The Influence of Traditional Residential Skywell Forms on Building Performance in Hot and Humid Regions of China—Taking Huangshan Area as an Example

Abstract

Skywells are crucial for climate regulation in traditional Chinese dwelling architecture, exhibiting significant variations across climatic regions. This study focuses on humid–hot China, using Huangshan, to explore skywell parameters’ impact on thermal comfort and energy efficiency. Field research on 24 buildings in the World Heritage Site Xidi, Hong Villages, and Chinese Historical Pingshan Village, combined with Grasshopper’s Ladybug tool, established a parametric model. Using orthogonal design, performance simulation, and Python-based machine learning, six morphological parameters were analyzed: width-to-length ratio, height-to-width ratio, orientation, hall depth, wing width, and shading width. After NSGA-II multi-objective optimization, the summer Percentage of Time Comfortable (P_TC) increased by 5.3%, 38.14 h; the Universal Thermal Climate Index (UTCI) relatively improved by 2%; energy consumption decreased by 8.6%, 0.14 kWh/m²; and the useful daylight illuminance increased by 28%, 128.4 h. This confirms the climate adaptability of courtyard-style buildings in humid–hot China and identifies optimized skywell parameters within the study scope.

1. Introduction

In 2018, data from the International Energy Agency showed that total energy consumption in buildings accounted for 40% of global energy consumption. In 2022, total energy consumption in buildings in China accounted for 44.8% of the country’s total energy consumption, with total energy consumption from building operations accounting for 21.7% of the country’s total energy consumption. In 2022, the Ministry of Ecology and Environment of China released the “National Strategy for Climate Change Adaptation 2035.” The rate of temperature rise in China is higher than the global average, and it is expected that global warming will continue through the middle of this century [1]. Climate warming has significantly reduced summer thermal comfort in residential buildings worldwide, thereby increasing the demand for temperature regulation [1]. In 2022, in China, during the operational phase, energy consumption in residential buildings accounted for 58% of total building energy consumption, with carbon emissions making up as much as 79%. Among them, traditional dwellings accounted for 32% of the total residential building area, equivalent to 19.5 billion m² [2]. Researching the optimization of the building performance of traditional dwellings is an important means to reduce energy consumption and improve dwelling comfort.

Traditional Chinese dwellings with courtyards mainly include courtyard-style dwellings and skywell-style dwellings. The width of the skywell typically ranges from 2.8 to 4.5 m, which is only one-third to one-half of the scale of northern courtyards in China [3]. Courtyard-style dwellings are commonly distributed in the cold northern regions of China, whereas skywell-style dwellings are commonly distributed in the hot and humid southern regions. In these hot and humid regions, where the climate is characterized by intense heat, high humidity, and strong solar radiation during summer, the traditional architectural design of skywells is particularly focused on addressing these environmental challenges [4]. Figure 1 shows different types of courtyard buildings in humid and hot regions during summer. The skywell spaces in these buildings often provide better environmental conditions than the outdoors during many periods of the day. Additionally, as a climate buffer layer, the skywell space helps to weaken or delay the impact of the outdoor climate on the main living areas to some extent. The skywell space plays a crucial role in climate regulation through shading, ventilation, and daylighting [5]. Understanding the interaction between thermal comfort and skywell design factors is key to passively improving building thermal comfort. Therefore, optimizing the morphology of skywell dwellings is the most effective method to enhance building performance in these regions.

In recent years, research on skywell design factors has mainly focused on several key categories: architectural form and skywell form factors, envelope factors, and window factors, among others. In the domain of courtyard building form factors, the parameters studied include plan aspect ratio, height-to-width ratio, depth of the main house, orientation, geometric shape factors, and various other elements (as shown in

Table 1. Architectural types, design parameters, research goals, and climate zones in existing studies (made by the authors).

Vintages	Author	Design Parameters	Objectives	Building Type	Climate Region
2015 [8]	Manioğlu, G.; Oral, G.K.	Width-to-length ratio (W/L)	Indoor thermal comfort	Courtyard house	Dry heat region
2015 [4]	Amirhosein Ghaffarianhoseini	Vegetation, wall orientation, height, albedo of courtyard	Tmrt and PTC (outdoor)	Courtyard public buildings (monasteries)	Hot and humid region
2016 [9]	Liu Sheng	Skywell height; length, width, and length of living space	Indoor natural ventilation	Skywell-style houses (Xiangxi “Yinzi” houses)	Hot and humid (hot summer and warm winter) region
2017 [10]	Farzaneh Soflaei	Urban texture, courtyard form, orientation, socio-cultural context, building materials, wall colors	Indoor comfort and energy efficiency	Courtyard houses (Iranian and Chinese traditional courtyards)	Dry heat region, dry cold region
2018 [11]	Rodríguez-Algeciras, J	Orientation, height, materials	Outdoor thermal comfort	Courtyard houses (traditional courtyard buildings)	Dry heat region
2022 [12]	Li Xueping	Wall materials, window materials	Indoor thermal comfort	Skywell houses (Huizhou style houses)	Hot in summer and cold in winter region
2022 [13]	Cheng He	Orientation, window U-value	Indoor thermal comfort	Office building	Hot in summer and cold in winter region
2022 [14]	Victoria Patricia López-Cabeza	Sunshade	UTCI (outdoor)	Courtyard houses (courtyard town houses)	Mediterranean climate region
2023 [7]	Chen Zhengshu	Building form, envelope, glazing, external factors	Indoor lighting and thermal comfort	Educational buildings	Cold region
2023 [15]	Eduardo Diz Mellado	Height-to-width ratio (WLR), orientation, yard geometry	Indoor cooling energy requirements	Courtyard house	Hot in summer and warm in winter
2023 [16]	Jie Han	Spatial layout and vegetation cover	PET and UTCI (outdoor)	Libraries (public buildings)	Hot in summer and cold in winter region
2023 [17]	Zheng Zhiyuan	Skywell width and length	Indoor air velocity	Skywell-style houses (traditional houses in Huangshan)	Hot in summer and cold in winter region
2023 [18]	Zhiqing Zhao	Feng shui layout	Outdoor air speed and pressure ratio	Educational building (White Deer Cave Academy, Jiangxi, China)	Hot summers and cold, wet winters region
2023 [19]	Yu Tianqi	Building materials	Indoor thermal comfort, outdoor thermal comfort	Skywell houses (central courtyard houses)	Hot in summer and cold in winter region
2024 [20]	Ruiheng Sun	Layout form (e.g., cluster, strip, ring, radial), aspect ratio	Outdoor wind speed ratio, wind shadow area, number of vortices	Courtyard dwelling houses (courtyard village residential compounds)	Cold regions of the Northeast
2024 [21]	Shan Wu	Architectural space, materials, structures	Wind speed, temperature, light, comfort	Skywell houses (traditional houses in Anhui)	Hot in summer and cold in winter region
2024 [22]	Hao Yongchun	Skywell width, height, angle, layout	Indoor lighting	Skywell-style houses (courtyard-type wood-frame houses)	Hot in summer and warm in winter region

). For skywell envelope and window factors, past studies have mainly emphasized key design elements such as the window U-value, wall materials and structure, the ratio of skylights to roof area, shading setups, skylight shapes and sizes, and the thickness of external insulation boards [7]. Among other uncategorized factors, the most significant one is the green coverage ratio. Based on a review of existing research, the selected key design factors include the aspect ratio (WLR: W/L), height-to-width ratio (HWR: H/W), orientation (OR), depth of the main house (HD), width of the side rooms (WW), wall U-value (thermal conductivity), eaves overhang coefficient (SW), and skywell green coverage rate. The research goals for skywell-style dwellings mainly focus on indoor and outdoor thermal comfort, daylighting, wind speed, energy consumption, etc., with most studies being single-objective research and some being multi-objective optimization, as shown in Table 1.

