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A Novel Framework for Optimizing Indoor Illuminance and Discovering Association of Involved Variables

A Novel Framework for Optimizing Indoor Illuminance and Discovering Association of Involved... buildings Article A Novel Framework for Optimizing Indoor Illuminance and Discovering Association of Involved Variables 1 , 2 3 4 Negar Heidari Matin * , Ali Eydgahi , Amin Gharipour and Payam Matin Gibbs College of Architecture, University of Oklahoma, Norman, OK 73019, USA Gameabove College of Engineering & Technology, Eastern Michigan University, Ypsilanti, MI 48197, USA; aeydgahi@emich.edu Ambassador Crawford College of Business and Entrepreneurship, Kent State University, Kent, OH 44240, USA; agharip1@kent.edu Department of Engineering and Aviation Sciences, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA; phmatin@umes.edu * Correspondence: negar.matin@ou.edu Abstract: The associations between various design variables affecting the visual performance of responsive facade systems are investigated in this study. First, we propose a data-driven approach to study practical aspects of illuminance optimization for responsive facades. In this approach, the hourly indoor illuminance data are combined with the location information to generate an objective function. This function is then utilized to evaluate the visual performance of responsive facade systems by matching a variety of facade angle movements to hourly sunshine patterns. Next, statistical tests were deployed to evaluate the role of design variables in different scenarios. The results provide detailed information about the design variables and their effects on visual comfort at 0.05 significant levels. On average, facade angles, facade configurations, facade orientations, and facade locations were significant in 100%, 41%, 87%, and 45% of different possible combinations of Citation: Matin, N.H.; Eydgahi, A.; scenarios/variables, respectively. Gharipour, A.; Matin, P. A Novel Framework for Optimizing Indoor Keywords: responsive facades; facade optimization; visual comfort; data-driven design; statistical tests Illuminance and Discovering Association of Involved Variables. Buildings 2022, 12, 878. https:// doi.org/10.3390/buildings12070878 1. Introduction Academic Editors: Wei-Ling Hsu, A building facade system is one of the most important contributors to occupant Teen-Hang Meen, Hsi-Chi Yang and comfort [1]. The performance of building facades contributes to 17 percent of occupants’ Wen-Der Yu visual comfort and 58 percent of occupants’ thermal comfort [2,3]. Traditional facades, Received: 5 April 2022 as static systems, are incapable of altering their performance over time in response to Accepted: 14 June 2022 frequent variations in weather [4–6]. The performance of dynamic facades developed by Published: 22 June 2022 advanced technologies can improve the limited response of static facades [7–9]. Facade Publisher’s Note: MDPI stays neutral systems have the potential to change their function, features, and behavior over time in with regard to jurisdictional claims in response to repeated weather changes using advanced control technologies [10]. If the published maps and institutional affil- design variables for a responsive facade system are optimized for specific objectives, such iations. as improved occupant visual comfort [11], the system can perform optimally. Occupants’ visual comfort optimization is not a straightforward process [12]. The number of variables involved and the complexity of interactions among the variables make the optimization problem a difficult task for designers [13,14]. Copyright: © 2022 by the authors. In the design process, three types of design variables must be considered: active Licensee MDPI, Basel, Switzerland. design variables, passive design variables, and environmental variables [13]. Active design This article is an open access article variables such as louver angles, the facade porosity, and facade granularity can adjust distributed under the terms and the response to external stimuli and interior elements [9]. In contrast, passive design conditions of the Creative Commons variables remain constant in response to external stimuli and interior elements, including Attribution (CC BY) license (https:// infiltration, window-to-wall ratio, glazing types, and wall insulation [15]. Furthermore, creativecommons.org/licenses/by/ parametric study of environmental variables such as climate zones, building locations, 4.0/). Buildings 2022, 12, 878. https://doi.org/10.3390/buildings12070878 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 878 2 of 22 facade orientations, and facade configurations can be implemented to develop multiple design scenarios [14]. Limited past studies developed mathematical models that incorporate active, passive, and environmental variables to optimize visual comfort in responsive facades [13–15]. However, no study has investigated the impact of the design variables and their associations with the optimization function in responsive facades. In this study, we present a double stage framework for investigating the associations between various design variables affecting the visual performance of responsive facade systems. First, we focused on louver adaptation angles in horizontal and vertical facade configuration. An objective function for obtaining optimal indoor illuminance is intro- duced, utilizing hourly adaptation angles. Compared to the previous objective functions, the proposed function can support all possible occupant activities with the required illu- minance ranges. Moreover, the proposed function can deliver an optimal solution even when multiple activities are conducted in the room in different timeframes. The brute force search algorithm is implemented to decide the optimum hourly angles for various facade configurations, orientations, and locations/climates. To find the maximum indoor illuminance, the proposed optimization function is calculated for increments of the facade variables and time. In the second stage, a proposed three-step framework is implemented to investigate the associations of various design variables with the optimal solution affecting the visual performance of responsive facade systems. The three main steps of the proposed framework are (1) defining scenarios, (2) performing statistical tests, and (3) evaluating the test results, which determines the association of the variables with the optimal solution. Since the proposed framework yields the optimum angles as its main outcome, the optimum angles are inputted in a facade control system. This potentially could not only improve control latency, but also reduce computational cost. However, it should be ex- plicitly noted that the cost of the hardware and required computational power were not considered in this study and would vary depending on the building specifications. 2. Materials and Methods 2.1. Experimental Settings A typical office room was designed using Rhinoceros version 6.0 developed by Robert McNeel & Associates (Seattle, WA, USA). The dimensions of the designed office were 4.0 m wide, 9.0 m deep, and 3.0 m high. The typical daylight zone is about 7.0 m deep from the window wall in common office spaces [16]. The thickness of walls, ceiling, and flooring elements are 0.15 m, 0.12 m, and 0.12 m, respectively. The depth of the office was chosen to be larger than the typical depth so that the effect of daylight remains visible for all variables [17]. Natural light was considered as the only source of light in the office room, with no artificial lighting inside. This simulated office room had a window opening of 2.6 m width and 3.6 m length. The window was made from double-glazed, clear glass with a visible light transmittance of 76% that was installed on the small side of the office room. The window-to-wall ratio before applying the responsive facade system was 78% (floor 2 2 area = 36.0 m and window area = 9.36 m representing a 26% glazing to floor ratio). Using the Grasshopper modeling tool, a responsive facade system was simulated parametrically and applied to the office window. The simulated office room could be rotated to face the four main cardinal directions (N, W, S, E) in order to create various design scenarios. The horizontal and vertical louver angles were able to be rotated hourly from 90 de- grees to +90 degrees in response to daylight patterns during the day. Horizontal and vertical louvers moved in a clockwise direction from 90 degrees to +90 degrees. The movement of louvers was divided into 60 steps with increments of 3 degrees. The designed facades considered for simulation consisted of 7 horizontal and 7 vertical louvers with dimensions of 3 m  0.26 m  0.18 m, as shown in Figure 1. The distances between louvers in the horizontal configuration were 0.40 m and in the vertical configuration were 0.50 m when Buildings 2022, 12, x FOR PEER REVIEW 3 of 22 movement of louvers was divided into 60 steps with increments of 3 degrees. The de- signed facades considered for simulation consisted of 7 horizontal and 7 vertical louvers with dimensions of 3 m × 0.26 m × 0.18 m, as shown in Figure 1. The distances between Buildings 2022, 12, 878 3 of 22 louvers in the horizontal configuration were 0.40 m and in the vertical configuration were 0.50 m when louvers were fitted on 0 degrees. It is assumed that the louvers were built from diffuse metal provided by DIVA, which corresponds to Radiance parameters louvers were fitted on 0 degrees. It is assumed that the louvers were built from diffuse of 0.9 specularity, 0.175 roughness, and 0.175 reflectance (RGB) in the DIVA plug-in. metal provided by DIVA, which corresponds to Radiance parameters of 0.9 specularity, 0.175 roughness, and 0.175 reflectance (RGB) in the DIVA plug-in. (a) (b) Figure 1. Standard south-facing office space with workstations. (a) Horizontal responsive louvers. Figure 1. Standard south-facing office space with workstations. (a) Horizontal responsive louvers. (b) Vertical responsive louvers. (b) Vertical responsive louvers. The DIVA daylight-modeling plug-in was utilized to measure indoor illuminance and its corresponding visual metric of Useful Daylight Illuminance (UDI). The DIVA is one of Grasshopper ’s plug-ins, which assists Grasshopper in conducting sustainability simulations, such as daylight analysis. Radiance is the core of the DIVA engine and was previously validated by other researchers [18–25]. It has been proven by Reinhart and Walkenhorst that Radiance-based simulation methods are able to efficiently and accu- rately model complicated daylighting elements [18]. It has also been demonstrated by Buildings 2022, 12, x FOR PEER REVIEW 4 of 22 The DIVA daylight-modeling plug-in was utilized to measure indoor illuminance and its corresponding visual metric of Useful Daylight Illuminance (UDI). The DIVA is one of Grasshopper′s plug-ins, which assists Grasshopper in conducting sustainability simulations, such as daylight analysis. Radiance is the core of the DIVA engine and was previously validated by other researchers [18–25]. It has been proven by Reinhart and Walkenhorst that Radiance-based simulation methods are able to efficiently and accu- rately model complicated daylighting elements [18]. It has also been demonstrated by Buildings 2022, 12, 878 4 of 22 Ng et al. [18] that Radiance can be used to predict the internal illuminance with a high degree of accuracy. Additionally, Yoon et al. [19] have stated that Radiance is validated computational software and is well known to provide reliable prediction results under Ng et al. [18] that Radiance can be used to predict the internal illuminance with a high various sky conditions. Furthermore, Reinhart and Andersen have shown that translu- degree of accuracy. Additionally, Yoon et al. [19] have stated that Radiance is validated cent materials can be modeled in Radiance with even higher accuracy than was demon- computational software and is well known to provide reliable prediction results under strated earlier [20–25]. various sky conditions. Furthermore, Reinhart and Andersen have shown that translucent A grid-based metric of indoor illuminance was developed by defining 220 sensors materials can be modeled in Radiance with even higher accuracy than was demonstrated located over a horizontal grid surface with a height of 0.8 m from the office floor, which earlier [20–25]. was within the average height of a work surface in an office. In both directions of the A grid-based metric of indoor illuminance was developed by defining 220 sensors surface, sensors were spaced approximately every 0.43 m apart. The interior of the office located over a horizontal grid surface with a height of 0.8 m from the office floor, which room was simulated using standard Radiance materials that included a generic floor was within the average height of a work surface in an office. In both directions of the with 20% reflectance, a generic ceiling with 70% reflectance, generic interior walls with surface, sensors were spaced approximately every 0.43 m apart. The interior of the office 50% reflectance, and generic furniture with 50% reflectance. room was simulated using standard Radiance materials that included a generic floor with It was assumed that the office would be occupied daily from 8:00 a.m. to 6:00 p.m. 20% reflectance, a generic ceiling with 70% reflectance, generic interior walls with 50% without daylight savings time. IESNA’s new Lighting Measurement IES LM-83-12 was reflectance, and generic furniture with 50% reflectance. in agreement with the occupancy schedule [17]. It was assumed that six workspaces It was assumed that the office would be occupied daily from 8:00 a.m. to 6:00 p.m. would be occupied during occupancy hours. The occupants would be performing regu- without daylight savings time. IESNA’s new Lighting Measurement IES LM-83-12 was in lar office work, including working on computers. The clear sky with the sun was as- agreement with the occupancy schedule [17]. It was assumed that six workspaces would be sum occupied ed as during sky condi occupancy tions. Ty hours. pical ann The uoccupants al meteorolog would icalbe da performing ta provided regular as an En offi ergyP ce work, lus Weather including File working (EPWon ) by computers. the U.S. Depar The clear tment o sky with f Energ theysun were was utassumed ilized for t ashsky e seconditions. lected cit- Typical annual meteorological data provided as an EnergyPlus Weather File (EPW) by the ies/climate zones. Three design scenarios were considered: (1) no louvers/no shade, (2) fixed U.S. Department horizontal and of Ener vergy tical wer loe uv utilized ers with for ze the ro-d selected egree an cities/climate gle, and (3) rzones. esponsThr ive ee horizon- design scenarios were considered: (1) no louvers/no shade, (2) fixed horizontal and vertical louvers tal and vertical louvers with hourly optimum angles, as shown in Figure 2. These scenar- with zero-degree angle, and (3) responsive horizontal and vertical louvers with hourly ios were repeated parametrically for four facade orientations (N, W, S, E) and different optimum angles, as shown in Figure 2. These scenarios were repeated parametrically for facade locations/climate zones. four facade orientations (N, W, S, E) and different facade locations/climate zones. Figure 2. The three design scenarios. (a) No shade/no louvers. (b) Fixed louvers with zero-degree Figure 2. The three design scenarios. (a) No shade/no louvers. (b) Fixed louvers with zero-degree angle. (c) Responsive louvers with hourly optimum angles. angle. (c) Responsive louvers with hourly optimum angles. Four cities