*Corr. Author’s Address: Government College of Engineering, Department of Mechanical Engineering, India , jpkn006@gmail.com 471
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484 Received for review: 2022-02-22
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-04-29
DOI:10.5545/sv-jme.2022.84 Original Scientific Paper Accepted for publication: 2022-05-12
Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
Prabhakaran, J.
 
−Jayabal, S.
Prabhakaran Jayasankar
*
−Jayabal Subbaian
Government College of Engineering, Department of Mechanical Engineering, India 
The air quality in a car’s cabin can be five times worse than that of residential and non-residential buildings, resulting in a variety of health 
issues, such as headache, sore throat, and nausea, which are all symptoms of in-vehicle air pollution. The monitoring of carbon dioxide, 
which is one of the principal pollutants in car cabins, is required before regulating it. The current research is focused on the recording 
of carbon dioxide levels for different levels of human load, air speed, and temperature. A statistical analysis and plots were obtained for 
recorded responses to determine air quality parameters for a minimum value of carbon dioxide level in a five-seat car cabin. Three algorithms 
(generalized reduced gradient (GRG), response surface methodology (RSM), and genetic algorithm (GA)) were successfully used in a 5-seat 
car to optimize the in-vehicle carbon dioxide level. The GRG method provided the minimum carbon dioxide level of 471.531 ppm for a one-
human load at an air speed of 2 m/s and a temperature of 24 °C. For varying human loads of 2,3,4, and 5, the GRG and GA methods provided 
carbon dioxide levels of 508.785 ppm, 580.722 ppm, 659.839 ppm and 769.016 ppm, respectively. Comparing all three techniques, the RSM 
provided carbon dioxide levels of 471.876 ppm, 508.865 ppm, 580.79 ppm, 659.905 ppm, and 769.362 ppm for human loads of 1, 2, 3, 4, 
and 5, respectively. This study will provide a platform for the researchers working on indoor air quality characteristics to apply soft computing 
techniques effectively for the evaluation of comfortable healthy environments and for the benefit of the passengers in car cabins.
Keywords: carbon dioxide, five-seat car, genetic algorithm, in-vehicle air quality, response surface methodology
Highlights
• 	 Carbon dioxide level for varying human loads, air speeds, and temperatures in a 5-seat car are studied.
• 	 Influence of air quality parameter on response is studied with the help of ANOVA and statistical plots.
• 	 Statistical analysis and regression equation are developed for the prediction of carbon dioxide levels.
• 	 Air quality characteristics for minimum values of response are obtained through familiar optimization algorithms.
0  INTRODUCTION
Human beings spend almost 80 % to 90 % of 
their time in confined spaces [1], such as houses, 
workplaces, classrooms, shopping malls, and theatres, 
as well as vehicles like cars. As a result, the indoor 
air quality (IAQ) of living spaces has become a matter 
of concern. The in-vehicle air quality (IVAQ) of 
automobiles, where pollution levels are much higher 
than the living indoor environments [2] to [4] is one 
such occupied space that has not been studied. The 
need for optimal indoor environmental quality (IEQ) 
is especially vital in all living and working places with 
vulnerable populations [5]. This is an area that needs 
to be seriously researched and studied to ensure better 
in-vehicle air quality for the passengers. Particulate 
matter (PM), carbon dioxide (CO
2
), carbon monoxide 
(CO), volatile organic compounds (VOCs), and other 
pollutants impair the IVAQ of the cabins. People 
employ varying degrees of temperature, velocity, 
and air-circulation modes for their preferences while 
commuting in a car with an air-conditioning system, 
without realizing the deleterious repercussions of 
those settings. The levels of pollutant concentration 
have higher values in indoor environments that 
use mechanical ventilation compared to natural 
ventilation [6]. These factors may lead to an increase 
in PM, the particle-health correlation has been 
thoroughly investigated and found to be both valid and 
confirmatory [7]. The carbon dioxide concentrations 
within inhabited living spaces are more than such 
concentrations outdoors, as people generate and 
exhale CO
2
.
The levels of the indoor-outdoor CO
2
 
