sustainability

Article
A Study on Parametric Design Method for Optimization of
Daylight in Commercial Building’s Atrium in Cold Regions
Yibing Xue and Wenhan Liu *

School of Architecture and Urban Planning, Shandong Jianzhu University, Jinan 250100, China;
xueyb@sdjzu.edu.cn
* Correspondence: 2020050218@stu.sdjzu.edu.cn

Abstract: With the development of urbanization, more and more commercial buildings are built
in cities, which is resulting in a large amount of building energy consumption that threatens the
ecological environment of the earth. Lighting energy in commercial buildings occupies a large
proportion of consumption, and improving the quality of natural daylight in commercial atriums
is of great significance for building energy efficiency as well as improving indoor comfort. This
paper proposes a method for optimizing the daylight quality of commercial atriums. Starting
from the perspective of parametric design, this paper investigates the current status and theoretical
research on the natural daylight of commercial atriums in cold regions, taking Jinan, China, as an
example. Dynamic daylight and glare simulations were performed using Rhino + Grasshopper and
Ladybug + Honeybee for every design parameter in the system, followed by correlation analysis and
multiple linear regression analysis using SPSS to determine the degree of influence of each design
parameter on the daylight quality of the atrium. Based on the results of the above analysis, the multi-
objective optimization plug-in Octopus is used to find the combination of design parameters that
can achieve the best indoor daylight. The results show that among a total of fourteen atrium design
parameters, seven of them are significantly correlated with atrium daylight, and after regression
Citation: Xue, Y.; Liu, W. A Study on analysis, it is found that the atrium design parameters affect the atrium daylight and glare in the
Parametric Design Method for following order: Skylight VT, Skylight ratio, Atrium inclination, Fabric coverage, Fabric VT, Wall
Optimization of Daylight in reflectivity, Roof reflectivity. The optimal design parameters for commercial atrium daylight quality
Commercial Building’s Atrium in are obtained according to the Pareto front solution set, which provides some reference and ideas for
Cold Regions. Sustainability 2022, 14, improving the optimization of commercial atrium daylight in cold regions of China.
7667. https://doi.org/10.3390/
su14137667 Keywords: daylight; atrium; parametric design; multi-objective optimization; sensitivity analysis
Academic Editors: Yuanda Cheng,
Peng Xue, Hanna J˛edrzejuk and Ji Li

Received: 31 May 2022

1. Introduction
Accepted: 20 June 2022
Published: 23 June 2022
At present, the world is facing a variety of problems such as an energy crisis, ecological
damage, and climate warming, while the construction sector occupies a large proportion of
Publisher’s Note: MDPI stays neutral
energy consumption, accounting for about one-third of the total social energy consump-
with regard to jurisdictional claims in
tion [1]. Most city dwellers spent nearly 90% of their time indoors. In 2008, only half of the
published maps and institutional affil-
world’s population lived in urbanized areas; however, they consumed nearly 67% of the
iations.
world’s energy. By 2030, the proportion is expected to increase to 73% [2,3]. Therefore, the
study of indoor comfort and energy saving will have a positive impact on the ecological
environment and human health [4]. In the light of the rapid development of China’s
Copyright: © 2022 by the authors.
urbanization and people’s high pursuit of material and spiritual life, cities in China have
Licensee MDPI, Basel, Switzerland. achieved the transformation from “production-oriented cities” to “life-oriented cities”, and
This article is an open access article urban commerce also proceeds on the path of rapid growth. Nowadays, retail-centered
distributed under the terms and business has grown into an indispensable part of the process of expanding domestic de-
conditions of the Creative Commons mand and optimizing the economic structure. More and more high-tech, luxurious and
Attribution (CC BY) license (https:// fashionable shopping malls are being built in cities, whose current application of colorful
creativecommons.org/licenses/by/ lights accounts for a lot of daylight energy consumption. Hence, it is important to improve
4.0/). the quality of natural daylight in commercial buildings.

Sustainability 2022, 14, 7667. https://doi.org/10.3390/su14137667 https://www.mdpi.com/journal/sustainability

Sustainability 2022, 14, 7667 2 of 22

Commercial buildings consume large amounts of energy, and this kind of consumption
is expected to increase in the future because artificial lighting is a key factor in high-level
energy consumption. The fact is that the application of artificial lighting generates heat and
causes cold, which increases cooling loads, which account for about 3–5% of the total energy
consumption. Decreasing the use of artificial lighting is of great significance for lowering
the total energy consumption in commercial buildings. A commercial building’s atrium not
only connects interior spaces but also is a place for social activities, thus bearing aesthetic
and iconic features as well as providing light to the core of the building [5]. Atriums
are widely used by designers in commercial building design because they usually have a
daylight roof, which is one of the most commonly used elements in the design of indoor
shopping malls. Its main purpose is to provide natural daylight for the atrium space and
the enclosed space of the corridors [6–8]. From the perspective of architectural design,
since an atrium is the core design point of commercial buildings, architects usually take
advantage of natural daylight, which not only can reduce daylight energy consumption
and heat dissipation but also creates a vibrant business atmosphere [9]. At present, atriums
have become a trend in modern commercial design because they absorb natural light and
connect adjacent spaces with the outside world [10]. Numerous studies have demonstrated
the use of natural daylight in commercial spaces to increase sales performance and office
rental value, improve building users’ health, and enhance customer satisfaction [11–13].
Natural daylight is both an essential part of green buildings and an important part
of passive design [14]. The use of natural daylight not only helps reduce the energy
consumption of lamps but also increases visual comfort, which is key to the improvement of
indoor environments. Achieving proper daylight can improve work performance, provide a
better environment for building users, and have a positive psychological impact on building
users [15–18]. At present, people increasingly prefer natural daylight to artificial lighting in
the built environment; sunlight has a positive impact on the physical and psychological
well-being of building users [19,20]. The color rendering index of natural light is the best
among all light sources, with daylight quality and energy-saving effect that are superior
to those of artificial lighting [21,22]. It has been confirmed that natural daylight improves
students’ learning and social skills in schools [23] and also contributes to the rehabilitation
of the elderly and other hospital patients [24,25]. Beneficial to physical health, appropriate
ultraviolet rays have the function of sterilization and disinfection [22]. However, excessive
sunlight exposure can also cause adverse effects, such as optic glare and overheating in
buildings, especially the adverse reactions in the human body stimulated by exposure to
sunlight. The discomfort caused by visual effects such as glare are more common than by
heating effect [26–29].
Since the atrium is the main area of natural daylight in shopping malls, the exploration
of changes in its design parameters plays a crucial role in optimizing the indoor daylight
performance of buildings [30]. Therefore, by selecting and extracting a large number of
atrium design parameters (e.g., atrium size, atrium inclination, atrium material, skylight
design, shading parameters) from a large number of studies related to atrium design
parameter variables. This paper uses the parametric software Rhino + Grasshopper to
build a parametric model of typical atrium daylight in cold regions of China. Specifically,
the paper:
(1) Adopts the Ladybug + Honeybee daylight simulation plug-in to perform dynamic
daylight and glare simulation.
(2) Conducts correlation analysis and multiple linear regression analysis for each design
parameter based on the simulation results to determine the impacts of different
parameters on atrium daylight.
(3) Uses the multi-objective optimization tool Octopus to calculate the optimal parameter
combination for optimizing atrium daylight.
The optimal combination of parameters can achieve the best annual daylight and
anti-glare effects, thereby improving the daylight performance of commercial buildings’
atriums in cold regions of China.
 Sustainability 2022, 14, x FOR PEER REVIEW 3 of 23

Sustainability 2022, 14, 7667 The optimal combination of parameters can achieve the best annual daylight and 3 of 22
anti-glare effects, thereby improving the daylight performance of commercial buildings’
atriums in cold regions of China.

2. Research
2. ResearchMethodology
Methodology and
and Model
Model Building
Building
2.1. Field Research on the Daylight of Commercial Building’s Atrium
2.1. Field Research on the Daylight of Commercial Building’s Atrium
2.1.1. Cold Regions of China
2.1.1. Cold Regions of China
Most of the cold regions in China are located in the north. The typical climate is cold
Most of the cold regions in China are located in the north. The typical climate is cold
winter and hot summer, which requires heat preservation in winter and heat insulation
winter and hot summer, which requires heat preservation in winter and heat insulation
in summer; at the same time, it is necessary to enhance solar radiation in winter and sun
in summer; at the same time, it is necessary to enhance solar radiation in winter and sun
shading and heat insulation in summer. Taking Jinan, China, as the research site and the
shading and heat insulation in summer. Taking Jinan, China, as the research site and the
atriumof
atrium ofaacommercial
commercialshopping
shopping center
center in Jinan
in Jinan as the
as the research
research object,
object, this paper
this paper aims aims
to to
investigate the optimization of daylight of a commercial building’s atrium
investigate the optimization of daylight of a commercial building’s atrium in a cold region in a cold region
of China.
of China.
The latest
The latestmethod
methodfor forevaluating
evaluating daylight
daylight performance
performance is climate-based
is climate-based daylight
daylight
modeling (CBDM), which is a dynamic method based on real daylight climate data hour hour
modeling (CBDM), which is a dynamic method based on real daylight climate data
by hour
by hour throughout
throughoutthe theyear,
year,making
making daylight
daylight simulation
simulation moremore accurate
accurate and reliable.
and reliable.
CBDMprovides
CBDM provides various
various metrics
metrics for evaluating
for evaluating daylightdaylight performance,
performance, such as
such as spatial spatial
day-
daylight
light autonomy
autonomy (sDA),
(sDA), annual
annual sunlight
sunlight exposure
exposure (ASE), (ASE), and useful
and useful daylight
daylight illuminance
illuminance
(UDI) [5–7,12,13,30,31].Therefore,
(UDI) [5–7,12,13,30,31]. Therefore, thethe Shandong
Shandong Jinan
Jinan (CSWD)
(CSWD) file downloaded
file downloaded from from
https://energyplus.net/weather
https://energyplus.net/weather (accessed on 23 on
(accessed November 2021) serves
23 November 2021)as the weather
serves as the file
weather
for
file the
for later daylight
the later simulation
daylight study.study.
simulation

2.1.2. Test
2.1.2. TestObjects
Objectsand
andSettings
Settings
According
Accordingtotodifferent
different locations,
locations,atriums
atriums generally can can
generally be classified into four
be classified into types:
four types:
enclosed
enclosedatriums,
atriums,semi-enclosed
semi-enclosed atriums, linear
atriums, atriums,
linear and and
atriums, attached atriums
attached (Figure
atriums 1).
(Figure 1).
The closed
closedatrium
atriumisisthe
theclassic
classicoror
standard
standardtype, andand
type, the the
most common
most one. one.
common It canItbe any
can be any
shape
shape onon the
theplane,
plane,such
suchasasa asquare,
square,rectangle,
rectangle,circle, or triangle.
circle, The The
or triangle. daylight roof or
daylight roof or
skylight
skylightisisthe
theonly
onlysource
sourceofofdaylight
daylightand view
and [32].
view [32].

