Research on the Optimization Design of the Atrium Space Form in University Libraries Based on the Coupling of Daylighting and Energy Consumption

Abstract

The atrium, as the core space of modern university libraries, is crucial for providing ample natural lighting and creating a comfortable spatial experience. It is also key to achieving the building’s green and low-carbon goals. However, designing the atrium of a university library faces a significant challenge: finding the right balance between ensuring good natural lighting and effectively reducing the energy consumption of the air conditioning system. This study aims to explore this balance and provide architects with various feasible design schemes. Firstly, a parametric typical model of the atrium space was established by researching 36 university libraries. Based on the Grasshopper platform in Rhino, the typical model was simulated for natural lighting and energy consumption, and the Wallacei plugin was used to couple the optimization parameters of the typical model with the optimization target parameters. The multi-objective optimization experiment of the typical model was carried out with the objectives of maximizing spatial daylight autonomy and the percentage of useful daylight illuminance, as well as minimizing air conditioning energy consumption. The experiment generated 2000 optimization solutions, and the analysis of the historical solution set revealed the complex non-linear relationship between optimization parameters and performance indicators. Moreover, three Pareto optimal solutions were selected as representative design schemes, providing valuable references for architects when designing the spatial form of the atrium.

1. Introduction

1.1. The Natural Lighting and Air Conditioning Energy Consumption of the Atrium

The atrium is the core space of modern university libraries and an essential place for teachers and students to learn and communicate [1]; it is often affected by the intense solar radiation and high temperatures typical of subtropical regions, which can lead to a decline in the quality of the light environment and an increase in the energy consumption of the air conditioning system [2,3]. Currently, the design of the atrium relies on the personal experience of architects, which limits the maximization of the physical performance of the atrium; at the same time, due to the progress of interdisciplinary collaboration and simulation methods, the design of the atrium requires further scientific research in balancing natural lighting and reducing air conditioning energy consumption [4]. Therefore, how to effectively utilize natural lighting and reduce air conditioning energy consumption in the library atrium’s design has become a critical issue that needs to be resolved in the current library space design.

Using theoretical analysis and software simulation as tools, in-depth research into the design methods of atriums can achieve more optimized architectural performance [5,6]. At the same time, thanks to the advancement of computer and machine learning technologies, the quantitative analysis of building performance has developed rapidly, and performance-driven computer-aided design methods will play an essential role in architectural design [7,8]. In the research on university library atriums, Wu et al. [9], based on performance simulation software such as Ladybug and Honeybee, explored the impact of the spatial form of university library atriums and the daylighting skylights on the natural lighting of the atriums. Wu et al. [10] investigated the effects of factors such as the ratio of skylight area and the height-to-width ratio on library atriums’ light and thermal performance, proposing design strategies for atrium space driven by light and thermal performance. In addition, some scholars have studied the daylighting and energy consumption of atriums in office buildings [11], commercial buildings [12,13], and hotel buildings [14,15] and proposed corresponding atrium design strategies. Mohsenin et al. [16], with the climate of Climate Zone 3 in the United States as the background, combined experimental simulation and scaled model methods to study the impact of the Well Index on atrium daylighting, providing valuable references for architects in atrium design. Pang et al. [14] used the method of CFD simulation to explore the influence of complex geometric parameters of the atrium on energy consumption of the hotel atrium, which provides a design strategy for the energy-saving design of hotel atrium. Mahsa Rastegari et al. [17] took the atrium of office buildings in Tehran as the research subject. They simulated the effects of the Well Index and the aspect ratio of the atrium on daylighting. Their research results indicate that the best daylighting effect is achieved when the Well Index is 1.3 and the aspect ratio is 0.5. B. Calcagni et al. [18] used the Radiance software simulation method to study the impact of the shape, orientation, and reflectivity of the atrium surface on the daylighting of adjacent spaces. They suggested that future research should comprehensively analyze the atrium’s thermal and optical environment.

