Cases of respiratory disease transmission in enclosed elevators have been reported frequently. In the postpandemic era, in order to mitigate the spread of respiratory diseases in moving elevators, a multiobjective genetic optimization method based on a response surface model is used to optimize the elevator ventilation. The ventilation parameters were optimized for three objectives: reducing carbon dioxide concentration, maintaining human thermal comfort, and achieving energy conservation. First, a response surface model is established using the computational fluid dynamics method and the Kriging model to correlate the design variables (air supply velocity in x, y, and z directions and air supply temperature) with the output function (CO_{2} concentration, average temperature, and average velocity). Subsequently, the Pareto optimal solution set of ventilation parameters was obtained by employing a multiobjective genetic algorithm. Finally, the optimal air supply velocity, angle, and temperature were obtained for both peak periods of elevator traffic (13 passengers) and other situations (4 passengers) when the elevator is moving up and down, which satisfy the objectives of health, comfort, and energy conservation.
NOMENCLATURE
 CFD

Computational fluid dynamics
 DCV

Demandcontrolled ventilation
 DoE

Design of experiments
 IAQ

Indoor air quality
 LHS

Latin hypercube sampling
 MOGA

Multiobjective genetic algorithm
 RSM

Response surface model
 RMSE

Root mean square error
 RAAE

Relative average absolute error
 R^{2}

Coefficient of determination
 UDF

Userdefined function
I. INTRODUCTION
Airborne transmission of respiratory infectious diseases has brought an impact on the use and management of elevators. The elevator cabin is enclosed, personnel are gathered, and the indoor environment is poorly ventilated, which increase the risk of virus transmission.^{1–3} Ito et al.^{4} demonstrated that the transmission of COVID19 in confined spaces was 18 times more prevalent than in outdoor environments. In the postpandemic era, the transmission of virus is mitigated through the normalized air conditioning methods, instead of imposing restrictions on passenger numbers and ride durations, or resorting to elevator shutdowns. It is recommended that the air volume be increased,^{5,6} although this may result in an increase in energy wastage due to overventilation of the constantairvolume ventilation system.^{7} Therefore, the accurate design of ventilation volume to maintain air quality in the elevator environment and harvest energy conservation is an urgent and challenging task.^{3}
It has been demonstrated that ventilation can dilute and displace infectious aerosols. However, the dilution of contaminants necessitates a substantial air volume, which in turn results in increased energy consumption. Furthermore, given the high passenger turnover and brief dwelling times within elevator cabins, the employment of substantial air volumes to fully eradicate indoor pollutants is not a viable option. Under these conditions, the energy conservation design of IAQ (Indoor air quality) is realized by optimizing the indoor air flow pattern. The exhaled pollutants by humans will exhibit a noticeable “selflocking phenomenon” in the breathing zone,^{8,9} which is also observed in an elevator cabin.^{3} In this case, we propose a way to decrease the height of the selflocking zone below that of the respiratory zone, thereby maintaining a low concentration in the zone.
Directly detecting and measuring the exhaled virus concentration is extremely difficult and slow.^{10,11} Fortunately, CO_{2} can be used as a good proxy for potential respiratory infectious disease transmission risk because its concentration is directly related to the respiratory activity of indoor people, which can affect the freshness of the air and the health and comfort of the occupants. A commonly used experimental method to demonstrate the validity of CO_{2} as an indicator of indoor environmental quality is to monitor changes in indoor CO_{2} concentrations under different ventilation conditions while recording the physiological responses, subjective comfort scores, or work efficiency of the occupants. Richardson^{12} measured CO_{2} in classrooms using portable carbon dioxide monitors; they found the probability of susceptible individuals acquiring airborne infectious diseases also increases when the concentration of exhaled air increases in the room with infectors present. The reason is that CO_{2} is coexhaled with aerosols containing pathogens by infectors.^{7} A study^{13} on tuberculosis outbreak in a university building showed that CO_{2} levels < 1000 ppm were associated independently with a decrease in tuberculosis incidence among contacts by 97%. Gilio et al.^{14} demonstrated a positive correlation between CO_{2} and a variety of indoor pollutants through measured data and statistical analyses, concluding that CO_{2} can be used as an indicator of indoor air quality. Thus, choosing the CO_{2} concentration as the indicator of virus concentration for infection control would be rational.
Demandcontrolled ventilation methods (DCV) is a widely used provision that can achieve energysaving control of indoor air quality (IAQ).^{15,16} The direction of elevator movement and the number of passengers is subject to stochastic variation. The vertical motion of the elevator generates airflow disturbances and pressure changes, which in turn alter the force exerted on the exhaled pollutants. Moreover, in the context of varying crowd densities, maintaining a constant airflow volume for ventilation may result in inadequate IAQ or excessive energy consumption and thermal discomfort.^{17,18} Fortunately, under the DCV framework, the ventilation rate is dynamically adjusted according to the actual ventilation demand. Li and Cai^{7} proposed a CO_{2}based demandcontrolled ventilation strategy that effectively limits the spread of COVID19 in indoor environments while achieving 30%–50% energysavings. Schibuola and Tambani^{19} proposed an effective approach for determining the optimal ventilation rate to control COVID19 infection risk based on realtime measurements of CO_{2} concentration, which resulted in a 72% reduction in energy consumption. The DCV system is capable of dynamically adjusting the ventilation volume according to the actual ventilation demand, thereby enabling the energy conservation control of IAQ.
In order to fulfill diverse ventilation demands, ventilation volumes will be meticulously designed. The multiobjective optimization design method enables the identification of the optimal solution of parameters to meet various ventilation requirements. Multiobjective optimization methods based on forward CFD calculations are frequently employed to identify solutions for mitigating the diffusion of indoor pollutants. Zhao et al.^{20} demonstrated the multiobjective optimization method to find optimal air supply inlet size and location and air supply parameters, which only takes 12 h to finish the design. Similarly, Bai^{21} established a natural ventilation performance prediction model by using response surface method, and adopted multiobjective genetic algorithm (MOGA) to quickly obtain the optimal solution. In short, the MOGA enables rapid determination of air supply parameters.
In conclusion, a DVCbased multiobjective optimization approach will be employed in order to mitigate the transmission of respiratory diseases in elevators. The objective is to reduce the concentration of pollutants in the breathing zone by optimizing the velocity, temperature and angle of the air supply.
Compared with existing studies, the proposed optimization approach has the following advantages and novelties:

