Performance-Oriented Passive Design Strategies for Shape and Envelope Structure of Independent Residential Buildings in Yangtze River Delta Suburbs

Abstract

The Yangtze River Delta is a relatively developed area with many detached houses in the suburbs. Such detached houses are usually 1–3 stories high, mostly self-built by local people. Due to the lack of passive design guidance in the design and construction process, these houses’ energy consumption is usually high. At present, residents in the area use air conditioners, fans, and other electrical equipment in their daily lives. This paper takes detached houses in the suburbs of Ningbo as the research objects, through performance simulation and big data mining of a large number of generated samples, and proposes a passive design strategy suitable for the local building form and envelope structure, which can guide local housing construction.

1. Introduction

1.1. Background

A massive quantity of housing construction and living consumption caused a colossal waste of resources. According to the “2018 Annual Report on China Building Energy Efficiency” [1], between 2000 and 2016, China’s total building energy consumption was about 899 million tons of standard coal. This number accounted for 20.6% of the country’s total energy consumption during these years.

From construction, use, and demolition, buildings consume innumerable energy during their entire life cycle. In this paper, passive design strategies were proposed for residential buildings in the Yangtze River Delta region to reduce building energy consumption.

1.2. Research Status

1.2.1. Passive Design Strategies

Passive design strategy plays an important role in energy efficiency and indoor environment quality improvement. Chen et al. conducted a comprehensive literature review on simulation-based passive design building optimization methods, and their research will guide decision-makers to achieve energy-efficient goals through an overall optimization process [2]. Elshafei et al. used simulation tools to find building orientations and shapes suitable for different climate zones in Egypt to improve indoor thermal comfort [3]. Intending to reduce energy consumption and improve thermal comfort and indoor air quality, Lee J combined genetic algorithm and CFD technology to optimize building geometry and HVAC systems [4]. Vargas et al. used DesignBuilder software to simulate the thermal performance of existing buildings in Mexico and evaluate the energy-efficient potential of different passive design strategies [5]. Chen et al. evaluated three passive design strategies. The findings suggested that passive design has great potential even in hot and humid areas if strategies are applied properly [6]. Brito-coimbra et al. reviewed the application of solar passive technology in building facade renovation in the Mediterranean climate. The study reviewed four passive solar technologies, namely glazing, sunshade, sunspace, and Trombe wall technologies [7]. Mushtaha et al. evaluated the impact of three passive design strategies, shading, natural ventilation, and insulation, on the building’s indoor temperature and cooling load [8]. Jung et al. conducted multi-objective optimization of passive design strategy for multi-story residential buildings in South Korea and identified key design factors [9]. Qiu et al. proposed a method combining data mining technology with parametric energy consumption simulation to explore the key design parameters of the envelope of passive solar office buildings in hot and humid climates [10]. Zune et al. reviewed passive design techniques used to achieve thermal comfort in Burmese dwellings. The effects of different passive design techniques on the thermal comfort of buildings under three climate conditions in Myanmar were compared [11]. Mahar et al. conducted a global sensitivity analysis of the effects of passive design parameters on comfort in cold and semi-arid climates. Simulations were conducted on a typical residential building in Pakistan to determine key design parameters for optimal thermal comfort [12]. Lin et al. proposed an optimal design method to minimize building energy consumption and visual discomfort based on a passive building in Shanghai. A total of 35 design parameters were considered. The results show that this method can reduce energy consumption and improve visual discomfort [13]. Shao et al. obtained the optimal combination of passive design parameters of rural dwellings in Zalantun through investigation, measurement, and simulation analysis, to improve the energy-efficient design and indoor thermal environment of rural residences [14].

1.2.2. Energy-Efficient Building Shape Design

In terms of energy-efficient building shape design at the beginning of the whole construction scheme, passive design is an effective method. According to Lin et al. [15], minor adjustments to the building shape can passively adapt the indoor to the wind environment, increasing the building’s natural ventilation capacity by more than 20%. A small change in the building orientation can also reduce the building’s annual load of air conditioning power consumption by about 15%. On the contrary, building energy technologies are much more expensive in the detailed design stage but may not produce substantial benefits. For example, the large-scale improvement of external wall insulation capacity can only reduce 1% to 5% of overall energy consumption. High-performance cooling and heating equipment units, with the investment increased by 40% to 60%, can only produce 4% to 6% of the energy-saving rate.