Figure 1.
Figure Differenttypes
1.Different typesofofatriums.
atriums.

Theenclosed
The enclosedfour-way
four-way atrium
atrium is chosen
is chosen for for
the the object
object of study.
of study. Compared
Compared with with
the the
other forms of atrium spaces, this kind of atrium is connected to
other forms of atrium spaces, this kind of atrium is connected to the interior in all fourthe interior in all four
directions.Light
directions. Lightcan
canonlyonly enter
enter through
through skylights,
skylights, without
without the side
the side windows
windows to assist
to assist in in
daylight,
daylight,which
whichisisthethemost
mostunfavorable
unfavorable situation
situationfor for
an indoor daylight
an indoor environment.
daylight environment.At At
the
the same
same time,
time,this
thisform
formexcludes
excludesthe thedaylight
daylight influence
influence of of
side windows
side windows andandallows for for a
allows
amore
moresystematic
systematicand andin-depth
in-depth study of of the
the degree
degreeof ofthe
theimpact
impactofofdaylight
daylight roof design
roof design on
on atrium
atrium daylight
daylight [33].
[33].
The
Theatrium
atriumof ofa shopping
a shoppingmallmall
in Jinan, China (Figure
in Jinan, 2), is selected
China (Figure 2), isasselected
the test object.
as the test
The plane
object. Theshape
planeof the
shapeatrium is rectangular,
of the with a lengthwith
atrium is rectangular, of 30am, a width
length of of
3024 m,m,a and
width of
a24height
m, andof about 20 m
a height offor 5 floors.
about 20 mThe forfield test ofThe
5 floors. illuminance
field testisof
conducted
illuminanceaccording to
is conducted
the Chinese daylight measurement specification “daylight
according to the Chinese daylight measurement specification “daylight Measurement Measurement Method
GB/T5699-2017”: The test time
Method GB/T5699-2017”: Thelasted fromlasted
test time 10:00amfrom to10:00
16:00pma.m.onto22 December
16:00 p.m. on2021, the
22 December
winter solstice day. The weather was full overcast. The test instrument was a FLUKE-941
2021, the winter solstice day. The weather was full overcast. The test instrument was a
illuminance meter, which is small, portable, and convenient for handheld measurement
FLUKE-941 illuminance meter, which is small, portable, and convenient for handheld
measurement and real-time recording of the illuminance value of the measurement point.
For the test, the measurement points were arranged in uniform layout along the length and
width of the atrium, the space between which was about 3 m. There were five measurement
points, whose distance from the indoor edge of the shopping mall was about 5 m. Along the
atrium axis were generated five horizontal and five vertical test sections. The measurement
took a horizontal plane 0.75 m above the ground as the reference plane (Figure 3).
 and
andreal-time
real-timerecording
recordingofofthe
theilluminance
illuminancevalue
valueofofthe
themeasurement
measurementpoint.point.For
Forthe
thetest,
test,
the
the measurement points were arranged in uniform layout along the length and widthofof
measurement points were arranged in uniform layout along the length and width
the
theatrium,
atrium,thethespace
spacebetween
betweenwhich
whichwas
wasabout
about3 3m.
m.There
Therewere
werefive
fivemeasurement
measurementpoints,
points,
Sustainability 2022, 14, 7667
whose
whose distance from the indoor edge of the shopping mall was about5 5m.
distance from the indoor edge of the shopping mall was about m.Along
Alongthethe4 of 22
atrium
atriumaxis
axiswere
weregenerated
generatedfive
fivehorizontal
horizontalandandfive
fivevertical
verticaltest
testsections.
sections.The
Themeasure-
measure-
ment
menttook
tooka ahorizontal
horizontalplane
plane0.75
0.75mmabove
abovethetheground
groundasasthe
thereference
referenceplane
plane(Figure
(Figure3).
3).

Figure
Figure2.2.Shopping
Shoppingmall
mallatrium
atriumphotos.
photos.
Figure 2. Shopping mall atrium photos.

Figure
Figure3.3.
Figure The
3.The test
Thetest equipment
testequipment
equipment and
and
and measuring
measuring
measuring point
point
point layout.
layout.
layout.

When
When measuring,
Whenmeasuring,
measuring,hold hold
holdthethe
the instrument
instrument
instrument to
totoreadread
read thethe
the illuminance
illuminance
illuminance value
valuevalue
and and
andrecord record
record atat at
the
the same time. After each measuring point stabilizes the instrument, read the data, and and
the same
same time.
time. After
After each
each measuring
measuring point
point stabilizes
stabilizes the the instrument,
instrument, read read
the the
data, data,
and
then
then quickly
thenquickly
quicklygogo tothe
gototo thenext
the next
next measuring
measuring
measuring point
point
point to measure.
totomeasure.
measure. This
This This process
process
process is repeated
isisrepeated
repeated twice, twice,
twice,
while
while attempting to make the measurement process as fast and accurate as possible. The The
while attempting
attempting toto make
make the
the measurement
measurement process
process as as
fast fast
and and accurate
accurate as as possible.
possible. The
illuminance
illuminancevalues
illuminance valuesofof
values ofallall
measuring
all measuring
measuring points are
points
points areaveraged
are totoobtain
averaged
averaged the
theaverage
to obtain
obtain the illuminance
average
average illuminance
illuminance
of the
ofofthe commercial
thecommercial building’s atrium.
building’satrium.
commercial building’s atrium.

2.1.3.
2.1.3.Testing
2.1.3. TestingResults
Testing Results
Results
The
The test resultsare
Thetest
testresults
results areshown
are ininin
shown
shown Table 1.1.1.
Table
Table

Table
Table1.
Table 1.1.Atrium
Atriumillumination
Atrium illuminationmeasurement
illumination measurement
measurementresults.
results.
results.
Time
Time Average
AverageIllumination
Time (lx)
Illumination Daylight
DaylightFactor
(lx)Average Illumination (lx) (DF)
Factor (DF) Outdoor
Daylight Factor (DF) Illumination
Outdoor Illumination
Outdoor (lx)
(lx)
Illumination (lx)
10:00
10:00 968
968 10:00 11.64%
11.64% 8313
8313
968 11.64% 8313
11:00
11:00 876.32
876.3211:00 876.32 11.90%
11.90% 11.90% 7362
7362 7362
12:00
12:00 686.64
686.6412:00 686.64 9.05%
9.05% 9.05% 7588
7588 7588
13:00
13:00 592.4
592.413:00 592.4 11.72%
11.72% 11.72% 5054
5054 5054
14:00
14:00 544.56
544.5614:00 544.56 10.63%
10.63% 10.63% 5125
5125 5125
15:00 397.6 15:00 397.6 11.46% 11.46% 3469 3469
15:00 397.6 11.46% 3469
16:00 299.44 11.14% 2688
16:00
16:00 299.44
299.44 11.14%
11.14% 2688
2688

2.2. Typical Model Building

2.2.1. Software Selection
At present, there is a variety of software with different functions for simulating indoor
daylight in buildings. Common daylight analysis software includes Lightscape, Desktop
Radiance, Daysim, DIVA, Lumen Micro, Ecotect, and Dialux [34]. Since this research
is based on the perspective of parametric design, Rhino + Grasshopper is selected as
the modeling software, assisted by Ladybug + Honeybee, the built-in building physical
environment simulation software in Grasshopper, as the tool for daylight performance
simulation. Its advantages include not only the Radiance + Dayism calculation engine to
ensure the accuracy of the annual daylight and glare simulation but also the convenience
of the parametric modeling function of Grasshopper to adjust the design parameters of
commercial buildings’ atriums, so as to explore their effect on indoor daylight. Finally, the
 as the modeling software, assisted by Ladybug + Honeybee, the built-in building physical
environment simulation software in Grasshopper, as the tool for daylight performance
simulation. Its advantages include not only the Radiance + Dayism calculation engine to
ensure the accuracy of the annual daylight and glare simulation but also the convenience
of the parametric modeling function of Grasshopper to adjust the design parameters of
Sustainability 2022, 14, 7667 5 of 22
commercial buildings’ atriums, so as to explore their effect on indoor daylight. Finally, the
multi-objective optimization software Octopus built into Grasshopper can also be used to
calculate the trade-off between annual daylight and glare simulation to achieve the best
results for the indoor
multi-objective daylight of asoftware
optimization commercial building’s
Octopus built atrium.
into Grasshopper can also be used to
calculate the trade-off between annual daylight and glare simulation to achieve the best
2.2.2. Typical
results for Model Parameter
the indoor Settings
daylight of a commercial building’s atrium.
According to the literature research and the field research of commercial buildings’
2.2.2. in
atriums Typical
Jinan,Model
a modelParameter Settings
of a typical commercial building’s atrium in a cold region is
established in Grasshopper
According (Figure 4).research
to the literature The specific
and design parameters
the field researchare shown in Table
of commercial buildings’
2. atriums in Jinan, a model of a typical commercial building’s atrium in a cold region is
established in Grasshopper (Figure 4). The specific design parameters are shown in Table 2.

Figure
Figure 4. Grasshopper
4. Grasshopper model
model buildbuild image.
image.

Table
Table 2. Typical
2. Typical model
model parameters
parameters (WI =(WI = Well
Well Index;
Index; VT = Visible
VT = Visible light transmittance).
light transmittance).