In general, there are still the following issues in the research on library atriums: (1) Most studies only focus on the impact of individual performance, such as the light environment and thermal environment on the design of the atrium, neglecting the coupling of multiple performance objectives and the relatively low efficiency of manual software simulation methods. (2) Most studies focus on the atriums of office and commercial buildings, with less attention given to the atriums of library buildings.

1.2. Multi-Objective Optimization

Studying atrium physical performance through software simulation could be more efficient. An increasing number of researchers have come to recognize that the optimized design of atriums is a complex issue that requires a comprehensive consideration of the impact of multiple optimization indicators. As a result, researchers are gradually adopting multi-objective optimization methods for atrium performance research [13,17,19,20,21,22]. Multi-objective optimization algorithms aim to find solutions that can simultaneously achieve optimal results in the face of multiple objective functions within a given search space; these solutions are known as Pareto optimal solutions [11,23,24]. Chaturvedi [25] used multi-objective optimization methods to study residential buildings, generating preferred schemes that reduced the annual energy consumption of the original residences by 9.24%, and the number of cooling set points unmet has been reduced by 45% compared to the base case. Xue et al. [26] explored the shading form of atriums through multi-objective optimization methods to obtain the best shading parameters and revealed the linear relationship between shading form and daylighting and energy consumption, providing a reference for the design of commercial atriums.

The reliability of the Wallacei plugin in multi-objective optimization has been verified in studies across various fields [27,28,29,30]. At the planning and design level, Li et al. [31], in response to the planning and design of new rural areas in China, proposed a community form multi-objective optimization framework based on energy consumption and thermal comfort models using the Wallacei plugin, generating a set of Pareto optimal solutions with better comprehensive performance. Liu et al. [30] used the Wallacei plugin to study the sunlight, energy consumption, and photovoltaic performance of urban blocks, constructing a multi-objective optimization framework for the design of urban block forms, and the solutions have significantly improved in all three optimization objectives. Bai et al. [28] focused on urban negative spaces. They used Wallacei for generative optimization design research, providing architects with various new design ideas in the early design stage of optimizing urban negative spaces. At the architectural optimization design level, Wu et al. [27] used the Wallacei plugin to explore residential building design methods with the goals of minimizing energy demand, maximizing photovoltaic power generation, and minimizing investment costs, further proving that multi-objective optimization methods can resolve conflicts between different optimization indicators. Ji et al. [4] used the Wallacei plugin for multi-objective optimization of natural daylighting and energy intensity in residential buildings, and the results showed that the preferred schemes had improved performance in all aspects. Multi-objective optimization algorithms provide strong support for architects in the decision-making process in the early stages of design, helping architects better balance various design factors [32,33,34]. In summary, Multi-objective optimization methods are widely applied in many fields, such as urban planning and architectural design, demonstrating great optimization potential in multi-performance coupling research. Future studies on atriums will involve the coupling of multiple performance objectives; therefore, adopting a multi-objective optimization research method can better balance the relationships between multiple performance objectives, enhancing the accuracy and efficiency of simulation optimization.

This article aims to achieve the following two objectives: (1) By relying on multi-objective optimization methods and integrating multiple simulation platforms, construct a methodological framework for the parametric design of university library atriums, daylighting and energy consumption simulation, and multi-objective optimization; (2) Taking the subtropical region as the research area, establish a typical model, set the parameters for the atrium form and optimization objectives, and conduct multi-objective optimization experiments to reveal the impact mechanism of the form optimization parameters and daylighting energy consumption of library atriums in subtropical regions, and selected three optimized solutions for in-depth analysis.

2. Methodology

2.1. Technical Route

This study employed Ladybug and Honeybee as the core tools for performance simulation, which are plugins based on the widely recognized computational engines of Radiance and Energy-Plus, the industry-standard energy analysis software. Using the Wallacei plugin enabled the effective integration of parametric models with performance simulation results, making the optimization process more efficient and accurate. The specific technical approach is divided into three stages (Figure 1):

(1)

Establishment of a typical model: We conducted a nationwide field survey of 36 university library atriums and collected and analyzed data to establish a typical parametric atrium model based on this information.