Therefore, the correct choice of the architectural form in the early stage of the whole scheme can make the design process clear and lay a good foundation for the subsequent design. It is a virtual node in the entire design process.

Shi put forward two performance-aided ideas for building design based on “performance” and “performance-driven.” Furthermore, Shi elaborated on its concepts, differences, technical difficulties, and other contents [16]. Sun and Han explained the top-down and down-top performance design concepts and proposed a green performance-oriented building digital design process with the technology platform [17]. Ji explored the possibility of scheme design using building performance as a form-generating factor and proposed a technical approach to obtain design schemes combining parameterized graphics and optimization algorithms [18]. Li et al. proposed a formal design method for energy efficiency improvement, taking the building’s internal and external energy changes as the starting point of shape design [19]. Pelken et al. proposed a performance-aided integrated software platform aimed at the early design stage, thereby promoting the integration of technical performance into the architectural design process [20]. Souza attempted to integrate performance simulation into architectural design and raised suggestions for improving various aspects [21].

1.2.3. Influence of the Shape on Performance

In terms of analyzing the influence factors of the shape on technical performance, Wu et al. used performance simulation to examine the influence of the shape factors such as building length and building height on the wind environment of the residential area [22]. Liu et al. [23] and Mechri et al. [24] used performance simulation to analyze the effects of floor area, shape factor, floor height, and other shape design factors on office building energy consumption. Lu et al. established a predictive model of hall sound quality parameters using a regression spline algorithm based on the data obtained by computer modeling simulation and then discussed the influence of shape factors on hall sound quality satisfaction such as width, height, and sidewall angle [25].

Regarding performance-based shape design decision assistance, Talbourdet et al. [26] and Lu et al. [27] researched office buildings and performing arts halls and used performance simulation to design a series of similar design solutions. The performance was compared to provide suggestions for the architect’s design modification.

Different performance goals, such as ventilation and energy consumption, are oriented to optimize the building shape automatically. In terms of automatic optimization of performance-oriented shapes, Li used a simplified physical model to calculate the natural lighting performance of the building’s atrium and then used genetic algorithms to optimize the shape of the atrium based on natural lighting performance [28]. Sun and Han used artificial neural networks to build performance prediction models for office buildings based on the data obtained from computer modeling simulations and then used genetic algorithms to optimize the geometric parameters of the shape based on light and heat performance [29]. Caldas and Santos et al. used performance simulation to calculate the natural lighting coefficient of the building interior and then used a genetic algorithm to optimize the roof and skylight shape with natural lighting as the guide [30]. Moreover, researchers such as Xie [31], You et al. [32], Trubiano et al. [33], Kim et al. [34], and Znouda et al. [35] adopted similar ideas to building design.

The use of digital technology to analyze and assist the technical performance of building shape design is frequently studied. Digital analysis-based performance analysis assistance for building shape design is an important research area in recent years. Therefore, architects analyze and improve building performance based on digital technology.

1.3. Focus

Based on the overview above, the combination of the techniques-performance simulation for a large number of samples generation and big data mining is not studied before. Besides, the shape and wall structure design modes of detached houses in the suburbs of the Yangtze River Delta region, including the districts around the city’s main urban areas, have not been researched either. Therefore, to summarize the construction guidelines, we take Ningbo’s rural area as an example, which is a typical city in the Yangtze River Delta region.

As described in Figure 1 and

Table 1. Surveyed village with the names and village types recorded.

No.	Village Name	Village Type	Number of Houses
1	Shangshejiaye village, Dayan town	hilly village, new (expanded) coexisting houses inside	80
2	Maoxin village, Gulin town	hilly village, preserved houses inside	389
3	Longguanxiangheng village, township	hilly village, preserved houses inside	723
4	Baibujie village, Lijiakeng, Zhangshui town	hilly village, new (expanded) coexisting houses inside	177
5	Longxi village, Longguan township	plain village, retaining new (expanded) coexisting houses inside	79
6	Renjiaxi village, Zhangqi town	plain village, preserved houses inside	653
7	Yongwang village, Zhenhai district	plain village, preserved houses inside	789
8	Tingshan village, Fenghua district	plain village, preserved houses inside	450
9	Dongqian lake Hanling	water village, whole village demolition	520
10	Dongqian lake city Yangcun	water village, preservation houses inside	409

, the survey chooses ten villages of different types in the suburbs of Ningbo.

