Introduction

Global hotel buildings are facing significant sustainability challenges, particularly in relation to SDGs 7.3, 8.9, 9.4, 11.3, and 12.51. Frequent redecoration and rebuilding cycles (every 2-5 years) contribute to high carbon emissions and material waste2, undermining energy efficiency (7.3)3, sustainable tourism (8.9)4, and building innovation (9.4)5. These issues are even more pronounced in budget chain hotels, as they are more sensitive to costs6,7. Prefabrication minimizes waste8, reduces construction time9, and lowers carbon footprints10, yet the mechanisms behind its success remain underexplored11. Many previous studies on carbon reduction in the hotel industry have primarily focused on the materialization and operational stages12,13. Within the materialization phase, most research has concentrated on improving carbon reduction efficiency through advancements in technology and materials14. However, fewer studies have explored the impact of architectural design11, specifically the 3D geometric proportions of buildings2, on carbon reduction efficiency15. Particularly, there has been limited attention on prefabricated construction16, a time-saving17, labor-efficient18, and material-saving approach to building construction19.

In recent years, prefabricated construction technologies have seen remarkable growth on a global scale, demonstrating a diversity of types and applications20. Based on structural forms and functional requirements, prefabricated construction can generally be categorized into precast concrete, modular steel construction21, BIM timber construction, hybrid structures, and fully modular buildings22. Precast concrete components—such as wall panels, beams, columns, and slabs—are among the most widely applied23. Modular steel construction is characterized by high-strength, lightweight modules24, while timber construction, including cross-laminated timber (CLT), and glued laminated timber (GLT), has gained broad recognition in North America and Europe25. Hybrid structures and fully modular buildings, on the other hand, integrate multiple materials and functional units to offer greater flexibility and adaptability for modern architectural demands26.

From a technological perspective, contemporary prefabricated construction benefits from several innovative advances, including building information modeling (BIM), robotics and automated manufacturing, the application of high-performance materials, the development of lightweight prefabricated components, and the adoption of modular construction systems27. BIM significantly enhances the precision of component design and the efficiency of construction management28. Automated and intelligent manufacturing technologies streamline factory production processes, reducing reliance on manual labor29. High-performance materials such as ultra-high-performance concrete (UHPC) and high-strength steel improve the durability and strength of prefabricated components30. Modular systems31, by pre-assembling complete units in factories and rapidly assembling them on-site, dramatically shorten construction timelines32.

In addition, intelligent prefabrication technologies have progressed rapidly, with robotic 3D printing emerging as a key innovation33. By combining industrial robotics with digital modeling and control systems, robotic 3D printing facilitates the direct fabrication of complex-shaped components without molds34. This not only enhances the geometric freedom and functional integration of prefabricated elements, but also reduces mold usage and material waste35. Particularly in precast concrete applications, layered robotic 3D printing can quickly produce high-performance, customized components36. When coupled with advanced materials such as low-carbon cement and fiber-reinforced concrete37, it also meets stringent environmental requirements38. Moreover, multi-robot collaborative printing has shown significant advantages in modular construction39. Walls, partitions, and even complex nodes can be formed entirely in the factory, then transported to the construction site for assembly40. This approach boosts productivity, lowers labor costs, and enhances safety on-site41. Looking forward, the integration of robotic 3D printing with the internet of things (IoT) and artificial intelligence (AI) is poised to drive prefabricated construction toward intelligent, flexible, and low-carbon solutions42. This will significantly enhance its adaptability and value in scenarios involving complex designs and rapid construction demands43.

The aim of this study is to explore how the optimal threshold of architectural 3D geometric proportions, through modeling, can help the prefabricated hotel model achieve greater carbon reduction targets. First, in response to the demand from mega-events, such as Osaka World Expo 2025, which necessitate the construction of new hotel chains to accommodate the influx of large numbers of visitors, prefabricated construction (a method with higher carbon reduction efficiency) should be prioritized. Second, if new hotels are built using prefabricated construction methods, the optimal carbon reduction efficiency threshold model derived in this study can be applied to guide the design and construction of these hotels. Third, in the case of hotel renovations, the carbon reduction efficiency threshold model presented in this research can similarly be used to identify the most suitable hotels for prefabricated technology upgrades, ensuring maximum carbon reduction with minimal material, labor, and resource waste. This approach serves three key purposes towards SDGs and its sustainable tourism44,45,46,47.