(2)

Simulation of the atrium’s physical environment: We performed detailed building performance simulations for the typical atrium model using the Ladybug and Honeybee plugins. The simulation results included the spatial daylight autonomy (sDA), the percentage of useful daylight illuminance (UDI), and the air conditioning energy consumption (E_C), providing a quantitative basis for assessing the daylighting quality and energy consumption level of the atrium.

(3)

Multi-objective optimization: Furthermore, we used the Wallacei plugin in conjunction with genetic algorithms to conduct multi-objective optimization of the atrium design. In this stage, we set optimization parameters and objectives and generated a set of Pareto optimal solutions through an iterative process. These solutions represent design schemes that balance natural daylighting and air conditioning energy consumption, and the best atrium morphological design schemes were further selected through performance analysis.

2.2. Construct the Typical Analytical Model

2.2.1. Survey Data Collection

The on-site and online survey was conducted from June 2023 to April 2024, focusing on the morphology and dimensions of the atriums in 36 university libraries in China. The purpose of the survey was to collect data to construct a typical model for subsequent analysis. The specific data collected included the floor-to-ceiling height (h), number of floors (c), and the length and width of the atrium (L₂ and L₁), as well as the width of the open spaces surrounding the atrium (w).

Table 1. List of atrium dimensions for each field research sample.

Name of Research Campus	h/m	w/m	L2/m	W2/m	Atrium Location Diagram
South China Agricultural University	4.5	8	48, 24	24, 16
South China Normal University (Shipai Campus)	4.5	8	16	16
Jinan University	4.5	4	48	32
South China University of Technology	5.4	4	36, 18	9, 9
Guangdong University of Technology	3.9	8	24	32
Guangzhou University	4.2	8	40	21
South China Normal University (University Town Campus)	3.6	8	24	18
Guangzhou University of Chinese Medicine	4.8	8	12	9
Xinghai Conservatory of Music	3.9	2	20	20
South China University of Technology (Wushan Campus)	4.5	6	26	15
Guangdong Pharmaceutical University	4.2	8	40	16
South University of Science and Technology of China	5.4	8	46	10
Southern Medical University	5.4	8	16	12
Shantou University	4.2	8	36	28
Guangzhou Medical University	4.8	6	18	18
Guangdong University of Foreign Studies (University Town Campus)	4.2	2	40	30
University of Foreign Studies (North Campus)	4.2	6	24	24
South China University of Technology (University Town Campus)	4.5	8	73	34
Chengdu University	4.2	8	32	32
Dongguan Vocational and Technical College	3.6	4	35	20
Guangdong University of Finance and Economics	3.2	8	38	38
Guangdong Academy of Fine Arts	4.2	4	27	13
Dalian University of Technology	4.8	10	38	24
Tsinghua University (Li Wenzheng Hall)	3.6	8	25	20
University (Law School)	3.6	8	16	16
Shenzhen University	4.2	2	20	20
Tianjin University	5.4	8	74	74
Wuhan University of Technology	3.6	8	36	27
The Chinese University of Hong Kong	3.4	4	16	10
Central University of Finance and Economics	4.5	8	40	24
Communication University of China	4	6	14	10
Nankai University	4.8	8	28	10
North China University of Technology	3.6	8	40	16
Zhejiang College of Tongji University	3.6	8	27	20
Anshun Polytechnic	5.7	8	24	24
College of Science and Technology, Xinjiang University	5.2	8	20	20

displays some of the morphological information of the atriums in the surveyed university libraries.

The field research data indicate that the floor plans of university libraries tend to utilize simple geometric shapes, with the rectangular layout being the most prevalent, accounting for 67% of the cases involving 24 examples. In terms of atrium design, there are various forms, including unidirectional, bidirectional, tridirectional, and tetra-directional atriums (Figure 2). According to the survey data, the tetra-directional atrium is the most common in university libraries, representing 72% of the cases involving 26 examples.

