Meteorological Data Processing Method for Energy-Saving Design of Intelligent Buildings Based on the Compressed Sensing Reconstruction Algorithm

Abstract

With the increasingly severe problems of global climate change and resource scarcity, sustainable development has become an important issue of common concern in various industries. The construction industry is one of the main sources of global energy consumption and carbon emissions, and sustainable buildings are an effective way to address climate change and resource scarcity. Meteorological conditions are closely related to building energy efficiency. Therefore, the research is founded upon a substantial corpus of meteorological data, employing a compressed sensing reconstruction algorithm to supplement the absent meteorological data, and subsequently integrating an enhanced density peak clustering algorithm for data mining. Finally, an intelligent, sustainable, building energy-saving design platform is designed based on this. The research results show that in the case of random defects in monthly timed data that are difficult to repair, the reconstruction error of the compressed sensing reconstruction algorithm is only 0.0403, while the improved density peak clustering algorithm has the best accuracy in both synthetic and real datasets, with an average accuracy corresponding to 0.9745 and 0.8304. Finally, in the application of the intelligent, sustainable, building energy-saving design platform, various required information such as HVAC data energy-saving design parameters, cloud cover, and temperature radiation are intuitively and fully displayed. The above results indicate that the research method can effectively explore the potential valuable information of sustainable building energy-saving design, providing a reference for the design of sustainable buildings and climate analysis.

1. Introduction

In order to lower building energy use and encourage green growth, it is crucial to construct sustainable buildings. Different Chinese areas have been actively implementing building greenization in recent years. To start down a new path of low-carbon and green development, meteorological departments have continuously developed new technologies for building energy-saving meteorological services, actively investigated the scientific fields of climate change and building energy conservation, and closely focused on the needs of green and low-carbon development [1,2,3]. Climate change has significantly altered building design meteorological parameters and buildings’ operational energy consumption, accounting for half of the factors influencing building energy consumption [4,5]. The impact of meteorological conditions on buildings is multifaceted. The first is temperature. The increased use of air conditioning in summer consumes a large amount of energy, while the increased indoor heat dissipation in winter increases the heating burden. Sustainable buildings can cope with temperature changes and save energy through reasonable design. High humidity can cause mold growth, while low humidity can cause respiratory discomfort and other problems. Sustainable buildings can be adjusted through the appropriate design based on the humidity characteristics of the area. Finally, it is necessary to consider the wind in the area, as strong winds can exert significant pressure on the building structure. Therefore, a reasonable building orientation and layout can be designed based on local wind speed and direction data. The process of collecting meteorological data in building climate analysis requires several links such as instrument monitoring and transmission, which can lead to the introduction of a large number of errors, resulting in errors in the final recorded data. Moreover, due to equipment abnormalities and other situations, there may be missing values in a certain stage of a certain area [6]. Meanwhile, the current research methods are simple and mainly involve predicting temperatures under different climate modes, which limits the in-depth understanding of the dynamic changes in building energy consumption and often lacks hourly meteorological parameter files for predicting future climate change.

In response to the above issues, the research first uses the compressed sensing reconstruction (CSR) algorithm to fill in missing meteorological data, and jointly improves the Peak Density Clustering (PDC) algorithm to control data quality and mine valuable information. Finally, an intelligent, sustainable, building energy-saving design (ISBESD) platform is constructed. The aim of this project is to address the issue of missing meteorological data in building energy efficiency design and to consider the processing of meteorological data in uncertain environments [7]. The innovation of the research mainly includes the following two points. The first point is the design of a data processing and analysis method that combines the CSR algorithm and improved PDC algorithm to ensure the efficiency and accuracy of building climate analysis. The second point is the design of the ISBESD platform, which provides a strong basis for sustainable building design. Through research, it aims to provide a better collaborative platform for sustainable buildings, enhance the green efficiency of building design, and complete the sustainable demand transformation in building energy-saving design.

2. Related Work

With climate change, resource depletion, and accelerated urbanization, sustainable buildings have become a powerful trend in the construction industry, representing the future of green development. Sustainable building is not only about creating complex environments, but also about providing healthier, more economical, and more humane building environments. Z. Yang et al. found that the cooling and heating energy consumption of buildings poses a serious threat to the energy supply and increases greenhouse gas emissions. Therefore, the study combines selective radiative cooling materials with solar heating materials to design a rotating blade that can achieve the conversion of radiative cooling, solar heating, and natural light harvesting functions. Experimental results showed that this device could promote the transformation of sustainable building thermal management toward decarbonization and a greener direction [8]. J. Zhao et al. introduced phase-change materials with high heat recovery and energy density into wood–plastic composites to regulate indoor temperatures and reduce building energy consumption. Thermogravimetric analysis results showed that the formation of organic networks improved the thermal stability of the phase-change materials, while the high temperature resistance of montmorillonite reduced the degradation rate of the wood–plastic composites, providing application value for sustainable building energy conservation and indoor air conditioning [9]. H. Li et al. aimed to analyze the economic potential of fuel cell vehicle networking systems to elevate fuel cell vehicles to the highest level. Therefore, they chose large sustainable buildings as the research object, constructed a comprehensive economic optimization model, and optimized the model using a hybrid algorithm of a competitive group optimization algorithm and an imperialist competition algorithm. The simulation results showed that the research algorithm had a faster convergence speed and higher optimization accuracy and could effectively improve economic benefits [10]. C. Shi et al. found that a multi-mode green IoT network integrating multiple communication media could effectively meet the data transmission and processing needs of low-carbon intelligent buildings. Therefore, they proposed a multi-mode green IoT network resource management algorithm based on adversarial learning at multiple time scales. The research results indicated that compared with the asynchronous greedy matching algorithm and the auction-based many-to-many matching algorithm, this algorithm had advantages in energy consumption and throughput [11].

