Big data-based optimized model of building design in the context of rural revitalization

1.1 Related works

In recent years, with the deepening of public BEC optimization, more experts and scholars have obtained many research results, thereby improving the optimization of public BEC. Li et al. found that traditional transfer learning methods posed a risk of privacy leakage to users. Therefore, a new method of joint learning was proposed based on traditional experimental methods. The new method could train data information and incorporate new aggregation algorithms during the training process to protect information from leakage. These experiments demonstrated that the new algorithm had higher accuracy and better information protection compared to traditional algorithms [8]. Mu found that air conditioning was an important energy consumption system in BEC. How to reduce energy consumption and improve usage efficiency of air-conditioning systems has become the focus of energy conservation and emission reduction. Therefore, they proposed a new BEC application technology based on traditional energy consumption prediction. New technology could reduce BEC and improve the efficiency of air conditioning. These experiments confirmed that the new method had a higher efficiency in reducing BEC compared to traditional algorithms [6]. Zhang found that traditional buildings had some inherent BEC during use, as well as unnecessary equipment energy consumption [9]. Therefore, to improve the energy consumption of traditional buildings, BEC parameters were optimized based on the genetic algorithm (GA, a search heuristic algorithm that mimics natural selection and genetics), and a new BEC optimization design model was obtained. These experiments demonstrated that this new model could reduce BEC and optimize BEC parameters [10]. Liu et al. believed that traditional optimization of public building design mainly focused on BEC, while BEC mainly focused on building data time series [11]. Therefore, a data processing algorithm based on artificial intelligence was proposed, which could provide a new database for mining BEC data. These experiments demonstrated that the new algorithm model could achieve analysis of energy data, improve energy utilization, and have better stability than traditional algorithms.

Zhao believed that there was a significant experimental error in traditional BEC prediction. Therefore, this study proposed a short-term energy consumption prediction method based on a regression tree on the basis of traditional energy consumption prediction [12]. The new method could use computer software to construct the BEC structure, obtain important BEC parameters, and use GA to extract BEC features. These experiments confirmed that the relative error of the new method was smaller, and the prediction of BEC was more accurate. Wenninger et al. believed that data-driven methods could accurately predict BEC data, but most studies did not study the prediction performance. Therefore, a new method based on artificial learning algorithms was proposed on this basis, which could predict and analyze energy consumption data. These experiments confirmed that the new algorithm could replace the traditional BEC prediction method [13]. Rongfang believed that the traditional BEC method was no longer able to meet the current BEC. Therefore, this study proposed a new BEC method based on traditional energy consumption. The new method could achieve monitoring of BEC by calculating the actual and theoretical support of energy. Simultaneously utilizing hot air circulation technology could achieve control and reduction of energy costs. These experiments confirmed that the new method could effectively predict the true value of BEC while controlling the use of energy [14]. Sun et al. believed that BEC was important in energy and resource utilization planning, but there was an imbalance between parameter optimization and accuracy changes in traditional BEC prediction planning [15]. Therefore, a light superposition-increasing framework was proposed. The new framework could fuse parameters to improve the predictive ability of the model. These experiments confirmed that the prediction accuracy of the new model was significantly better than that of traditional models [15]. In the study by Shen et al., the optimization of the ecological performance of a building using a superposition model and an MO model significantly improved the optimization of the building, with a 39% increase in the solar gain index, but the reduction in building costs still needs to be improved [16]. Markarian et al. (2024), conversely, used a machine learning-based BPS agent approach to significantly improve the energy prediction capability and thermal comfort of the building, with a 34% improvement in thermal comfort and 1,266 times faster computation than the conventional method [17]. However, further exploration was still needed in terms of cost reduction and performance optimization [17].

In summary, the optimization of public building models in rural revitalization mainly involves optimizing the energy consumption of buildings. Although many current studies have optimized BEC, there are still problems with insufficient precision and predictive ability. Therefore, this study proposes a new algorithm model to address the precision and accuracy. Moreover, proxy replacement is carried out on the model while controlling costs to achieve optimal design of public buildings.

