error rates of the WSR analysis model for the cost control method of building seismic structures and the project cost management method based on BIM technology are 16.9% and 16.7%, respectively. The author compares the cost control method of building antiseismic structure and the project cost management method based on BIM technology by using WSR analysis model. The error value is small, and the error rate is controlled within 10%, meeting the requirements of investment estimation. In addition, the evaluation speed of the three methods is compared, and the results are shown in Figure 4.Figure 4
Comparison of evaluation speed of different methods.When evaluating the same target, the evaluation speed of the author’s method requires less time than the WSR analysis model for the cost control method of building seismic structures and the engineering cost management method based on BIM technology, and the evaluation efficiency is high [20]. The main reason is that the learning rate of the neural network in the proposed method is set more appropriately, and the BP neural network has the characteristics of distributed data storage, parallel data processing, good fault-tolerant performance of information processing, and strong adaptive ability of data processing.


## 5. Conclusion

This paper proposes an intelligent evaluation method for the feasibility model of project cost based on the Internet of Things. High-rise buildings are the key development direction of future building projects, and the cost of this project is of great significance for investment. Therefore, this paper uses BP neural network to study the cost evaluation model of high-rise buildings. First of all, this paper constructs the evaluation index system using the gray correlation analysis method. Secondly, this paper determines the network structure by analyzing the characteristics of the neural network, adjusts its weight value with gradient descent method, and sets the learning rate. Finally, this paper introduces the cost parameters into the trained neural network and constructs the final evaluation model.



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*Source: 3420723-2022-10-06.xml*