3.1 Digital analysis of intelligent building based on BIM technology
A digital tool used in engineering design, construction, and management is referred to as BIM technology. Through the integration of building data and information models, this technology is shared and transferred throughout the whole life cycle of project design, operation, and maintenance. In order to improve production efficiency, reduce costs, and accelerate construction time, engineers and technicians must be able to correctly understand and respond to all types of building information [17, 18]. Figure 1 displays the advantages of BIM technology.
In Fig. 1, the advantages of BIM technology mainly include visualization, parameterization, simulation, collaboration and inheritance. Visualization can graphically present architectural design through threedimensional modeling, so that architects, designers, owners and other related personnel can understand and evaluate architectural design schemes more intuitively, thus better meeting the needs of users. Parameterization can model and manage various parameterizations in architectural design, such as size, material and quality, and the relationship between different parameters. Finally, the design scheme can be quickly adjusted by modifying the parameters to improve the design efficiency and accuracy. Simulation means that the technology evaluates the feasibility and optimization direction of the architectural scheme by simulating various situations of the architectural design scheme, such as structure, energy consumption, and lighting. Collaboration means that this technology can coordinate all links among architects, structuralists, electromechanical engineers and other professions in the process of architectural design. Inheritance means that BIM can inherit and manage all kinds of information and data in architectural design scheme, thus facilitating later maintenance and management. For instance, to achieve the intelligent operation and management of the building, all types of characteristics, materials, equipment, and other information of the architectural design scheme are connected with the maintenance management system [19–21]. As a result, Fig. 2 illustrates the precise methods used in this paper's usage of BIM technology to digitally and visually represent the intelligent building.
In Fig. 2, firstly, building information is collected, including architectural design drawings, engineering specifications, technical specifications and related documents. This information contains a detailed description of the structure, layout, materials and equipment of the building, among which the extraction and processing of BIM data are shown in Table 1. Secondly, create a threedimensional model. Based on the collected building information, a threedimensional model of the building can be made using BIM software or modeling tools. At this stage, it is necessary to model all components of the building, including the structure, appearance, electromechanical equipment, piping system, etc., and accurately express the geometric shape, size and position of the building through the modeling function [22]. Next, associate the attribute information. In addition to geometric modeling, it is also necessary to associate relevant attribute information with the building model. This attribute information may include building materials, quantities, costs, and safety risks during construction. By associating attribute information, the building model can be transformed into an intelligent model with rich information, which provides a data basis for subsequent cost prediction [23]. Finally, after building model creation and attribute association are completed, tools such as BIM software or virtual reality technology can be used for visual display.
Table 1
BIM data extraction and processing
Step

Specific implementation method

Data fetch

Extract geometric information, attribute information, component relationship and spatial topology of buildings from BIM model;

Data cleaning and preprocessing

Remove duplicate data, fill in missing values, handle abnormal values, etc., and meanwhile normalize or standardize the data to ensure that the data is within the same order of magnitude;

Data feature selection

By statistical analysis, feature importance evaluation or domain expert knowledge, the features with high correlation and predictive ability are selected.