In the field of architectural research, Orthogonal Design of Experiments (ODOE) and related statistical analysis methods have become important research tools for exploring building thermal comfort optimization and strategies for improving thermal comfort. In recent years, many studies have cleverly applied the ODOE framework, combined with statistical techniques such as analysis of variance (ANOVA), orthogonal post hoc range analysis, linear estimation, and multivariate regression models, to analyze the impact of various design factors on building performance. Guoxiang Huang’s [23] research (2017) focused on the impact of street canyon types on building cooling and heating comfort. Through the integrated application of ODOE and linear estimation methods, the study revealed the connection between street morphology and thermal comfort needs. Shuhan Yang [24] focused on residential areas in northern China, systematically evaluating the contribution of key factors such as building layout, pavement layout, and vegetation layout to summer thermal comfort. Subsequently, Shanguo Zhao [25] further expanded the application scope of ODOE by using orthogonal post hoc range analysis techniques to explore the significant impact of cool roof thermal parameters on building thermal comfort. These studies fully demonstrate the powerful potential of orthogonal experimental design and related statistical analysis methods in building technology research.

In 2022, Wu, Haoran and Zhang, Tong [26] applied the multi-objective optimization (MOO) method, combining parametric modeling, building performance simulation (such as EnergyPlus and Radiance), and genetic algorithms (SPEA-2 and HypE), focusing on the integrated impact of parameters such as openable window area ratio (OWR), window-to-wall ratio (WWR), solar heat gain coefficient (SHGC), shading depth, and wall thickness. They studied the co-optimization problem between energy efficiency, visual comfort, and thermal comfort performance of building envelopes in China’s hot summer and cold winter climate zone [26]. Sharma, Shubhkirti, and Kumar, Vijay, reviewed the evolution, current status, and future development direction of multi-objective optimization (MOO) techniques, focusing on the performance comparison and application areas of evolutionary algorithms (such as NSGA-II, SPEA2, and MOEA/D) and swarm intelligence algorithms (such as MOPSO, MOACO, and MMPOA), covering over ten fields including energy, data mining, and mechanical engineering [27]. In 2024, Ding Zhikun and Wang Zhan used BIM technology and the MC-NSGA II algorithm, integrating building performance simulation (Design Builder) and machine learning (BP neural networks), to study the multi-objective optimization of envelope retrofitting in existing public buildings, covering energy consumption, carbon emissions, thermal comfort, and economic factors [28]. The feasibility of multi-objective optimization in building performance optimization has been validated in previous studies.

Existing research provides many factors that can be studied and offers a variety of available research tools and methods. However, in specific research fields, much attention has been given to the role of morphological parameters in regulating the microclimate, but the core design elements of skywell-style dwellings that affect thermal comfort and building energy consumption have not been clearly identified. Moreover, most studies only analyze either the outdoor thermal environment or the indoor thermal environment, overlooking the integrated effect of the space formed by the hall and skywell in skywell-style dwellings on thermal buffering and passive energy saving.

This study focuses on the building performance of traditional dwellings in hot and humid regions, systematically analyzing factors such as the skywell aspect ratio, height-to-width ratio, skywell orientation, depth of the main house, width of the side rooms, eaves overhang coefficient, wall U-value, and the skywell naturalization index. The study aims to identify which of these influencing factors are the main determinants of the performance of such dwellings and to uncover the impact patterns of the key factors on building performance. Energy consumption (E), Universal Thermal Climate Index (UTCI), Percentage of Time Comfortable (P_TC), and useful daylight illuminance (UDI) are selected as optimization objectives. Through simulations, the study quantifies the microclimate regulation and energy-saving effects of different design schemes, proposes optimized design parameters, and reveals the balance mechanism between comfort, energy consumption, and daylighting under a cooling-first strategy in skywell-style dwellings during summer. This study achieves the optimization of building performance in climate-adaptive design for traditional dwellings, providing valuable decision-making and design insights for the renovation of traditional skywell-style dwellings in hot and humid regions.

2. Materials and Methods

2.1. Research Framework

As shown in Figure 2, the framework of the study proposed in this research is demonstrated.

2.2. Study Area and Target Audience

In tropical humid regions, summer temperatures are relatively high, with the average temperature in the hottest month exceeding 25 °C. The annual average relative humidity is also high, typically ranging from 70% to 80%. Huangshan is one of the representative cities in China’s tropical humid regions. As shown in Figure 3, Huangshan’s annual average temperature is 16.3 °C, and the annual average relative humidity is 78%. The city experiences five months each year with the average maximum temperature exceeding 30 °C. On the summer solstice, the solar altitude at noon reaches its lowest value of 82°02′. Under such humid and warm conditions, with a long summer and no severe cold, the passive energy-saving design of dwelling buildings focuses on summer heat insulation [29]. This study selects three villages in the Huangshan region, with Xidi and Hongcun being World Heritage Sites, and Pingshan being a famous historical and cultural village in China. This study focuses on three well-preserved and strictly protected villages in the Huangshan region. As shown in Figure 4, these villages were all established during the Ming and Qing dynasties, with their architectural complexes intact. They represent the most iconic traditional skywell-style residences in regions characterized by hot and humid conditions.

Based on the village floor plan, sample points were set using a random sampling method. The survey was conducted by combining traditional craftsmanship with modern technology: through repeated on-site observations, manual measurements (using tape measures and laser rangefinders), sketches, and detailed textual and photographic documentation, supplemented by drone aerial photography to obtain bird’s-eye views of the building clusters and roof condition data, Figure 5 is an actual photograph of a skywell in Huangshan. Various building information was systematically collected, from which blueprints were drawn and models established. Through the survey of 24 traditional dwellings (as shown in

Table 2. Field research on residential data (documented and created by the authors).

