Sensitivity Analysis of Envelope Design for Rural Dwellings in Cold Regions of China: An Orthogonal Experiment-Based Approach

Abstract

To improve the energy efficiency and indoor environmental quality of rural dwellings in China’s cold regions, this study selected a typical rural dwelling in Linyi, Shandong Province, as a case study. Integrating field measurements with parametric simulations, the Orthogonal Experimental Design method was employed to systematically evaluate the impacts of 12 envelope design parameters on building energy demand (ED_tot, ED_H, ED_C), thermal comfort (PNT_ave), daylight performance (UDI_ave), and economic outcomes (retrofit cost and return on investment, ROI). Three sets of orthogonal experiments with varying value ranges (Case 1–3) were conducted. The results revealed that U-Window and SHGC are the most critical factors influencing energy demand and thermal comfort, while light transmittance (Trans) exerts the greatest influence on daylighting. The economic analysis demonstrated that window material is the primary determinant of retrofit costs, whereas building depth and the south window-to-wall ratio (WWR-South) significantly affect ROI. Additional range and variance analyses quantified the significance of each parameter and revealed nonlinear influence patterns. This research provides data support and decision-making references for the energy-efficient retrofit and multi-objective optimization of rural dwellings in cold regions, offering strong practical implications.

1. Introduction

1.1. Research Background

Recent data indicate that the building sector accounts for about 37% of global energy consumption and roughly 40% of global carbon dioxide emissions [1]. In 2022, operational energy consumption in China’s building sector accounted for approximately 21% of the country’s total energy use [2], while overall building energy consumption represented 46.7% of national energy consumption [3]. With ongoing economic growth, China’s building energy demand is projected to rise by around 50% by 2060 [4]. Reducing emissions in the building sector is therefore vital for meeting China’s targets of peaking carbon emissions by 2030 and achieving carbon neutrality by 2060 [5]. However, owing to insufficient scientific design guidance and relatively low construction quality, rural dwellings often consume more energy than urban buildings [6]. Rural China spans vast areas, with rural residents making up 36.11% of the total population [7]. According to the Ministry of Housing and Urban–Rural Development of China, by 2030, the average rural housing area per capita will reach 45 m², and the total rural housing area will expand to 22 billion m² [8]. Therefore, promoting the sustainable development of rural dwellings is a critical element of China’s energy conservation and emission reduction strategies.

Most rural dwellings in China are self-built by residents and lack systematic scientific design guidance as well as energy-saving measures. As a result, their thermal performance is often poor, and problems with the indoor thermal environment are significant [9]. These issues are especially severe in northern cold regions, where rural dwellings face greater challenges in both indoor thermal conditions and energy consumption [7,10]. Numerous studies have shown that key design parameters of rural dwellings—such as the thermal performance of building envelopes, window-to-wall ratio, and aspect ratio—play an essential role in improving the indoor thermal environment and reducing energy demand [11]. Therefore, this study uses rural dwellings in Shandong Province as a case study to systematically examine the design parameters of rural houses in cold regions of China, analyzing their influence patterns and relative weights on building energy demand, thermal comfort, daylight, and economic outcomes.

1.2. Literature Review

Due to differences in construction methods, materials, and usage patterns, rural dwellings in China exhibit significant disparities from urban residences in terms of indoor thermal environment and thermal comfort. Extensive field studies have consistently documented that rural houses often suffer from poor and highly fluctuating indoor thermal conditions [12,13,14]. For instance, surveys in severe cold regions revealed that indoor temperatures in winter frequently drop below 16 °C, leading to pronounced thermal discomfort [14]. This situation necessitates performance optimization strategies tailored specifically for rural housing. While reducing energy demand remains essential, improving thermal comfort must be given equal priority, alongside other critical objectives such as daylighting and cost-effectiveness, given the economic and technical constraints in rural areas [2].

To address these challenges, researchers have implemented various optimization strategies in diverse climatic contexts. Simulation-based optimization has proven particularly effective. For example, Duan applied such methods to optimize key envelope and form parameters of rural dwellings in Dalian and other cold regions, reporting substantial improvements: thermal comfort time increased by approximately 41%, and annual energy demand was reduced by around 80.96% [7]. These findings underscore the pivotal role of building performance simulation tools, such as the Ladybug Tools plugin within the Grasshopper platform, which integrates validated engines like EnergyPlus and Radiance [15]. To further enhance computational efficiency, machine learning-based surrogate modeling techniques have been widely adopted to replace time-consuming physical simulations, often achieving prediction accuracy (R²) above 0.95 while reducing computation time by orders of magnitude [16,17,18]. Collectively, these studies validate the considerable potential and necessity of performance optimization for rural buildings at the early design stage.

In the context of retrofits, enhancing building performance generally requires a combination of active and passive strategies [19]. For active technologies, such as air source heat pumps (ASHP) [20] and photovoltaic (PV) systems [21,22], economic costs must be carefully evaluated. Nevertheless, given the relatively constrained economic conditions in rural areas, passive design strategies hold significant promise due to their low cost and climate adaptability. Climate-responsive design, a key approach to addressing climate change, primarily employs passive strategies to harmonize buildings with specific climatic conditions, thereby reducing energy consumption and carbon emissions [23,24,25,26,27]. Common passive measures focus on optimizing the building envelope and exploiting natural conditions, including the use of high-performance insulation materials like EPS and aerogel [28,29,30,31], low-emissivity (low-e) glazing [32,33], shading devices [34], and region-specific constructions such as sunspaces [35,36,37].

However, when attempting to simultaneously optimize multiple envelope parameters to achieve conflicting objectives such as minimizing energy consumption, maximizing thermal comfort, and minimizing cost, inherent trade-offs emerge [38,39,40]. This complexity makes multi-objective optimization (MOO) a mainstream approach for addressing such architectural design problems [41,42,43]. MOO frameworks, such as those based on the NSGA-II algorithm, have been successfully applied to identify Pareto-optimal solutions for rural buildings, demonstrating the ability to balance, for instance, a 34.42% reduction in energy use with a 11.35% improvement in comfort metrics [44].

