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Abstract

This paper focuses on the use of Bayesian networks for the industrial thermal comfort issue, specifically in industries in Northern Argentina. Mined data sets that are analyzed and exploited with WEKA and ELVIRA tools are discussed. Thus, networks giving the predictive value of thermal comfort for different pairs of indoor temperature and humidity values according to activity, time, and season, verified in the workplace, were obtained. The results obtained were compared to other statistical models of linear regression used for thermal comfort, thus observing that comfort temperature values are within a same range, yet the network offered more information since a range of options for interior design parameters (temperature/relative humidity) was offered for different work, time, and season conditions. Additionally, if compared with static models of heat exchange, the contribution of Bayesian networks is noted when considering a context of actual operability and adaptability conditions to the environment, which is promising for developing thermal comfort intelligent systems, especially for the development of sustainable settings within the Industry 4.0 paradigm.
applied
sciences
Article
Study and Application of Industrial Thermal Comfort
Parameters by Using Bayesian Inference Techniques
Patricia I. Benito * , Miguel A. Sebastián and Cristina González-Gaya


Citation: Benito, P.I.; Sebastián, M.A.;
González-Gaya, C. Study and
Application of Industrial Thermal
Comfort Parameters by Using
Bayesian Inference Techniques. Appl.
Sci. 2021,11, 11979. https://doi.org/
10.3390/app112411979
Academic Editor: Cesare Biserni
Received: 29 November 2021
Accepted: 14 December 2021
Published: 16 December 2021
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This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Department of Construction and Manufacturing Engineering, ETS Ingenieros Industriales, Universidad Nacional
de Educación a Distancia (UNED), C/Juan del Rosal 12, 28040 Madrid, Spain; msebastian@ind.uned.es (M.A.S.);
cggaya@ind.uned.es (C.G.-G.)
*Correspondence: pbenito16@alumno.uned.es
Abstract:
This paper focuses on the use of Bayesian networks for the industrial thermal comfort issue,
specifically in industries in Northern Argentina. Mined data sets that are analyzed and exploited
with WEKA and ELVIRA tools are discussed. Thus, networks giving the predictive value of thermal
comfort for different pairs of indoor temperature and humidity values according to activity, time,
and season, verified in the workplace, were obtained. The results obtained were compared to
other statistical models of linear regression used for thermal comfort, thus observing that comfort
temperature values are within a same range, yet the network offered more information since a
range of options for interior design parameters (temperature/relative humidity) was offered for
different work, time, and season conditions. Additionally, if compared with static models of heat
exchange, the contribution of Bayesian networks is noted when considering a context of actual
operability and adaptability conditions to the environment, which is promising for developing
thermal comfort intelligent systems, especially for the development of sustainable settings within the
Industry 4.0 paradigm.
Keywords:
thermal comfort; industrial building; occupational risk; Bayesian inference; sustainability;
energy saving; Industry 4.0
1. Introduction
Industrial Revolution 4.0 is based on Information and Communications Technology
(ICT), Internet of Things (IoT), artificial intelligence (AI) linked to Big Data and algorithms
used to process them, robotics, and cloud services, among others, to optimize processes
and achieve more efficiency and productivity [13].
Within this great Industry 4.0 paradigm, occupational health and safety and the issue
of thermal comfort are included.
ISO 7730 Standard defines thermal comfort, also known as hygrothermal comfort, as
“that mental condition in which thermal environment satisfaction is expressed” [
4
], which
is a subjective concept and thus very difficult to assess. It is even defined by its oppo-
site concept—hygrothermal discomfort, which is climate discomfort due to temperature,
humidity, or air velocity.
From a physiological standpoint, a person experiences thermal comfort when their
organism does not need to use their body temperature autoregulation mechanisms [5].
Hygrothermal comfort has major impact on both people’s health and environmental
sustainability. The application handbook of Law 13059, Hygrothermal Conditioning of Build-
ings from the Housing Institute of Buenos Aires, describes that adequate levels of thermal
comfort are essential for maintaining health, moderating humidity condensation effects,
and saving energy [6].
Additionally, the Ministry of Health of Argentina [
7
] mentions that the World Health
Organization defines occupational health as a multidisciplinary activity aimed at promoting
and protecting workers’ health by disease and accident prevention and at controlling
Appl. Sci. 2021,11, 11979. https://doi.org/10.3390/app112411979 https://www.mdpi.com/journal/applsci
Appl. Sci. 2021,11, 11979 2 of 17
risk prevention and safety at work. It aims at creating and promoting healthy and safe
work as well as comfortable work environments, emphasizing the mental, physical, and
social wellbeing of workers and promoting the optimization and maintenance of their
work capacity.
Taking into consideration the general importance of the subject and the World Health
Organization recommendations about occupational health as for hygrothermal comfort,
the following issues about the air conditioning installation project are considered.
In this sense, Néstor Quadri [
8
] suggests designing and calculating heating, venti-
lation, and air conditioning (HVAC) installations in which the following factors should
be considered:
Building factors: dimensions and sun orientation of the premises, total transmittance
coefficients on walls, floors and ceilings, room distribution;
Purposes of premises: number of people, type of activity and time schedule, lighting,
equipment and motor-driven machines, and other heat-emitting sources;
Design parameters: outdoor temperature and relative humidity determined in the
premises, indoor temperature, and relative humidity. In closed spaces, air velocity has
no decisive influence since its values for comfort conditions may vary from 5 to 8 m/s,
and in summer, velocities up to 12 m/s may be acceptable.
Both building factors and the purpose of the premises can be determined with some
precision, while design parameters related to indoor temperature and relative humidity for
people to be at thermal comfort cannot if we consider the concept’s subjective factor.