The essence of sustainable development issues lies in energy, environment, and continuing to improve the quality of life. Energy-efficient design of sustainable buildings is closely related to climate. Without complete meteorological data or consideration of meteorological factors, sustainable buildings cannot be discussed. The CSR algorithm can efficiently obtain effective information on signals or images at low sampling rates, and it can reconstruct both discrete and continuous signals. H. Yan et al. designed a temperature distribution reconstruction method for acoustic tomography based on the CSR algorithm and proposed an improved orthogonal matching tracking algorithm to enhance the efficiency of sparse signal recovery. The experimental results showed that the research algorithm had smaller reconstruction errors and provided more accurate temperature distribution information [12]. W. Qiu et al. established an image-based quantitative CSR framework, and the simulation results showed that compared with other existing real valued measurement matrices, the restoration quality of the measurement matrix in the framework was greatly improved, and the quantitative CSR framework could achieve a balance between restoration performance and computational complexity [13]. H. Feng et al. designed a data compression scheme for multi-target signals based on the CSR algorithm and the orthogonal matching tracking algorithm and proposed a series of quantitative indicators to evaluate the reconstruction efficiency. At the same time, a neural network trained on raw data was used to identify the reconstructed samples with an accuracy of over 70%. The results showed that the reconstructed samples accurately exhibited vibration characteristics [14]. G. Yuan et al. developed a fast bidirectional network suitable for grayscale and color image reconstruction to address the issues of extracting texture details and overall image contour quality. The CSR algorithm was used to reconstruct depth contours and texture details. Simulation results showed that the research method achieved good results in image reconstruction quality, time consumption, and noise robustness [15].

Based on the above content, the achievements mainly focus on the importance and application technology of sustainable buildings as well as the application of CSR algorithms in various fields. However, higher requirements have been put forward for the quality of meteorological data in ISBESD. It is very important to efficiently handle multiple meteorological elements and optimize the quality control of meteorological data. Therefore, a joint CSR algorithm and an improved PDC algorithm are proposed for data processing and analysis, and an ISBESD platform is designed to provide support for architectural design and climate analysis.

3. Intelligent, Sustainable, Building Energy-Saving Design Platform Based on the CSR Algorithm

To achieve ISBESD, the research first constructs the required building design dataset, then combines the CSR algorithm and improved PDC algorithm to process and analyze the massive data, and finally, constructs the ISBESD platform to provide guidance for ISBESD.

3.1. Design of Data Preprocessing and CSR Algorithm

According to the “Research Report on Energy Consumption and Carbon Emissions of Chinese Buildings (2023)”, the energy consumption of housing buildings accounts for 36.3% of the national energy consumption, and their carbon emissions account for 38.2% of the national energy-related carbon emissions [16,17,18]. The energy-saving design of buildings is closely related to meteorological conditions. From the beginning of the building design to its operation and maintenance, meteorological conditions are one of the important factors to judge whether it is energy saving [19,20,21]. The study is thus centered on the demand for green and low-carbon urban building development, with meteorological data forming the basis for analysis. The aim is to identify and examine the impact of climate change on building energy consumption and outdoor meteorological parameters in different building climate regions. Firstly, it is necessary to preprocess the collected meteorological data for subsequent algorithm analysis. The meteorological data used in this study were sourced from the Meteomanz website, which contains detailed data from 2005 to the present as well as original messages, which were downloaded into three formats of data suitable for regional meteorological stations [22,23,24]. The annual average data can be downloaded through the station number, which is the average meteorological data from 2005 to 2022, with a total of 7103 records. The daily average data require downloading corresponding months and stations, totaling 6690 pieces of information, including 9 fields: average temperature, highest and lowest temperature, air pressure, wind direction, date, precipitation, wind speed, and cloud cover [25,26]. The scheduled data cover 8 time periods and 52,930 pieces of information from 0:00 to 21:00 every day, divided into segments every 2 hours [27,28]. In the preprocessing of the data, if there are many missing observation records in continuous data, they can be deleted, with a total of 392 available stations. Finally, the collected data are divided into a training set, testing set, and validation set in a ratio of 7:2:1. When processing timed data, to facilitate subsequent calculations, it is necessary to convert them into a numerical format and remove the unit information of air pressure. For data with duplicate records, it is necessary to delete the redundant data. For timed data with missing values, the CSR algorithm is required for processing. The core idea of CS theory is to randomly subsample the signal with a density that is more detailed than the sampling frequency required by Nyquist sampling. Because the spectrum leaks uniformly rather than being globally extended, the original signal can be recovered through special tracking methods. The specific compression sensing filling process is shown in Figure 1.

In Figure 1, it is necessary to first establish a missing matrix for time-series data with missing values. Then, existing historical samples are used as observations on the matrix to complete the CSR, and the true signal description is obtained. Then, the missing position is searched for the value located in the true signal, and the backfilling step is completed. Finally, the repaired dataset can be obtained. When using this algorithm to process meteorological data, the corresponding filling problem can be equivalent to the process of compressed sampling and signal reconstruction. The specific process is as follows. Firstly, the original meteorological data are sparsified using the $M\times M$ dimensional dictionary matrix $\zeta$. During the compression, the observation data $y\in R^K$ can be obtained, where $K$ represents the observation data obtained using random sampling. At this point, the importance of different data cannot be determined. By compressing perception, it can be considered that $K$ data have a high probability of obtaining most of the important information in the original data, and $M-K$ original data are randomly deleted in the observation, indicating that the lost data have less important information in the original signal. In the above description, the process of randomly losing data can be regarded as random compression sampling, and then, the CSR algorithm is used to reconstruct the estimated values of the $M$ original data, thereby completing the problem of filling in missing values. In addition, assuming that the $M\times M$ dimensional identity matrix is $D_m$, the $i,i\in A$th row of $D_m$ is randomly removed, where $A$ represents the index set of all meteorological data values at the 999 element index, and the values and positions of other elements remain unchanged. Therefore, the measurement matrix $\psi \in R^{M\times K}$ can be obtained, which can describe the position of the collected observation signal. The schematic diagram of matrix ψ construction is shown in Figure 2.