concentration differential grow as the ventilation rate 
(i.e., supply of fresh air into the house) per individual 
reduces [8], As a result of the limited and closed aspect 
of public transit, contaminants accumulate and lead to 
rises in concentrations [9]. There is no major change 
in indoor CO
2
 levels with changes in the average 
outdoor temperature [10]. There are a few factors 
that lead to the increase in cabin CO
2
 levels. Various 
ventilation fan speeds may lead to variations in cabin 
CO
2
 concentrations [11]. The month of the year when 
testing is being conducted will also have a significant 
impact on CO
2
 levels in vehicles [12]. When the mode 
of travel is a subway rather than normal open roads 
the concentration levels will be high [13]. The CO
2 
that the inhabitants breathe enters their bloodstream 
and creates respiratory problems, harms their health, 
and even leads to premature deaths [14] and [15]. This 
not only affects human health; it also triggers nutrition 
imbalances in plants that are exposed to higher levels 
of CO
2
 [16]. As the amount of CO
2
 inside the vehicle 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
472 Prabhak aran,	J.	−Ja yabal,	S.
Fig. 1.  CO
2
's effect on human decision-making
cabin rises, so does the danger of an accident caused 
by the driver’s tiredness and reduced agility [17]. Fig. 
1 sourced from the research article documented by 
Satish et al. [18] shows the influence of the increase in 
CO
2
 levels in human decision making.
CO
2
 is a widely used and practical metric 
for determining air quality [19]. As of  September 
2021 [20], the worldwide average ambient CO
2
 
concentration level was at 413.30 ppm. The 
permissible amounts of CO
2
 in air-conditioned 
space for human beings are defined by ASHRAE 
Standard-62 [21]. According to ASHRAE 
(American Society of Heating, Refrigerating, and 
Air-Conditioning Engineers), the maximum CO
2
 
level limit is 700 ppm over ambient surroundings 
continuously. Even though the value does not apply to 
CO
2
 levels inside cars, it is still significant because a 
car is a confined space. In comparison to other small 
environments, automobile exposure is more difficult 
to comprehend because it is influenced by several 
interconnected factors, such as ventilation, motorway 
type, vehicle type, and self-pollution [22]. 
Many strategies are used to improve the 
IAQ for the inhabitants, and many researchers [23] 
and [24] have sought to optimise heating, ventilation, 
and air-conditioning (HVAC) systems for indoor 
conditions. Researchers have proved that productivity 
has a significant relationship with indoor air quality 
[25]. Different monitoring techniques should be 
applied for natural and mechanical ventilation, as 
both have different characteristics [26]. Prior research 
in IVAQ optimization has been documented, but 
the optimization of input parameters for the vehicle 
cabin to minimize CO
2
 levels concerning occupants 
in a subcompact car is very limited. In this article, 
algorithms were used for optimization.
1  EXPERIMENTS
1.1  Air Quality Parameters and their Characteristics
In the modelling process, some parameters gathered 
are irrelevant or redundant. As a result, before 
constructing the predictive model, parameter selection 
is critical. In data mining, the availability of irrelevant 
or redundant parameters can obscure primary patterns 
[27], As a result, before beginning an experiment, 
identifying the right parameters is essential. On 
indoor air quality metrics, the Environmental 
Protection Agency (EPA), ASHRAE, and Leadership 
in Energy and Environmental Design (LEED) are all 
interrelated. The conditions for a healthy environment 
of particulate matter are 10 micrometres or less in 
diameter of 50 µg/m³ and 2.5 micrometres or less 
in diameter of 15 µg/m³. The humidity is below 60 
%, ideally ranging from 30 % to 50 % (EPA). CO 
concentration should be less than 9 ppm and CO
2 
is about 700 ppm above open-air air levels, and it is 
about 1000 ppm to 1200 ppm, and the temperature is 
20.3 °C to 23.3 °C in winter and 23.9 °C to 26.9°C 
in summer (ASHRAE). The air quality parameters, 
such as air speed and temperature, were varied at 
different levels for varying human loads and CO
2
 
characteristics were measured accordingly.
1.2  Assumptions 
To avoid ambiguity and maintain a regulated 
atmosphere inside the vehicle, the following 
assumptions were made, and similar ones were 
proposed to be applicable by Thirumal et al. [28] for 
optimizing IAQ characteristics using a multi-objective 
genetic algorithm.  