In general, the parameters used when calculating air conditioning installations are
obtained from charts and/or tables based on controlled experiences under ideal conditions
and for a specific population. In this sense, the American Society of Heating, Refrigerating
and Air-Conditioning Engineers (ASHRAE), with the help of different universities and
official entities, carried out experiences to see different people’s reactions under different
temperature, relative humidity, and air movement conditions. The results were used to
create a comfort chart linking psychometric conditions to human reactions [9].
When using indoor temperature and relative humidity values to calculate installations,
actual working conditions, regional customs, and local weather characteristics are not taken
into consideration.
So far, mathematical methods and statistical analysis techniques, by means of charts
and/or equations, are used to determine hygrothermal comfort parameters [1014].
However, they do not show the complexity and relationships of hygrothermal comfort
expressed by people.
In an experiment carried out by Ma, N. et al. [
15
], they propose a Bayesian approach
by applying a neural network (BNN) to build a predictive model for the occupants’ thermal
preference indoor. The authors found that this model is better than conventional thermal
comfort models, yet they assessed that it provides roughly reliable predictions, according
to the occupants’ preferences.
This paper proposes the use of Bayesian inference techniques [
16
,
17
], which create
a model of the event being studied by means of a variable set and its dependence rela-
tionships. Bayesian inference allows determining the posterior probability of unknown
variables, based on known variables, and provides information through graphic presenta-
tion of probabilistic relationships as for how the domain variables relate. These variables
can be occasionally construed as cause–effect relationships in different fields of knowledge,
and particularly in the thermal comfort field. Expert involvement can help in building
these models and determining the conditional probability of network nodes; however, the
models can also be determined by means of machine learning.
In this particular study, a Bayesian network was used to determine the thermal comfort
parameters in industrial settings that allow improving the work environment, reducing
occupational risks, and increasing energy efficiency.
Appl. Sci. 2021,11, 11979 3 of 17
2. Background
As main background, the Fanger model published in the British Journal of Industrial
Medicine can be mentioned [
10
]. It assesses thermal comfort status based on predictive mean
vote (PMV) and predictive percentage of dissatisfied (PPD). The predictive mean vote is
calculated by means of clothing insulation, metabolic rate, and environment characteristics
(temperature, radiant temperature, relative humidity, and air velocity). This rate allows
the determination of people dissatisfied with the environment, showing major progress in
comparison with other thermal comfort rates. Nonetheless, as it is performed in controlled
chambers with young people of European or North American descent (physiological model)
at rest, it does not consider the lack of local thermal comfort, actual operability conditions,
or regional working habits. Diego-Mas, J.A. [
11
] considers that the calculation of PMV
and PPD allows the identification of thermal discomfort events perceived by the body.
Moreover, there are a series of factors, such as drafts, differences in vertical temperature,
and the existence of hot or cold ceilings, walls, or floors, that may cause discomfort in
workers even when the overall situation has been assessed as satisfactory by the Fanger
method. Thus, he concludes that the assessment should be completed with the study of
“local thermal discomfort” in such cases.
According to ISO 7730 Standard: Ergonomics of the thermal environment [
4
], another
limitation of the Fanger model applicability is that the predictive mean vote (PMV) rate
should only be used to assess thermal environments in which the variables in the calculation
are within specific intervals of a metabolic rate (46 and 232 W/m
2
), clothing insulation (0
and 0.31 m
2
K/W), air temperature (10
C and 30
C), mean radiant temperature (10
C
and 40 C), air velocity (0 and 1 m/s), and water vapor pressure (0 and 27 HPa).
From another approach, adaptive models (Brager, G. and De Dear, R. [
12
], Nicol, F. and
Humphreys. M. [
13
]) consider the outdoor climate to determine the preferences of indoor
comfort, where the person is not a passive receptor but part of a dynamic system with the
environment. These two theoretical approaches (Gómez-Azpeitia, L. et al. [
14
]) have not
delivered answers for establishing design parameters of air conditioning installations.
Furthermore, Atmaca and Koçak [
18
] found that thermal environment conditions are
one of the most important factors in workplaces from a productivity, occupational safety,
and human health standpoint. In the simulation, they used an energy balance model to
determine the thermal comfort area. They identified that the optimal operational tempera-
ture decreases while metabolic activity levels increase. This research paper considers air
velocity, yet there is no evidence of the relative humidity influence.
Another background study is the experience provided by Sun et al., focusing on the
combination between ambient temperature and the temperature of facilities while being
ventilated by an air-conditioning unit. In this case, they used 18 test subjects and three
temperature combinations, with low air speed to reduce one variable. For the authors, the
results imply that the adoption of local ventilation could improve thermal comfort while
consuming less energy, compared with the traditional air conditioning mode, which creates
a uniform comfortable environment by setting air temperature at 26 C [19].
The results of a case study in the History Museum of Valencia, Spain, about the
thermal comfort of its visitors stressed the limitations of the Fanger model when used in
this type of building, highlighting the need for further research in this field [
20
]. Activity
incidence, building conditions for art preservation, and their impact on people whose
clothing is fitted for outdoor temperature and does not guarantee their comfort within the
building during warm season are stressed.
Several studies on thermal comfort were carried out in educational institutions of
different levels. The study performed by Singh, M.K. et al. [
21
], compiling 93 research
papers on the subject, found that students were dissatisfied with the thermal environment
and preferred a colder temperature in all education levels. This study shows that it is
necessary to establish a different set of guidelines or standards for students of different ages
in different educational levels in order to satisfy their thermal comfort needs or preferences.
Appl. Sci. 2021,11, 11979 4 of 17
Another study conducted by Martínez-Molina et al. on a post-occupancy thermal
comfort assessment in a primary school focused on the building’s energy adaptation and
improvement. A post-occupancy evaluation (POE), in which the sample size was the
classroom [
22
], was performed. Standard PMV and PPD values for both students and
teachers were calculated, and then, a survey about their comfort level was conducted.
Results show that the children’s thermal comfort status is different from that of adults
and highlight the concept’s subjectivity. Once again, age incidence is stressed and further
shows the need to find other tools to get closer to reality.