2.1 BEC optimization design and model construction

Big data algorithm is a collective term for various data processing algorithms, and the whole algorithm model may include multiple algorithms. In public building design, it is hoped that buildings can be designed with low cost, high safety, and high comfort. However, many of the characteristics of buildings are contradictory, and this problem of multiple contradictory relationships is called MOP. In practical applications, MO can only achieve one optimal solution, so in the optimization design of public buildings, the optimal solution can only be achieved for as many objectives as possible. An optimal solution is a set of solutions that balances all objective functions in an MO problem. In the study, the velocity and position updates of the particles are influenced by adjusting the parameters to guide the particles to search the solution space to find the optimal solution. BBMOPSO-A is an upgraded algorithm used in PSO to solve multi-objective optimal solutions [18]. This algorithm achieves the optimal solution of the population by iterating on the demand particle population. Eqs. (1) and (2) is the conventional formula for particle speed update and its position:

In Eqs. (1) and (2), t represents the number of iterations of the algorithm, w represents the weight of inertia, c 1 and c 2 represent the learning factors of the algorithm, r 1 and r 2 represent numbers between 0–1, pb i , j represents the best advantage that an individual appears in i and j throughout the entire algorithm, gb i , j represents the global optimal advantage that appears in i and j throughout the entire algorithm, and v i , j represents the update speed of the algorithm in i and j . In the PSO algorithm, the inertia weights affect the global search ability of the particles. The individual learning factor and the learning factor reflect the particle’s own experience and the group experience adjustment speed, respectively. The random number helps the particle to jump out of the local optimum. Eqs. (1) and (2) are traditional formulas for updating particle velocity and position in the PSO algorithm. The uniqueness of the solution in the above equation may depend on the choice of the initial position and velocity of the particles, as well as the setting of the parameters, but if the objective function is not convex or multimodal, there may be multiple local optimal solutions.

These formulas are used to initialize the velocity and position of the particles and then find the optimal solution through an iterative process. Figure 1 shows the conventional PSO calculation.

Figure 1

PSO process.

In Figure 1, when inputting the numerical values of PSO, the input data is first initialized. Then, its optimal fitness is found by calculating the fitness of data. Then, it determines the particle speed and position and finally determines whether the optimal solution is met. When calculating the optimal solution for weight values, if the update speed is too high, the global optimal solution may be missed. If the speed is too low, the global optimal solution may not be obtained. The inertia weight represents the search efficiency of PSO. When the inertia weight is large, it is helpful for the algorithm’s global search, and when the inertia weight is small, it is helpful for the algorithm’s local search ability. Therefore, setting an appropriate speed update can make the optimal solution of this algorithm faster [19].

The introduction of radial basis function neural networks (RBFNNs) is a neural network algorithm to solve the linear and nonlinear problems of input and output functions in PSO. The basic algorithm process is that the radial basis function connects neurons through input functions, and its calculation can be expressed as [20]

In Eq. (3), h j represents the output function value in neuron j , x represents the vector value of the input function, c j represents the central position of the function in neuron j , and σ j represents the extended value of the central function. Eq. (4) represents the aggravating weight in the k -th neuron

In Eq. (4), W k j represents the weight burst values of hidden layer neurons j and k , m represents the number of hidden layer functions, and y k represents the weighted value of the function [21]. Eq. (3) is a formula for introducing RBFNNs to solve linear and nonlinear problems of input and output functions in PSO. Eq. (3) represents the output function value of neurons in RBFNN, and Eq. (4) represents the weight value of neurons in the hidden layer. RBFNN enhances the ability of the algorithm to solve complex nonlinear problems by providing a nonlinear mapping. In PSO, RBFNN is commonly used for global search guidance, local search refinement, and dynamic tuning of algorithm parameters. RBFNNs can achieve dissociative activation in the input and output spaces through the judgment of linear and nonlinear functions. To some extent, it can solve the linear problem of BBMOPSO-A. Adding radial basis function algorithm to BBMOPSO-A can help solve nonlinear problems in multi-objective particle swarm optimization (MOPSO) and improve its efficiency. BBMOPSO-A mainly solves BEC and improves user comfort. BEC optimization is the design of building room orientation information, window information, heat transfer coefficient, personnel information, lighting information, equipment information, air conditioning information, etc. When optimizing energy use in public buildings, design variables can include the thermal performance of building envelope structures, equipment energy use, occupant activities, and building operating parameters. The range of values for each design variable is determined by actual engineering constraints and physical limitations. Therefore, the optimization of the spatial domain is crucial, and at the beginning of the algorithm, the initial position of the particle swarm is usually randomly distributed within the optimization domain. Second, the BBMOPSO-A explores the solution space by updating the velocity and position of the particles. If it is found that there is no better solution within the current optimization domain, it is possible to consider expanding the optimization domain to explore more possible solutions. The above method is to optimize the spatial domain. Therefore, it can achieve the maximum optimization coefficient. Figure 2 shows the BEC structure.

