Using the Taguchi Method and Grey Relational Analysis to Optimize Ventilation Systems for Rural Outdoor Toilets in the Post-Pandemic Era

Abstract

This study addresses the issue of poor air quality and thermal comfort in rural outdoor toilets by proposing a ventilation system powered by a building-applied photovoltaic (BAPV) roof. A numerical model is established and validated through comparison with the literature and experimental data. Based on a consensus, four influential variables, namely, inlet position, outlet height, supply air temperature, and ventilation rate, are selected for optimization to achieve multiple objectives: reduction in ammonia concentration, a predicted mean vote (PMV) value of 0, minimization of age of air, and energy consumption. The present study represents a pioneering effort in integrating the Taguchi method, computational fluid dynamics (CFD), and grey relational analysis to concurrently optimize the influential variables for outdoor toilet ventilation systems through design and simulation. The results indicate that all four variables exhibit nearly equal importance. Ventilation rate demonstrates a dominant effect on ammonia concentration and significantly impacts the age of air and energy consumption, while supply air temperature noticeably influences PMV. The optimal scheme features an inlet at center top position, an outlet height of 0.2 m, a supply air temperature of 12 °C and a ventilation rate of 20 times/h. This scheme improves ammonia concentration by 18.9%, PMV by 6.8%, and age of air by 30.0% at a height of 0.5 m, while achieving respective improvements by 18.9%, 5.5%, and 22.2% at a height of 1.5 m. The BAPV roof system generates an annual electricity output of 582.02 kWh, which covers the energy consumption of 358.1 kWh for toilet ventilation, achieving self-sufficiency. This study aims to develop a zero-carbon solution for outdoor toilets that provides a safe, comfortable, and sanitary environment.

1. Introduction

One of the Sustainable Development Goals set by the United Nations is to ensure universal access to clean drinking water and sanitation facilities by 2030. According to Water for Prosperity and Peace—2024 United Nations World Water Development Report, 3.5 billion individuals worldwide lack access to safe and properly managed sanitation facilities [1]. Among them, 419 million people still practice open defecation, predominantly in rural areas, accounting for 91% of this population [2]. Furthermore, there is a growing demand for outdoor toilets in diverse settings such as construction sites, mountainous regions, remote islands, sports facilities, emergency shelters, and other areas lacking sewage systems [3]. Therefore, it is imperative and highly significant to develop innovative solutions for sanitary outdoor toilets that can provide a safe and hygienic environment. Currently, the majority of outdoor toilets in rural China are relatively rudimentary. In recent years, despite many being equipped with flushing systems in urbanized village areas, most outdoor toilets scattered across vast and remote rural regions lack proper drainage infrastructure. Furthermore, there is a dearth of standardized disinfection mechanisms in place; instead, it entirely relies on whether the users can regularly disinfect or not. Additionally, the construction structure is relatively simplistic; mechanical ventilation systems or air conditioning/heating devices are absent in most rural toilets, leading to inadequate ventilation and particularly uncomfortable thermal conditions during winter and summer seasons.

1.1. Previous Studies on Toilets

Zhang [4] conducted experiments and numerical simulations to investigate the impact of ventilation mode and vent location on ammonia and hydrogen sulfide concentrations, aiming to improve toilet air quality. Tung [5] designed a negative pressure wall exhaust system to examine the influence of ventilation volume and toilet location on the odor concentration and distribution within toilets, while evaluating the effectiveness of odor removal using local air quality index and odor removal efficiency. Gundlach [6] utilized computational fluid dynamics (CFD) simulation to optimize toilet dimensions. Ammonia concentration [7,8,9] is considered as the most critical indicator for accessing toilet air quality, with levels not exceeding 100 mg/m³ in order to ensure human health protection. A survey analysis of rural China’s “toilet revolution” reveals that frequently cited obstacles include issues related to toilet design.

Previous studies [10,11,12] have primarily focused on optimizing the air quality of indoor/outdoor public toilets with sewage systems using the CFD method. However, in the post-COVID-19 era, enhancing ventilation [13] plays a crucial role in mitigating infection risks and elevating overall indoor safety levels. Therefore, ensuring effective ventilation is critical for achieving better toilet air quality; however, it also leads to higher energy consumption [14,15,16]. Given that toilets are frequently occupied spaces, maintaining thermal comfort becomes paramount, especially in severely cold and cold areas. Air quality, thermal comfort, and energy conversation are widely recognized as key indicators for evaluating the effectiveness [17] of ventilation systems.

1.2. Ventilation to Improve Indoor Air Quality

Ventilation plays a pivotal role in achieving optimal indoor air quality [17]. The implementation of demand-controlled ventilation [18] effectively reduces energy consumption. Mechanical ventilation [19] facilitates the expulsion of indoor pollutants and promotion of indoor air quality. Asif [15] employed the transient mass balance, steady-state, and decay methods to calculate ventilation rates for evaluating and comparing different ventilation mechanisms in office buildings. Ameen [17] numerically simulated a corner-based impinging jet ventilation system in an office environment to assess its performance regarding local thermal comfort and indoor air quality. Su [16] investigated the relationship between ventilation time/frequency/volume and indoor air quality to effectively optimize the design and operation strategies for ventilation systems. Tognon [20] utilized a combined simulation approach to evaluate various control strategies for hybrid ventilation systems targeting annual energy demand reduction and risk mitigation in both residential and educational buildings, revealing that a hybrid ventilation system has the potential to reduce energy consumption while maintaining a healthy indoor environment.

1.3. Using Photovoltaics to Generate Electricity

Toilets serve as primary and hazardous environments for the transmission of respiratory and gastrointestinal infections [12]. Therefore, ensuring a high ventilation rate is imperative to guaranteeing safe, pollution-free conditions and mitigating potential health risks, resulting in significant energy consumption for ventilation. Furthermore, in regions with severely cold and cold climates, it is a fundamental requirement to ensure thermal comfort during toilet use, leading to substantial heating energy consumption as well. Photovoltaic (PV) technology utilizes the photovoltaic effect of semiconductor materials to directly convert solar energy into electricity. Due to its clean, safe and renewable characteristics, PV has emerged as the most widely adopted form of new energy [21,22]. With continuous advancements in PV materials over recent decades, PV technology has rapidly developed [23,24,25] with reduced cost and improved generation efficiency. Roofs [26] have been identified as the preferred location for PV installation, followed by south-facing deployment, particularly in high-latitude regions.