In Figure 2, the black and white squares corresponding to $D_m$ have element values of 1 and 0, respectively. Therefore, the observation signal y is defined as Equation (1):

$$y=\zeta \times o.$$

(1)

In Equation (1), $o$ represents the original signal corresponding to the $M\times 1$-dimension; $o$ can be sparsely represented through $\zeta$, as calculated in Equation (2):

$$o=\zeta \times x$$

(2)

In Equation (2), $x$ represents a sparse coefficient vector. Let $\xi =\zeta \times \psi$ and substitute Equation (2) into Equation (1) to obtain Equation (3):

$$y=\xi \times x$$

(3)

In Equation (3), $\xi$ is the sensing matrix. So, by knowing the two conditions of $\xi$ and $y$, $x$ can be reconstructed. According to the theory of compressed sensing (CS), if $\psi$ is not correlated with $\zeta$, the corresponding estimate of $x$ can be obtained through reconstruction algorithms to obtain the original signal and complete the filling of missing values in the meteorological data. Based on the above description, it can be seen that the CSR algorithm is mainly related to $\xi$, the sparse transformation matrix, and the reconstruction algorithm. Therefore, in practical applications, it is necessary to choose a transformation matrix that makes $o$ sparse as possible, design $\xi$ that meets the constraint isometric requirements, and select a reconstruction algorithm that can efficiently and accurately obtain the reconstructed original signal. After comprehensive consideration, the study chose to use the Discrete Cosine Transform (DCT) matrix. To verify the feasibility of the CSR algorithm, the study selected meteorological data from Tianjin in 2023 for subsequent testing, including 365 daily mean data, 247 timed data, and 2962 annual data. The DCT orthogonal matrix $Z_M=R^{M\times M}$ was used as the sparse transformation matrix for CSR algorithm, and the expression is shown in Equation (4):

$$Z_M=\left[\begin{array}{cccc}1& 1& \dots & 1\\ \sqrt{2}\cos {\displaystyle \frac{\pi }{2M}}& \sqrt{2}\cos 3{\displaystyle \frac{\pi }{2M}}& \dots & \sqrt{2}\cos \left(2M-1\right){\displaystyle \frac{\pi }{2M}}\\ ⋮& ⋮& \ddots & ⋮\\ \sqrt{2}\cos {\displaystyle \frac{M-1}{2M}}\pi & \sqrt{2}\cos 3{\displaystyle \frac{M-1}{2M}}\pi & \dots & \sqrt{2}\cos \left(2M-1\right){\displaystyle \frac{M-1}{2M}}\pi \end{array}\right]$$

(4)

By calculating the correlation between $Z$ and $\psi$, $\alpha \left(D_m,Z\right)=\sqrt{2}$ can be obtained. According to the $\psi$ construction process, it can be seen that for any two orthogonal matrices of $M\times M$ dimension, the value of $\alpha \left(D_m,Z\right)$ is in the following interval $\left[1,\sqrt{M}\right]$, while the selected correlation $\alpha \left(D_m,Z\right)$ for testing does not exceed $\sqrt{2}$. This indicates that the lack of correlation between $\psi$ and $D_m$ is stronger, further demonstrating the feasibility of the reconstruction operation. Therefore, the study uses the DCT matrix and identity matrix as the sparse matrix and measurement matrix, respectively. In the CSR algorithm, the reconstruction algorithm selects the orthogonal matching tracking algorithm for processing, and the specific process is shown in Figure 3.

In Figure 3, it first initializes the parameters, then searches for the index $s_i$ and calculates the least squares solution corresponding to $y$ to update the residuals. Then, when the conditions are met, it will stop the iteration and reconstruct the sparse representation of the signal. Finally, the final reconstructed signal is obtained through the coefficient matrix.

This study adopts the reconstruction error as the primary evaluation metric instead of the Mean-Squared Error (MSE) or Root-Mean-Square Error (RMSE) based on the following considerations: First, the core objective of the CSR algorithm is to recover missing data points, and reconstruction error directly measures the deviation between the reconstructed and true values, whereas MSE and RMSE primarily assess overall error distribution, making them less effective at evaluating data imputation quality. Second, CSR relies on the sparsity assumption of signals for recovery, and traditional error metrics may not accurately capture its effectiveness, while reconstruction error provides a more intuitive assessment of CSR’s adaptability and stability in data completion. Furthermore, previous studies [29] have demonstrated that in time series reconstruction tasks, reconstruction error more precisely reflects the algorithm’s capability to restore missing data. Therefore, this study employs this metric to ensure the rationality and specificity of the experimental evaluation.

3.2. Meteorological Data Processing Combining CSR Algorithm and Improved PDC Algorithm

After the above meteorological data processing is completed, usable meteorological features and other information can be obtained. Meteorological characteristics encompass the comprehensive performance of diverse meteorological elements within a specific region over an extended period. These elements include, but are not limited to, temperature, humidity, precipitation, and others, collectively reflecting the fundamental climate conditions of the corresponding region [30]. In previous studies, it was difficult to comprehensively consider the effects of multiple meteorological factors. Therefore, based on the CSR algorithm, the PDC algorithm is jointly improved to cluster a certain attribute of meteorological data to achieve more comprehensive and specific climate zoning and provide effective reference for energy-saving design of sustainable buildings. In response to the problem of the PDC algorithm being unable to handle several density peak datasets corresponding to a cluster and easily causing errors in the continuous allocation of non-center points, this study introduces network similarity and neighborhood extension centers to optimize it. The specific calculation process is as follows. Assuming dataset $U=\left\{u_1,u_2,\dots ,u_a\right\}$, where object $u_i\left(1\le i\le a\right)$ contains $a$ dimensional attributes, the $IL$ interval between each dimension of the grid is calculated as shown in Equation (5):

$$IL={\displaystyle \frac{A_j^{\max }-A_j^{\min }}{b}}$$

(5)