Atrium Parameters
Atrium Parameters Value Value
Length Length 30 m 30 m
Width Width 30 m 30 m
Height Height 15
15 m (4 floors) m (4 floors)
WI WI 1 1
Area 900 m2
Area 900 m 2
Indoor reflectivity 0.8/0.5/0.2
Indoor reflectivity
Atrium shape
0.8/0.5/0.2 Rectangle
Atrium shape
Skylight ratio Rectangle 0.5
Skylight ratio
Skylight VT 0.5 0.6
Skylight Form
Skylight VT 0.6 Flat skylight
Shading system
Skylight Form 50% coverage fabric shade
Flat skylight
Shading system 50% coverage fabric shade
2.3. Verification
Sustainability 2022, 14, x FOR PEER REVIEW of Daylight Model 6 of 23
2.3. Verification of Daylight
The measured Model
illuminance data will be used for verifying the illuminance simulation
The measured
results illuminance
of the typical modeldata[35],will
sobeasused for verifying
to determine thethe illuminance
reliability simulation
of the typical model
results of the typical
established. Under model
the [35],outdoor
same so as toilluminance
determine the reliabilitythe
conditions, of illuminance
the typical model
of typi-
the typical
established. Under the same outdoor illuminance conditions, the illuminance of the
cal model is simulated on an hourly basis using L + H (Ladybug + Honeybee), and then athen a
model is simulated on an hourly basis using L + H (Ladybug + Honeybee), and
correlationanalysis
correlation analysis between
between thethe illuminance
illuminance value
value is obtained
is obtained fromfrom the simulation,
the simulation, and and
themeasured
the measureddata dataareare conducted
conducted to verify
to verify whether
whether the two
the two are significantly
are significantly relatedrelated
and and
whetherthe
whether theestablishment
establishmentofofthethetypical
typical model
model is is reliable.
reliable. The The specific
specific analysis
analysis is shown in
is shown
Figure
in Figure5).5).

Figure
Figure5.5.Typical
Typicalmodel
modelreliability analysis.
reliability analysis.

Due to the influence of skylight stains and window frames, and the presence of long
hours of artificial lighting and partial shading from other buildings at the atrium site, there
is a certain error between the measured illuminance and the software simulation value;
the Pearson correlation calculated by correlation analysis is 0.955, with sig = 0.01 less than
Sustainability 2022, 14, 7667 6 of 22

Due to the influence of skylight stains and window frames, and the presence of long
hours of artificial lighting and partial shading from other buildings at the atrium site, there
is a certain error between the measured illuminance and the software simulation value;
the Pearson correlation calculated by correlation analysis is 0.955, with sig = 0.01 less than
0.05. The results indicate that there is a significant correlation between the established
typical model daylight and real building daylight in cold regions of China, and subsequent
daylight simulations can be performed.

3. Dynamic Daylight and Glare Simulation

3.1. Investigation on Design Parameters of Atrium Daylight and Light-Environment
Evaluation Index
After the typical model is established, it is necessary to determine the design parame-
ters affecting the quality of light for the study. Common design parameter variables usually
include orientation, window-to-wall ratio, window material, and shading length [36].
Through the analysis of relevant literature research, the design parameters that affect
atrium daylight are analyzed and screened with the specific results shown in Table 3.

Table 3. Research on atrium daylight literature. (Definition of Abbreviations: WI = Well index;

VT = Visible light transmittance; PAR = Plane aspect ratio; SAR = Space aspect ratio; WWR = Window
to wall ratio; DF = Daylight factor; ADF = Average daylight factor; UDI = Useful Daylight Illumi-
nance; DA = Daylight Autonomy; CDA = Continuous Daylight Autonomy; sDA = Spatial Daylight
Autonomy; ASE = Annual Sunlight Exposure; DGP = Daylight glare probability).

Author Year Independent Variable Dependent Variable

B.Calcagni [10] 2004 WI; Skylight VT; Skylight Form DF
Ran Yi [32] 2009 PAR; SAR; WI DF
Jiangtao Du [35] 2011 Atrium Reflectance; PAR ADF
Illumination; DF;
Stanley K.H. Chow [18] 2013 Atrium Size; daylight Control
Energy Consumption
Atrium Size; Skylight VT; Skylight
Abdelsalam Aldawoud [37] 2013 Energy Consumption
Ratio; Climate
Umberto Berardi [7] 2014 Skylight VT; Shading System DF; UDI; DGP
WI; Skylight Form; Atrium Reflectivity;
Mahsan Mohsenin [12] 2015 sDA; ASE
Skylight VT
Mohsen Ghasemi [8] 2015 Atrium Shape; Atrium Size ADF
Milica Vujošević [38] 2017 Atrium Shape; Shading System Energy Consumption
DA; Glare Index;
Wessam El-Abd [6] 2018 Skylight Ratio; Skylight VT
Energy Consumption
Ignacio Acosta [39] 2018 Atrium Height; Skylight VT DF
Francesco De Luca [40] 2018 Skylight Orientation; Skylight VT CDA; UDI
Jie Li [13] 2019 Atrium Shape; Atrium Size; Skylight Ratio sDA; DA
Kareem S.Galal [41] 2019 Skylight VT sDA; ASE; UDI
Energy Consumption; DF;
Omar S.Asfour [31] 2020 WWR; Shading System; Skylight
sDA; ASE
Skylight Form; Skylight Ratio;
Mohamed Marzouk [42] 2020 sDA; ASE; UDI
Skylight Orientation
Mahsa Rastegari [30] 2021 WI; Atrium Size DA; UDI
Zhengyu Fan [33] 2021 Skylight Material; Skylight Ratio DA; UDI
Om Prakash [43] 2021 Atrium Shape; Skylight Orientation DF; Energy Consumption
Atrium Shape; Atrium Inclination;
Lili Dong [44] 2022 DF; Illumination Uniformity
Skylight Size
Mohamed Marzouk [45] 2022 Skylight VT; Skylight Size sDA; ASE

It can be seen from the table that the design parameters that affect atrium daylight
as independent variables are mostly atrium size, skylight ratio, skylight VT, and shading
system, while the daylight indicators in the dependent variables were mostly DF and
illuminance uniformity in earlier years. In recent years, dynamic daylight evaluation
Sustainability 2022, 14, 7667 7 of 22

indexes such as sDA, ASE, and UDI are frequently used, while glare evaluation often takes
DGP as the evaluation index.
Therefore, the variable setting of this study has taken the independent variables and
dependent variables selected in these studies into full consideration, so as to achieve a
more precise and comprehensive research conclusion.

3.2. Determination of Design Parameters and Variables Affecting Atrium Daylight

3.2.1. Design Parameters of Atrium
Atrium design parameters are the main components of atrium space. In recent years,
there have been increasing studies on the optimization of atrium geometry, but the daylight
performance has not been fully studied, and such research on daylight performance usually
focuses on fixed architectural geometry [36]. The correct use of building design parameters,
as well as other elements such as shading, energy efficient glazing, room geometry, and
building systems, will significantly reduce building energy consumption and improve
building physical performance [46]. Common types of atrium geometries include circular,
rectangular, and triangular, and different floor plans affect the amount of daylight entering
the building. Additionally, the height of the atrium has an unavoidable effect on the
incoming daylight, with WI or well index, which is related to the floor number, being
regarded as an important variable [30].
First, the plane shape of the atrium is the design parameter that needs to be considered
most in the early stage of the design. Once it is determined, it cannot be easily changed in
the later stage. Now, its design is mostly based on the needs about shape and appearance,
while it is rarely considered in combination with daylight performance. Second, the profile
inclination of the atrium is also one of the factors affecting the daylight of the atrium.
Daylight performance was measured in terms of atrium proportions as defined by the Well
Index (WI) used to characterize atriums, a quantifier describing atrium proportions. The
equation is WI = H(W + L)/2 WL. According to this equation, the well index (WI) of a
square atrium is measured by the length, width, and height of the atrium [12]. Based on
the common commercial atrium design dimensions in China, a range of atrium dimensions
is set, and the effects of different WI on atrium lighting under different dimensions are also
studied. Third, the indoor reflectivity of the atrium is also one of the important factors
affecting daylight. According to the requirements of Chinese regulations, ceilings, walls,
and floors have different reflectance value ranges. Therefore, the atrium design parameters
of size and reflectivity are set as the independent variables for the research (Table 4).

Table 4. Atrium design parameter values.

Atrium Design Parameter Value

Length 10–50 m
Width 10–50 m
Atrium size (AS)
Height 10–30 m
WI 0.2–3.0
Atrium inclination (AI) AI 60–120◦
Roof 0.60–0.90
Indoor reflectivity (IR) Wall 0.30–0.80
Floor 0.10–0.50

3.2.2. Design Parameters of Daylight Roof

The setting of external windows in a building plays a decisive role in daylight, and the
daylight performance of a window system largely depends on factors such as window type
and size, window orientation, and window opening ratio [47]. In atrium designs, window
systems often come in the form of skylights. The skylight has a crucial impact on daylight,
energy consumption, and the visual comfort of the atrium. The selection of its design
parameters is part of the basic decision in the early design stage. Usually, parameters such
as skylight form, orientation, and glass size in skylight design [27,48] are difficult to adjust
Sustainability 2022, 14, 7667 8 of 22

later. Therefore, the design of daylight must be carefully studied and become part of the
overall design process, with consideration of multiple aspects at the same time.
First, the roof form. Skylights usually adopt a flat-top roof, single-slope roof, double-
slope roof, or four-slope roof, and changing the slope of the skylights will also affect the
effect of indoor daylight. Second, the window opening ratio of the skylight, that is, the
ratio of the skylight area to the area of the atrium roof, has a crucial impact on indoor
daylight. The larger the window opening ratio, the better the indoor illumination but the
more serious the glare, and vice versa. Third, another important design parameter is the
transmittance of skylight glass, which directly affects the luminous flux of sunlight entering
the room through the glass, and has a significant effect on indoor daylight. The specific
range of daylight roof design parameters is shown in Table 5.

Table 5. Skylight design parameter values.