1.4. Application of Taguchi Method in Fluid Dynamics

The Taguchi method [27] is widely employed in medicine, chemistry, industry, manufacturing, and other fields [28,29,30,31,32] to enhance product quality and process efficiency by achieving optimal system design with minimal experimentation [33,34].

Scholars have utilized the Taguchi method combined with numerical simulation to investigate fluid dynamics-related issues. For instance, Radhakrishnan [35] optimized four key design parameters (turbine diameter, axial clearance, blade height, and blade number) to enhance power performance of a turbine. Fatahian [36] applied the Taguchi method along with an analysis of variance (ANOVA) to optimize the experimental design variables, which consists of five factors with three levels, for enhancing the output power of the two rotors in the deflection system. Xu [37] proposed an optimization approach that integrates CFD modeling and the Taguchi method to quantitatively investigate the impact of stirring speed and aeration rate on impeller performance through numerical simulation. Rasekh [38] conducted a sensitivity analysis on vertical axis wind turbines using both Taguchi and CFD methods.

Haghshenaskashani [39] employed the Taguchi method to optimize operational performance of an impingement jet ventilation system based on CFD simulation in the building environment. Shokrollahi [40] utilized the Taguchi method to conduct multi-objective optimization of thermal comfort, indoor air quality, and energy conservation in an underfloor air distribution system. The optimization focused on diffuser position, return air height, air exchange volume, supply air temperature, and diffuser blade angle. Fatahian [41] combined the Taguchi method with CFD analysis to investigate parameters such as particle mass flow rate, inlet velocity, inlet temperature, and turbulence intensity with the aim of maximizing separation efficiency. Metzger [42] applied the Taguchi method to optimize the operational characteristics of a novel individual ventilated air terminal design by considering supply air temperature, speed, and flow rate to achieve overall optimal performance in terms of thermal comfort, indoor air quality, and energy efficiency.

1.5. Multi-Objective Optimization with Taguchi-Based Grey Relational Analysis

CFD simulation and experimental measurements [4] using a tracker gas (SF6) are commonly employed in the field of ventilation. Evaluation indexes for optimizing ventilation systems encompass air quality, odor removal efficiency [3], and ventilation rate [13]. However, most studies traditionally address and optimize multiple objectives separately [14,15,18], leading to single-objective optimization results.

Similarly, the Taguchi method is suitable for single-objective optimization, while multiple quality analysis methods are necessary for multi-objective optimization [43]. Grey relational analysis is a multi-factor analysis method that can overcome the limitations of the Taguchi method in optimizing multiple quality characteristics [44,45]. Fung [46] combined the Taguchi method with grey relational matrix analysis to identify the most influential factors on injection molding process and determine the most vulnerable wear properties. Niu [47] utilized the Taguchi method and grey correlation analysis to optimize air distribution and reduce indoor temperature in data centers. To enhance indoor natural ventilation efficiency, Yin [48] employed the Taguchi method to classify factors affecting air exchange volume and efficiency and applied grey correlation analysis to determine multiple optimal design schemes. Canbolat [49] utilized both the Taguchi method and grey correlation analysis to establish an important parameter sequence affecting energetic and exergetic performance in absorption refrigeration systems. Yuce [50] adopted a combination of the Taguchi method and variance analysis to find an optimal solution for drought risk or age of air while employing grey correlation analysis to identify an optimal solution considering both aspects.

In summary, this study focuses on rural outdoor toilets as the research subject and aims to achieve multi-objective optimization of air quality, thermal comfort, and energy conservation by targeting ammonia concentration, PMV, age of air, and energy consumption. The Taguchi method, grey relational analysis, and CFD simulation are employed simultaneously to establish a numerical model for toilet design and identify the optimal design variables.

2. Materials and Methods

This study establishes a numerical model of typical rural outdoor toilets in Xining City, Qinghai Province, China using CFD software (Airpak 3.0.16). Qinghai Province is situated on the Qinghai–Tibet Plateau in Northwestern China, as depicted in Figure 1, and experiences a plateau continental climate characterized by cold meteorological conditions. Four indicators (ammonia concentration, PMV value, age of air, and energy consumption) are adopted as optimization objectives for ventilation systems. After converting multiple objectives into a single target through grey relational analysis, the Taguchi method is employed to identify the optimized scheme.

2.1. CFD Simulation Preparation

In China, rural outdoor toilets are typically standalone structures equipped with squatting pots. In this study, we establish a physical model for an outdoor toilet, as depicted in Figure 2. The x, y, z coordinates (0.8, 0.5, 0.45) represent the mouth and nose positions in squatting posture, while (0.8, 1.5, 0.45) correspond to standing posture; these points serve as the targets for multi-objective optimization. Although some approximations have been made to the fine structures of the toilet to simplify the modeling process, our model remains fundamentally consistent with actual dimensions to effectively reduce simulation cycles without compromising accuracy.

2.1.1. Physical Parameters

The targeted toilet is situated on the outskirts of Xining, the capital city of Qinghai Province in Northwestern China. The outlet is designed to be positioned on the north side of the toilet, while the door is located on the south side. Based on the wind rose diagram of Xining City, only a small portion experiences northwest winds, whereas the majority of wind direction originates from the southeast. The average outdoor wind speed in winter and summer seasons amounts to 1.4 m/s, with prevailing winds originating from the southeast [51]. The outdoor temperature remains below 27 °C all year round; therefore, typical winter conditions were selected for subsequent simulation purposes. In winter, when simulating typical conditions, it is assumed that outdoor air temperature drops to −11.9 °C with an air convection heat transfer coefficient of 23 W/(m²·K). The source of toilet odor can be attributed to its drainage pipe, which has been simplified as an air supply outlet with a diameter of 110 mm and a velocity of 0.1 m/s [52].

Table 1. Physical model parameters of the outdoor toilet.