Name	Number	Total Area (m2)	Skywell				Aspect Ratio H/W	Aspect Ratio W/L	Percentage of Skywell Area	Type
			Area (m2)	Length (L/m)	Width (W/m)	Enclosed Height (H/m)
Six-roomed hall	1	108.32	17	2.7	6.194	6.749	1.09	2.294	0.157	three sides enclosing the skywell
Light blue cloud house	2	136.36	26.88	5.583	4.688	2.683	0.572	0.84	0.197	four sides enclosing the skywell
Hu Peace House	3	145	16.21	2.81	5.98	7.51	1.256	2.128	0.112	four sides enclosing the skywell
Stewart’s house 1	4	77.11	19.91	6.57	3.03	8.434	2.783	0.461	0.258	three sides enclosing the skywell
Stewart’s house 2	5	73.49	16.27	5.29	3.031	8.434	2.783	0.573	0.221	three sides enclosing the skywell
Hu Guoliang House	6	108.33	15.05	3.157	4.815	7.741	1.608	1.525	0.139	four sides enclosing the skywell
Tudor Hall	7	76.04	16.73	2.52	6.475	6.307	0.974	2.569	0.22	three sides enclosing the skywell
South side of Kuang Gu House	8	76.83	6.63	1.87	3.1	6.779	2.187	1.658	0.086	three sides enclosing the skywell
North side of Kuang Gu House	9	86.32	22.58	6.9	3.3	7.383	2.237	0.478	0.262	three sides enclosing the skywell
Hu Xianfeng’s house 1	10	108.12	17.46	2.749	6.39	5.717	0.895	2.324	0.161	four sides enclosing the skywell
Hu Xianfeng’s house 2	11	59.51	11.41	5.87	1.971	6.052	3.071	0.336	0.192	three sides enclosing the skywell
Lam Ping House	12	77.13	21.71	3.738	6.16	5.308	0.862	1.648	0.281	three sides enclosing the skywell
Chen Wangming ① right 1	13	40.09	11.34	2.7	2.1	4.24	2.019	0.778	0.283	three sides enclosing the skywell
Chen Wangming ① left 1	14	90.21	13.32	2.2	6.242	8	1.282	2.837	0.148	four sides enclosing the skywell
East house left 1	15	96.88	21.79	7.145	3.05	8.4	2.754	0.427	0.225	three sides enclosing the skywell
East house left 2	16	64.62	13.99	4.272	3.23	7.1	2.198	0.756	0.216	three sides enclosing the skywell
East house right 1	17	87.17	10.41	2.388	4.324	8	1.85	1.811	0.119	three sides enclosing the skywell
Da-fu House	18	142.5	34.46	4.553	7.458	7.292	0.978	1.638	0.242	four sides enclosing the skywell
Room 006, Back Creekside	19	23.02	3.988	2.232	1.787	7.3	4.085	0.801	0.173	three sides enclosing the skywell
Injeong-ri House	20	98.74	18.65	6.068	3.054	7.262	2.378	0.503	0.189	three sides enclosing the skywell
Chak Kin Wo House	21	71.81	18.93	2.97	6.35	6.803	1.071	2.138	0.264	three sides enclosing the skywell
Hu Siwen House	22	45.5	9.000	2.500	3.600	6.900	1.917	1.440	0.198	three sides enclosing the skywell
Chen Wangming ②	23	65.4	22.360	4.300	5.200	7.100	1.365	1.209	0.342	four sides enclosing the skywell
Supply and marketing house	24	149.02	23.308	5.240	4.448	6.499	1.461	0.849	0.156	three sides enclosing the skywell
Average value		86.974	16.886	4.014	4.416	6.833	1.547	1.358	0.197
Maximum values		142.5	34.46	7.145	7.458	8.434	1.131	2.837	0.283
Minimum value		23.02	3.988	1.87	1.787	2.683	1.501	0.336	0.119
Percentage of four sides enclosing the skywell: 29%					Percentage of three sides enclosing the skywell: 71%

) and the analysis presented in Figure 6, it was found that the traditional dwellings in the selected area are mainly divided into two forms, with the “凹 (rooms on three sides enclosing the skywell)” type accounting for 71%, far more than the “回 (rooms on all four sides enclosing the skywell)” type. As shown in Table 2, the surveyed dwellings typically have a land area in the 70–90 m² range, with an average of 86 m². The building height is generally around 6.8 m, and most buildings are two stories. The skywell area is usually within the 10–20 m² range, with an average of 17.6 m². The average length of the skywell is 4 m, and the average width is 4.4 m. Based on these analysis results, a typical dwelling model was constructed, as shown in Figure 7. Figure 7① shows the actual building model, built according to the actual situation. Figure 7② is a plan view of the actual building model, Figure 7③ is the simplified 3D model used for simulation, with relevant building parameters set as shown in

Table 3. Basic model parameter table (made by the authors).

Name	Total Area of the Compound	Skywell Area	Skywell Length	Skywell Width	Enclosed Building Height	Skywell Aspect Ratio	Skywell Aspect Ratio
numerical value	86.9	17.6	4	4.4	6.8	1.54	0.9

, and Figure 7④ is a building courtyard group composed of basic individual buildings.

2.3. Establishment of a Parametric Simulation System

With the rapid development of building performance simulation and optimization technologies (such as building thermal comfort simulation and optimization), their application scope has been continuously expanding, and they are now widely used in related research and practical fields. Grasshopper 2.0 is a parametric plugin based on Rhinoceros, which integrates model development, performance simulation, and automated optimization search into a single BESO plugin. Its Ladybug module encapsulates a series of building physics equations (such as thermal comfort, sunlight, and ventilation) into “operators” (i.e., components) to enable efficient simulation and analysis of building performance. When calculating comfort and lighting, OpenStudio v1.10.0, EnergyPlus 25.1.0, and Radiance 6.0a will be called. This study uses the Ladybug and Honeybee modules to analyze building performance.

2.4. Method Validation

To verify the effectiveness of the parametric model developed in this study in terms of thermal response reliability, the conclusions of Diz-Mellado et al. (2023) [15] regarding the relationship between courtyard geometry and cooling energy consumption were selected as a benchmark reference. Their research concluded, through a combination of actual monitoring and three simulations using the official Spanish energy certification tool HULC, that when the courtyard height-to-width ratio (H/W) increased to the range of 1.92–2.12, a significant thermal buffering effect occurred. The peak temperature difference (ΔTmax) between the courtyard and the outdoor environment reached 14.4 °C, and the cooling energy consumption was reduced by 18% compared to the baseline model (p < 0.01) [15].

In this study, the boundary conditions of the original research were fully replicated. The solar radiation model used the Perez diffuse algorithm, the ground reflectance was set to 0.35, and the wind speed profile followed a logarithmic distribution. The parametric model’s height-to-width ratio was fixed at H/W = 1.92. The simulation results showed that in terms of thermal buffering performance, the temperature difference between the atrium and the outdoor environment was ΔTmax = 12 °C, with cooling energy consumption reduced by 14% compared to the baseline model. This confirms the accuracy of the parametric simulation system in building performance calculation and energy consumption prediction.

While Ladybug Tools enables integrated thermal and daylight analysis through EnergyPlus 25.1.0 and Radiance 6.0a, its accuracy for shaded environments requires validation. The related literature reveals its limitations: Discrepancies in mean radiant temperature (T_mrt) algorithms between tools caused UTCI differences of up to 10.9 °C, significantly impacting thermal comfort predictions [14]. To mitigate these, relative differences are prioritized over absolute values. At the same time, when presenting the results, the uncertainty or numerical error is indicated.