Figure 1 shows one typical surveyed village, while the following is the table for the surveyed village, which summarizes the village names and village types.

There lie two problems. Firstly, for the hot and humid summer in this area, the housing construction urgently needs guidance on building energy efficiency. Recently, the energy-efficient method used in this district is the simple means of making the ratio of enclosure area/volume as a reference. Still, the complicated relationship between shape and wall structure and energy consumption is influenced by the orientation, local climate, and human activities. Secondly, based on the review of a small number of samples, the current passive building research and the best design mode selected will inevitably lead to comparatively inaccurate conclusions by comparing the results of a large number of samples. There is currently no passive design study for data analysis of performance simulation results of a large number of samples. Therefore, this paper established a large number of samples for performance simulation, used a big data analysis method to deal with the output of performance simulation, and uses innovative research modes to fill the gaps in the existing body of research. The conclusion of this paper can guide the local construction design.

2. Materials and Methods

Figure 2 is the flow chart of this study. The main work is divided into three parts: data investigation, performance simulation and data analysis

2.1. Performance Simulation and Sample Generation

Sufficient samples are the basis of research. Rhinoceros/Grasshopper has the advantage of quickly generating numerous examples that other software is inconvenient. The program in Rhino/GH is used to generate samples. Thresholds and intervals for the width, depth, and height are set to generate standard building models. These building models are connected to the performance simulation program. The insulation samples are also generated in Rhino. The variables are the thickness of the air layer and the thermal insulation layer. The output is connected with Ladybug + Honeybee and the data preview part.

EnergyPlus is the core used by most current energy simulation software, ensuring the reliability of the results. The energy simulation engine in DIVA is EnergyPlus. DIVA was used as a performance simulation tool in this study. DIVA’s advantage is that it can be linked to Grasshopper and can calculate the energy consumption of multiple samples simultaneously. This unique advantage of DIVA will greatly assist this study.

The idea of performance simulation is as follows: First, we select the material of the envelope structure and set the parameters of different materials. Secondly, we connect it to the core computing unit for calculation. In the core computing unit, the operator can select the calculated indicators, output the result, and present the results in a visual form.

2.2. ANN-Based Data Analysis

There is a complex relationship between the input variables (width, depth, height, the thickness of L-shape, material thickness) and the output variables (energy consumption, the thermal performance of the wall). Therefore, the ANN is adopted to obtain the complicated relationship between variables.

The use of ANN to process large amounts of data is reliable because it is a highly adaptive learning system. The system uses external input to modify the information it has obtained or its internal structure to learn. It is a nonlinear, adaptive information processing system composed of a large number of interconnected processing units. The ANN can learn from a large number of sample data. The larger the number of samples is, the more iterations happen, the more it is trained, and the closer to reality the result is.

In this paper, the Owl plug-in is used for ANN experiments. The reason for using Owl is as follows. Firstly, Owl is a plug-in of Grasshopper, which has a seamless connection with the energy consumption calculated by DIVA. Secondly, the relationship between the operators can be elaborated through Owl. Thirdly, the results can be directly displayed in Rhinoceros and Grasshopper.

Width, depth, and height are taken as the input variables, and energy consumption is taken as the output variables. The ANN model is obtained by training the sample data. Energy consumption can be predicted by the trained model.

3. Experiments

3.1. Building Form

According to surveys, the building outlines are rectangular and L-shaped. For the rectangle ones, the width range of the buildings is 3.30 m to 14.43 m, the depth span is between 3.90 m and 11.10 m, and the height ranks from 2.60 m to 3.00 m. For the L-shape, the thickness domain is 3.00 m to 5.00 m.