from different climate zones in the United States, namely, Miami (FL), Phoenix (AZ), Boston (MA), and Milwaukee (WI), were selected using K-cluster analysis along with an elbow method [26,27]. Annual meteorological data of the selected cities were adopted to simulate the hourly indoor illuminance associated with the multiple scenarios considered. Based on the ASHRAE classification, Miami and Phoenix represent the very Hot-Humid (1A) and Hot-Dry (2B) climates, respectively. Boston and Milwaukee represent Cool-Humid (5A) and Cold-Humid (6A) climates, respectively [28]. Hourly indoor illuminances were calculated at 220 predefined sensors for every 8760 h of a year, while the responsive louver angles were parametrically changed incrementally from90 to +90 . The measurements were repeated for four facade orientations, horizontal Buildings 2022, 12, x FOR PEER REVIEW 5 of 22 Four cities from different climate zones in the United States, namely, Miami (FL), Phoenix (AZ), Boston (MA), and Milwaukee (WI), were selected using K-cluster analysis along with an elbow method [26,27]. Annual meteorological data of the selected cities were adopted to simulate the hourly indoor illuminance associated with the multiple scenarios considered. Based on the ASHRAE classification, Miami and Phoenix repre- sent the very Hot-Humid (1A) and Hot-Dry (2B) climates, respectively. Boston and Mil- waukee represent Cool-Humid (5A) and Cold-Humid (6A) climates, respectively [28]. Buildings 2022, 12, 878 Hourly indoor illuminances were calculated at 220 predefined sensors for every 5 of 22 8760 h of a year, while the responsive louver angles were parametrically changed incre- mentally from −90 to +90°. The measurements were repeated for four facade orienta- tions, horizontal and vertical facade configurations, and four cities/climate zones. The and vertical facade configurations, and four cities/climate zones. The simulations ran simulations ran 37,843,200 times to calculate and stored raw indoor illuminance values 37,843,200 times to calculate and stored raw indoor illuminance values at 8,325,504,000. at 8,325,504,000. The stored output data of the DIVA plug-in were transferred and stored in the Postgres- The stored output data of the DIVA plug-in were transferred and stored in the SQL database. Then, R software was utilized to apply the brute force search algorithm Postgres-SQL database. Then, R software was utilized to apply the brute force search al- based gorithm based on the pro on the proposed objective posed objective func function to find tionthe to find the optim optimum louver um lo angles uver angles [29–31]. After calculating [29–31]. Aft indoor er calcul illuminance, ating indoor UDI illumina is calculated nce, UDI is as ca alcu metric, lated as which a metr repr ic, whi esents ch repre- both indoor sents both indoor illuminance level and discomfort glare in one scheme, as widely uti- illuminance level and discomfort glare in one scheme, as widely utilized in the field. lized in the field. Figure 3 shows the flow and execution of the data in the simulation. Figure 3 shows the flow and execution of the data in the simulation. Figure 3. Structure of the simulation runs. Figure 3. Structure of the simulation runs. 2.2. The Proposed Framework—Stage 1 2.2. The Proposed Framework—Stage 1 The UDI is a measure of the annual light quantity accessible in a certain interior The UDI is a measure of the annual light quantity accessible in a certain interior space. space. The annual average of UDI may be used to evaluate the annual performance of a The annual average of UDI may be used to evaluate the annual performance of a facade. facade. The UDI metric, which depends on both active and passive variables, is consid- The UDI metric, which depends on both active and passive variables, is considered as a ered as a dependent variable for establishing an objective function [28–31]. The UDI is dependent variable for establishing an objective function [28–31]. The UDI is calculated calculated not only as lower and upper thresholds but also as a useful value depending not only as lower and upper thresholds but also as a useful value depending on the range on the range of illuminance. The lower and upper thresholds and the useful value of of illuminance. The lower and upper thresholds and the useful value of UDI are denoted UDI are denoted as UDIunderlit, UDIoverlit, and UDIuseful, respectively [32]. In general, UDI is as UDI , UDI , and UDI , respectively [32]. In general, UDI is defined as a defined as a weigh underlit t overlit ed average as fol useful lows [30]: weighted average as follows [30]: ∑( . ) UDI = (1) ∑( ) (wf t ) i i i where ti is the time when the illumina UDI nce E= is calculated, and wfi is the weighting factor, (1) å (t ) which depends on the range of the calculated illuminance E. It should be noted that the weighting factor wfi is selected based on the range of the calculated illuminance E. For where t is the time when the illuminance E is calculated, and wf is the weighting factor, i i instance, as shown below, for the upper threshold, UDIoverlit is calculated as below after which depends on the range of the calculated illuminance E. It should be noted that the weighting factor wf is selected based on the range of the calculated illuminance E. For instance, as shown below, for the upper threshold, UDI is calculated as below after overlit wf is selected depending on how the illuminance E value compares to the upper limit of illuminance specified in standards: 1 if E > E Upper limit UDI with wf = (2) overall i 0 if E  E Upper limit In a similar way, the lower threshold UDI is calculated as: underlit 1 if E < E  E Lower limit Upper limit UDI with wf = (3) Usefull i 0 if E  E _ E > E Lower limit Upper limit Buildings 2022, 12, 878 6 of 22 Similarly, UDI is calculated as: useful 1 if E < E Daylight Lowelimit UDI with wf = (4) Underlit i 0 if E  E Daylight Lower limit To optimize indoor illuminance, an objective function is established in the following general form as: Obj = F(Active variables, Passive variables, Environmental variables )dx (5) general In this study, an objective function with active variables that can adapt the hourly daylight pattern is proposed. The illuminance includes the useful, overlit, and underlit ranges as the function constraints. These constraints divide interior space into three zones with three different levels of indoor illuminance appropriate for three distinct human activities. The goal of the proposed objective function is to increase the area of useful range for the different human activities and to decrease the area of undesirable ranges. Two configurations of responsive facades, facades with horizontal louvers and facades with vertical louvers, were considered. The selected configurations are the most influen- tial among various types of responsive facades with high visual performance in facade orientations [33–36]. Let S = s , . . . , s represent a specific set of human activities in a desired range 1 j of illuminance. H = {h , h , . . . , h } denotes hour of the day, and E(x, ) indicates the 1 2 k indoor illuminance for a specific point x located in the room for a louver angle of . Then, depending on whether or not the value of E(x, ) lays on one of the desired ranges, a new indication function I is calculated for a specific point of x in the room and louver angle (x,) by using Equation (3): 1 when E x,  is in the range of activity j ( ) I(x, ) = (6) 0 otherwise It should be noted that I indicates some indoor illuminance since it is based on the (x,) value of E(x, ). Depending on the importance of the human activities, which correspond to the illuminance ranges defined in S, a weighting factor W may be defined in a matrix form as: 2 3 w  w 1jsj 6 7 . . W = . . . (7) 4 5 . . w  w jHj1 jHjjsj The rows of the weighting factor are associated with the different human activities as defined in S. Thus, there are as many columns as the numbers of human activities as defined in S and denoted by jSj. The weighting factors of columns are associated with the different hours of the day as defined in H and denoted by |H| for which E(x, ) is calculated. The hours considered were from 8:00 a.m. to 6:00 p.m. For a given hour of h, the weighting factors associated with the human activities are obtained by calculating a weighted average of values of the indication function I for the (x,) entire points in the room. As shown in Equation (8), the weighted average can be considered as a new indoor illuminance function and be presented as a new metric, sAUDI : jsj w I(x, ) hj j=1 sAUDI (x, ) = dx (8) x2X where N denotes the total number of points in the room. X Buildings 2022, 12, x FOR PEER REVIEW 7 of 22 considered as a new indoor illuminance function and be presented as a new metric, sAUDIh: || ∑ ( ) (8) ( ) sAUDI x, θ = dx Buildings 2022, 12, 878 ∈ 7 of 22 where N denotes the total number of points in the room. The final objective function, AUDI, which is a function of the point x, the louvre an- The final objective function, AUDI, which is a function of the point x, the louvre angle gle θ, and the hour h, is computed by adding the calculated sAUDIh for all the hours, as , and the hour h, is computed by adding the calculated sAUDI for all the hours, as presented in Equation (9): presented in Equation (9): AUDI(x, θ,h) = sAUDI dh (9) AUDI(x, , h) = sAUDI dh (9) h2H 2.3. The Proposed Framework—Stage 2 2.3. The Proposed Framework—Stage 2 While the first stage of the framework aims to find the optimum angle by using Equation (6), the second stage investigates the role of various input variables in the op- While the first stage of the framework aims to find the optimum angle by using timum daylight illuminance. There are three steps in this stage, entitled scenario genera- Equation (6), the second stage investigates the role of various input variables in the optimum tion, hypothesis test assignment, and hypothesis test conduction and evaluation, as daylight illuminance. There are three steps in this stage, entitled scenario generation, shown in Figure 4. The scenario generation step includes the following: hypothesis test assignment, and hypothesis test conduction and evaluation, as shown in Figure 4. The scenario generation step includes the following: 1. A dependent variable is selected from the visual comfort and maximum visual comfort calculations of Equation (9). 1. A dependent variable is selected from the visual comfort and maximum visual comfort 2. An independent variable is chosen from active variables or environmental varia- calculations of Equation (9). bles. 2. An independent variable is chosen from active variables or environmental variables. 3. Other input variables are fixed at specific values. 3. Other input variables are fixed at specific values. Figure 4. Stage 2 of the framework. Figure 4. Stage 2 of the framework. As an example, in order to investigate whether the office orientation impacts the As an example, in order to investigate whether the office orientation impacts the values values of the maximum visual comfort, the office orientation and the maximum hourly of the maximum visual comfort, the office orientation and the maximum hourly visual visual comfort are considered as the independent variable and dependent variables, re- comfort are considered as the independent variable and dependent variables, respectively. spectively. Each design scenario needs a specific statistical test based on the type of the indepen- Each design scenario needs a specific statistical test based on the type of the inde- dent and dependent variables. Therefore, the second step assigns a statistical test from the pendent and dependent variables. Therefore, the second step assigns a statistical test list of available statistical tests based on the different experimental settings (scenarios) and from the list of available statistical tests based on the different experimental settings the type of the dependent and independent variables. The statistical tests available for this (scenarios) and the type of the dependent and independent variables. The statistical tests step include ANOVA, the Kruskal–Wallis, and Chi-squared [37–39]. available for this step include ANOVA, the Kruskal–Wallis, and Chi-squared [37–39]. Finally, the third step evaluates the results of the statistical test based on the obtained p-value, which measures the difference between the involved populations in the conducted test. A p-value greater than 0.05 indicates statistical insignificance. Thus, if the p-value calculated was below 0.05, the result was considered as statistically significant. All statistical analyses were carried out using R v.3.4.0 [40]. The complete list of the variables is provided in Table 1. Using the statistical tests presented in Table 1, the impacts of several independent variables on visual comfort were investigated. These independent variables include adaptation angles, type of rotational motion of the louvers (horizontal or Buildings 2022, 12, 878 8 of 22 vertical), orientations of responsive facade systems, and the range of the rotational angles of the louvers’ motion. Some of the independent variables mentioned are active variables and others are environmental. Table 1. Experimental settings for scenario generation. Independent Variable Dependent Variable Fixed Variables Assigned Test Scenarios Fixed facade City and Visual comfort Rotational Motion One-way ANOVA 384 Responsive facade with metric—UDI Orientation Adaptation angle Month of the year Horizontal louvers City Visual comfort and Orientation One-way ANOVA 192 metric—UDI Vertical louvers Month of the year City Building orientation Max visual comfort Rotational Motion Kruskal–Wallis 96 Month of the year Positive angles City and Max visual comfort Rotational Motion Chi squared 32 negative angles Orientation 3. Results The percentage values of the indoor illuminance function %sAUDI for the three different human activities of s , s , and s associated with the three different illuminance 2 3 ranges and for both horizontal and vertical louvers on two specific days of 21 June and 21 December are presented in Tables 2–5. The three different human activities of s , s , and 1 2 s associated with the three different illuminance ranges are introduced in Equation (7). s where 300 Lux  E x,   1000 Lux ( ) < 1 S = s where E(x, )  300 Lux (10) s where 1000 Lux  E(x, ) As shown in Table 2, at 12:00 p.m. on 21 June, the percentage value of sAUDI associated with the target range of s (where illuminance is between 300 Lux and 1000 Lux) is calculated as 36%. This value indicates that 36% of the working space area had the desired indoor illuminance (as specified for s human activity) if an optimum angle of32 degrees was chosen for south-facing horizontal louvers for that specific time of the year. The hourly optimum angles and sAUDI associated with ranges s , s , and s for all 2 3 h 1 the locations investigated including Miami, Phoenix, Boston, and Milwaukee on 21 June for the entire facade orientations are shown in Tables 6–11. Figure 5 shows the percentage values of sAUDI associated with ranges s , s , and h 1 2 s for a south-orientated office in Phoenix on 21 June when the responsive louvers were set at an optimum angle of 32 degrees. Furthermore, the percentage values of sAUDI on 21 June associated with ranges s , s , and s are illustrated in Figure 6a–c for four facade 1 2 3 orientations (N, W, S, E). Additionally, the visual representation of the estimated indoor illuminance in the office considered is depicted in Figure 7. It is observed that the area which experiences the targeted illuminance range s increases as a responsive facade with an optimum angle is utilized as opposed to a fixed louver system. Buildings 2022, 12, 878 9 of 22 Table 2. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 June-Phoenix-Horizontal louvers. June-21st-Horizontal Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 43 35.455 62.727 1.818 75 43.182 3.182 53.636 46 31.364 58.636 10.000 49 39.091 59.545 13.64 9:00 40 31.818 59.545 8.636 80 40.455 4.545 55.000 43 30.000 54.091 15.909 46 35.909 55.909 8.182 10:00 40 30.455 51.364 18.182 53 41.818 1.818 56.364 43 31.364 53.636 15.000 46 35.455 54.545 10.000 11:00 44 30.000 54.545 15.455 60 48.636 2.273 49.091 40 33.182 55.909 10.909 44 34.091 54.545 11.364 12:00 32 36.364 24.091 39.545 63 47.727 6.364 45.909 46 33.182 55.455 11.364 46 33.636 50.909 15.455 13:00 32 36.818 23.182 40.000 60 32.273 30.455 37.273 44 32.727 57.727 9.545 46 32.273 50.455 17.273 14:00 26 33.182 28.636 38.182 46 34.545 51.818 13.636 46 35.000 55.000 10.000 60 47.727 9.091 43.182 15:00 46 32.727 55.455 11.818 43 37.273 59.091 3.636 46 35.455 56.818 7.727 63 47.727 4.545 47.727 16:00 46 31.818 58.636 9.545 43 38.182 60.000 1.818 46 34.091 57.273 8.636 86 41.818 4.091 54.091 17:00 43 34.091 60.000 5.909 49 39.091 58.182 2.727 43 32.273 57.727 10.000 77 41.818 2.273 55.909 18:00 43 33.636 63.636 2.727 49 36.818 61.818 1.364 43 31.364 58.182 10.455 43 45.000 4.545 50.455 Table 3. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 June-Phoenix-Vertical louvers. June-21st-Vertical Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 32 26.818 54.545 18.636 66 43.636 4.545 51.818 34 26.818 52.273 20.909 69 27.273 55.909 16.818 9:00 12 26.818 47.727 25.455 80 41.364 2.273 56.364 32 25.909 47.727 26.364 69 27.273 50.909 21.818 10:00 26 26.818 46.818 26.364 89 40.909 5.909 53.182 32 26.818 46.818 26.364 77 27.273 50.000 22.727 Buildings 2022, 12, 878 10 of 22 Table 3. Cont. June-21st-Vertical Facade-Phoenix Orientations South East North West 11:00 14 25.909 41.818 32.273 83 31.818 23.182 45.000 29 27.727 47.273 25.000 80 26.818 48.636 24.545 12:00 46 25.455 46.364 28.182 75 25.455 38.636 35.909 32 26.364 46.818 26.818 77 26.818 47.273 25.909 13:00 32 25.455 44.091 30.455 57 25.455 47.273 27.273 32 27.273 48.182 24.545 69 25.455 47.273 27.273 14:00 34 26.818 43.636 29.545 83 28.636 45.455 25.909 26 28.182 46.818 25.000 52 26.818 44.545 28.636 15:00 29 27.727 47.273 25.000 86 29.545 48.182 22.273 0 28.182 47.273 24.545 80 31.364 24.091 44.545 16:00 14 28.182 47.273 24.545 77 30.909 49.091 20.000 3 27.727 47.273 24.545 89 35.909 10.000 54.091 17:00 17 28.182 51.818 20.000 77 30.909 52.273 16.818 40 28.182 53.182 18.636 66 39.545 4.091 56.364 18:00 37 27.273 51.818 20.909 66 27.273 57.727 15.000 40 27.273 55.455 17.273 57 42.273 3.182 54.545 Table 4. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for 1 2 3 21 December-Phoenix-Horizontal louvers. December-21st-Horizontal Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 9:00 49 28.182 52.273 19.545 46 35.455 30.000 34.545 12 35.455 64.545 0.000 80 37.727 60.909 1.364 10:00 0 31.818 20.000 48.182 89 30.909 22.727 46.364 0 40.455 59.545 0.000 90 37.727 57.727 4.545 11:00 3 41.818 3.182 55.000 43 30.000 51.364 18.636 3 41.818 55.000 3.182 86 35.455 54.091 10.455 12:00 14 41.818 2.727 55.455 49 31.818 52.273 15.909 37 40.000 59.545 0.455 49 37.273 59.545 3.182 13:00 43 45.455 5.909 48.636 46 34.545 63.182 2.273 0 39.545 51.364 9.091 49 34.091 58.636 7.273 14:00 14 41.818 3.182 55.000 46 35.000 60.909 4.091 40 39.545 60.455 0.000 46 31.364 50.909 17.727 15:00 0 41.818 2.727 55.455 46 35.909 62.727 1.364 40 39.091 60.909 0.000 83 30.909 25.909 43.182 Buildings 2022, 12, 878 11 of 22 Table 4. Cont. December-21st-Horizontal Facade-Phoenix Orientations South East North West 16:00 0 31.364 20.455 48.182 52 35.455 64.545 0.000 0 35.909 57.273 6.818 83 32.273 15.000 52.727 17:00 52 27.727 55.000 17.273 86 30.455 60.000 9.545 12 30.455 60.000 9.545 49 35.000 28.182 36.818 18:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 Table 5. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 December-Phoenix-Vertical louvers. Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 9:00 1 31.364 56.818 11.818 37 35.000 47.273 17.727 43 26.818 72.273 0.909 60 25.455 72.727 1.818 10:00 17 33.182 16.818 50.000 72 31.364 24.091 44.545 20 30.000 62.273 7.727 83 28.182 64.545 7.273 11:00 3 44.545 3.182 52.273 57 27.727 34.545 37.727 12 31.818 58.182 10.000 69 27.727 63.182 9.091 12:00 46 44.091 5.000 50.909 80 28.182 50.909 20.909 20 32.273 53.182 14.545 63 27.727 54.545 17.727 13:00 52 41.818 3.636 54.545 80 28.636 55.000 16.909 14 32.273 54.545 13.182 89 27.727 55.455 16.818 14:00 43 45.000 4.545 50.455 66 28.636 50.909 20.455 0 30.909 51.818 17.273 54 26.364 52.273 21.364 15:00 9 42.273 2.273 55.455 86 28.182 54.545 17.273 9 28.636 54.091 17.273 60 27.273 31.818 40.909 16:00 29 34.545 15.909 49.545 86 29.091 59.545 11.364 12 28.636 59.545 11.818 57 30.000 0.055 44.545 17:00 46 26.818 57.727 15.455 89 23.182 65.455 11.364 32 22.727 65.455 11.818 40 32.273 46.818 20.909 18:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 Buildings 2022, 12, 878 12 of 22 Table 6. The hourly optimum angles and their associated %sAUDI on 21 June in MiamiHorizontal Louvers. June21st-Horizontal Facade-Miami Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 37 33.64 64.09 2.27 86 43.63 4.54 51.81 43 29.54 62.72 7.72 52 35.00 64.54 0.45 9:00 49 33.64 60.45 5.90 80 40.45 5.00 54.54 43 31.81 52.27 15.90 43 35.90 60.45 3.63 10:00 46 30.00 57.27 12.72 63 45.45 1.36 53.18 46 29.54 56.81 13.63 49 35.00 53.18 11.81 11:00 43 29.55 50.90 19.54 57 49.54 1.81 48.63 46 31.36 52.72 15.90 46 35.00 50.00 15.00 12:00 46 28.64 56.81 14.54 57 35.45 23.63 40.90 43 30.45 55.90 13.63 46 30.90 55.45 13.63 13:00 32 35.00 24.54 40. 75 36.36 22.72 40.90 29 32.27 28.18 39.54 60 38.18 19.54 42.27 14:00 43 29.09 51.81 19.09 46 28.63 30.45 40.90 49 29.54 57.27 13.18 69 31.36 24.54 44.09 15:00 49 30.91 66.81 22.72 46 33.18 63.63 3.18 43 30.90 60.00 9.09 63 34.09 54.00 41.81 16:00 43 30.91 59.54 9.54 54 36.81 59.54 3.63 43 29.54 55.90 14.54 54 45.90 68.18 48.63 17:00 32 29.55 70.00 0.45 54 29.09 70.90 3.18 32 29.54 70.00 0.04 46 30.90 59.09 0.00 18:00 37 30.00 69.54 0.45 72 30.45 69.09 3.63 43 30.00 70.00 0.00 46 37.27 53.18 3.63 Table 7. The hourly optimum angles and their associated %sAUDI on 21 June in Miami-Vertical louvers. June-21st-Vertical Facade-Miami Orientations South East North West %AUDI %AUDI %AUDI %AUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 32 26.82 55.00 18.18 80 40.00 13.63 46.36 17 25.91 55.00 19.09 77 26.81 60.00 13.18 9:00 6 27.27 46.81 25.90 80 41.36 2.72 55.90 34 26.82 48.18 25.00 60 27.72 52.72 19.54 10:00 29 25.45 50.00 24.54 80 32.27 22.27 45.45 26 25.91 47.27 26.81 69 26.36 50.90 22.72 11:00 3 25.45 42.27 32.27 89 25.91 33.18 40.90 6 25.45 43.18 31.36 69 25.90 46.81 27.27 Buildings 2022, 12, 878 13 of 22 Table 7. Cont. June-21st-Vertical Facade-Miami Orientations South East North West 12:00 20 23.18 47.27 29.54 54 23.64 46.36 30.00 32 23.64 49.54 26.81 77 24.09 50.90 25.00 13:00 3 23.64 43.18 33.18 89 23.64 43.63 32.72 34 24.09 45.90 30.00 26 23.18 45.00 31.81 14:00 32 22.72 46.36 30.90 54 22.73 46.81 30.45 40 22.73 46.81 30.45 52 22.27 46.81 30.90 15:00 20 24.55 50.45 25.00 72 25.45 54.54 20.00 0 25.00 49.09 25.90 52 23.63 46.81 29.54 16:00 17 25.45 50.90 23.63 77 28.64 51.36 20.00 40 25.91 52.72 21.36 86 25.90 30.45 43.63 17:00 32 19.55 65.90 14.54 54 19.09 69.54 11.36 0 19.09 64.54 16.36 60 19.54 66.36 14.09 18:00 34 20.45 65.45 14.09 57 20.45 65.90 13.63 3 22.27 60.45 17.27 54 26.36 54.54 19.09 Table 8. The hourly optimum angles and their associated %sAUDI on 21 June in Boston-Horizontal louvers. June-21st-Horizontal Facade-Boston Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 46 32.27 60.45 7.27 75 41.82 3.18 55.00 43 33.18 56.81 10.00 46 38.63 60.90 0.00 9:00 43 31.36 54.09 14.54 86 41.36 3.18 55.45 46 34.09 59.09 6.81 46 38.63 56.81 4.54 10:00 40 30.45 49.54 20.00 60 45.45 5.90 48.63 46 35.00 59.54 5.45 43 36.81 59.09 4.09 11:00 29 32.27 31.81 35.90 -63 36.82 22.72 40.45 43 39.55 60.00 0.00 43 37.72 59.09 3.18 12:00 26 37.73 22.27 40.00 46 32.73 51.36 15.90 46 36.36 59.54 4.54 49 35.00 49.09 15.90 13:00 26 35.00 27.27 37.72 46 36.36 55.45 8.18 46 39.55 59.54 0.00 46 35.45 49.09 15.45 14:00 46 31.82 52.27 15.90 46 36.36 55.45 8.18 43 37.27 61.81 3.18 63 45.00 10.45 44.54 15:00 40 31.36 50.45 18.18 43 37.73 60.00 2.27 46 33.64 58.63 6.81 60 43.63 2.72 53.63 16:00 43 32.27 57.27 10.45 46 38.64 59.54 1.81 46 33.64 59.54 4.54 80 41.81 4.09 54.09 17:00 40 33.18 60.45 6.36 49 39.55 0.00 60.45 40 30.45 58.63 10.90 43 45.45 5.00 49.54 18:00 40 32.27 67.72 0.00 52 34.09 0.00 65.54 40 28.64 59.54 11.81 43 44.09 6.81 49.09 Buildings 2022, 12, 878 14 of 22 Table 9. The hourly optimum angles and their associated %sAUDI on 21 June in BostonVertical louvers. June-21st-Vertical Facade-Boston Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 46 38.64 60.90 0.00 49 42.73 4.54 52.72 32 27.73 51.81 20.45 86 27.27 54.54 18.18 9:00 46 35.64 56.81 45.45 80 41.82 4.54 53.63 37 28.64 51.81 19.54 86 29.09 50.90 20.00 10:00 43 36.82 59.09 4.09 86 34.09 20.90 45.00 23 28.64 49.54 21.81 69 29.54 50.90 19.54 11:00 43 37.73 59.09 3.18 72 30.00 34.54 35.45 6 30.91 49.09 20.00 83 29.09 51.81 19.09 12:00 49 35.00 49.09 15.90 63 28.64 46.36 25.00 0 29.09 46.81 24.09 80 28.18 47.27 24.54 13:00 46 35.45 49.09 15.45 86 30.91 48.63 20.45 34 30.91 49.09 20.00 54 28.18 48.18 23.63 14:00 63 45.00 2.72 53.63 86 30.00 49.09 20.09 6 29.09 51.36 19.54 72 29.54 30.45 40.00 15:00 60 43.64 4.09 54.09 86 30.45 49.09 20.45 23 27.73 47.27 25.00 75 32.72 16.81 50.45 16:00 80 41.82 5.00 49.54 89 30.00 50.90 19.09 29 28.64 51.36 20.00 -80 39.09 3.63 57.27 17:00 43 45.45 6.81 49.09 72 30.00 54.09 15.90 29 27.27 45.90 26.81 49 42.27 3.18 54.54 18:00 43 44.09 10.45 49.09 66 25.91 60.90 1.31 17 27.73 44.54 27.72 -46 40.00 5.90 54.09 Table 10. The hourly optimum angles and their associated %sAUDI on 21 June in Milwaukee-Horizontal louvers. June21st-Horizontal Facade-Milwaukee Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 43 30.45 59.09 10.45 -69 43.64 1.81 54.54 40 31.45 59.09 10.45 46 35.91 61.81 2.27 9:00 40 30.00 51.81 18.18 69 40.91 0.00 59.09 43 31.00 51.81 18.18 46 35.45 56.36 8.18 10:00 40 31.36 49.54 19.09 63 45.00 3.18 51.81 43 32.36 49.54 19.09 43 38.18 59.09 2.72 11:00 43 31.36 50.45 18.18 60 35.91 22.27 41.81 40 31.36 50.45 18.18 43 38.18 59.09 2.72 12:00 26 34.55 27.72 37.72 49 33.18 51.36 15.45 26 35.55 27.72 37.72 49 35.45 53.18 11.36 Buildings 2022, 12, 878 15 of 22 Table 10. Cont. June21st-Horizontal Facade-Milwaukee Orientations South East North West 13:00 26 32.73 30.90 36.36 46 35.91 56.81 7.27 26 33.73 30.90 36.36 46 34.09 51.36 14.54 14:00 40 32.73 50.90 16.36 46 38.18 60.45 1.36 40 33.73 50.90 16.36 60 35.45 24.09 40.45 15:00 40 31.36 54.09 14.54 49 41.36 58.18 0.06 40 32.36 54.09 14.54 66 45.00 5.00 50.00 16:00 43 32.73 59.54 7.72 49 41.82 58.18 0.00 43 33.73 59.54 7.72 83 43.64 3.63 52.72 17:00 40 34.09 60.09 5.00 49 39.09 60.90 0.01 40 35.09 60.90 5.00 43 46.82 5.45 47.72 18:00 40 33.64 65.45 0.00 52 35.91 63.18 0.00 40 34.64 65.45 0.00 46 41.82 5.43 52.72 Table 11. The hourly optimum angles and their associated %sAUDI on 21 June in MilwaukeeVertical louvers. June-21st-Vertical Facade-Milwaukee Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 34 25.45 54.09 20.45 90 40.45 10.00 49.54 32 25.45 52.27 22.27 80 25.91 54.54 19.54 9:00 34 25.91 49.09 25.00 89 40.00 6.36 53.63 9 27.73 46.81 25.45 69 27.27 50.90 21.81 10:00 40 28.18 46.81 26.81 77 35.91 14.54 49.54 14 29.55 48.18 22.27 75 29.09 51.36 19.54 11:00 43 29.09 44.09 30.00 49 29.55 41.81 28.63 14 30.00 50.00 20.00 86 29.55 51.36 19.09 12:00 34 28.64 41.36 29.54 83 29.09 45.45 25.45 12 30.91 50.45 18.63 89 29.09 50.90 20.00 13:00 32 28.18 42.27 24.54 75 30.45 49.54 20.00 12 30.00 50.90 19.09 80 28.18 47.27 24.54 14:00 29 29.09 46.36 20.45 77 31.82 51.81 16.36 6 30.45 52.72 16.81 43 28.64 45.45 25.90 15:00 34 29.09 50.45 16.36 77 31.36 52.72 15.90 20 29.55 54.09 16.36 89 33.18 20.00 46.81 16:00 34 28.64 55.00 14.54 69 32.27 53.63 14.09 9 29.55 55.00 15.45 83 39.55 3.18 57.27 17:00 40 28.18 57.27 19.54 69 30.45 55.45 14.09 29 27.73 56.81 15.45 46 42.27 5.90 51.81 18:00 37 27.27 53.18 7.27 57 25.00 60.90 14.09 40 26.36 45.45 28.18 66 37.73 5.45 56.81 Buildings 2022, 12, x FOR PEER REVIEW 16 of 22 Buildings 2022, 12, 878 16 of 22 Buildings 2022, 12, x FOR PEER REVIEW 16 of 22 Figure 5. The %sAUDIh for three different human activities of s , s , and s for south facade orien- Figure 5. The %sAUDI for three different human activities of s , s , and s for south facade Figure 5. The %sAUDIh for three different human activities of s , s , and s for south facade orien- h 1 2 3 tations calculated for 21 June in Phoenix. tations orientations calculat calculated ed for 21for June in Phoenix. 21 June in Phoenix. (a) (a) (b) (b) Figure 6. Cont. Buildings 2022, 12, x FOR PEER REVIEW 17 of 22 Buildings 2022, 12, x FOR PEER REVIEW 17 of 22 Buildings 2022, 12, 878 17 of 22 (c) Figure 6. The %sAUDIh associated with s1, s2, and s3 for horizontal responsive louvers with opti- (c) mum angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) Figure 6. The %sAUDIh associated with s1, s2, and s3 for horizontal responsive louvers with opti- Figure 6. The %sAUDI associated with s , s , and s for horizontal responsive louvers with optimum h 1 2 3 North. mum angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) North. North. (a) Fixed louvers (a) Fixed louvers (b) Responsive louvers with an optimum angle Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in (b) Responsive louvers with an optimum angle Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in the office categorized with the three ranges of indoor illuminance s1, s2, and s3 for (a) fixed louvers the office categorized with the three ranges of indoor illuminance s , s , and s for (a) fixed louvers 1 2 3 Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in and (b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade and (b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade the office categorized with the three ranges of indoor illuminance s1, s2, and s3 for (a) fixed louvers in Phoenix. and ( in Phoenix. b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade in Phoenix. To examine the significance of the optimum adaptation angle (as an active variable) To examine the significance of the optimum adaptation angle (as an active variable) on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- To examine the significance of the optimum adaptation angle (as an active variable) tical tests were performed, and the results are shown in Table 6. The p-values less than tical tests were performed, and the results are shown in Table 6. The p-values less than on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- 0.05 demonstrate significant differences between the facade of fixed louvers of a 0- 0.05 demonstrate significant differences between the facade of fixed louvers of a 0-degree tical tests were performed, and the results are shown in Table 6. The p-values less than angle (base case) and the vast majority of the responsive facades of horizontal configuration 0.05 demonstrate significant differences between the facade of fixed louvers of a 0- for all orientations examined in the city of Phoenix. This suggests that applying the opti- mal adaptation angles to the responsive facade of horizontal configuration leads to more Buildings 2022, 12, 878 18 of 22 desirable indoor illuminance for the majority of cases. The p-value of greater than 0.05 in Table 12 suggests that there were no