Name	Number	Size/m	Type	Value
Room	1	1.2 × 0.9 × 2.0	Room	0.079 mg/m3
Wall 1	2	2.0 × 0.9	Wall	-
Wall 2	2	2.0 × 1.2	Wall	-
Wall 3	2	1.2 × 0.9	Wall	-
Inlet	1	To be simulated	Opening	-
Outlet	1	To be simulated	Vent	-
Pollution source	1	de 110 mm	Opening	0.05 mg/m3, 0.1 m/s

provides details regarding inner parameters of the toilet’s physical model while material parameters are presented in

Table 2. Material parameters.

Material	Density (kg/m3)	Specific Heat (J/(kg·K))	Heat Conductivity Coefficient (W/(m·K))	Viscosity Coefficient (kg/(m·s))	Molecular Weight (kg/kmol)
NH3	0.7710	2080	0.02470	10.039	17
Wall of toilet	1800	917.6	0.04	/	/
Door of toilet	700	1050	0.4	/	/

.

2.1.2. CFD Simulation

CFD software (Airpak 3.0.16) is utilized in this study to evaluate the ventilation effect of various conditions, accurately simulating airflow, air quality, heat transfer, pollution, and comfort [53] within the ventilation system. To ensure both accuracy and computational efficiency of simulation results, a pressure-based solver and indoor zero equation [54] are employed for simulating airflow distribution. Notably, the residual errors for velocity, energy, and species in the continuity equation are maintained at 10⁻³, 10⁻³, 10⁻³, 10⁻³, 10⁻⁶, and 10⁻⁶ in the x, y, and z directions, respectively. A three-dimensional hexa-unstructured mesh with refined element sizes at the inlet, vent, and chamber, respectively, is applied to optimize grid generation speed and quality. Mesh independence verification is conducted using models with mesh numbers of 50,385, 64,179, and 153,543. The average relative difference between the current mesh (50,385 cells) and finer mesh (153,543 cells) is found to be less than 3%, indicating that a mesh number of 50,385 is suitable for this study.

The inlet and outlet are positioned for the setup of velocity and outflow. These specific locations will be stimulated for optimization in Section 3.1 and Section 3.2 for these specific locations. The coupling surface is located on the interior surface of the toilet wall, while the second boundary condition is selected on the exterior surface.

2.1.3. Validation of the CFD Model

The experimental data were obtained from the research conducted by He et al. [55,56], in which they conducted experiment within a precisely controlled environmental chamber with controllable wall boundaries. The dimensions of the experimental chamber were 2 m × 2 m × 2 m. A manikin was positioned inside the chamber, featuring a sensible heat dissipation power of 75.69 W under a mechanical ventilation rate of 82 m³/h, equivalent to 10 air changes per hour.

This setup closely mimics toilet ventilation conditions, making it ideal for validating simulation models. Figure 3 illustrates the experimental model along with measurement locations (pole 1–5). For numerical simulations, a pressure-based solver combined with an indoor zero equation, as described in Section 2.1.2, was utilized alongside a mesh number of 78,997. Comparisons between temperature and velocity obtained from numerical simulation and experimental results are presented in Figure 4, respectively.

Experiments and simulation data at poles 3 and 4 are compared respectively because pole 3 is adjacent to the manikin, while pole 4 represents the surrounding location. The measured temperature and velocity results are used to verify the accuracy of simulations specifically at positions of pole 3 and pole 4. In Figure 4, it can be observed that the simulation results are generally consistent with the experimental results, exhibiting similar transformation trends; however, discrepancies arise in areas characterized by significant temperature and velocity gradient. It should be noted that such discrepancies are common when conducting experiments under these conditions. This is relatively easy to understand; even minor positional errors can lead to inaccuracies, and it is also necessary to consider the precision of the experimental measurement instruments. Therefore, employing an indoor zero equation model enables us to obtain accurate results for this study.

2.2. Optimization Objectives

An optimal indoor environment is characterized by satisfactory air quality and thermal comfort. Given that ammonia, age of air, and PMV serve as crucial indicators for evaluating toilet pollutants, air freshening, and human thermal sensation, respectively, these three indicators have been chosen as optimization objectives to enhance both air quality and thermal comfort. Furthermore, fan power consumption plays a critical role in reducing toilet energy consumption and carbon emissions; thus, it has been identified as another optimization objective, which can be facilitated by PV roof systems for energy conservation purposes. Therefore, the selected optimization objectives encompass “ammonia concentration”, “PMV value”, “age of air”, and “energy consumption”. The subsequent sections will provide further elaboration on the PMV value and age of air.

2.2.1. PMV

Predicted mean vote (PMV) can be utilized to forecast the average response of a large population. Fanger established a relationship between PMV values and the disparity between actual heat flow from the body in a given environment and the heat flow necessary for optimal comfort [57], as described by Equations (1) and (2). Here, the dimensionless quantity $f_{cl}$ represents the clothing area factor, while $t_{cl}$ denotes the clothing surface temperature measured in degrees Celsius.

$$\begin{array}{l}PMV=[0.303\exp (-0.036M)+0.028]\{M-W-3.96\times {10}^{-8}{f}_{cl}[(t_{cl}+273{)}^4\\ -({\mathrm{t}}_{\mathrm{r}}+273{)}^4]-f_{cl}{h}_c(t_{cl}-t)-3.05\times {10}^{-3}[5733-6.96(M-W)-{\mathrm{P}}_{\mathrm{a}}]\\ -0.42(M-W-58.15)-1.7\times {10}^{-5}[5876-{\mathrm{P}}_{\mathrm{a}}]-0.0014M(34-t)\}\end{array}$$

(1)

$$h_c={\left\{\begin{array}{l}2.38(t_{cl}-t)\\ 12.1\sqrt{{\mathrm{v}}_{\mathrm{a}\mathrm{r}}}\end{array}\right.}^{0.025}\begin{array}{l}2.38{(t_{cl}-t)}^{0.025}>12.1\sqrt{{\mathrm{v}}_{\mathrm{a}\mathrm{r}}}\\ 2.38{(t_{cl}-t)}^{0.025}\le 12.1\sqrt{{\mathrm{v}}_{\mathrm{a}\mathrm{r}}}\end{array}$$

(2)

The thermal sensation scale listed in

Table 3. Relationship between PMV values and thermal comfort for human beings.