Results

Comprehensive exploratory analysis

To comprehensively identify the factors influencing per-3D-unit-volume carbon emission intensity, conducted with a detailed analysis across 2main categories, 4 sub-categories, and 23 smaller factors. These include the building geometry factors category, which consists of length/area/volume factors (8 sub-categories), number factors (2 sub-categories), and ratio factors (5 sub-categories); and the carbon emission efficiency category, which includes carbon emission factors (8 sub-categories) (Fig. 1 Note: Per-3D-Unit-Volume Carbon Emission Intensity in Prefabricated Construction (Per3DCEICPC) / Conventional Construction (Per3DCEICC), Total-3D-Volume Carbon Emission Intensity in Prefabricated Construction (Total3DCEICPC) / Conventional Construction (Total3DCEICC)).

Fig. 1
Fig. 1
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Sankey diagram flow overview 1 and 2 of hotel factors.

From the 2D and 3D scatter plots (Fig. 2a, b Note: In the Geometry Type, A refers to a quadrilateral, B refers to a hexagon, C refers to a pentagon, D3 refers to a triangle, E8 refers to an octagon, and F9 refers to polygons with nine or more sides.), significant differences in the distribution of Per3DCEICC (kgCO₂/m³) and Per3DCEIPC (kgCO₂/m³) across different geometry types (A, B, C, D, E, F) are evident. Buildings of geometry type A generally exhibit higher Per3DCEICC values, while geometry type B buildings show lower Per3DCEIPC values. Buildings of geometry type C display a greater carbon emission variance, with the ratio (Per3DCEICC - Per3DCEIPC) / Per3DCEICC reaching 0.4545. In contrast, the D, E, and F building types demonstrate a more balanced carbon emission density, with smaller ratio differences, highlighting the variability in carbon emissions across different building types.

Fig. 2: 2D and 3D scatter plots of Per3DCEICC, Per3DCEIPC, and the ratio with Geometry Type colors.
Fig. 2: 2D and 3D scatter plots of Per3DCEICC, Per3DCEIPC, and the ratio with Geometry Type colors.
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a The 2D scatter plot compares Per3DCEIPC (carbon emission intensity in prefabricated construction) against Per3DCEICC (carbon emission intensity in conventional construction), with different Geometry Types represented by colors: red (A), green (B), blue (C), purple (D), yellow (E), and orange (F). Each point is labeled with a unique building identifier. b The 3D scatter plot shows Per3DCEICC on the x-axis, Per3DCEIPC on the y-axis, and the ratio (Per3DCEICC−Per3DCEIPC)/Per3DCEICC on the z-axis. The points are color-coded by Geometry Types, offering insights into the spatial relationships between carbon emission intensities and geometric properties.

Screening potential factors analysis

Heatmap analysis (Fig. 3a) reveals the relationship between architectural features and carbon emission intensity. Per3DCEICC (kgCO₂/m³), representing carbon emission intensity in traditional buildings, correlates with several architectural factors. A strong positive correlation (0.75) is found between building volume (m³) and Per3DCEICC, suggesting that larger buildings generally exhibit higher carbon emissions due to increased material usage and energy consumption. Total building area (m²) also shows a positive correlation (0.67) with Per3DCEICC, indicating that larger buildings consume more energy and generate higher emissions. The correlation between building footprint area (m²) and Per3DCEICC is 0.43, demonstrating that buildings with larger footprints tend to have higher carbon emissions. Additionally, a positive correlation (0.43) is observed between area/perimeter and Per3DCEICC, suggesting that buildings with less efficient spatial layouts (higher area/perimeter ratios) tend to have higher carbon emissions. Conversely, a negative correlation (-0.37) is found between height/perimeter*L and Per3DCEICC, implying that more efficient building shapes (higher height-to-perimeter ratios) result in lower carbon emissions. While the correlation between height/area*L and Per3DCEICC is weak (-0.16), it still suggests that optimizing the height-to-area ratio can help reduce carbon emission intensity. Finally, the number of edges (L) shows a negative correlation (-0.31) with Per3DCEICC, indicating that simpler building forms (fewer edges) may contribute to reduced energy consumption and emissions. In conclusion, efficient spatial utilization (lower area/perimeter) helps reduce carbon emission intensity. Simplified building forms (fewer number of edges) and higher form efficiency (higher height/perimeter*L) are associated with lower carbon emission intensity. To further reduce carbon emissions, building designs should optimize area/perimeter, increase height/perimeter*L, and minimize the number of edges (L). These analyses offer valuable guidance for future architectural design, particularly in prefabricated construction, by optimizing these factors to achieve low-carbon, sustainable building goals.