significant differences between the responsive facade with optimum adaption angles and the responsive facade with fixed louvers of a 0-degree angle. This case is associated with the month of December for the south orientation and suggests that for this specific time of the year, and for such an orientation, applying opti- mum adaptation angles does not lead to more desirable indoor illuminance as compared to the fixed facade. A similar approach was used for the responsive facade of vertical configurations for the city of Phoenix for all main orientations. It was observed that applying optimum adaptation angles led to more desirable indoor illuminance for facades of vertical configuration. One-way ANOVA statistical tests were conducted for four cities of Miami, Phoenix, Boston, and Milwaukee in both horizontal and vertical layouts. Table 12. Significant differences between fixed facade (FF) and responsive facade (RF) with horizontal louvers. T- Month City Type Orientation Mean_FF SD_FF Mean_RF Mean_Rf p-Value Significant Statistic January Phoenix Horizontal South 0.33 0.06 0.35 0.35 0.001 4.970 Yes February Phoenix Horizontal South 0.31 0.05 0.34 0.34 0.004 3.660 Yes Macrh Phoenix Horizontal South 0.27 0.02 0.35 0.35 0.002 4.130 Yes April Phoenix Horizontal South 0.30 0.03 0.32 0.32 0.000 5.810 Yes May Phoenix Horizontal South 0.31 0.03 0.33 0.33 0.002 4.210 Yes June Phoenix Horizontal South 0.28 0.02 0.33 0.33 0.000 6.360 Yes July Phoenix Horizontal South 0.29 0.02 0.33 0.33 0.000 8.580 Yes August Phoenix Horizontal South 0.28 0.06 0.31 0.31 0.000 5.230 Yes September Phoenix Horizontal South 0.28 0.02 0.34 0.34 0.005 3.590 Yes October Phoenix Horizontal South 0.26 0.08 0.32 0.32 0.001 4.690 Yes November Phoenix Horizontal South 0.31 0.10 0.33 0.33 0.007 3.480 Yes December Phoenix Horizontal South 0.33 0.06 0.36 0.36 0.057 2.280 Yes To evaluate the significance of rotation direction of the louver angle, both optimum positive and negative adaption angles were considered as the independent variables. Different orientations and cities were considered for both positive and negative adaptation angles to generate 32 scenarios for both horizontal and vertical louvers. Then, Chi-squared tests were utilized. The results for Phoenix are shown in Table 13, which demonstrates that Chi-squared tests delivered significantly low p-values (p < 0.05), indicating there were significant differences between the optimum positive and negative adaptation angles for both horizontal and vertical louvers in all four facade orientations. Table 13. Significant differences between positive and negative optimum adaptation angles in the city of Phoenix. City Type Orientation Statistic p-Value Significant Phoenix Horizontal North 140.01 3  10 Yes Phoenix Vertical North 139.38 4  10 Yes Phoenix Horizontal West 139.62 Yes 3  10 Phoenix Vertical West 139.62 3  10 Yes Phoenix Horizontal South 139.93 3  10 Yes Phoenix Vertical South 139.99 Yes 3  10 Phoenix Horizontal East 139.93 3  10 Yes Phoenix Vertical East 140.02 3  10 Yes Buildings 2022, 12, 878 19 of 22 To study the role of horizontal versus vertical louvers, 192 distinct scenarios were considered and one-way ANOVA tests were performed. The results are shown in Table 14, providing different ranges of p-values depending on month of the year. Thus, the difference between horizontal and vertical louvers is significant for only those months of the year when the p-value is below 0.05. For the remaining months, the difference was found to be insignificant. Table 14. Significant differences between horizontal and vertical louvers for the months of January, February, June, July, November, and December. Mean SD Mean SD T- Month City Orientation p-Value Significant Imp_H Imp_H Imp_V hmp_V Statistic January Phoenix South 5.66 3.32 36.70 42.02 0.0445 2.329 Yes February Phoenix South 9.37 8.12 18.51 9.58 0.0258 2.414 Yes March Phoenix South 26.51 20.01 13.30 7.05 0.0604 2.065 No April Phoenix South 7.61 5.24 12.31 7.02 0.0779 1.857 No May Phoenix South 5.96 5.82 6.64 4.18 0.7449 0.330 No June Phoenix South 20.59 12.57 6.89 4.94 0.0033 3.515 Yes July Phoenix South 13.65 6.11 8.95 4.64 0.0461 2.122 Yes August Phoenix South 17.73 23.74 11.88 5.58 0.4220 0.831 No September Phoenix South 23.12 20.38 14.87 8.43 0.2362 1.240 No October Phoenix South 30.18 34.00 11.27 8.83 0.1009 1.786 No November Phoenix South 9.87 13.33 27.39 17.95 0.0179 2.599 Yes December Phoenix South 10.75 11.50 29.27 20.69 0.0362 2.346 Yes To determine the significance of the four key orientations of building facades, 96 sce- narios were considered that included both horizontal and vertical louvers. Kruskal–Wallis tests were applied to the scenarios and the results are shown in Table 15, which shows significant differences for all four facade orientations. The tests were repeated for four different cities, and similar results were achieved. Table 15. Significant differences among different building orientations including south-facing, north- facing, east-facing, and west-facing in Phoenix. Month City Type T-Statistic p-Value Significant January Phoenix Horizontal 28.19 3  10 Yes February Phoenix Horizontal 28.79 2  10 Yes March Phoenix Horizontal 26.78 7  10 Yes April Phoenix Horizontal 34.89 Yes 1  10 May Phoenix Horizontal 32.95 3  10 Yes June Phoenix Horizontal 34.61 1  10 Yes July Phoenix Horizontal 35.86 8  10 Yes August Phoenix Horizontal 35.86 4  10 Yes September Phoenix Horizontal 30.62 Yes 1  10 October Phoenix Horizontal 16.19 Yes 1  10 November Phoenix Horizontal 26.31 8  10 Yes December Phoenix Horizontal 23.46 3  10 Yes Buildings 2022, 12, 878 20 of 22 4. Conclusions In this study, we developed an objective function and a data-driven approach to investigate the contribution of different design variables to the visual performance of responsive facades. A computer model of an office with specific responsive facades (in the form of louvers) was constructed as an architectural space. For a specific hour of a day, the louvers were set to a specific adaptation angle, and a simulation was conducted to estimate the indoor illuminance. For the same selected hour, the simulation was repeated for a range of different adaptation angles to estimate the associated indoor illuminance. The data collected on indoor illuminance were fed into the proposed objective function to deliver the optimum adaptation angle for the selected hour. This process was repeated for all hours of a day and all days of a year. The study was also repeated for several design variables, including the location of the office, orientation of the office, and the facade’s configuration being vertical or horizontal. Statistical tests were implemented to investigate the significance of the design variables on the visual comfort under different scenarios. In limited cases, and under specific circumstances, some design variables were found to be insignificant. The results of this study indicate that obtaining and deploying optimum adaptation angles could lead to significantly desired levels of visual comfort. Implementing the proposed approach could help designers achieve higher levels of visual comfort, although the specifics of the design variables (such as location, orientation, and facade configuration) must be considered during the design process. Author Contributions: N.H.M., conceptualization, methodology, software, draft preparation, and writing; A.E., validation, reviewing, and editing; A.G., writing, methodology, analysis, data curation; P.M., writing, reviewing, validation, and editing. All authors have read and agreed to the published version of the manuscript. Funding: This project was funded by the Faculty Investment Program (FIP) Provided by the Vice President for Research and Partnership at the University of Oklahoma. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Aksamija, A. Design methods for sustainable, high-performance building facades. Adv. Build. Energy Res. 2015, 10, 240–262. [CrossRef] 2. Grobman, Y.J.; Capeluto, I.G.; Austern, G. External shading in buildings: Comparative analysis of daylighting performance in static and kinetic operation scenarios. Arch. Sci. Rev. 2017, 60, 126–136. [CrossRef] 3. Wagdy, A.; Fathy, F.; Altomonte, S. Evaluating the daylighting performance of dynamic facades by using new annual climate- based metrics. Proceeding of the 36th International Conference on Passive and Low Energy Architecture, Los Angeles, CA, USA, 11–13 July 2016. 4. Selkowitz, S.E.; Aschehoug, Ø.; Lee, E.S. Advanced interactive facade: Critical elements for future green buildings. In Proceedings of the GreenBuild, the Annual USGBC International Conference and Expo, Philadelphia, PA, USA, 20–22 November 2013. 5. Kim, K.; Jerratt, C. Energy performance of an adaptive facade system. J. Archit. Res. 2011, 179–186. [CrossRef] 6. Sørensen, L.S. Heat Transmission Coefficient Measurements in Buildings Utilizing a Heat Loss Measuring Device. Sustainability 2013, 5, 3601–3614. [CrossRef] 7. Veliko, K.; Thun, G. Responsive Building Envelopes: Characteristics and Evolving Paradigms in Design and Construction of High- Performance Homes; Routledge Press: New York, NY, USA, 2013. 8. Heidari Matin, N.; Eydgahi, A.; Shyu, S.; Matin, P. Evaluating visual comfort metrics of responsive facade systems as educational activities. Proceeding of the ASEE Annual Conference & Exposition Proceedings, Salt Lake City, UT, USA, 23–27 July 2018. [CrossRef] 9. Matin, N.H.; Eydgahi, A. Technologies used in responsive facade systems: A comparative study. Intell. Build. Int. 2019, 14, 54–73. [CrossRef] Buildings 2022, 12, 878 21 of 22 10. Heidari Matin, N.; Eydgahi, A.; Shyu, S. Comparative analysis of technologies used in responsive building facades. In Proceedings of the ASEE Annual Conference & Exposition Proceedings, Columbus, OH, USA, 24–27 June 2018. 11. Zemella, G.; Faraguna, A. Evolutionary Optimization of Facade Design; Springer: London, UK, 2014. [CrossRef] 12. Loonen, R.C.G.M.; Trcka, ˇ M.; Cóstola, D.; Hensen, J.L.M. Climate adaptive building shells: State-of-the-art and future challenges. Renew. Sustain. Energy Rev. 2013, 25, 483–493. [CrossRef] 13. Shan, R. Climate Responsive Facade Optimization Strategy. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, USA, 2016. 14. Matin, N.H.; Eydgahi, A. A data-driven optimized daylight pattern for responsive facades design. Intell. Build. Int. 2021, 1–12. [CrossRef] 15. Shan, R.; Junghans, L. “Adaptive radiation” optimization for climate adaptive building facade design strategy. Build. Simul. 2018, 11, 269–279. [CrossRef] 16. Ochoa, C.E.; Capeluto, I.G. Evaluating visual comfort and performance of three natural lighting systems for deep office buildings in highly luminous climates. Build. Environ. 2006, 41, 1128–1135. Available online: https://www.academia.edu/309066 0/Evaluating_visual_comfort_and_performance_of_three_natural_lighting_systems_for_deep_office_buildings_in_highly_ luminous_climates (accessed on 12 June 2022). [CrossRef] 17. Reinhart, C.F.; Walkenhorst, O. Validation of dynamic RADIANCE-based daylight simulations for a test office with external blinds. Energy Build. 2001, 33, 683–697. [CrossRef] 18. Ng, E.Y.-Y.; Poh, L.K.; Wei, W.; Nagakura, T. Advanced lighting simulation in architectural design in the tropics. Autom. Constr. 2001, 10, 365–379. [CrossRef] 19. Yoon, Y.; Moon, J.W.; Kim, S. Development of annual daylight simulation algorithms for prediction of indoor daylight illuminance. Energy Build. 2016, 118, 1–17. [CrossRef] 20. Reinhart, C.F.; Andersen, M. Development and validation of a Radiance model for a translucent panel. Energy Build. 2006, 38, 890–904. [CrossRef] 21. Reinhart, C.F.; Jakubiec, A.; Ibarra, R. Definition of a reference office for standardized evaluations of dynamic facade and lighting technologies. Proc. Build. Simul. 2013, 5, 560–580. 22. Mardaljevic, J. Validation of a lighting simulation program under real sky conditions. Light. Res. Technol. 1995, 27, 181–188. [CrossRef] 23. Mardaljevic, J. Daylight Simulation: Validation, Sky Models and Daylight Coefficients. Ph.D. Thesis, De Montfort University, Leicester, UK, 2000. 24. Mardaljevic, J. The BRE-IDMP dataset: A new benchmark for the validation of illuminance prediction techniques. Light. Res. Technol. 2001, 33, 117–134. [CrossRef] 25. Mardaljevic, J. Verification of program accuracy for illuminance modelling: Assumptions, methodology and an examination of conflicting findings. Light. Res. Technol. 2004, 36, 217–239. [CrossRef] 26. Gharipour, A.; Liew, A.W.-C. An integration strategy based on fuzzy clustering and level set method for cell image segmentation. In Proceedings of the 2013 IEEE International Conference on Signal, Communication and Computing, KunMing, China, 5–8 August 2013. [CrossRef] 27. Gharipour, A.; Liew, A.W.-C. Level set-based segmentation of cell nucleus in fluorescence microscopy images using correntropy- based K-means clustering. In Proceedings of the 2015 International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, Australia, 23–25 November 2015. [CrossRef] 28. Pacific Northwest National Laboratory (NPPL). U.S. Department of Energy, Annual Site Environmental Report; The U.S. Department of Energy: Oak Ridge, TN, USA, 2015; p. 155. 29. Lorenz, C.-L.; Packianather, M.; Spaeth, A.B.; De Souza, C.B. Artificial Neural Network-Based Modelling for Daylight Evaluations. In Proceedings of the SimAUD 2018, Delft, The Netherlands, 4–7 June 2018; 2018; Volume 2, pp. 1–8. [CrossRef] 30. Yi, H.; Kim, M.-J.; Kim, Y.; Kim, S.-S.; Lee, K.-I. Rapid Simulation of Optimally Responsive Façade during Schematic Design Phases: Use of a New Hybrid Metaheuristic Algorithm. Sustainability 2019, 11, 2681. [CrossRef] 31. Trakhtenbrot, B. A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms. IEEE Ann. Hist. Comput. 1984, 6, 384–400. [CrossRef] 32. Tabadkani, A.; Banihashemi, S.; Hosseini, M.R. Daylighting and visual comfort of oriental sun responsive skins: A parametric analysis. Build. Simul. 2018, 11, 663–676. [CrossRef] 33. Reinhart, C.F.; Weissman, D.A. The daylit area—Correlating architectural student assessments with current and emerging daylight availability metrics. Build. Environ. 2012, 50, 155–164. [CrossRef] 34. Nabil, A.; Mardaljevic, J. Useful daylight illuminances: A replacement for daylight factors. Energy Build. 2006, 38, 905–913. [CrossRef] 35. Nabil, A.; Mardaljevic, J. Useful daylight illuminance: A new paradigm for assessing daylight in buildings. Light. Res. Technol. 2005, 37, 41–57. [CrossRef] 36. Chauvel, P.; Collins, J.; Dogniaux, R.; Longmore, J. Glare from windows: Current views of the problem. Light. Res. Technol. 1982, 14, 31–46. [CrossRef] 37. Ostertagová, E.; Ostertag, O. Methodology and Application of One-way ANOVA. Am. J. Mech. Eng. 2013, 1, 256–261. [CrossRef] 38. Wong, A.; Wong, S. A Cross-Cohort Exploratory Study of a Student Perceptions on Mobile Phone-Based Student Response System Using a Polling Website. Int. J. Educ. Dev. Using Inf. Commun. Technol. 2016, 12, 58–78. Buildings 2022, 12, 878 22 of 22 39. Hailemeskel Abebe, T. The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology. Math. Lett. 2019, 5, 33–40. [CrossRef] 40. R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2014; Available online: http://www.R-project.org/ (accessed on 12 June 2022). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Buildings Multidisciplinary Digital Publishing Institute

A Novel Framework for Optimizing Indoor Illuminance and Discovering Association of Involved Variables