Despite the development of MOO frameworks, their effectiveness largely hinges on a critical preliminary step: parameter sensitivity analysis (SA). Accurate SA can identify key parameters that significantly influence multiple objectives, thereby considerably narrowing the optimization search space and improving MOO efficiency [45]. However, existing SA methods in architectural studies present notable limitations. First, they are often relatively coarse, relying on one-variable-at-a-time (OVAT) approaches or simple regression analyses, which are inefficient and insufficient for capturing complex interactions among multiple parameters [44]. For instance, OVAT methods can misleadingly underestimate the importance of a parameter that only has a significant effect in combination with others. Second, the depth of analysis is often inadequate, typically restricted to ranking parameter significance without investigating the nonlinear influence trends or underlying physical mechanisms. This lack of depth limits the practical applicability of the results for guiding design decisions.

To overcome these limitations, this study introduces an efficient and systematic sensitivity analysis framework based on Orthogonal Experimental Design (OED). This approach can accurately quantify the main effects of multiple envelope design parameters on energy consumption, thermal comfort, daylighting, and cost using a minimal number of simulation runs, while clearly revealing the influence trends of each parameter across different value ranges. Consequently, it provides a more robust and in-depth decision-making foundation for subsequent multi-objective optimization, specifically addressing the identified gaps in the context of cold-region rural dwellings.

1.3. Research Objectives

This study aims to develop an efficient and systematic sensitivity analysis framework based on Orthogonal Experimental Design (OED) to address the limitations of existing methods in the multi-objective optimization of rural dwellings. The framework quantitatively evaluates the impacts of envelope design parameters on conflicting objectives such as energy consumption, thermal comfort, daylighting, and cost. It not only identifies key parameters but also elucidates their underlying mechanisms, providing essential theoretical support and variable selection strategies for subsequent high-precision multi-objective optimization, thereby enhancing both the efficiency and reliability of the optimization process.

The specific technical objectives are as follows:

• Develop a parametric simulation and experimental design platform: Based on a typical rural dwelling model and the Grasshopper/Ladybug Tools performance simulation environment, key envelope design variables (e.g., envelope U-values, window-to-wall ratios, building aspect ratios) and their feasible ranges are determined. Appropriate orthogonal arrays are then selected to construct the simulation experiment matrix.
• Quantify parameter sensitivity significance: Range analysis and Analysis of Variance (ANOVA) are employed to precisely calculate the main effect contributions of each design parameter on multiple performance indicators, including indoor heating and cooling loads, percentage of annual comfortable time (PNT_ave), daylight (UDI_ave), renovation cost, and return on investment (ROI).
• Reveal parameter influence patterns and trends: Based on orthogonal experiment results, plots of the relationships between key parameter variations and performance responses are generated to qualitatively and quantitatively describe influence trends, while integrating building physics principles to explain underlying mechanisms.
• Establish optimization decision support: Transform the sensitivity analysis results into clear decision-making information and develop parameter selection rules for guiding multi-objective optimization. Priority is given to “driving” parameters that exhibit high sensitivity across multiple objectives, thereby significantly reducing the search space and computational cost of subsequent optimization algorithms.

2. Materials and Methods

2.1. Case Study Building and On-Site Measurement

This study utilizes a validated baseline model of a typical rural dwelling in Linyi, Shandong Province, which was originally developed and calibrated in our previous work [7]. Linyi lies in a cold climate zone, characterized by distinct seasonal variations, with hot and humid summers and cold, dry winters. The selected building type is widely distributed in the local rural context and is considered highly representative [46]. The dwelling is constructed with a brick–concrete structure and primsarily oriented along the north–south axis (Figure 1). Its envelope design reflects the common construction practices of rural houses in the region [2]. Detailed information on materials and structural components is presented in

Table 1. Material construction and thermal properties of the envelope of the case study model (Source: [7]).

Envelope	Construction	R (m2⋅K/W)
Exterior wall	5 mm cement mortar + 240 mm clay brick + 5 mm cement mortar + 10 mm lime plaster	0.34
Interior Wall	10 mm lime plaster + 240 mm clay brick + 10 mm lime plaster	0.34
Roof	50 mm clay tile + 30 mm cement mortar + 100 mm Clay and grass + 10 mm asphalt felt	0.29
Floor	10 mm lime plaster + 240 mm clay tile + 10 mm lime cement mortar	0.34
Ceiling	50 mm plasterboard	0.07
Exterior window	3 mm single pane plain glass	0.001

.

This dwelling was selected as a typical case due to its high representativeness of rural dwellings in the cold region of Shandong Province. Preliminary field surveys and literature reviews [7] indicated a high degree of homogeneity in this region regarding spatial layout (main rooms facing south on the north side), structural system (brick–concrete), and envelope construction practices. The selected building is a common prototype, and its baseline condition accurately reflects the typical thermal performance level prevalent in the local rural building stock [10]. Consequently, the findings derived from this case study are highly relevant to this specific building typology.

For the purpose of this simulation study, the architectural model was simplified to focus on the primary living spaces. The analysis concentrates on the three south-facing rooms on the north side of the courtyard (ROOM-a/b/c), as they represent the core functional area common to this building typology and are the main consumers of energy for heating and cooling. Among them, ROOM-a and ROOM-c function as bedrooms, while ROOM-b serves as a living room. All three rooms are primarily daylit and ventilated through windows only on the south facade, with a baseline window-to-wall ratio (WWR) of 0.15.

To obtain realistic indoor thermal environment data for validating the accuracy of subsequent simulation models, one-week field measurements were conducted in the main living spaces of the case dwelling during both winter (December) and summer (August) of 2022. The instruments employed included a TR-72nw thermometer (with a temperature accuracy of ±0.5 °C). Measurement points were positioned at a height of 1.5 m above the floor at the center of each room, avoiding doors, windows, and heat sources to minimize local disturbances. Data were recorded at 10 min intervals (Figure 2).

