fuzzy logic model to classify effectiveness of daylighting in an office with a movable blind system

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Building and Environment 69 (2013) 22e34

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Building and Environment

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Fuzzy logic model to classify effectiveness of daylighting in an officewith a movable blind system

Tu�gçe Kazanasmaz*

Department of Architecture, _Izmir Institute of Architecture, Urla 35430, Izmir, Turkey

a r t i c l e i n f o

Article history:Received 26 April 2013Received in revised form13 July 2013Accepted 16 July 2013

Keywords:DaylightingFuzzy logicUniformityBuildingMovable blind

* Tel.: þ90 232 7507063.E-mail addresses: [email protected], tugcekazan

0360-1323/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.buildenv.2013.07.011

a b s t r a c t

This study estimated daylight illuminance and classified its effectiveness in an office with a movableblind system. First, measurements were carried out to validate and apply a simulation model usingDIALux. Second, the simulation model was constructed utilizing physical properties similar to those ofthe case office. Third, the simulation model provided the daylighting calculations in terms of the slatangles of the movable blind system. A fuzzy model was later employed using the Mamdani fuzzyinference system. Four inputs, namely, hour, angle, distance and location, were fuzzified in this model.The daylight illuminance at specific points was successfully estimated by implementing fuzzy rules,resulting in a prediction power of 87%. To test the distribution of daylight illuminance inside the office,effectiveness classes of uniformity were constructed by this model in accordance with daylightingstandards and design norms. Regarding the movable blind system, slat angles of 30� and 45� providedmore uniformly distributed daylight than other angles throughout standard working hours. Thus, ac-cording to the degree of match between the simulated and fuzzy models, the majority of the uniformityoutcomes of the fuzzy model fully fit the simulation outcomes. Because the fuzzy model successfullyestimated the daylight illuminance and its distribution (uniformity), it could be easily employed toexamine early architectural design schemes.

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1. Introduction

Daylight penetration and its even distribution throughout aspace are basic considerations made in building design. Both definethe effectiveness of daylighting. A sufficient amount of daylightreduces the demand for electrical lighting and provides a healthyvisual environment. Moreover, daylighting results in enhancedenergy efficiency and visual acuity [1e5]. Apart from the benefitprovided by daylight’s intensity, uniformly distributed daylightdoes not give rise to glaring surfaces and enhances visual qualityand comfort [6e9,10]. Consequently, the primary physical measureuse to quantify this phenomenon is illuminance. The estimation ofuniformly distributed daylight is necessary, both in early architec-tural design processes and in daylighting performance evaluationstudies [5,11e13]. Foreseeing further deficiencies regardingdaylighting, i.e., incorrect window dimensions or misuse of a blindsystem, can be avoided in the early design stage. While evaluatingthe daylighting performance of an existing interior, any visual

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comfort problems related to daylight may be assessed straightfor-wardly and rapidly.

The literature reveals several techniques for predicting daylightilluminance. Contemporary techniques that have been used overthe years include the construction of scale models and the use ofanalytical formulas and simulation tools. An overview of thesemethods was presented in previous studies by the author [14,15].The strengths and weaknesses of these techniques were explainedby reviewing selected studies. Recent methodologies, such asartificial intelligence [14], simulation tools such as Radiance, DIA-Lux, etc. [12,16e18] and a trial simulation tool named Codyrun [19],have been introduced to predict indoor illuminance by acceptingthe irrefutable nature of daylighting and by simplifying itscomplexity for the ease of design. Several studies of daylightingmetrics and rules of thumb have also been proposed to overcomeinitial design problems [1,2,20]. Gagne et al. [10] suggested aninteractive design expert system for daylighting design, whichmight be used in the early design phase. This systemwas developedas an alternative to simulation tools to guide users inmaking designmodifications. This tool was defined as a “virtual daylightingconsultant”, including a daylighting knowledge-base and a fuzzyrule-based decision-making logic. The former involved information

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T. Kazanasmaz / Building and Environment 69 (2013) 22e34 23

about the impact of design conditions on daylighting, while thelatter is for the decision on the main effect on design actions toimprove daylighting conditions [10]. Reinhart and Wienold [5]proposed a new method for conducting integrated daylightingdesign analysis and thereby examine annual daylight availability,visual comfort and energy use together with dynamic simulationpotentials. The authors named this tool ‘the daylighting dashboard’.It is known that there are many variables affecting daylight illu-minance in a space [8,9,14]. In consideration of the all of the factorsoutlined above, this study aimed to estimate daylight illuminancesimply by utilizing fewer variables, relative to the number of vari-ables typically used in other methods, obtained from architecturaldrawings and using time data and to classify the distribution ofilluminance (the daylighting effectiveness) in an office with amovable blind system by fuzzy logic modeling.