Therefore, the experiment on building shape is in four aspects: (1) for the rectangular shape—the relationship between the dimension (width, depth, height) and the energy consumption; (2) for the rectangular shape—the width–depth ratio with height and the energy consumption; (3) for the L-shape—the relationship between dimension (width, depth, thickness) and energy consumption; (4) for the rectangular shape—roof slope angle with floor height and energy consumption. According to the results, the best design mode can be obtained. The following content is a detailed description of the first aspect. The other three are neglected for the methods used are similar, and the results are given directly.

3.1.1. Sample Generation

The values of width, depth, and height are used as input variables.

Table 2. The combined values of the width and depth with the height of 2.60 m.

	Depth (m)	3.30	3.80	4.30	4.80	5.30
Width (m)
3.90		3.30 × 3.90	3.80 × 3.90	4.30 × 3.90	4.80 × 3.90	5.30 × 3.90
4.40		3.30 × 4.40	3.80 × 4.40	4.30 × 4.40	4.80 × 4.40	5.30 × 4.40
4.90		3.30 × 4.90	3.80 × 4.90	4.30 × 4.90	4.80 × 4.90	5.30 × 4.90
5.40		3.30 × 5.40	3.80 × 5.40	4.30 × 5.40	4.80 × 5.40	5.30 × 5.40
5.90		3.30 × 5.90	3.80 × 5.90	4.30 × 5.90	4.80 × 5.90	5.30 × 5.90
6.40		3.30 × 6.40	3.80 × 6.40	4.30 × 6.40	4.80 × 6.40	5.30 × 6.40
6.90		3.30 × 6.90	3.80 × 6.90	4.30 × 6.90	4.80 × 6.90	5.30 × 6.90
7.40		3.30 × 7.40	3.80 × 7.40	4.30 × 7.40	4.80 × 7.40	5.30 × 7.40
7.90		3.30 × 7.90	3.80 × 7.90	4.30 × 7.90	4.80 × 7.90	5.30 × 7.90
8.40		3.30 × 8.40	3.80 × 8.40	4.30 × 8.40	4.80 × 8.40	5.30 × 8.40
8.90		3.30 × 8.90	3.80 × 8.90	4.30 × 8.90	4.80 × 8.90	5.30 × 8.90
9.40		3.30 × 9.40	3.80 × 9.40	4.30 × 9.40	4.80 × 9.40	5.30 × 9.40
9.90		3.30 × 9.90	3.80 × 9.90	4.30 × 9.90	4.80 × 9.90	5.30 × 9.90
10.40		3.30 × 10.40	3.80 × 10.40	4.30 × 10.40	4.80 × 10.40	5.30 × 10.40
10.90		3.30 × 10.90	3.80 × 10.90	4.30 × 10.90	4.80 × 10.90	5.30 × 10.90
11.10		3.30 × 11.10	3.80 × 11.10	4.30 × 11.10	4.80 × 11.10	5.30 × 11.10

shows the combined values of the width and depth for the standard building models. Due to the large amount of data, only the combined width and depth values with the height of 2.60 m are shown. Among them, the width, depth, and height are modeled with an interval of 50 cm, that is, 23 × 15 × 14 = 4830 models are established.

Figure 3 is a schematic diagram of the width, depth, and height combination. As shown on the right, buildings of the same height are located on the same plane. 23 groups of models for width subdivisions are established in the X direction and 15 groups for depth in the Y direction. Because there are too many models to display, we used the computer to form a three-dimensional matrix.

3.1.2. Performance Simulation

Table 3. Simulation parameters settings.

Parameter	Value
Human density	0.05 people/m2
Equipment energy consumption	12.00 W/m2
Lighting energy consumption	12.00 W/m2
Illumination	300.00 lx
Heating and cooling limit	100.00 W/m2
Wall	0.26 m brick wall
Roof	150 mm reinforced concrete + 50 mm rock wool insulation
Roof slope	45 degrees
Ground	300 mm concrete

shows the parameter settings in this work:

The thermal indicators related to energy consumption include the following five categories: human heat dissipation index, lighting heat dissipation index, thermal index of electrical appliances, thermal gain and loss index of the envelope structure, and air heat balance index.

The authors simulated 4830 samples. According to the survey, the width of the sample was 3.30–14.43 m, the depth was 3.90–11.10 m, and the height was 2.60–9.00 m.