Reducing the concentration of CO_{2} in the breathing zone by using less air volume, thereby decreasing the likelihood of passenger infection and maintaining thermal comfort.

The individual density and the elevator's motion are taken into consideration. The results are more in line with reallife scenarios, enabling automatic adjustment of elevator ventilation in various operating scenarios.
II. MULTIOBJECTIVE OPTIMIZATION METHOD FOR SUPPLY AIR PARAMETERS
The multiobjective optimization of supply air parameters involves response surface construction and multiobjective computations in two steps. The MOGA scheme will be obtained through the ANSYS Workbench platform, using the Design Exploration module for parameter optimization calculations.
The simplified optimization process is shown in Fig. 1.
A. Response surface prediction model
Response surface methodology (RSM) is a mathematical and statistical technique that uses information about known sample points to construct an approximate mathematical model.^{22} RSM provides an objective function for correlating output responses with the number of selected input parameters.^{23} It has a significant advantage as it reduces the number of experiments essential in predicting the optimum condition.^{24,25} To construct a response surface model, there are three steps involved: determining the objective function and optimizing parameters of the response surface, design of experiments (DoE), and selecting the method for constructing the response surface model.
1. Optimizing parameters
In optimization problems, the aim is to determine a set of design variables that can achieve the optimal values of design objectives while satisfying certain constraints. Therefore, the first step is to determine the objective functions based on the design objectives and consider them as output parameters. Next, the critical parameters that have a significant impact on the objective functions are selected as design variables and constraints, and they are considered as input parameters.
2. Sensitivity analysis
When investigating the impact of multiple variables on an objective, sensitivity analysis is commonly used to evaluate the extent of their impact. This includes both local and global sensitivity analysis. Local sensitivity analysis allows control variable experiments to determine the impact of individual parameters on the objectives. However, it is not conducive to quantitatively determining the sensitivity of each parameter, thus failing to identify critical parameters. Global sensitivity analysis aims to investigate the impact of various input parameters on the design objectives and calculate the sensitivity index for each parameter, thereby identifying critical parameters that have a significant impact on the model. Sensitivity analysis can be employed to reduce the computational cost of the optimization process by identifying critical factors prior to optimization.
3. Design of experiments and constructing methods
The $ \theta k$ in the unknown parameters is used to fit the model, M is the number of design variables, and $ x k i$ and $ x k j$ are the kth components of sample points $ x i$ and $ x j$.
Based on the above results, this research chooses LHS method as the DoE method and adopts the Kriging method to construct the response surface model.
4. Prediction accuracy
Since it is an approximate model, it is crucial to evaluate and validate the prediction accuracy of the response surface model in detail. The commonly used statistical indicators for analyzing the prediction accuracy of response surface models include root mean square error (RMSE), relative average absolute error (RAAE), and coefficient of determination (R^{2}).^{27} Among these, RMSE, RAAE, and R^{2} primarily reflect the overall prediction accuracy of the response surface model. This prediction model will also adopt the above indicators for validation and analysis.
B. Multiobjective optimization genetic algorithm