The implementation of movable blind systems has beenextensively recommended due to the systems’ ability to providevisual comfort and daylight for user’s appraisal and to meet peakelectric demand. Movable blind systems are reliable and econom-ical devices in satisfying energy-saving requirements and totalenergy use [3e8]. Several studies have been conducted on thedesign and performance of these devices in terms of visual comfortand their effect on thermal comfort and energy performance[12,13,18,21]. Specifically, Hu and Olbina focused on automatedblind systems and aimed to construct an illuminance-based ANNmodel to select the optimal slat angles [18]. Additionally, theliterature reveals various studies on the use of a fuzzy logicapproach in automated blind control in the daylighting sector. Inthis context, fuzzy controllers have been proposed to achieve op-timum daylight intensity and energy savings [22e25]. If properlyintegrated into a fenestration system, movable blind systems pre-vent unwanted heat gain during the cooling period and allow heatgain during the heating period. In particular, the applications of

Fig. 1. An example of fuzzy rule

movable blind systems in buildings located in hot-humid regionswith mostly clear-sky conditions are favorable for improvingdaylighting uniformity and visual comfort. Movable blind systemsare composed of different materials and are designed in varioussizes [6e8]. In view of their common use in hot-humid regions andtheir design alternatives, the estimation of the effectiveness ofmovable blind systems with respect to daylight distribution in in-teriors has become a major research issue, particularly regardinghow a movable blind system performs in terms of daylighting orwhat slat angle leads uniform illuminance. Such inquiries should beaddressed during the very early stages of design by simple andstraightforward examination of architectural drawings. Thus, afuzzy model was developed to evaluate daylight distribution, andits effectiveness was assessed.

2. Background of fuzzy logic

2.1. Fuzzy logic concept

The practice of fuzzy logic derives from the transformation ofverbal expressions into analytical information for use in computingprocesses. This mathematical tool then categorizes variables intocertain degrees of subsets based on the theory that “an event occurswith a relative graded membership” [26]. Thus, a fuzzy inferencesystem (FIS) constructs a model that provides outcomes withmeaningful decision-making implications as a result of these cate-gories of imprecise data and vague statements of verbal information[26,27]. This model helps to categorize the complexity of real-worldtasks into simple units. The prediction of daylight illuminance is onesuch task. This methodology was applied in a previous study by theauthor in the field of architecture [28]; however, the problem in thisstudy depends on the optimum estimation and classification of fuzzysets with respect to the effectiveness of daylighting.

system with defuzzification.

T. Kazanasmaz / Building and Environment 69 (2013) 22e3424

There are generally four steps thatmust be followed to constructa fuzzy model. First, fuzzification transforms input data into gradesof membership through membership functions of a fuzzy set. Themembership function matches a degree (grade) to a linguistic termsuch as “low” or “medium”. Theremay be one or moremembershipfunctions. Each input value is associated with a value (an infinitenumber in the interval [0 1]) between 0 and 1. Fuzzy membershipfunctions may be triangular or trapezoidal in form for the ease ofapplication [26e30]. Second, fuzzy rules are constructed to deter-mine all possible relations between input and output data in thefuzzy knowledge (rule) base. These IF/THEN rules with AND/ORconnectors determine the uncertainties, nonlinear relationshipsand/ormodel complexity of the descriptive fuzzy inference process.The fuzzy concept does not involve numerical equations and modelparameters. Therefore, Mamdani, a type of rule system inwhich theresult of a fuzzy rule is expressed verbally, was applied in this study.In detail, “the fuzzy numbers of the antecedent of the rule arecombined according to the AND/OR operators that may be used inthe syntax of the rule, respectively, to produce a new fuzzy num-ber” [26]. An example of this process specific to this study issummarized in Fig. 1. Third, a fuzzy inference engine operates withfuzzy rules to diagram the outputs through deduction based oninputs. The engine performs mathematical computations such asapplying min or prod activation operators. Finally, defuzzificationdisplays the fuzzy output as a meaningful crisp value (a number).