2.2. Simulation Setup and Validation

In this study, building performance simulations were carried out using the Ladybug Tools plugin suite within the Rhino/Grasshopper visual programming platform. The toolkit integrates validated simulation engines, including EnergyPlus for energy demand and thermal comfort analysis, and Radiance for daylighting evaluation, thereby enabling seamless linkage between parametric modeling and performance assessment. A parametric model of the case dwelling was developed in Grasshopper based on its actual dimensions, construction details, and material properties. To ensure consistency between simulation and measured conditions, outdoor meteorological data collected during the field campaigns were applied as boundary conditions. The calibration parameters of the simulation model are summarized in

Table 2. Simulation parameters settings for the case study model (Source: [7]).

People (p/m2)	Lighting (W/m2)	Equipment (W/m2)	Ventilation (m3/s per Person)	Infiltration (m3/s per m2 Facade)
0	0	0	0	0.0001

. The internal heat gains and ventilation rates listed in Table 2 were set to zero or minimal values during the simulation calibration phase. This was a deliberate strategy to isolate the overall thermal response of the building envelope to external conditions by eliminating unmeasured and variable internal loads. This approach facilitates a more accurate calibration of the model against the measured data, which was collected under controlled, unoccupied conditions. The calibration parameters for the simulation model are summarized in Table 2. For key unknown parameters, such as the infiltration rate, a calibration process was undertaken. A range of values (0.001, 0.003, and 0.006 m³/s·m²) recommended by Ladybug Tools for naturally ventilated buildings were tested against the measured data. The value of 0.0001 m³/s·m² was ultimately selected as it yielded the highest model agreement. This very low value accurately reflects the nearly airtight conditions during the measurement campaign, where all windows and doors were intentionally kept closed and sealed to isolate the envelope’s thermal performance.

To ensure high consistency between the simulation and the measured conditions, the outdoor meteorological data used as boundary conditions were modified using on-site monitoring data. Specifically, the actual air temperature data recorded by the outdoor TR-72nw logger was used to replace the temperature data in the standard EPW file for the corresponding period. This approach eliminates errors arising from regional climate differences, allowing the model calibration to more accurately reflect the thermal performance of the building envelope itself.

The Willmott index of agreement ($d_w$) was employed to assess the calibration performance. This index provides a standardized measure of prediction accuracy, with values ranging from 0 to 1. A score of 0 denotes complete divergence between simulated and observed data, whereas a score of 1 represents perfect concordance. In practice, models with $d_w$ values greater than 0.6 are typically regarded as having acceptable predictive capability. The calculation is expressed as follows:

$$d_w=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(M_i-O_i\right)}^2}{{\sum }_{i=1}^n{\left(\left|M_i-\overline{O}\right|+\left|O_i-\overline{O}\right|\right)}^2}}$$

(1)

where $M_i$ represents the simulated results, $O_i$ represents the observed values, $\overline{O}$ is the mean of the observed values, and $n$ is the number of samples.

The model validation outcomes are presented in Figure 3, where the y-axis represents the indoor air temperature used for calibration. The results demonstrate good agreement between simulated and measured data in both summer and winter. For ROOM-b, the calculated Willmott index of agreement was 0.70 in summer and 0.95 in winter; for ROOM-c, it was 0.72 in summer and 0.82 in winter. All values exceed the acceptable threshold of 0.6, indicating that the established model reliably predicts the building’s thermal performance and is suitable for subsequent parametric simulation studies.

This calibrated model, which accurately reflects the actual thermal performance of the case-study building (with envelope properties as defined in Table 1), serves as a validated baseline for all subsequent parametric sensitivity analyses.

The parameter settings in Table 2 were designed to ensure the accuracy of the model calibration. The specific selection of an unoccupied dwelling for on-site measurement, with windows closed and no occupancy or equipment use, was intended to prevent any interference from occupant activities and equipment on the measured data. This approach allowed us to accurately capture the pure thermal response of the building envelope to external weather conditions, providing a high-quality dataset for model validation.

After the model was successfully validated, all parametric simulations were conducted using realistic operational parameters based on field surveys to reflect actual living conditions:

• Natural ventilation and HVAC strategy: To simulate occupant behavior, windows were set to open automatically for natural ventilation when the outdoor temperature was between 18 °C and 26 °C. The HVAC system was activated for heating when the indoor temperature dropped below 18 °C and for cooling when it exceeded 26 °C.
• Internal Loads: The occupant, lighting, and equipment power densities used in the simulations are provided in

  Table 3. Interior rooms design loads of simulation mode (Source: [7]).

  People (p/m2)	Lighting (W/m2)	Equipment (W/m2)	Ventilation (m3/s per Person)	Infiltration (m3/s per m2 Facade)
  0.04	5	3.8	0.01	0.0001

  .
• Operational Schedules: The operating schedules for these loads, based on field surveys, are provided in

  Table 4. Program setting of simulation model (Source: [7]).

  Time		0	1	2	3	4	5	6	7	8	9	10	11
  Occupancy (p/m2)	ROOM-a/c	1	1	1	1	1	1	1	0.5	0.5	0	0	0
  	ROOM-b	0	0	0	0	0	0	0	0.5	0.5	1	1	1
  Activity (W/p)	ROOM-a/b/c	120	120	120	120	120	120	120	120	120	120	120	120
  Lighting (W/m2)	ROOM-a/c	0	0	0	0	0	0	1	0.5	0	0	0	0
  	ROOM-b	0	0	0	0	0	0	0.5	1	0	0	0	0
  Equipment	ROOM-a/c	0	0	0	0	0	0	0	1	1	0	0	0
  	ROOM-b	0	0	0	0	0	0	0	0.5	1	1	0.5	0.5
  Time		12	13	14	15	16	17	18	19	20	21	22	23
  Occupancy (p/m2)	ROOM-a/c	0	0	0	0	0	0	0	0	0	0.5	1	1
  	ROOM-b	1	1	1	1	1	1	1	1	1	0.5	0	0
  Activity (W/p)	ROOM-a/b/c	120	120	120	120	120	120	120	120	120	120	120	120
  Lighting (W/m2)	ROOM-a/c	0	0	0	0	0	0	0	0	0	1	1	0
  	ROOM-b	0	0	0	0	0	0	0	1	1	0.5	0	0
  Equipment	ROOM-a/c	0	0	0	0	0	0	0	0	0	1	1	0
  	ROOM-b	1	1	0.5	0.5	0.5	0.5	1	1	1	0.5	0	0

  .