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
473 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
•	 When the car’s doors were closed, the leak is 
negligible. The air-conditioning is set in fresh air 
supply mode. 
•	 The CO
2
 may vary based on location and 
environmental conditions. Within the car, volatile 
organic component pollutants are not present. 
•	 Before beginning the experiment, the indoor 
regulated space is allowed to reach equilibrium 
with the outdoor circumstances. 
•	 Pollen, dander, dust solids, and particulate matter 
are not considered. 
•	 Tobacco smoking, dust particles, and further 
unknown elements are not present in the space. 
•	 The fan motor’s input current and air speed will 
change when the engine rpm changes. Hence, the 
average air speeds were approximated as (1, 2, 3, 
4, 5, 6, 7 and 8) m/s.
1.3  Experimental Set-Up
1.3.1  Description of Locale
The assessment was recorded in an important roadway 
of the Karaikudi municipality, which is the 20
th
 highest 
urban accumulation of Tamilnadu with a population 
of 106,714 (2011 census survey data). It is a heritage 
town situated in Sivagangai District, Tamilnadu, India. 
Fig. 2 shows the location of the town. This place can 
be accessible by the Tiruchirappalli–Rameswaram 
highway that passes through Karaikudi. This locus is 
located at 10.07° N latitude and 78.78° E longitude. 
The average maximum temperature is about 34° C 
(~93° F), and the average lowest temperature is about 
24° C (~75° F); the twelve-monthly middling rainfall 
in Karaikudi is about 920 millimetres, the topography 
of the place is predominantly flat and some gravel 
areas are also found in the surroundings.  The area of 
the municipality is about 33.75 km².
1.3.2  Measurements
To measure in-vehicle carbon dioxide concentration 
a portable IAQ CO
2
 meter, the Extech device (Model 
CO250) by FLIR commercial systems Inc., USA, 
has been utilized. A similar experimental setup and 
equipment were used by Ayyakkannu et al. [29] for 
measuring in-vehicle pollutants. This measuring 
device works with the theory of the non-dispersive 
infrared (NDIR) technique. The device can assess 
up to a maximum range of 5000 ppm with 1 ppm 
resolution. The device was positioned in the centre of 
the car cabin at breathing level. The instrument was 
Fig. 2.  Location of Karaikudi town and experimental test route

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
474 Prabhak aran,	J.	−Ja yabal,	S.
calibrated and field-tested before the measurement of 
CO
2
. The measuring instrument is set to record data at 
a one-minute time interval; the data is then transferred 
to a laptop PC with an acquisition software provided 
by the device manufacturer to record the CO
2
 values 
from the instrument. The schematic sketch is shown in 
Fig. 3, this set-up is used for carrying out our research. 
A five-seat hatchback car was chosen; it has air-
conditioning with a variable temperature from 18 °C 
to 25 °C and with recirculation modes.
Three tests are carried out for each human load 
varying from one to five, as the CO
2
 concentration 
will significantly increase according to the number 
of passengers [30]. The mean values of three tests 
were considered for the final optimization of the 
parameters. The route at Karaikudi, where the test was 
carried out was about 13 km per cycle, which includes 
a college road with trees, traffic signals, a petrol 
station, road junctions, and a bus stand. The test route 
is shown in Fig. 2.
1.3.3  Design of Experiments and Regression Line
The design of experiments for the study was designed 
using full factorial design and regression modelling in 
statistical software. In each comprehensive trial run 
or repetition of the studies, the full factorial design 
establishes experimental points utilizing all feasible 
combinations of the levels of the components. The 
vertices of a hypercube in the n-dimensional design 
space are determined by the least and highest values of 
each of the factors. These factors are the experimental 
design points in a full factorial design; therefore, these 
experimental points are also known as factorial points.
Regression analysis is a type of predictive 
modelling approach that focuses on the correlation 
between a dependent (target) and an independent 
variable (predictor). This technique is used for the 
prediction of the finding of the fundamental effect 
relationship between the variables. The quartic non-
linear regression model was suggested due to the 
better value of correlation coefficient and fitting to the 
data points. The refined model is also developed for 
predicting carbon dioxide levels for various human 
loads, which are further used for finding the better 
value of air quality parameters.
1.4  Search Optimization Methods
Among the various algorithms, the statistical, gradient, 
and metaheuristic algorithms are popularly used by 
most researchers for finding the optimum value of 
responses. The familiar algorithms in the above three 
categories are effectively chosen for finding indoor 
air quality characteristics in the present investigation. 
Response surface methodology (RSM) is based on 
indirect optimization self-organization; GRG is the 
most commonly used reduced gradient method to 
solve nonlinear problems, which finds a local optimal 
solution; genetic algorithm (GA solves optimization 
problems based on a natural selection process derived 
form biological evaluation; it uses high-level search 
procedures for minimization of response variables.
Fig. 3.  Schematic sketch of the experimental setup