Forgiarini, R. and Ghisi, E. [
23
] performed studies in office buildings with air condition-
ers and mixed mode ventilation, and they used analytical and adaptive models for thermal
comfort. For the authors, the analytical model overestimated users’ sensation of cold and
did not adequately predict the percentage of thermal dissatisfaction. As such, they recom-
mended adapting a broader range of indoor thermal conditions than those recommended
by ASHRAE 55-2013 during the functioning of air-conditioning, while the application of
the adaptive model would prove inadequate for buildings with air-conditioning, although
this finding was not conclusive due to a lack of sufficient data.
In the same research line, Jia, X. et al. [
24
] noted that: “...there is no consensus among
previous studies on how to assess thermal comfort on occupants in mixed mode (MM)
buildings. This study aims at comparing the PMV-PPD and the adaptive model appli-
cability in MM buildings and assessing if the occupants’ thermal perception varies with
different functioning modes...”. The results showed that the analytical model was not fitted
for MM buildings and that the adaptive model proved better applicability in cooling mode
with air conditioners than with natural ventilation.
Studies by Gallardo, A. et al. showed that the PMV model predicts to some extent the
thermal sensation of occupants but fails to estimate the temperature at which occupants
feel comfortable [25].
According to Piasecki, M. et al. [
26
], “it was noted that the panelists showed better
thermal comfort sensation at lower temperatures than would result from the traditional
Fanger distribution, so the authors proposed the experimental function of percentage of
dissatisfied (PPD) = f(PMV)”. It is another case that highlights the need to review the
methodology for assessing thermal comfort in the face of new challenges.
Based on this background, the research study on thermal comfort has been mainly
conducted on two models—the mathematical and the adaptive—from a conceptual and
methodological standpoint.
In the mathematical model, also known as the quantitative method, the person–
environment heat exchange is studied by measuring the physiological variations expe-
rienced by test subjects in controlled chambers. Thermal balance equations linked to
physiological values obtained through experience are solved to predict comfort sensation.
As it has been stated, the model reference is Povl Ole Fanger [
10
]. This model is fitted for
evaluating thermal comfort in constantly conditioned buildings.
Adaptive models are based on qualitative methods using observation, surveys, and/or
interviews in actual operability settings, mostly offices and houses, for data mining. They
record all possible details about clothing type, people’s characteristics, activity, and tem-
perature. In general, the tools used for this model were statistics aiming at determining
which temperatures most people were comfortable with, related to outdoor temperature
but excluding design parameters such as indoor relative humidity (RH). Table 1shows a
summary of authors, models, and limitations:
Appl. Sci. 2021,11, 11979 5 of 17
Table 1. Thermal comfort models and their limitations.
Author Model Method Techniques Tools Limitations
Fanger, P.O. [10]Mathematical/
Analytical Quantitative Experimental
Lab experiment
Controlled conditions
for data collection by
means of measurements
Static model of heat
exchange
People resting
Mechanically conditioned
buildings
Not industry specific
It does not consider
human adaptability to the
environment
Brager, G. and De Dear, R. [12]
Nicol, F. and Humphreys, M.
[13]
Adaptative Qualitative Field
Experimentation
Statistical models are
used. In general, linear
regression
It is subjective
They consider comfort
temperature based on
outdoor dry-bulb
temperature
They do not consider RH%
Not industry specific
Gomez-Azpeitia, L. et al. [14]
Singh, M.K. et al. [21]Review papers
Data search and
location
Decision criteria
Analysis and
evaluation
They review and
compare the prevailing
quantitative and
qualitative approaches
Literature review papers
show the limitations of the
models used, which
cannot offer hygrothermal
comfort
The quantitative and qualitative methods studied show that the issue of thermal
comfort has yet to be solved [
14
]. Even though the adaptive model shows a better answer
to the problem when compared with the Fanger model due to its simplicity, its great
disadvantage is the variety of intervening domain variables, which have been included in
case studies. Some of these have been introduced as background in this paper due to their
impact on the studied variable, and they are summarized as follows in Table 2:
Table 2. Contributions to the thermal comfort models.
Authors Characteristics Limitations
Atmaca, I. y Koçak, S. [18]
Sun et al. [19]
Martínez-Molina et al. [20,22]
Forgiarini, R. and Ghisi, E. [23]
Jia, X. et al. [24]
Gallardo, A. et al. [25]
Piasecki, M. et al. [26]
Authors introduce case
studies for different building
types and/or specific aims,
with mechanical
conditioning, natural
ventilation, or mixed mode.
They use the qualitative
and/or quantitative method
to determine the thermal
comfort level or to compare
and/or verify both methods.
From these studies, it can be
concluded that there still are
many domain areas that are
not included in thermal
comfort analysis.
The limitations of both the
qualitative and quantitative
approaches are presented.
3. Problem Statement
As observed in the background, research has been based on the Fanger model, statisti-
cal techniques, and/or compared case studies.
Even though qualitative methods hinder generalization, a meta-analysis that statis-
tically combines several studies can be conducted since there is a great amount of data.
Additionally, there can be publication bias if studies with negative results or those that
could not be published are not considered.
As shown in Tables 1and 2summarizing the current literature, the methods used in
the cases presented show limitations for hygrothermal comfort.
If the following aspects are considered, new alternatives are needed to study the
complex weave of relationships when determining industrial comfort parameters:
concept subjectivity;
significance of the topic for health;
thermal comfort significance for occupational health and safety and its impact on
productivity;
Appl. Sci. 2021,11, 11979 6 of 17
model limitations when applied in industries;
and energy resource optimization for thermal comfort.
Therefore, previous experiences from studies in western and eastern areas of Ar-
gentina [
27
,
28
] were capitalized on, and the standards and guidelines regulating thermal
comfort [
29
33
] were analyzed. This study shows the lack of regulations for air condi-
tioning installations in industrial buildings regarding indoor design parameters, in which
geographical region, season, time schedule, activity, and subjective value are essential
to consider.