2.3. Orthogonal Experimental Design for Sensitivity Analysis

To systematically and efficiently examine the effects of multiple envelope parameters on building performance, this study adopted Orthogonal Experimental Design (OED) as the primary method for sensitivity analysis.

(1)

Selection of design parameters and determination of levels

Drawing on the previous literature and local practices, twelve key envelope design parameters were identified for sensitivity analysis (

Table 5. Distribution of Design Variable Values.

Variables	Range of Change	Variables	Range of Change
Depth (m)	3~7.2 (0.6/step)	U-Roof	0.1~2.1 (0.4/step)
WWR-East	0.1~0.9 (0.1/step)	U-Ceiling	0.5~4.5 (0.5/step)
WWR-South	0.1~0.9 (0.1/step)	U-Window	0.4~5.2 (0.6/step)
WWR-West	0.1~0.9 (0.1/step)	SHGC	0.1~0.9 (0.1/step)
WWR-North	0.1~0.9 (0.1/step)	t-vis	0.1~0.9 (0.1/step)
U-Wall	0.1~2.1 (0.4/step)	Trans	0.1~0.9 (0.1/step)

). To maintain a manageable experimental scale, three representative levels were assigned to each parameter. The feasible value ranges were determined based on a comprehensive review of local practices and building codes, with the final simulated ranges appropriately expanded to explore influence trends under broader boundary conditions. Given the wide variation in these ranges, three separate orthogonal experiments (Case 1, Case 2, Case 3) were conducted to avoid overly broad intervals in a single experiment and to comprehensively capture parameter variability and potential nonlinear effects. The factor levels for this first round of simulations, focused on building performance, are detailed in

Table 6. Orthogonal experiment factor levels for building performance objectives.

	Case 1			Case 2			Case 3
Depth (m)	3	4.1	5.2	5	6.1	7.2	3	5.1	7.2
WWR-North	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
WWR-South	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
WWR-West	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
WWR-East	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
U-Wall (W/m2·K)	0.1	0.6	1.1	1.1	1.6	2.1	0.1	1.1	2.1
U-Roof (W/m2·K)	0.1	0.6	1.1	1.1	1.6	2.1	0.1	1.1	2.1
U-Ceiling (W/m2·K)	0.5	1.5	2.5	2.5	3.5	4.5	0.5	2.5	4.5
U-Window (W/m2·K)	0.4	1.6	2.8	2.8	4	5.2	0.4	2.8	5.2
SHGC	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
t-vis	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9
Trans	0.1	0.3	0.5	0.5	0.7	0.9	0.1	0.5	0.9

. It is critical to note that these three cases represent different value-level sets applied to the same building model, not different buildings.

A second round of orthogonal simulations was conducted for the economic analysis (evaluating retrofit cost and ROI). This round utilized the same experimental matrix for the first eight parameters concerning building geometry and opaque envelope insulation (Depth through U-Ceiling). The key modification was applied to the four window performance parameters (U-Window, SHGC, t-vis, Trans), which were replaced by a single categorical variable, Window material, representing five specific glazing types with fixed properties and costs (

Table 7. Orthogonal experiment factor levels for Cost and ROI objectives.

	Case 1			Case 2			Case 3
Window materials	Low-E triple glazing	Low-E double glazing	Double glazing	Double glazing	Low-E single glazing	Single glazing	Low-E triple glazing	Double glazing	Single glazing

). Their specific U-values and unit costs are detailed in

Table 8. Thermal performance and unit cost of window materials.

Window Material	U-Value (W/m2·K)	Cunit (CNY/m2)
Single glazing	5.68	140
Low-E single glazing	3.84	200
Double glazing	2.83	538
Low-E double glazing	1.4	750
Low-E triple glazing	0.68	1250

. For the opaque envelope components, the U-values from Round 1 were retained. The cost for walls and roof was calculated based on the thickness of Expanded Polystyrene (EPS) insulation required to achieve those specific U-values. EPS was selected as the representative insulation material because prior studies have shown that commonly used insulation materials exhibit only minor differences in both cost and payback period [7], making EPS a robust and simplified choice for this economic analysis. The unit cost of EPS is 442 CNY/m³, with the cost calculated based on the thickness required to achieve a specific U-value. This two-round approach effectively decouples the physical performance analysis from the economic analysis, allowing for a clear assessment of how design decisions impact both performance and cost.

In the parametric simulations, for each run defined by the orthogonal array, the designated design variables (e.g., U-values of the wall, roof, and windows) were assigned the levels specified in Table 5 (for performance objectives) and Table 6 (for economic objectives), effectively replacing the corresponding baseline values from the validated model (Table 1). The thermal properties of all other building components not considered as variables (e.g., internal walls, floor) were kept constant at their baseline values throughout all simulations.

(2)

Selection of orthogonal table: Given that the study considered 12 variables, each with three levels, the L27 (313) orthogonal array was employed. This design requires only 27 simulation runs while still providing a balanced representation of all parameter–level interactions, thereby offering a dramatic improvement in efficiency compared to a full factorial design (313 = 1,594,323 runs).

(3)

Determination of optimization objectives

The simulation-derived performance indicators were defined as optimization objectives:

(i)

Annual cooling and heating load (kWh): including summer cooling, winter heating, and total annual load.

(ii)

Percentage of Neutral Time (PNT_ave): the mean proportion of thermally neutral hours across all rooms, based on the APMV model.

(iii)

Useful Daylight Illuminance (UDI_ave): the average share of daylight illuminance falling within the useful range across all rooms.

(iv)

Investment cost (Cost): the capital expenditure associated with each renovation scheme.