Based on the survey data, we found that in the design of library atriums, the H-shaped section (Figure 3b) is the most common, accounting for 83% of the cases involving 30 examples. In contrast, the other section forms shown in Figure 3a,c are less common, with a combined total of only 17%. As for the design of skylights, flat-top skylights are widely popular due to their structural simplicity and efficient daylighting performance, accounting for 58% of the cases involving 21 examples.

Figure 4 presents the average dimensions of the atriums surveyed: the average floor-to-ceiling height and the width of the open space are 4.3 m and 6.5 m (Figure 4a), respectively. The average lengths of the longer and shorter sides of the atriums are 31 m and 21 m (Figure 4b), respectively. Among the buildings surveyed, those with four stories have the highest proportion, accounting for 28%.

2.2.2. Establish Typical Model

The field survey of 36 university libraries aims to establish typical models for atriums in libraries, which requires considering various factors such as regional climate, culture, and user characteristics. Therefore, the survey cases are focused on the Chinese region. Suppose other regions worldwide need to research the daylighting, energy consumption, and other performance aspects of atriums. In that case, they can also establish typical models based on the research methods presented in this paper.

By analyzing the floor plans of 36 university libraries, we found that the layout of library buildings typically consists of 3 main parts: the atrium, the open space surrounding the atrium, and the reading rooms, with the depth of the reading rooms mostly 18 m. This study focuses on the four-sided atriums in university library buildings with a rectangular floor plan. Fixed parameters, including the building floor dimensions (78 m by 68 m), floor-to-ceiling height (4.5 m), number of floors (4), skylight type (flat-top skylight), and the width of the open space surrounding the atrium (6 m) were set for the typical model.

According to relevant Chinese building standards [35,36], the area of skylights in public buildings should not exceed 20% of the building’s footprint area, and the area of a single fire compartment in multi-story buildings should not exceed 5000 square meters. Therefore, we have set the variable parameters as the skylight plan dimensions (W₂ × L₂ = 600 square meters) and the atrium plan dimensions (0 < W₁ × L₁ ≤ 20% S). The specific parameter settings of the typical and three-dimensional models are shown in

Table 2. Parameters setting for typical model.

	Model Parameters	Notes
Plan Dimensions	78 m × 68 m	Fixed Parameters
Floor-to-ceiling Height (h)	4.5 m
Number of Floors (c)	4 floors
Skylight Form	Flat-top skylight
Open Space Distance (w)	6 m
Atrium Plan Dimensions	W2·L2 = 600 m2	Variable Parameters (W1, W2, L1, L2)
Skylight Plan Dimensions	0 < W1·L1 ≤ 20%S

and Figure 5a,b.

2.3. Research Region

To establish climatic parameters for subsequent optimization analysis, this study selected the subtropical region of China as the scope of research. In this area, the intensity of solar radiation is high in summer and relatively lower in winter. The sun reaches its peak value in summer, which lasts for a long time, with the average temperature of the hottest month ranging from 20 to 29 degrees Celsius, leading to intense solar radiation and high-temperature weather in summer [35]. This region’s intense solar radiation and long daylight hours impact the thermal comfort and lighting conditions inside buildings. Therefore, natural daylighting and air consumption have become the main assessment indicators when comprehensively evaluating the indoor environment of buildings. Guangzhou, as a large city with representative climatic characteristics of this region, has strong solar radiation from May to September, with the highest solar radiation value reaching 1024 W/m² and the average solar radiation value being 150 W/m² [37]. At the same time, the EPW file of Guangzhou was chosen as the source of climatic data to provide a basis for simulation analysis.

2.4. Daylighting and Energy Consumption Simulation Optimization Analysis

2.4.1. Enclosure Structural Parameter Settings

The parameters of the enclosure structure significantly impact the air conditioning energy consumption of the atrium space. Following the requirements of relevant building codes [36,38], we have set the parameters for the enclosure structure and skylight material as follows (

Table 3. Parameters setting for enclosure structure.