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buildings Article A Novel Framework for Optimizing Indoor Illuminance and Discovering Association of Involved Variables 1 , 2 3 4 Negar Heidari Matin * , Ali Eydgahi , Amin Gharipour and Payam Matin Gibbs College of Architecture, University of Oklahoma, Norman, OK 73019, USA Gameabove College of Engineering & Technology, Eastern Michigan University, Ypsilanti, MI 48197, USA; aeydgahi@emich.edu Ambassador Crawford College of Business and Entrepreneurship, Kent State University, Kent, OH 44240, USA; agharip1@kent.edu Department of Engineering and Aviation Sciences, University of Maryland Eastern Shore, Princess Anne, MD 21853, USA; phmatin@umes.edu * Correspondence: negar.matin@ou.edu Abstract: The associations between various design variables affecting the visual performance of responsive facade systems are investigated in this study. First, we propose a data-driven approach to study practical aspects of illuminance optimization for responsive facades. In this approach, the hourly indoor illuminance data are combined with the location information to generate an objective function. This function is then utilized to evaluate the visual performance of responsive facade systems by matching a variety of facade angle movements to hourly sunshine patterns. Next, statistical tests were deployed to evaluate the role of design variables in different scenarios. The results provide detailed information about the design variables and their effects on visual comfort at 0.05 significant levels. On average, facade angles, facade configurations, facade orientations, and facade locations were significant in 100%, 41%, 87%, and 45% of different possible combinations of Citation: Matin, N.H.; Eydgahi, A.; scenarios/variables, respectively. Gharipour, A.; Matin, P. A Novel Framework for Optimizing Indoor Keywords: responsive facades; facade optimization; visual comfort; data-driven design; statistical tests Illuminance and Discovering Association of Involved Variables. Buildings 2022, 12, 878. https:// doi.org/10.3390/buildings12070878 1. Introduction Academic Editors: Wei-Ling Hsu, A building facade system is one of the most important contributors to occupant Teen-Hang Meen, Hsi-Chi Yang and comfort [1]. The performance of building facades contributes to 17 percent of occupants’ Wen-Der Yu visual comfort and 58 percent of occupants’ thermal comfort [2,3]. Traditional facades, Received: 5 April 2022 as static systems, are incapable of altering their performance over time in response to Accepted: 14 June 2022 frequent variations in weather [4–6]. The performance of dynamic facades developed by Published: 22 June 2022 advanced technologies can improve the limited response of static facades [7–9]. Facade Publisher’s Note: MDPI stays neutral systems have the potential to change their function, features, and behavior over time in with regard to jurisdictional claims in response to repeated weather changes using advanced control technologies [10]. If the published maps and institutional affil- design variables for a responsive facade system are optimized for specific objectives, such iations. as improved occupant visual comfort [11], the system can perform optimally. Occupants’ visual comfort optimization is not a straightforward process [12]. The number of variables involved and the complexity of interactions among the variables make the optimization problem a difficult task for designers [13,14]. Copyright: © 2022 by the authors. In the design process, three types of design variables must be considered: active Licensee MDPI, Basel, Switzerland. design variables, passive design variables, and environmental variables [13]. Active design This article is an open access article variables such as louver angles, the facade porosity, and facade granularity can adjust distributed under the terms and the response to external stimuli and interior elements [9]. In contrast, passive design conditions of the Creative Commons variables remain constant in response to external stimuli and interior elements, including Attribution (CC BY) license (https:// infiltration, window-to-wall ratio, glazing types, and wall insulation [15]. Furthermore, creativecommons.org/licenses/by/ parametric study of environmental variables such as climate zones, building locations, 4.0/). Buildings 2022, 12, 878. https://doi.org/10.3390/buildings12070878 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 878 2 of 22 facade orientations, and facade configurations can be implemented to develop multiple design scenarios [14]. Limited past studies developed mathematical models that incorporate active, passive, and environmental variables to optimize visual comfort in responsive facades [13–15]. However, no study has investigated the impact of the design variables and their associations with the optimization function in responsive facades. In this study, we present a double stage framework for investigating the associations between various design variables affecting the visual performance of responsive facade systems. First, we focused on louver adaptation angles in horizontal and vertical facade configuration. An objective function for obtaining optimal indoor illuminance is intro- duced, utilizing hourly adaptation angles. Compared to the previous objective functions, the proposed function can support all possible occupant activities with the required illu- minance ranges. Moreover, the proposed function can deliver an optimal solution even when multiple activities are conducted in the room in different timeframes. The brute force search algorithm is implemented to decide the optimum hourly angles for various facade configurations, orientations, and locations/climates. To find the maximum indoor illuminance, the proposed optimization function is calculated for increments of the facade variables and time. In the second stage, a proposed three-step framework is implemented to investigate the associations of various design variables with the optimal solution affecting the visual performance of responsive facade systems. The three main steps of the proposed framework are (1) defining scenarios, (2) performing statistical tests, and (3) evaluating the test results, which determines the association of the variables with the optimal solution. Since the proposed framework yields the optimum angles as its main outcome, the optimum angles are inputted in a facade control system. This potentially could not only improve control latency, but also reduce computational cost. However, it should be ex- plicitly noted that the cost of the hardware and required computational power were not considered in this study and would vary depending on the building specifications. 2. Materials and Methods 2.1. Experimental Settings A typical office room was designed using Rhinoceros version 6.0 developed by Robert McNeel & Associates (Seattle, WA, USA). The dimensions of the designed office were 4.0 m wide, 9.0 m deep, and 3.0 m high. The typical daylight zone is about 7.0 m deep from the window wall in common office spaces [16]. The thickness of walls, ceiling, and flooring elements are 0.15 m, 0.12 m, and 0.12 m, respectively. The depth of the office was chosen to be larger than the typical depth so that the effect of daylight remains visible for all variables [17]. Natural light was considered as the only source of light in the office room, with no artificial lighting inside. This simulated office room had a window opening of 2.6 m width and 3.6 m length. The window was made from double-glazed, clear glass with a visible light transmittance of 76% that was installed on the small side of the office room. The window-to-wall ratio before applying the responsive facade system was 78% (floor 2 2 area = 36.0 m and window area = 9.36 m representing a 26% glazing to floor ratio). Using the Grasshopper modeling tool, a responsive facade system was simulated parametrically and applied to the office window. The simulated office room could be rotated to face the four main cardinal directions (N, W, S, E) in order to create various design scenarios. The horizontal and vertical louver angles were able to be rotated hourly from 90 de- grees to +90 degrees in response to daylight patterns during the day. Horizontal and vertical louvers moved in a clockwise direction from 90 degrees to +90 degrees. The movement of louvers was divided into 60 steps with increments of 3 degrees. The designed facades considered for simulation consisted of 7 horizontal and 7 vertical louvers with dimensions of 3 m  0.26 m  0.18 m, as shown in Figure 1. The distances between louvers in the horizontal configuration were 0.40 m and in the vertical configuration were 0.50 m when Buildings 2022, 12, x FOR PEER REVIEW 3 of 22 movement of louvers was divided into 60 steps with increments of 3 degrees. The de- signed facades considered for simulation consisted of 7 horizontal and 7 vertical louvers with dimensions of 3 m × 0.26 m × 0.18 m, as shown in Figure 1. The distances between Buildings 2022, 12, 878 3 of 22 louvers in the horizontal configuration were 0.40 m and in the vertical configuration were 0.50 m when louvers were fitted on 0 degrees. It is assumed that the louvers were built from diffuse metal provided by DIVA, which corresponds to Radiance parameters louvers were fitted on 0 degrees. It is assumed that the louvers were built from diffuse of 0.9 specularity, 0.175 roughness, and 0.175 reflectance (RGB) in the DIVA plug-in. metal provided by DIVA, which corresponds to Radiance parameters of 0.9 specularity, 0.175 roughness, and 0.175 reflectance (RGB) in the DIVA plug-in. (a) (b) Figure 1. Standard south-facing office space with workstations. (a) Horizontal responsive louvers. Figure 1. Standard south-facing office space with workstations. (a) Horizontal responsive louvers. (b) Vertical responsive louvers. (b) Vertical responsive louvers. The DIVA daylight-modeling plug-in was utilized to measure indoor illuminance and its corresponding visual metric of Useful Daylight Illuminance (UDI). The DIVA is one of Grasshopper ’s plug-ins, which assists Grasshopper in conducting sustainability simulations, such as daylight analysis. Radiance is the core of the DIVA engine and was previously validated by other researchers [18–25]. It has been proven by Reinhart and Walkenhorst that Radiance-based simulation methods are able to efficiently and accu- rately model complicated daylighting elements [18]. It has also been demonstrated by Buildings 2022, 12, x FOR PEER REVIEW 4 of 22 The DIVA daylight-modeling plug-in was utilized to measure indoor illuminance and its corresponding visual metric of Useful Daylight Illuminance (UDI). The DIVA is one of Grasshopper′s plug-ins, which assists Grasshopper in conducting sustainability simulations, such as daylight analysis. Radiance is the core of the DIVA engine and was previously validated by other researchers [18–25]. It has been proven by Reinhart and Walkenhorst that Radiance-based simulation methods are able to efficiently and accu- rately model complicated daylighting elements [18]. It has also been demonstrated by Buildings 2022, 12, 878 4 of 22 Ng et al. [18] that Radiance can be used to predict the internal illuminance with a high degree of accuracy. Additionally, Yoon et al. [19] have stated that Radiance is validated computational software and is well known to provide reliable prediction results under Ng et al. [18] that Radiance can be used to predict the internal illuminance with a high various sky conditions. Furthermore, Reinhart and Andersen have shown that translu- degree of accuracy. Additionally, Yoon et al. [19] have stated that Radiance is validated cent materials can be modeled in Radiance with even higher accuracy than was demon- computational software and is well known to provide reliable prediction results under strated earlier [20–25]. various sky conditions. Furthermore, Reinhart and Andersen have shown that translucent A grid-based metric of indoor illuminance was developed by defining 220 sensors materials can be modeled in Radiance with even higher accuracy than was demonstrated located over a horizontal grid surface with a height of 0.8 m from the office floor, which earlier [20–25]. was within the average height of a work surface in an office. In both directions of the A grid-based metric of indoor illuminance was developed by defining 220 sensors surface, sensors were spaced approximately every 0.43 m apart. The interior of the office located over a horizontal grid surface with a height of 0.8 m from the office floor, which room was simulated using standard Radiance materials that included a generic floor was within the average height of a work surface in an office. In both directions of the with 20% reflectance, a generic ceiling with 70% reflectance, generic interior walls with surface, sensors were spaced approximately every 0.43 m apart. The interior of the office 50% reflectance, and generic furniture with 50% reflectance. room was simulated using standard Radiance materials that included a generic floor with It was assumed that the office would be occupied daily from 8:00 a.m. to 6:00 p.m. 20% reflectance, a generic ceiling with 70% reflectance, generic interior walls with 50% without daylight savings time. IESNA’s new Lighting Measurement IES LM-83-12 was reflectance, and generic furniture with 50% reflectance. in agreement with the occupancy schedule [17]. It was assumed that six workspaces It was assumed that the office would be occupied daily from 8:00 a.m. to 6:00 p.m. would be occupied during occupancy hours. The occupants would be performing regu- without daylight savings time. IESNA’s new Lighting Measurement IES LM-83-12 was in lar office work, including working on computers. The clear sky with the sun was as- agreement with the occupancy schedule [17]. It was assumed that six workspaces would be sum occupied ed as during sky condi occupancy tions. Ty hours. pical ann The uoccupants al meteorolog would icalbe da performing ta provided regular as an En offi ergyP ce work, lus Weather including File working (EPWon ) by computers. the U.S. Depar The clear tment o sky with f Energ theysun were was utassumed ilized for t ashsky e seconditions. lected cit- Typical annual meteorological data provided as an EnergyPlus Weather File (EPW) by the ies/climate zones. Three design scenarios were considered: (1) no louvers/no shade, (2) fixed U.S. Department horizontal and of Ener vergy tical wer loe uv utilized ers with for ze the ro-d selected egree an cities/climate gle, and (3) rzones. esponsThr ive ee horizon- design scenarios were considered: (1) no louvers/no shade, (2) fixed horizontal and vertical louvers tal and vertical louvers with hourly optimum angles, as shown in Figure 2. These scenar- with zero-degree angle, and (3) responsive horizontal and vertical louvers with hourly ios were repeated parametrically for four facade orientations (N, W, S, E) and different optimum angles, as shown in Figure 2. These scenarios were repeated parametrically for facade locations/climate zones. four facade orientations (N, W, S, E) and different facade locations/climate zones. Figure 2. The three design scenarios. (a) No shade/no louvers. (b) Fixed louvers with zero-degree Figure 2. The three design scenarios. (a) No shade/no louvers. (b) Fixed louvers with zero-degree angle. (c) Responsive louvers with hourly optimum angles. angle. (c) Responsive louvers with hourly optimum angles. Four cities from different climate zones in the United States, namely, Miami (FL), Phoenix (AZ), Boston (MA), and Milwaukee (WI), were selected using K-cluster analysis along with an elbow method [26,27]. Annual meteorological data of the selected cities were adopted to simulate the hourly indoor illuminance associated with the multiple scenarios considered. Based on the ASHRAE