PMV	−3	−2	−1	0	1	2	3
Thermal comfort of human	Cold	Cool	Slightly cool	Neutral	Slightly warm	Warm	Hot

is widely recognized and accepted within the scientific community. PMV values can be computed based on the simulated results obtained through Airpak software (Version 3.0.16). In this study, a human metabolic rate of 1.0 met (equivalent to sitting or relaxing state) is utilized. The clothing thermal resistance is set at 2.0 clo, which is equal to 0.31 (m²·K)/W. Additionally, the relative humidity is maintained at 30%.

2.2.2. Age of Air

The age of air pertains to the duration during which a specific quantity of outdoor air remains confined within a building or zone. Analyzing the distribution of the age of air aids in identifying areas with stagnant indoor airflow and evaluating ventilation efficiency. Typically, the age of air in a building is determined using tracer gas methodology, which can be replaced with CFD simulation [58].

2.3. Grey Relational Analysis

2.3.1. Steps of Grey Relational Analysis

Multi-objective optimization can be converted into single-objective optimization through grey relational analysis, which involves a series of seven steps: (1) determining both the reference sequence that reflects the characteristics of system behaviors and the comparative sequence that affects system behaviors; (2) normalizing both the reference sequence and comparative sequence; (3) establishing the deviation sequence; (4) formulating the grey relational coefficient sequence; (5) calculating grey relational grade (GRG); (6) ranking the grey relational grade; and (7) converting a multi-objective optimization problem to a single-objective one.

In this study, the optimization objectives encompass minimizing ammonia concentration, reducing the age of air, lowering energy consumption, and achieving a PMV value of 0. Sixteen orthogonal schemes are subsequently designed and described in detail in Section 3.2.1 and Table 6. The reference sequence is denoted as Equation (3), while the comparative sequence is represented by Equation (4). x1(1)~x1(4) represents the objective values of Scheme 1 for ammonia concentration, PMV, age of air, and energy consumption; similarly, x16(1)~x16(4) denotes the objective values of Scheme 16.

$$X_0={\left(0,0,0,0\right)}^T$$

(3)

$$(X_1,X_2,\dots ,X_{16})={\left(\begin{array}{cccc}{x}_1(1)& x_2(1)& \cdots & x_{16}(1)\\ x_1(2)& x_2(2)& \cdots & x_{16}(2)\\ x_1(3)& x_2(3)& \cdots & x_{16}(3)\\ x_1(4)& x_2(4)& & x_{16}(4)\end{array}\right)}_{4\times 16}$$

(4)

Ammonia concentration, age of air, and energy consumption are normalized according to Equation (5). PMV is normalized as per Equation (6). The normalized reference sequence is assumed to be ${\left(1,1,1,1\right)}^T$.

$$x_i^{*}(k)={\displaystyle \frac{\max x_i(k)-x_i(k)}{\max x_i(k)-\min x_i(k)}}{,}_{\hspace{1em}k=1,2,3,4; i=1,2,\dots 16}$$

(5)

$$x_i^{*}(k)=1-{\displaystyle \frac{\left|x_i(k)-0\right|}{\max [\max (x_i(k))-0,0-\min (x_i(k))]}}$$

(6)

The deviation sequence is calculated according to Equation (7).

$${\Delta }_{0,i}(k)=‖x_0^{*}(k)-x_i^{*}(k)‖={\left(\begin{array}{cccc}{\Delta }_{0,1}(1)& {\Delta }_{0,2}(1)& \cdots & {\Delta }_{0,16}(1)\\ {\Delta }_{0,1}(2)& {\Delta }_{0,2}(2)& \cdots & {\Delta }_{0,16}(2)\\ {\Delta }_{0,1}(3)& {\Delta }_{0,2}(3)& \cdots & {\Delta }_{0,16}(3)\\ {\Delta }_{0,1}(4)& {\Delta }_{0,2}(4)& \cdots & {\Delta }_{0,16}(4)\end{array}\right)}_{4\times 16}$$

(7)

The grey relational coefficient is calculated according to Equations (8)–(10). ζ, the distinguishing coefficient [59], is used to adjust the correlation coefficient, with a larger distinguishing coefficient indicating a greater influence on the target and leading to better analysis results. Typically, it is set at 0.5 [60,61]. The sequence of grey relational coefficient is described by Equation (11).

$${\xi }_{0,i}(k)={\displaystyle \frac{{\Delta }_{\min }+\zeta {\Delta }_{\max }}{{\Delta }_{0,i}(k)+\zeta {\Delta }_{\max }}}$$

(8)

$${\Delta }_{\min }=\underset{\forall j\in i}{{\displaystyle \min }}\underset{\forall \in k}{{\displaystyle \min }}‖x_0^{*}(k)-x_j^{*}(k)‖$$

(9)

$${\Delta }_{\max }=\underset{\forall j\in i}{{\displaystyle \max }}\underset{\forall \in k}{{\displaystyle \max }}‖x_0^{*}(k)-x_j^{*}(k)‖$$

(10)

$$({\xi }_{0,1},{\xi }_{0,2},\dots ,{\xi }_{0,16})={\left(\begin{array}{cccc}{\xi }_{0,1}(1)& {\xi }_{0,2}(1)& \cdots & {\xi }_{0,16}(1)\\ {\xi }_{0,1}(2)& {\xi }_{0,2}(2)& \cdots & {\xi }_{0,16}(2)\\ {\xi }_{0,1}(3)& {\xi }_{0,2}(3)& \cdots & {\xi }_{0,16}(3)\\ {\xi }_{0,1}(4)& {\xi }_{0,2}(4)& \cdots & {\xi }_{0,16}(4)\end{array}\right)}_{4\times 16}$$

(11)

GRG represents the degree of correlation between the comparative sequence and reference sequence, which is calculated by using Equation (12). A higher value of GRG, closer to 1, indicates a stronger alignment between the test results and the ideal data. ${\beta }_k$ denotes the weight of each factor based on relative importance, which can be calculated per Equation (19) in Section 2.3.2.

$${\gamma }_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1}^n{\beta }_k{\xi }_{0,i}(k)}$$

(12)

The highest value of GRG is assigned an order of 1, thereby enabling the conversion of multi-objective optimization into a single-objective optimization.