Multiobjective genetic algorithms can find globally optimal compromise solutions when dealing with competitive or conflicting objectives. In order to attain the relative optimal solutions for each objective function, the Pareto optimal solution method is recommended. The control running parameters of the Pareto optimal solution method include setting parameters such as the number of initial samples, the number of samples per iteration, and the maximum allowable Pareto percentage.^{28}
The convergence and stopping criteria for optimization can be set based on the maximum allowed Pareto percentage and the maximum number of iterations. If the maximum allowed Pareto percentage is too low (<30%), the optimization calculation may converge too early; if this value is too high (>80%), the convergence speed of the process will be slow. The maximum number of iterations can also be used as a stopping criterion. If the optimization has not converged when reaching this number, the iteration will stop.
III. MULTIOBJECTIVE VENTILATION OPTIMIZATION IN MOVING ELEVATOR
The operation direction of the elevator and the number of passengers exhibit a degree of randomness. In order to regulate the air volume according to the number of passengers, air supply regulation schemes for daily passenger situations (4 passengers) and full load situations (13 passengers) in different moving directions will be obtained, respectively.
There is a mediumspeed elevator with a load capacity of 1000 kg (13 passengers at full load) suitable for ordinary residential use, with an operating speed of 1.5 m/s. A simplified elevator model with dimensions of 1500 × 1600 × 2350 mm^{3} (X × Z × Y) was established using Ansys Space Claim 18.0,^{29} as shown in Fig. 2.
In the elevator car, there are four asymptomatic infected passengers, with index patient A marked in red and the other patients marked in blue. They are evenly distributed, have a height of 1.65 m, and breathe through their noses and exhaled pollution. The region proximal to the nose and mouth, where passengers are exposed to a significant volume of ambient air, is defined as the respiratory zone.^{2} The breathing zone is the region encompassing the nose and mouth, through which a substantial volume of air can be inspired (X × Z × Y: 400 × 200 × 200 mm^{3}). The top of the elevator contains an air inlet, and according to the national standard “Safety Code for Elevator Manufacture and Installation” (GB 7588–2003),^{30} the area of the air supply port should be greater than 1% of the elevator's effective area. Therefore, the air inlet size is set to 400 × 40 mm^{2}, and the sizes of other parts are summarized in Table I.
Name .  Number .  Parameters . 

Elevator  1  Size: X × Z × Y: 1500 × 1600 × 2350 mm^{3} 
Passenger: A–D  4  Height: 1.65 m 
Nose  4  Area: 50 mm^{2} 
Inlet: 1  1  Size: X × Z: 400 × 40 mm^{2} 
Light: 2 and 3  2  Size: X × Z: 20 × 400 mm^{2} 
Outlet: 4  1  Size: X × Y: 6 × 2100 mm^{2} 
Door: 5 and 6  2  Size: X × Y: 447 × 2100 mm^{2} 
Breathing zone  4  Size: X × Z × Y: 400 × 200 × 200 mm^{3} 
Name .  Number .  Parameters . 

Elevator  1  Size: X × Z × Y: 1500 × 1600 × 2350 mm^{3} 
Passenger: A–D  4  Height: 1.65 m 
Nose  4  Area: 50 mm^{2} 
Inlet: 1  1  Size: X × Z: 400 × 40 mm^{2} 
Light: 2 and 3  2  Size: X × Z: 20 × 400 mm^{2} 
Outlet: 4  1  Size: X × Y: 6 × 2100 mm^{2} 
Door: 5 and 6  2  Size: X × Y: 447 × 2100 mm^{2} 
Breathing zone  4  Size: X × Z × Y: 400 × 200 × 200 mm^{3} 
After establishing the model, Fluent is employed to set boundary conditions using numerical calculation methods for investigating the flow field distribution and CO_{2} concentration in the elevator. The mathematical model adopted at present is the same as our previous work.^{2} The comprehensive mathematical model includes the Mass equation, Navier–Stokes equations and RNG k–ε equations.
The CO_{2} concentration at the air supply and door opening is set to 400 ppm (i.e., volume/mole fraction: 0.04%). The concentration of exhaled CO_{2} from the mouth is set at 45 000 ppm (4.5%).^{36,37}
Simulation of working conditions are listed in Table II.
Boundary name .  Type .  Parameter .  Component boundary conditions . 