As Kralikova and Wessely [
34
] note, human beings have attempted to create thermally
comfortable spaces for many years, and the components of successfully doing so include
air temperature, humidity, and air speed inside the space; however, they add that the
understanding of what makes a space comfortable is still evolving, and we are discovering
that these components only represent a part of the thermal comfort conundrum.
For this issue, and trying to offer a solution for these vacancies, the use of probabilistic
techniques is proposed.
To illustrate, a case study performed in the northern area of Argentina, whose mined
data are published in ResearchGate, is presented [35,36].
4. Study Case—Northern Area of Argentina
Based on the proposed, the aim was to analyze the behavior of Bayesian techniques
for prediction and better result exploitation to prove field experiments. In this case, it is in
the northern area of Argentina, where the weather is primarily subtropical, dry, and warm;
however, there are some areas with a wet season in which heavier rainfall events occur in
the summer, with relative humidity >50%.
The experiment was performed in six companies from different businesses (veneer
plants, and textile, metal-mechanic, and tobacco sectors) in the northern area of Argentina
by observing and recording:
Season of the year (summer/winter);
Time schedule.
For the summer season, cooling loads varied according to solar time; so, data mining
was performed three times, at 10.00 h, 15.00 h, and 18.00 h, to consider the variable impact.
For the winter season, solar time contributes to heating loads, so data mining was
performed only at 10.00 h. Variables included:
Activity (Light-Moderate-Heavy);
Indoor Temperature (C);
Indoor Relative Humidity (%);
Geographical region;
Thermal comfort status—1 to 10 range where:
1: completely uncomfortable;
10: completely comfortable.
Data mining was performed by a simple interview about thermal comfort, with the
following form, named Table 3.
Appl. Sci. 2021,11, 11979 7 of 17
Table 3. Thermal Comfort Interview.
Thermal Comfort Form—Summer/Winter
Region:
Company/Institution
Address:
Email Address:
Area:
Activity:
Day and Time:
Personnel Temperature
(C)
Relative Humidity
(%)
Status
(1 to 10)
Specifications for the survey were as follows:
To state, before starting the survey, that the answers are anonymous for employees
and company, and that the results are only part of a research;
Minimum answering time to not interfere with personal activities;
To contemplate that the respondents have similar clothing or wear a uniform;
To contemplate that air velocity has no determining influence [8];
Temperature and relative humidity measurements are taken with a hygrometer spe-
cially designed for long-term follow-up of indoor climate conditions. This device used
for air quality has a temperature sensor with a measuring range of 0–50
C—resolution
0.1
C (
±
0.15
C from 0 to 20
C and
±
0.1
C from 20 to 50
C) and a relative humidity
(RH) sensor with a measuring range of 0–100% RH—resolution 0.1% RH (
±
1.5% RH
from 0 to 80% RH).
Comfort status is divided into three categories:
Low Comfort: Status from 1 to 4;
Medium Comfort: Status 5, 6, and 7;
High Comfort: Status 8, 9, and 10.
Subsequently, the Bayesian network techniques proposed were applied, with WEKA [
37
]
and ELVIRA [38] tools.
Finally, the results obtained were validated, thus offering thermal comfort recommenda-
tions.
5. Materials and Methods
First, data preparation was done, thus creating the files to be exploited by WEKA
and ELVIRA [
39
,
40
] tools. WEKA is a collection of automated learning and data prepro-
cessing algorithms (Witten, I. et al. [
41
]) developed by the University of Waikato in New
Zealand and has tools for data reprocessing, classification, regression, clustering, associa-
tion rules, and visualization. It is an open-source software under the general public license
of GNU (GPL).
ELVIRA is the result of a project funded by the Interministry Commission of Science
and Technology (CICYT) and the Ministry of Science and Technology of Spain, of which
researchers from different Spanish universities—the Universidad de Educación a Distancia
(UNED) among others—were part. The tool “is used for editing and evaluating probabilistic
chart models, specifically Bayesian networks and influence diagrams” (Díez Vegas, F. [
42
]).
Second, the data analysis was performed using the WEKA tool in Explorer mode,
which allows data preprocessing, filter application, classification, clustering, association
rule, attribute selection, and data visualization tasks (García Morate, D. [
43
]). As an
example, Figure 1shows the main window with a data file loaded with summer data. It is
later replicated with winter data [39,40].
Appl. Sci. 2021,11, 11979 8 of 17
Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 17
Figure 1. Main window of WEKA Explorer with a loaded data file.
Third, a classification algorithm, J48 [43], was used to make a decision tree. In this
sense, in an ideal situation with an infinite number of cases, predictions on quality meas-
urements of model behavior would be perfect. In all practicality, the data set must be di-
vided. Thus, stratified cross-validation was used. It is used when data are divided in an
“n” number of parts and, for each division, the classier is built with the remaining n1
parts, and it is tested. The procedure is repeated for each of the parts. A cross-validation
is said to be stratified when each of the parts has characteristics of the original sample.
The sample attribute is then selected—generally the last one on the list, which is the vari-
able to be determined in the classification. Cross-validation results for the J48 Classifier
are available on ResearchGate [39,40].
When finished, a decision tree is shown in the “Visualize tree” option if it was created
from the classifier. Figure 2a,b shows the decision trees for summer and winter, respec-
tively.
(a)
Figure 1. Main window of WEKA Explorer with a loaded data file.
Third, a classification algorithm, J48 [
43
], was used to make a decision tree. In this
sense, in an ideal situation with an infinite number of cases, predictions on quality mea-
surements of model behavior would be perfect. In all practicality, the data set must be
divided. Thus, stratified cross-validation was used. It is used when data are divided in an
“n” number of parts and, for each division, the classifier is built with the remaining n
1
parts, and it is tested. The procedure is repeated for each of the parts. A cross-validation is
said to be stratified when each of the parts has characteristics of the original sample. The
sample attribute is then selected—generally the last one on the list, which is the variable
to be determined in the classification. Cross-validation results for the J48 Classifier are
available on ResearchGate [39,40].