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
475 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
1.4.1  Response Surface Method
The RSM is a commonly used arithmetical and 
mathematical approach for developing and evaluating 
a process in which many factors impact the response 
of interest. This strategy aims to optimize the response 
time. The development of an approximation model 
for the true response surface is required for the 
RSM to be used in reality [31]. The RSM searches 
for a suitable approximation relationship between 
input and output variables to find the best operating 
conditions for a system or a portion of the factor field 
that complies with the requirements. The RSM was 
used to optimize the conditions of the experiment 
by the author Yan et al. [32] for the optimization and 
analysis of CO
2 
surface assimilation by imidazole and 
tetraethylenepentamine operative sorbent material.
The RSM includes three stages (i.e., design, 
analysis, and optimization) using statistical software; 
a non-linear regression equation was developed and 
optimized using this approach for varying human 
loads in the present investigation. The ANOVA Table 
and statistical plots were also generated to study the 
individual, interaction, and higher-order effects of air 
quality parameters.
1.4.2 Generalized Reduced Gradient
The generalized reduced gradient (GRG) method is 
a nonlinear inequality constraint-aware expansion 
of the reduced gradient method. In this method, a 
quest path is found in which the current dynamic 
limitations remain precisely effective for any move. 
Microsoft Excel uses three solving methods such as 
GRG Nonlinear for problems that are smoothing 
nonlinear, LP Simplex for problems that are linear, 
and Evolutionary for non-smooth problems. GRG 
is used to find the optimum CO
2 
level for various 
human loads by setting quadratic estimates, forward 
derivatives, and Newton search in the solver option. 
The max time was set to 100 seconds for 100 iterations 
with the precision value of 0.000001, the tolerance 
was set to 5 % and the convergence was 0.0001in the 
Microsoft Excel Solver.
1.4.3 Genetic Algorithm
A genetic algorithm is a search heuristic based on 
Charles Darwin’s natural-evolution hypothesis. 
This algorithm mimics natural selection, in which 
the fittest individuals are chosen for reproduction 
to create the next generation. GA have been used to 
solve a wide variety of systematic, engineering, and 
financial problems. GA are robust because they can 
find the global optimum in a multimodal landscape 
[33]. The initial population, fitness function, selection, 
crossover, and mutation are the five phases considered 
in a genetic algorithm.
MATLAB’s R2016a graphical user interface 
was used to find the minimum value of the function. 
The double vector population type opted with the 
population type was left to default at 50 for five or 
fewer variables; otherwise, it was 200. The creation 
function was constrained dependent on keeping the 
initial population, initial scores, and initial range 
as default. For the fitness-scaling function, rank 
was chosen. The stochastic uniform was set for the 
selection function. In the reproduction section, elite 
count and cross-over fraction were default. Mutation 
and crossover functions are constraint-dependent. 
Migration direction is forward keeping fraction and 
interval values as default 0.2 and 20, respectively. 
For the constraint parameters, the nonlinear constraint 
algorithm Augmented Lagrangian is used with an 
initial penalty and penalty factor as default. The 
hybrid function was set to none, and the stopping 
criteria were completely used with default settings. 
2  RESULTS AND DISCUSSION
2.1  Experimental Observation of Air Quality Characteristics 
The three factors that are varied in three levels  
(5 × 8 × 8 = 320) contributed 320 experimental runs 
as per full factorial design. The standard deviation 
for human load, air speed, and temperature are 1.42, 
2.29 and 2.29, respectively. A minimum value of 460 
and a maximum value of 949 were observed in carbon 
dioxide level. The mean and standard deviations for 
the recorded value of responses are 633 and 128.9, 
respectively (Eq. (1)).
 x
x
n
xx
n



 
,, 
2
 (1)
where x is mean, n number of observations, x 
individual observations, and σ standard deviation. 
The observation of the highest frequency for 320 data 
in 18 bins was obtained, which is shown in Fig. 4. The 
frequency is calculated using number of counts in the 
histogram range specified in x axis whereas proportion 
is calculated using the Eq. (2).
 Proportion
Frequency
=
n
. (2)

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
476 Prabhak aran,	J.	−Ja yabal,	S.
The proportion and density plots are also obtained 
in correlation with recorded values of carbon dioxide 
levels. The CO
2
 level is ranged from 460 ppm to 949 
ppm and the corresponding frequency values up to 60 
and proportion up to 0.2 are plotted.
2.2  Development of NLRM for Carbon Dioxide Level
The design is built, and response data is added to 
formulate a polynomial model of response design 
by including individual, interaction, and lower and 
higher-order terms. The polynomial degree of four, 
which is in the form of a quartic function was observed 
based on the best fit and the coefficient of correlation 
of 0.9975. The statistical summary of factors and 
response are in Table 1.
 fx ax bx cx dx e   
432
. (3)
The adjusted R
2
 associates the explanatory 
power of regression replicas with varying numbers 
of predictors, whereas the projected R
2
 shows how 
well a regression model predicts fresh observations’ 
responses. The predicted R
2 
of 0.9968 is in satisfactory 
agreement with the adjusted of 0.9972 due to the 
variance of less than 0.2. The subgroup sample 
standard deviation divided by the subsection mean, 
multiplied by 100, yields the percentage of the CV 
plot point. In practice, the percentage of CV is the 
proportion of the mean that the standard deviation.
The model F-value of 3389.3 shows the model is 
considerable. There is only a 0.01 per cent probability 
that an F-value of this massive might appear due to 
noise. Model terms with P-values less than 0.0500 are 
noteworthy. x
1
, x
3
, x
1
 x
2
, x
1
 x
3
, x
1
2
, x
3
2
, x
1
 x
2
 x
3
, x
1
2
x
2
, 
x
1
2
x
3
, x
1
3
, x
1
2
 x
2
2
, x
1
2
 x
3
2
, x
1
3
x
2
, x
1
3
 x
3
, x
1
 x
2
3
, x
1
 x
3
3
, 
x
1
4
, x
3
4
 are significant model terms in this scenario. 
The model terms are not significant if the value is 
larger than 0.1000. The model decrease may enhance 
your model if there are several irrelevant model terms 
(not involving those necessary to support hierarchy). 
The nonlinear regression model was developed using 
statistical software, as given in Eq. (4).
f(x) = + 10021.14279 + 1030.93478 × x
1
 