2.3.2. Weight Calculation Based on Shannon Entropy

Shannon entropy [62,63,64,65] is a widely used method for determining weights that assigns weights to different measurement indicators to enhance the accuracy and objectivity of the measurement results.

Firstly, the sum of all attributing factors in the analysis sequence is calculated as Equation (13).

$$D(k)={\displaystyle \sum _{i=1}^m{x}_k(i)}$$

(13)

Secondly, the entropy of each factor can be represented by Equations (14)–(16).

$$e_k={\displaystyle \frac{1}{0.6478\times m}}{\displaystyle \sum _{i=1}^m{U}_e}(x)$$

(14)

$$U_e(x)=x{e}^{(1-x)}+(1-x)e^x-1$$

(15)

$$x={\displaystyle \frac{x_i(k)}{D(k)}}$$

(16)

Thirdly, the total value of entropy is calculated based on Equation (17).

$$E={\displaystyle \sum _{i=1}^n{e}_k}$$

(17)

Then, the relative weight can be computed using Equation (18).

$${\lambda }_k={\displaystyle \frac{1}{m-E}}(1-e_k)$$

(18)

Finally, the weight of each attribute is determined by employing the normalization method, as described in Equation (19).

$${\beta }_k={\displaystyle \frac{{\lambda }_k}{{\displaystyle {\sum }_{i=1}^n{\lambda }_i}}}$$

(19)

2.4. Taguchi Method

The Taguchi method employs the concept of a quality loss function to quantitatively assess the degradation in product quality. A signal-to-noise ratio (S/N) is utilized to transform the quality loss function model into an index for measuring the robustness of design factors. The optimal combination of design factors is determined through Taguchi orthogonal testing. Figure 5 illustrates the flowchart depicting the steps involved in implementing the Taguchi method.

2.4.1. Signal/Noise Ratio

S/N evaluates the discrepancy between the actual value and the target value. A larger S/N ratio indicates a smaller deviation of an actual value from an ideal one, resulting in reduced fluctuation. S/N can be calculated [59] using Equations (20) and (21).

$$\mathrm{S}/\mathrm{N}=10\lg \left({\displaystyle \frac{1}{{\sigma }^2}}\right)(\mathrm{dB})$$

(20)

$${\sigma }^2={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(y_i-O\right)}^2}$$

(21)

The static S/N includes the characteristics of larger-the-better, smaller-the-better, and nominal-the-type, without considering the quality characteristics of the input–output relationship. In this study, ammonia concentration, age of air, and energy consumption exhibit the characteristic of smaller-the-better, while PMV demonstrates the nominal-the-type characteristic. Since the target values for ammonia concentration, age of air, energy consumption, and PMV are all zero, the calculation of the S/N ratio can be simplified as Equation (22).

$${\mathrm{S}/\mathrm{N}}_{\left(smaller-the-better\right)}=10\lg \left({\displaystyle \frac{1}{{\sigma }^2}}\right)=-10\lg \left({\sigma }^2\right)=-10\lg \left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{y}_i^2}\right)$$

(22)

2.4.2. Multi-Factor Analysis of Variance

The ANOVA is a statistical tool used to assess the relative significance of different parameters influencing system performance in a given dataset [66]. Its objective is to categorize experimental results into groups based on a common variable/parameter and an objective function/response. ANOVA optimization can be achieved through three distinct approaches. The first approach involves obtaining the F-value by calculating F-test [67], identifying the impact of parameters on output, and estimating the contribution of each factor to the total variation [68]. The second method employs Pareto analysis, also known as Pareto ANOVA, for analyzing parameter contributions that affect the output or response [69]. The third approach utilizes Sobol sensitivity analysis, which decomposes the model output variance into the sum of the input parameter variances to increase dimensionality [70]. In this study, we adopt the first approach, consisting of four steps: (1) calculation of between-group variation using between sum of squares (BSS) and between mean squares (BMS); (2) calculation of within-group variation using within sum of squares (WSS) and within mean squares (WMS); (3) calculation of F-test statistic from BMS to WMS; and (4) obtaining F-test value (F) [71].

2.5. Multi-Objective Optimization Process

This article employs CFD simulation, the Taguchi method, and grey relational analysis concurrently to optimize four variables and achieve an optimal balance of the four objectives. Sixteen orthogonal schemes with four variables at four levels were simulated using a validated numerical model. Grey relational analysis is used to transform the multiple-objective optimization into a single-objective GRG (grey relational grade) optimization. The Taguchi method is employed to calculate the S/N ratio for each GRG scheme and determine the optimal scheme.

The process of multi-objective optimization is depicted in Figure 6. A numerical model of the toilet is established within the Airpak environment. Simulations are conducted using orthogonal numerical schemes proposed by the Taguchi orthogonal method. Grey relational analysis and weight calculation based on Shannon entropy are applied to the simulation results of ammonia concentration, PMV, age of air, and energy consumption in order to transform multi-objective optimization into a single-objective GRG optimization. S/N analysis of GRG is employed for selecting the optimal design variables, while ANOVA of S/N is utilized to determine the significance of each variable. The optimized scheme is validated through comparison with a control group and serves as a basis for implementing the PV system and clean energy supply.

3. Results and Discussion

Despite the multitude of factors influencing the indoor air quality (IAQ) and predicted mean vote (PMV) of outdoor toilets, which are primarily influenced by ventilation systems, the operation of the ventilation system depends on four crucial factors: inlet location, outlet height, supply air temperature, and ventilation rate. The inlet location and outlet height determine airflow and distribution, while the ventilation rate affects the speed and quantity of air exchange; all three significantly impact indoor air quality. Moreover, the supply air temperature typically determines the temperature level within indoor spaces and consequently influences human thermal comfort. Therefore, this thesis selects these four variables as parameters for static analysis.

Consequently, particular emphasis has been placed on optimizing the positioning of inlet and outlet vents. Taking into consideration the four optimization objectives, including reducing ammonia concentration, achieving a PMV value of 0, and minimizing the age of air, all these goals are primarily influenced by the ventilation system. Therefore, our initial focus is on optimizing the inlet position, followed by determining the optimal height of the outlet from ground level, supply air temperature, and ventilation rate.