When finished, a decision tree is shown in the “Visualize tree” option if it was created
from the classifier. Figure 2a,b shows the decision trees for summer and winter, respectively.
Fourth, to execute ELVIRA, the data files were built from the WEKA decision trees
for the northern area in summer and winter, as mentioned in “Evaluation, using Algo-
rithms, of Thermal Comfort Levels in the Industrial Area of the Region of Buenos Aires,
Argentina” [28].
As mentioned, ELVIRA allows editing and assessing probabilistic graphic models—
specifically, Bayesian networks [
42
]. The Bayesian inference is a probabilistic reasoning
that spreads the evidence effects through the network to know the “a posteriori” variable
probability [
17
]. Bayesian classifiers can be considered a special case of a Bayesian network,
in which there is a specific variable (class) and the rest of the variables are attributes.
Bayesian classifiers are widely used due to the advantages they offer, such as, their
simplicity for building and understanding, their reliability when assessing irrelevant
attributes, and their pondering of several properties to provide a final prediction.
In this study, data preprocessing was performed, followed by machine learning
operations, in which the Naive-Bayes classifier (NBC) was chosen. This simple Bayesian
classifier construes attributes as independent (i.e., there are no arches among them), as
can be seen in Figure 3, so the probability can be obtained by the product of individual
conditional probabilities of each attribute from the class node [17].
Appl. Sci. 2021,11, 11979 9 of 17
Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 17
Figure 1. Main window of WEKA Explorer with a loaded data file.
Third, a classification algorithm, J48 [43], was used to make a decision tree. In this
sense, in an ideal situation with an infinite number of cases, predictions on quality meas-
urements of model behavior would be perfect. In all practicality, the data set must be di-
vided. Thus, stratified cross-validation was used. It is used when data are divided in an
“n” number of parts and, for each division, the classier is built with the remaining n1
parts, and it is tested. The procedure is repeated for each of the parts. A cross-validation
is said to be stratified when each of the parts has characteristics of the original sample.
The sample attribute is then selected—generally the last one on the list, which is the vari-
able to be determined in the classification. Cross-validation results for the J48 Classifier
are available on ResearchGate [39,40].
When finished, a decision tree is shown in the “Visualize tree” option if it was created
from the classifier. Figure 2a,b shows the decision trees for summer and winter, respec-
tively.
(a)
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 17
(b)
Figure 2. (a) Classifier Tree Visualizer—Summer. (b) Classifier Tree Visualizer—Winter.
Fourth, to execute ELVIRA, the data files were built from the WEKA decision trees
for the northern area in summer and winter, as mentioned in “Evaluation, using Algo-
rithms, of Thermal Comfort Levels in the Industrial Area of the Region of Buenos Aires,
Argentina” [28].
As mentioned, ELVIRA allows editing and assessing probabilistic graphic models—
specifically, Bayesian networks [42]. The Bayesian inference is a probabilistic reasoning
that spreads the evidence effects through the network to know the “a posteriori” variable
probability [17]. Bayesian classifiers can be considered a special case of a Bayesian net-
work, in which there is a specific variable (class) and the rest of the variables are attributes.
Bayesian classifiers are widely used due to the advantages they offer, such as, their
simplicity for building and understanding, their reliability when assessing irrelevant at-
tributes, and their pondering of several properties to provide a final prediction.
In this study, data preprocessing was performed, followed by machine learning op-
erations, in which the Naive-Bayes classifier (NBC) was chosen. This simple Bayesian clas-
sifier construes attributes as independent (i.e., there are no arches among them), as can be
seen in Figure 3, so the probability can be obtained by the product of individual condi-
tional probabilities of each attribute from the class node [17].
Figure 3. Bayesian network.
Figure 2. (a) Classifier Tree Visualizer—Summer. (b) Classifier Tree Visualizer—Winter.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 17
(b)
Figure 2. (a) Classifier Tree Visualizer—Summer. (b) Classifier Tree Visualizer—Winter.
Fourth, to execute ELVIRA, the data files were built from the WEKA decision trees
for the northern area in summer and winter, as mentioned in “Evaluation, using Algo-
rithms, of Thermal Comfort Levels in the Industrial Area of the Region of Buenos Aires,
Argentina” [28].
As mentioned, ELVIRA allows editing and assessing probabilistic graphic models—
specifically, Bayesian networks [42]. The Bayesian inference is a probabilistic reasoning
that spreads the evidence effects through the network to know the “a posteriori” variable
probability [17]. Bayesian classifiers can be considered a special case of a Bayesian net-
work, in which there is a specific variable (class) and the rest of the variables are attributes.
Bayesian classifiers are widely used due to the advantages they offer, such as, their
simplicity for building and understanding, their reliability when assessing irrelevant at-
tributes, and their pondering of several properties to provide a final prediction.
In this study, data preprocessing was performed, followed by machine learning op-
erations, in which the Naive-Bayes classifier (NBC) was chosen. This simple Bayesian clas-
sifier construes attributes as independent (i.e., there are no arches among them), as can be
seen in Figure 3, so the probability can be obtained by the product of individual condi-
tional probabilities of each attribute from the class node [17].
Figure 3. Bayesian network.
Figure 3. Bayesian network.
Then, in “Inference” mode, ELVIRA shows the networks with a priori probabilities [
42
].
From these inference networks, by choosing type of activity and time of day, different
indoor temperature and relative humidity values can be tested, thus obtaining the thermal
comfort level for those parameters.
Appl. Sci. 2021,11, 11979 10 of 17
Even though the simple Bayesian classifier works very well in many fields of knowl-
edge and is very accurate, its performance decreases when attributes are not conditionally
independent as expected [17]. This issue has not been shown in this study.