3.2. Thermal Performance of the Envelope

3.2.1. Survey

According to surveys, the enclosing structures of detached houses in the Yangtze River Delta region suburbs are divided into six types: brick walls, block walls, weaving walls, wooden boards, rammed earth walls, and stone walls.

According to the Ningbo government [36], rural housing construction in Ningbo is mainly divided into three stages: Field surveys of typical villages in the outskirts of Ningbo in the Yangtze River Delta region found that 19% of the houses were built before 1949, and this type of building was mainly brick–wood, stone–wood, and stone structures. Between 1949 and 1990, 37% of the houses were built. Buildings of this type are primarily brick–concrete structures. 44% of the houses built after 1990 account for most of the buildings. This type of building is mainly brick–concrete structures, supplemented by frame structures.

It can be seen from this that the enclosing structure of detached houses in the suburbs of Ningbo is mainly brick walls and block walls. Striped clay walls, wooden boards walls, rammed earth walls, and stone walls are used less frequently in modern times. Therefore, this section takes the brick and block walls as the research objects. After the authors’ experiments, the simulation data of the block wall is the same as the brick wall, so it will not be described once again. Therefore, this section will discuss the performance simulation of brick walls in detail.

Through investigation, it was found that the outer wall has no insulation method but is simply plastered inside and the envelope structure outside. That is bound to affect the thermal insulation performance of the building significantly. Therefore, it is necessary to perform appropriate thermal insulation treatment on the building envelope.

At present, energy-efficient and thermal insulation measures for building walls in China are divided into three categories: internal insulation, sandwich insulation, and external insulation.

In the early days of implementing building energy-efficient design standards, the Chinese adopted the method of internal insulation. Internal insulation means the additional insulation material is added to the interior wall of the building space to achieve energy-saving purposes. However, the problems with internal insulation are also apparent. The thermal efficiency is low, and the insulation layer fixed indoors brings much trouble to the secondary decoration and hanging facilities. Once a quality problem occurs, it will cause great distress to the resident during the repair.

Sandwich insulation is the use of layered treatment on the outer retaining wall to form a “wall insulation layer-wall” system to achieve the purpose of heat preservation and energy efficiency. The top three high-rise residential areas in Beijing, built in the early 1980s, are typical examples.

External wall insulation is the addition of insulation materials on the outside of the building’s exterior wall to achieve energy-saving purposes. External wall insulation technology is a kind of building energy-efficient technology that is being vigorously promoted at present. Compared with internal insulation, external insulation has better energy-efficient effects. The exterior insulation technology is suitable for new buildings and the energy-efficient reconstruction of existing buildings. The outer insulation material is coated on the outside of the main structure, which can effectively protect the main construction of the building and prolong the service life of the building. At the same time, it eliminates the phenomenon of condensation and mildew on the indoor side of the exterior wall and improves the comfort of the indoor living environment.

Therefore, the choice of sandwich insulation and external insulation is better. In contrast, the internal insulation is abandoned due to low thermal efficiency and is unsuitable for reconstruction. Therefore, this section adapts sandwich insulation and external insulation for research.

Air interlayer is currently being developed as a new external wall insulation technology because the heat transfer in closed air interlayers has the most substantial proportion of radiative heat transfer and the smaller portion of convection and heat conduction. Layers have significant advantages for wall insulation. Gao introduced that air interlayers can improve the thermal insulation performance of external walls [37].

The left side of Figure 4 shows the construction method of the brick wall, which is mainly plastered with 0.01 m inside and outside the 0.24 m brick wall. The middle picture is the external thermal insulation treatment of the existing brick wall, and an air interlayer and a thermal insulation layer are placed outside the existing brick wall. However, since the air interlayer needs to be implemented in an external insulation board, a metal keel thermal bridge is generated. To minimize the impact of the thermal bridge, the thermal insulation structure of the brick wall is further adjusted in the right picture. Two layers of air interlayer and one layer of thermal insulation are placed in the middle of a skin brick to form a “brick wall + air interlayer + thermal insulation layer + air interlayer + brick wall “sandwich-like insulation layer. They used the outer air interlayer to reduce the impact of the thermal layer keel thermal bridge.

This section studies the two different insulation measures mentioned above.