Inlet  Velocityinlet  P1: Velocity in xdirection (m/s)  Mole fraction: 
P2: Velocity in ydirection (m/s)  
CO_{2}: 0.04%  
P3: Velocity in zdirection (m/s)  Air: 99.96%  
P4: Temperature (K)  
Light  Wall  Temperature equals to 300 K  ⋯ 
Outlet  Pressureoutlet  Mole fraction:  
Eqs. (3.1) and (3.2)  CO_{2}: 0.04%  
Temperature equals to 298 K  Air: 99.96%  
Door; wall (floor, ceiling, etc.)  Wall  ⋯  ⋯ 
Passenger: A–D  Wall  Heat transfer coefficient: 4.5 W·m^{−2} °C^{−1}  ⋯ 
Mouth: A–D  
Nose: A–D  Velocityinlet  Mole fraction:  
Eqs. (3.3)–(3.6)  CO_{2}: 4.5%  
Temperature equals to 307 K  Air: 95.5% 
Boundary name .  Type .  Parameter .  Component boundary conditions . 

Inlet  Velocityinlet  P1: Velocity in xdirection (m/s)  Mole fraction: 
P2: Velocity in ydirection (m/s)  
CO_{2}: 0.04%  
P3: Velocity in zdirection (m/s)  Air: 99.96%  
P4: Temperature (K)  
Light  Wall  Temperature equals to 300 K  ⋯ 
Outlet  Pressureoutlet  Mole fraction:  
Eqs. (3.1) and (3.2)  CO_{2}: 0.04%  
Temperature equals to 298 K  Air: 99.96%  
Door; wall (floor, ceiling, etc.)  Wall  ⋯  ⋯ 
Passenger: A–D  Wall  Heat transfer coefficient: 4.5 W·m^{−2} °C^{−1}  ⋯ 
Mouth: A–D  
Nose: A–D  Velocityinlet  Mole fraction:  
Eqs. (3.3)–(3.6)  CO_{2}: 4.5%  
Temperature equals to 307 K  Air: 95.5% 
A. Construction of response surface model
1. Optimizing parameters in moving elevator
a. Objective function
The exhaled pollutants by humans will exhibit a noticeable selflocking phenomenon in the breathing height zone,^{8,9} which is also observed in an elevator.^{3} The prolonged presence of exhaled pollutants will greatly increase the risk of interpersonal disease transmission. Therefore, in order to suppress the accumulation of pollutants in the breathing zone and reduce the risk of exposure to passengers, the optimization design of air supply velocity, temperature, and angle will be focused.
During the optimization process of elevator air supply parameters, the response surface output variable is the subsequent optimization target. According to our previous research,^{2} approximately 50% of pollutants tend to accumulate in the elevator above a height of 1.5 m. This height, however, is located within the breathing zone of passengers, posing a threat to their health. Therefore, it is imperative to reduce the concentration of CO_{2} at the height of 1.5 m. The objective of optimizing the air supply parameters is to reduce the concentration of CO_{2} in the area, prevent the accumulation of CO_{2} from locking the breathing zone, and maintain overall thermal comfort. The effect of positioning the selflocking zone below the breathing zone is depicted in Fig. 3.
Type .  Number .  Name .  Unit . 

Output variable  P5  CO_{2} molar fraction  ⋯ 
(Plane: Y = 1500 mm)  
P6  Average temperature  K  
P7  (Plane: Y = 1500 mm)  m/s  
Air flow average velocity  
P8  Average velocity (control group)  m/s  
(Plane: Y = 1300 mm) 
Type .  Number .  Name .  Unit . 