Skylight Design Parameter Value

Skylight Ratio (SR) 0.10–0.90
Skylight VT (SV) 0.10–0.90

3.2.3. Design Parameters of the Shading System

While the atrium skylight brings natural daylight, it often also causes more solar
radiation, giving rise to indoor overheating. Therefore, the atrium skylight is usually
equipped with a shading system to prevent overheating and glare in summer. Yet again,
excessive shading can reduce the indoor illuminance. When designing a skylight, it is
necessary to take both the indoor cooling effect and the indoor illuminance into account.
Common building shading systems include slatted shading, louvers and roller shutters [49]
(Figure 6). Louver shading can protect building users from direct solar glare, and
Sustainability 2022, 14, x FOR PEER REVIEW 9 of louvers
23
are composed of multiple horizontal, vertical, or slanted slats of different shapes and surface
finishes [50]. Louvers can be external or internal; they are used to partially or completely
block the sun
completely rays,
block theand
sun the
rays,size
andparameters of the shutters
the size parameters as well as well
of the shutters the shading angle are
as the shad-
controlled
ing in controlled
angle are studies [51,52]. Shading
in studies fabrics
[51,52]. are widely
Shading used
fabrics are to shade
widely usedexterior
to shadewindows
exte- to
improve
rior visual
windows and thermal
to improve visualcomfort, control
and thermal the amount
comfort, controlofthe
solar radiation,
amount of solarand enhance
radia-
building
tion, and interior
enhance privacy.
buildingThe mainprivacy.
interior optical The
properties characterizing
main optical propertiessunshade fabrics are
characterizing
sunshade fabrics are visible
visible transmittance transmittance
(VT) and (VT) and
coverage [53]. The coverage [53]. The
specific design specific design
parameters of thepa-
shading
rameters
system areof the
shownshading system
in Table 6. are shown in Table 6.

Louverand
Figure6.6.Louver
Figure andfabric
fabric shading.
shading.

Shadingsystem
6. Shading
Table 6. systemdesign
design parameter
parameter values.
values.

Shading System
Shading SystemDesign
DesignParameter
Parameter ValueValue
Shade type
Shade type louver shade; fabric shade
louver shade; fabric shade
Louver
Louverwidth
width(LW)
(LW) 50–300 mm
50–300 mm
Louver
Louverinclination
inclination(LI)
(LI) −60–60◦
−60–60°
Fabric
Fabric coverage(FC)
coverage (FC) 0.10–0.90
0.10–0.90
FabricVT
Fabric VT(FV)
(FV) 0.10–0.90
0.10–0.90

3.3. Dynamic Daylight and Glare Evaluation Index

3.3.1. Dynamic Daylight Evaluation Index
With the development of research on architectural daylight, the traditional static day-
light evaluation indicators have been unable to meet the design requirements of architec-
tural daylight, and dynamic daylight evaluation has gradually become an important in-
dicator of the quality of natural daylight in buildings. The dynamic daylight evaluation is
Sustainability 2022, 14, 7667 9 of 22

3.3. Dynamic Daylight and Glare Evaluation Index

3.3.1. Dynamic Daylight Evaluation Index
With the development of research on architectural daylight, the traditional static
daylight evaluation indicators have been unable to meet the design requirements of archi-
tectural daylight, and dynamic daylight evaluation has gradually become an important
indicator of the quality of natural daylight in buildings. The dynamic daylight evaluation
is mainly done by loading the typical climate data for the area where the research object
is located throughout the year, constructing the Perez sky model, and simulating and
calculating the building’s annual (8760 h) daylight simulation, glare, and other daylight
problems, so that the index can more truly reflect the natural daylight situation of the
building throughout the year. Compared with the traditional static daylight evaluation
index, dynamic daylight indexes based on climate-based daylight modeling can yield a
building’s year-round daylight performance. Climate-based daylight modeling (CBMD)
allows for quantitative performance predictions based on local weather data. The resultant
annual illuminance records are reduced to s comprehensive annual index [54].
The dynamic daylight evaluation index has been widely used in the recent research
on daylight performance, such as DA, sDA, UDI, and ASE. The DA index was originally
proposed by the Swiss Electric Association in 1989 and was further developed to measure
the percentage of occupied hours [55]. UDI is defined as the illuminance falling in the
range of 100–2000 lx [56]. Yu Bian et al. investigated the daylight performance index
in Guangzhou, engaging in a comparative analysis of DA and DF, and compared the
DA and DF values of four main facades of a side daylight room in Guangzhou through
field measurements; they found that the actual tested DA and DF data deviated from the
simulated values and concluded that DA was a more applicable daylight performance
index than DF [57]. This annual daylight simulation evaluation index uses DA as well as
sDA to evaluate the commercial atrium indoor daylight. On account of the high illuminance
value and good daylight effect of the atrium, the sDA threshold can be set to 1000 lx, i.e.,
sDA1000, 50%, and the reference level of sDA is shown in Table 7.

Table 7. sDA rating evaluation.

sDA Level Value

Inappropriate <0.55
Acceptable 0.55–0.75
Satisfactory >0.75

3.3.2. Glare Evaluation Index

Visual comfort is an important concern in interior daylight design, which is mainly
related to sunlight intensity. People are more tolerant of uncomfortable glare from sunlight
than from artificial lighting. The external window arrangement especially will affect the
subjective impression of glare because daylight glare mainly comes from windows [58].
Regarding daylight glare, different glare indices have been proposed and analyzed, but
the luminance-based terms and metrics using vertical illuminance are physically different
and therefore cannot quantify daylight discomfort glare in the same way. Simulation
methods have been developed and are able to quantify glare using existing evaluation
metrics such as daylight glare probability [28], and currently common glare evaluation
metrics include DGI, UGR, CGI, VCP, and DPG [53,58,59]. Among them, daylight glare
probability or DGP is considered a reasonable index of the daylight discomfort glare, so the
glare evaluation aspect of the dynamic evaluation index is evaluated by DGP. The concept
of DGP, proposed in 2006 by Jan Wienold of Fraunhofer Institute for Solar Energy Systems
(ISE) and Jens Christoffersen of Danish Building Research Institute (SBI), considers both
the overall brightness of the field of view and the effects of glare and contrast [60,61].
Therefore, the glare evaluation index in this simulation study uses the discomfort glare
probability (DGP), and the design outdoor illuminance is uniformly set to 50,000x. DGP
Sustainability 2022, 14, 7667 10 of 22

is used to measure the glare index caused by daylight glare, and the rating evaluations of
DGP is shown in Table 8. The equation is as follows [62]:

L2s,i ωs,i
DGP = 5.87 × 10−5 + Ev + 9.18 × 10−2 log (1 + ∑ )
i Ev1.87 Pi2

where Ev is the vertical eye illuminance [lux]: Ls the luminance of source [cd/m2 ]; ω s is the
solid angle of source; P is the position index.

Table 8. DGP glare rating evaluations.

DGP Level Value

Imperceptible <0.35
Perceptible 0.35–0.40
Disturbing 0.40–0.45
Intolerable >0.45

3.4. Simulation Process

After determining the design parameters under study and the evaluation indexes for
the simulation study, the next step is to bring the design parameter battery into Grasshopper
and run the L + H (Ladybug + Honeybee) built-in daylight simulation engine
Sustainability 2022, 14, x FOR PEER REVIEW 11 to obtain
of 23
different lighting indexes according to the 14 design parameters determined in the previous
section grouped for simulation. This process was repeated until all single variables were
analyzed, and the corresponding data were subsequently obtained (Figure 7).

Figure 7. The
Figure The simulation
simulationprocess
processdiagram.
diagram.

4.
4. Results andDiscussion
Results and Discussion
According
According totothe
thethree
threemain
maintypes
typesof of design
design parameters
parameters selected
selected (atrium
(atrium designdesign
pa- pa-
rameters, skylightdesign
rameters, skylight design parameters,
parameters, shading
shading design
design parameters)
parameters) (Tables (Tables
4–6), L +4–6),
H (La-L + H
(Ladybug + Honeybee)
dybug + Honeybee) waswas used
used to simulate
to simulate dynamic
dynamic daylight
daylight and glare,
and glare, andcorre-
and the the corre-
sponding
sponding daylight evaluation
evaluation index
index data
data were
were obtained;
obtained;then
thenSPSS
SPSSwas
wasused
usedtotoanalyze
analyze the
the correlation
correlation of each
of each parameter.
parameter.

4.1.
4.1. Atrium DesignParameters
Atrium Design ParametersSimulation
Simulation
4.1.1.
4.1.1. Atrium SizeSimulation
Atrium Size SimulationAnalysis
Analysis
In this section,the
this section, thedimensions
dimensionsofof thethe atrium
atrium areare explored,
explored, andand the length,
the length, width,width,
height,
height, and WI WIofofthe
theatrium
atriumarearesimulated
simulated separately
separately forfor daylight
daylight simulation.
simulation. The typical
The typical
reference model isis30
reference model 30mmininlength,
length,3030mm in in width,
width, 15 15 m height,
m in in height,
andand 0.5WI.
0.5 in in Each
WI. Each
parameter study only controls
parameter controls univariate
univariateforforsimulation,
simulation,and
andthe
thespecific
specificsimulation
simulationpro-
process
cess results
and and results arefollows
are as as follows (Figures
(Figures 8 and
8 and 9). 9).
As can
can be
be seen
seenfrom
fromthetheline
linegraph, thethe
graph, length, width,
length, andand
width, height of the
height of atrium size size
the atrium
were not significantly correlated with sDA, and WI was significantly correlated
were not significantly correlated with sDA, and WI was significantly correlated with sDA; with sDA;
only the
only the atrium
atrium length
lengthwaswasnot
notsignificantly
significantly correlated with
correlated DGP.
with DGP.
 height, and WI of the atrium are simulated separately for daylight simulation. The typical
reference model is 30 m in length, 30 m in width, 15 m in height, and 0.5 in WI. Each
parameter study only controls univariate for simulation, and the specific simulation pro-
cess and results are as follows (Figures 8 and 9).
As can be seen from the line graph, the length, width, and height of the atrium size
Sustainability 2022, 14, 7667 11 of 22
were not significantly correlated with sDA, and WI was significantly correlated with sDA;
only the atrium length was not significantly correlated with DGP.