(v)

Return on Investment (ROI): the economic return relative to the associated cost.

ROI in the economic analysis was defined as the inverse of the Simple Payback Period (SPP), calculated as

$$\mathrm{ROI}={\displaystyle \frac{C_{\mathrm{savings},\mathrm{annual}}}{\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}}={\displaystyle \frac{1}{\mathrm{SPP}}}$$

(2)

where $C_{\mathrm{savings},\mathrm{annual}}$ is the annual energy cost saving (CNY/year), $\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}$ is the total retrofit investment cost (CNY), and $\mathrm{SPP}$ is the simple payback period (years).

This approach represents a static economic assessment that does not consider the time value of money (i.e., no discount rate is applied). While less precise than dynamic analysis methods, it is well-suited for relative comparison during the preliminary screening phase of design alternatives. It effectively reveals the relative impact of different retrofit parameters on economic performance, providing an intuitive basis for sensitivity analysis. The calculation was based on the following assumptions:

(a)

Energy Price: Energy savings were converted into monetary savings based on the residential electricity tariff (0.55 CNY/kWh) in Linyi.

(b)

Measure Lifetime: The retrofit measures (e.g., insulation, windows) were assumed to have a service life consistent with the building itself, aiming to evaluate the long-term energy savings over the building’s lifespan.

(c)

Discount Rate: As a static analysis, a discount rate was not applied.

(d)

Sensitivity analysis method: Three sets of orthogonal experiments, each consisting of 27 simulations, were systematically evaluated.

(i)

Deviation analysis ($\overline{K_i}$): $\overline{K_i}$ notes the mean deviation under each level. Comparing the three $\overline{K_i}$ values reveals the response trend of an objective to changes in a given variable. A wider spread among the $\overline{K_i}$ values indicates a stronger effect of that variable.

(ii)

Range analysis (R): For each parameter, the mean deviations across levels were calculated, and the sensitivity ranking was determined according to the range (R-value). A larger R-value reflects a greater influence of the parameter on the objective.

Through these approaches, the study not only identified the most influential parameters but also clarified their impact trends and interaction patterns across multiple performance indicators.

3. Results and Analysis

3.1. The Impact of Design Variables on Building Performance

As illustrated in Figure 4, the variable impact trends derived from the three orthogonal experiment sets exhibit distinct differences, confirming the rationality and necessity of partitioning the experiments into three groups with distinct parameter ranges. This strategy not only capitalizes on the efficiency and accuracy of orthogonal design in assessing parameter significance but also effectively mitigates the risk of misjudgment associated with inappropriate single-range settings. It should be noted that the influence trends and relative strengths of the variables shown in Figure 4 are derived from range analysis within the orthogonal experimental design. The range (R-value), which is the difference between the maximum and minimum mean of the objective at different factor levels, serves as the quantitative metric for assessing the significance of each parameter’s influence. A larger R-value indicates a stronger effect of the parameter on the performance objective.

Furthermore, Figure 4 facilitates the identification of dominant variables across different performance objectives, with the results summarized and interpreted as follows:

• Energy Demand (ED_tot, ED_H, ED_C)

The analysis reveals a clear hierarchy of parameter influence on energy demand. For the ED_tot, the U-Window consistently emerges as the most significant factor across cases. This underscores the critical importance of window thermal performance in cold regions. Physically, windows typically constitute the weakest thermal bridge in the building envelope due to their higher thermal transmittance compared to insulated walls. The heat transfer process through windows, governed by conduction, convection, and longwave radiation, leads to substantial heat loss during the long heating season. Therefore, improving window U-value directly reduces this dominant heat loss pathway.

A more nuanced pattern is observed when analyzing ED_H and ED_C demands separately. For ED_C, SHGC is the dominant factor. This is physically sound because the SHGC directly governs the amount of solar shortwave radiation transmitted through the glazing, which is converted to heat within the space. A high SHGC allows excessive solar heat gain to enter the building during summer, significantly increasing the sensible cooling load. This effect is particularly pronounced for south and west-facing windows, which receive abundant solar irradiation. Secondary influences include WWR-South, WWR-North, and WWR-West, as larger glazing areas on these orientations admit more solar heat. This collectively highlights that controlling solar heat gain is the key strategy for reducing cooling energy consumption.

Conversely, for ED_H, both U-Window and SHGC exhibit the strongest influence. While a low U-Window is crucial for minimizing conductive and convective heat loss, as explained above, SHGC plays a dual role. A higher SHGC is beneficial during the heating season by allowing passive solar heat gain, which offsets part of the heating demand. This creates a trade-off: a high SHGC increases cooling load but decreases heating load. The optimal SHGC thus depends on the balance between heating and cooling seasons. Secondary but substantial influences come from WWR-South, U-Wall, U-Roof, and U-Ceiling. In contrast, parameters related to visible light (t-vis and Trans) show relatively minor effects on energy demand.

2.

Thermal Comfort (PNTave)

The influence of design variables on PNT_ave strongly correlates with their impact on energy demand, as both are governed by the fundamental principles of heat balance. Unsurprisingly, SHGC and U-Window remain the two most influential factors, far exceeding the effects of other variables. This is because SHGC directly affects the solar radiant heat gain, a major component of the indoor thermal load that influences the mean radiant temperature (MRT). Simultaneously, U-Window determines the rate of heat exchange through the glazing and the interior surface temperature of the window. A lower U-value results in a higher interior surface temperature in winter, reducing cold radiant draught and improving local thermal comfort near windows. Their combined effect is critical for maintaining overall thermal stability and comfort. Secondary influences include U-Wall, U-Roof, WWR-South, and Depth, as they also significantly affect the overall thermal buffering capacity and heat loss/gain of the dwelling. The remaining variables exert comparatively minor impacts.

3.

Daylight Performance (UDIave)

As expected, Trans overwhelmingly dominates UDI_ave, demonstrating that selecting glazing with a high Trans value is the most direct and effective measure for improving indoor daylight availability. A higher Trans value directly increases the illuminance level across the indoor space, thereby expanding the zone where daylight levels fall within the useful range (UDI). The Depth of the room and the WWR-South also exert considerable influence. A greater room depth reduces light penetration from the primary façade due to the inverse-square law and inter-reflections, while a larger WWR-South increases the aperture size, allowing more daylight to enter.