Fig. 2. A schematic layout of the case office

The literature on fuzzy logic offers more detailed information [26e34]. In this study, to evaluate the prediction accuracy of the pro-posed model, the measured illuminance outputs were comparedwith the estimated ones and the illumination divergence error wascalculated.

3. The case office

The case office is located in a three-story educational buildingof the Faculty of Architecture (_Izmir Institute of Technology) on ahilly site (latitude 38.19�; longitude 26.37�). The offers measure4.5 m in length and 5.5 m in width, as schematically shown inFig. 2a. The story height is 3.8 m. This office has one exterior wallwith two identical double-glazed windows (1.9 m � 2.0 m) facingeast. The fenestration is composed of white aluminum profiles.The floor covering material is white marble, the walls are paintedin acrylic light beige and the ceiling is white. The glass hemi-sphericalehemispherical transmittance, normalenormal trans-mittance and wall surface hemisphericalehemisphericalreflectance values in the office were measured on-site accordingto the daylighting performance evaluation method mentioned byFontoynont [35]. The first transmittance was 94%, the secondtransmittance was 90% and the reflectance of the wall materialwas 89%. According to the literature, non-specular surfaces forfloors with 20e50% reflectance, for walls with 40e70% reflectance

(a) and photos of the blind system (b).


and for ceilings with 70e90% reflectance are recommended bythe IESNA lighting standards [36]. The exterior movable blindsystem is composed of white horizontal slats placed 10 cm apartas shown in Fig. 2b. The slats are able to move within two guidingprofiles. These slats are connected to each other by steel cables.Each slat can move along its axis up to 180�.

According to climatic data for _Izmir, the solar azimuth and solaraltitude are, respectively, 125.4� and 4.9� at 9 a.m., 148.3� and 21.0�

at 11 a.m., 177.6� and 38.0� at 1 p.m. and 177.6� and 28.0� at 3 p.m.on December 21st.

Fig. 3. Fuzzy membership functions for (a) hour, (b) an

4. Method

4.1. Field measurements

All measurements of daylight illuminance were conducted at15 reference points by following certain practical guidanceoffered by the Chartered Institution of Building Services Engi-neers (CIBSE). The number of measurement points and theirlocations were also determined according to the CIBSE byconsidering the ratio between room size and height. Reference

gle, (c) distance, (d) location and (e) illuminance.

Table 1An example of 20 fuzzy rule sets randomly selected from the total 108 sets.

Hour Distance Angle Location Illuminance

L L L L VVLL L L H VLH H L M HL M L H LM M L L HM L L H MVL H M L VLM M H M VLL H M L ML H H H LH L M L VVLL M L H VVHM M L M VVHH M H H VVLM M M H LVL H L H MH L L H LVL H H H VVLH M L M MH H H L VVL


points were located at the center of equal divisions of the floorarea [37]. Fig. 2 displays the layout of the measurement points.The measurements were carried out in November and in June,mainly covering prevailing conditions such as cloudy skies inNovember and clear skies in June. The external illuminanceswere measured according to the method mentioned by Fon-toynont [35]. They ranged from 4.8 klux to 6 klux, and from16 klux to 20 klux, respectively. The cloudy-sky condition re-sembles the weakest external condition experienced, whichleads to the minimum level of daylight inside the room. Byutilizing this type of sky condition, the model tested the worst-case scenario in terms of daylight level. The clear-sky conditionwas also taken into account because it represents the case inwhich a blind system is used to control sunlight. A digitallightmeter with a silicon photodiode detector was used for fieldmeasurements. The constant height for each reading was set to0.8 m from the floor to define the working plane. Measurementswere taken 0.5 m away from walls/columns/partitions, and gridpoints were positioned with equal spacings (Fig. 2). Moreover, aluminance meter was required to determine the transmittanceof the glazing and the brightness of finishing surfaces asobserved within the field of view.