Sustainability 2022, 14, x FOR PEER REVIEW 12 of 23

Sustainability 2022, 14, x FOR PEER REVIEW 12 of 23

Figure 8.
Figure 8. Atrium
Atriumsize
sizediagram.
diagram.

Figure 9. Simulation results for atrium size.

Figure 9. Simulation results for atrium size.

4.1.2. Atrium
Figure Inclination
9. Simulation Simulation
results for atrium size. Analysis
4.1.2.In
Atrium Inclination
this section, Simulation
the atrium Analysis
profile inclination is explored, and the daylight simulation
is 4.1.2.
In Atrium
performed Inclination
for
this section, thetheatriumSimulation
atrium profileAnalysis
profile inclinationis variable.
inclination explored, The atrium
and the areasimulation
daylight is controlled to
be the In
is performedthis section,
same, for
and thethe theprofile
atriumatrium profile
profile inclination
inclination
inclination isis
explored,
variable.
angle Theto
taken andbethe
atrium daylight
area
60–120° simulation
is controlled
and testedtoat
be10° in-
theis performed
same, and for
the the
profileatrium profile
inclination inclination
angle is variable.
taken to be The
60–120 ◦ andarea
atrium testedis at 10 ◦ intervals
controlled to
tervals (Figure 10); the simulation process and results are as follows (Figure 11).
be the10);
(Figure same,
theand the profile inclination
simulation angle is taken to be 60–120° and
11).tested at 10° in-
As shown by the lineprocess
graph,andthe results
atriumare as follows
inclination (Figure
angle was significantly correlated
tervals
As (Figureby
shown 10);
the the simulation
line graph, process
the atriumand results areangle
inclination as follows
was (Figure 11). correlated
significantly
with both sDA and
As shown by the DGP.
line graph, the atrium inclination angle was significantly correlated
with both sDA and DGP.
with both sDA and DGP.

Figure
Figure 10.
10.
Figure
Atrium
10.Atrium
inclination
Atrium inclination
inclination diagram.
inclination
inclination inclination diagram.
diagram.
 Sustainability 2022, 14, 7667 12 of 22
Figure 10. Atrium inclination inclination diagram.

Sustainability 2022, 14, x FOR PEER REVIEW 13 of 23

The
Sustainability 2022, 14, x FOR PEER typical reference models of roof, wall, and floor reflectance are set to 0.8, 13
REVIEW 0.5,
of and
23 0.2,
Sustainability 2022, 14, x FOR PEERFigure
REVIEW11. Simulation results of atrium inclination. 13 of 23
and each parameter is studied by controlling only a single variable for simulation
Figure 11. Simulation results of atrium inclination. (Figure
12).
4.1.3. Indoor Reflectivity Simulation Analysis
From
The
4.1.3. thisthe
typical
Indoor
In line graph,
reference
Reflectivity
section, the it can
models be of
seen
of roof,
Simulation
reflectance thethat
wall, and all three
floor
Analysis
interior reflectances
reflectance
materials ofare are
thesetatriumsignificantly
to 0.8, 0.5,
is and 0.2,corre-
investigated,
The
lated
and typical
with
each thereference
DGP,
parameter ismodels
while ofby
only
studied roof,
the wall,reflectivity
roof
controllingand floor
only a reflectance
is not
single are for
set simulation
significantly
variable to 0.8, 0.5, and
correlated 0.2,
with
(Figure the
and the
In reflectance
this of the
section, theroof, walls, and floor
reflectance of of the
the atriummaterials
interior are simulated of for
the daylight.
atrium The
is investig
and
12).
sDA, each
and parameter
the wallmodelsis studied
and floor by controlling
reflectivities only a single variable for simulation (Figure
typical reference of roof, wall, andare significantly
floor reflectancecorrelated with
are set to 0.8, 0.5,the
andsDA.
0.2, and
12).the
and reflectance
From of the
the line graph, roof, walls,
that and floor of the atrium are simulated for day
each parameter is studied it
bycan be seen
controlling onlyall three
a singlereflectances are significantly
variable for corre-
simulation (Figure 12).
latedFrom the DGP,
with the line graph,
while itonly
canthe
be roof
seen reflectivity
that all three reflectances
is not are significantly
significantly corre-
correlated with the
From
lated the line graph, itonly
can be seen that all three reflectances are significantly correlated
sDA, and the wall and floor reflectivities are significantly correlated with the sDA. the
with the DGP, while the roof reflectivity is not significantly correlated with
with
sDA,the DGP,
and while
the wall only
and thereflectivities
floor roof reflectivity is not significantly
are significantly correlatedcorrelated with the sDA,
with the sDA.
and the wall and floor reflectivities are significantly correlated with the sDA.

Figure 12. Simulation results of indoor reflectivity.

Figure
4.2. 12.Simulation
Skylight
Figure 12. Simulation results of
Design Parameters
results of indoor reflectivity.
Simulation
indoor reflectivity.
Figure 12. Simulation results of indoor reflectivity.
4.2.1.
4.2. Skylight
4.2.Skylight RatioParameters
SkylightDesign
Design Simulation
Parameters Analysis
Simulation
Simulation
4.2. Skylight
InSkylight
this Design
section, Parameters Simulation
4.2.1.
4.2.1. Skylight Ratiothe
Ratio skylightAnalysis
Simulation
Simulation ratio is explored and tested at 0.1 intervals, and the spe-
Analysis
4.2.1.
cific Skylight Ratio
simulation processSimulation
and Analysis
results
InInthis
thissection,
section,the
theskylight ratioare
skylightratio as follows
isis explored
explored and
and(Figures
tested at13
0.1and 14). and
intervals,
intervals, and the
the spe-
specific
In
simulation this section,
process
cific simulation the skylight
and results
process ratio
are as
and results is explored
arefollows and
(Figures
as follows tested at
13 and
(Figures 0.1 intervals,
14).14).
13 and and the spe-
cific simulation process and results are as follows (Figures 13 and 14).

Figure 13. Skylight ratio diagram.

Figure 13. Skylight ratio diagram.
Figure 13. Skylight ratio diagram.
Figure 13. Skylight ratio diagram.

Figure 14.Simulation
Figure14. Simulation results of the
results of the skylight
skylightdesign
designparameters.
parameters.
Figure 14.14.
Figure Simulation
Simulationresults
results of theskylight
of the skylightdesign
design parameters.
parameters.
4.2.2. Skylight VT Simulation Analysis
4.2.2. Skylight
4.2.2. SkylightVTVTSimulation Analysis
Simulation Analysis
In this section, the visible light transmittance of the skylight is explored and tested at
0.1In In thissection,
this
intervals,section, the
the
and the visiblesimulation
visible
specific light
lighttransmittance
transmittance
process andof of
the skylight
the
results are asisfollows
skylight explored and tested
is explored
(Figure and at
tested
13). The at
0.1 intervals,
0.1linear
intervals, and the specific
and thebetween
relationship simulation
specificskylight
simulation process
process
VT and and results
andratio
skylight are
results as follows
are asas
is similar, (Figure
follows 13).
shown(Figure The
13). The
by the line
linear
graph.
linear relationship between
Both designbetween
relationship skylight
parameters VTVTand
andskylight
are significantly
skylight ratio
correlated
skylight iswith
ratio similar,
sDA as shown
and
is similar, DGP.
as by theby
shown line
the line
graph. Both design parameters are significantly correlated with sDA and DGP.
graph. Both design parameters are significantly correlated with sDA and DGP.
 Sustainability 2022, 14, 7667 13 of 22

4.2.2. Skylight VT Simulation Analysis

In this section, the visible light transmittance of the skylight is explored and tested at
0.1 intervals, and the specific simulation process and results are as follows (Figure 13). The
linear relationship between skylight VT and skylight ratio is similar, as shown by the line
graph. Both design parameters are significantly correlated with sDA and DGP.
Sustainability 2022, 14, x FOR PEER REVIEW 14 of 23

4.3. Shading System Design Parameters Simulation

Sustainability 2022, 14,
Sustainability x FOR
2022, 14, xPEER
4.3.1.
REVIEW
FOR PEER
Louver
REVIEW
Width Simulation Analysis 14 of 14
23 of 23
50–300This
mm, and the test is conducted every 50 mm, and the specific simulation process is
section explores the louver width in the louver shading system, where the typical
asreference
follows (Figure 15). ◦
model louver inclination is 90 , the louver width variable takes the range of
50–300
50–300 mm,
50–300mm,andand
mm, andthe
the thetest
test istestisisconducted
conducted every
everyevery
conducted 50mm,
50 mm,
50 mm,the
and and
and thespecific
specific
specific
the simulation
simulation process
simulation process
is is is
process
as as
follows
follows(Figure 15).
(Figure 15).
as follows (Figure 15).

Figure 15. Louver width diagram.

Figure
Figure15. 15.
Louver width
Louver diagram.
width diagram.
4.3.2. Louver
Figure 15. Inclination
Louver width Simulation Analysis
diagram.

4.3.2. This
4.3.2.
Louver section
Louver explores
Inclination
Inclination the louver
Simulation
Simulation inclination in the louver shading system, in which
Analysis
Analysis
4.3.2. Louver Inclination Simulation Analysis
the This
typical
This reference
section model
exploresthethe louver width is 200 mm, the shading
louver inclination variable takes
section
This explores
section explores thelouver
louver inclination
inclination
louver in
in the
inclination inthe
thelouver
louver louvershading system,
system,
shading in
inwhich
in which
system, whichthe
the value
thetypical
typical range
reference of 30–150°
model and
louver is tested
width every
isis200 15°, and the specific simulation process and
reference
the typical model
reference louver
model width
louver width ismm,
200 mm,
200 the
mm,thelouver
louver
the inclination
louverinclinationvariable
inclination takes
variable
variable takes
takesthe
isvalue
the as follows
value range (Figure
rangerange
of30–150
of 30–150°16).and is tested
◦ tested every
every 15°,◦
15 and andthe
,15°, thespecific simulation
specific simulation process
process andand is as
the value of 30–150° and is tested every and the specific simulation process and
is as From
follows
follows the line
(Figure
(Figure graph
16).
16).
is as follows (Figure 16). (Figure 17), it can be seen that the relationship between louver
From
inclination
From theangle
From line
the graph
and
theline
line (Figure
sDA
graph
graph is 17), it
parabolic
(Figure
(Figure canit
17),
17), be
canseen
itand
can there that
be seen
be seenis the
no
that
that relationship
significant between
linear
therelationship
the relationship louver
correlation;
between
between thus,
louver
louver
inclination
louver
inclination angle
shading
inclination and
angle
angle sDA
hasand
and is
sDA parabolic
difficulties
sDAis is parabolicand
parabolic there
in the subsequent
andthere
and is no significant
thereisisstudy. linear
nosignificant
no significant correlation;
linear
linear thus,
correlation;
correlation; thus,thus,
louver
louvershading
louvershading hashas
shading difficulties in the
hasdifficulties
difficulties insubsequent
in the
the subsequent
subsequent study. study.
study.