In summary, the sensitivity analysis conducted across three distinct value ranges provides a robust and nuanced understanding of how envelope design parameters govern the performance of rural dwellings in cold regions. The results collectively underscore a hierarchical influence structure, where key fenestration properties (U-Window, SHGC, and Trans) overwhelmingly dominate the objectives of energy demand, thermal comfort, and daylighting, respectively. This hierarchy confirms the pivotal role of windows as the primary mediator between the indoor environment and external climatic conditions. Furthermore, the significant, albeit secondary, influence of opaque envelope insulation (U-Wall, U-Roof) and building geometry (Depth, WWR-South) highlights that an integrated design approach—optimizing both transparent and opaque components along with the building form—is essential for achieving high performance. The methodological approach of employing multiple orthogonal arrays has proven effective in capturing potential nonlinearities and range-dependent effects, thereby enhancing the reliability of the findings. These insights offer clear practical implications: prioritizing the selection of high-performance windows, characterized by low U-Window, an appropriate SHGC, and high Trans, should be the foremost strategy in retrofits and new designs, followed by careful consideration of insulation levels and south-facing fenestration design to holistically balance energy efficiency, indoor environmental quality, and economic viability.

3.2. The Impact of Design Variables on Cost and ROI

In the second part of the analysis, the study evaluates the economic feasibility of the proposed renovation strategies. To ensure accurate estimation of total renovation costs and return on investment (ROI), the design variables from the orthogonal experiments were refined to reflect actual material selections and their corresponding costs. The economic assessment primarily considers energy consumption expenses and initial renovation investments. Since rural residents generally maintain relatively fixed daily routines, variations in lighting-related energy use are minimal. Consequently, this section emphasizes the interplay between renovation costs, ROI, and energy demand.

Specifically, ceiling materials were excluded from the analysis due to their negligible contribution to the overall renovation budget. For wall and roof insulation, expanded polystyrene (EPS) was adopted as a representative material, as prior studies have shown that commonly used insulation materials display only minor differences in both performance and cost [7], making EPS a robust reference option. For glazing, five types of glass with distinct thermal and optical properties were considered, each assigned a unique identifier to facilitate coding and analysis within the orthogonal table.

To minimize biases in trend and significance evaluation arising from overly broad parameter ranges in a single orthogonal experiment, three independent orthogonal experiments (Case 1, Case 2, Case 3) were conducted. The design principle was to vary the factor ranges across the three cases in order to examine whether factor effects change with range width and to detect potential nonlinear or threshold behaviors. Specifically, Case 1 focused on the lower half of the design range, Case 2 on the upper half, and Case 3 uniformly spanned the entire range. This “local–local–global” arrangement enables assessment of whether factor effects remain consistent across different ranges (e.g., linear or monotonic trends) and whether certain factors exhibit critical thresholds at extreme values, thereby offering more nuanced guidance for engineering decision-making.

For clarity, each subplot in Figure 5 presents three segmented lines corresponding to the three orthogonal experiments (Case 1/Case 2/Case 3). The three points at the front of the x-axis represent Case 1, those at the back represent Case 2, and the three evenly spaced points correspond to Case 3. Thus, the three lines in each subplot do not represent repetitions of the same factor at identical levels, but rather the response curves of that factor across different value ranges, thereby enabling direct comparison of range effects. Figure 6 shows the bar chart of factor influences (F-values) derived from the three orthogonal experiments, with each experiment distinguished by color. The F-values were obtained using one-way ANOVA to quantify the explanatory power of each factor on the variability of the response variables (total renovation cost and ROI). Based on the F_α distribution table (F_0.25 = 1.66, F_0.1 = 3.11, F_0.05 = 4.46, F_0.01 = 8.65), the significance levels were classified as follows: F > F_0.01: extremely significant; F_0.01 > F > F_0.05: significant; F_0.05 > F > F_0.1: moderately significant; F_0.1 > F > F_0.25: minor but not significant; F < F_0.25: no effect. Figure 6 reports only the factors with F > F_0.1.

As shown in Figure 5, the response curves of design variables on Cost and ROI differ substantially across the three scenarios (Case 1/Case 2/Case 3). The range of each three-point line allows for a qualitative assessment of variable influence, which can be cross-validated with the F-values presented in Figure 6: larger ranges correspond to higher sensitivity of the variable to the output.

With respect to Cost, Figure 5a shows that Depth, U-Wall, U-Roof, U-Ceiling, and Window material display decreasing trends as the x-axis values increase, whereas most other variables generally exhibit upward trends. For ROI, Depth and WWR-South rise with increasing x-axis values, while most other variables show declining trends. In the optimization process, the objective is to enhance building performance and maximize ROI while keeping costs under control. Increasing Depth reduces the envelope area, thereby lowering costs. Although Depth has only a limited direct effect on energy demand, it exerts a strong influence on ROI, which initially increases and subsequently decreases with larger Depth. The window-to-wall ratios (WWRs) in all four orientations increase renovation costs as their values rise, since high-performance glazing is considerably more expensive than other envelope components. Moreover, all WWRs influence energy demand to varying degrees, thereby exerting significant impacts on ROI across cases, with WWR-South showing the strongest effect. The remaining four material-related variables generally exhibit declining trends for both Cost and ROI, with window material exerting the most pronounced effect—substantially greater than that of other variables. Overall, although high-performance envelope components raise renovation costs, they also deliver higher ROI. Therefore, optimization decisions should simultaneously account for actual energy savings and economic returns.