2.5. Determination of Orthogonal Test Factors

The full-scale simulation involves 8 design parameters, each with 4 research levels, resulting in 65,536 possible conditions to test. Each simulation takes 8.2 min, requiring a total of 8960 h of computation time. To reduce the computational effort, the orthogonal experiment method was employed, following specific rules [30] to select representative samples from the full-scale experimental combinations. Using the special orthogonal table developed by Genichi Taguchi [31], the L32(4⁸) orthogonal table was used to replace the full-factorial design, requiring only 32 typical conditions to be tested, which is 0.049% of the full-scale scheme. This design ensures the orthogonality of the 8-factor, 4-level system and has been verified to cover 95.1% of the parameter space. Through analysis with the generalized linear model, main effect factors and interaction terms with a statistical significance of p-value less than 0.01 and statistical power greater than 0.85 can be effectively identified. As a result, the experimental resource consumption is reduced by 99.95%.

Based on the literature review, potential influencing factors related to morphology and the building envelope were selected as variables for the orthogonal experiment. Since the local skywell (天井) is completely open to the sky, factors related to skylights (such as window-to-wall ratio and window materials) were excluded. However, the building’s interior features windows facing the skywell to admit natural light and air into the room space, so the interior windows were retained in the basic model. The interior windows are made of pine wood and ordinary glass, fully open to the skywell, and the proportions and materials used for these windows have become a local tradition. Therefore, in this study, the parameters of the windows were not considered as variable independent factors. Other factors applicable to skywell-style dwelling buildings were all retained. In previous studies, the courtyard green coverage ratio has often been employed as an important factor. However, this factor is not directly applicable to skywell-style dwellings, as the skywell area typically accounts for only one-tenth to one-fourth of that found in traditional northern Chinese courtyards. Moreover, the microclimatic conditions within skywells are significantly constrained by their relatively high height-to-width ratios, rendering them unsuitable for conventional vegetation planting. Nevertheless, field surveys indicate that 89.6% of the sampled skywells feature a composite arrangement of water jars and potted landscapes. Accordingly, this study introduces the Courtyard Naturalization Index (CNI)—defined as the ratio of the combined surface area of water features and the projected area of potted plants to the skywell floor area—as a substitute for conventional green coverage metrics.

This orthogonal experiment aims to systematically identify the significant factors affecting the performance of skywell-type dwelling buildings and to determine the hierarchical structure of their primary and secondary effects. To ensure the reliable identification of influential factors, the parameter ranges were deliberately broadened based on the statistical essence of factor screening: wide-range parameter perturbation enhances the variance analysis’s ability to detect weak-effect factors, thereby avoiding the omission of impactful variables due to overly narrow ranges. Length-to-width ratio: continuous gradient from 0.5 to 2; height-to-width ratio: divided into four equal gradients, from 0.5 to 2; orientation: based on true south (0°), with 4 levels rotating 30° towards the east and west; main building depth: starting from 3 m, increasing by 2 m up to 9 m; wing room width: from 2 m to 8 m, increasing by 2 m; wall U-value: starting at 0.25 W/(m²·K), increasing by 0.25 W/(m²·K) up to 1 W/(m²·K); eaves overhang coefficient: starting at 0.8, increasing by 0.3 in an arithmetic progression up to 1.7; atrium naturalization index: continuous gradient from 0.2 to 0.8. All parameters are designed with four evenly spaced levels, covering geometric proportions, spatial dimensions, wall U-values, and spatial orientation. This configuration is suitable for multivariate orthogonal experimental analysis, as shown in

Table 4. Factor level design for experimental parameters (made by the authors).

Design Consideration Level		1	2	3	4
Width-Length Ratio (W/L)	A	0.5	1	1.5	2
Height-Width Ratio (H/W)	B	0.5	1	1.5	2
Orientation (OR)	C	−45°	−15°	15°	45
Depth of the hall (HD)	D	3	5	7	9
Width of wing room (WW)	E	2	4	6	8
Wall U-value (U)	F	0.25	0.5	0.75	1
Eave projection factor (SW)	G	0.8	1.1	1.4	1.7
Skywell naturalization index (SNI)	H	0.2	0.4	0.6	0.8

SNI: skywell naturalization index (${\displaystyle \frac{{\mathrm{A}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}+{\mathrm{A}}_{\mathrm{b}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{a}\mathrm{i}}}{{\mathrm{A}}_{\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{t}\mathrm{y}\mathrm{a}\mathrm{r}\mathrm{d}}}}$).

.

According to relevant references [32,33,34], additional parameters affecting the research objectives—such as operational parameters and climatic conditions—must also be considered. The human activities listed in the table are based on field research and represent the activities most frequently performed by local residents at home. In accordance with the Thermal Design Code for Civil Buildings (GB 50176-2016 [29]) data from the hottest months, July and August, were used. The city is located in the hot and humid region of China, characterized by hot, humid summers. Therefore, building design must prioritize heat protection during the summer. The climate dataset was loaded into the Ladybug plugin of Grasshopper to define the climate parameters. The original meteorological data were jointly compiled by the National Meteorological Information Center of the China Meteorological Administration and Tsinghua University. The settings for building operation parameters and climate conditions are shown in

Table 5. Residential energy simulation parameter settings (documented and created by the authors).

Architectural Parameters			Housing Parameters
Roof material	Ceramic tiles and pinewood: 3.22 W/(m2·K)		Number of inhabitants per household	4 persons/household
Wall material	External wall	Brick: 2.09 W/(m2·K)	Home-based activities per capita metabolic rate	Sitting/sleeping	2.45 mL/(kg·min)
	Interior wall	Pinewood: 0.11 W/(m2·K)		Standing/relaxing	3.5 mL/(kg·min)
				Cooking	6.475 mL/(kg·min)
Outer window material	Pine window frame with plate glass: 4.36 W/(m2·K)			Clean the room	6.475 mL/(kg·min)
Building structure	Brick and wood construction		Electric power consumption	14 W/m2
			Air-conditioning temperature in summer	26 °C
Analogous time period		15 July–15 August

.

2.6. Selection of Evaluation Indicators

After establishing the model and defining the variables, it is necessary to determine the performance evaluation indicators for the optimization objectives, which will be used to assess the performance variations of dwellings.

Spatial Daylight Autonomy (sDA) and useful daylight illuminance (UDI) are dynamic evaluation indices that have been widely used internationally in recent years to assess daylight performance in architectural spaces [34]. Compared to sDA, UDI is more adaptable to visual comfort, making it particularly suitable for evaluating architectural design factors. In this study, the UDI value is adopted as an evaluation indicator. UDI represents the percentage of the year during which a specific point indoors receives natural illuminance within a defined physiologically comfortable range. The lower and upper threshold values for this range are set at 100 lux and 2000 lux, respectively [35].

$$\mathrm{U}\mathrm{D}\mathrm{I}={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}\left({\mathrm{E}}_{\mathrm{i}}\right)}{\mathrm{T}}}$$

where UDI is the percentage of useful daylight illuminance (%); N is the total number of hours in a year; Time (E_i) is the duration during the i-th hour when the illuminance E_i falls within the specified range (e.g., 100 lux ≤ E_i < 2000 lux); T is the total duration considered (in hours).

Using the Ladybug tool on the Grasshopper platform, the average UDI data for all rooms in the parametric model during the hottest summer month were calculated, and the UDI values corresponding to different skywell design schemes were statistically analyzed.