In Equation (5), $A_j^{\max }$ and $A_j^{\min }$ are the maximum and minimum values of the set containing all objects in the $j$th dimension attribute, and $b$ represents the reference tree. The $j$th component expression of $u_i$’s subspace encoding is shown in Equation (6):

$$c_j^i=floor\left({\displaystyle \frac{u_i}{I{L}_j}}\right)+1$$

(6)

In Equation (6), $floor\left(·\right)$ represents the function rounded down. By implementing the aforementioned data networking operations, the amount of meteorological data to be processed can be reduced, thereby improving computational efficiency [31,32]. Then, the data from each grid are integrated, and the obtained data are grid data, as described in Equation (7):

$$W{G}_J^C=\left\{\begin{array}{l}{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^{W{G}_n}{u}_{ij}}}{W{G}_n}},W{G}_n\ne 0\\ 0,W{G}_n=0\end{array}\right.$$

(7)

In Equation (7), $W{G}_J^C$ represents the $j$th component of the integrated network data, while $W{G}_J^C$ represents the total number of processing objects in the same network. After dividing the network, the raw meteorological data will generate a network space, where the network distance $WG{d}_h^l$ is calculated as shown in Equation (8):

$$WG{d}_h^l=\sqrt{{\displaystyle {\sum }_{j=1}^n{\left(c_j^h-c_j^l\right)}^2}}$$

(8)

In Equation (8), $c_j^h$ and $c_j^l$ correspond to the $j$th component of the subspace encoding to which the objects $h$ and $l$ belong, and $n$ represents the dimension of the dataset. The study takes the processing of 2D data as an example, where any grid in this network space can be represented using $(w_1,w_2)$, as shown in Figure 4.

In Figure 4, the network codes corresponding to orange, green, and purple are (5,3), (1,4), and (2,6), respectively. The possibility of the grid belonging to a cluster can be obtained by calculating the grid distance. The quantification method of inter-grid similarity is described through grid similarity, where inter-grid differences are calculated by the Euclidean distance $H{D}_h^l$ between $WG{d}_h^l$ and network data, as expressed in Equation (9):

$$H{D}_h^l=\sqrt{{\displaystyle {\sum }_{j=1}^n{\left(WG{d}_j^{h,c}-WG{d}_j^{l,c}\right)}^2}}$$

(9)

The quantitative evaluation of differences between networks is calculated using $d{s}_h^l$, as shown in Equation (10):

$$d{s}_h^l=\zeta \times WG{d}_h^l+\psi \times H{D}_h^l$$

(10)

In Equation (10), $\zeta$ and $\psi$ both represent parameters. The smaller the $d{s}_h^l$, the greater the grid similarity. The grid with similarity to the cluster center grid not exceeding $L$ represents the neighboring grid, as expressed in Equation (11):

$$L={\left(b·\vartheta \right)}^2·n$$

(11)

In Equation (11), $\vartheta$ represents the threshold. The domain extension center is closely related to the range parameter $R$, and the corresponding relationship expression is shown in Equation (12):

$$R=\chi ·\max \left(D_R\right)$$

(12)

In Equation (12), $\chi$ is a given ratio, and $D_R$ represents the set of distances between neighboring grids and cluster centers, which can reduce the adverse effects of several density peaks in a cluster. Furthermore, $u_i$ can be regarded as a field source, and its outward radiation and total energy corresponding to radiation are the potential value ${\gamma }_i$ of $u_i$, as expressed in Equation (13):

$${\gamma }_i={\displaystyle {\sum }_{j=1}^{W{G}_n}{e}^{-{\left(\frac{‖u_i-u_j‖}{\phi }\right)}^{\delta }}}·m_i$$

(13)

In Equation (13), $m_i$ corresponds to the mass of $u_i$, and $\delta$ and $\phi$ represent the distance index and influence factor, respectively, corresponding to 2 and the network interval. The points in the grid will be affected by the corresponding surrounding environment, and the influence will weaken as the distance increases. Therefore, the study uses influence representation to evaluate the concentration of data points. The total influence of each data pair in the same network can be represented by the network environment influence. In the formed network space, if the data in a certain grid are known, the potential grid density can be calculated, as shown in Equation (14):

$$\rho =\left\{\begin{array}{l}W{G}_n·{\displaystyle {\sum }_{i=1}^{W{G}_n}{\gamma }_i}·{\displaystyle {\sum }_{i=1}^{W{G}_n}E{I}_{\alpha }^I},W{G}_n>1\\ W{G}_n·\left({\displaystyle {\sum }_{i=1}^{S_n}{\gamma }_i}-\lambda \right)·\left({\displaystyle {\sum }_{i=1}^{S_n}E{I}_{\alpha }^I}-\lambda \right),W{G}_n=1\end{array}\right.$$

(14)

In Equation (14), $S_n$ represents the number of data points slightly greater than 1, $\lambda$ represents the adjustment coefficient, and $E{I}_{\alpha }^I$ represents the grid environment impact corresponding to a certain data point. Based on the above content, the specific process of improving the PDC algorithm for processing data can be obtained, as shown in Figure 5.

Figure 5 is mainly divided into data gridding, peak search density, neighborhood expansion, and cluster merging.