Figure16.16.
Figure TheThe louver inclination diagram.
Figure 16.louver inclination
The louver diagram.
inclination diagram.
Figure 16. The louver inclination diagram.

Figure 17. 17.

Figure
FigureThe
17.simulation
The
The results
simulation
simulation of louver
results
results of shading
of louver
louver system.
shading
shading system.
system.
Figure 17. The simulation results of louver shading system.
4.3.3. Fabric
4.3.3.
4.3.3. Coverage
Fabric
Fabric Coverage Simulation
Coverage Simulation
Simulation Analysis
Analysis
Analysis
4.3.3. Fabric
This section
This Coverage
explores
Thissection
section Simulation
the
explores
explores fabric
thefabric
the Analysis
coverage
fabric in theinfabric
coverage
coverage shading
in the
the fabric
fabric system,
shading
shading where the typ-
system,
system, where where
the typ-the
ical reference
typical
ical model
reference
reference fabric
model
model VT
fabric is
fabricVT0.6VTand
is is
0.6 the
0.6
and fabric
and
the coverage
the fabric
fabric variable
coverage
coverage takes values
variable
variable
This section explores the fabric coverage in the fabric shading system, where the takes in
takes
valuesthe
values
in in
the typ-
range
the of 0.1–0.9
range
range of of and is
0.1–0.9
0.1–0.9 andtested
and
is isattested
tested 0.1atintervals,
at
0.1 0.1 and the
intervals,
intervals, and specific
and
the thesimulation
specific
specific process
simulation
simulation and
process re-
process
and and
re-
ical reference model fabric VT is 0.6 and the fabric coverage variable takes values in the
sults are asare
results
sults follows
as (Figures
as follows
follows 18 and
(Figures
(Figures 181819).
and19).
and 19).
range of 0.1–0.9 and is tested at 0.1 intervals, and the specific simulation process and re-
sults are as follows (Figures 18 and 19).

Figure 18. Fabric

Figure coverage
18. Fabric diagram.
coverage diagram.
 Figure 17. The simulation results of louver shading system.

4.3.3. Fabric Coverage Simulation Analysis

This section explores the fabric coverage in the fabric shading system, where the typ-
Sustainability 2022, 14, 7667
ical reference model fabric VT is 0.6 and the fabric coverage variable takes values in the
14 of 22
range of 0.1–0.9 and is tested at 0.1 intervals, and the specific simulation process and re-
sults are as follows (Figures 18 and 19).

Sustainability 2022, 14, x FOR PEER REVIEW 15 of 23

Figure 18. Fabric coverage diagram.

Figure 18. Fabric coverage diagram.

Figure 19. The simulation results for the fabric shading system.
Figure 19. The simulation results for the fabric shading system.
4.3.4. Fabric VT Simulation Analysis
4.3.4.InFabric VT Simulation
this section, Analysis
the visible light transmittance of the skylight is explored and tested
at 0.1In this section,
intervals, the specific
and the visible light transmittance
simulation of the
process and skylight
results are is
asexplored and tested
follows (Figure 18). at
0.1 intervals,
From and the
the line graph, it isspecific simulation
clear that process
the coverage andshading
of fabric results is
are as followscorrelated
significantly (Figure 18).
with
FromVT thewith
lineboth sDA
graph, and
it is DGP,
clear sothe
that fabric shading
coverage ofisfabric
moreshading
suitable is
forsignificantly
the next orthogonal
correlated
test as well as the sensitivity analysis than louver shading.
with VT with both sDA and DGP, so fabric shading is more suitable for the next orthogo-
nal test as well as the sensitivity analysis than louver shading.
4.4. Sensitivity Analysis of Design Parameters
SensitivityAnalysis
4.4. Sensitivity analysis of
can determine
Design the most important parameters related to building
Parameters
performance, and the focus of the subsequent sustainable building design and optimization
Sensitivity analysis can determine the most important parameters related to building
concentrate can be concentrated on this part of the design parameters. The adoption of
performance, and the focus of the subsequent sustainable building design and optimiza-
sensitivity analysis in the early stage of design can improve the efficiency of building
tion concentrate can be concentrated on this part of the design parameters. The adoption
performance optimization [19,63]. Correlation analysis and multiple linear regression
of sensitivity
equations are analysis
commonly in used
the early
datastage of design
analysis methods,canand
improve the efficiency
the standardized of building
regression
performance
coefficient optimization
(SRC) can provide [19,63]. Correlation
the impact analysis design
of architectural and multiple
parameterslinearon regression
indoor
equations are commonly used data analysis methods, and the standardized
daylight. Ranking sensitivities of key parameters is also informative for design strategies. regression
coefficient an
Combining (SRC) can provide
appropriate the impact
sensitivity program ofwith
architectural design parameters
building simulation on indoor
software offers an
daylight.and
effective Ranking
valuablesensitivities of keythe
tool for ranking parameters is also informative
design parameters according to fortheir
design strategies.
importance
Combining
for an appropriate
indoor daylight in a shortsensitivity
time [64–67]. program with building
Paulo Filipe de Almeida simulation softwareetoffers
Ferreira Tavares al.
an effective
utilized and valuable
sensitivity analysis totool for ranking
consider the design
the indoor thermalparameters
performanceaccording to their
changes caused byim-
different
portancetypes of exterior
for indoor walls, in
daylight roofs, glazed
a short windows,
time [64–67].and shading,
Paulo Filipe anddetoAlmeida
determine the
Ferreira
degree
Tavaresofet influence of each
al. utilized parameter
sensitivity [68]. Hangxin
analysis Li et al.
to consider theproposed a methodperformance
indoor thermal of multi-
stage
changessensitivity
causedanalysis to identify
by different typesthe key design
of exterior parameters
walls, for design
roofs, glazed optimization.
windows, The
and shading,
key building design parameters were subsequently optimized using
and to determine the degree of influence of each parameter [68]. Hangxin Li et al. pro- a genetic algorithm
to minimize
posed the optimization
a method of multi-stage objective [69]. Before
sensitivity analysisthetosensitivity
identify the analysis, the correlation
key design parameters
analysis of each atrium design parameter was first conducted
for design optimization. The key building design parameters were subsequently to screen out the design opti-
parameters
mized using with significant
a genetic correlations
algorithm on the atrium
to minimize daylight quality
the optimization (annual
objective [69].daylight
Before the
and anti-glare level) for the subsequent study (Table 9).
sensitivity analysis, the correlation analysis of each atrium design parameter was first con-
The correlation analysis is carried out for each design parameter. After excluding the
ducted to screen out the design parameters with significant correlations on the atrium
design parameter variables of no obvious significance, the result is that the fabric shading
daylight quality (annual daylight and anti-glare level) for the subsequent study (Table 9).
system was selected as the study object, and WI, Atrium inclination, Wall reflectivity, Floor
reflectivity, Skylight ratio, Skylight VT, and fabric shading system parameter variables
Table 9. Correlation analysis of atrium parameters. (AS = Atrium size; WI = Well index; AI = Atrium
were obtained, where the WI parameter involved multivariate changes and affected the
inclination; RR = Roof reflectivity; WR = Wall reflectivity; FR = Floor reflectivity; SR = Skylight ratio;
atrium area change so the WI variable was not considered; the following processes include
SV = Skylight visible transmittance; LW = Louver width; LI = Louver inclination; FC = Fabric
a orthogonal experimental design using SPSS to carry out random sampling combination
coverage; FV = Fabric visible transmittance), (* means that the sig. of the parameter with sDA and
to obtain corresponding indicators of daylight, a multiple linear regression analysis to
DGP are less than 0.05, i.e., significantly correlated).
calculate the regression coefficient of each design parameter to analyze the degree of
sDA DGP
Design Parameter
Pearson Sig. Pearson Sig.
Length 0.298 0.626 0.852 0.067
Width 0.830 0.082 0.954 0.012
Sustainability 2022, 14, 7667 15 of 22

influence of the different design parameter variables on the annual daylight and glare in
commercial buildings’ atriums. A total of 81 sets of parameter combinations are obtained
from the orthogonal design and are further processed by L + H (Ladybug + honeybee) to
simulate annual daylight and glare in order to obtain the dependent variables sDA and
DGP. The data will be brought into SPSS to calculate the results of the multiple linear
regression equation:
Y = B0 + β1 X1 + β2 X2 + . . . + βn Xn
B0 is the constant term, β1 , β2 , β3 , . . . , βn is called Y corresponding to X1 , X2 , X3 , . . . ,
Xn regression coefficient.
After the simulation, the data results were analyzed by multiple linear regression and
the following results were obtained.