classification, Miami and Phoenix represent the very Hot-Humid (1A) and Hot-Dry (2B) climates, respectively. Boston and Milwaukee represent Cool-Humid (5A) and Cold-Humid (6A) climates, respectively [28]. Hourly indoor illuminances were calculated at 220 predefined sensors for every 8760 h of a year, while the responsive louver angles were parametrically changed incrementally from90 to +90 . The measurements were repeated for four facade orientations, horizontal Buildings 2022, 12, x FOR PEER REVIEW 5 of 22 Four cities from different climate zones in the United States, namely, Miami (FL), Phoenix (AZ), Boston (MA), and Milwaukee (WI), were selected using K-cluster analysis along with an elbow method [26,27]. Annual meteorological data of the selected cities were adopted to simulate the hourly indoor illuminance associated with the multiple scenarios considered. Based on the ASHRAE classification, Miami and Phoenix repre- sent the very Hot-Humid (1A) and Hot-Dry (2B) climates, respectively. Boston and Mil- waukee represent Cool-Humid (5A) and Cold-Humid (6A) climates, respectively [28]. Buildings 2022, 12, 878 Hourly indoor illuminances were calculated at 220 predefined sensors for every 5 of 22 8760 h of a year, while the responsive louver angles were parametrically changed incre- mentally from −90 to +90°. The measurements were repeated for four facade orienta- tions, horizontal and vertical facade configurations, and four cities/climate zones. The and vertical facade configurations, and four cities/climate zones. The simulations ran simulations ran 37,843,200 times to calculate and stored raw indoor illuminance values 37,843,200 times to calculate and stored raw indoor illuminance values at 8,325,504,000. at 8,325,504,000. The stored output data of the DIVA plug-in were transferred and stored in the Postgres- The stored output data of the DIVA plug-in were transferred and stored in the SQL database. Then, R software was utilized to apply the brute force search algorithm Postgres-SQL database. Then, R software was utilized to apply the brute force search al- based gorithm based on the pro on the proposed objective posed objective func function to find tionthe to find the optim optimum louver um lo angles uver angles [29–31]. After calculating [29–31]. Aft indoor er calcul illuminance, ating indoor UDI illumina is calculated nce, UDI is as ca alcu metric, lated as which a metr repr ic, whi esents ch repre- both indoor sents both indoor illuminance level and discomfort glare in one scheme, as widely uti- illuminance level and discomfort glare in one scheme, as widely utilized in the field. lized in the field. Figure 3 shows the flow and execution of the data in the simulation. Figure 3 shows the flow and execution of the data in the simulation. Figure 3. Structure of the simulation runs. Figure 3. Structure of the simulation runs. 2.2. The Proposed Framework—Stage 1 2.2. The Proposed Framework—Stage 1 The UDI is a measure of the annual light quantity accessible in a certain interior The UDI is a measure of the annual light quantity accessible in a certain interior space. space. The annual average of UDI may be used to evaluate the annual performance of a The annual average of UDI may be used to evaluate the annual performance of a facade. facade. The UDI metric, which depends on both active and passive variables, is consid- The UDI metric, which depends on both active and passive variables, is considered as a ered as a dependent variable for establishing an objective function [28–31]. The UDI is dependent variable for establishing an objective function [28–31]. The UDI is calculated calculated not only as lower and upper thresholds but also as a useful value depending not only as lower and upper thresholds but also as a useful value depending on the range on the range of illuminance. The lower and upper thresholds and the useful value of of illuminance. The lower and upper thresholds and the useful value of UDI are denoted UDI are denoted as UDIunderlit, UDIoverlit, and UDIuseful, respectively [32]. In general, UDI is as UDI , UDI , and UDI , respectively [32]. In general, UDI is defined as a defined as a weigh underlit t overlit ed average as fol useful lows [30]: weighted average as follows [30]: ∑( . ) UDI = (1) ∑( ) (wf t ) i i i where ti is the time when the illumina UDI nce E= is calculated, and wfi is the weighting factor, (1) å (t ) which depends on the range of the calculated illuminance E. It should be noted that the weighting factor wfi is selected based on the range of the calculated illuminance E. For where t is the time when the illuminance E is calculated, and wf is the weighting factor, i i instance, as shown below, for the upper threshold, UDIoverlit is calculated as below after which depends on the range of the calculated illuminance E. It should be noted that the weighting factor wf is selected based on the range of the calculated illuminance E. For instance, as shown below, for the upper threshold, UDI is calculated as below after overlit wf is selected depending on how the illuminance E value compares to the upper limit of illuminance specified in standards: 1 if E > E Upper limit UDI with wf = (2) overall i 0 if E  E Upper limit In a similar way, the lower threshold UDI is calculated as: underlit 1 if E < E  E Lower limit Upper limit UDI with wf = (3) Usefull i 0 if E  E _ E > E Lower limit Upper limit Buildings 2022, 12, 878 6 of 22 Similarly, UDI is calculated as: useful 1 if E < E Daylight Lowelimit UDI with wf = (4) Underlit i 0 if E  E Daylight Lower limit To optimize indoor illuminance, an objective function is established in the following general form as: Obj = F(Active variables, Passive variables, Environmental variables )dx (5) general In this study, an objective function with active variables that can adapt the hourly daylight pattern is proposed. The illuminance includes the useful, overlit, and underlit ranges as the function constraints. These constraints divide interior space into three zones with three different levels of indoor illuminance appropriate for three distinct human activities. The goal of the proposed objective function is to increase the area of useful range for the different human activities and to decrease the area of undesirable ranges. Two configurations of responsive facades, facades with horizontal louvers and facades with vertical louvers, were considered. The selected configurations are the most influen- tial among various types of responsive facades with high visual performance in facade orientations [33–36]. Let S = s , . . . , s represent a specific set of human activities in a desired range 1 j of illuminance. H = {h , h , . . . , h } denotes hour of the day, and E(x, ) indicates the 1 2 k indoor illuminance for a specific point x located in the room for a louver angle of . Then, depending on whether or not the value of E(x, ) lays on one of the desired ranges, a new indication function I is calculated for a specific point of x in the room and louver angle (x,) by using Equation (3): 1 when E x,  is in the range of activity j ( ) I(x, ) = (6) 0 otherwise It should be noted that I indicates some indoor illuminance since it is based on the (x,) value of E(x, ). Depending on the importance of the human activities, which correspond to the illuminance ranges defined in S, a weighting factor W may be defined in a matrix form as: 2 3 w  w 1jsj 6 7 . . W = . . . (7) 4 5 . . w  w jHj1 jHjjsj The rows of the weighting factor are associated with the different human activities as defined in S. Thus, there are as many columns as the numbers of human activities as defined in S and denoted by jSj. The weighting factors of columns are associated with the different hours of the day as defined in H and denoted by |H| for which E(x, ) is calculated. The hours considered were from 8:00 a.m. to 6:00 p.m. For a given hour of h, the weighting factors associated with the human activities are obtained by calculating a weighted average of values of the indication function I for the (x,) entire points in the room. As shown in Equation (8), the weighted average can be considered as a new indoor illuminance function and be presented as a new metric, sAUDI : jsj w I(x, ) hj j=1 sAUDI (x, ) = dx (8) x2X where N denotes the total number of points in the room. X Buildings 2022, 12, x FOR PEER REVIEW 7 of 22 considered as a new indoor illuminance function and be presented as a new metric, sAUDIh: || ∑ ( ) (8) ( ) sAUDI x, θ = dx Buildings 2022, 12, 878 ∈ 7 of 22 where N denotes the total number of points in the room. The final objective function, AUDI, which is a function of the point x, the louvre an- The final objective function, AUDI, which is a function of the point x, the louvre angle gle θ, and the hour h, is computed by adding the calculated sAUDIh for all the hours, as , and the hour h, is computed by adding the calculated sAUDI for all the hours, as presented in Equation (9): presented in Equation (9): AUDI(x, θ,h) = sAUDI dh (9) AUDI(x, , h) = sAUDI dh (9) h2H 2.3. The Proposed Framework—Stage 2 2.3. The Proposed Framework—Stage 2 While the first stage of the framework aims to find the optimum angle by using Equation (6), the second stage investigates the role of various input variables in the op- While the first stage of the framework aims to find the optimum angle by using timum daylight illuminance. There are three steps in this stage, entitled scenario genera- Equation (6), the second stage investigates the role of various input variables in the optimum tion, hypothesis test assignment, and hypothesis test conduction and evaluation, as daylight illuminance. There are three steps in this stage, entitled scenario generation, shown in Figure 4. The scenario generation step includes the following: hypothesis test assignment, and hypothesis test conduction and evaluation, as shown in Figure 4. The scenario generation step includes the following: 1. A dependent variable is selected from the visual comfort and maximum visual comfort calculations of Equation (9). 1. A dependent variable is selected from the visual comfort and maximum visual comfort 2. An independent variable is chosen from active variables or environmental varia- calculations of Equation (9). bles. 2. An independent variable is chosen from active variables or environmental variables. 3. Other input variables are fixed at specific values. 3. Other input variables are fixed at specific values. Figure 4. Stage 2 of the framework. Figure 4. Stage 2 of the framework. As an example, in order to investigate whether the office orientation impacts the As an example, in order to investigate whether the office orientation impacts the values values of the maximum visual comfort, the office orientation and the maximum hourly of the maximum visual comfort, the office orientation and the maximum hourly visual visual comfort are considered as the independent variable and dependent variables, re- comfort are considered as the independent variable and dependent variables, respectively. spectively. Each design scenario needs a specific statistical test based on the type of the indepen- Each design scenario needs a specific statistical test based on the type of the inde- dent and dependent variables. Therefore, the second step assigns a statistical test from the pendent and dependent variables. Therefore, the second step assigns a statistical test list of available statistical tests based on the different experimental settings (scenarios) and from the list of available statistical tests based on the different experimental settings the type of the dependent and independent variables. The statistical tests available for this (scenarios) and the type of the dependent and independent variables. The statistical tests step include ANOVA, the Kruskal–Wallis, and Chi-squared [37–39]. available for this step include ANOVA, the Kruskal–Wallis, and Chi-squared [37–39]. Finally, the third step evaluates the results of the statistical test based on the obtained p-value, which measures the difference between the involved populations in the conducted test. A p-value greater than 0.05 indicates statistical insignificance. Thus, if the p-value calculated was below 0.05, the result was considered as statistically significant. All statistical analyses were carried out using R v.3.4.0 [40]. The complete list of the variables is provided in Table 1. Using the statistical tests presented in Table 1, the impacts of several independent variables on visual comfort were investigated. These independent variables include adaptation angles, type of rotational motion of the louvers (horizontal or Buildings 2022, 12, 878 8 of 22 vertical), orientations of responsive facade systems, and the range of the rotational angles of the louvers’ motion. Some of the independent variables mentioned are active variables and others are environmental. Table 1. Experimental settings for scenario generation. Independent Variable Dependent Variable Fixed Variables Assigned Test Scenarios Fixed facade City and Visual comfort Rotational Motion One-way ANOVA 384 Responsive facade with metric—UDI Orientation Adaptation angle Month of the year Horizontal louvers City Visual comfort and Orientation One-way ANOVA 192 metric—UDI Vertical louvers Month of the year City Building orientation Max visual comfort Rotational Motion Kruskal–Wallis 96 Month of the year Positive angles City and Max visual comfort Rotational Motion Chi squared 32 negative angles Orientation 3. Results The percentage values of the indoor illuminance function %sAUDI for the three different human activities of s , s , and s associated with the three different illuminance 2 3 ranges and for both horizontal and vertical louvers on two specific days of 21 June and 21 December are presented in Tables 2–5. The three different human activities of s , s , and 1 2 s associated with the three different illuminance ranges are introduced in Equation (7). s where 300 Lux  E x,   1000 Lux ( ) < 1 S = s where E(x, )  300 Lux (10) s where 1000 Lux  E(x, ) As shown in Table 2, at 12:00 p.m. on 21 June, the percentage value of sAUDI associated with the target range of s (where illuminance is between 300 Lux and 1000 Lux) is calculated as 36%. This value indicates that 36% of the working space area had the desired indoor illuminance (as specified for s human activity) if an optimum angle of32 degrees was chosen for south-facing horizontal louvers for that specific time of the year. The hourly optimum angles and sAUDI associated with ranges s , s , and s for all 2 3 h 1 the locations investigated including Miami, Phoenix, Boston, and Milwaukee on 21 June for the entire facade orientations are shown in Tables 6–11. Figure 5 shows the percentage values of sAUDI associated with ranges s , s , and h 1 2 s for a south-orientated office in Phoenix on 21 June when the responsive louvers were set at an optimum angle of 32 degrees. Furthermore, the percentage values of sAUDI on 21 June associated with ranges s , s , and s are illustrated in Figure 6a–c for four facade 1 2 3 orientations (N, W, S, E). Additionally, the visual representation of the estimated indoor illuminance in the office considered is depicted in Figure 7. It is observed that the area which experiences the targeted illuminance range s increases as a responsive facade with an optimum angle is utilized as opposed to a fixed louver system. Buildings 2022, 12, 878 9 of 22 Table 2. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 June-Phoenix-Horizontal louvers. June-21st-Horizontal Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 43 35.455 62.727 1.818 75 43.182 3.182 53.636 46 31.364 58.636 10.000 49 39.091 59.545 13.64 9:00 40 31.818 59.545 8.636 80 40.455 4.545 55.000 43 30.000 54.091 15.909 46 35.909 55.909 8.182 10:00 40 30.455 51.364 18.182 53 41.818 1.818 56.364 43 31.364 53.636 15.000 46 35.455 54.545 10.000 11:00 44 30.000 54.545 15.455 60 48.636 2.273 49.091 40 33.182 55.909 10.909 44 34.091 54.545 11.364 12:00 32 36.364 24.091 39.545 63 47.727 6.364 45.909 46 33.182 55.455 11.364 46 33.636 50.909 15.455 13:00 32 36.818 23.182 40.000 60 32.273 30.455 37.273 44 32.727 57.727 9.545 46 32.273 50.455 17.273 14:00 26 33.182 28.636 38.182 46 34.545 51.818 13.636 46 35.000 55.000 10.000 60 47.727 9.091 43.182 15:00 46 32.727 55.455 11.818 43 37.273 59.091 3.636 46 35.455 56.818 7.727 63 47.727 4.545 47.727 16:00 46 31.818 58.636 9.545 43 38.182 60.000 1.818 46 34.091 57.273 8.636 86 41.818 4.091 54.091 17:00 43 34.091 60.000 5.909 49 39.091 58.182 2.727 43 32.273 57.727 10.000 77 41.818 2.273 55.909 18:00 43 33.636 63.636 2.727 49 36.818 61.818 1.364 43 31.364 58.182 10.455 43 45.000 4.545 50.455 Table 3. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 June-Phoenix-Vertical louvers. June-21st-Vertical Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 32 26.818 54.545 18.636 66 43.636 4.545 51.818 34 26.818 52.273 20.909 69 27.273 55.909 16.818 9:00 12 26.818 47.727 25.455 80 41.364 2.273 56.364 32 25.909 47.727 26.364 69 27.273 50.909 21.818 10:00 26 26.818 46.818 26.364 89 40.909 5.909 53.182 32 26.818 46.818 26.364 77 27.273 50.000 22.727 Buildings 2022, 12, 878 10 of 22 Table 3. Cont. June-21st-Vertical Facade-Phoenix Orientations South East North West 11:00 14 25.909 41.818 32.273 83 31.818 23.182 45.000 29 27.727 47.273 25.000 80 26.818 48.636 24.545 12:00 46 25.455 46.364 28.182 75 25.455 38.636 35.909 32 26.364 46.818 26.818 77 26.818 47.273 25.909 13:00 32 25.455 44.091 30.455 57 25.455 47.273 27.273 32 27.273 48.182 24.545 69 25.455 47.273 27.273 14:00 34 26.818 43.636 29.545 83 28.636 45.455 25.909 26 28.182 46.818 25.000 52 26.818 44.545 28.636 15:00 29 27.727 47.273 25.000 86 29.545 48.182 22.273 0 28.182 47.273 24.545 80 31.364 24.091 44.545 16:00 14 28.182 47.273 24.545 77 30.909 49.091 20.000 3 27.727 47.273 24.545 89 35.909 10.000 54.091 17:00 17 28.182 51.818 20.000 77 30.909 52.273 16.818 40 28.182 53.182 18.636 66 39.545 4.091 56.364 18:00 37 27.273 51.818 20.909 66 27.273 57.727 15.000 40 27.273 55.455 17.273 57 42.273 3.182 54.545 Table 4. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for 1 2 3 21 December-Phoenix-Horizontal louvers. December-21st-Horizontal Facade-Phoenix Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 9:00 49 28.182 52.273 19.545 46 35.455 30.000 34.545 12 35.455 64.545 0.000 80 37.727 60.909 1.364 10:00 0 31.818 20.000 48.182 89 30.909 22.727 46.364 0 40.455 59.545 0.000 90 37.727 57.727 4.545 11:00 3 41.818 3.182 55.000 43 30.000 51.364 18.636 3 41.818 55.000 3.182 86 35.455 54.091 10.455 12:00 14 41.818 2.727 55.455 49 31.818 52.273 15.909 37 40.000 59.545 0.455 49 37.273 59.545 3.182 13:00 43 45.455 5.909 48.636 46 34.545 63.182 2.273 0 39.545 51.364 9.091 49 34.091 58.636 7.273 14:00 14 41.818 3.182 55.000 46 35.000 60.909 4.091 40 39.545 60.455 0.000 46 31.364 50.909 17.727 15:00 0 41.818 2.727 55.455 46 35.909 62.727 1.364 40 39.091 60.909 0.000 83 30.909 25.909 43.182 Buildings 2022, 12, 878 11 of 22 Table 4. Cont. December-21st-Horizontal Facade-Phoenix Orientations South East North West 16:00 0 31.364 20.455 48.182 52 35.455 64.545 0.000 0 35.909 57.273 6.818 83 32.273 15.000 52.727 17:00 52 27.727 55.000 17.273 86 30.455 60.000 9.545 12 30.455 60.000 9.545 49 35.000 28.182 36.818 18:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 Table 5. Hourly optimum angles and the associated sAUDI for three different human activities of s , s , and s and four facade orientations calculated for h 1 2 3 21 December-Phoenix-Vertical louvers. Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 9:00 1 31.364 56.818 11.818 37 35.000 47.273 17.727 43 26.818 72.273 0.909 60 25.455 72.727 1.818 10:00 17 33.182 16.818 50.000 72 31.364 24.091 44.545 20 30.000 62.273 7.727 83 28.182 64.545 7.273 11:00 3 44.545 3.182 52.273 57 27.727 34.545 37.727 12 31.818 58.182 10.000 69 27.727 63.182 9.091 12:00 46 44.091 5.000 50.909 80 28.182 50.909 20.909 20 32.273 53.182 14.545 63 27.727 54.545 17.727 13:00 52 41.818 3.636 54.545 80 28.636 55.000 16.909 14 32.273 54.545 13.182 89 27.727 55.455 16.818 14:00 43 45.000 4.545 50.455 66 28.636 50.909 20.455 0 30.909 51.818 17.273 54 26.364 52.273 21.364 15:00 9 42.273 2.273 55.455 86 28.182 54.545 17.273 9 28.636 54.091 17.273 60 27.273 31.818 40.909 16:00 29 34.545 15.909 49.545 86 29.091 59.545 11.364 12 28.636 59.545 11.818 57 30.000 0.055 44.545 17:00 46 26.818 57.727 15.455 89 23.182 65.455 11.364 32 22.727 65.455 11.818 40 32.273 46.818 20.909 18:00 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 89 0.000 100.000 0.000 Buildings 2022, 12, 878 12 of 22 Table 6. The hourly optimum angles and their associated %sAUDI on 21 June in MiamiHorizontal Louvers. June21st-Horizontal Facade-Miami Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 37 33.64 64.09 2.27 86 43.63 4.54 51.81 43 29.54 62.72 7.72 52 35.00 64.54 0.45 9:00 49 33.64 60.45 5.90 80 40.45 5.00 54.54 43 31.81 52.27 15.90 43 35.90 60.45 3.63 10:00 46 30.00 57.27 12.72 63 45.45 1.36 53.18 46 29.54 56.81 13.63 49 35.00 53.18 11.81 11:00 43 29.55 50.90 19.54 57 49.54 1.81 48.63 46 31.36 52.72 15.90 46 35.00 50.00 15.00 12:00 46 28.64 56.81 14.54 57 35.45 23.63 40.90 43 30.45 55.90 13.63 46 30.90 55.45 13.63 13:00 32 35.00 24.54 40. 75 36.36 22.72 40.90 29 32.27 28.18 39.54 60 38.18 19.54 42.27 14:00 43 29.09 51.81 19.09 46 28.63 30.45 40.90 49 29.54 57.27 13.18 69 31.36 24.54 44.09 15:00 49 30.91 66.81 22.72 46 33.18 63.63 3.18 43 30.90 60.00 9.09 63 34.09 54.00 41.81 16:00 43 30.91 59.54 9.54 54 36.81 59.54 3.63 43 29.54 55.90 14.54 54 45.90 68.18 48.63 17:00 32 29.55 70.00 0.45 54 29.09 70.90 3.18 32 29.54 70.00 0.04 46 30.90 59.09 0.00 18:00 37 30.00 69.54 0.45 72 30.45 69.09 3.63 43 30.00 70.00 0.00 46 37.27 53.18 3.63 Table 7. The hourly optimum angles and their associated %sAUDI on 21 June in Miami-Vertical louvers. June-21st-Vertical Facade-Miami Orientations South East North West %AUDI %AUDI %AUDI %AUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 32 26.82 55.00 18.18 80 40.00 13.63 46.36 17 25.91 55.00 19.09 77 26.81 60.00 13.18 9:00 6 27.27 46.81 25.90 80 41.36 2.72 55.90 34 26.82 48.18 25.00 60 27.72 52.72 19.54 10:00 29 25.45 50.00 24.54 80 32.27 22.27 45.45 26 25.91 47.27 26.81 69 26.36 50.90 22.72 11:00 3 25.45 42.27 32.27 89 25.91 33.18 40.90 6 25.45 43.18 31.36 69 25.90 46.81 27.27 Buildings 2022, 12, 878 13 of 22 Table 7. Cont. June-21st-Vertical Facade-Miami Orientations South East North West 12:00 20 23.18 47.27 29.54 54 23.64 46.36 30.00 32 23.64 49.54 26.81 77 24.09 50.90 25.00 13:00 3 23.64 43.18 33.18 89 23.64 43.63 32.72 34 24.09 45.90 30.00 26 23.18 45.00 31.81 14:00 32 22.72 46.36 30.90 54 22.73 46.81 30.45 40 22.73 46.81 30.45 52 22.27 46.81 30.90 15:00 20 24.55 50.45 25.00 72 25.45 54.54 20.00 0 25.00 49.09 25.90 52 23.63 46.81 29.54 16:00 17 25.45 50.90 23.63 77 28.64 51.36 20.00 40 25.91 52.72 21.36 86 25.90 30.45 43.63 17:00 32 19.55 65.90 14.54 54 19.09 69.54 11.36 0 19.09 64.54 16.36 60 19.54 66.36 14.09 18:00 34 20.45 65.45 14.09 57 20.45 65.90 13.63 3 22.27 60.45 17.27 54 26.36 54.54 19.09 Table 8. The hourly optimum angles and their associated %sAUDI on 21 June in Boston-Horizontal louvers. June-21st-Horizontal Facade-Boston Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 46 32.27 60.45 7.27 75 41.82 3.18 55.00 43 33.18 56.81 10.00 46 38.63 60.90 0.00 9:00 43 31.36 54.09 14.54 86 41.36 3.18 55.45 46 34.09 59.09 6.81 46 38.63 56.81 4.54 10:00 40 30.45 49.54 20.00 60 45.45 5.90 48.63 46 35.00 59.54 5.45 43 36.81 59.09 4.09 11:00 29 32.27 31.81 35.90 -63 36.82 22.72 40.45 43 39.55 60.00 0.00 43 37.72 59.09 3.18 12:00 26 37.73 22.27 40.00 46 32.73 51.36 15.90 46 36.36 59.54 4.54 49 35.00 49.09 15.90 13:00 26 35.00 27.27 37.72 46 36.36 55.45 8.18 46 39.55 59.54 0.00 46 35.45 49.09 15.45 14:00 46 31.82 52.27 15.90 46 36.36 55.45 8.18 43 37.27 61.81 3.18 63 45.00 10.45 44.54 15:00 40 31.36 50.45 18.18 43 37.73 60.00 2.27 46 33.64 58.63 6.81 60 43.63 2.72 53.63 16:00 43 32.27 57.27 10.45 46 38.64 59.54 1.81 46 33.64 59.54 4.54 80 41.81 4.09 54.09 17:00 40 33.18 60.45 6.36 49 39.55 0.00 60.45 40 30.45 58.63 10.90 43 45.45 5.00 49.54 18:00 40 32.27 67.72 0.00 52 34.09 0.00 65.54 40 28.64 59.54 11.81 43 44.09 6.81 49.09 Buildings 2022, 12, 878 14 of 22 Table 9. The hourly optimum angles and their associated %sAUDI on 21 June in BostonVertical louvers. June-21st-Vertical Facade-Boston Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 46 38.64 60.90 0.00 49 42.73 4.54 52.72 32 27.73 51.81 20.45 86 27.27 54.54 18.18 9:00 46 35.64 56.81 45.45 80 41.82 4.54 53.63 37 28.64 51.81 19.54 86 29.09 50.90 20.00 10:00 43 36.82 59.09 4.09 86 34.09 20.90 45.00 23 28.64 49.54 21.81 69 29.54 50.90 19.54 11:00 43 37.73 59.09 3.18 72 30.00 34.54 35.45 6 30.91 49.09 20.00 83 29.09 51.81 19.09 12:00 49 35.00 49.09 15.90 63 28.64 46.36 25.00 0 29.09 46.81 24.09 80 28.18 47.27 24.54 13:00 46 35.45 49.09 15.45 86 30.91 48.63 20.45 34 30.91 49.09 20.00 54 28.18 48.18 23.63 14:00 63 45.00 2.72 53.63 86 30.00 49.09 20.09 6 29.09 51.36 19.54 72 29.54 30.45 40.00 15:00 60 43.64 4.09 54.09 86 30.45 49.09 20.45 23 27.73 47.27 25.00 75 32.72 16.81 50.45 16:00 80 41.82 5.00 49.54 89 30.00 50.90 19.09 29 28.64 51.36 20.00 -80 39.09 3.63 57.27 17:00 43 45.45 6.81 49.09 72 30.00 54.09 15.90 29 27.27 45.90 26.81 49 42.27 3.18 54.54 18:00 43 44.09 10.45 49.09 66 25.91 60.90 1.31 17 27.73 44.54 27.72 -46 40.00 5.90 54.09 Table 10. The hourly optimum angles and their associated %sAUDI on 21 June in Milwaukee-Horizontal louvers. June21st-Horizontal Facade-Milwaukee Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 43 30.45 59.09 10.45 -69 43.64 1.81 54.54 40 31.45 59.09 10.45 46 35.91 61.81 2.27 9:00 40 30.00 51.81 18.18 69 40.91 0.00 59.09 43 31.00 51.81 18.18 46 35.45 56.36 8.18 10:00 40 31.36 49.54 19.09 63 45.00 3.18 51.81 43 32.36 49.54 19.09 43 38.18 59.09 2.72 11:00 43 31.36 50.45 18.18 60 35.91 22.27 41.81 40 31.36 50.45 18.18 43 38.18 59.09 2.72 12:00 26 34.55 27.72 37.72 49 33.18 51.36 15.45 26 35.55 27.72 37.72 49 35.45 53.18 11.36 Buildings 2022, 12, 878 15 of 22 Table 10. Cont. June21st-Horizontal Facade-Milwaukee Orientations South East North West 13:00 26 32.73 30.90 36.36 46 35.91 56.81 7.27 26 33.73 30.90 36.36 46 34.09 51.36 14.54 14:00 40 32.73 50.90 16.36 46 38.18 60.45 1.36 40 33.73 50.90 16.36 60 35.45 24.09 40.45 15:00 40 31.36 54.09 14.54 49 41.36 58.18 0.06 40 32.36 54.09 14.54 66 45.00 5.00 50.00 16:00 43 32.73 59.54 7.72 49 41.82 58.18 0.00 43 33.73 59.54 7.72 83 43.64 3.63 52.72 17:00 40 34.09 60.09 5.00 49 39.09 60.90 0.01 40 35.09 60.90 5.00 43 46.82 5.45 47.72 18:00 40 33.64 65.45 0.00 52 35.91 63.18 0.00 40 34.64 65.45 0.00 46 41.82 5.43 52.72 Table 11. The hourly optimum angles and their associated %sAUDI on 21 June in MilwaukeeVertical louvers. June-21st-Vertical Facade-Milwaukee Orientations South East North West %sAUDI %sAUDI %sAUDI %sAUDI h h h h Hours Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s Opt. Angle s s s 1 2 3 1 2 3 1 2 3 1 2 3 8:00 34 25.45 54.09 20.45 90 40.45 10.00 49.54 32 25.45 52.27 22.27 80 25.91 54.54 19.54 9:00 34 25.91 49.09 25.00 89 40.00 6.36 53.63 9 27.73 46.81 25.45 69 27.27 50.90 21.81 10:00 40 28.18 46.81 26.81 77 35.91 14.54 49.54 14 29.55 48.18 22.27 75 29.09 51.36 19.54 11:00 43 29.09 44.09 30.00 49 29.55 41.81 28.63 14 30.00 50.00 20.00 86 29.55 51.36 19.09 12:00 34 28.64 41.36 29.54 83 29.09 45.45 25.45 12 30.91 50.45 18.63 89 29.09 50.90 20.00 13:00 32 28.18 42.27 24.54 75 30.45 49.54 20.00 12 30.00 50.90 19.09 80 28.18 47.27 24.54 14:00 29 29.09 46.36 20.45 77 31.82 51.81 16.36 6 30.45 52.72 16.81 43 28.64 45.45 25.90 15:00 34 29.09 50.45 16.36 77 31.36 52.72 15.90 20 29.55 54.09 16.36 89 33.18 20.00 46.81 16:00 34 28.64 55.00 14.54 69 32.27 53.63 14.09 9 29.55 55.00 15.45 83 39.55 3.18 57.27 17:00 40 28.18 57.27 19.54 69 30.45 55.45 14.09 29 27.73 56.81 15.45 46 42.27 5.90 51.81 18:00 37 27.27 53.18 7.27 57 25.00 60.90 14.09 40 26.36 45.45 28.18 66 37.73 5.45 56.81 Buildings 2022, 12, x FOR PEER REVIEW 16 of 22 Buildings 2022, 12, 878 16 of 22 Buildings 2022, 12, x FOR PEER REVIEW 16 of 22 Figure 5. The %sAUDIh for three different human activities of s , s , and s for south facade orien- Figure 5. The %sAUDI for three different human activities of s , s , and s for south facade Figure 5. The %sAUDIh for three different human activities of s , s , and s for south facade orien- h 1 2 3 tations calculated for 21 June in Phoenix. tations orientations calculat calculated ed for 21for June in Phoenix. 21 June in Phoenix. (a) (a) (b) (b) Figure 6. Cont. Buildings 2022, 12, x FOR PEER REVIEW 17 of 22 Buildings 2022, 12, x FOR PEER REVIEW 17 of 22 Buildings 2022, 12, 878 17 of 22 (c) Figure 6. The %sAUDIh associated with s1, s2, and s3 for horizontal responsive louvers with opti- (c) mum angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) Figure 6. The %sAUDIh associated with s1, s2, and s3 for horizontal responsive louvers with opti- Figure 6. The %sAUDI associated with s , s , and s for horizontal responsive louvers with optimum h 1 2 3 North. mum angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) angles for south, east, north, and west facades on 21 June in Phoenix. (a) East, (b) West, (c) North. North. (a) Fixed louvers (a) Fixed louvers (b) Responsive louvers with an optimum angle Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in (b) Responsive louvers with an optimum angle Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in the office categorized with the three ranges of indoor illuminance s1, s2, and s3 for (a) fixed louvers the office categorized with the three ranges of indoor illuminance s , s , and s for (a) fixed louvers 1 2 3 Figure 7. Indoor illuminance distribution (on the assumed horizontal grid surface considered) in and (b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade and (b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade the office categorized with the three ranges of indoor illuminance s1, s2, and s3 for (a) fixed louvers in Phoenix. and ( in Phoenix. b) responsive louvers set with the optimum angle utilized at noon on 21 June for south facade in Phoenix. To examine the significance of the optimum adaptation angle (as an active variable) To examine the significance of the optimum adaptation angle (as an active variable) on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- To examine the significance of the optimum adaptation angle (as an active variable) tical tests were performed, and the results are shown in Table 6. The p-values less than tical tests were performed, and the results are shown in Table 6. The p-values less than on the maximum visual comfort, 384 scenarios were generated. One-way ANOVA statis- 0.05 demonstrate significant differences between the facade of fixed louvers of a 0- 0.05 demonstrate significant differences between the facade of fixed louvers of a 0-degree tical tests were performed, and the results are shown in Table 6. The p-values less than angle (base case) and the vast majority of the responsive facades of horizontal configuration 0.05 demonstrate significant differences between the facade of fixed louvers of a 0- for all orientations examined in the city of Phoenix. This suggests that applying the opti- mal adaptation angles to the responsive facade of horizontal configuration leads to more Buildings 2022, 12, 878 18 of 22 desirable indoor illuminance for the