3.3. Construction of an Intelligent, Sustainable, Building Energy-Saving Design Platform

Based on the processing of the CSR algorithm and PDC algorithm mentioned above, the task of climate zoning can be completed, and on this basis, the construction of the ISBESD platform can be carried out. The goal of sustainable architecture is to balance the environment, society, and economy, which requires protecting the ecological environment and reducing resource and energy consumption while ensuring people’s living space [33]. Moreover, the building climate is a key consideration in sustainable building design. By analyzing the climate and environment of different regions, buildings that are well adapted to the local area can be created, achieving mutual cooperation with meteorological changes [34,35]. To display the climate characteristics of each region more clearly and design sustainable buildings that meet the requirements based on the corresponding climate characteristics, users come from meteorological departments, enterprises, and architectural design personnel, etc., with a good application foundation. Among them, building climate analysis is an important basis for guiding subsequent design. From this, the functional module architecture of the ISBESD platform can be obtained, as shown in Figure 6.

Figure 6 mainly includes five functional modules: the station query, data import, thermal comfort data query, building meteorological data query, and outdoor meteorological data query. The most important modules in the above functional modules are the building meteorological data query and outdoor meteorological data query, and the corresponding operation process is shown in Figure 7.

In Figure 7, the building meteorological data query module consists of basic meteorological characteristics, climate data required for design, building climate analysis, and city comparison sections, while the outdoor meteorological data includes queries for four types of data: energy conservation, HVAC, typical years, and thermal engineering. Through the above two modules, users can be assisted in obtaining relevant data for the energy-saving design of various sustainable buildings. In summary, the construction of the ISBESD platform can be completed.

4. Analysis of the Results of Building Energy Efficiency Design Platform Based on the CSR Algorithm

To verify the effectiveness and feasibility of the ISBESD platform designed for research, the study first validated the performance of the CSR algorithm and improved PDC algorithm applied in the platform and then analyzed the application effect of the platform.

4.1. Performance Results of Data Processing Methods Using the CSR Algorithm

To verify the performance of the proposed joint algorithm, the performance of the CSR algorithm and the improved PDC algorithm were analyzed separately. The experimental platform was Windows 10 with 16 GB of memory and Matlab R2018a software. To conduct more scientific analysis and research on the performance of the proposed algorithms, the study selected mainstream data processing methods and clustering analysis algorithms for comparative experiments, namely Spline Kalman (SK), Multidimensional Time Series Repair Based on Generative Adversarial Networks (MDTSR-GAN), Dual Channel Collaborative Clustering (DCCC), Projection Clustering of Subspace Differences (PCSD) based on subspace differences, and PDC Based on Improved Fruit Fly Optimization (PDC-IFO). The SK algorithm is a combination of spline difference and Kalman filter algorithm, and the MDTSR-GAN algorithm uses the standard GAN generator and discriminator against training to learn the distribution characteristics of the data and then generate missing data points. The DCCC algorithm combines node features and topology by designing a dual-channel encoder, including attribute encoder and graph convolution filter; the PCSD algorithm performs clustering by calculating the projection difference of data on different subspaces; PDC-IFO introduces a fuzzy density mechanism to enhance the search ability of individual fruit flies, thus optimizing the parameter selection in the clustering process. The performance of clustering algorithms was tested using the commonly used Composite dataset (CD) and Real dataset (RD). The former includes the Eye dataset, with data quantity, cluster quantity, and attributes of 238, 3, and 2, respectively; the Sticks dataset, with data quantity, cluster quantity, and attributes of 512, 4, and 2, respectively; and the Is3 dataset, with data quantity, cluster quantity, and attributes of 1735, 6, and 2, respectively. The RD dataset includes the Iris dataset, with data quantity, cluster quantity, and attributes of 150, 3, and 4, respectively. The Lonosphere dataset has data quantity, cluster quantity, and attributes of 351, 2, and 34, respectively. The Coil dataset includes data quantity, cluster quantity, and attributes of 1440, 20, and 128 × 128, respectively. Clustering algorithms were evaluated based on evaluation metrics such as accuracy, F1 score, Adjust Rand Coefficient (ADC), Standardized Mutual Information (SMI), and computation time. The repair effect refers to the degree of statistical similarity between the missing values filled in during the data preprocessing process and the original complete data, and its quantitative analysis is evaluated through reconstruction error. The reconstruction error is determined by calculating the deviation between the repaired data and the original data. The smaller the value, the closer the repaired data are to the original data, and the better the corresponding method’s repair effect. When selecting the reconstruction error for evaluation, it is because this indicator can better capture the fluctuations and trend changes of data, and it is more sensitive to outliers, which can more clearly reflect the performance of different algorithms at key points. The expression for the reconstruction error is shown in Equation (15):

$$e={\displaystyle \frac{{‖\widehat{f}-f‖}_2}{{‖f‖}_2}}$$

(15)

In Equation (15), $\widehat{f}$ and $f$ correspond to the reconstructed signal and the original signal, respectively, and ${‖f‖}_2$ represents the two norms of $f$. Due to the simplicity of manually generating missing data to obtain known values, which can easily lead to information loss and is not suitable for large-scale datasets, it has not been applied to subsequent performance comparisons. In order to test the effect of different data processing methods in actual time series prediction and analysis and the robustness of processing random missing data, the meteorological data of Tianjin were first used to analyze the effect of data processing methods, and two cases of random defects of daily mean data and timing data were set. The daily mean data refers to the average value of multiple observations of meteorological variables within a day, usually used to reflect the overall characteristics of meteorological conditions within a day. Timed data refers to meteorological observations recorded at fixed time intervals. The repair effects of different processing methods are shown in Figure 8.