To evaluate these measurements, literature regarding certainlighting standards was reviewed. According to DIN 5034 [38], theuniformity values for daylit interiors should satisfy the followingequations;

Dmin=Dmax > 0:67 (1)

and

Dmin=Davg > 0:5 (2)

In addition, several recommendations regarding daylightingilluminance vary among various countries because standardizationof daylighting is a complex task that has yet to be resolved. Thepredictable and unpredictable characteristics and dynamic natureof daylight in terms of its intensity and color are the drivers for itscomplexity. It is widely accepted that the characteristics and qualityof daylight are superior to those of electric lighting. Althoughminimum illuminance is defined as 300 lux for offices according tothe CIBSE standards [37], the recommended daylight levels in theGerman DIN 5034-4 standard range from 250 lux to 500 lux fornormal tasks and from 750 lux to 1000 lux for difficult tasks [38].Daylight requirements are cited explicitly by Boubekri [39] andLicht [38].

Fig. 4. Comparison of measured and simulated results; (a) under cloudy-sky condition,(b) under clear-sky condition.

4.2. DIALux modeling

DIALux is a simulation tool that is used for electric lightingdesign practice and energy research, mainly to estimate powerconsumption. The tool operates using technical data for a widerange of lamps. It calculates illuminance with the necessary powerload. However, although the program calculates and evaluates en-ergy consumption, it should be noted that the operation of electriclighting systems is not independent of daylighting systems andshading components. The schedule of daylight availability andpenetration time reduce the operating time of artificial lighting,which is why both daylighting and artificial lighting should bedesigned collectively. Furthermore, a design tooldpreferably asimulation tool to meet today’s demandsdshould be used to testthese factors in the early design phase. This tool wouldmake it easyto determine the dimensions and the form of shading componentsor daylighting systems or window apertures required. Other vari-able conditions or daylighting complications such as insufficient

Fig. 5. Schematic sections of slat angles.


illuminance, glare or an excessive amount of direct sunlight (sun-patch) at any time during the year [4e6,11e13] can be estimatedcorrectly by comparing DIALux outputs with the values recom-mended by common standards. To date, DIALux has been a usefultool for analyzing and designing daylighting. Its advantage lies inthe integration of the use of real electric lighting fixtures from themarket (for real applications) with daylighting analysis. The skymodels of DIALux, i.e., clear, overcast and partially overcast sky, arein accordance with CIE 110-1994 “Spatial Distribution of Daylight eLuminance Distributions of Various Reference Skies” [40]. Theprogram performs calculations according to DIN 5034 and CIEpublication 110 by considering location, time, orientation anddaylight obstruction [41]. Geographical location is defined by lati-tude and longitude, and time is determined according to GMT. Inthis study, measurements and simulations were carried out underclear-sky conditions in summer and cloudy (overcast)-sky condi-tions in winter.

4.3. Fuzzy logic modeling

A fuzzy model was constructed by employing the original dataobtained from DIALux modeling and considering the recom-mended illuminance for offices mentioned in the CIBSE standards[37]. The fuzzy rules and their membership functions were con-structed by considering expert opinion and the data set gatheredfrom the sample. MATLAB software was used to execute mathe-matical algorithms to construct the model. The input parametershour, angle, distance and locationwere fuzzified in fuzzy subsets toobtain the degree of illuminance effectiveness. Hour, which de-termines the position of the sun, was the most significant variable[36]. The slat angle was the key indicator of the movable blind

Fig. 6. Distribution of illuminance for a slat angle of 30� at (a) 9 a.m., (b

system’s performance. The blind position defined the amount ofdaylight penetration [8]. The remaining two parameters identifiedeach reference point. The illuminance measured at these pointsdefined the pattern of light distribution. The hour range was9 a.m.e3 p.m., and the four subsets into which it was sub-divideddvery low (VL), low (L), medium (M) and high (H)dwereconsidered to have triangular membership functions, as shown inFig. 3a. However, angle was considered to have amaximumvalue of7, and the three subsets into which it was subdivideddlow (L),medium (M) and high (H)dwere considered to have triangularmembership functions, as shown in Fig. 3b. Similarly, themaximumvalues of distance and locationwere 5 and 3, respectively. The threesubsets into which they were divideddlow (L), medium (M) andhigh (H)dwere considered to have triangular membership func-tions, as shown in Fig. 3c, d. Finally, the maximum illuminance wasdetermined to be 2000 lux, and the then subsets into which it wassubdivided were considered to have triangular membership func-tions, as shown in Fig. 3e.