	Enclosure Structure	Set Value
Thermal Transmittance [W/(m2·K)]	Roof (Coating 10 mm + Waterproof Cement 15 mm + XPS 100 mm + EPS 30 mm + Reinforced Concrete 200 mm)	0.40
	Interior Walls	Adiabatic
	Exterior Walls	Adiabatic
	Floor	Adiabatic
	Skylight (6 mm HLT low-e + 12 mm Air + 6 mm Glass)	1.92
Material Reflectance	Ceiling	0.75
	Interior Walls	0.60
	Floor	0.30

and

Table 4. Skylight glass material parameter settings.

Skylight Glass Parameters (6 mm HLT low-e + 12 mm Air + 6 mm Glass)
Solar Heat Gain Coefficient	Shading Coefficient	Visible Light Transmittance Ratio	Thermal Transmittance [W/(m2·K)]
0.26	0.30	0.72	1.92

):

2.4.2. Morphological Optimization Parameter Settings

In this study, we referred to the literature where other scholars selected optimization parameters in atrium research and chose the skylight area ratio (AR, Figure 6a), height-to-width ratio (SAR, Figure 6b), profile inclination angle (θ, Figure 6c,d), and well index (WI, Figure 6a) as optimization parameters for atrium design [10,14,18,26,32,39]. The selection of these parameters aims to deeply explore how they affect the daylighting and energy consumption of the atrium, thereby guiding the optimized design of the atrium. The specific parameter settings are presented in Figure 6 shows each parameter in a diagrammatic way.

$$\mathrm{T}={\displaystyle \frac{\mathrm{W}1·\mathrm{L}1}{\mathrm{S}}}(\mathrm{S}:\mathrm{a}\mathrm{b}, \mathrm{A}\mathrm{R} \le 20\%)$$

(1)

$$\mathrm{SAR}={\displaystyle \frac{2\mathrm{H}}{\mathrm{L}1+\mathrm{L}2}}$$

(2)

$${\mathrm{\theta }}_1= {\tan }^{-1}{\displaystyle \frac{2\mathrm{H}}{(\mathrm{W}1-\mathrm{W}2)}}$$

(3)

$${\mathrm{\theta }}_1={\tan }^{-1}{\displaystyle \frac{2\mathrm{H}}{(\mathrm{L}1-\mathrm{L}2)}}$$

(4)

$$\mathrm{WI}={\displaystyle \frac{\mathrm{H}·(\mathrm{W}1+\mathrm{L}1+\mathrm{W}2+\mathrm{L}2)}{(\mathrm{W}1+\mathrm{L}1)(\mathrm{W}2+\mathrm{L}2)}}$$

(5)

$$\mathsf{\theta }={\displaystyle \frac{\mathsf{\theta }1+\mathsf{\theta }2}{2}}$$

(6)

2.4.3. Settings of Optimize Performance Indicator

Daylighting evaluation indicators are generally divided into two major categories: static daylighting evaluation indicators and dynamic daylighting evaluation indicators. Consistent with most similar studies, this research selected dynamic daylighting evaluation indicators for analysis, including spatial daylight autonomy (sDA) and the percentage of useful daylight illuminance (UDI) [40]. Considering the high air conditioning energy consumption in the atriums of libraries in subtropical areas during summer, we also introduced annual air conditioning energy consumption (Ec) as an indicator for energy consumption evaluation.

sDA measures the proportion of time in which the illuminance in a room meets the requirements for at least half of the workspace within a specified time. The higher the value of this indicator, the better the natural daylighting effect inside the room. UDI measures the proportion of time in which the illuminance on the workspace is within the suitable range [41]. According to relevant standards, the illuminance standard for reading areas is 300 lx [42]. Therefore, we set the suitable range for UDI between 300 lx and 2000 lx [41]. While meeting the daylighting requirements, a lower value of Ec reflects the superior energy-saving performance of the indoor environment.