 – 254.83387 × x
2
 – 1784.46657 × x
3
 
 – 2.82325 × x
1
 × x
2
 – 213.63461 × x
1
 × x
3
 
 + 32.61305 × x
2
 × x
3
 + 261.08873 × x
1
² 
 + 10.19365 × x
2
² + 130.89552 × x
3
² 
 –1.15965 × x
1
 × x
2
 × x
3
 + 4.79252 × x
1
² × x
2
 
 + 0.610780 × x
1
² × x
3
 + 0.559092 × x
1
 × x
2
² 
 + 10.14499 × x
1
 × x
3
² – 0.205609 × x
2
² × x
3
 
a)           b) 
Fig. 4.  Histogram for response; a) frequency, and b) proportion
Table 1.  Statistical summary of factors and response
Factor/ Response Name Minimum Maximum Coded Low Coded High Mean Std. Dev.
Factor 1 Human load [No.] 1 5 -1 ↔ 1.00 +1 ↔ 5.00 3.00 1
Factor 2 Air speed [m/s] 1 8 -1 ↔ 1.00 +1 ↔ 8.00 4.50 2
Factor 3 Temperature [°C] 18 25 -1 ↔ 18.00 +1 ↔ 25.00 21.50 2
Response CO
2
 [ppm] 460 949 - - 632.88 128.87

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
477 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
 – 1.43142 × x
2
 × x
3
² – 62.51457 × x
1
³ 
 – 1.24080 × x
2
³ – 4.31326 × x
3
³ – 0.192815 × x
1
² × x
2
² 
 + 0.012856 × x
1
² × x
2
 × x
3
 – 0.172513 × x
1
² × x
3
² 
 – 0.030896 × x
1
 × x
2
² × x
3
 + 0.028628 × x
1
 × x
2
 × x
3
² 
 + 0.005322 × x
2
² × x
3
² – 0.448041 × x
1
³ × x
2
 
 + 0.803695 × x
1
³ × x
3
 + 0.090972 × x
1
 × x
2
³ 
 – 0.143119 × x
1
 × x
3
³ + 0.004359 × x
2
³ × x
3 
 
+ 0.020725 × x
2
 × x
3
³ + 4.00456 × x
1
4
 
 + 0.048793 × x
2
4
 + 0.053101 × x
3
4
  .
               
(4)
The sequential p-value is less than 0.0001 and 
the difference between the adjusted and predicted 
coefficient of correlation is 0.0004 which indicated 
the best fit of the quartic model for 320 values 
of carbon dioxide level (Table 2). The sequential 
p-value is < 0.0001 for linear, two-factor interaction, 
quadratic, cubic, quartic, and quintic models. The best 
fit is selected based on the higher value of coefficient 
of correlation.
Table 2.  Fit summary and selection of model
Source
Sequential 
p-value
Adjusted R² Predicted R² Remarks
Linear < 0.0001 0.891 0.8889 -
2FI < 0.0001 0.9197 0.917 -
Quadratic < 0.0001 0.9935 0.9933 -
Cubic < 0.0001 0.9942 0.9938 -
Quartic < 0.0001 0.9972 0.9968 Suggested
Fifth < 0.0001 0.9985 0.9981 Aliased
2.3  ANOVA, Diagnostics and Statistical Plots
The model includes the overall model test for 
significance and how much variance in the reaction 
is described by the model. Individual factors are 
removed from the model and tested separately. The 
residual indicates how much variation in the response 
remains unaccounted for. The degree to which the 
model predictions differ from the observed is referred 
to as “lack of fit”. The amount of variation between 
replicate runs is known as “pure error”. The degree 
of variation around the mean of the observations is 
shown by the corrected total. The individual effect 
of human load and temperature, combined effect of 
air speed and temperature, are significant terms in 
ANOVA listed in Table 3. The second-order effect 
of human load with air speed and temperature is also 
significant.
The normal probability plot shows whether the 
residuals have a normal distribution and, as a result, 
follow a straight line. For better analysis, scatter 
with normal data in an s-shaped curve showed the 
transformation response as shown in Fig. 5a. A graph 
of anticipated response values versus actual response 
values can be used to spot a value, or a collection 
of values, that the model cannot predict is shown 
in Fig. 5b. The assumption of constant variance is 
tested by plotting the residuals against the ascending 
expected response values as shown in Fig. 5c. A 
studentized residual is calculated by dividing the 
residual by an estimate of its standard deviation. 
The standard deviation for each residual is computed 
with the observation excluded. A plot of the residuals 
against the experimental run order to look for hidden 
variables that could have influenced the response 
during the experiment is shown in Fig. 5d. Internally 
studentized residuals are defined for each observation 
as an ordinary residual divided by an estimate of its 
standard deviation.
Cook’s distance is a measurement of how much 
the entire regression function changes when the i
th
 