Figure 2

Energy consumption composition of public buildings.

In Figure 2, the conventional BEC includes air conditioning energy consumption, heating energy consumption, and water, electricity, and wind energy consumption. The energy consumption of air conditioning includes water pumps, cold water units, and air conditioning. Heating energy consumption includes boiler energy consumption. Water and electricity consumption also includes water and air pipelines. BBMOPSO-A is an algorithm used early on to change the optimization coefficients of parameter changes and control parameters. The optimization of BEC mainly solves the optimal solution of building parameters. The particle update speed and update trend of the algorithm affect the parameter changes of BEC [22] in the following equation:

where N represents the Gaussian distribution of the function. It is possible to achieve the optimal solution for multi-objective parameters by changing different parameters. Eq. (5) introduces a Gaussian distribution function to update the velocity and position of particles in the algorithm. Eq. (5) is used to adjust the update speed and update trend of particles, which affects the parameter changes of BEC. The inertia weights help the particles to maintain the motion trend and promote the global search; the individual learning factor and the learning factor guide the particles to move toward their own historical optimal position and the global optimal position, respectively. Eq. (5) enhances the global search capability and ability to avoid local optima of BBMOPSO-A by introducing the Gaussian distribution function [23]. Moreover, the random number increases the randomness of the search and helps the particles to jump out of the local optimal position. By expanding the algorithm parameters, the following equation Eq. (6) is obtained:

Eq. (6) removes and reduces the weights and learning factors of the source function based on the original Eq. (5). Eq. (6) is designed to improve the performance of the algorithm by adjusting the velocity update rule for the particles, either by introducing new parameters or by adjusting the existing ones to improve the algorithm’s exploration and exploitation capabilities. When using this new formula to solve multi-objective problems, it is necessary to update the algorithm’s position in the following equation:

In Eq. (7), r 3 represents a random value from 0 to 1. Eq. (7) is used to update the position of the algorithm to avoid wasting resources and introduces a random value for updating the position and extremum points of particles within a given interval of the Gaussian function. The parameters of Eq. (5) function in concert to optimize the global and local search capabilities of the algorithm. Conversely, Eq. (6) utilizes the novel velocity values to directly modify the position of the particles. Finally, Eq. (7) facilitates the particles’ transition out of local optima and exploration of new search regions by introducing greater randomness into the search process. When the individual limit values are close to or even equal to the global limit values, the algorithm’s Gaussian distribution will approach the global limit values as the algorithm values are resolved. This will cause areas that have already been explored or calculated to be recalculated, resulting in resource waste. Therefore, in response to the above issues, the original BBMOPSO-A is improved to obtain a new algorithm update formula in Eqs. (8)–(10).

In Eqs. (8)–(10), T represents the maximum iteration, x j up and x j low represent the limited domain range between the j -th decision variables, f m max and f m min represent the maximum and minimum values at the objective function m , f m ( pb i ( t ) ) and f m ( Gb i ( t ) ) represent the global range extreme points and individual range extreme points at the objective function m , pro − d represents the perturbation factor of the global extremum and individual extremum, and δ j represents the degree of approximation between the global extremum and the individual extremum. In the PSO algorithm, the role of inertia weights is to regulate the motion tendency of the particles, which affects the global and local search capabilities of the algorithm. Although the inertia weight in traditional PSO algorithms is usually positive, the weight is not always positive. On the contrary, the adjustment of weights is dynamic, aiming to optimize the global search ability and convergence performance of the algorithm by introducing strategies such as perturbation factors and approximation degree. Therefore, the value of the weights can be adjusted according to the specific needs of the optimization problem, rather than being fixed and invariant. Eqs. (8)–(10) introduce the perturbation factors of global and individual extremes and their approximations. These factors are used to evaluate the probability of the algorithm to find the optimal solution and the global exploration capability during the computation. To find the maximum and minimum values in a given interval, it is necessary to define the objective function, determine the search interval, initialize the particle swarm, evaluate the particles, update the individual and global optimums, and iteratively update the particle velocities and positions. When the individual extreme value is closest to the global extreme value, the feasibility of the perturbation factor is optimal at the maximum perturbation probability. Therefore, the probability of finding the optimal solution increases as the algorithm computes. When the perturbation factor value of the algorithm increases, the probability of the algorithm being perturbed decreases, and the global exploration ability of the algorithm increases [24].