Output variable  P5  CO_{2} molar fraction  ⋯ 
(Plane: Y = 1500 mm)  
P6  Average temperature  K  
P7  (Plane: Y = 1500 mm)  m/s  
Air flow average velocity  
P8  Average velocity (control group)  m/s  
(Plane: Y = 1300 mm) 
b. Design variables and constraints
In this case, parameters (air supply velocity, air supply angle, and air supply temperature) that have a significant impact on both the concentration of exhaled pollutants and human comfort were selected as key input variables.^{3}
The range and unit information for these optimization variables is shown in Table IV.
Type .  Number .  Name .  Unit .  Codomain .  Constraint condition . 

Input variable  P1  x direction velocity  m/s  77  $ P 1 \xd7 P 1 + P 2 \xd7 P 2 + P 3 \xd7 P 3 \u2264 4$(normal situation: 4 passengers) 
P2  y direction velocity  m/s  70  
P3  z direction velocity  m/s  77  $ P 1 \xd7 P 1 + P 2 \xd7 P 2 + P 3 \xd7 P 3 \u2264 7$(other situation: 13 passengers)  
P4  Air supply temperature  K  292–302  ⋯ 
Type .  Number .  Name .  Unit .  Codomain .  Constraint condition . 

Input variable  P1  x direction velocity  m/s  77  $ P 1 \xd7 P 1 + P 2 \xd7 P 2 + P 3 \xd7 P 3 \u2264 4$(normal situation: 4 passengers) 
P2  y direction velocity  m/s  70  
P3  z direction velocity  m/s  77  $ P 1 \xd7 P 1 + P 2 \xd7 P 2 + P 3 \xd7 P 3 \u2264 7$(other situation: 13 passengers)  
P4  Air supply temperature  K  292–302  ⋯ 
2. Sensitivity analysis of air supply parameters in elevator
The parameter correlation analysis module of ANSYS is employed in this study to perform a global sensitivity analysis of supply air parameters. Commonly utilized approaches for global sensitivity analysis encompass regressionbased, variancebased, and screeningbased approaches. The regressionbased method was selected for its convenience and costeffectiveness in calculating sensitivity indicators for multiple parameters simultaneously. In the regression analysis, either the Pearson correlation coefficient or Spearman rank correlation coefficient is employed to represent the sensitivity index of each parameter. The Pearson correlation coefficient method evaluates the linear relationship between two continuous variables using their real values. Furthermore, it assesses the correlation between two statistical variables based on their ranking and monotone equation. Given the complex linear and nonlinear relationships response surface results between supply air input parameters and optimization objectives, it is evident that the Spearman method is more appropriate for this study.
The correlation coefficient $r$ in Spearman's method has a value range of [−1, 1]. A positive $r$ indicates a positive correlation between supply air parameters and elevator air quality optimization objectives, while a negative $r$ indicates a negative correlation. The magnitude of the correlation coefficient reflects the strength of the correlation: $ r\u226b0.8$ represents an extremely high correlation; $0.6\u226a r\u226a0.8$ suggests a high correlation. The sensitivity results of elevator air supply optimization parameters are presented in Table V.
.  x direction velocity (m/s) .  y direction velocity (m/s) .  z direction velocity .  Inlet ambient air temperature (K) .  

up .  down .  up .  down .  up .  down .  up .  down .  
Temperature (K)  0  0  0  0.833  0  0  0.851  0.511 
CO_{2} concentration  0.591  0  0  −0.595  0.592  0  0  0 
y direction velocity (m/s)  −0.738  0  0  0  −0.574  0  0  0 
.  x direction velocity (m/s) .  y direction velocity (m/s) .  z direction velocity .  Inlet ambient air temperature (K) .  