point is removed from the model fitting (Fig. 6a). The 
plot of the residuals versus any factor if the variation 
not accounted for by the model varies depending 
on the level of the factor is in Fig. 6b. The response 
surface plot and contour plot for the interaction of 
variables are shown in Figs. 6c and d, respectively. 
Surface plots are diagrams of three-dimensional 
data that shows a functional relationship between a 
designated dependent variable and two independent 
variables. A contour plot is a graphical technique 
for representing a 3-dimensional surface by plotting 
constant z slices called “contours”.
2.4 Optimization of Carbon Dioxide Level
2.4.1  RSM Optimization for Minimum Value of Carbon 
Dioxide Level
The human load is set to 1, 2, 3, 4, and 5, whereas 
the air speed and temperature are set in range as 
criteria and the minimization of carbon dioxide was 
carried out using response surface methodology. 
The minimum value of carbon dioxide levels for 
various human loads in accordance with air speed and 
temperature are given in Table 4. The optimization 
looks for a set of factor values that satisfies all the 
criteria for each of the responses and factors at the 
same time. The desirability function indicates the 
desirable limits for each response. The maximum 
value of air speed and low value of temperature is 
needed for getting the minimum value of CO
2
 level 
in a 5-seat car. The minimum value of air speed and 
upper limit of temperature provided a minimum value 
of carbon dioxide of 472. The setting of air speed and 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
478 Prabhak aran,	J.	−Ja yabal,	S.
2.4.2 GRG Optimization for Minimum Value of Carbon 
Dioxide Level
The minimum CO
2
 concentration value of 471.537 
ppm was achieved in accordance with air speed and 
temperature of 2 m/s and 24 °C, respectively, for 
a single human load using the GRG technique. In a 
comparison of the three optimization methods utilized 
for one human load, among RSM (471.876), GRG 
(471.537), and GA (471.611), the lowest CO
2 
level 
temperature for an intermediate value of human loads 
are effectively determined using response surface 
optimization. The maximum value of air speed and 
lower limit of temperature provided a minimum value 
of carbon dioxide of 769.362 ppm for the maximum 
capacity of the vehicle.
Table 3.  ANOVA for response and significance of factors
Source Sum of Squares df Mean Square F-value p-value Remarks
Model 5.29E+06 34 1.55E+05 3389.3 < 0.0001 Significant
x
1
3.76E+05 1 3.76E+05 8202.13 < 0.0001
x
2
145.96 1 145.96 3.18 0.0755
x
3
6182.8 1 6182.8 134.82 < 0.0001
x
1
 × x
2
851.29 1 851.29 18.56 < 0.0001
x
1
 × x
3
5184.82 1 5184.82 113.06 < 0.0001
 x
2
 × x
3
31.56 1 31.56 0.6882 0.4075
 x
1
² 461.81 1 461.81 10.07 0.0017
x
2
² 33.99 1 33.99 0.7412 0.39
x
3
² 532.36 1 532.36 11.61 0.0008
x
1
 × x
2
 × x
3
296.12 1 296.12 6.46 0.0116
x
2
² × x
3
2296.85 1 2296.85 50.08 < 0.0001
x
1
² × x
3
1101.23 1 1101.23 24.01 < 0.0001
x
1
 × x
2
² 15.47 1 15.47 0.3374 0.5618
x
1
 × x
3
² 0.7741 1 0.7741 0.0169 0.8967
 x
2
² × x
3
3.98 1 3.98 0.0867 0.7686
x
2
 × x
3
² 54.02 1 54.02 1.18 0.2787
x
1
³ 594.83 1 594.83 12.97 0.0004
x
2
³ 0.4001 1 0.4001 0.0087 0.9256
x
3
³ 162.26 1 162.26 3.54 0.061
x
1
² × x
2
² 699.53 1 699.53 15.25 0.0001
 x
1
² × x
2
 × x
3
4.08 1 4.08 0.089 0.7657
x
1
² × x
3
² 559.98 1 559.98 12.21 0.0006
x
1
 × x
2
² × x
3
67.35 1 67.35 1.47 0.2266
x
1
 × x
2
 × x
3
² 57.83 1 57.83 1.26 0.2624
x
1
² × x
3
² 4 1 4 0.0871 0.768
x
1
³ × x
2
971.26 1 971.26 21.18 < 0.0001
x
1
³ × x
3
3125.25 1 3125.25 68.15 < 0.0001
x
1
 × x
2
³ 393.27 1 393.27 8.58 0.0037
x
1
 × x
3
³ 973.35 1 973.35 21.22 < 0.0001
x
2
³ × x
3
2.37 1 2.37 0.0517 0.8203
x
2
 × x
3
³ 53.58 1 53.58 1.17 0.2807
x
1
4
8445.27 1 8445.27 184.15 < 0.0001
x
2
4
172.39 1 172.39 3.76 0.0535
x
3
4
204.18 1 204.18 4.45 0.0357
Residual 13070.01 285 45.86