UTCI (Universal Thermal Climate Index) is an index used to evaluate thermal comfort [36], and in this study, it is applied to assess the thermal comfort of the connected spaces between the skywell and the main hall. Based on a human thermal balance model, UTCI integrates various meteorological parameters that affect thermal comfort or thermal stress into a single temperature value. The comfort range of UTCI lies between 9 °C and 26 °C, within which the human body experiences no significant thermal stress and perceives a comfortable environment. The calculation formula is as follows:

$${\mathrm{T}}_{\mathrm{m}\mathrm{r}\mathrm{t}}={\left[{\left({\mathrm{T}}_{\mathrm{g}}+273.14\right)}^4+{\displaystyle \frac{\left(1.10\times {10}^8{{\mathrm{v}}_{\mathrm{a}}}^{0.6}\right)}{{\mathsf{\epsilon }\mathrm{D}}^{0.4}}}\times \left({\mathrm{T}}_{\mathrm{g}}-{\mathrm{T}}_{\mathrm{a}}\right)\right]}^{1/4}$$

(1)

$$\mathrm{U}\mathrm{T}\mathrm{C}\mathrm{I}={\mathrm{T}}_{\mathrm{a}}+\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}\left({\mathrm{T}}_{\mathrm{a}},{\mathrm{T}}_{\mathrm{m}\mathrm{r}\mathrm{t}},{\mathrm{v}}_{\mathrm{a}},\mathrm{R}\mathrm{H}\right)=\mathrm{f}\left({\mathrm{T}}_{\mathrm{a}},{\mathrm{T}}_{\mathrm{m}\mathrm{r}\mathrm{t}},{\mathrm{v}}_{\mathrm{a}},\mathrm{R}\mathrm{H}\right)$$

(2)

where T_g, T_a, D, V_a, ε, and RH represent globe temperature (°C), air temperature (°C), globe diameter (meters), wind speed (m/s), emissivity, and relative humidity (%), respectively.

Using the Ladybug tool on the Grasshopper platform, UTCI data for the continuous space between the skywell and the main hall during the hottest summer month were calculated, and the UTCI values corresponding to different skywell design schemes were statistically analyzed.

This study uses the Percentage of Time Comfortable (P_TC) to evaluate indoor thermal comfort [37]. P_TC reflects the proportion of time during which occupants perceive the indoor environment to be within a comfortable range. Scientific studies have shown that humans feel most comfortable when the ambient temperature is between 18 °C and 25 °C and the relative humidity is between 40% and 70% [38]. The study area’s hottest summer period is defined as the 720 h from July 15 to August 15. The proportion of time during this period in which both indoor temperature and humidity meet the comfort criteria is recorded as the P_TC value used in this study. A higher P_TC value indicates a higher level of residential comfort. The calculation formula is as follows:

$${\mathrm{P}}_{\mathrm{T}\mathrm{C}}={\displaystyle \frac{Total comfort hours}{Total number of hours recorded}}\times 100\mathrm{\%}$$

Using the Ladybug tool on the Grasshopper 2.0 platform and based on the OpenStudio v1.10.0 engine, this study calculates and records the hourly temperature and humidity data for each room during the hottest summer month. From these data, the P_TC values corresponding to different skywell design schemes are determined.

In this study, the metric E is selected to represent the energy consumption of skywell-style dwelling buildings during the hottest summer month. A lower E value indicates a better energy-saving performance of the building [39], with the unit being kWh/m².

Using the Ladybug tool on the Grasshopper platform, the energy consumption of dwelling spaces during the hottest summer month is calculated, and the E values corresponding to different skywell design schemes are recorded.

2.7. Establishment of the Orthogonal Experiment Table

If all design factors and levels were to be fully combined for a comprehensive experiment, the time cost of using simulation software would be significantly higher [40]. Compared to full-scale experiments, orthogonal tests are an efficient technique to reduce the number of trials using a scientific process, and the main idea is to select representative samples from the full set of experimental combinations according to specific rules [40].

Table 6. L32(4⁸) orthogonal design table (32 rows in total, 23 rows omitted, made by the authors).

Serial Number	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5	Factor 6	Factor 7	Factor 8
1	1	1	1	1	1	1	1	1
2	1	1	2	2	4	4	3	3
3	1	2	3	4	1	2	3	4
4	1	2	4	3	4	3	1	2
5	1	3	1	3	2	4	2	4
6	1	3	2	4	3	1	4	2
7	1	4	3	2	2	3	4	1
8	1	4	4	1	3	2	2	3
9	2	1	3	4	3	4	2	1
	…	…	…	…	…	…	…	…

presents the L32(4⁸) orthogonal test designed using the statistical analysis software SPSS (version 22.0), where each design factor includes four levels of variables.

Based on the target values of each design scheme, the range analysis method is used to determine the influence of each control factor on the design outcomes [41]. The specific steps are as follows [42]:

(1)

Calculate the sum of the evaluation indices for design schemes when factor j is at level l, denoted as K_jl.

$$K_{jl}=\sum _{i=1}^n{y}_i\times {\delta }_{ijl}$$

${\mathrm{y}}_{\mathrm{i}}$: The overall score of the i-th design scheme (obtained using the Borda method or other evaluation methods).

$${\mathsf{\delta }}_{\mathrm{i}\mathrm{j}\mathrm{l}}:\left\{\begin{array}{c}1 If factor j takes level 1 in scheme i\\ 0 Otherwise\end{array}\right.$$

(2)

Calculate the average value of the evaluation index for factor j at level l, denoted as k_jl.

$$k_{jl}={\displaystyle \frac{K_{jl}}{r_{jl}}}$$

${\mathrm{r}}_{\mathrm{j}\mathrm{l}}$: Number of replicates in the orthogonal experiment for factor j at level l.

(3)

Calculate the range R_j of factor j.

$${\mathrm{R}}_{\mathrm{j}}=\mathrm{m}\mathrm{a}\mathrm{x}\left({\mathrm{k}}_{\mathrm{j}1},{\mathrm{k}}_{\mathrm{j}2},\dots {\mathrm{k}}_{\mathrm{j}\mathrm{t}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{k}}_{\mathrm{j}1},{\mathrm{k}}_{\mathrm{j}2},\dots {\mathrm{k}}_{\mathrm{j}\mathrm{t}}\right)$$

t: The total number of levels of factor j.