2.4.4. Settings of Personnel and Equipment Parameters

The indoor population density and the parameters of related equipment can significantly affect daylighting and air conditioning energy consumption. Based on the requirements of relevant coding requirements [38,43], the settings for human activity and equipment parameters are shown in

Table 5. Human activity and equipment parameters.

Parameter	Setting
Occupant density (m2/person)	5
Room summer set temperature (°C)	26
Power consumption (W/m2·K)	10
Fresh air volume [m3/(h·person)]	30
COP	4.5
Test grid size (m)	2 m × 2 m
Illuminance sensor height (m)	0.75

.

2.5. Settings of Wallacei Plugin

Optimization parameters and performance indicators must be integrated into the Wallacei plugin for processing.

Table 6. Settings for Wallacei plugin.

Generation Size	Generation Count	Crossover Probability	Mutation Probability	Random Seed
50	40	0.9	0.05	1

displays the settings for parameters in the genetic algorithm, including the number of generations, population size, crossover probability, mutation probability, and random seed. After the parameter settings are completed, the Wallacei plugin is run to obtain the Pareto optimal solutions, which include model morphology, optimization parameters, and performance indicator data. The experiment generated 2000 solutions, taking 41 h, 40 min, and 26 s, with an average computation time of approximately 1 min and 33 s per individual. The optimization experiment was completed on a computer with an AMD Ryzen 5 5600X six-core @3.70 GHz processor (produced by AMD Company in China), 16 GB RAM, and an NVIDIA GeForce RTX 3060 Ti graphics card.

3. Result

The 2000 solutions generated by the experiment are displayed in a parallel coordinates plot (Figure 7), where the vertical axis represents the range of optimized performance indicators. Each line segment represents a solution, with its color gradient from blue to red, symbolizing the completion of the iteration process. According to the plot, we can observe that the range of the complete spatial daylight autonomy (sDA) in the historical solution set is between 0.41 and 0.68, the range of the useful daylight illuminance (UDI) is between 0.24 and 0.36, and the range of the annual cooling energy consumption (E_C) extends from 56.39 kWh/m² to 66.43 kWh/m².

Figure 8 displays a selection of the generated optimization solutions, providing detailed optimization parameters and performance indicator data for these solutions.

4. Discussion

4.1. Analysis of Interrelationship between Optimization Parameters and Performance Indicators

The following discussion will delve into the atrium design schemes obtained from the experimental simulation. We have utilized Origin software (2022) for data visualization to display the interrelationship between optimization parameters and performance indicators. Figure 9 illustrates the relationship between the optimization parameters and performance indicators for each architectural atrium scheme during the simulation process, with each point in the graph representing a specific optimization solution.

Generally, an sDA indicator greater than 0.6 signifies good natural daylighting within the interior. In the historical solution set, when sDA reaches 0.68, the atrium’s natural daylighting effect is optimal, with the corresponding atrium design parameters being WI = 0.55, AR = 0.19, θ₁ = 53°, θ₂ = 95°, and SAR = 0.42. Figure 9 shows that WI, θ, and SAR generally exhibit an inverse relationship with the sDA, while AR shows a direct proportionality with the sDA. To achieve ample natural daylighting in the atrium, the preferable range for WI is 0.47–0.60 (see Figure 9a); for AR, it is 0.14–0.19 (see Figure 9b); for θ, the optimal range is 68°–85° (see Figure 9c), where the atrium section often takes a “V” shape; and for SAR, the preferable range is 0.28–0.68 (see Figure 9d).

The higher the value of the UDI indicator, the better the daylighting effect inside the room. The range of UDI in the experimental simulation results is 0.24–0.36, which is relatively low. The reason is that the open space surrounding the atrium, as part of the simulation area, is too wide, leading to insufficient illuminance of less than 300 lx in some local simulated areas, thus causing the overall UDI value to be low. Based on the UDI simulation results, the study selected the solution set when the UDI indicator exceeds 0.34. The effective natural daylighting inside the room is good at that point.