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
479 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
was attained in GRG methods. The carbon dioxide 
levels of 508.785 ppm, 580.722 ppm, 659.839 ppm 
and 769.016 ppm were obtained for human loads 2, 3, 
4 and 5, respectively. 
When compared with RSM, GRG provided 
a minimum value of carbon dioxide level for all 
levels of human load. The search procedure in GRG 
found a better value of results when compared with 
statistical-based optimization. RSM is a mathematical 
and statistical technique for the empirical model 
building which predicted better value of responses 
using indirect optimization based on self-organization 
whereas the Newton method used a root-finding 
approach by polynomial approximation using Taylor’s 
series. The air speed of 7 m/s and temperature of 18 °C 
were obtained for a minimum value of carbon dioxide 
level of 769.016 ppm in GRG and GA methods.
2.4.3  GA Optimization for Minimum Value of Carbon 
Dioxide Level
The minimum CO
2
 concentration of 471,611 ppm for 
one human load was obtained for the air speed of 2 
m/s and a temperature of 24 °C using the GA method, 
which was slightly higher than the optimum value 
(471.537 ppm) obtained using the GRG method. 
The lowest ideal value for a five-person capacity is 
769,016 at an air speed of 7 m/s and a temperature 
of 18 °C, respectively. The carbon dioxide levels of 
508.785 ppm, 580.722 ppm, 659.839 ppm and 769.016 
ppm were obtained for human loads 2, 3, 4, and 5 
respectively which is the same as the results obtained 
using the GRG method. When comparing the results 
acquired using the GA method in MATLAB software 
to the obtained results using RSM optimization in 
Design-Expert software, the GA approach produced 
Fig. 5.  Plot of residuals; a) normal % probability, b) predicted vs. actual, c) residuals vs. predicted, and d) residuals vs. run

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
480 Prabhak aran,	J.	−Ja yabal,	S.
Fig. 6.  Design plots; a) Cook’s distance, b) residual vs. factor, c) 3D surface plot, and d) contour plot
Table 4.  Optimum values of CO
2
 level for various human loads and confirmation of responses
Sl. No. Algorithm
Factors CO
2
 [ppm]
Absolute percentage of error
Airspeed [m/s] Air temp. [°C] Predicted response Experimental response
1
RSM
2 24 471.876 479.983 1.7
2 3 21 508.865 503.832 0.2
3 3 20 580.79 586.231 0.9
4 6 19 659.905 671.376 1.7
5 8 18 769.362 752.263 2.2
6
GRG
2 24 471.537 479.983 1.8
7 3 21 508.785 503.832 0.9
8 3 19 580.722 586.231 0.9
9 6 19 659.839 671.376 1.7
10 7 18 769.016 777.847 1.1
11
GA
2 24 471.611 479.983 1.3
12 3 21 508.785 503.832 0.9
13 3 20 580.722 589.124 0.9
14 6 19 659.839 671.376 1.7
15 7 18 769.016 777.847 1.1