Table 9. Correlation analysis of atrium parameters. (AS = Atrium size; WI = Well index; AI = Atrium
inclination; RR = Roof reflectivity; WR = Wall reflectivity; FR = Floor reflectivity; SR = Skylight
ratio; SV = Skylight visible transmittance; LW = Louver width; LI = Louver inclination; FC = Fabric
coverage; FV = Fabric visible transmittance), (* means that the sig. of the parameter with sDA and
DGP are less than 0.05, i.e., significantly correlated).

sDA DGP
Design Parameter
Pearson Sig. Pearson Sig.
Length 0.298 0.626 0.852 0.067
Width 0.830 0.082 0.954 0.012
AS
Height −0.842 0.074 −0.996 0
WI * −0.927 0.023 −0.879 0.049
Atrium design parameter
AI AI * 0.916 0.004 0.998 0
RR 0.872 0.128 0.966 0.034
IR WR * 0.977 0.001 0.999 0
FR * 0.988 0.002 1.000 0
SR SR * 0.911 0.001 0.989 0
Skylight design parameter
SV SV * 0.953 0 1.000 0
LW * −0.971 0.001 −0.986 0
Louver
LI −0.044 0.91 −0.892 0.001
Shading design parameter
FC * −0.964 0 −1.000 0
Fabric
FV * 0.981 0 1.000 0

4.4.1. sDA Multiple Regression Equation

After the orthogonal test and the multiple linear regression calculation, the linear
regression equation of sDA is:

Y = −114.907 + 0.902X1 + 17.228X2 − 11.448X3 + 77.749X4 + 90.823X5 − 36.707X6 + 13.739X7

According to the analysis of the results of the following graphs (Tables 10 and 11;
Figure 20), X1 is Atrium inclination, X4 is Skylight ratio, X5 is Skylight VT, X6 is Fabric
coverage, and the sig of these variables are all less than 0.05, indicating that these parameters
are significantly correlated in the regression equation. Meanwhile, X2 is Wall reflectivity, X3
is Floor reflectivity, and X7 is Fabric VT, all of which have sig greater than 0.05, indicating
that they are not significantly correlated in the regression equation; VIF < 5 indicates
that there is no multicollinearity between the parameters. The model residuals, which
basically obeyed a normal distribution, indicated that the error of this equation was within
a reasonable range. Therefore, the linear regression equation established by the model is
statistically significant.
SPSS software was used to fit the multiple linear regression and the coefficient of the
model fit; R2 = 0.778, indicating a good model fit, and DW = 2.117, indicating that there is
no correlation between the independent variables in this model, i.e., a valid regression.
 Table 10. The sDA multiple linear regression model.

Adjusted R Durbin-
Model R R Square Sig.
Square Watson
sDA
Sustainability 2022, 14, 7667 0.882 0.778 0.757 2.117 16 of 22 0.000

Table 11. The sDA multiple linear regression equation analysis. (AI = Atrium inclination; WR
Table 10. The sDA multiple linear regression model.
reflectivity; FR = Floor reflectivity; SR = Skylight ratio; SV = Skylight visible transmittance
Fabric coverage; FV = Fabric visible transmittance). Adjusted R Durbin-
Model R R Square Sig.
Square Watson
Unstandardized
sDA 0.882 0.778 0.757 2.117 0.000
Standardized Collinearity Statis
Coefficients
Model Coefficients t Sig.
Table 11. TheStd.
sDA multiple linear regression equation analysis. (AI = Atrium inclination; WR = Wall
B reflectivity; FR = Floor reflectivity;Beta Tolerance
SR = Skylight ratio; SV = Skylight visible transmittance; FC = Fabric
V
Error
coverage; FV = Fabric visible transmittance).
(Constant) −114.907 16.04 −7.164 0
AI 0.902 Coefficients
Unstandardized 0.114 Standardized 0.436 7.913 Sig. 0 Collinearity Statistics
1 1
Model t
WR B 17.228 Std. Error 14.384 Coefficients Beta
0.066 1.198 0.235Tolerance 1VIF 1
(Constant)
FR −114.907
−11.448 16.04 17.867 −0.035 − 7.164
−0.641 0 0.524 1 1
AI 0.902 0.114 0.436 7.913 0 1 1
SRWR 77.749 14.384 9.097
17.228 0.066 0.471 1.198 8.546 0.235 0 1 11 1
SVFR −11.448
90.823 17.867 9.097 − 0.035 0.551 − 0.641 9.983 0.524 0 1 1 1 1
SR 77.749 9.097 0.471 8.546 0 1 1
FCSV −36.707 9.097 9.097
90.823 0.551 −0.223 9.983 −4.035 0 0 1 11 1
FVFC −36.707
13.739 9.097 9.097 −0.223 0.083 −4.035 1.51 0 0.135 1 11 1
FV 13.739 9.097 0.083 1.51 0.135 1 1

Figure 20. The sDA Histogram of the model’s residual distribution and P-P diagram of the model’s
Figure 20. The sDA Histogram of the model’s residual distribution and P-P diagram of the m
normalised residuals.
normalised residuals.
4.4.2. DGP Multiple Regression Equation
AfterMultiple
4.4.2. DGP the orthogonal test and Equation
Regression the multiple linear regression calculation, the linear
regression equation of DGP is:
After the orthogonal test and the multiple linear regression calculation, the lin
Y = −31.332
gression + 0.36X
equation is:2 − 2.808X3 + 31.263X4 + 48.024X5 − 16.877X6 + 12.954X7
+ 4.223X
of1DGP
According
Y = −31.332 + 0.36X to the
1 + 4.223X 2 − analysis
2.808X3of+ 31.263X
the results
4 +of48.024X
Tables 12
5 −and 13 and6 +Figure
16.877X 21, 7these
12.954X
parameters sig are greater than 0.05, indicating that they are not significantly correlated
in According
the regressionto the analysis
equation; VIF < 5 of the results
indicates of is
that there Tables 12 and 13 and
no multicollinearity Figure
between the 21, the
parameters. The model residuals, which basically obeyed normal distribution,
rameters sig are greater than 0.05, indicating that they are not significantly correla indicated
that the error of this equation was within a reasonable range. Therefore, the linear regression
theequation
regression equation;
established by theVIF < is
model 5 statistically
indicates significant.
that there is no multicollinearity betwe
parameters. The model residuals, which basically obeyed normal distribution, ind
that the error of this equation was within a reasonable range. Therefore, the linear r
sion equation established by the model is statistically significant.
SPSS software was used to fit the multiple linear regression and the coefficient
model fit; R2 = 0.872, indicating a good model fit, DW = 2.156, indicating that ther
correlation between the independent variables in this model, i.e., a valid regression
 Table 12. The DGP multiple linear regression model.

Adjusted R Durbin-
Model R R Square Si
Square Watson
Sustainability 2022, 14, 7667 DGP 0.934 0.872 0.860 2.156 17 of 22 0.0

Table 13. DGP multiple linear regression equation analysis. (AI = Atrium inclination; WR
Table 12. The DGP multiple linear regression model.
reflectivity; FR = Floor reflectivity; SR = Skylight ratio; SV = Skylight visible transmittanc
Fabric coverage; FV = Fabric visible transmittance).Adjusted R Durbin-
Model R R Square Sig.
Square Watson
Unstandardized
DGP 0.934 0.872 0.860 2.156 0.000
Standardized Collinearity Stati
Coefficients
Model Coefficients t Sig.
Table 13. DGPStd. multiple linear regression equation analysis. (AI = Atrium inclination; WR = Wall
B Beta Tolerance V
reflectivity; FRError
= Floor reflectivity; SR = Skylight ratio; SV = Skylight visible transmittance; FC = Fabric
coverage; FV = Fabric visible transmittance).
(Constant) −31.332 5.34 −5.867 0
AI 0.36 Coefficients0.038Standardized0.397
Unstandardized 9.492 0Collinearity Statistics
1
Model t Sig.
WR B 4.223 Std. Error 4.789 Coefficients Beta
0.037 0.882 0.381
Tolerance 1
VIF
FR
(Constant) −31.332−2.808 5.34 5.948 −0.02 −5.867 −0.472 0 0.638 1
AI 0.36 0.038 0.397 9.492 0 1
SR
WR 4.223
31.263 4.789 3.029 0.037 0.432 0.882 10.322 0.381 0 1 111
SV
FR −2.80848.024 5.948 3.029 −0.02 0.663 −0.472 15.856 0.638 0 1 11
SR 31.263 3.029 0.432 10.322 0 1
FC
SV 48.024
−16.877 3.029 3.029 0.663 −0.233 15.856 −5.572 0 0 1 111
FV
FC −16.87712.954 3.029 3.029 −0.233 0.179 −5.572 4.277 0 0 1 11
FV 12.954 3.029 0.179 4.277 0 1 1

Figure 21. The DGP histogram of the model’s residual distribution and the DGP P-P diagram of the
Figure 21.normalized
model’s The DGPresiduals.
histogram of the model’s residual distribution and the DGP P-P diagra
model’s normalized residuals.
SPSS software was used to fit the multiple linear regression and the coefficient of the
model fit; R2 = 0.872, indicating a good model fit, DW = 2.156, indicating that there is no
4.4.3. Sensitivity Analysis of Atrium Design Parameters
correlation between the independent variables in this model, i.e., a valid regression.
After the sDA and DGP multiple linear regression analysis, the standardized
4.4.3. Sensitivity Analysis of Atrium Design Parameters
cients beta of each design parameter was obtained, and then the degree of influ
After the sDA and DGP multiple linear regression analysis, the standardized coeffi-
each parameter on the target evaluation index can be seen, i.e., sensitivity analysis
cients beta of each design parameter was obtained, and then the degree of influence of each
22). From the
parameter figure,
on the targetitevaluation
can be seen
indexthat theseen,
can be mosti.e.,influential parameter
sensitivity analysis on22).
(Figure the atriu
light
Fromisthe
Skylight
figure, it VT, followed
can be by most
seen that the Skylight ratio,
influential Atriumoninclination,
parameter and Fabric
the atrium daylight is co
Skylight VT, followed by Skylight ratio, Atrium inclination,
while the remaining design parameters have less influence. and Fabric coverage, while the
remaining design parameters have less influence.
 Sustainability
Sustainability 2022,
2022, 14,14, x FOR PEER REVIEW
7667 19 of 23
18 of 22

Figure Sensitivityanalysis
Figure 22. Sensitivity analysisofofthe
theatrium
atrium design
design parameters.
parameters.