Analysis of Figure 10 shows that when the optimized indicator UDI is 0.36 in the historical solution set, the effective natural daylighting in the atrium is the best, with the atrium design parameters being WI = 0.49, AR = 0.16, θ₁ = 54°, θ₂ = 92°, and SAR = 0.36. Figure 10 shows that WI, θ, SAR, and sDA indicators generally have an inverse relationship, while AR and sDA indicators generally show a direct proportionality. To achieve sufficient effective natural daylighting, the preferable range for WI is 0.49–0.63 (Figure 10a); for AR, it is 0.09–0.19 (Figure 10b); for θ, the preferable range is 72°–89° (Figure 10c), where most atrium sections take a “V” shape; the preferable range for SAR is 0.3–0.68 (Figure 10d).

The lower the value of the E_C, the better the energy-saving effect of the indoor environment. In the experimental simulation results, the E_C indicator ranges from 56.39 kWh/m² to 66.43 kWh/m². Based on the simulated air conditioning energy consumption data, the study selected the solution set with Ec below 62 kWh/m² as the preferred solution.

In the solution set, when the optimized Ec indicator reaches 56.39 kWh/m², the air conditioning energy consumption of the atrium is at its lowest. The corresponding atrium design parameters at this time are WI = 0.59, AR = 0.07, θ₁ = 84°, θ₂ = 133°, and SAR = 1.37. Analysis reveals that WI, θ, and SAR generally show an inverse relationship with the EC indicator, while AR generally shows a direct proportionality with the Ec indicator. To keep the air conditioning energy consumption of the atrium at a lower level, the recommended range for WI is 0.55–0.72 (see Figure 11a); for AR, it is 0.07–0.14 (see Figure 11b); for θ, the recommended range is 81°–108° (see Figure 11c), where the atrium section mostly takes an “A” shape, which helps reduce energy consumption; the recommended range for SAR is 0.38–1.47 (see Figure 11d).

4.2. Selected Optimized Solutions Analysis

This study selected three representative optimized solutions for in-depth analysis based on the optimality and balance of natural daylighting and air conditioning energy consumption.

As shown in Figure 12a, in the 3D model diagram of solution NO.1143, the atrium dimensions are L₂ = 24 m, W₂ = 25 m, and the top skylight dimensions are L₁ = 20 m, W₁ = 32 m, with a skylight area ratio of AR = 0.11. The section inclination angles are θ₁ = 98° and θ₂ = 78°, respectively, which deviate little from 90°, which indicates that under these design parameters, the atrium achieves a good balance in the three optimization indicators, providing ample natural daylighting while maintaining low air conditioning energy consumption (see Figure 12b).

Figure 13a displays the 3D model diagram of solution NO.1762, with the atrium dimensions of L₂ = 28 m, W₂ = 22 m, the top skylight dimensions of L₁ = 50 m, W₁ = 14 m, and the skylight area ratio of AR = 0.18. The section inclination angles are θ₁ = 54° and θ₂ = 95°, giving the atrium a “V” shape in the east–west direction. This design significantly enhances the natural daylighting performance of the atrium (see Figure 13b), with the sDA value being the highest recorded in the solution set and the UDI value outperforming other schemes. However, it is important to note that the E_C value of this scheme is also close to the highest in the historical solution set, implying relatively high energy consumption for the atrium.

Figure 14a presents the 3D model diagram of solution NO.1864, with the atrium dimensions of L₂ = 40 m, W₂ = 15 m, the top skylight dimensions of L₁ = 62 m, W₁ = 14 m, and the skylight area ratio of AR = 0.16. The section inclination angles are θ₁ = 55° and θ₂ = 92°, giving the atrium section a “V” shape in the east–west direction. According to the analysis in Figure 14b, compared to solution NO.1143, the atrium section inclination angle in solution NO.1864 has been reduced, significantly enhancing the UDI in the simulated area and reaching the maximum value recorded in the solution set.