majority of cases. The p-value of greater than 0.05 in Table 12 suggests that there were no significant differences between the responsive facade with optimum adaption angles and the responsive facade with fixed louvers of a 0-degree angle. This case is associated with the month of December for the south orientation and suggests that for this specific time of the year, and for such an orientation, applying opti- mum adaptation angles does not lead to more desirable indoor illuminance as compared to the fixed facade. A similar approach was used for the responsive facade of vertical configurations for the city of Phoenix for all main orientations. It was observed that applying optimum adaptation angles led to more desirable indoor illuminance for facades of vertical configuration. One-way ANOVA statistical tests were conducted for four cities of Miami, Phoenix, Boston, and Milwaukee in both horizontal and vertical layouts. Table 12. Significant differences between fixed facade (FF) and responsive facade (RF) with horizontal louvers. T- Month City Type Orientation Mean_FF SD_FF Mean_RF Mean_Rf p-Value Significant Statistic January Phoenix Horizontal South 0.33 0.06 0.35 0.35 0.001 4.970 Yes February Phoenix Horizontal South 0.31 0.05 0.34 0.34 0.004 3.660 Yes Macrh Phoenix Horizontal South 0.27 0.02 0.35 0.35 0.002 4.130 Yes April Phoenix Horizontal South 0.30 0.03 0.32 0.32 0.000 5.810 Yes May Phoenix Horizontal South 0.31 0.03 0.33 0.33 0.002 4.210 Yes June Phoenix Horizontal South 0.28 0.02 0.33 0.33 0.000 6.360 Yes July Phoenix Horizontal South 0.29 0.02 0.33 0.33 0.000 8.580 Yes August Phoenix Horizontal South 0.28 0.06 0.31 0.31 0.000 5.230 Yes September Phoenix Horizontal South 0.28 0.02 0.34 0.34 0.005 3.590 Yes October Phoenix Horizontal South 0.26 0.08 0.32 0.32 0.001 4.690 Yes November Phoenix Horizontal South 0.31 0.10 0.33 0.33 0.007 3.480 Yes December Phoenix Horizontal South 0.33 0.06 0.36 0.36 0.057 2.280 Yes To evaluate the significance of rotation direction of the louver angle, both optimum positive and negative adaption angles were considered as the independent variables. Different orientations and cities were considered for both positive and negative adaptation angles to generate 32 scenarios for both horizontal and vertical louvers. Then, Chi-squared tests were utilized. The results for Phoenix are shown in Table 13, which demonstrates that Chi-squared tests delivered significantly low p-values (p < 0.05), indicating there were significant differences between the optimum positive and negative adaptation angles for both horizontal and vertical louvers in all four facade orientations. Table 13. Significant differences between positive and negative optimum adaptation angles in the city of Phoenix. City Type Orientation Statistic p-Value Significant Phoenix Horizontal North 140.01 3  10 Yes Phoenix Vertical North 139.38 4  10 Yes Phoenix Horizontal West 139.62 Yes 3  10 Phoenix Vertical West 139.62 3  10 Yes Phoenix Horizontal South 139.93 3  10 Yes Phoenix Vertical South 139.99 Yes 3  10 Phoenix Horizontal East 139.93 3  10 Yes Phoenix Vertical East 140.02 3  10 Yes Buildings 2022, 12, 878 19 of 22 To study the role of horizontal versus vertical louvers, 192 distinct scenarios were considered and one-way ANOVA tests were performed. The results are shown in Table 14, providing different ranges of p-values depending on month of the year. Thus, the difference between horizontal and vertical louvers is significant for only those months of the year when the p-value is below 0.05. For the remaining months, the difference was found to be insignificant. Table 14. Significant differences between horizontal and vertical louvers for the months of January, February, June, July, November, and December. Mean SD Mean SD T- Month City Orientation p-Value Significant Imp_H Imp_H Imp_V hmp_V Statistic January Phoenix South 5.66 3.32 36.70 42.02 0.0445 2.329 Yes February Phoenix South 9.37 8.12 18.51 9.58 0.0258 2.414 Yes March Phoenix South 26.51 20.01 13.30 7.05 0.0604 2.065 No April Phoenix South 7.61 5.24 12.31 7.02 0.0779 1.857 No May Phoenix South 5.96 5.82 6.64 4.18 0.7449 0.330 No June Phoenix South 20.59 12.57 6.89 4.94 0.0033 3.515 Yes July Phoenix South 13.65 6.11 8.95 4.64 0.0461 2.122 Yes August Phoenix South 17.73 23.74 11.88 5.58 0.4220 0.831 No September Phoenix South 23.12 20.38 14.87 8.43 0.2362 1.240 No October Phoenix South 30.18 34.00 11.27 8.83 0.1009 1.786 No November Phoenix South 9.87 13.33 27.39 17.95 0.0179 2.599 Yes December Phoenix South 10.75 11.50 29.27 20.69 0.0362 2.346 Yes To determine the significance of the four key orientations of building facades, 96 sce- narios were considered that included both horizontal and vertical louvers. Kruskal–Wallis tests were applied to the scenarios and the results are shown in Table 15, which shows significant differences for all four facade orientations. The tests were repeated for four different cities, and similar results were achieved. Table 15. Significant differences among different building orientations including south-facing, north- facing, east-facing, and west-facing in Phoenix. Month City Type T-Statistic p-Value Significant January Phoenix Horizontal 28.19 3  10 Yes February Phoenix Horizontal 28.79 2  10 Yes March Phoenix Horizontal 26.78 7  10 Yes April Phoenix Horizontal 34.89 Yes 1  10 May Phoenix Horizontal 32.95 3  10 Yes June Phoenix Horizontal 34.61 1  10 Yes July Phoenix Horizontal 35.86 8  10 Yes August Phoenix Horizontal 35.86 4  10 Yes September Phoenix Horizontal 30.62 Yes 1  10 October Phoenix Horizontal 16.19 Yes 1  10 November Phoenix Horizontal 26.31 8  10 Yes December Phoenix Horizontal 23.46 3  10 Yes Buildings 2022, 12, 878 20 of 22 4. Conclusions In this study, we developed an objective function and a data-driven approach to investigate the contribution of different design variables to the visual performance of responsive facades. A computer model of an office with specific responsive facades (in the form of louvers) was constructed as an architectural space. For a specific hour of a day, the louvers were set to a specific adaptation angle, and a simulation was conducted to estimate the indoor illuminance. For the same selected hour, the simulation was repeated for a range of different adaptation angles to estimate the associated indoor illuminance. The data collected on indoor illuminance were fed into the proposed objective function to deliver the optimum adaptation angle for the selected hour. This process was repeated for all hours of a day and all days of a year. The study was also repeated for several design variables, including the location of the office, orientation of the office, and the facade’s configuration being vertical or horizontal. Statistical tests were implemented to investigate the significance of the design variables on the visual comfort under different scenarios. In limited cases, and under specific circumstances, some design variables were found to be insignificant. The results of this study indicate that obtaining and deploying optimum adaptation angles could lead to significantly desired levels of visual comfort. Implementing the proposed approach could help designers achieve higher levels of visual comfort, although the specifics of the design variables (such as location, orientation, and facade configuration) must be considered during the design process. Author Contributions: N.H.M., conceptualization, methodology, software, draft preparation, and writing; A.E., validation, reviewing, and editing; A.G., writing, methodology, analysis, data curation; P.M., writing, reviewing, validation, and editing. All authors have read and agreed to the published version of the manuscript. Funding: This project was funded by the Faculty Investment Program (FIP) Provided by the Vice President for Research and Partnership at the University of Oklahoma. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Aksamija, A. Design methods for sustainable, high-performance building facades. Adv. Build. Energy Res. 2015, 10, 240–262. [CrossRef] 2. Grobman, Y.J.; Capeluto, I.G.; Austern, G. External shading in buildings: Comparative analysis of daylighting performance in static and kinetic operation scenarios. Arch. Sci. Rev. 2017, 60, 126–136. [CrossRef] 3. Wagdy, A.; Fathy, F.; Altomonte, S. Evaluating the daylighting performance of dynamic facades by using new annual climate- based metrics. Proceeding of the 36th International Conference on Passive and Low Energy Architecture, Los Angeles, CA, USA, 11–13 July 2016. 4. Selkowitz, S.E.; Aschehoug, Ø.; Lee, E.S. Advanced interactive facade: Critical elements for future green buildings. In Proceedings of the GreenBuild, the Annual USGBC International Conference and Expo, Philadelphia, PA, USA, 20–22 November 2013. 5. Kim, K.; Jerratt, C. Energy performance of an adaptive facade system. J. Archit. Res. 2011, 179–186. [CrossRef] 6. Sørensen, L.S. Heat Transmission Coefficient Measurements in Buildings Utilizing a Heat Loss Measuring Device. Sustainability 2013, 5, 3601–3614. [CrossRef] 7. Veliko, K.; Thun, G. Responsive Building Envelopes: Characteristics and Evolving Paradigms in Design and Construction of High- Performance Homes; Routledge Press: New York, NY, USA, 2013. 8. Heidari Matin, N.; Eydgahi, A.; Shyu, S.; Matin, P. Evaluating visual comfort metrics of responsive facade systems as educational activities. Proceeding of the ASEE Annual Conference & Exposition Proceedings, Salt Lake City, UT, USA, 23–27 July 2018. [CrossRef] 9. Matin, N.H.; Eydgahi, A. Technologies used in responsive facade systems: A comparative study. Intell. Build. Int. 2019, 14, 54–73. [CrossRef] Buildings 2022, 12, 878 21 of 22 10. Heidari Matin, N.; Eydgahi, A.; Shyu, S. Comparative analysis of technologies used in responsive building facades. In Proceedings of the ASEE Annual Conference & Exposition Proceedings, Columbus, OH, USA, 24–27 June 2018. 11. Zemella, G.; Faraguna, A. Evolutionary Optimization of Facade Design; Springer: London, UK, 2014. [CrossRef] 12. Loonen, R.C.G.M.; Trcka, ˇ M.; Cóstola, D.; Hensen, J.L.M. Climate adaptive building shells: State-of-the-art and future challenges. Renew. Sustain. Energy Rev. 2013, 25, 483–493. [CrossRef] 13. Shan, R. Climate Responsive Facade Optimization Strategy. Ph.D. Dissertation, University of Michigan, Ann Arbor, MI, USA, 2016. 14. Matin, N.H.; Eydgahi, A. A data-driven optimized daylight pattern for responsive facades design. Intell. Build. Int. 2021, 1–12. [CrossRef] 15. Shan, R.; Junghans, L. “Adaptive radiation” optimization for climate adaptive building facade design strategy. Build. Simul. 2018, 11, 269–279. [CrossRef] 16. Ochoa, C.E.; Capeluto, I.G. Evaluating visual comfort and performance of three natural lighting systems for deep office buildings in highly luminous climates. Build. Environ. 2006, 41, 1128–1135. Available online: https://www.academia.edu/309066 0/Evaluating_visual_comfort_and_performance_of_three_natural_lighting_systems_for_deep_office_buildings_in_highly_ luminous_climates (accessed on 12 June 2022). [CrossRef] 17. Reinhart, C.F.; Walkenhorst, O. Validation of dynamic RADIANCE-based daylight simulations for a test office with external blinds. Energy Build. 2001, 33, 683–697. [CrossRef] 18. Ng, E.Y.-Y.; Poh, L.K.; Wei, W.; Nagakura, T. Advanced lighting simulation in architectural design in the tropics. Autom. Constr. 2001, 10, 365–379. [CrossRef] 19. Yoon, Y.; Moon, J.W.; Kim, S. Development of annual daylight simulation algorithms for prediction of indoor daylight illuminance. Energy Build. 2016, 118, 1–17. [CrossRef] 20. Reinhart, C.F.; Andersen, M. Development and validation of a Radiance model for a translucent panel. Energy Build. 2006, 38, 890–904. [CrossRef] 21. Reinhart, C.F.; Jakubiec, A.; Ibarra, R. Definition of a reference office for standardized evaluations of dynamic facade and lighting technologies. Proc. Build. Simul. 2013, 5, 560–580. 22. Mardaljevic, J. Validation of a lighting simulation program under real sky conditions. Light. Res. Technol. 1995, 27, 181–188. [CrossRef] 23. Mardaljevic, J. Daylight Simulation: Validation, Sky Models and Daylight Coefficients. Ph.D. Thesis, De Montfort University, Leicester, UK, 2000. 24. Mardaljevic, J. The BRE-IDMP dataset: A new benchmark for the validation of illuminance prediction techniques. Light. Res. Technol. 2001, 33, 117–134. [CrossRef] 25. Mardaljevic, J. Verification of program accuracy for illuminance modelling: Assumptions, methodology and an examination of conflicting findings. Light. Res. Technol. 2004, 36, 217–239. [CrossRef] 26. Gharipour, A.; Liew, A.W.-C. An integration strategy based on fuzzy clustering and level set method for cell image segmentation. In Proceedings of the 2013 IEEE International Conference on Signal, Communication and Computing, KunMing, China, 5–8 August 2013. [CrossRef] 27. Gharipour, A.; Liew, A.W.-C. Level set-based segmentation of cell nucleus in fluorescence microscopy images using correntropy- based K-means clustering. In Proceedings of the 2015 International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, Australia, 23–25 November 2015. [CrossRef] 28. Pacific Northwest National Laboratory (NPPL). U.S. Department of Energy, Annual Site Environmental Report; The U.S. Department of Energy: Oak Ridge, TN, USA, 2015; p. 155. 29. Lorenz, C.-L.; Packianather, M.; Spaeth, A.B.; De Souza, C.B. Artificial Neural Network-Based Modelling for Daylight Evaluations. In Proceedings of the SimAUD 2018, Delft, The Netherlands, 4–7 June 2018; 2018; Volume 2, pp. 1–8. [CrossRef] 30. Yi, H.; Kim, M.-J.; Kim, Y.; Kim, S.-S.; Lee, K.-I. Rapid Simulation of Optimally Responsive Façade during Schematic Design Phases: Use of a New Hybrid Metaheuristic Algorithm. Sustainability 2019, 11, 2681. [CrossRef] 31. Trakhtenbrot, B. A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms. IEEE Ann. Hist. Comput. 1984, 6, 384–400. [CrossRef] 32. Tabadkani, A.; Banihashemi, S.; Hosseini, M.R. Daylighting and visual comfort of oriental sun responsive skins: A parametric analysis. Build. Simul. 2018, 11, 663–676. [CrossRef] 33. Reinhart, C.F.; Weissman, D.A. The daylit area—Correlating architectural student assessments with current and emerging daylight availability metrics. Build. Environ. 2012, 50, 155–164. [CrossRef] 34. Nabil, A.; Mardaljevic, J. Useful daylight illuminances: A replacement for daylight factors. Energy Build. 2006, 38, 905–913. [CrossRef] 35. Nabil, A.; Mardaljevic, J. Useful daylight illuminance: A new paradigm for assessing daylight in buildings. Light. Res. Technol. 2005, 37, 41–57. [CrossRef] 36. Chauvel, P.; Collins, J.; Dogniaux, R.; Longmore, J. Glare from windows: Current views of the problem. Light. Res. Technol. 1982, 14, 31–46. [CrossRef] 37. Ostertagová, E.; Ostertag, O. Methodology and Application of One-way ANOVA. Am. J. Mech. Eng. 2013, 1, 256–261. [CrossRef] 38. Wong, A.; Wong, S. A Cross-Cohort Exploratory Study of a Student Perceptions on Mobile Phone-Based Student Response System Using a Polling Website. Int. J. Educ. Dev. Using Inf. Commun. Technol. 2016, 12, 58–78. Buildings 2022, 12, 878 22 of 22 39. Hailemeskel Abebe, T. The Derivation and Choice of Appropriate Test Statistic (Z, t, F and Chi-Square Test) in Research Methodology. Math. Lett. 2019, 5, 33–40. [CrossRef] 40. R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2014; Available online: http://www.R-project.org/ (accessed on 12 June 2022).

Journal

BuildingsMultidisciplinary Digital Publishing Institute

Published: Jun 22, 2022

Keywords: responsive facades; facade optimization; visual comfort; data-driven design; statistical tests

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