6. Results
The results from thermal comfort levels based on conditioned environment temper-
ature and relative humidity, considering activity, time of day and season variables, are
shown in the inference networks in Figures 4and 5for the northern area of Argentina,
where probability for each value is presented in two forms: (a) by means of a number and
(b) by means of a bar proportional to the probability. Since no new data were introduced,
the probabilities are a priori (Díez Vegas, F. [
42
]), where the only probability calculated is
thermal comfort. These networks belong to the “initial case”.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 17
Then, in “Inference” mode, ELVIRA shows the networks with a priori probabilities
[42]. From these inference networks, by choosing type of activity and time of day, different
indoor temperature and relative humidity values can be tested, thus obtaining the thermal
comfort level for those parameters.
Even though the simple Bayesian classifier works very well in many fields of
knowledge and is very accurate, its performance decreases when attributes are not condi-
tionally independent as expected [17]. This issue has not been shown in this study.
6. Results
The results from thermal comfort levels based on conditioned environment temper-
ature and relative humidity, considering activity, time of day and season variables, are
shown in the inference networks in Figures 4 and 5 for the northern area of Argentina,
where probability for each value is presented in two forms: (a) by means of a number and
(b) by means of a bar proportional to the probability. Since no new data were introduced,
the probabilities are a priori (Díez Vegas, F. [42]), where the only probability calculated is
thermal comfort. These networks belong to the “initial case”.
Figure 4. ELVIRA—Inference Network—A priori probabilities—Northern area, Summer.
Figure 5. ELVIRA—Inference Network—A priori probabilities—Northern area, Winter.
Figure 4. ELVIRA—Inference Network—A priori probabilities—Northern area, Summer.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 17
Then, in “Inference” mode, ELVIRA shows the networks with a priori probabilities
[42]. From these inference networks, by choosing type of activity and time of day, different
indoor temperature and relative humidity values can be tested, thus obtaining the thermal
comfort level for those parameters.
Even though the simple Bayesian classifier works very well in many fields of
knowledge and is very accurate, its performance decreases when attributes are not condi-
tionally independent as expected [17]. This issue has not been shown in this study.
6. Results
The results from thermal comfort levels based on conditioned environment temper-
ature and relative humidity, considering activity, time of day and season variables, are
shown in the inference networks in Figures 4 and 5 for the northern area of Argentina,
where probability for each value is presented in two forms: (a) by means of a number and
(b) by means of a bar proportional to the probability. Since no new data were introduced,
the probabilities are a priori (Díez Vegas, F. [42]), where the only probability calculated is
thermal comfort. These networks belong to the “initial case”.
Figure 4. ELVIRA—Inference Network—A priori probabilities—Northern area, Summer.
Figure 5. ELVIRA—Inference Network—A priori probabilities—Northern area, Winter.
Figure 5. ELVIRA—Inference Network—A priori probabilities—Northern area, Winter.
From these inference networks, specific temperature, relative humidity, activity, time
schedule, and season values were tested to know the predictive value of thermal comfort.
Thus, the first evidence case was generated and identified with a color. If another value set
Appl. Sci. 2021,11, 11979 11 of 17
were to be introduced, a second evidence case would be generated with a different color.
These evidence cases can be filed and affect the network. Figure 6shows the first evidence
case for summer.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 17
From these inference networks, specific temperature, relative humidity, activity, time
schedule, and season values were tested to know the predictive value of thermal comfort.
Thus, the first evidence case was generated and identified with a color. If another value
set were to be introduced, a second evidence case would be generated with a different
color. These evidence cases can be filed and affect the network. Figure 6 shows the first
evidence case for summer.
Figure 6. ELVIRA—Inference Network—First evidence case—Northern area, Summer.
Table 4 shows data and probabilities taken from the inference network in Figure 6
for the first evidence case.
Table 4. Results from the first evidence case—Summer.
Season Time Temperature R.H.% Activity Comfort
Summer 18.00 h. >25 °C and 30 °C >52% and 74% Moderate 100% Medium
Figure 7 shows the first evidence case for winter as example:
Figure 6. ELVIRA—Inference Network—First evidence case—Northern area, Summer.
Table 4shows data and probabilities taken from the inference network in Figure 6for
the first evidence case.
Table 4. Results from the first evidence case—Summer.
Season Time Temperature R.H.% Activity Comfort
Summer 18.00 h. >25 C and
30 C
>52% and
74% Moderate 100%
Medium
Figure 7shows the first evidence case for winter as example:
With the data mined from the first evidence case for winter, the following information
was obtained: at 10.00 h, and with temperatures ranging from 19
C to 25
C and relative
humidity < 54%, comfort is high for light activities, as shown in Table 5.
It allows “the graphic observation of how each finding’s impact affects the probabilities
of other variables, which helps to understand how a Bayesian network works and, if we
want to improve net reliability, we can modify the structure or probabilities when the
results are not those expected” [42].
Appl. Sci. 2021,11, 11979 12 of 17
Figure 7. ELVIRA—Inference Network—First evidence case—Northern area, Winter.
Table 5. Results from the first evidence case—Winter.
Season Time Temperature R.H.% Activity Comfort
Winter 10.00 h >19 C and
25 C54% Light 100% High
7. Discussion
The thermal comfort results from the inference networks were compared with the
work environments selected for data mining.
Furthermore, new values obtained from the surveys in different industries of the
northern area were tested, thus creating new evidence cases whose results are comparable
with those provided by the staff in the working environment, so no correction to the
network probabilities was necessary.
It can be noted that, apart from the possible building design optimization, thermal
comfort depends on temperature, work type, time of day, season, and relative humid-
ity percentage.
In the northern area of Argentina, due to its warm subtropical climate, staff can
endure maximum temperatures of up to 30
C within humidity limits without their optimal
comfort level being affected. It can be concluded that human beings have a certain climate
adaptability.
It is also worth noting that comfort parameters are similar for both summer and winter
as for the different activities in the northern area. It can be concluded that this characteristic
is due to such adaptability.