up .  down .  up .  down .  up .  down .  up .  down .  
Temperature (K)  0  0  0  0.833  0  0  0.851  0.511 
CO_{2} concentration  0.591  0  0  −0.595  0.592  0  0  0 
y direction velocity (m/s)  −0.738  0  0  0  −0.574  0  0  0 
Table V demonstrates a strong positive correlation between the average temperature in the breathing zone (height of 1.5 m plane) and intake air temperature during upward elevator movement. The CO_{2} concentration at the same level is found to correlate positively with the xdirection velocity (0.591) and negatively with the zdirection velocity (0.592). The ydirection velocity at the breathing zone exhibits a high negative correlation of −0.738 with the xdirection velocity and −0.574 with the zdirection velocity. Based on the above analysis, it is evident that adjusting the air supply temperature can effectively create thermal comfort for passengers within the breathing zone (1.5 m plane). Furthermore, adjusting the air supply velocity in both the x and z directions can result in a reduction of pollutant concentration within the breathing zone and decrease the height of the selflocking zone.
The average temperature in the breathing zone is positively correlated with the air supply velocity in the $y$ direction and the air supply temperature during downward elevator movement, showing a very high positive correlation with a ydirection velocity of 0.833. Additionally, there is a negative correlation of 0.595 between CO_{2} concentration and ydirection velocity on the same plane. The above analysis demonstrates that the adjustment of air supply temperature and ydirection velocity can moderately create the thermal comfort of individuals and mitigate the concentration of pollutants in the breathing zone.
3. Design of experiments and construction methods in moving elevator
The reason for using the LHS method for experimental design is that it allows for efficient and homogeneous sampling of sample points in the parameter space, resulting in a better estimate of the overall parameter with a smaller number of trials. Therefore, in this case, the LHS method was used as the experimental design method to construct 25 experimental points within a specified range for each parameter. The Kriging method was employed to construct a response surface model. Using the Design Exploration module in ANSYS Workbench, relevant parameters for the Kriging algorithm were set on top of a Fluent computational model. The kernel variable type was set to “variable.” The output parameter “CO_{2} concentration” may vary gently or abruptly, and setting it to variable means that the most appropriate kernel type can be chosen flexibly to optimize the predictive performance of the model. To improve the accuracy of the prediction model, the maximum number of refinement points allowed was set to 5. The maximum predicted relative error was set at 5% to ensure that the final design meets the design requirements for passenger health, comfort, and energy efficiency.
B. Multiobjective ventilation optimization calculation
A multiobjective genetic algorithm will be employed to optimize the four ventilation parameter variables (velocity in the x, y, and z directions, and air supply temperature) within the optimization model of the elevator air supply parameters. The optimal solutions are ultimately derived from the Pareto solution set.
In this case, the selection operator was set to 0.5, and the default parameters for the crossover and mutation operators were 0.01 and 0.98, respectively^{28} Based on the four input parameter values in this case research, the initial sample size was set to 100, and the number of samples per iteration was set to 20. For most examples, values between 55% and 75% were more suitable, and a value of 70% was selected with a convergence stability setting of a default of 2% in this experiment. In this research, the maximum number of iterations allowed was set to 20. After the optimization of each air supply parameter for the elevator, three alternative results will be generated based on the Pareto optimal solution set. The MOGA parameter setting is shown in Table VI.
Initial sample size .  Number of samples per iteration .  Max allowable Pareto percentage (%) .  Convergence stability (%) .  Maximum number of iterations . 

100  20  70  2  20 
Initial sample size .  Number of samples per iteration .  Max allowable Pareto percentage (%) .  Convergence stability (%) .  Maximum number of iterations . 

100  20  70  2  20 
The optimization process of elevator air supply parameters is shown in Fig. 4.
IV. RESULTS AND DISCUSSION
A. Validation and analysis of the response surface model
Based on the Kriging algorithm, the predicted accuracy of the response surface for the elevator's updown movement under normal conditions (4 passengers) is shown in Table VII.
.  Temperature (K) (Y = 1500 mm) .  CO_{2} molar fraction (Y = 1500 mm) .  Average velocity (Y = 1300/1500 mm) . 

Coefficient of determination (best value = 1)  1  1  1 
Verification points  
Root mean square error (best value = 0)  2.0459 × 10^{−9} (up)  4.0543 × 10^{−13} (up)  2.3968 × 10^{−9} (up) 
1.8971 × 10^{−9} (down)  3.2268 × 10^{−13} (down)  3.5691 × 10^{−9} (down)  
Verification points  
Relative maximum absolute error (best value = 0%)  0  0  0 
Verification points  
Relative average absolute error (best value = 0%)  0  0  0 
Verification points 
.  Temperature (K) (Y = 1500 mm) .  CO_{2} molar fraction (Y = 1500 mm) .  Average velocity (Y = 1300/1500 mm) . 

Coefficient of determination (best value = 1)  1  1  1 
Verification points  
Root mean square error (best value = 0)  2.0459 × 10^{−9} (up)  4.0543 × 10^{−13} (up)  2.3968 × 10^{−9} (up) 
1.8971 × 10^{−9} (down)  3.2268 × 10^{−13} (down)  3.5691 × 10^{−9} (down)  
Verification points  
Relative maximum absolute error (best value = 0%)  0  0  0 
Verification points  
Relative average absolute error (best value = 0%)  0  0  0 
Verification points 
According to Table VIII, the response surface constructed using the Kriging method can achieve optimal results in terms of accuracy error. The predictive accuracy of the response surface model was investigated in reference.^{39} The results demonstrated that the response surface model under this algorithm is considered to have high prediction accuracy when the root mean square error is reduced to within 5%. Therefore, the Kriging algorithm chosen for constructing the response surface of this elevator is appropriate.
.  Scheme .  Air supply temperature (K) .  Air supply velocity (m/s) .  Air supply angle . 