Therefore, improving the algorithm requires the following steps. First, the population size and iteration times of the algorithm are calculated. Moreover, the particle positions and extreme points are updated within the given Gaussian function interval. The required BEC parameter values are set. The calculated function parameter values are used to solve for the optimal value of the objective function through data parameter software. The dataset information of the algorithm is updated. The dataset signal is saved in an external function. Based on the allocation situation in the reserve dataset, particle selection is carried out for each dataset. Moreover, the extreme values of particles are determined through dominance relationships. Figure 3 shows the flowchart of this algorithm.

Figure 3

Algorithm model flowchart.

In Figure 3, the model parameters of the required building are first determined. Then, the model parameters are inputted into the algorithm and initialized. The initialized data is analyzed. The results are programmed using data software. Then, the written program is used to update the position of particles. The numerical values are imported by the written program. The software program is used to analyze the encoding results. Finally, the data standard is determined to terminate the algorithm. To optimize the computation time of the algorithm, this study adopts the strategy of introducing an agent-based model. The inertia weights, individual learning factor, and social learning factor in the PSO algorithm are adjusted. The RBFNN is used to deal with the nonlinear problem. The particle velocity and position update rules are improved. Parallel computation and early termination conditions are also used to reduce unnecessary iterations.

2.2 Design of proxy model for BBMOPSO-A

The ideal auxiliary model mainly replaces the model of the algorithm, replacing high-cost algorithms to achieve, because the ideal model can replace higher cost functions to calculate the target. Although the computational complexity and workload of the ideal auxiliary model far exceed the real objective function, the cost of the ideal auxiliary model is lower. For traditional objective optimization algorithm-assisted models, there are currently assisted social learning PSO, automatic learning PSO, and domain development-assisted evolutionary algorithms. Although traditional auxiliary proxy algorithms can calculate model accuracy and computational costs, they cannot solve the MO problem of the objective function. Data collection is an important component of proxy-assisted models. Figure 4 shows the proxy model data collection [25].

Figure 4

Data collection structure.

In Figure 4, the data collection structure consists of data collection, user interface, and data evaluation system. The components of each data collection structure can exchange data with each other, thus achieving high data utilization. It is important for proxy auxiliary model data collection models. When optimizing the proxy auxiliary model of MOPSO, it is necessary to provide an auxiliary model optimization method for building energy-saving designs based on traditional MOPSO. Then, different reserve sets are used to help the changing proxy auxiliary model optimize management decisions. The model management decisions and prediction accuracy are balanced, and the model management decisions are integrated into the system to obtain a new proxy-assisted MOPSO.

For the proxy auxiliary optimization model of MOPSO, it is necessary to first build the basic framework of the model and improve the algorithm model proposed in the previous section while ensuring the particle swarm position and management content of the auxiliary model. Figure 5 shows the improved model.

Figure 5

Proxy-assisted model.