The external window of the Ningbo country house is mostly square. The square window size is mainly a combination of 0.95 m, 1.20 m, 1.50 m, and 1.80 m. Based on the square window, the width of the square window is sometimes expanded to the room width and height below the cornice on the second floor to get a better view and natural lighting. The size of the east and west window is the usual square window size, or there are no windows to avoid sun exposure. The common windowsill height is 0.90 m.

3.2.2. Performance Simulation

The thermal performance of the wall is divided into two parts: summer and winter. This article only uses summer heat insulation as an example.

The method of generating a large number of samples is as described above. Some of the generated models are shown in Figure 5.

With Ladybug + Honeybee, after setting the material, thermal conductivity, and thermal storage coefficient, we set the indoor and outdoor temperatures of a large number of samples. According to the current national standard [38], the indoor design temperature of the living space during the day in summer is 26.00 °C, and the average temperature of the hottest month in Ningbo is 30.10 °C (Figure 6).

The thermal parameter setting of building envelope is shown in

Table 4. Thermal parameter setting of building envelope.

Parameter	Value
Thermal conductivity of brick wall	0.81 W/(m·K)
Thermal storage coefficient of brick wall	10.53 W/(m2·K)
Thermal conductivity of EPS board	0.04 W/(m·K)
Thermal storage coefficient of EPS board	0.36 W/(m2·K)
Thermal conductivity of air interlayer	0.023 W/(m·K)
Thermal storage coefficient of air interlayer	0.00 W/(m2·K)

[39]:

4. Results

4.1. Building Form

Using ANN, Owl was used to analyze the relationship between the four (three input data of width, depth, height, and one output data of energy consumption).

The generated results are expressed by a cube model, in which the X, Y, and Z-axis values are the width, depth, and height of each sample.

Figure 7 is a schematic diagram of the data analysis of 4830 samples. The X-axis is the width (3.30 m to 14.43 m), Y-axis is the depth (3.90 m to 11.10 m), Z-axis is the height (2.60 m to 9.00 m), and the model color represents the energy consumption value from green to red to indicate 2.26 × 10⁷ J/m² to 1.37 × 10⁹ J/m², i.e., 6.28 kWh/m² to 379.87 kWh/m².

The energy consumption and corresponding width, depth, and height values are accurately captured below, according to the colors in Figure 7.

Mesh1 in Figure 8 is the envelope generated by grabbing corresponding points of the same energy consumption value using Grasshopper. The boundary of the surface is the junction of red and yellow. The energy consumption on Mesh1 is 9.47 × 10⁸ J/m². The coordinates of the intersection points A, B, C, and D are (3.30, 3.90, 6.06), (3.30, 11.10, 8.49), (3.52, 11.10, 8.87), (7.75, 3.90, 9.00). When the width, depth, and height values are above Mesh1, the energy consumption is the largest, and the range is 9.47 × 10⁸–1.37 × 10¹⁰ J/m². Within this range, the energy consumption rapidly increases with width and height but gradually increases with depth.

It shows that the combination of the width, depth, and height of the building above Mesh1 leads to higher energy consumption, i.e., the building size within this range is inappropriate.

Simultaneously, Mesh2 in Figure 9, with the corresponding energy consumption of 4.86 × 10⁸ J/m². Coordinates of Intersect points are E (3.30, 3.90, 3.50), F (3.30, 11.10, 4.78), G (7.97, 11.10, 9.00), H (14.43, 6.35, 9.00), I (14.43, 3.90, 6.31). When the value of width and depth is outside the range of Mesh2, changing the floor’s width, depth, or height contributes relatively less to the energy consumption. At this time, the energy consumption is also low (2.26 × 10⁷–4.86 × 10⁸ J/m²). It is advisable to take the building size value within this range.

It shows that changing the building width, depth, and floor height between Mesh1 and Mesh2 brings considerable energy. As shown in Figure 10, when the values of width, depth, and height change between Mesh1 and Mesh2, the energy consumption gradually decreases from 1.37 × 10⁹ J/m² to 9.47 × 10⁸ J/m². Within this range, the energy consumption falls with the increased width and depth, and the energy consumption gradually increases with the rise in height. It is not advisable to take the building size within this range.