4 passengers  1  293  2.50  ZOX: 1.83° 
YOX: 1.32°  
2  293  2.54  ZOX: 12.54°  
YOX: 80.94°  
3  293  2.93  ZOX: 45.96°  
YOX: 20.56°  
13 passengers  1  293  6.77  ZOX: 15.36° 
YOX: 20.56° 
.  Scheme .  Air supply temperature (K) .  Air supply velocity (m/s) .  Air supply angle . 

4 passengers  1  293  2.50  ZOX: 1.83° 
YOX: 1.32°  
2  293  2.54  ZOX: 12.54°  
YOX: 80.94°  
3  293  2.93  ZOX: 45.96°  
YOX: 20.56°  
13 passengers  1  293  6.77  ZOX: 15.36° 
YOX: 20.56° 
The specific threedimensional graph of the response surface is presented in Figs. 5 and 6. The horizontal coordinates are defined as the elevator's air supply temperature and velocity in the x, y, and z directions. The vertical coordinate is set as CO_{2} concentration (represented in mole fraction, e.g., 8 × 10^{−5} is 0.008%).
B. Optimization result analysis
In order to satisfy the convergence and constraints of the optimization calculation, three alternative air supply regulation schemes are obtained for four lift operation scenarios, respectively. The output results show that the CO_{2} mole fraction is below 0.01% (100 ppm), which is onetenth of the set target concentration threshold. The yvelocity in the breathing zone is in the range of 0–0.3 m/s, with an average temperature of approximately 293 K. All of these values met the optimization objectives.
Among the three alternative results of the air supply parameters for each operating condition, the air supply temperature is consistently 293 K. However, the air supply velocity varies.

Optimization results of the air supply parameters when the elevator is moving upward
Table VIII presents the optimal results of the air supply velocity and angle when the elevator moves upward. Figures 7 and 8 show the results of the air supply angles when carrying 4 and 13 passengers, respectively, during the elevator moving upward. The red indicator line in the figures indicates the air supply direction, and the angles shown represent the angle formed by decomposing the velocity into the ZOX plane and YOX plane with the center of the air inlet as the origin.
As shown in Fig. 7, when four passengers take the elevator up, all three alternative results have velocity within 3 m/s, which are 2.50, 2.54, and 2.93 m/s, respectively. However, there are significant differences in the velocity of the airflow in each direction, leading to different results for the air supply angle. Among them, the deflection angles in the ZOX plane are 1.83°, 12.54°, and 45.96°, respectively, while those in the YOX plane are 1.32°, 80.94°, and 20.56°, respectively.
Three alternative results were obtained when the elevator carrying 13 passengers moving upward. The discrepancy in air supply velocity and angle is less than 0.1%, resulting in essentially identical results, one of which is depicted in Fig. 8. The resultant velocity is approximately 6.77 m/s, the ZOX plane deflection angle is approximately 15.36°, and the YOX plane deflection angle is approximately 20.56°.
The minimum air supply velocity scheme that meets energy conservation requirements is considered the optimal solution. For the elevator scenario of carrying 4 passengers moving upward, the optimal air supply regulation scheme selects alternative scheme 1, for the 13 passengers' scenario, the final optimized solution is also to select alternative result 1.

Optimization results of the air supply parameters when the elevator is moving downward
Table IX shows the optimized results of the air supply during the elevator moving downward. Figures 9 and 10 show the results of the air supply angle when an elevator is carrying 4 passengers and 13 passengers, respectively.
.  Scheme .  Air supply temperature (K) .  Air supply velocity (m/s) .  Air supply angle . 

4 passengers  1  293  3.95  ZOX: 21.1° 
YOX: 36.58°  
13 passengers  1  293  6.83  ZOX: 29.19° 
YOX: 53.28°  
2  293  6.46  ZOX: 22.26°  
YOX: 28.17°  
3  293  6.55  ZOX: 25.2°  
YOX: 31.53° 
.  Scheme .  Air supply temperature (K) .  Air supply velocity (m/s) .  Air supply angle . 