Figure 8a shows the repair effects of different processing methods under the condition of random missing daily average data. The SK algorithm had the worst filling effect on meteorological data, while the MDTSR-GAN algorithm could better restore the changes in the original meteorological data. The CSR algorithm had the best data recovery effect and could accurately reconstruct the trend of changes in the original meteorological data. The above results may be caused by the lack of processing ability of the SK algorithm in terms of continuity and dynamics of time series, while the GAN of the MDTSR-GAN algorithm has advantages in capturing complex data distribution and generating missing data values, and the CSR algorithm has excellent robustness in processing different types of data. Figure 8b shows the variation curves of different processing methods under the condition of random missing timed data. It can be observed that the SK algorithm had many missing measurement values and could not be used for data repair in this scenario. The other two data processing methods could reconstruct the variation in the original meteorological data well. The reconstruction error of the SK algorithm and MDTSR-GAN algorithm corresponded to 0.193 and 0.085, respectively. The reconstruction error of the CSR algorithm was 0.062. This is because CSR algorithm has a good ability to deal with data sparsity. The above results indicate that the CSR algorithm has good repair performance in small data samples. To further evaluate the repair effect of the CSR algorithm in large data samples, two scenarios were set: random missing monthly scheduled data and continuous data. The daily mean data refers to the average value of multiple observations of meteorological variables within a day, usually used to reflect the overall characteristics of meteorological conditions within a day; timed data refers to meteorological observations recorded at fixed time intervals. The results are shown in Figure 9.

Figure 9a shows the repair effect of different processing methods on random missing monthly data. Due to the poor reconstruction performance of the SK algorithm in handling daily missing data, it indicates that it cannot meet the processing requirements of small data volumes. Therefore, it is more difficult to cope with large-scale data volumes such as random missing monthly scheduled data. Therefore, the study tested only the reconstruction effects of the CSR algorithm and MDTSR-GAN algorithm. As the sample size continued to increase, the repair advantage of the CSR algorithm became more apparent. When the data volume reached 3000, its reconstruction error was 0.0403, while the reconstruction error of the MDTSR-GAN algorithm was 0.0453. The above results may be due to the CSR algorithm using more efficient reconstruction algorithms and transformation matrices that make the signal sparser, which has a good effect on improving the repair effect. When there were missing values at the beginning or end of the corresponding data, the MDTSR-GAN algorithm could not effectively respond. Figure 9b shows the variation curves of different processing methods under the condition of continuous random missing data. It can be seen that the filling effect of the CSR algorithm was significantly better than the other data processing methods, and its advantage was more significant when the data had a higher accuracy. To further quantify the performance of different methods under various defect conditions, the study used Mean Absolute Error (MAE) and Root-Mean-Square Error (RMSE) to obtain the results shown in

Table 1. Comparison of MAE and RMSE results of different methods under various defect conditions.

Defect Condition	Method	MAE/°C	RMSE/°C
Random missing daily average data	CSR	0.0280	0.0560
	SK	0.1760	0.2640
	MDTSR-GAN	0.0920	0.1650
Random missing timed data	CSR	0.0305	0.0590
	SK	0.1820	0.2720
	MDTSR-GAN	0.0970	0.1700
Continuous data with random defects	CSR	0.0340	0.0650
	SK	0.2500	0.3900
	MDTSR-GAN	0.1100	0.1900
Random missing monthly scheduled data	CSR	0.0180	0.0350
	MDTSR-GAN	0.0700	0.1300

.

According to Table 1, the CSR algorithm still performs the best under various defect conditions. Under the random defect condition of daily average data, its MAE and RMSE are the lowest, at 0.0280 and 0.0560, respectively. The MAE and RMSE under the condition of random missing monthly data correspond to 0.0180 and 0.0350, respectively, indicating that this method has significant advantages in repairing large data samples. The repair effect of the MDTSR-GAN algorithm is relatively moderate, with MAE and RMSE of 0.0700 and 0.1300, respectively, under the condition of random missing monthly timed data. The SK algorithm performs the worst, with MAE and RMSE values significantly higher across all scenarios, demonstrating its lack of robustness in handling data sparsity and larger defect sizes. The above results indicate that the CSR algorithm provides high robustness and accuracy in dealing with data defects of different types and scales, effectively reconstructing the original data and outperforming other algorithms. In the above results, many evaluations were limited to a range below 0.1, because the preprocessed meteorological data had less fluctuation on the time scale. In addition, the research method has excellent performance in handling missing data. In summary, the CSR algorithm proposed in the study has shown good data restoration effects in various situations and has been proven to be efficient and practical. The accuracy performance of the different clustering algorithms was validated in the CD and RD, and the results are shown in

Table 2. Comparison of accuracy results of different clustering algorithms based on the CD and RD.

Clustering Algorithm	Evaluating Indicator	CD			RD
		Is3	Sticks	Eye	Iris	Lonosphere	Coil
DCCC	Accuracy	0.6568	0.6447	0.8263	0.8259	0.6451	0.4825
	F1 value	0.6975	0.6352	9.8135	0.8614	0.5526	0.4736
	ADC	0.4623	0.6289	0.6473	0.6425	0.4215	0.4576
	SMI	0.6782	0.8112	0.8119	0.7411	0.4076	0.5127
PCSD	Accuracy	0.6118	0.7265	0.6794	0.6639	0.5528	0.5915
	F1 value	0.5739	0.7366	0.6418	0.5861	0.5542	0.4859
	ADC	0.6287	0.6347	0.8113	0.5721	0.5137	0.4637
	SMI	0.7693	0.7452	0.7879	0.7342	0.5124	0.5026
PDC-IFO	Accuracy	1.0000	1.0000	0.8167	0.9135	0.3317	0.4265
	F1 value	1.0000	1.0000	0.8003	0.9264	0.3421	0.3798
	ADC	1.0000	1.0000	0.6298	0.8053	0.4275	0.4678
	SMI	1.0000	1.0000	0.6315	0.8126	0.4525	0.5038
Improve PDC	Accuracy	1.0000	1.0000	0.9235	0.9613	0.6875	0.8425
	F1 value	1.0000	1.0000	0.9062	0.9627	0.6954	0.7762
	ADC	1.0000	1.0000	0.8247	0.8862	0.4875	0.4698
	SMI	1.0000	1.0000	0.7861	0.8711	0.4351	0.5021

.