5. Conclusions and Future Work

As global warming continues to intensify, the temperatures in subtropical regions will be in a state of constant rise during the summer, which will have a significant impact on the energy consumption of buildings in these areas. Therefore, it is crucial to conduct coupled research on the performance of building daylighting, energy consumption, and carbon emissions and summarize optimized design parameters and strategies through numerical analysis.

This study’s main contributions are as follows: (1) The study proposed a parametric design optimization method for library atrium spaces that couples natural daylighting with air conditioning energy consumption; (2) The study obtained multiple solutions’ optimization parameters and indicators through multi-objective optimization experiments, revealing the complex non-linear relationship between optimization parameters and performance indicators; (3) From the 2000 solutions generated by the experiments, the study selected three Pareto optimal solutions, which can provide multiple sustainable options for the early stages of architectural design, enhancing the efficiency of architects. The study concludes the following:

• WI, θ, and SAR show an inverse relationship with sDA, UDI, and E_C indicators, while AR shows a direct proportionality with these indicators. When WI = 0.55, AR = 0.07, θ₁ = 53°, θ₂ = 95°, and SAR = 0.42, sDA reaches its maximum value of 0.68, indicating the optimal natural daylighting effect in the atrium.
• When WI = 0.55, AR = 0.19, θ₁ = 53°, θ₂ = 95°, and SAR = 0.42, the sDA reaches its maximum value of 0.68, indicating the best natural daylighting effect in the atrium. When WI = 0.49, AR = 0.16, θ₁ = 54°, θ₂ = 92°, and SAR = 0.36, UDI reaches its maximum value of 0.36, indicating the best effective natural daylighting in the atrium; when WI = 0.59, AR = 0.07, θ₁ = 84°, θ₂ = 133°, and SAR = 1.37, E_C is minimized to 56.39 kWh/m², indicating the lowest air conditioning energy consumption in the atrium.
• Increasing the length of the atrium’s east–west skylights and reducing the profile aspect ratio (SAR) can significantly enhance natural daylighting in the atrium; when the profile inclination angle is less than 90°, reducing the east–west section inclination angle of the atrium can improve indoor natural daylighting; when the section inclination angle is greater than 90°, increasing the north–south section inclination angle of the atrium can effectively reduce indoor energy consumption.

Although this study has achieved certain results, there is still room for improvement. First, the study determined a typical model by surveying the atriums of university libraries in China. Future research can expand the scope of the survey to summarize more comprehensive and universally applicable typical models. Secondly, current research mainly focuses on coupling the light environment and thermal environment in library atriums. Future research can couple multiple performance evaluation indicators such as daylighting, energy consumption, carbon emissions, wind environment, and indoor air quality to achieve a more comprehensive optimization. Thirdly, the determination of optimization parameters was based on reading a large number of the related domestic and international research literature. In the future, sensitivity analysis can be introduced to accurately assess the impact of these optimization parameters on performance indicators, thereby improving the efficiency of the optimization process and the accuracy of the results. Through these improvements, we can further enhance architectural design’s scientific and practical nature and provide strong support for realizing more efficient and environmentally friendly library architectural design.

Table 7. List of abbreviations and acronyms used in this article.

Abbreviation	Explanation
sDA	The spatial daylight autonomy
UDI	The percentage of useful daylight illuminance
EC	The air conditioning energy consumption
h	Floor-to-ceiling height
c	Number of floors
L2	East–west atriums length
W2	North–south atriums length
w	Open space distance
H	Floor-to-ceiling height
L1	East–west skylight length
W1	North–south skylight length
S	The base area
a	The north–south length of the building
b	The east–west length of the building
AR	The skylight area ratio
SAR	Height-to-width ratio
θ1	The east–west section inclination angle of the atrium
θ2	The north–south section inclination angle of the atrium
θ	Section inclination angle
WI	The well index
CFD	Computational fluid dynamics

shows the abbreviations and explanation of the studies, which will help readers better understand the article.