3.1. Inlet Position Optimization

This study models eleven inlet positions distributed across the ceiling and upper part of the backwall, as depicted in Figure 7. The outlet is located at a height of 15 cm from the bottom of the wall, with a supply air temperature of 18 °C and an air circulation of 20 times/h. Both inlet and outlet have dimensions measuring 120 mm × 120 mm.

Combined with the previous literature listed in

Table 4. Diverse heights explored in relevant research.

Reference	Height (m)
Wang C H, et al. [50]	0.9, 1.5
Zhang Z H, et al. [2]	0.9, 1.5
Tung Y, et al. [5]	1.56, 0.4, 1.16
Ameen A, et al. [15]	0.6, 1.1, 1.7

, ammonia concentration, PMV, and age of air are calculated at coordinates (0.8, 0.5, 0.45) and (0.8, 1.5, 0.45), as illustrated in Figure 8. The S/N ratios of the simulation results are depicted in Figure 9.

According to the equations presented in Section 2.2, the weights assigned to ammonia concentration, PMV, and age of air are 0.33384, 0.33283, and 0.33333, respectively, at a height of 0.5 m, while at a height of 1.5 m, these weights change slightly to 0.33362, 0.33310, and 0.33328, respectively. These results indicate that all three evaluation indicators demonstrate nearly equal importance in assessing the given parameters’ impact on system performance. The GRG and S/N values for each of the eleven schemes at both heights (i.e., 0.5 m and 1.5 m) are presented in Figure 10.

The results depicted in Figure 9 demonstrate that Scheme 1 to 5 (i.e., the positions of center, upper right, upper middle, upper left, and left middle on the ceiling) exhibit excellent thermal comfort and indoor air quality at both heights of 0.5 m and 1.5 m. Among these five positions, upper right and upper left are symmetrical and yield similar effects. Consequently, for subsequent multi-objective optimization purposes, we select four positions, center, upper middle, upper left, and left middle, as inlet locations.

3.2. Multi-Objective Optimization

The Taguchi method and CFD are employed to design and simulate orthogonal schemes, while ANOVA and grey relational analysis are utilized to determine the optimal scheme.

3.2.1. Taguchi Orthogonal Design

The optimization of the toilet ventilation system involves the selection of four influential factors: inlet position, outlet height, supply air temperature, and ventilation rate. In addition to the four inlet positions mentioned in Section 3.1, there are four levels for other factors, as presented in

Table 5. Associated factors and level definitions.

Level	Factor
	Inlet Position	Outlet Height (m)	Supply Air Temperature (°C)	Ventilation Rate (1/h)
1	Center top	0.12	12	12
2	Upper middle top	0.15	14	15
3	Upper left top	0.18	16	18
4	Left middle top	0.2	18	20

.

In order to minimize the number of simulations, an orthogonal experiment table of $L_{16}\left(4^4\right)$ was designed, as illustrated in

Table 6. Orthogonal simulation schemes.

	Column	Inlet Position	Outlet Height (m)	Supply Air Temperature (°C)	Ventilation Rate (1/h)
Number
1		1 (center top)	1 (0.12)	1 (12)	1 (12)
2		1	2 (0.15)	2 (14)	2 (15)
3		1	3 (0.18)	3 (16)	3 (18)
4		1	4 (0.20)	4 (18)	4 (20)
5		2 (upper middle top)	1	2	3
6		2	2	1	4
7		2	3	4	1
8		2	4	3	2
9		3 (upper left top)	1	3	4
10		3	2	4	3
11		3	3	1	2
12		3	4	2	1
13		4 (left middle top)	1	4	2
14		4	2	3	1
15		4	3	2	4
16		4	4	1	3

, which reduces simulation times from 256 to 16.

3.2.2. Numerical Simulation Results

The numerical simulation results of the above 16 schemes at heights of 0.5 m and 1.5 m, respectively, are depicted in Figure 11. Identifying an optimal scheme that comprehensively addresses reduced ammonia concentration, minimal age of air, low energy consumption, and a PMV value of 0 poses considerable complexity.

The analysis of means (ANOM) is employed to determine the preference level for each variable at two different heights. The parameter effect of a specific level refers to the extent of variation at which the parameter causes the S/N ratio to deviate from its overall mean. For the four levels under the ‘inlet position’ factor, the average S/N ratio is computed as described in Equations (23)–(26). This method can be extended to calculate the mean S/N ratio for other factors, and the ANOM for the S/N ratio is depicted in Figure 12 and Figure 13. Here, A, B, C, and D represent four variables, respectively—inlet position, outlet height, supply air temperature, and ventilation rate—while 1, 2, 3, and 4 denote four levels of each variable. $\eta$ represents values of simulation results, while the subscripts 1 to 16 correspond to the simulation schemes listed in Table 6.

$$m_{A1}={\displaystyle \frac{1}{4}}\left({\eta }_1+{\eta }_2+{\eta }_3+{\eta }_4\right)$$

(23)

$$m_{A2}={\displaystyle \frac{1}{4}}\left({\eta }_5+{\eta }_6+{\eta }_7+{\eta }_8\right)$$

(24)

$$m_{A3}={\displaystyle \frac{1}{4}}\left({\eta }_9+{\eta }_{10}+{\eta }_{11}+{\eta }_{12}\right)$$

(25)

$$m_{A4}={\displaystyle \frac{1}{4}}\left({\eta }_{13}+{\eta }_{14}+{\eta }_{15}+{\eta }_{16}\right)$$

(26)

No significant correlation was observed between ammonia concentration and age of air at the heights of 0.5 m and 1.5 m, while the trends of PMV and energy consumption exhibit similarity. Notably, energy consumption demonstrates a direct association solely with supply air temperature and ventilation rate, resulting in identical ANOM values for S/N ratio at both heights.

At a height of 0.5 m, A4, B4, C1, and D4 demonstrate the highest mean S/N values for ammonia concentration, indicating minimal odor at these levels. Similarly, A1, B4, C4, and D4 establish the most comfortable thermal environment. A2, B1, C1, and D4 result in the lowest age of air. The combination of C1 and D1 consumes the lowest amount of energy.