Fig. 3: Screening potential factors analysis of Per3DCEICC and Per3DCEIPC.
Fig. 3: Screening potential factors analysis of Per3DCEICC and Per3DCEIPC.
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a Correlation matrix of building features and Per3DCEICC (carbon emission intensity in conventional construction), showing correlations between building attributes and Per3DCEICC with color intensity indicating correlation strength. b Correlation heatmap for building attributes and Per3DCEIPC (carbon emission intensity in prefabricated construction), similar to Panel a but reflecting the relationship with Per3DCEIPC. c Radar chart comparing the correlation between Per3DCEICC, Per3DCEIPC, and building attributes like volume, height, and number of rooms. d Top 10 forms based on Per3DCEICC, showing the most significant building forms contributing to carbon emission intensity in conventional construction. e Top 10 forms based on Per3DCEIPC, showing the significant building forms for prefabricated construction.

Heatmap analysis (Fig. 3b) reveals the relationship between architectural features and carbon emission intensity. Building footprint area and total building area show a strong positive correlation with Per3DCEIPC, indicating that larger building areas are associated with higher carbon emission intensity per unit volume in prefabricated buildings. Building height per floor also correlates positively with Per3DCEIPC, suggesting that taller buildings tend to have higher emissions due to increased material and energy consumption. Similarly, building volume strongly correlates with Per3DCEIPC, indicating that as building volume increases, carbon emission intensity per unit volume rises, likely due to the additional materials and construction processes required. The area/perimeter ratio shows a negative correlation (-0.22) with Per3DCEIPC, suggesting that buildings with a lower area-to-perimeter ratio are more efficient in reducing carbon emissions. Ideal designs should minimize excessive complexity in shapes to reduce emissions. Height/perimeter*L also has a negative correlation (-0.20) with Per3DCEIPC, implying that balancing building height and perimeter can optimize energy use and reduce carbon emissions. Conversely, height/area*L shows a positive correlation (0.26) with Per3DCEIPC, indicating that higher volume-to-area ratios may require more materials, increasing carbon emissions. Therefore, building designs, especially for prefabricated structures, should avoid excessively high height-to-area ratios to reduce energy and resource demand. Number of edges (L) shows a weak correlation (0.05) with Per3DCEIPC, indicating that the number of edges has a limited effect on carbon emissions. However, simplifying the building’s geometry by reducing complexity can still contribute to lowering emissions. In conclusion, optimizing architectural design factors such as the area/perimeter ratio and height/perimeter*L can effectively reduce carbon emission intensity. Maintaining a lower area-to-perimeter ratio and optimizing the balance between building height and perimeter are key to minimizing carbon emissions. The positive correlation between height/area*L indicates that avoiding overly high building-to-area ratios helps reduce carbon emissions. The limited impact of L (number of edges) on carbon emissions suggests that the complexity of a building’s geometry (i.e., the number of edges) has a minimal effect on emissions, although the number of edges can still influence the building’s esthetic and functional characteristics, offering opportunities for creative architectural design with more complex forms.

Comparison of the correlations (Fig. 3 c, d, e) between Per3DCEICC and Per3DCEIPC show different correlations with various architectural features, such as the area/perimeter ratio, building height, and the number of floors. Through radar charts, we can observe the changes in the two carbon emission indicators across multiple dimensions, providing feedback on architectural design. Per3DCEICC exhibits a strong correlation with certain building features, such as building volume and the number of floors, possibly due to more complex building forms (e.g., higher floors and larger areas) leading to higher carbon emission intensity. In contrast, the correlation curve for Per3DCEIPC shows a slightly different pattern, indicating that certain building features—particularly in prefabricated buildings, which focus more on design optimization and resource efficiency—have a lesser impact on carbon emissions. For example, the area/perimeter ratio has a smaller effect on emissions. Additionally, the complexity of the building’s geometric shape (geometry type) has a relatively minor impact on carbon emission intensity, suggesting that prefabricated buildings have better potential for optimization in their design. The different performances of Per3DCEICC and Per3DCEIPC suggest that architectural design may have varying impacts on carbon emission intensity in prefabricated versus traditional buildings. Features such as building shape, volume, and perimeter have a reduced impact on carbon emission intensity in prefabricated buildings, which indicates a higher potential for design optimization. By adopting modular designs that adhere to specific geometric ratios (such as the area/perimeter ratio and geometry type), prefabricated buildings can more effectively control and reduce carbon emissions. More importantly, these ratios give prefabricated buildings a significant advantage over traditional buildings when designing more complex shapes, allowing for better sustainability and efficiency in the design process.