The subdivisions of the input variables were defined explicitlydepending on the nature of the data and the existing literature.Similarly, the subsets of fuzzy variations in illuminance resemblethe values of relevant norms and guidelines. They represent basicclassifications that capture detailed deviations in any illuminancedistribution.

The fuzzy rule base, representing the relationships betweenthe inputs, i.e., hour, angle, distance and location, and the output,i.e., illuminance, was then constructed. Fuzzy rules were intui-tively applied by taking into account the measured and simulateddata. They were also inferred from general knowledge presentedin the literature [8,37e39]. The commonly used Mamdani rulesystem was employed in this study. The system is used to relate

) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (cloudy-sky condition in winter).

Fig. 7. Distribution of illuminance for a slat angle of 30� at (a) 9 a.m., (b) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (clear-sky condition in summer).


the input variables to the output variable verbally by constructingfuzzy rules [13e16]. The antecedent part of a ruledthe partbeginning with IF, up to THENdincluded a statement on hour,angle, distance and location, whereas the consequent partdthepart beginning with THEN, up to the enddincluded a statementon illuminance. For example,

‘IF the hour is ‘Low’, the angle is ‘Low’, the distance is ‘Medium’ andthe location is ‘Low’, THEN the illuminance is ‘Low’.

There were a total of 108 fuzzy rule sets, 20 of which wererandomly selected and summarized in Table 1. The following fuzzyinferencing engine operators were used: the min operator wasemployed to determine the firing strength of each rule, the maxcomposition operator was used to combine fuzzy output sets fromeach fired rule into a single fuzzy output set; and the centroidmethod was employed for defuzzification.


5. Model application and discussion

5.1. Comparison of measurements and DIALux modeling

The simulation model was built on the DIALux platform. Theactual locations of furniture and window openings were modeledas shown in Fig. 2. The color and reflectance of surface materialswere selected carefully to resemble the actual materials correctly. Aset of simulation outputs was then compared with the measure-ments to validate and finalize the DIALux model. Then, the cor-rected simulations were carried out. The field measurementsconducted in November and June were incorporated into thisprocess. The error rate was determined and the model validatedaccording to the method applied by Kim and Chung [17]. First, therelative errors at each measurement point were determined sepa-rately. Second, the minimum, maximum and mean RE values for all

) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (cloudy sky condition in winter).

Fig. 10. Fuzzy results versus simulation results for (a) cloudy-sky condition in winterand (b) clear-sky condition in summer.


slat positions were determined. Third, regression lines created forscatter plots of the gathered data represented the degree of rela-tionship between the measurement and simulation results. Spe-cifically, the Relative Error (RE) between the two results wascalculated at each reference point using the following formula:

RE ¼ ½ðME� SEÞ=ME� � 100% (3)

where ME is the measured illuminance at a reference point and SEis the matching simulated illuminance determined by DIALux.Based on this calculation, the minimum RE value was 3% at pointC4, and the maximum RE value was 43% at point B1 for all slatpositions. The mean value of RE at the measurement points for allangles ranged from 5% to 30%. The simulated results closelymatched the measurement results. In the linear regression analysisperformed to estimate the relationship between the measured andsimulated results, the coefficient of determination (R2) valuesranged from 96% to 97%. To correct the simulated findings, acorrection factor (CF) and corrected simulation (CS) value wererecalculated at each point. The value of CF was the average value ofthe relative errors at each point. The value of CS was the simulatedilluminance obtained by placing CF instead of RE in Eq. (3). In otherwords, each measured illuminance was multiplied by the meanvalue of RE defined for each point by Eq. (4):

CS ¼ simulation results� CF at each point (4)

where CF is the mean value of the relative errors at each point [17].The results of the corrected simulations were then compared

with themeasurement results. This comparison showed that the REvalue ranged from 1% to 24%. Moreover, the R2 values ranged from96% to 98% for the corrected simulation values (Fig. 4). Because theDIALux model was calibrated and finalized with relative errors of2e4%, trial models were applied for fuzzy model construction.