5.
5. Multi-Objective Optimizationofof
Multi-Objective Optimization Daylight
Daylight
Multi-objective optimizationuses
Multi-objective optimization usesthe
theoptimization
optimizationtool tooltotocalculate
calculatethe
theoptimal
optimalpa-param-
eter combination
rameter combination andandcancangreatly
greatly improve
improvedesigners’
designers’ efficiency
efficiency andandaccuracy
accuracy inin building
build-
performance
ing performance simulation.
simulation.InInthe the process
process ofof adopting
adoptinga aparametric
parametric daylight
daylight design,
design, the the
computer
computer is is only
onlyusedusedforforthe
the repetitive,
repetitive, heavy,
heavy, andand demanding
demanding calculations
calculations and analyses.
and analyses.
The
The range
range of of independent
independentvariables
variables having
having been
been setset before,
before, the the calculator
calculator can iteratively
can iteratively
calculate by
calculate by itself,
itself,so
soasastotoobtain
obtainthe theparameter
parameter combination
combination indicative of the
indicative ofbest effecteffect
the best
of daylight [70,71]. To date, commonly used multi-objective computing
of daylight [70,71]. To date, commonly used multi-objective computing methods include methods include
genetic algorithms,
genetic algorithms, annealing
annealing algorithms,
algorithms, and and evolutionary
evolutionaryalgorithms,
algorithms,suchsuchasasMicro-
Micro-GA,
GA, NSGA-II, MATLAB, Multiopt2, GenOpt, Galapagos,
NSGA-II, MATLAB, Multiopt2, GenOpt, Galapagos, Octopus, and Wallace [72–74]. Octopus, and Wallace [72–74]. The
The Pareto
Pareto frontier
frontier solution
solution setconsidered
set is is considered to be
to be a trade-off
a trade-off solution
solution amongconflicting
among conflictingobjec-
objectives in the design. Under the premise of multiple objectives,
tives in the design. Under the premise of multiple objectives, Pareto means that no Pareto means thatobjective
no
objective can be improved to the detriment of other objectives [75,76].
can be improved to the detriment of other objectives [75,76]. Rizki A. Mangkuto et al. pro- Rizki A. Mangkuto
et al. proposed
posed a simulation a simulation
study tostudy
exploreto explore the influence
the influence of WWR,of WWR,wall wall reflectivity,
reflectivity, andandexterior
exterior window orientation on various daylight indicators and
window orientation on various daylight indicators and the daylight energy consumptionthe daylight energy con-
sumption of buildings in tropical climates, and they obtained the parity through a multi-
of buildings in tropical climates, and they obtained the parity through a multi-objective
objective optimization method and the Pareto frontier solution set [77]. Tarek Rakha et al.
optimization method and the Pareto frontier solution set [77]. Tarek Rakha et al. provided
provided an optimization procedure with the goal of maximizing daylight uniformity by
an optimization procedure with the goal of maximizing daylight uniformity by controlling
controlling the geometry of the ceiling [78]. Anxiao Zhang et al. introduced a study on the
the geometry of the ceiling [78]. Anxiao Zhang et al. introduced a study on the optimization
optimization of daylight energy consumption in school buildings in cold regions: The op-
of daylight energy consumption in school buildings in cold regions: The optimal solution
timal solution was obtained through the use of Grasshopper to control building geometric
was obtained
parameters, thethrough
adoption theof use of Grasshopper
Ladybug and Honeybee to control buildingmaterial
to add building geometric parameters,
properties,
the
andadoption of Ladybug
the subsequent and Honeybee
combination of energy toconsumption,
add building daylight,
material andproperties, and the sub-
multi-objective
sequent combination
optimization tools [23]. of energy consumption, daylight, and multi-objective optimization
tools This
[23].research uses a novel parametric multi-objective optimization tool, Octopus, be-
This
cause it can research
achieve uses a novel parametric
the multi-objective multi-objective
optimization optimization
in a more accurate tool, Octopus,
and comprehen-
because
sive way when setting the independent variables as the design parameters of thecomprehen-
it can achieve the multi-objective optimization in a more accurate and above
sive way when
sensitivity analysissetting
and thethe independent variables
dependent variables as as
sDAtheanddesign
DGP.parameters
The followingof the above
pro-
sensitivity analysis and the dependent variables as sDA and
cesses include respective calculations of the maximum sDA and the minimum DGP to DGP. The following processes
include
achieve therespective
best effectcalculations of the maximum
of indoor daylight, sDA of
the parameters and
thethe minimum
genetic DGPand
algorithm, to the
achieve
the
finalbest effect of indoor
multi-objective daylight,
optimization the parameters
calculation of the genetic algorithm, and the final
(Table 14).
multi-objective optimization calculation (Table 14).
After thirteen iterations of Octopus, the computation is automatically stopped and the
Pareto frontier solution set is obtained (Table 15, Figure 23). After the comparison of the
results, among them, Group 3 and Group 4 have the best daylight effects, 90.89% and 88.56%
of sDA and 37.67% and 39.63% of DGP, respectively, both meeting the maximum annual
daylight effect and being lower than the DGP requirement of 0.4, and their corresponding
design parameter combination can also be used as a reference.
 Table 14. Octopus optimized parameter settings.

Optimization Parameters Value

Elitism 0.7
Mut.Probablity 0.01
Sustainability 2022, 14, 7667 19 of 22
Mutation Rate 0.1
Crossover Rate 0.9
Population Size 20
Table 14. Octopus optimized parameter settings.
Max Generation 20
Optimization Parameters Value
After thirteen iterations of Octopus, the computation is automatically stopped and
Elitism 0.7
the Pareto frontier solution set is obtained (Table 15, Figure 23). 0.01
Mut.Probablity After the comparison of
the results, among them,Rate
Mutation Group3 and Group4 have the best daylight0.1 effects, 90.89% and
88.56% of sDA and 37.67%
Crossover and 39.63% of DGP, respectively, both0.9
Rate meeting the maximum
annual daylightPopulation
effect andSize
being lower than the DGP requirement20of 0.4, and their corre-
sponding design Max Generation
parameter 20
combination can also be used as a reference.

Table 15.
Table 15. Pareto
Pareto frontier
frontier solution.
solution. (AI
(AI= =Atrium
Atriuminclination;
inclination;WR
WR = Wall reflectivity;
= Wall FRFR
reflectivity; = Floor re-
= Floor
flectivity; SR = Skylight ratio; SV = Skylight visible transmittance; FC = Fabric coverage; FV = Fabric
reflectivity; SR = Skylight ratio; SV = Skylight visible transmittance; FC = Fabric coverage; FV = Fabric
visible transmittance).
visible transmittance).
Group AI WR FR SR SV FC FV sDA DGP
Group AI WR FR SR SV FC FV sDA DGP
1 117.00 0.34 0.30 0.69 0.29 0.58 0.39 70.11% 35.77%
21 117.00
117.00 0.34
0.31 0.30
0.17 0.69
0.69 0.29
0.36 0.58
0.75 0.39
0.41 70.11%
81.78% 35.77%
36.57%
2 117.00 0.31 0.17 0.69 0.36 0.75 0.41 81.78% 36.57%
33 119.00
119.00
0.60
0.60
0.17
0.17
0.68
0.68
0.30
0.30
0.51
0.51
0.39
0.39
90.89%
90.89%
37.67%
37.67%
44 91.00
91.00 0.65
0.65 0.27
0.27 0.89
0.89 0.37
0.37 0.50
0.50 0.13
0.13 88.56%
88.56% 39.63%
39.63%
55 118.00
118.00 0.60
0.60 0.36
0.36 0.68
0.68 0.30
0.30 0.50
0.50 0.39
0.39 91.00%
91.00% 40.50%
40.50%
66 118.00
118.00 0.60
0.60 0.17
0.17 0.84
0.84 0.30
0.30 0.76
0.76 0.76
0.76 100.00%
100.00% 42.70%
42.70%

Figure 23. Pareto Frontier Images.

Images.

6. Conclusions
6. Conclusions
As the
As the most
mostcommon
commonpartpartofofcommercial
commercial buildings, thethe
buildings, atrium design
atrium hashas
design a critical im-
a critical
pact on the quality of natural daylight in the building interior. After simulation, correlation
impact on the quality of natural daylight in the building interior. After simulation, corre-
and linear
lation regression
and linear analyses
regression were performed
analyses on fourteen
were performed atriumatrium
on fourteen designdesign
parameters
parame- to
investigate the effect of each design parameter on the daylight quality of the commercial
ters to investigate the effect of each design parameter on the daylight quality of the com-
atrium. atrium.
mercial The results
The show
resultsthat Skylight
show VT, Skylight
that Skylight ratio, Atrium
VT, Skylight inclination,
ratio, Atrium and Fabric
inclination, and
coverage have the greatest influence on atrium daylight quality, while the remaining pa-
Fabric coverage have the greatest influence on atrium daylight quality, while the remain-
rameters have a smaller degree of influence. The standardized regression coefficients of SV,
ing parameters have a smaller degree of influence. The standardized regression coeffi-
SR, AI, and FC affecting atrium daylight are 0.551, 0.471, 0.436, and −0.223, respectively;
cients of SV, SR, AI, and FC affecting atrium daylight are 0.551, 0.471, 0.436, and −0.223,
the standardized regression coefficients affecting atrium glare are 0.663, 0.432, 0.397, and
respectively; the standardized regression coefficients affecting atrium glare are 0.663,
−0.233, respectively. The Pareto front solution set was obtained by filtering the results
0.432, 0.397, and −0.233, respectively. The Pareto front solution set was obtained by filter-
combined with the evaluation reference criteria. Among many results, the parameter
ing the results combined with the evaluation reference criteria. Among many results, the
combination with the best daylight and anti-glare effect reached 90.89% of sDA and 37.67%
of DGP, which is obviously a satisfactory indoor daylight index for the atrium. Based on
the parametric design, this study proposes a method for exploring the optimization of
daylight in commercial atria in cold regions of China, which hopefully can provide some
reference and ideas for future atrium daylight design.
Sustainability 2022, 14, 7667 20 of 22

Supplementary Materials: The following supporting information can be downloaded at: https://www.
mdpi.com/article/10.3390/su14137667/s1, File S1: Table Data.
Author Contributions: Conceptualization, Y.X.; Data curation, W.L.; Formal analysis, W.L.; Investigation,
W.L.; Methodology, W.L.; Project administration, Y.X.; Supervision, Y.X.; Validation, Y.X.; Writing—
original draft, W.L.; Writing—review & editing, Y.X. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no funding.
Data Availability Statement: Data has been added to the Supplementary Materials.
Conflicts of Interest: The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in this paper.

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