(4)

Ranking rule for the degree of influence of factors.

$${\mathrm{R}}_{\mathrm{j}1}>{\mathrm{R}}_{\mathrm{j}2}>\dots \dots >{\mathrm{R}}_{\mathrm{j}\mathrm{m}} \mathrm{T}\mathrm{h}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r} {\mathrm{j}}_1 \mathrm{i}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}$$

2.8. Multi Objective Optimization

Multi-objective optimization (MOO) refers to considering multiple conflicting or contradictory objectives simultaneously in an optimization problem and using optimization algorithms to find a set of optimal solutions that best satisfy all objectives. To better balance different influencing factors, multi-objective optimization is introduced into the process of architectural design and renovation. Multi-objective optimization methods can be divided into two main categories: traditional optimization algorithms and intelligent optimization algorithms. In intelligent optimization algorithms, the genetic algorithm [43] (GA) is a series of search algorithms inspired by natural evolution theory. By mimicking the processes of natural selection and reproduction, it provides high-quality solutions to various problems involving search, optimization, and learning. A multi-objective optimization problem can be expressed as follows [44]:

$$\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{F}\left(\mathrm{x}\right)={\left[{\mathrm{f}}_1\left(\mathrm{x}\right),{\mathrm{f}}_2\left(\mathrm{x}\right),{\mathrm{f}}_3\left(\mathrm{x}\right),\dots {\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right),\right]}^{\mathrm{T}}, \mathrm{x}\mathsf{ϵ}\mathsf{\Omega }$$

$$\mathrm{s}.\mathrm{t}.\left\{\begin{array}{c}{\mathrm{g}}_{\mathrm{i}}\left(\mathrm{x}\right)\le 0,j=\mathrm{1,2},\dots ,P;\\ {\mathrm{h}}_{\mathrm{k}}\left(\mathrm{x}\right)=0,k=\mathrm{1,2},\dots Q;\end{array}\right.$$

where M represents the number of objective functions, P is the number of inequality constraints, Q is the number of equality constraints, Ω is the decision (variable) space, x is a candidate solution, and F is a vector containing M objective functions. “s.t.” denotes the two types of constraints in a multi-objective optimization problem; when the constraints are satisfied, it means the solution is feasible, and vice versa [45].

f₁ (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CNI_i) = min(E)

f₂ (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CNI_i) = min(−P_TC)

f₃ (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CNI_i) = min(−UDI)

f₄ (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CNI_i) = min(UTCI)

m_inF(x) = [f1 (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CN_ii), f2 (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CN_ii), f3 (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CN_ii), f4 (WLR_i, HWR_i, OR_i, HD_i, WW_i, U_i, SW_i, CN_ii)]^T, i ∈ ∞

where f₁, f₂, f₃, and f₄ are the four objective optimization functions; i is the number of skywell morphology types; WLR_i, HWR_i, OR_i, HD_i, WW, U_i, SW_i, and CNI_i represent the corresponding aspect ratio, height-to-width ratio, orientation, depth of halls, width of wing rooms, wall U-value, eave-out factor, and greenness index of the skywell, respectively, for each scheme and skywell greening index.

This study employs the NSGA-II algorithm embedded in the Wallacei plugin to perform multi-objective optimization of Huangshan dwellings. The main objective is to determine the optimized geometric parameters of the skywell in hot and humid regions, aiming to achieve a good building performance while minimizing the use of active energy-saving measures. Four optimization objectives were considered: E, UTCI, P_TC, and UDI. Within the Grasshopper environment, the Wallacei multi-objective optimization module was used to filter design factors, link the independent variable control module with the objective module, and conduct iterative optimization searches through the simulation platform to identify optimal solutions. The skywell design parameters were controlled via sliders in the plugin, with design variables defined on the left panel and evaluation metrics placed on the right panel. Each iteration simulated and evaluated 50 solutions over 20 generations, resulting in a total of 1000 solutions.

In this multi-objective optimization analysis, both the P_TC and UDI indicators aim to maximize their values for optimal performance, which is contrary to the default behavior of the Wallacei multi-objective optimization algorithm that optimizes towards smaller target values. Therefore, the negative values of these two indicators are used during optimization. The actual physical meaning of this is that when the optimization algorithm drives the indicators towards smaller values, the corresponding original P_TC, UDI values approach larger values.

3. Results

3.1. Analysis of Orthogonal Experiment Results

After conducting range analysis and variance analysis on the results of the orthogonal experiment, the sensitivity and significance of various influencing factors on building performance were determined.

The combination schemes of the orthogonal experiment table are input into Grasshopper, where continuous simulations are run for the 32 design factor schemes in the orthogonal experiment table to derive the UDI, UTCI, P_TC, and E for each combination. The research results are then loaded into SPSS (version 26) for analysis of the influence of different design factors on energy consumption. After exporting the analysis results, a sensitivity analysis is performed. First, range analysis is used to determine the order of influence of the skywell design factors on each building objective value. Then, ANOVA (analysis of variance) is used to determine the significance of the skywell design parameters for each objective parameter.

3.1.1. Range Analysis

Through range analysis, the parameters with the highest sensitivity to the impact on building performance were identified, and a general trend was observed, as shown in Figure 8.

At the same time, as shown in Figure 8, when the length-to-width ratio approaches 0.5, the proportion of indoor thermal comfort time in the skywell building is the highest. As the height-to-width ratio increases, the proportion of indoor thermal comfort time in the skywell building is also the highest. The skywell building has the highest proportion of indoor thermal comfort time when oriented directly south in the summer. The main building depth, when close to 9 m, results in the highest proportion of indoor thermal comfort time.

Table 7. Range analysis of influencing factors on dependent variables (made by the authors).

	A	B	C	D	E	F	G	H	Max	Min
UDI	10.71	10.50	3.25	30.73	11.14	5.74	9.70	9.04	30.73	3.25
UTCI	0.45	0.83	0.07	0.09	0.25	0.09	0.30	0.13	0.83	0.07
E	0.25	0.62	0.18	0.19	0.89	0.13	0.61	0.16	0.89	0.13
PTC	3.68	20.69	1.57	5.56	10.69	1.13	2.51	1.96	20.69	1.13

indicates that, in traditional buildings of hot and humid regions, the influence of design factors on the four objectives (UTCI, UDI, P_TC, and E) varies significantly. For UTCI, the height-to-width ratio of the skywell is the dominant factor, followed by the length-to-width ratio, with orientation having the least effect (B > A > G > E > F > D > H > C). For UDI, the depth of the main hall exerts the greatest influence, followed by the width of the side rooms, while the skywell naturalization index has the smallest impact (D > E > A > B > G > F > C > H). For P_TC, the skywell height-to-width ratio again shows the strongest effect, followed by the width of the side rooms, with the wall U-value having the least impact (B > E > D > A > G > H > C > F). For E, the width of the side rooms ranks first, followed by the skywell height-to-width ratio, while the wall U-value has minimal influence (E > B > G > A > D > C > H > F).

3.1.2. ANOVA

Through analysis of variance, the significance of each factor’s impact on building performance was identified.

Range analysis reveals the relative influence of each skywell design factor on energy consumption; however, it does not determine whether these effects are statistically significant [46]. Therefore, an analysis of variance (ANOVA) was conducted to identify the factors that have a significant impact on skywell energy consumption. The orthogonal experimental data were analyzed using SPSS, and the results are presented in

Table 8. Significance record (authors’ original records).

		F	p			F	p
UDI	A	1.701	0.253	UTCI	A	5.435	0.042 *
	B	1.935	0.212		B	12.098	0.003 *
	C	0.151	0.926		C	0.076	0.97
	D	11.52	0.004 *		D	0.152	0.925
	E	1.444	0.309		E	1.141	0.409
	F	0.632	0.618		F	0.163	0.919
	G	1.512	0.293		G	1.348	0.342
	H	1.156	0.392		H	0.239	0.866
E	A	1.471	0.303	PTC	A	3.006	0.104
	B	7.96	0.012 *		B	78.057	0 *
	C	0.668	0.598		C	0.663	0.601
	D	0.756	0.553		D	5.72	0.027 *
	E	16.906	0.001 *		E	20.887	0.001 *
	F	0.395	0.761		F	0.245	0.862
	G	8.038	0.011 *		G	1.288	0.351
	H	0.516	0.684		H	0.791	0.536

Note: The F-value is used to compare variances and assess whether the effect of a factor on the dataset variation is significant [47], while the p-value tests the statistical significance of this effect in the ANOVA. An asterisk (*) indicates that the p-value reaches the 0.05 significance level.