Simulation results at 9 a.m., 11 a.m., 1 p.m. and 3 p.m. wereobtained for overcast-sky conditions on December 21st and clear-sky conditions on June 21st. The daylight calculations were iter-ated for each slat angle of the movable blind, i.e., �60, �45, �30�,0�, 30�, 45� and 60�; schematic sections of the blind angles areshown in Fig. 5 and the distribution of illuminance in Figs. 6e9. Thetotal number of data sets obtained from DIALux was 375.


5.2. Fuzzy model application

A fuzzy logic algorithm was applied to predict daylight illumi-nance in an office with a movable blind system as mentionedpreviously. The objective of the study was to classify the degree of

) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (clear sky condition in summer).


effectiveness according to the slat angles of the movable blind,where effectiveness is the indicator of daylight distribution in aspace; thus, predicting the illuminance at each reference point wasthe essential step.

Taking the simulated illuminance of the reference points intoconsideration, the daylight illuminance values were predicted bythe fuzzy model. An example of this Mamdani fuzzy inferencesystem based on three rules was illustrated in the previous section(Fig. 1). The fuzzy subsets for the input and output variables areshown in Fig. 3. The total number of data sets that were used totest the model was 375. The model was executed in the fuzzy logictoolbox in MATLAB. The prod and centroid methods wereemployed as the inference operator and for defuzzification,respectively. The predicted illuminance that falls into any subset isshown in Fig. 3d.

Fig. 11. Distribution of Emin, Emax and Eavg values determined yielded by simulated

The relative error obtained by the model was 11%. The modelpredicted the simulation values with a high rate of accuracy, nearly87% for randomly selected data sets (Fig. 10). The fuzzy outcomes fitthe simulation outcomes very well. However, the uniformity valuesdeviated extremely.

Overall, the findings obtained under cloudy- and clear-skyconditions showed similarities. Here, the focus will be on the re-sults obtained for the clear-sky condition and their differences fromthe other findings obtained for the cloudy-sky condition. The dis-tributions of Emin, Emax and Eavg determined from the simulated andfuzzy models as a function of slat angle are shown in Fig. 10(cloudy-sky condition in winter) and Fig. 11 (clear-sky conditionin summer). Whereas the fuzzy model constructed under thecloudy-sky condition estimated the Emin, Emax and Eavg values moreaccurately at slat angles of 0�, 30� and 45� than the values at other

and fuzzy models as a function of slat angle (cloudy-sky condition in winter).


angles, the model under the clear-sky condition yielded more ac-curate results at slat angles of 30�, 45� and 60�. Even the Emax valuesdeviated for the most part. Another distinctive finding is that themajority of the Eavg values yielded by the fuzzy model closelymatched the average illuminance calculated by simulation. Indeed,under the clear-sky condition, the average daylight illuminancesatisfied the daylighting standards and norms for normal tasks formost of the standard working period (starting at 9 a.m. until 3 p.m.)at all angles, unlike that determined by the model under thecloudy-sky condition. Regarding the Emax values at points near thewindow zone, most of the slat angles provided a daylight illumi-nance above 1200e1600 lux. In general, the majority of the slatangles were successful in avoiding sunpatches during workinghours. In fact, sunpatches were observed only at point C2 (i.e.,nearly 16 klux) at slat angles of�30�, 0�, 30�, 45� and 60� at specific

Fig. 12. Distribution of Emin, Emax and Eavg values yielded by simulated and fu

hours, as obtained in the simulation model. Thus, this situationaffected the illuminance at nearby points in the room. The fuzzymodel failed to capture such deviations in illuminance (Figs. 6e8).The points displaying sunpatches were eliminated in analyzing theuniformity values (Fig. 12).

The uniformity values of the simulated and fuzzy modelsimplied that none of the U1 (uniformity 1 ¼ Emin/Emax) valueswere in overall agreement with current daylighting requirementsand design criteria mentioned in the literature [8,35,38]. How-ever, with only a few exceptions, all U2 (uniformity 2 ¼ Emin/Eavg)values were relevant. Thus, three uniformity effectiveness classeswere proposed with respect to the standard uniformity ratiosmentioned in the literature [8,35,38]. Uniformity ratios thatranged from 0.30 to 0.49 defined the poorly effective class, thosethat ranged from 0.50 to 0.59 defined the moderately effective

zzy models as a function of slat angle (clear-sky condition in summer).


class and those that ranged from 0.60 to 0.70 defined the highlyeffective class.