In Figure 5, the proxy-assisted model first updates the particle positions of MOPSO, saves the iterative optimal solution, and calculates the target value generated by the particles by using the proxy model instead of the real function. The external storage set iteratively updates the generated target values and then introduces local guidance and individual guidance. The second part is mainly responsible for improving and controlling the data functions. The representative solution selection mechanism has been added, and the real target values are selected from the new reserve set by updating and evaluating the real values using BEC simulation software. The proxy model can initiate system mechanisms through algorithm updates. After building the proxy model, system data sampling is conducted. Eq. (11) represents the specific sampling settings

In Eq. (11), q represents the sample point that appears and n represents the n -th dimensional space. Eq. (11) is employed for the optimization of data sampling management decisions in the proxy-assisted model, the determination of the occurrence of sample points, and the sampling process in the d-dimensional space. When sampling occurs, the initial sample interval is first divided into q initial sample points. Then, each decision point is changed through a set of intervals. x 1 decision points are extracted. Then, all the points are combined to implement the set S . Points are randomly selected in the set S , and feasible solutions from the set are brought into the real objective function. Such a feasible solution is a sample point. By using the above method, the sampling process is stopped until q sample points are generated. When updating the predicted average of the proxy model, the error function generated is represented by

In Eq. (12), f ˆ j ( x i ′ ) represents the fitted values of j objective functions generated by the proxy model, f j ( x i ′ ) represents the objective function value of the frames number calculated by energy-consuming software, and E ( f , EP ) represents the average prediction error of the proxy function model in the set EP . Eq. (12) is employed to calculate the prediction error of the surrogate model and to generate the function distance of the dataset, thereby evaluating the prediction accuracy of the surrogate model. In practice, the likelihood of zero function values can be reduced through data pre-processing, model tuning, thresholding, and post-processing measures. After calculating the error function, the function distance of the dataset will be generated through two savings sets. Eq. (13) is a dataset metric formula [26]

In Eq. (13), A represents the dataset A = { a 1 , ⋯ , a p } , B represents the dataset B = { b 1 , ⋯ , b q } , and h ( A , B ) in the distance formula is represented by

In Eq. (14), ∣ a i − b j ∣ represents the distance norm directly between a i and b j and h ( A , B ) represents the functional distance from A to B . Eq. (15) represents the reverse distance

Eq. (15) shows the inverse function distance formula from A to B . By calculating the distance, the position difference between two datasets can be obtained, thereby better updating the dataset. Eqs. (13)–(15) are utilized to calculate the distance between datasets. Eq. (13) is the distance formula, Eq. (14) represents the direct distance norm, and Eq. (15) represents the reverse distance formula. By increasing the sample size, a new decision sample L can be obtained, which can represent the updated data sample values and training parameters. Eq. (16) is L

In Eq. (16), l max and l min represent the maximum and minimum values of the sample size, respectively. By setting the size of the sample size, the richness of the proxy sample can be enriched. After calculating the distance and setting the sample size, BBMOPSO-A is calculated. Figure 6 shows the calculation process of this algorithm.

Figure 6

Algorithm calculation flowchart.

In Figure 6, the initialization of data sample points is first carried out, and the threshold of the sample parameter update algorithm is set. After calculation, the predicted value of the particle’s objective function is obtained, and the predicted value of the function is stored in the reserve set for updating. By calculating the distance from the dataset, it is determined whether to update or train the proxy model. If the distance is small, the updated model is calculated, and if the distance is large, the updated model is not recalculated. The updated model is updated by individual and global extreme points. Then, the distance between the updated points is calculated to determine if the optimal solution conditions are met. If they are met, the process ends. If not, the parameters and bounds are updated again.

The parallel part of this research includes the development and application of the BBMOPSO-A, agent model design, performance evaluation, and application to building energy optimization problems, with the goal of optimizing the design of public buildings in the context of rural revitalization and reducing BEC using big data algorithms.

Meanwhile, the study also includes the application of hybrid difference techniques to achieve higher order convergence approximation through adaptive Shishkin grids and error analysis for nonlinear singularly perturbed problems to ensure uniform second-order convergence [27]. In addition, adaptive mesh analysis based on monitor functions provides highly accurate spatio-temporal convergence for parabolic systems, while a reaction matrix-based triangular partitioning method is validated through numerical experiments to reduce computational costs and ensure convergence of the algorithm [28,29]. The study also proposes a higher order numerical method for solving polynomial time partitioned partial integral differential equations with initial layer singularities with stability and convergence analysis [30,31]. Finally, the solvability of nonlinear models involving the p-Laplacian operator is studied, the existence of a unique solution is proved, and the stability of the fractional order boundary problem is verified by numerical experiments [32,33].