According to Figure 6, the significance ranking of factors influencing total renovation cost (Cost) is as follows: Case 1: Window material (56.02) > U-Wall (19.57) > U-Roof (16.89) > WWR-South (6.44) > WWR-North (5.55) > Depth (4.77). Case 2: Window Material (421.57) > WWR-South (8.80) > WWR-North (6.49) > WWR-East (5.28) > WWR-West (3.61) > Depth (1.71). Case 3: Window Material (37.43) > WWR-South (6.12) > WWR-North (5.01) > Depth (3.67) > U-Roof (3.59) > WWR-West (2.58) > WWR-East (2.37) > U-Wall (1.68).

Regarding ROI, the significance ranking of factors is as follows: Case 1: Depth (4.78) > U-Wall (4.21) > Window Material (3.87) > U-Ceiling (3.42) > WWR-North (2.42) ≈ WWR-East (2.41). Case 2: Window Material (824.88) > WWR-South (13.18) > U-Wall (6.37) > U-Roof (6.11) > Depth (2.98) > WWR-East (2.72) > U-Ceiling (2.35). Case 3: Window Material (6.62) > U-Ceiling (3.49) > WWR-South (2.37) > U-Wall (2.08).

Overall, based on three sets of orthogonal experiments with different variable ranges, this study systematically assessed the impacts of renovation design variables on both economic and energy performance. The results demonstrate that window material selection is the most dominant factor influencing total renovation cost, consistently producing very high F-values across all cases. In addition, U-Wall and U-Roof as well as WWR-South and WWR-North also exert significant effects on cost. With respect to ROI, window material remains highly influential, while Depth and U-Ceiling show notable effects under specific value ranges.

The stratified experimental design (Case 1, Case 2, Case 3) effectively captured potential range effects and nonlinear behaviors of design factors. Window material consistently exhibited significant influence across all cases, underscoring its central role in economic feasibility. By contrast, variables such as building depth and the south-facing window-to-wall ratio displayed varying effects across different value ranges, suggesting that optimal renovation strategies should be context-dependent and tailored to specific design conditions.

The findings suggest that effective renovation design should prioritize the adoption of high-performance window systems, which can simultaneously improve energy efficiency and economic returns. Moreover, building depth and window-opening strategies—particularly the south façade window-to-wall ratio—should be carefully adjusted to balance energy-saving potential with cost control. In addition, building performance optimization based on multi-range orthogonal experimental design provides more detailed and actionable insights, offering strong support for cost-effective, high-return renovation strategies in rural residential buildings.

4. Discussion

This study provides a comprehensive understanding of how envelope design parameters shape the energy, environmental, and economic performance of rural dwellings in cold regions. By systematically applying Orthogonal Experimental Design (OED) across multiple value ranges, the analysis generates nuanced insights that move beyond those of conventional sensitivity studies.

First, the strong influence of window-related parameters—U-value, SHGC, and transmittance—across multiple objectives highlights the central role of fenestration systems in rural building energy efficiency. This finding is consistent with prior research stressing the importance of glazing in severe climates [38,39]. Our multi-range analysis further demonstrates that their effects are nonlinear and vary across value intervals. For example, the impact of SHGC on cooling load reduction is most pronounced at mid-range levels, indicating that simply maximizing or minimizing this parameter is not universally effective. Such nonlinearity underscores the need for context-specific design strategies rather than one-size-fits-all recommendations.

A deeper analysis reveals that the influence weights of the design parameters are not static but exhibit significant range dependency and interactions. A key finding is the strong interaction between the WWR and the thermal properties of the envelope components, which leads to a dynamic shift in the dominant influencing factors across different design value ranges.

In Case 1, characterized by lower parameter values including smaller window-to-wall ratios, the building’s heat loss/gain is primarily governed by the opaque envelope components (walls, roof). Consequently, the U-Wall emerges as the most significant factor for energy demand. However, in Cases 2 and 3, where parameters like WWR-South increase to higher values, the thermal performance of the transparent envelope becomes critically important. The influence of U-Window and SHGC surpasses that of the wall, becoming the dominant factors.

The building physics mechanism underlying this phenomenon is that windows are typically the thermal weak point in the building envelope, with a much higher U-value per unit area than an insulated wall. When the window area is small, its contribution to the total envelope area and overall heat transfer is minor; thus, improving wall insulation yields the greatest benefit. However, when the window area is significantly increased, its thermal disadvantage is proportionally amplified. The share of total heat flow through the windows rises substantially, making their performance parameters the decisive factor for overall energy consumption. This finding has a crucial implication for design practice: for buildings with small windows, priority should be given to optimizing wall insulation, whereas for designs with large window areas, high-performance windows must be the primary strategy.

Second, the economic analysis highlights the trade-off between upfront investment and long-term savings. Although high-performance windows raise initial costs, their dominant influence on ROI demonstrates that these investments are economically justified over the building lifecycle. This is particularly relevant in rural settings where financial constraints often drive low-cost choices. Our results indicate that targeted investments in elements such as windows and south-facing glazing can deliver disproportionate returns, providing a strong rationale for subsidies or financial incentives in rural retrofit programs.

The notable effects of building depth and south-facing window-to-wall ratio on both energy outcomes and ROI highlight the importance of early-stage architectural design. Unlike material-based interventions, these geometric parameters involve minimal direct costs yet strongly affect performance. Enhancing awareness of these factors among builders and designers could therefore yield substantial improvements in rural building stock at little additional expense.

Furthermore, this study offers clear, practical guidance for enhancing the performance of opaque envelopes (U-Wall, U-Roof), which constitute the largest surface area of single-story rural dwellings. The improvement pathway is direct: adding insulation materials such as Expanded Polystyrene (EPS), with the thickness calibrated to achieve the target U-value, as modeled in our economic analysis. Crucially, our sensitivity results identify the specific design contexts where this strategy is most impactful. When window areas are limited (e.g., lower WWR values as in Case 1) or when project budgets are constrained, prioritizing investments in wall and roof insulation becomes a highly cost-effective primary measure, as the influence of U-Wall and U-Roof on heating demand is most pronounced under these conditions. This allows for the development of context-tailored retrofit pathways, ensuring efficient allocation of limited resources.