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
481 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
lower results due to the metaheuristic approach 
(High-level search procedure). In addition, when 
compared to RSM, the air velocity for the five human 
load conditions is lowered by one level in the GA 
optimization technique. The GA plots for optimization 
plotting fitness value vs. generation are shown in 
Fig. 7. The values are obtained in between 50 to 100 
generations for the better value of fitness. The same 
value of best fitness and mean fitness was obtained 
which indicated the minimum value of carbon dioxide 
level for various human loads.
2.4.4  Confirmation of Optimum Conditions
The experiments were conducted for the optimum 
conditions obtained using RSM, GRG, and GA 
methods; the carbon dioxide levels values were 
reordered and compared with the optimum values. 
The comparison graph of experimental results and 
predicted results are shown in Fig. 8. The blue, 
green, and yellow lines indicated the optimum value 
of carbon dioxide levels for RSM, GRG, and GA, 
respectively, whereas the orange, red, and violet lines 
indicated the experimental value of carbon dioxide 
levels for RSM, GRG, and GA, respectively. RSM 
predicted carbon dioxide levels of 471.876 ppm, 
508.865 ppm, 580.79 ppm, 659.905 ppm, and 769,362 
ppm for human loads 1, 2,3,4, and 5 and the same 
is confirmed with experimental values of 479.983 
ppm, 503.832 ppm, 586.231 ppm, 671.376 ppm, 
and 752.263 ppm. The absolute percentage error of 
values 1.8, 0.9, 0.9, 1.7, and 1.1 for human loads 1, 
2, 3, 4, and 5 were obtained using the GRG method. 
GA predicted carbon dioxide levels of 471.611 ppm, 
Fig. 7.  GA plot for optimization of carbon dioxide level for different human load

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
482 Prabhak aran,	J.	−Ja yabal,	S.
508.785 ppm, 580.722 ppm, 659.839 ppm, and 
769.016 ppm for human loads 1,2,3,4, and 5 and 
the same is confirmed with experimental values of 
479.983 ppm, 503.832 ppm, 589.124 ppm, 671.376 
ppm, 777.847 ppm, respectively.
The absolute ratio of error is determined using the 
following formulation.
 
Percentage of error =
Experimental valueO ptimum value
Experim
 
e entalv alue
. (5)
a)        
b) 
c)        
Fig. 8.  Confirmation testing comparative graph between optimum and experimental value for all three algorithms;  
a) RMS, b) GRG, and c) GA

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)7-8, 471-484
483 Optimization of in-Vehicle Carbon Dioxide Level in a 5-Seat Car
The absolute percentage of error is less than 2.5, 
indicating good level of accuracy in the confirmation 
of results the maximum absolute percentage of error 
of 2.2 in RSM, 1.8 in GRG and 1.7 in GA were 
obtained. The close prediction of experimental value 
with the predicted value was obtained. 
3  CONCLUSION
Experimental runs were carried out for different 
values of human load, air speed, and temperature, 
and the observed value of carbon dioxide levels were 
recorded. Response surface design, analysis, and 
optimization were done to find the minimum value 
of carbon dioxide levels for various human loads 
and corresponding air velocity and temperature. In 
addition, with response surface methodology, the 
generalized reduced gradient and genetic algorithm 
are also used to find the minimum value of carbon 
dioxide levels in the present investigation. The 
minimum carbon dioxide level of 471.531 ppm for 
one human load was obtained for the air speed of 
2 m/s and a temperature of 24 °C using the GRG 
method. The carbon dioxide levels of 508.785 ppm, 
580.722 ppm, 659.839 ppm and 769.016 ppm were 
obtained for human loads 2, 3, 4 and 5, respectively, 
using GRG and GA methods. The experiment was 
conducted for the optimum value of IV AQ parameters, 
and the corresponding CO
2
 level was measured. The 
absolute percentage of error was found for all three 
algorithms, which resulted in the genetic algorithm 
providing a better value of results for the current 
problem. Other indoor air quality characteristics, 
such as relative humidity, particulate matter, carbon 
monoxide level, and oxygen level may be optimised 
using the optimization techniques, and the optimal 
value for comfort and healthy living in an enclosed 
environment can be found. These methods can be 
used to determine the optimal inlet HVAC parameters 
such as inlet velocity, the quantity of fresh air supply, 
type of filtration, and required temperature for various 
human loads in a confined area. This application 
could lead to a better and healthier indoor living 
environment. Even though this method has a wide 
range of applications, the IAQ characteristics vary 
from place to place, and values in different countries 
may deviate at a significant pace depending on the 
environmental circumstances and abrupt climate 
changes of that country as well as the region under 
study. In the future, the same study can be extended to 
other vehicle cabins, such as those of SUVs or seven-
seat cars, trucks, buses and even trains by varying 
different passenger loads, elevation of location under 
study, ventilation type, and outside environmental 
weather conditions. It is also concluded that breathing 
clean air is a vital aspect of investigation for enhanced 
human health during the Covid-19 pandemic.
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