Digitization and visualization of building information is the basic step to establish BIM intelligent building model. By means of digitalization and visualization, complex information of buildings can be presented in a structured way, and accurate input data can be provided for subsequent cost prediction models. The establishment of this intelligent building model not only improves the visualization effect of information, but also provides important support for the digital transformation and intelligent development in the building field.
3.2 ENN algorithm and its optimization
Recurrent neural network (RNN), sometimes referred to as ENN, is a type of recursive neural network [24]. In order for the neural network's basic structure to describe and predict sequence data, it incorporates cyclic connections. Input, hidden, and output layers make up the ENN. The hidden layer's cyclic connections between neurons let the network recall its previous state and information. The ENN method is capable of updating and transmitting data across time. The network gets the inputs for the current time step's input data and the hidden state from the previous time step before updating the hidden layer's state by activating the function [25, 26]. In the following time step, the hidden layer's state is transmitted to it, and it is also utilized as the input for the output layer. As a result, the network can use the input sequence's temporal sequence information to anticipate future results. Eq. (1) displays the ENN's actual expression.
$$y\left( k \right)=g\left( {{w_3}x\left( k \right)} \right)$$
1
$$x\left( k \right)=f\left( {{w_1}{x_c}\left( k \right)+{w_2}\left( {u\left( {k  1} \right)} \right)} \right)$$
2
$${x_c}\left( k \right)=x\left( {k  1} \right)$$
3
In Eq. (1), y refers to the output vector of m dimension. x refers to the ndimensional hidden layer node vector. u refers to the input vector of r dimension. \({x_c}\)refers to ndimensional feedback state vector. \({w_3}\) refers to the weight matrix of the connection between the hidden layer and the output layer. \({w_2}\) refers to the weight matrix of the connection between the input layer and the hidden layer. \({w_1}\) refers to the weight matrix of the connection from the receiving layer to the hidden layer. g (*) is the conduction function of the output neuron. It is a linear weighted combination of hidden layer output. Purelin function is usually used. f (*) refers to the conduction function of neurons in the hidden layer, usually using S function. k refers to the moment when the sample is taken. The training error function e of ENN can be expressed as Eq. (4):
$$e \approx \sum\limits_{{k=1}}^{m} {{{\left( {{y_k}  {{\bar {y}}_k}} \right)}^2}}$$
4
In the above equation, \({y_k}\) refers to the ideal output data of ENN. \({\bar {y}_k}\) refers to the actual output of the neural network. m refers to the number of samples trained by the neural network. The specific ENN algorithm flow is shown in Fig. 3.
Figure 3 shows a nonlinear mapping from n independent variables to m dependent variables using an ENN. The receiving layer in this neural network receives the intelligent building data through the zeroth layer, and the output layer receives it through the hidden layer. Each layer's input intelligent building data is integrated linearly with the threshold and offset values between them before being output to the following layer via an activation function operation. Through the threshold connection with the intermediate layer, the associated layer sends back the output of the receiving layer and hidden layer at the current moment. When there is a discrepancy between the output of the network and the anticipated outcome, it is determined whether the error satisfies the standards for accuracy and whether the number of training steps satisfies those standards. If not, the network will modify its weight and offset values layer by layer until it reaches the required level of error accuracy, at which point it will reverse the error between the two.
However, ENNs are susceptible to the gradient disappearance or explosion problem, particularly when working with lengthy time series. This could prevent the network from successfully capturing longterm dependencies. Additionally, because of its relatively simplistic structure, neural networks might not be able to adapt to complicated situations or huge data sets. In order to reduce the impact of the "sawtooth phenomenon" on the network, prevent the occurrence of local optimal solutions, and increase the network's predictive accuracy, Particle Swarm Optimization (PSO), one of the evolutionary thinking algorithms, is introduced here when forecasting the construction cost of intelligent buildings [27, 28]. Figure 4 depicts the PSO fusing ENN's algorithm flow.
Figure. 4 Flow chart of optimization algorithm based on PSO and ENN
When the ENN in Fig. 4 is optimized by PSO, the particle swarm is initially initialized. Each randomly generated particle in a group represents a different parameter setting for an ENN. Each particle has two pieces of information: its present position and speed, and a fitness calculation. ENN is built using the parameter combinations that correspond to each particle, and training is carried out using training data. Each particle's fitness is determined by assessing the network's performance metric (such as error or accuracy). The third step entails updating the particle position and velocity. To come up with a better answer, the positions and velocities of each particle are modified. Each particle has an optimal location that is estimated for both its individual optimal position (historical optimal fitness) and its overall optimal position (optimal fitness across the entire particle swarm). Equations (5) and (6) display the pace and location of updating particles:
$$v\left( {t+1} \right){\text{ }}={\text{ }}wv\left( t \right){\text{ }}+{\text{ }}{c_{1{\text{ }}}}{r_1}\left( {{p_{best}}{\text{ }}  {\text{ }}position\left( t \right)} \right){\text{ }}+{\text{ }}{c_2}{r_2}\left( {{g_{best}}{\text{ }}  {\text{ }}position\left( t \right)} \right)$$
5
$$position\left( {t+1} \right){\text{ }}={\text{ }}position\left( t \right){\text{ }}+{\text{ }}v\left( {t+1} \right)$$
6