Detecting key factors analysis

Through heatmap correlation analysis (Fig. 4 a), the relationships between four architectural features—area/perimeter, height/perimeter*L, height/area*L, and L (number of edges)—and the target variable (Per3DCEICC - Per3DCEIPC) / Per3DCEICC (%) (the ratio of carbon reduction efficiency between prefabricated and traditional construction) were analyzed. The correlation between area/perimeter and carbon reduction efficiency (%) is -0.08, indicating a minimal impact on carbon reduction efficiency. This suggests that the area/perimeter ratio has little effect on the carbon reduction benefits of prefabricated construction compared to traditional methods. In contrast, height/perimeter*L shows a strong positive correlation (0.73) with carbon reduction efficiency, indicating that optimizing the 3D ratio adjusted for the height-to-perimeter ratio enhances carbon reduction benefits. Similarly, height/area*L has a perfect positive correlation (1.00) with carbon reduction efficiency, demonstrating that increasing this ratio significantly improves the carbon reduction efficiency of prefabricated construction. The correlation between L (number of edges) and carbon reduction efficiency (%) is weak (0.17), suggesting that the complexity of the building form has a minimal effect on carbon reduction efficiency, likely due to its limited contribution to overall carbon emission reduction. The strong correlations between height/perimeter*L and height/area*L with the target variable indicate the importance of optimizing building form and spatial efficiency. In particular, enhancing the height-to-area ratio is crucial for improving the carbon reduction efficiency of prefabricated construction. Conversely, the weak correlation between area/perimeter and carbon reduction efficiency, and the minimal impact of L (number of edges), highlight that spatial efficiency and form complexity play a less significant role in reducing carbon emissions. By optimizing height/area*L and height/perimeter*L, the carbon reduction efficiency of prefabricated buildings can be significantly improved, offering a substantial advantage over traditional construction methods.

Fig. 4: Detecting key factors analysis of (Per3DCEICC−Per3DCEIPC)/Per3DCEICC.
Fig. 4: Detecting key factors analysis of (Per3DCEICC−Per3DCEIPC)/Per3DCEICC.
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a The correlation matrix of building features and carbon emissions intensity, showing correlations between building attributes (e.g., footprint area, height) and carbon intensity. Red shades indicate positive correlations, blue indicates negative correlations. b Loadings of features on principal components (PC1, PC4, PC5, PC7) showing the contribution of each feature to these components. c The elbow method for determining the optimal number of clusters (K) in K-means clustering, where K=3 is identified as optimal. d K-means clustering (K=3) in 2D space, color-coded by cluster membership (red, green, blue), showing the distribution of data points using the first two principal components (PC1 and PC2).

Principal component analysis (PCA) (Fig. 4 b) reveals that PC1 and PC2 together explain approximately 68.35% of the total variance, making them the most important principal components that capture the main variability in the data. PC3 to PC7 collectively account for 22.42% of the variance, indicating that these components also influence the data’s variability. From PC8 to PC13, their contributions are relatively small, suggesting that only the first few principal components should be considered for further analysis. In PC1, area/perimeter has a loading of -0.29, indicating a strong negative contribution. Height/perimeter*L has a loading of +0.14, showing a positive but minor correlation. Height/area*L has a loading of +0.23, suggesting a slight positive contribution to PC1, while L (number of edges) has a loading of +0.05, indicating a minimal contribution. In PC4, Area/Perimeter has a loading of +0.03, showing a very small contribution. Height/perimeter*L has a loading of +0.26, indicating a positive correlation and suggesting that the efficiency of building form plays a notable role in this principal component. Height/area*L has a loading of +0.05, contributing minimally to PC4. L has a loading of +0.48, which represents a strong contribution, indicating that the number of edges in the building has a significant impact on this principal component. In PC5, Area/perimeter has a loading of -0.27, showing a negative correlation. Height/perimeter*L has a loading of -0.35, demonstrating a strong negative impact. Height/area*L has a loading of -0.04, with a minor contribution. L has a loading of -0.26, indicating a negative impact, suggesting that the number of edges influences this principal component. In PC7, Area/Perimeter has a loading of +0.01, contributing almost nothing. Height/perimeter*L has a loading of -0.25, showing a strong negative correlation. Height/area*L has a loading of +0.11, reflecting a slight positive correlation. L has a loading of +0.14, indicating a small positive contribution to PC7.