The J48 WEKA classifier obtained results corresponding to those informed in the
study areas and was the basis for the network formulation with ELVIRA software and the
result verification.
The use of Bayesian inference techniques reduces error probabilities for the results
obtained with statistical analysis and offers a greater number of temperature–humidity
relationships based on the variables (activity, time of day, season) to reach a specific
comfort level.
To verify what has been previously mentioned, a comparative study between different
adaptive models (Gómez-Azpeitia, L. et al. [
14
]) and the values obtained from the data
mined in the study area by using linear regression techniques was performed. In the case
of adaptive models, comfort temperature (tn) was calculated based on outdoor mean tem-
perature (tme) [
44
]. For linear regression technique calculations, a partial data set [
45
] was
Appl. Sci. 2021,11, 11979 13 of 17
used without distinguishing activity type, time schedule, season, or humidity percentage.
Tables 6and 7respectively show results for summer and winter.
Table 6.
Comfort temperatures (tn) for summer obtained from adaptive models and linear regression.
Author tn = m ×(tme)+b tem (C) tn (C)
Humphreys (1976) [14] tn = 0.534 ×(tme) + 11.9 27.8 26.7
Auliciems (1981) [14] tn = 0.31 ×(tme) + 17.6 27.8 26.2
Griffiths (1990) [14] tn = 0.534 ×(tme) + 12.1 27.8 26.9
Nicol et al. (1993) [14] tn = 0.38 ×(tme) + 17.0 27.8 27.6
Brager- De Dear (1998) [14] tn = 0.31 ×(tme) + 17.8 27.8 26.4
Humphreys-Nicol (2000) [14] tn = 0.54 ×(tme) + 13.5 27.8 28.5
Linear regression-North Zone
tn = 0.541
×
(tme) + 11.97
27.8 27.0
Table 7.
Comfort temperatures (tn) for winter obtained from adaptive models and linear regression.
Author tn = m ×(tme) + b tem (C) tn (C)
Humphreys (1976) [14] tn = 0.534 ×(tme) + 11.9 22.6 24.0
Auliciems (1981) [14] tn = 0.31 ×(tme) + 17.6 22.6 24.6
Griffiths (1990) [14] tn = 0.534 ×(tme) + 12.1 22.6 24.2
Nicol et al. (1993) [14] tn = 0.38 ×(tme) + 17.0 22.6 25.6
Brager- De Dear (1998) [14] tn = 0.31 ×(tme) + 17.8 22.6 24.8
Humphreys-Nicol (2000) [14] tn = 0.54 ×(tme) + 13.5 22.6 25.7
Linear regression-North Zone
tn = 0.541
×
(tme) + 11.97
22.6 24.2
When analyzing Tables 6and 7, it can be noted that the differences between the
obtained results are not significantly different between the adaptive models and those
obtained from linear regression in our case study [
45
]. However, it should be considered
that results calculated with linear regression were obtained from a partial data set since
adaptive models only provide one comfort temperature without considering variables such
as time of year, time schedule, or activity in the conditioned industry premises.
If these results are compared with those obtained—for example, with the first evi-
dence case from Bayesian networks (Tables 4and 5)—it can be concluded that they are
within the same range, yet the network provides more information such as temperature,
relative humidity percentage, activity type, time schedule, and time of year for a specific
comfort probability.
On the other hand, the Fanger or quantitative method does not consider the actual
working conditions since it is based on a static model of heat exchange, nor does it consider
human environment adaptability.
The Bayesian inference model’s contribution is offering a variety of design parameter
alternatives (indoor temperature/relative humidity percentage relationships) for different
working conditions in industries while considering time and season.
8. Conclusions
ICTs, especially those techniques linked to AI use in the Industry 4.0 context, are an
opportunity to improve thermal comfort levels—specifically, data analysis and calculated
probability prediction algorithms from data mining [1,2].
These analysis techniques can be extended and repeated in any geographical area if
the software used are fed with data and characteristics from the area.
Having a work methodology for determining industrial thermal comfort parameters
for any geographical area would be an asset for those designing heating, ventilation, and air
conditioning (HVAC) installations, thus allowing the use of different temperature/relative
humidity pairs to obtain the same hygrothermal comfort level.
According to a research study on energy efficiency conducted by Khalilnejad, A.;
French, R.; and Abramson, A. [
46
], commercial buildings “consumed 36% of electricity, or
Appl. Sci. 2021,11, 11979 14 of 17
1.35 trillion kWh, in the United States in 2017, and almost 30% of that energy was wasted.
Much of this loss can be linked to inefficient heating, ventilation, and air conditioning
(HVAC) systems. If operational conditions are improved, significant energy savings can be
achieved”.
HVAC installation design by using specific parameters as those obtained from the
work methodology in our study can imply energy savings since systems would not over-
work, thus increasing energy efficiency [47,48].
The National Program of Rational and Efficient Energy Use of Argentina (Decree
140/2007) [
49
] shares this aim. The decree item related to industries mentions its aim as
“contributing to increase the area’s competitiveness by introducing management tools that
would reduce costs due to the efficient use of energy and product resources”.
For occupational health and safety professionals, it allows access to tools for improv-
ing working positions, which would prevent risks and diseases, to improve the employees’
wellbeing and quality of life and thus boosting performance due to the workers’ hygrother-
mal comfort [6,7].
The limitations observed while conducting the study are the difficulty of data mining,
which was performed with personal interviews, and verification at the workplace, which
was very time-consuming. On the other hand, the data mined did not consider the basal
physiological factors related to thermal comfort.
Therefore, an interesting line of work to follow is the programming of a mobile
application that would allow the recording of indoor temperature, indoor relative humidity
of the conditioned premises, and comfort status of a person in their workplace by means of
voice command, without conducting personal interviews. It would allow a greater amount
of real-time data that could be easily obtained in any workplace.