4 passengers  1  293  3.95  ZOX: 21.1° 
YOX: 36.58°  
13 passengers  1  293  6.83  ZOX: 29.19° 
YOX: 53.28°  
2  293  6.46  ZOX: 22.26°  
YOX: 28.17°  
3  293  6.55  ZOX: 25.2°  
YOX: 31.53° 
Three alternative results were obtained when the elevator carrying four passengers moving downward, which differ in velocity magnitude and angle from the results obtained when upward. The discrepancy in three air supply velocity and angle is also less than 0.1%, one of which is depicted in Fig. 9. The resultant velocity is about 3.95 m/s, approximately 1.5 times the magnitude of the upward velocity result. The ZOX plane deflection angle is approximately 21.1°, and the YOX plane deflection angle is approximately 36.58°.
According to Fig. 10, when 13 passengers take the elevator down, three alternative results all have velocity within 7 m/s, specifically at 6.83, 6.46, and 6.55 m/s, with a deviation from the results of going up being relatively small, about 0.02%. However, there are significant differences in the velocity magnitudes in different directions, resulting in different angles of air supply. Specifically, the deflection angles of the ZOX plane are 29.19°, 22.26°, and 25.2°, and those of the YOX plane are 53.28°, 28.17°, and 31.53°.
According to the air supply velocity and energy efficiency, the final optimized solution for carrying four passengers in the elevator going down condition is selected from the alternative solution 1. The final optimized solution for carrying 13 passengers is selected from alternative solution 2.
The above summary and charts show that when the elevator is moving up, the air supply angle should be directed toward the Xpositive direction, which is more conducive to controlling pollutants and meeting human comfort requirements. The deflection angle during down trips can be adjusted to meet the optimization goals for air supply parameters, according to the number of passengers. At the same time, all optimized results have a supply air temperature of approximately 293 K, indicating that within the adjustable temperature range (292–302 K), lower temperatures are more conducive to pollutant control. These results suggest a precise regulation scheme to mitigate the transmission of respiratory infectious diseases in elevators during the postpandemic era.
V. CONCLUSION
To mitigate indoor exhaled pollutants to restrict the spread of respiratory diseases in moving elevators, in this research, a multiobjective genetic optimization method based on response surface models is used to optimize the elevator air supply velocity, angle, and temperature parameters, which can reduce the concentration of pollutants in the breathing zone of passengers, ensure human thermal comfort, and save energy during elevator moving upward and downward. This work provides assistance in formulating ventilation strategies in healthy cities in the postpandemic era, which contributes to the sustainable development of green cities. The main conclusions are as follows:
The supply air regulation schemes have been obtained for both peak periods of elevator traffic (13 passengers) and other situations (4 passengers). The air supply temperature in all cases was set at 293 K.

Peak periods of elevator traffic:
① When the elevator is fully loaded and moving upward, the air supply velocity is 6.77 m/s, and the air supply angles are a ZOX plane deflection angle of 15.36° and a YOX plane deflection angle of 20.56°.
② When the elevator is fully loaded and moving downward, the air supply velocity is 6.46 m/s, and the air supply angles are a ZOX plane deflection angle of 22.26° and a YOX plane deflection angle of 28.17°.

Other situations:
① When the elevator is carrying four passengers during an upward journey, the air supply velocity is 2.50 m/s, and the air supply angles are a ZOX plane deflection angle of 1.83° and a YOX plane deflection angle of 1.32°.
② When the elevator is carrying four passengers during a downward journey, the air supply velocity is 3.95 m/s, and the air supply angles are a ZOX plane deflection angle of 21.1° and a YOX plane deflection angle of 36.58°.
Future studies should aim to compare the energy consumption of various ventilation methods. In addition, the movement of the elevator is random. Therefore, future research should also be devoted to the investigation of the laws of elevator random motion.
ACKNOWLEDGMENTS
This research was supported by the Technology Innovation Special Foundation of Hubei Province (2023BCB106). The numerical calculation was supported by the HighPerformance Computing Center of Wuhan University of Science and Technology.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Dan Mei: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Xinwen Zhang: Data curation (equal); Writing – original draft (equal); Writing – review & editing (equal). Chenxia Wang: Software (equal); Validation (equal). Li Liu: Investigation (equal). Jiaqian Li: Investigation (equal).
DATA AVAILABILITY
The data that support the findings of this study are available within the article.