In PC1 and PC5, the features area/perimeter and height/perimeter*L contribute significantly to the principal components, with height/perimeter*L showing a negative correlation in PC5. In PC4, the loading of L is the strongest, highlighting the significant role of building complexity (i.e., the number of edges) in this principal component. In PC7, height/perimeter*L shows a negative correlation, while L has a minor positive impact. These relationships between the principal components and architectural features suggest that building spatial form, structural complexity (such as the number of edges), and design efficiency (such as the area-to-perimeter ratio) are key factors influencing the carbon emission efficiency of both prefabricated and traditional construction.

The K-means clustering analysis (Fig. 4 c, d Table 1) reveals distinct differences in the average carbon emission intensity across three clusters, measured by the formula (Per3DCEICC - Per3DCEIPC) / Per3DCEICC (%). Specifically, Cluster 0 shows an average carbon emission intensity difference of 0.374, Cluster 1 exhibits 0.390, and Cluster 2 demonstrates 0.382. Notably, Cluster 1 displays a higher carbon emission intensity difference, suggesting that buildings in this cluster experience a more significant reduction in carbon emissions when utilizing prefabricated construction compared to traditional construction. The differences in carbon emission reduction between Clusters 0 and 2, however, are comparatively smaller. The spatial distributions of the three clusters indicate notable variations in architectural features. Cluster 0, characterized by lower spatial efficiency and simpler building forms, is associated with an area/perimeter greater than 1.25, height/perimeter*L values below 0.20, and height/area*L values under 0.07. Additionally, the number of edges (L) ranges from 3 to 6, reflecting a simpler form. Cluster 1, which features higher spatial efficiency and moderately complex buildings, has an area/perimeter between 0.7 and 2.85, height/perimeter*L values ranging from 0.09 to 0.22, and height/area*L values between 0.05 and 0.13. The number of edges (L) in this cluster is more complex, ranging from 4 to 9. In contrast, Cluster 2, with higher spatial efficiency and more complex building forms, is characterized by an area/perimeter of less than 1.0, height/perimeter*L values exceeding 0.20, and height/area*L values above 0.25. The number of edges (L) in this cluster ranges from 4 to 9, indicating a moderate level of complexity. Clusters 1 and 2, exhibiting higher spatial efficiency and more complex building forms, demonstrate more significant carbon emission reduction benefits. In contrast, Cluster 0, with simpler building forms and lower spatial efficiency, shows relatively smaller carbon reduction benefits. The optimal threshold combinations suggest that enhancing carbon reduction benefits in prefabricated construction can be achieved by optimizing area/perimeter, height/perimeter*L, height/area*L, and L (number of edges), particularly by focusing on the characteristics found in Cluster 2.

Table. 1 Distribution of features for each cluster (interval analysis)
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Discussion

Future-oriented architectural design can greatly benefit from a more refined application of optimal geometric threshold combinations, especially in enhancing building performance, energy efficiency, and carbon emissions reduction. While the results presented in this study highlight promising trends, it is important to note that further validation is required across a broader range of building types and geographical locations to ensure robustness. Optimizing the area/perimeter ratio with a lower threshold (e.g., less than 1.5) can improve spatial efficiency and reduce overall energy demand, but the extent of reduction is context-dependent and may vary based on local climate and operational characteristics. The role of higher values for height/perimeter*L (3D Ratio) in leading to more compact and efficient building forms should be considered within the specific limits of different building types. The number of edges (L) can also impact the complexity of the building design. Maintaining a moderate range (e.g., 4 to 6 edges) can strike a balance between efficiency and complexity, helping to optimize energy use while ensuring structural integrity.

Furthermore, optimizing the height/area*L (3D Ratio) can enhance spatial and energy efficiency, helping to design more compact buildings with higher floor area ratios, reducing energy consumption and lowering carbon emissions. However, these optimizations should be adapted to the specific constraints and requirements of the building context, including environmental factors and the intended building use. These optimizations also play a critical role in addressing the challenges of climate change and urbanization, as they reduce building energy demand and overall carbon footprint. Yet, the degree of these effects should be validated in diverse geographical and operational contexts to ensure that they are not overstated. Ultimately, the thoughtful integration of these optimal geometric combinations will contribute to more energy-efficient, low-carbon, and sustainable building designs, aligning with global sustainability goals and improving the performance and comfort of buildings.