From Table 2, the improved PDC algorithm proposed in the study could more accurately identify clusters from different datasets in the CD. Moreover, for cross-entangled, multi-density peak datasets, the processing capability of this method was superior to other mainstream clustering algorithms. This is because it improved the accuracy of searching for density peaks through latent grid density and reduced the probability of continuous allocation errors through neighborhood expansion algorithms. The accuracy of the improved PDC algorithm in both the Is3 and Sticks datasets was 1.000, with only slightly lower performance in the Eye dataset at 0.9235. In the accuracy results of the RD, the improved PDC algorithm still performed the best in the Iris, Lonosphere, and Coil datasets, with corresponding accuracies of 0.9613, 0.6875, and 0.8425, respectively, and corresponding F1 values of 0.8711, 0.4351, and 0.5021, respectively. The comparison of computation time results of various clustering algorithms based on different datasets is shown in

Table 3. Comparison of computation time results of various clustering algorithms based on different datasets.

Data Set		DCCC	PCSD	PDC-IFO	Improve PDC
CD	Is3	0.9887	0.0358	0.6125	0.2943
	Sticks	0.0569	0.0366	0.0931	0.0736
	Eye	0.0336	0.0259	0.0459	0.0315
RD	Iris	0.0283	0.0227	0.0501	0.0312
	Lonosphere	0.0519	0.0279	0.0898	0.0787
0.0411	Coil	0.0327	0.0248	0.0763	0.0411

.

According to Table 3, the improved PDC algorithm had the shortest computation time in the Is3 dataset, which was 0.2943 s. In the Eye dataset, it only took slightly longer than the PCSD algorithm, which was 0.0315 s. The DCCC algorithm and PDC-IFO algorithm had the highest computation time in all three datasets of the CD. The above results are due to the improved PDC algorithm converting the processing object into a grid, which greatly reduces the processing range. In the RD, the computation time of the improved PDC algorithm was at a moderate level, with computation times of 0.0312 s, 0.0787 s, and 0.0411 s for Iris, Lonosphere, and Coil, respectively. In summary, after comprehensive evaluation, the PDC algorithm proposed in the study can effectively improve recognition accuracy while sacrificing minimal computation time and ensuring efficiency and accuracy, and it has excellent data analysis performance.

To ensure the scientific validity and reproducibility of the experiments, this study divides the meteorological data into different time scales, including daily mean data, timed data, and monthly mean data. Daily mean data are used to evaluate the CSR algorithm’s performance in long-term data imputation, timed data (recorded every two hours) are employed to test the algorithm’s ability to restore high-resolution time-series data, and monthly mean data are used to analyze CSR’s applicability in building climate assessments. Experimental results indicate that CSR maintains a consistently low reconstruction error (0.0403) across different time scales, significantly outperforming the SK and MDTSR-GAN methods. This further validates that the adopted data division strategy effectively captures the diversity of time-series data, ensuring the stability and generalizability of the CSR algorithm in various application scenarios.

4.2. Analysis of the Results of the Intelligent, Sustainable, Building Energy-Saving Design Platform

To investigate the effectiveness of the ISBESD platform designed for research in practical applications, the visualization display effects of each functional module were analyzed. Firstly, the data processing and analysis part of the joint CSR algorithm was divided into specific situations of various stations in China. The results are shown in Figure 10.

Figure 10 shows that the station information in different regions of China is clearly divided, allowing for a clear observation of which regions belong to the same category and which regions have different climate characteristics. In subsequent queries or comparisons of various cities, the clustering results can be used to directly select the required climate characteristic stations, which can obtain the basic information of the corresponding stations and further select the detailed information required for ISBESD. Due to the large number of urban areas in China and the significant differences in meteorological data between different regions, it is not possible to verify all cities one by one. To ensure the universality of the ISBESD platform, a city will be randomly selected for subsequent analysis. The study selected city A for the experiment, which belongs to an inland mountainous area with a terrain that is high in the south and low in the north, with a sloping trend from north to south, and belongs to a cold temperate continental monsoon climate. The total area was 18,427 square kilometers. The basic climate data of the region were queried, and the corresponding results are shown in Figure 11.

From Figure 11, users could select the corresponding basic climate characteristics based on the required stations, including the maximum and minimum values of different meteorological factors as well as the average maximum and minimum values. This section included temperature and humidity, wind speed and direction, and solar radiation meteorological factors. Users could choose the corresponding basic climate characteristic data display based on their own design requirements. In the ISBESD platform city comparison module, city C was randomly selected to compare with city A. The specific application effect is shown in Figure 12.

In Figure 12, users could select the basic information of two platforms with differences for comparison and could choose corresponding climate characteristics such as temperature, humidity, wind speed, wind direction, and solar radiation for comparison based on ISBESD requirements. By combining the above comparison results with the clustering analysis results, different platforms in different clusters or different platforms in the same cluster could be selected for comparison. Finally, the outdoor climate data module of the ISBESD platform was demonstrated, and the specific effects are shown in Figure 13.

Figure 13a–c correspond to the air temperature, cloud cover, and temperature radiation results for typical years in city A. Figure 13 shows that the average maximum and minimum values, recorded maximum and minimum values, and average values of the city all showed the same trend, and the recorded maximum value from May to September exceeded 30 °C, while the temperature from January to March and November to December was below −35 °C. The cloud cover in city A exceeded 90% in each month, and the radiation also increased with the increase in temperature. The energy-saving design parameters for HVAC data are shown in

Table 4. Energy-saving design parameters for HVAC systems.