The simulation results at a height of 1.5 m demonstrate that the highest S/N values are observed for A2, B2, C3, and D3 in terms of ammonia concentration; for A1, B4, C4, and D4 in terms of PMV; and for A1, B3, C4, and D4 in terms of age of air.

The simulation of influential factors for the outdoor toilet ventilation system result in inconstancy among the four-objective optimization scenarios, causing an inability to determine the optimal factor level. Therefore, grey relational analysis is applied to identify the factor levels that achieve multi-objective optimization at both heights, as described in subsequent sections.

3.2.3. ANOVA of S/N

The analysis of variance is employed to interpret the impact and contribution of four variables with respect to the four objectives at two different heights. An ANOVA of S/N was conducted using the calculation method described in Section 2.1.2. Taking the ammonia concentration at a height of 0.5 m as an example,

Table 7. ANOVA of S/N for ammonia concentration at a height of 0.5 m.

Design Variable	Degree of Freedom	Quadratic Sum	Mean Quadratic Sum	Variance Ratio	Contribution Rate
Inlet position	4	0.009	0.003	0.25263	0.03%
Outlet height	4	0.028	0.009	0.75789	0.08%
Supply air temperature	4	0.058	0.019	1.6	0.16%
Ventilation rate	4	35.285	11.762	990.484	99.74%
Error	0
Total	16	35.38
(Error)	8	0.095	0.011875

presents the ANOVA results for S/N. The contribution rates of inlet position, outlet height, supply air temperature and ventilation rate are 0.02%, 0.08%, 0.16%, and 99.74%, respectively, indicating that ventilation rate is the most influential factor affecting ammonia concentration at a height 0.5 m. The ANOVA results for all objectives are summarized in

Table 8. ANOVA results of S/N for four objectives.

Design Variable	Ammonia Concentration		PMV		Age of Air		Energy Consumption
	0.5 m	1.5 m	0.5 m	1.5 m	0.5 m	1.5 m	0.5 m	1.5 m
Inlet position	0.03%	0.03%	1.36%	11.66%	3.08%	48.85%	/	/
Outlet height	0.08%	0.08%	0.90%	2.45%	1.22%	10.14%	/	/
Supply air temperature	0.16%	0.17%	71.50%	73.24%	1.99%	6.24%	21.14%	21.14%
Ventilation rate	99.74%	99.72%	26.24%	12.65%	93.70%	34.76%	78.86%	78.86%

.

The ANOVA results presented in Table 8 indicate that ventilation rate exerts a dominant effect on ammonia concentration, while supply air temperature exhibits a significant influence on PMV. Both ventilation rate and inlet position greatly affect the age of air. Notably, ventilation rate plays a more crucial role in energy consumption.

3.2.4. GRG and S/N Analysis

According to the equations presented in Section 2.3, a comparative sequence is established and normalized, followed by the calculation of grey relational coefficient and weight for each factor. At a height of 0.5 m, the weights assigned to ammonia concentration, PMV, age of air, and energy consumption are determined as 0.24996, 0.24992, 0.25008, and 0.25004, respectively, while at a height of 1.5 m, these values become 0.24991, 0.25009, 0.25000, and 0.25000, respectively—indicating that all four factors hold practically equal importance.

GRG is calculated based on Equation (12) and the corresponding outcomes are described in Figure 8. Due to its larger-the-better characteristic, the S/N of GRG can be calculated using Equation (27), and the results are illustrated in Figure 14.

$${S/N}_{\left(\mathit{larger}-the-better\right)}=10\lg \left({\displaystyle \frac{1}{{\sigma }^2}}\right)=-10\lg \left({\sigma }^2\right)=10\lg \left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{y}_i^2}\right)$$

(27)

GRG and S/N exhibit a similar trend at both heights of 0.5 m and 1.5 m. Scheme 6 demonstrates a distinct advantage over other schemes at a height of 0.5 m, while showing a slight disadvantage compared with Scheme 1 at a height of 1.5 m. Considering squatting pots are more frequently installed and time-consuming comparing to standing types in actual toilet usage, it is anticipated that air quality and thermal comfort play a more crucial role at a height of 0.5 m than at 1.5 m. Therefore, Scheme 6 is considered as the optimal solution with an inlet position located at the upper middle top, outlet height set to 0.12 m, supply air temperature maintained at 12 °C, and ventilation rate set to 20 times/h.

The simulation results for both Scheme 6 and Scheme 1 at coordinate z = 0.45 m are depicted in Figure 15.

3.3. Optimization Scheme Validation

3.3.1. Optimization Effect

To validate the degree and effectiveness of the optimization, the middle level in the orthogonal table [72] is selected as the control group (i.e., an inlet position at center top, an outlet height of 0.16 m, supply air temperature of 15 °C, and ventilation rate of 16 times/h). The simulation results are presented in Figure 16: 6.25 ppm for ammonia concentration, −1.47 for PMV, 229.42 s for age of air, and 388.36 W for energy consumption at a height of 0.5 m. Similarly, at a height of 1.5 m, the corresponding values are recorded as 6.19 ppm, −1.09, 90.09 s, and 388.36 W, respectively.

At a height of 0.5 m, the optimal scheme slightly compromises energy savings in favor of improving air quality and thermal comfort, resulting in a 17.4% decrease in ammonia concentration, a 4.1% enhancement in PMV, and a 36.8% reduction in age of air compared with the control group. However, at a height of 1.5 m, the optimal scheme exhibits diminished performance as it achieves only a 17.4% reduction in ammonia concentration while experiencing worsened PMV and age of air compared with the control group.

The comparison results at a height of 1.5 m can be explained as follows: due to its proximity to the wall of the inlet position in the optimal scheme, airflow development is insufficient at a height of 1.5 m, where it generates attached jet streams that deteriorate PMV and age of air.

3.3.2. Optimal Scheme Revision

To improve the unsatisfactory PMV value and age of air at a height of 1.5 m, design variables of the optimal scheme were revised. Based on the ANOM analysis of S/N described in Figure 12 and Figure 13,

Table 9. The optimal factor levels.