On the other hand, the application of 3D printing in prefabricated construction has the potential to bring about significant improvements. While 3D printing offers higher precision, flexibility, and efficiency, its full potential in reducing carbon emissions is still being explored and requires further empirical data to validate the broader claims of sustainability. Optimizing geometric threshold combinations through 3D printing can enhance building performance, but the actual environmental benefits should be confirmed through large-scale case studies. 3D printing enables the manufacturing of complex shapes that were previously difficult or expensive to produce with traditional methods; however, the long-term carbon footprint and material efficiency benefits of 3D printing in construction require further investigation. Moreover, 3D printing technology can help reduce material consumption by producing parts only when needed, thereby minimizing waste and improving sustainability. It also allows for the creation of more sustainable building materials, reducing waste and enhancing material efficiency. 3D printing addresses supply chain challenges by enabling on-demand production, reducing transportation and storage costs. As the technology advances, integrating artificial intelligence with 3D printing can lead to smart building materials with self-regulating, self-repairing, and adaptive capabilities. Additionally, 3D printing supports modular construction, enabling faster construction with higher quality and lower maintenance costs. The use of sustainable materials, such as biodegradable and recycled materials, is also on the rise, contributing to the reduction of the overall environmental impact of construction.

Through the study of optimal geometric thresholds, this research presents a framework for improving carbon reduction in prefabricated hotel designs. However, the model presented here should be considered as an initial step. Real-world applications must take into account the variability in operational practices, energy systems, and local climates. Further data from diverse case studies are required to generalize these findings across a wider range of buildings and ensure that the identified thresholds are universally applicable. The study suggests that prefabricated construction, which offers higher carbon reduction efficiency, should be prioritized in response to the demand for new hotel chains in mega-events, such as the Osaka World Expo. The optimal carbon reduction efficiency threshold model can guide the design and construction of new hotels using prefabricated methods, ensuring that they achieve maximum energy efficiency. For hotels requiring renovation, the model can identify the most suitable buildings for prefabricated technology upgrades, helping to achieve maximum carbon reduction with minimal material, labor, and resource waste. The successful implementation of prefabricated hotels in Hangzhou during the Asian Games provides a model for other cities hosting international events, such as the Osaka World Expo, where sustainable development is a priority. Prefabricated construction and renovation technologies enhanced construction efficiency, reduced environmental impact, and delivered better economic returns. These technologies also contributed to the enhancement of the brand reputation of the hotels during the event, demonstrating the broader economic and environmental benefits of incorporating sustainable construction methods.

Most previous studies have primarily focused on improving carbon reduction efficiency through technological and material advancements, with relatively few studies exploring the impact of architectural design—specifically the 3D geometric proportions of buildings—on carbon reduction efficiency. This is particularly true in the context of prefabricated construction, which is known for its time, labor, and material-saving benefits. This study addresses this gap by using multidimensional algorithms to derive an optimal threshold model for maximizing carbon reduction efficiency in prefabricated construction, based on a hotel building database. The 3D ratio data in the model are primarily associated with the following variables: area/perimeter, ranging from 0.7 to 2.85, indicating moderate spatial efficiency; height/perimeterL (3D Ratio), ranging from 0.09 to 0.22, suggesting relatively simple building forms; height/areaL (3D Ratio), ranging from 0.05 to 0.13, indicating higher spatial efficiency; and L (number of edges), ranging from 4 to 9, indicating greater complexity. By studying optimal geometric threshold models for building 3D forms, this research aims to achieve higher carbon reduction goals for prefabricated hotel models. The objectives are: first, to address the demand for new hotel chains for mega-events such as the Osaka World Expo, where prefabricated construction, with its superior carbon reduction efficiency, should be prioritized; second, the optimal carbon reduction efficiency threshold model can guide the design and construction of new hotels using prefabricated methods; and third, for hotel renovations, the model can identify which buildings are most suitable for prefabricated technology upgrades, ensuring maximum carbon reduction with minimal material, labor, and resource waste. This study provides a practical design model for the future of prefabricated construction, particularly for large-scale global applications, while contributing theoretically to the research of prefabricated technologies, including robot 3D printing and conventional construction methods.

Methods

This study employs multidimensional algorithms for a two-level data analysis. The first step involves a comprehensive exploratory analysis of factors and carbon emission intensity, focusing on screening potential factors, and detecting key factors. In the second step, the focus shifts to in-depth analysis of Ratio factors and carbon reduction efficiency ((Per3DCEICC-Per3DCEIPC)/Per3DCEICC(%)), aiming to identify the optimal threshold model affecting carbon reduction efficiency. The methods used for this analysis include Sankey diagram analysis, 2D and 3D scatter plot analysis, heatmap correlation analysis, and principal component analysis (PCA).

Multidimensional algorithms

Sankey Diagram Analysis

A Sankey diagram is a flow visualization tool that helps represent the magnitude of flows between different categories. It’s used to visualize the distribution and proportions of quantities like energy, money, or material. Key Formula (Flow Proportions):

$${S}_{{out}}={S}_{{in}}$$
(1)

Where \({S}_{{out}}\) and \({S}_{{in}}\) represent the flow into and out of a system, respectively. These values are usually proportionally represented by the width of the arrows in the Sankey diagram.