.

3.2. Multi-Objective Optimization Results

Through analysis of the SD graph generated by multi-objective optimization, a preliminary judgement can be made as to whether building performance has been optimized.

The optimal solutions were compared with the baseline model to assess improvements in each objective (P_TC, UTCI, E, and UDI). Based on the range and variance analyses of the orthogonal experiment, factors F and H (wall U-value and skywell naturalization index) were consistently found to have the least influence on all four objectives. These low-impact factors were excluded from subsequent analyses, and the remaining factors were retained as the optimal set of design parameters (

Table 9. Screening and retention of influencing factors (made by the authors).

Optimization Goals	Design Factor Rankings	A	B	C	D	E	F	G	H
UDI	D > E > A > B > G > F > C > H	√	√	√	√	√	×	√	×
UTCI	B > A > G > E > F > D > H > C	√	√	×	√	√	×	√	×
E	E > B > G > A > D > C > H > F	√	√	√	√	√	×	√	×
PTC	B > E > D > A > G > H > C > F	√	√	√	√	√	×	√	×

).

This study analyzes the multi-objective optimization data generated by the Ladybug toolset through a Python 3.13 and Grasshopper collaborative computing framework. Using a genetic algorithm, 50 individuals were set per generation for 20 iterations, resulting in 1000 optimization solutions containing six independent variables and four dependent variables. During the data analysis phase, a Python-based machine learning process was constructed: first, the 1000 sets of multidimensional data were cleaned using pandas [48], and the linear correlation between design parameters and performance metrics was revealed through the Pearson correlation coefficient matrix [49]. The XGBoost algorithm was then used to build a model [50], and the SHAP values were analyzed to quantify the nonlinear impact weights of design parameters on performance objectives [51]. Finally, the fast non-dominated sorting algorithm from the pymoo library was used to extract the Pareto front solutions [52].

Figure 9 shows the comparison of four optimization objectives distribution between the initial generation (First Gen, red) and the final generation (Last Gen, blue) during the optimization process. Three major building performance aspects have been optimized.

As shown in Figure 9, three objectives have been optimized to some extent, one objective optimization is not ideal. The blue lines in Graphs ①, ②, ③, and ④ have all shifted to the left. In multi-objective optimization programs, a shift to the left indicates that the data has been optimized, and the objectives have been optimized [53]. Graphs ①, ②, ③, and ④ represent the SD plots of the optimization results for UDI, UTCI, E, and P_TC, respectively. However, as can be seen from Graphs ①, ②, and ④, the optimization levels for UDI, UTCI, and P_TC are not very high. Graph ③ shows that building energy consumption has been significantly optimized, and the standard deviation has decreased. All E optimization results are positive (range: [0.01]~[3.34]), the negative coordinates in the graph merely indicate this statistical distribution characteristic, and the actual E values always satisfy the physical constraint of E ≥ 0.

The skywell dwellings in the Huangshan region have evolved over time to develop climate-adaptive architectural and skywell forms. Since the initial parameters for the multi-objective optimization in this study were derived from the average values obtained through field surveys of local skywell dwellings, UDI and P_TC have been optimized, but not to a great extent, and UTCI has not been optimized, thereby demonstrating the climate-adaptive comfort of traditional local architecture [53]. Since the building energy consumption settings are based on the provisions of the “Energy Conservation Design Standards for dwelling Buildings in Hot Summer and Cold Winter Regions” (JGJ 134-2010 [54]), as shown in the table, during the optimization process, as illustrated in Figure 9③, E gradually decreases and eventually stabilizes at a relatively small value.

3.3. Pareto Optimal Solution Analysis

By comparing feasible solutions and Pareto solutions, we can verify the conclusions of the SD diagram analysis and confirm whether the building performance has been optimized.

Figure 10 compares the performance of feasible solutions and Pareto solutions in each objective. To better describe the overall distribution of optimization objectives, this study analyzes the mean and median of the optimization objectives. The mean reflects the average level of feasible and Pareto solutions but is susceptible to the influence of extreme values. The median, on the other hand, describes the concentration of feasible and Pareto solutions, including extreme values. By combining both the mean and median, a more comprehensive view of the average distribution of feasible and Pareto solutions can be provided.

In Figure 10③, the Pareto solutions for E are more concentrated at lower values, with the mean being lower than the feasible solutions and the median slightly lower than the feasible solutions. In Figure 10①,②,④, the Pareto solutions for UTCI, P_TC comfort time percentage, and UDI have both mean and median values greater than those of the feasible solutions. As the E value decreases, the P_TC and UDI increase—indicating better building renovation performance. The Pareto solutions are concentrated in the set of solutions with better renovation effects. The median and average values of UTCI increase, but more than 90% of the Pareto solution set remains within the comfort range, proving the climate adaptability of local buildings. For all four optimization objectives shown in Figure 10, except for UTCI, the mean and median of the Pareto solution are better than the feasible solution, and the overall optimization results are good.

To obtain the optimal parameter values for skywell-type residences in hot and humid regions, this study uses the Topsis and Vikor comprehensive evaluation methods to conduct a ranking analysis of the Pareto solutions. Additionally, Python is used to calculate the Borda count [55] for the comprehensive ranking of each Pareto feasible solution. Figure 11 shows the Topsis and Vikor evaluation scores, as well as the final comprehensive evaluation scores. Each vertical axis represents the ranking sequence, variables, or intervals of objectives, and each solution is represented by a polyline that connects the variable values from the ranking sequence to the performance values of the objectives. Figure 11 shows that the solution with WLR = 1.6, HWR = 2.6, OR = −20°, SW = 0.5, WW = 2.4, and HD = 2 has the highest comprehensive ranking. This solution, compared to the simulation values of the typical model in

Table 10. Comparison of building performance before and after optimization (drawn by the authors).

Objectives	UDI	UTCI	E	PTC
Typical Models	63.67%	22.08 °C	1.62 kwh/m2	54.84%
Optimized Model	81.5%	21.64 °C	1.48 kwh/m2	57.8%
Performance Improvement Value	28% (128.4 h)	2%	8.6% (0.14 kWh/m2)	5.3% (38.14 h)

, achieves a 28% improvement in UDI for summer living space, 128.4 h; a 2% improvement in UTCI; an 8.6% reduction in E, 0.14 kWh/m², and a 5.3% increase in P_TC, 38.14 h.

3.4. Correlation Analysis

By plotting scatter figures, we analyzed the trends in how each factor affects various building performance characteristics within their respective ranges of variation. At the same time, we used SHAP analysis to rank all factors according to their influence on four building performance characteristics.