v(t + 1) is the next generation speed, position(t + 1) is the next generation position. w is the inertia weight. c1 and c2 are learning factors. r1 and r2 are random numbers. pbest is the individual optimal position of particles, and gbest is the global optimal position of the whole particle swarm.
The fourth step is to evaluate the stopping circumstances. The stopping criteria, such as completing the specified number of iterations or achieving the predetermined fitness level, are assessed. The optimization process ends if the stop condition is satisfied; else, the second step is returned to carry on the iteration.
The fifth step is to present the findings. The optimized ENN model's parameters are chosen to correspond to the particle that has the highest fitness.
Therefore, the PSO algorithm can be optimized and improved according to specific problems and needs in this paper when it is applied to the construction cost prediction of intelligent buildings. The performance and convergence speed of the algorithm can be improved by adjusting the values of inertia weight, learning factor, and random number, as well as by introducing adaptive strategies.
3.3 Intelligent building construction cost prediction model based on BIM and ENN
In this paper, BIM technology is introduced and a BIM intelligent building model is built in order to accurately anticipate the construction cost of intelligent buildings. After the intelligent building has undergone pretreatment, the PSO algorithm optimizes the ENN, leading to the creation of the intelligent building's construction cost model. The data information in BIM intelligent building model is imported into ENN as input data, and the construction cost of intelligent building is predicted by optimizing the parameters of neural network. The concrete intelligent building construction cost prediction model based on BIM and ENN is shown in Fig. 5.
As shown in Fig. 5, this model uses BIM technology to digitize and visualize information about the building's construction, electromechanical system, and pipeline. People can obtain a multitude of buildingrelated information, such as material costs, labor costs, equipment rental costs, and so forth, using the BIM model. Then, to guarantee the accuracy and consistency of the data, the BIM intelligent building model's data is preprocessed. This includes data cleaning, the removal of aberrant values, the filling in of missing values, and other procedures. Second, ENN uses the preprocessed BIM data as its input data. The weight and threshold of the ENN are two of the parameters that are optimized using the PSO technique. Finally, the construction cost of intelligent buildings is predicted using the improved ENN model. ENN can learn the correlation between architectural elements and construction cost by receiving BIM data as input. The model can then forecast construction costs based on the input BIM data.
When using PSO algorithm to optimize ENN, taking a threelayer network as an example, its coding length S can be expressed as Eq. (7) according to real coding rules:
$$S={S_1} \cdot {S_2}+{S_2} \cdot {S_3}+{S_2} \cdot {S_2}+{S_2}+{S_3}$$
7
\({S_1}\) refers to the number of neurons in the zeroth layer of the network, \({S_2}\) refers to the number of neurons in the middle layer of the network and \({S_3}\) refers to the number of neurons in the output layer of the network.
Further set the algorithm parameters. The size of the initial population determines the convergence speed and search quality of the final result, but the size of the initial population has an opposite effect on the two. Therefore, it is necessary to reasonably set the value of the initial population number popu, which cannot be too large or too small. The size FF of the subpopulation can be expressed as Eq. (8):
$$FF=popu/\left( {B\_size+T\_size} \right)$$
8
\(B\_size\) refers to the number of superior subgroups, and \(T\_size\) refers to the number of temporary subgroups.
Fitness function, as an important index of individual search evolution, usually follows simple calculation, universal application, positive value and continuity when selecting this parameter. Usually, the trained network selects the training data for prediction, and the mean square error of the prediction output result is inverted as the fitness value val of the current individual, as shown in Eq. (9):
$$val=\frac{1}{{mse\left( {T  A} \right)}}$$
9
T refers to the expected output value of training data and A refers to the predicted output value of training data.
With the help of this model, researchers may extract building information using BIM technology and anticipate construction costs using ENNs. The ENN's performance and accuracy are increased by using the PSO algorithm to optimize its parameters. This model offers a useful technique for estimating construction costs in the area of intelligent buildings and supports the digital and intelligent growth of construction companies.
3.4 Simulation experiment evaluation
The information price of hotrolled grade III seismic steel bars (HRB400E1825mm) in Xi'an from April 2019 to October 2022 is chosen as the research data in order to assess the effectiveness of the intelligent building construction cost prediction model based on BIM and ENN. The paper proposes the rolling prediction approach, with a time frequency of four, in order to realize the longterm prediction of the model and guarantee the timeliness of the outcomes. Due to the significant price fluctuations in steel bar, each node's fluctuation value might vary by up to 800 yuan per ton, and there is some variation in the data. Prior to network training in this paper, the original data must be normalized. Eq. (10) illustrates how dimensionless data processing often uses the maximumminimum standardization method to compress the original data to [1, 1]:
$${x_k}=\left( {{x_k}  {x_{\hbox{min} }}} \right)/\left( {{x_{\hbox{max} }}  {x_{\hbox{min} }}} \right)$$
10
\({x_{\hbox{min} }}\) refers to the minimum value in the data sequence, \({x_{\hbox{min} }}=  1\). \({x_{\hbox{max} }}\) refers to the maximum value in the sequence, \({x_{\hbox{max} }}=1\).
The research algorithm is compared with the ENN, BP neural network [29], LSTM algorithm [30], and the model algorithm proposed by Li et al. (2023) in terms of fitting effect, root mean squared error (RMSE), and determination coefficient (R2) in order to assess the performance of the model built in this paper.