2D and 3D Scatter Plot Analysis

Scatter plots are used to visualize the relationship between two or more variables, showing how one variable is affected by another. A 3D scatter plot extends this analysis to three variables, providing a visual representation in three dimensions. 2D Scatter Plot (for two variables x and y):

$${\rm{y}}={\rm{f}}({\rm{x}})$$
(2)

Where: y: Dependent variable, x: Independent variable.

3D Scatter Plot (for three variables x, y, and z):

$${\rm{z}}={\rm{f}}({\rm{x}},{\rm{y}})$$
(3)

Heatmap Correlation Analysis

Heatmaps are used to visualize data matrices, with the intensity of the color representing the magnitude of values. In correlation heatmaps, colors show the strength and direction of the correlation between variables. Key Formula (Pearson Correlation Coefficient):

$$r=\frac{\left(\varSigma \left({x}_{i}-\bar{x}\right)\left({y}_{i}-\bar{y}\right)\right)}{\sqrt{\varSigma {\left({x}_{i}-\bar{x}\right)}^{2}\varSigma {\left({y}_{i}-\bar{y}\right)}^{2}}}$$
(4)

Where: \({x}_{i}\), \({y}_{i}\): Data points for variables X and Y, \(\bar{x}\), \(\bar{y}\): Means of X and Y, r: Pearson correlation coefficient

The heatmap will use color gradients to show r, with values near +1 or −1 indicating strong positive or negative correlation, and values near 0 indicating little or no correlation.

Principal Component Analysis (PCA)

Principal Component Analysis (PCA) is a dimensionality reduction technique used to transform high-dimensional data into a lower-dimensional space while retaining as much variance as possible. It finds the principal components (PCs) that explain the most variance in the data. Key Formula (PCA Eigenvalue Decomposition):

$${Cv}=\lambda v$$
(5)

Where: C: Covariance matrix of the dataset, \({C\; v}\): Eigenvector (principal component), \(\lambda {v}\): Eigenvalue representing the variance explained by the eigenvector

Carbon emissions calculation

Based on the review of carbon emission calculation, buildings life cycle can be divided into four stages: material production, on-site installation, renovation, and dismantling48,49,50,51. Therefore, the calculation of the total carbon emissions of a building is as follows:

$$W={W}_{1}+{W}_{2}+{W}_{3}+{W}_{4}+{W}_{5}$$
(6)

where \(W\) is the total carbon emissions of building; \({W}_{1}\) is the carbon emissions in the production phase ; \({W}_{2}\) is the carbon emissions in the transportation phase; \({W}_{3}\) is the carbon emissions in the on-site installation stage; \({W}_{4}\) is the carbon emissions in the renovation stage; \({W}_{5}\) is the carbon emissions in the dismantling stage.

Production phase

The materials production phase (Conventional Construction) equation is as follows:

$${{W}_{1}=W}_{p}=\mathop{\sum}\limits_{i=1}^{n}{M}_{i}{F}_{i}$$
(7)

Where \({W}_{p}\) is the carbon emissions in the production stage; \({W}_{t}\) is the carbon emissions in the transportation stage; \({M}_{i}\) is the consumption of the i-th material (kg or m³); \({F}_{i}\) is the carbon emission factor corresponding to the i-th material (kgCO2e/unit quantity of material);

The materials production phase (Prefabricated Construction) equation is as follows52,53,54:

$${C}_{51}=\mathop{\sum}\limits_{g=1}^{n}{M}_{g}{F}_{g}$$
(8)

\({M}_{g}\) is the consumption of material for producing the g-th prefabricated component; \({F}_{g}\) is the carbon emission factor of the g-th prefabricated component (kgCO2/m³).

Transportation phase

The transportation phase (Conventional Construction) equation is as follows:

$${{W}_{1}=W}_{t}=\mathop{\sum}\limits_{i=1}^{n}{M}_{i}{D}_{i}{T}_{i}$$
(9)

Where \({D}_{i}\) is the average transportation distance of the i-th material (km); \({T}_{i}\) is the carbon emission factor per unit weight of the i-th material for the transportation mode of the i-th material(kgCO2e/kg·km).

The transportation phase (Prefabricated Construction) equation is as follows52,53,54:

$${C}_{52}=\mathop{\sum}\limits_{t=1}^{n}{M}_{t}{D}_{t}{T}_{t}$$
(10)

\({D}_{t}\) is the average transportation distance for the t-th prefabricated component (km); \({T}_{t}\) is the carbon emission factor per unit volume of the t-th prefabricated component for the transportation mode of the t-th material (kgCO2e/ m³·km).