4.2. Thermal Performance of the Envelope

As shown in Figure 11, an excerpt from Ladybug + Honeybee, the left side of each model represents the inner surface of the envelope structure, and the right side represents the outer surface of the envelope structure. The colors are black to red, indicating that the heat flux value is small to large.

Owl was used to analyze the relationship between two inputs and one output. The inputs are the thickness of the air interlayer and the thickness of the insulation layer, and the output is the heat flux on the inner surface of the envelope structure. The calculation iteration is 10,000.

The generated results are expressed by a three-dimensional coordinate model. The values of the X, Y, and Z axes respectively show the thickness of the air interlayer, the thickness of the thermal insulation layer, and the heat flux on the inner surface of the envelope structure. The resulting three-dimensional coordinate model is shown below. In the big data model trained by the artificial neural network, the three-dimensional coordinates corresponding to each point are the thickness of the air interlayer, the thickness of the insulation layer, the heat flux value of the inner surface of the envelope structure, and the inner surface of the envelope structure corresponding to it. Color-coded data can also track heat flux values.

Figure 12 is a schematic diagram of data analysis after training using the envelope structure’s inner surface heat flux value with 40,000 random samples. Among them, the X-axis is the thickness of the air interlayer (value range is 0.00–0.20 m), the Y-axis is the thickness of the insulation layer (value range is 0.00–0.20 m), and the Z-axis is the heat flux (value of the inner surface of the envelope structure) (The range is 1.86 W/m² to 8.47 W/m²). The color of the heat flux value on the inner surface of the envelope structure changes from green to red to indicate that the energy consumption ranges from low to high, from 1.86 W/m² to 8.47 W/m².

As the color of the three-dimensional coordinate model shows, as the thickness of the insulation layer continues to increase, the value of the heat flux on the inner surface of the envelope structure decreases sharply and then gradually decreases. As the thickness of the air interlayer increases, decreasing surface heat flux does not change much.

As shown in Figure 13, Curve1 is the yellow–green boundary of the color of the three-dimensional coordinate model. At this time, the envelope structure’s corresponding internal surface heat flux is 3.84 W/m². The curve Curve1 intersects the three-dimensional coordinate model at A (0.00, 0.04, 3.84) and B (0.20, 0.05, 3.84). It can be seen from the figure that when the thickness of the insulation layer is greater than 0.05 m, the heat flux value of the inner surface of the envelope structure is small. At this time, the rate of change of the heat flux on the inner surface of the envelope structure begins to slow down. The change of the air interlayer has little effect on the heat flux change on the inner surface of the envelope structure.

Figure 14 is the front view of the figure above. This diagram represents the relationship between the thickness of the air interlayer and the heat flux on the inner surface. Curve2 is the relationship between the thickness of the air interlayer and the heat flux on the inner surface of the envelope structure when the thickness of the insulation layer is 0.0064 m. As shown in the figure, Curve2 showed a strong downward trend and a gentle movement. In the figure, point C is the turning point of Curve2. At this time, the abscissa of point C is 0.024. When the thickness of the EPS insulation layer is 0.0064 m, the optimal thickness of the air interlayer is 0.024 m.

After experiments, when the thickness of the insulation layer is changed from 0.00 m to 0.20 m, the optimal air interlayer thickness is about 0.024 m. Because the experimental methods are the same, this section will not have repeated discussions and only give conclusions.

It can be known from the above experiments that the index that affects the summer insulation performance of the envelope structure under the external insulation method is mainly the thickness of the insulation layer. When the EPS insulation board is selected as the insulation layer, the optimal insulation layer thickness is 0.05 m, and the optimal air interlayer thickness is 0.024 m. The air interlayer influences the summer insulation of the envelope structure, but the effect is not significant.

5. Discussion

5.1. Building Form

From the above experiments, we can intuitively find out that changes in the energy consumption of the independent rectangular residential buildings in the suburbs of the Yangtze River Delta region with the changes in width, depth, and height. The discussion on the results is as follows:

(1)

For rectangular buildings, the larger the building area is, the lower the building energy consumption per unit area will be within the limited building size (width: 3.30 m to 14.43 m, depth: 3.90 m to 11.10 m, height: 2.60 m to 9.00 m);

(2)

When the width of the rectangular is higher than 7.97 m (X coordinate of point G) and the depth is higher than 6.35 m (Y coordinate of point H), the energy consumption per unit area is the lowest. At this point, increasing width and depth has almost no impact on the energy consumption; and

(3)

Energy consumption increases with the increase of rectangular building height. The influence of building height on energy consumption decreases with the increase of building width and depth. Therefore, on the premise of meeting the housing needs, reducing building height, and increasing building width and depth will lead to lower energy consumption.