Methodologically, employing three orthogonal arrays with varying value ranges effectively captured complex parameter behaviors, including interactions and threshold effects. This represents a clear advance over traditional one-factor-at-a-time approaches and even standard orthogonal designs confined to single ranges. The consistent identification of window material as the most influential factor across all cases strengthens the robustness of this conclusion, while range-dependent variations in other parameters offer practical guidance for diverse design contexts.

While this study systematically reveals the influence mechanisms of envelope parameters via orthogonal experimental design, several limitations should be acknowledged. Firstly, the simulations were based on fixed indoor conditions and predetermined operational schedules. This simplification, while necessary to manage complexity, fails to fully capture the highly adaptive and stochastic nature of occupant behavior in rural settings. For instance, occupant-driven window opening could occur more frequently and for longer durations than modeled. Moreover, the heat generated from intermittent, high-capacity heating devices, such as solid fuel stoves commonly used in winter, differs significantly from the consistent space heating modeled in this study. These strong occupant-driven interventions could potentially override or mitigate the impacts of passive envelope design in real-world scenarios, a crucial context for applying our findings. Secondly, the analysis relied on Typical Meteorological Year data and did not account for climate change. A warming climate may further reduce heating demand while drastically increasing cooling needs, thereby shifting the relative importance and optimal combination of design parameters (e.g., SHGC vs. insulation levels). Future work should, therefore, focus on integrating stochastic occupant behavior models and future climate projection data into the framework. Multi-objective optimization performed on this more dynamic foundation will be essential for developing more robust, adaptive, and practical design strategies.

Despite these limitations, this study advances the field by establishing a robust framework for parameter sensitivity analysis in rural building design. The results provide actionable guidance for prioritizing retrofit strategies and design measures in cold-region rural housing. Future research could build on this foundation by integrating occupant behavior models, climate projections, and multi-objective optimization to develop comprehensive design guidelines that support sustainable rural development.

5. Conclusions

This study systematically evaluated the sensitivity of envelope design parameters for rural dwellings in cold regions of China by integrating on-site measurements with a multi-range orthogonal experimental design. The results demonstrate that the transparent components of the building envelope—specifically, window performance parameters—exert a decisive influence on overall building performance.

Key findings are summarized as follows:

U-Window and SHGC were identified as the most significant factors influencing ED_tot and PNT_ave. This conclusion is consistent with fundamental physical mechanisms: windows typically represent the weakest thermal bridge in the building envelope, accounting for a substantial proportion of total heat loss. Consequently, reducing the window U-value directly mitigates heat transfer during both heating and cooling seasons. Simultaneously, a higher SHGC provides beneficial passive solar heat gain during the heating season, effectively reducing heating demand, but it also increases cooling loads in summer, presenting a typical trade-off between winter and summer performance. In contrast, Trans of windows overwhelmingly dominated daylighting performance (UDI_ave). A higher Trans value directly increases indoor illuminance levels, significantly expanding the zone of useful daylight. The influence of other parameters on various objectives was relatively secondary: while the thermal insulation of opaque envelopes (U-values of walls, roof, and ceiling) and building geometry (Depth, WWR) exhibited certain impacts on energy consumption and comfort, their contributions were consistently lower than those of the window parameters. Furthermore, this study found that the separate effect of visible light transmittance (t-vis) on all indicators was negligible.

Economic analysis revealed distinct drivers for retrofit cost and ROI. Window material—integrating its U-value, SHGC, and Trans properties—was the dominant factor determining total retrofit cost, with high-performance double- or triple-pane Low-E glass significantly increasing the initial investment. Although high-performance windows elevate costs, they also substantially enhance energy savings, thereby improving long-term economic returns. In comparison, building Depth and the south window-to-wall ratio (WWR-South) significantly influenced ROI. Increasing the building depth reduces the external envelope area, lowering construction costs, and its impact on ROI exhibited a nonlinear trend of initial increase followed by a decrease. Enhancing the south-facing window proportion increases passive solar heat gain in winter, thereby improving economic returns. Synthesizing the results from the three orthogonal experiments shows that the sensitivity ranking of ROI varies across value ranges: in some scenarios, window material had the greatest effect on ROI, while in others, building depth and the south WWR were the critical factors. This indicates that optimization must simultaneously consider the synergistic effects between window performance and building geometry.

While the critical role of fenestration in building performance is an established tenet, this study advances the field by quantifying its context-dependent and nonlinear behavior, thereby transitioning from a principle to a actionable design strategy. The sensitivity hierarchy (U-Window > SHGC > Trans) and their identified interaction with geometry (e.g., WWR-South, Depth) provide a stratified decision-making framework. To achieve the proposed holistic optimization, a two-stage process is recommended: First, parameter screening and prioritization based on the quantified sensitivity rankings, focusing on the dominant fenestration properties. Second, directed multi-objective optimization (MOO), where algorithms like NSGA-II are deployed with a reduced search space to efficiently resolve the key trade-offs—such as that between SHGC’s impact on heating versus cooling demand—while synergistically adjusting the secondary yet cost-effective geometric parameters (Depth, WWR-South) to control envelope area and leverage passive solar gains.

These conclusions are highly consistent with the experimental data: window-related parameters consistently ranked at the top in influencing all performance objectives, validating the accuracy of the analysis. Furthermore, the influences of many parameters exhibited nonlinear and range-dependent characteristics. For instance, when the window-to-wall ratio is small, the thermal performance of the opaque envelope (e.g., U-values) has a more pronounced effect on energy consumption; however, as the window ratio increases, window performance (U-value, SHGC) becomes the dominant factor. This further substantiates the necessity of employing a multi-range experimental design to avoid biases inherent in single-range analyses.

In summary, this research provides data support and decision-making references for the optimization of building envelopes in cold-region rural dwellings. A clear hierarchy of parameter importance has been established: priority should be given to selecting window systems with low U-values, moderate SHGC, and high Trans, followed by improving the insulation of the opaque building envelope and rationally adjusting the building depth and south WWR. This approach enhances energy efficiency and comfort while maintaining economic viability. These findings offer significant guidance for the energy-efficient retrofit and multi-objective design optimization of rural dwelling.