On-site installation stage

On-site installation stage is divided into construction machinery and workers. The equation is as follows55,56,57

$${W}_{3}={C}_{j}+{C}_{r}$$
(11)
$${C}_{j}={E}_{j}{R}_{j}{F}_{j}$$
(12)
$${C}_{r}={Q}_{r}{F}_{r}$$
(13)

Where \({C}_{j}\) is the carbon emissions produced by the operation of construction machinery; \({C}_{r}\) is the carbon emissions produced by labor consumption; \({E}_{j}\) is the quantity of the j-th construction machinery; \({R}_{j}\) is the energy consumption per unit shift of the j-th construction machinery; \({F}_{j}\) is the carbon emission factor of the energy corresponding to the j-th construction machinery (kgCO2e/kwh); \({Q}_{r}\) is the labor consumption (man-days); \({F}_{r}\) is the labor carbon emission factor (kgCO2/man-day).

Renovation stage

The renovation stage in this study mainly focuses on the secondary decoration of the building. The renovation phase is divided into the material production, transportation, and installation. The equation is as follows:

$${W}_{4}={C}_{31}+{C}_{32}+{C}_{33}$$
(14)
$${C}_{31}=\mathop{\sum}\limits_{c=1}^{n}{M}_{c}{F}_{c}$$
(15)
$${C}_{32}=\mathop{\sum}\limits_{c=1}^{n}{M}_{c}{D}_{c}{T}_{c}$$
(16)
$${C}_{33}=\mathop{\sum}\limits_{x=1}^{m}{c}_{x}$$
(17)
$${C}_{x}=\mathop{\sum}\limits_{y=1}^{n}{c}_{{xy}}{Q}_{{xy}}$$
(18)

Where \({C}_{31}\) is the carbon emissions in the decoration material production stage; \({C}_{32}\) is the carbon emissions in the decoration material transportation stage; \({C}_{33}\) is the carbon emissions in the decoration material construction stage; \({M}_{c}\) is the consumption of the c-th decoration material (kg); \({F}_{c}\) is the carbon emission factor corresponding to the c-th decoration material (kgCO2e/unit quantity of material); \({D}_{c}\) is the average transportation distance of the c-th decoration material (km);, \({T}_{c}\) is the carbon emission factor per unit weight of the c-th decoration material or the transportation mode of the c-th decoration material(kgCO2e/kg·km). \({C}_{x}\) is the carbon emissions generated by the x-th inventory in the decoration construction stage; \({c}_{{xy}}\) is the volume of work for the y-th quantity within the x-th inventory in the decoration construction stage, \({Q}_{{xy}}\) is the carbon emissions generated per unit for the y-th quantity within the x-th inventory in the decoration construction stage (y = 1, 2, 3,…, n).

Dismantling stage

For comparative analysis of the carbon emissions per unit, elements such as building area, building height, floor-to-floor height, number of residential units, and usable area can be selected. Based on a review of previous research, this paper chooses to use the carbon emission per unit volume of the building to compare the carbon emission intensity of 55 Hanting hotels. The characteristic of carbon intensity is the carbon emission per unit building area. Therefore, the calculation formula for the carbon emission intensity per unit volume is as follows:

$$P=\frac{W}{V}$$
(19)

Where \(P\) is carbon emission intensity per unit volume of the building(kgco2/m³), V is the volume of building (m³).

Data sources

The research subject of this study is all Hanting hotels in Hangzhou. Data sources including online hotel reservation platforms such as Ctrip, Dianping, and Qunar. Currently, the mainstream methods for data collection include using Python for rule-based collection and using web crawler tools for collection. As of September 30, 2014, Hanting Hotels had 1,547 hotels in 282 cities of China, forming a densely distributed hotel network system. By January 2024, Hanting Hotels had spread to over 1,000 cities in China with more than 3,600 stores. The research subject of this study is the 55 Hanting Hotels within the Hangzhou. To comprehensively identify the factors influencing carbon emission efficiency per unit volume in buildings, we conducted a detailed analysis across two main categories, four sub-categories, and 23 smaller factors. These include the Building Geometry Factors category, which consists of Length/Area/Volume Factors (8 sub-categories), Number Factors (2 sub-categories), and Ratio Factors (5 sub-categories); and the Carbon Emission Efficiency category, which includes Carbon Emission Factors (8 sub-categories).