Objective	0.5 m Height				1.5 m Height
	A	B	C	D	A	B	C	D
Ammonia concentration	4	4	1	4	2	2	3	3
PMV	1	4	4	4	1	4	4	4
Age of air	2	1	1	4	1	3	4	4
Energy consumption	\	\	1	1	\	\	1	1

illustrates the optimal factor levels reflected by the maximum S/N for four objectives. The most frequently mentioned factor levels comprises A1, B4, C1, and D4, which are referred to as the revised optimal scheme.

The revised optimal scheme yields an ammonia concentration of 5.07 ppm, a PMV value of −1.37, an age of air of 160.64 s, and an energy consumption of 420.44 kWh at a height of 0.5 m. Similarly, at a height of 1.5 m, the values are 5.02 ppm, −1.03, and 70.12 s, respectively, as depicted in Figure 17.

Compared with the control group, both air quality and thermal environment are enhanced at heights of 0.5 m and 1.5 m, albeit at the expense of energy conservation. At a height of 0.5 m, there is an improvement in ammonia concentration by 18.9%, PMV by 6.8%, and age of air by 30.0%. Similarly, at a height of 1.5 m, these improvements amount to 18.9%, 5.5%, and 22.2%, respectively, thus evidencing that the revised optimal scheme significantly improved the toilet environment with an inlet position at center top, outlet height of 0.2 m, supply air temperature of 12 °C, and ventilation rate of 20 times/h.

3.4. Photovoltaic Roof System

To mitigate municipal electricity consumption and alleviate the adverse impact on energy conservation of the optimal scheme, two approaches, namely, a building-integrated photovoltaic (BIPV) system and building-attached photovoltaic (BAPV) system, can be employed for PV system installation on toilet roofs.

3.4.1. PV Power Generation

Due to its lower investment cost and more convenient structure compared to BIPV, the BAPV roof was selected for this study, as demonstrated in Figure 18. Monocrystalline silicon solar panels are installed on the toilet roof to convert solar energy into electricity for powering the ventilation system. The PV panels have an inclination angle of 30°, which is considered preferable local performance for solar collectors, covering an area of 1.25 m². The PV system efficiency is measured at 20.4%, with a highly efficient inverter efficiency at 97% and a miscellaneous loss of only 5%. In calculation of electricity production, the tilted solar irradiance method proposed by Perez [73] in 1990 is taken into account. The annual electricity generated by the BAPV roof system amounts to 582.02 kWh, which is calculated using RETScreen (a PV design software program popular in the industry, version Expert), as depicted in Figure 19.

3.4.2. Ventilation Energy Consumption

According to the 2019 Qinghai Province Population and Family Development Report, the average household size in the region is 3.9 individuals per household. Statistics from the World Toilet Organization indicate that an individual typically visits toilets 6~8 times a day. Considering a household with four members, and each person visiting seven times daily for about 5 min per visit, it can be estimated that a household toilet ventilation system operates for approximately 851.67 h annually.

The optimal scheme suggests an electric power consumption of 420.44 W based on a supply air temperature of 12 °C and ventilation rate of 20 times/h. Taking into account annual usage time, the combined annual ventilation energy consumption is approximately 358.07 kWh, which can be covered by PV electricity production.

The optimized design variables applied to outdoor toilet ventilation systems in Qinghai province, China presented in this study, can serve as a reproducible model for other cold regions, providing valuable insights for implementing concrete measures towards achieving the goals set forth by the Toilet Revolution initiative.

4. Conclusions

This study aims to efficiently improve the outdoor toilet environment by proposing an optimized scheme with a BAPV roof-powered ventilation system through pioneering efforts in developing and validating of its numerical model through integrated application of the Taguchi method, computational fluid dynamics (CFD), and grey relational analysis. Specifically, the optimization process focuses on influential variables that affect both ventilation effectiveness and thermal comfort. Based on our research findings, we derived the following conclusions:

The optimization of system performance hinges on four influential variables: inlet position, outlet height, supply air temperature, and ventilation rate. These factors are evaluated by multiple objectives (ammonia concentration, PMV, age of air, and energy consumption), each carrying nearly equal weight at both 0.5 m and 1.5 m heights in this context. The complex statistical and experimental (simulation experiment) approach yielded anticipated results: ventilation rate has a dominant impact on ammonia concentration, while supply air temperature significantly influences PMV. Both the ventilation rate and inlet position have a significant effect on the age of air, while the former plays a more crucial role in determining energy consumption.

The inlet location is recommended to be positioned on the ceiling rather than on the walls—specifically at the center top, upper right, upper middle, upper left, and left middle. In the optimal scheme, it features a center top as the inlet position, an outlet height of 0.2 m, a supply air temperature of 12 °C, and a ventilation rate of 20 times/h. This configuration effectively improves ammonia concentration, PMV, and age of air by 18.9%, 6.8%, and 30.0%, respectively, at a height of 0.5 m, and by 18.9%, 5.5%, and 22.2%, respectively, at a height of 1.5 m; however, it comes at the expense of energy conservation. Consequently, a BAPV roof is proposed with an inclination angle of 30, covering an area measuring 1.25 m² that achieves system efficiency up to 20.4%. This setup generates an annual electricity output of 582.02 kWh, which covers the energy consumption equivalent to 358.07 kWh, thereby achieving zero-carbon operation in toilet ventilation.

By utilizing numerical simulation of the Taguchi method, computational fluid dynamics (CFD), and gray relational analysis to optimize indoor air quality and thermal comfort with zero-carbon emission practices in rural toilets, this study marks a departure from previous studies that solely focused on indoor air quality while neglecting thermal comfort and energy conservation or only analyzed one or two influential factors. This research comprehensively considers various factors that could potentially impact the indoor air quality of toilets and achieves an optimal balance of air quality, thermal comfort, and energy consumption. Its findings contribute towards enhancing toilet standards in cold and harsh climates. However, it should be noted that this study specifically concentrates on cold regions; thus, further analysis might be required for hot regions in order to obtain applicable results.

In summary, this article offers valuable insights into the construction of rural hygienic outdoor toilets and standalone facilities, serving as a reference for building temporary outdoor toilets in urban areas and emergency shelters. It aims to develop a zero-carbon solution that caters to the needs of a vast population by ensuring a more safe, comfortable, and sanitary environment.