As shown in Figure 12, increasing the WLR, HD, HWR, or SW of the skywell typically reduces UDI and UTCI and decreases E. This reduction in E primarily stems from the expanded shadow coverage [56] and reduced direct solar radiation [57] resulting from the increased parameters, effectively lowering the thermal load. However, these changes weaken ventilation efficiency, leading to a decrease or uneven distribution of P_TC, which can easily create areas of stagnant heat and humidity [58]. Specifically, the decrease in UDI is due to uneven light distribution or increased attenuation; the reduction in UTCI is directly related to the significant blocking of solar radiation [59]; and the general decrease in E is the result of reduced radiative heat load. There are two exceptions: when the shading width is excessively increased, although radiant heat is reduced, the steam trap effect paradoxically increases the total energy consumption E; when the bay width is increased, the volume of the indoor space requiring temperature control rigidly increases, directly leading to a higher cooling energy consumption E. The increase in P_TC is primarily due to the statistical range effect (including more self-shadowed areas) rather than actual improvement.

Figure 13 displays the correlation coefficients between each influencing factor and the four objectives. From Figure 13①, it can be seen that the impact of OR on the four objectives is not very significant.

Figure 13② shows the SHAP value impact analysis. The horizontal axis represents the SHAP values of the design variables, with values greater than zero indicating a positive correlation and values less than zero indicating a negative correlation [60]. The vertical axis ranks the influencing factors based on the magnitude of their impact, from top to bottom. Figure 13 shows that the most important variable is SW, followed by WLR, with OR being the least important. The conclusions drawn from the orthogonal experiment are not entirely consistent with those from the multi-objective optimization, because the range of factors in the orthogonal experiment was expanded, while the range of values for the multi-objective optimization factors was based on the maximum and minimum values obtained from field surveys.

Single-variable analysis indicates that linear regression fits poorly, suggesting that there are complex nonlinear relationships and interactions between building performance parameters and comfort metrics [46]. Building systems are inherently multi-parameter coupled systems, and single-variable linear models can only reflect local trends and cannot capture the complex global interaction network. This complexity highlights the importance of multi-objective optimization—it is necessary to use a systematic approach to find the balance between parameters rather than relying on simple linear rules.

4. Discussion

This study identified the core influencing factors of skywell-type dwelling building performance in humid and hot regions of China through orthogonal experiments, and revealed the quantitative relationship between the core parameters of skywell-type dwellings and passive performance through multi-objective optimization. The findings provide a scientific basis for the green renovation of traditional dwellings and the selection of parameters for new buildings in hot and humid regions. The specific conclusions are as follows.

4.1. Parameter Sensitivity and Optimization Mechanisms

The sensitivity of each parameter to building performance was clarified, and the optimal parameter combination within the study scope was determined. Based on an L32(4⁸) orthogonal experimental design, the sensitivity differences of various parameters were quantified. The skywell length-to-width ratio, skywell height-to-width ratio, room width, hall depth, and eaves overhang coefficient were identified as the most sensitive factors. Orientation had only a limited influence on summer indoor performance in hot and humid regions. Using the NSGA-II multi-objective optimization algorithm, the optimal parameter combination was determined as follows: WLR = 1.6, HWR = 2.6, OR = −20°, SW = 0.5, WW = 2.4, and HD = 2. This configuration improved the UDI of summer living spaces by 28%, increased UTCI by 2%, reduced E by 8.6%, and increased P_TC by 5.3%.

4.2. Geographical Climate Adaptation Characteristics

This study employed UDI, UTCI, E, and P_TC as evaluation metrics to investigate the building performance of two distinct spatial areas: the physically undivided continuous space formed by the skywell and central hall, and the indoor spaces within skywell buildings. The research fully considered the differences between skywell dwellings in the hot–humid region of China and courtyard residences in the northern region. Through parametric modeling and simulation, using average values from field surveys as initial inputs, the study confirmed the climatic adaptability of skywell dwellings in China’s hot, humid region.

4.3. Design Guidelines and Methodology

This study provides specific parameter data for the design of new skywell-type buildings in humid and hot regions of China, improving the efficiency of design personnel in formulating renovation plans and providing precise parameter guidelines for new buildings.

Through the statistical analysis, the following conclusions were drawn: the priority control parameters for new buildings are the height-to-width ratio, the depth of the main building, and room width as key regulating parameters; the dynamic balancing parameters are the skywell length-to-width ratio and the eaves overhang coefficient. An “orthogonal screening–multi-objective optimization” technical framework was established. In the early stages of building design, these conclusions can be used to optimize control of the parameters. These parameters are inherent properties of the building and will not increase construction costs, while contributing to the long-term sustainable improvement of passive energy-saving capabilities once the building is completed. At present, the Chinese government encourages the development of energy-efficient buildings and provides financial support. Implementing highly efficient energy-saving strategies aligns with national policies aimed at reducing costs and improving efficiency.

4.4. Limitation

This study has certain limitations in terms of universality, statistical methods, and simulation tools.

The methodological framework established in this study is applicable to most performance optimization research of detached dwellings. However, the specific conclusions are only valid for courtyard-style dwellings in the hot and humid regions of China. The study focuses on self-built dwellings, and the conclusions are not applicable to integrated housing and dwellings without courtyards. Given the significant climatic and architectural differences across various regions of China, the research findings should not be directly generalized nationwide.

This study only focused on the main effect relationships between various building parameters and building performance, and did not examine the interaction effects between different building parameters. Future research could further investigate the interaction effects between various building parameters.

The simulation tools used in the study have a certain degree of error in the calculation of UTCI. Future work should integrate hybrid validation frameworks (e.g., coupling Ladybug with localized ENVI-met 5.6.1 domains) to address known constraints in T_mrt and shading efficacy simulation.

This study used a fixed occupancy schedule, which does not fully reflect dynamic behavior in real-life scenarios. Future research could combine behavior modeling tools to improve prediction accuracy. Integration of stochastic behavior modeling tools (e.g., Occupant Behavior Simulator) with Monte Carlo sampling could be used to quantify behavioral uncertainty impacts.

5. Conclusions

This study identified the core influencing factors affecting the building performance of traditional skywell-style dwellings in hot and humid regions of China. Through optimization analysis, the optimal architectural parameters within the research scope were determined, thereby validating the climatic adaptability of skywell-style dwellings. Although the research focused on traditional skywell-style residences representative of China’s hot and humid regions, the identified design principles and performance patterns are equally applicable to modern buildings within the same climatic zone.

In the absence of clear construction guidelines, the design and renovation of dwelling buildings may lead to excessive long-term operational costs. This study provides practical design and retrofit recommendations, reducing the trial-and-error costs and enabling efficient energy-saving retrofits and sustainable construction practices.

Although the specific quantitative conclusions of this study apply only to China’s hot and humid regions, skywell-style buildings, characterized by the absence of physical barriers between skywells and main halls, are prevalent across a broad geographic range from hot, humid areas of China to Southeast Asia. Future studies can explore and validate the applicability of these findings in Southeast Asia and other regions sharing similar climatic characteristics.

Research on skywell-style architecture highlights the skywell’s significance as a product of China’s millennia-old architectural tradition, which has focused on climate adaptability. Demonstrating the climatic adaptability of skywells carries substantial implications for the sustainable development of global cultural heritage sites and plays a crucial role in preserving and protecting regional cultural identity amid rapid economic growth and rural revitalization.