On this basis, the authors summarize the following design modes:

(1)

Regardless of whether they are rectangular buildings or L-shaped buildings, the building height should be reduced, and the building width and depth should be increased as much as possible. It is recommended that the building width be higher than 5.54 m and the depth be higher than 4.75 m.

(2)

Based on this study, the suggested building heights and corresponding optimal width-to-depth ratios are summarized in

Table A1. The suggested combination of height and width/depth.

Floor	Height (m)	Width/Depth
1	2.60	1.09
	2.70	1.13
	2.80	1.16
	2.90	1.16
	3.00	1.15
2	5.20	0.93
	5.30	0.92
	5.40	0.91
	5.50	0.95
	5.60	0.94
	5.70	0.93
	5.80	0.90
	5.90	0.92
	6.00	0.90
3	7.80	0.96
	7.90	0.96
	8.00	0.96
	8.10	0.96
	8.20	0.97
	8.30	0.97
	8.40	0.98
	8.50	0.93
	8.60	0.94
	8.70	0.95
	8.80	0.95
	8.90	0.96
	9.00	0.96

in Appendix A. Overall, the width-to-depth ratio ranges from 0.90 to 1.16. When the building height is between 2.6 m and 3 m, the width-to-depth ratio is higher than 1.09, and when the building height is higher than 5.2 m, the width-to-depth ratio is lower than 1.

(3)

For L-shape, the building thickness should be greater than 4.23 m.

(4)

The lower the building roof angle, the lower the energy consumption is, and the most energy-efficient flat roof. If a sloping roof shape design is required, the building roof angle should be as low as 29.98°.

5.2. Thermal Performance of the Envelope

The discussion about the thermal performance is as follows:

(1)

The increase in the thickness of the air interlayer and the thermal insulation layer can improve the wall’s thermal insulation performance in the summer and winter seasons. Furthermore, the thickness changes in the thermal insulation in summer are similar to that in winter. With the increase of the thickness of the air interlayer and the thermal insulation layer, the thermal insulation effect has shown a trend of first improvement and then stabilization.

(2)

The change in the thickness of the thermal insulation layer has a more significant impact on the thermal insulation. With the increase in the thickness of the thermal insulation layer, the heat flux on the inner surface of the envelope structure first showed a sharp decrease and then gradually flattened. It can be known from the calculation that when the EPS (Expanded Polystyrene) insulation board is selected for external insulation, the optimal thickness of the insulation layer is 0.05 m; when the EPS insulation board is selected for sandwich insulation, the optimal thickness of the insulation layer is 0.037 m.

(3)

The change in the thickness of the air interlayer has less influence on the thermal insulation effect. With the increase of the thickness of the air interlayer, the change of the heat flux on the inner surface of the envelope structure shows a trend of rapid decrease and then gentleness. It can be known from the calculation that when the EPS insulation board is selected for external insulation, the optimal thickness of the air interlayer is 0.024 m; when the EPS insulation board is selected for sandwich insulation, the optimal thickness of the air interlayer is 0.013 m.

(4)

The comparison between the optimal thickness of the brick wall insulation layer and the air interlayer in the external insulation and sandwich insulation structure. The “+ 10 mm plastering” sandwich insulation method is better than the “10 mm plastering + 115 mm brick wall + 10 mm plastering + 115 mm brick wall + air interlayer + insulation layer” outer insulation method.

6. Conclusions

Existing studies mainly focus on the research of individual buildings. In this study, parameterization technology and performance simulation techniques are used to obtain the relationship between the variables of building form and thermal performance, and energy consumption. Based on the simulation results, the best design pattern is summarized to provide practical solutions for the actual project. Based on this study, the following important results are obtained: (1) Optimal building height, width, and depth; (2) Pptimal width-to-depth ratio of the building under different heights; (3) Optimal thickness of insulation and air interlayer.