Another contribution, as a new research line, would be including the records of basal
physiological parameters in the inference model.
In the Industry 4.0 context, if an application for interacting with users and working
environment conditions and physiological parameters linked to thermal comfort with
sensors was integrated with mobile devices, data that could be independently mined with
automated learning techniques would be obtained to allow thermal system interaction and
control in an intelligent control loop.
Therefore, all devices (air conditioners, enclosures, ventilations, etc.) would be started
to modify environmental hygrothermal conditions to achieve comfort status in the Industry
4.0 paradigm.
In this sense, Diogo Cardoso and Luís Ferreira mention that “artificial intelligence tools,
specifically automated learning, show great potential for analyzing great amounts of data,
now readily available, to reduce upkeeping costs and increase operational performance
and decision-making support” [50].
All of what has been previously mentioned would mean industry/company benefits,
thus boosting economic growth in line with the environment and supporting sustainable
development by improving energy efficiency for thermal comfort.
Author Contributions:
Conceptualization, P.I.B.; methodology, P.I.B., M.A.S. and C.G.-G.; inves-
tigation, P.I.B., M.A.S. and C.G.-G.; resources, P.I.B.; writing—original draft preparation, P.I.B.;
writing—review and editing, P.I.B., M.A.S. and C.G.-G.; supervision, M.A.S. and C.G.-G.; project
administration, P.I.B., M.A.S. and C.G.-G. All authors have read and agreed to the published version
of the manuscript.
Funding: Universidad Nacional de Educación a Distancia (UNED).
Data Availability Statement:
Links to publicly archived datasets: Thermal Comfort—Northern area of
Argentina—Summer, ResearchGate, 2021, https://doi.org/10.13140/RG.2.2.28981.60642.https://www.
researchgate.net/publication/355651806_Thermal_Comfort_-_Northern_area_of_Argentina-Summer (ac-
cessed on 4 November 2021). Thermal Comfort—Northern area of Argentina—Winter, ResearchGate,
2021, https://doi.org/10.13140/RG.2.2.20592.99848.https://www.researchgate.net/publication/355651
613_Thermal_Comfort_-_Northern_area_of_Argentina_-_Winter (accessed on 4 November 2021). Ther-
Appl. Sci. 2021,11, 11979 15 of 17
mal Comfort—Northern area of Argentina—Input Data WEKA—Summer, ResearchGate, 2021, https://
doi.org/10.13140/RG.2.2.17440.71688.https://www.researchgate.net/publication/356007548_Thermal_
Comfort-_Northern_area_of_Argentina-_Input_Data_WEKA_-Summer (accessed on 4 November 2021).
Thermal Comfort—Northern area of Argentina—Input Data WEKA—Winter, ResearchGate, 2021, https://
doi.org/10.13140/RG.2.2.13043.25125.https://www.researchgate.net/publication/355652295_Thermal_
Comfort-_Northern_area_of_Argentina-_Input_Data_WEKA_-_Winter (accessed on 4 November 2021).
Dataset—Comfort Temperature—Northern area of Argentina-Linear Regression, ResearchGate, 2021, https:
//doi.org/10.13140/RG.2.2.35692.49288.https://www.researchgate.net/publication/355652081_Data_
set_-_Comfort_Temperature_-_Northern_area_of_Argentina-Linear_Regression (accessed on 4 Novem-
ber 2021).
Acknowledgments:
This paper is based on the ongoing research of the lead author’s Ph.D. thesis,
under preparation at the Escuela Internacional de Doctorado, Universidad Nacional de Educación a
Distancia (UNED); the authors, therefore, wish to express their gratitude for the support from that
Institution. Additionally, the authors thank the Secretariat of Science and Technology, Universidad
de Morón, for its support through the 2016-PID 01-002 project.
Conflicts of Interest: The authors declare no conflict of interest.
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... In recent years, the number of studies on the effects of the indoor thermal environment on human physical and mental health has increased. The studies focused on different aspects of the theme, such as assessing the indoor thermal environment in specific locations (classrooms, workplaces) [6,7], using electronic sensors for monitoring and improving the thermal sensation [8], using IT instruments for the modelling and prediction of thermal comfort [9][10][11], or the effects of heat-related illness on mental health [12]. ...
... ISO 7730:2005 Standard defines thermal comfort, also known as hygrothermal comfort, as "that condition of mind which expresses satisfaction with the thermal environment" [13], which is a subjective concept and thus very difficult to assess [2,10]. Thermal comfort is determined by six environmental and personal factors, which may be independent of each other but determine the employee's thermal comfort by their synergic effects [14][15][16]. ...
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... Together with the alternative models, several statistical methods have been applied to analyze thermal comfort, such as discriminant analysis [21], Bayesian statistics [22], Griffiths analysis [23], logistic regression [24], and structural equations [25]. Another relevant technique is the analysis of variance (ANOVA) that investigates the influences of some experimental conditions, errors, and significance of factors [26] and cluster analysis that classifies objects into homogeneous groups according to their level of similarity [27]. ...
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The Predicted Mean Vote (PMV) has discrepancies in relation to the thermal reality of the environment; thus, adaptive models serve to improve this estimate. In this context, this research aimed to verify the performance of PMV and adaptive models under different conditions in Brazil from an analysis of variance and to further classify individuals into clusters according to their feelings of thermal comfort. Through ASHRAE’s Global II Thermal Comfort Database, users of offices and classrooms in Brasilia, Recife, Maceió, and Florianópolis were investigated. The results of ANOVA showed that the PMV model did not represent the thermal reality of any of the cities investigated, and the cluster analysis showed how most people felt thermally in relation to indoor environments.
... Related to the topic of "sustainable and green manufacturing", Benito et al. [11] developed an article focused on the use of Bayesian networks to address the industrial thermal comfort issue, specifically in industries in northern Argentina. Mined data sets were analyzed and exploited with WEKA and ELVIRA tools. ...
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