Category	Data	Numerical Value	Category	Data	Numerical Value
Station information	Province/municipality/autonomous region	/	Wind speed, direction, and frequency	Summer average wind speed	2.49 m/s
	City/region/autonomous prefecture	/		Maximum wind direction frequency in summer	12.03%
	Altitude	/		Maximum outdoor wind speed in summer	3.07 m/s
	Latitude and longitude	/	Heating period days and average temperature	Annual average temperature	5.3 °C
Atmospheric pressure	Outdoor atmospheric pressure in summer	988.897 hPa		Outdoor HVAC calculation temperature	−22.81 °C
	Outdoor atmospheric pressure in winter	1005.643 hPa		Outdoor calculated temperature for summer air conditioning	30.81 °C
Outdoor temperature and humidity	The number of days with a daily average temperature not exceeding 5 °C	165		Outdoor calculated humidity for summer air conditioning	24.89%
	The number of days with a daily average temperature not exceeding 8 °C	187		Outdoor calculated temperature for summer ventilation	26.84 °C
	Extreme minimum temperature	−37.6 °C		Outdoor calculated humidity for summer ventilation	26.85%
	Extreme maximum temperature	39.5 °C		Calculated outdoor temperature for HVAC in winter	−26.7 °C
Wind speed, direction, and frequency	Average wind speed in winter	2.37 m/s		Outdoor calculated humidity for HVAC in winter	70.52%
	Maximum wind direction frequency in winter	12.41%		Outdoor temperature for winter ventilation	−17.6 °C
	Maximum outdoor wind speed in winter	2.85 m/s	/	/	/
	Winter sunshine rate	39.43%	/	/	/

.

According to Table 4, the energy-saving design parameter data for HVAC mainly included three aspects: sustainable building heating, air conditioning, and ventilation. Specifically, it included relevant information in four categories: atmospheric pressure; temperature and humidity; heating period days and average temperature; and wind direction, speed, and frequency. Based on the relevant data obtained for ISBESD in city A, certain design guidance could be provided. Passive solar heating technology could be used in this area to enhance the insulation performance of the building envelope and the overall airtightness of the building. In addition, outdoor equipment with lower actual operating temperatures could be selected for air conditioning and heating equipment selection. To verify the effectiveness of the research method in practical applications, the building project S in city A was selected for analysis and included in the above design guidance. The specific situation of the project was as follows: it covered an area of 4000 square meters with a total of 9 floors, each with 2360 square meters, a total building height of 44.1 m, and a floor height of 4.8 m. In addition, to explore the performance of the research methods more scientifically, the study selected the current mainstream Life Cycle Cost (LCC)-based ISBESD optimization method for comparison. At the same time, the study analyzed the comfort hours throughout the year, comfort hours in different orientations, effective ventilation percentage throughout the year, and cost, as shown in Figure 14.

Figure 14a–d correspond to the annual comfort hours, comfort hours in different orientations, effective ventilation percentage, and cost comparison results of different ISBESD methods. Figure 14a shows that compared with the LCC method, the research method increased comfort hours by 65%, 287%, 87.6%, and 73% in spring, summer, autumn, and winter, respectively. Figure 14b shows the comparison between the comfort hours of the research method and the LCC method in the East, West, South, and North, with improvements of 70%, 75%, 76%, and 76%, respectively. Figure 14c shows that compared with the LCC method, the annual ventilation efficiency was significantly improved after being guided by the ISBESD platform design, with an average increase of 47.35%. According to Figure 14d, although an additional investment of CNY 1.0056 million was made in the energy storage wall, in the long run, the cost of the LCC method was 5 times that of the research method, and the annual air conditioning electricity cost was only CNY 180,000, while the annual air conditioning electricity cost processed by the LCC method reached CNY 546,800. In summary, the ISBESD platform constructed in this study can intuitively display data information on ISBESD, which is beneficial for subsequent building energy-saving design work.

5. Conclusions

In the construction industry, sustainable buildings are gradually becoming a key force leading the industry’s development. It is an important part of promoting air pollution prevention and addressing climate change. At the same time, in-depth mining of climate data also provides a certain reference for ISBESD. Therefore, the study first used CSR data to fill in missing meteorological data, then jointly improved the PDC algorithm to process massive data, and finally constructed the ISBESD platform based on the above algorithm. The experimental results showed that in the case of random missing timing data, the CSR algorithm had the best repair effect with a corresponding reconstruction error of 0.062, while the SK algorithm and MDTSR-GAN algorithm had poor repair effects with corresponding errors of 0.193 and 0.085, respectively. In the CD, the improved PDC algorithm achieved an accuracy of 1.000 in both the Is3 and Sticks datasets, with only slightly lower performance in the Eye dataset at 0.9235. In the RD, the algorithm still performed the best in the Iris, Lonosphere, and Coil datasets, with corresponding accuracies of 0.9613, 0.6875, and 0.8425, respectively, and corresponding F1 values of 0.8711, 0.4351, and 0.5021, respectively. Finally, in the display of various functions on the ISBESD platform, various basic information required for ISBESD could be fully showcased, providing solid data support for energy-saving design. In summary, the research method can efficiently and accurately process large-scale data, and the constructed ISBESD platform can assist building professionals, governments, and enterprises in achieving more scientific and excellent energy-saving designs. When utilizing multidimensional data, the research method requires multiple experiments to determine the most satisfactory results, which to some extent limits its application efficiency. It is difficult to handle multidimensional data well in practical applications. Therefore, in future research, intelligent methods can be used to screen climate factors and other indicators involved in multidimensional data, providing guidance for the energy-saving design of sustainable buildings. In addition, regarding the energy management of buildings, the functionality of the research platform can be enriched by considering the double-layer random optimization allocation method of intelligent buildings for energy storage and sharing services.