Table 3 summarizes all of the uniformity classes for all slatangles. The fuzzy model was able to successfully predict theuniformity classes for slat angles of 30� and 45�. When the blind’sslat angle was 0�, the model was also successful under thecloudy-sky condition (Table 2). Concerning the simulation model,when slat angles of 0�, 30�, 45� and 60� were used, daylight wasdistributed both poorly and highly inside the office throughoutthe working period. The fuzzy model results were lower or higherthan but similar to the simulated results at specific hours. Eventhe U2 values nearly fell into the satisfying and preferred uni-formity class. The lowest matching uniformity values were ob-tained by the fuzzy model at a slat angle of 0�. Thus, according tothe degree of match for the simulated and fuzzy models, themajority of the uniformity outcomes of the fuzzy model fully fitthe simulation outcomes. The majority of the uniformity valuesfor the resting slat angles did not fully match the simulation re-sults because of the deviation in U2 values at 0 and 60� and thedeviation in U1 values at �60�, �45� and �30�. In general, ahigher degree of matching among uniformity values was achievedunder the cloudy-sky condition than under the clear-sky condi-tion. This result can be attributed to the difficulty in controllingdirect sunlight versus diffuse light. It is necessary to reconsider

Table 2Uniformity values yielded by the simulated and fuzzy models as a function of slat angle

Angle Hour Simulation model Fuzzy model

Emin/Emax

U1Emin/EavgU2

Emin/Emax U1 Emin/Eavg U2

�60 9.00 0.23 0.53 0.39 0.5711.00 0.23 0.53 0.42 0.5913.00 0.23 0.53 0.46 0.63

15.00 0.23 0.53 0.30 0.45

�45 9.00 0.24 0.54 0.50 0.68

11.00 0.24 0.54 0.38 0.60

13.00 0.24 0.54 0.38 0.5715.00 0.24 0.54 0.40 0.65

�30 9.00 0.29 0.58 0.40 0.5811.00 0.29 0.58 0.44 0.67

13.00 0.29 0.58 0.44 0.66

15.00 0.29 0.58 0.33 0.48

0 9.00 0.42 0.69 0.44 0.6111.00 0.41 0.69 0.41 0.6413.00 0.41 0.69 0.47 0.6715.00 0.41 0.69 0.33 0.49

30 9.00 0.46 0.72 0.44 0.6311.00 0.46 0.71 0.40 0.6013.00 0.46 0.72 0.43 0.6115.00 0.46 0.71 0.35 0.55

45 9.00 0.44 0.70 0.32 0.57

11.00 0.44 0.70 0.44 0.6013.00 0.44 0.70 0.50 0.6715.00 0.44 0.70 0.47 0.74

60 9.00 0.42 0.69 0.25 0.50

11.00 0.42 0.69 0.60 0.61

13.00 0.42 0.69 0.60 0.76

15.00 0.42 0.70 0.49 0.69

the design of the blind system in terms of its form and its size.Further analysis is recommended for developing a new blindsystem design that tracks sun angles.

Slat angles of 30� and 45� provided a more uniform daylightingdistribution than the other angles did throughout the workingperiod. Thus, it was concluded that these angles represented themost suitable design alternatives that would be preferred in thearchitectural design of offices that are located in similar areas andexhibit similar climate and orientation characteristics. The data setsused in this fuzzy model included data gathered under both thecloudy-sky and clear-sky conditions. The former allowed for theelimination of extreme deviations in daylight illuminance duringwinter. Thus, the illuminance was close to the minimum levelsconsidered valid for the design process. However, as because themain function of a blind is to control sunlight under clear skies, thefindings focused on the latter condition. Additionally, the illumi-nances complied with the recommended levels under this condi-tion, although the U1 values did not.

6. Discussion

To summarize, the DIALux and fuzzy logic models developed inthis study were used to estimate the daylight illuminance andclassify the uniformity rates in an existing office with a movable

(cloudy-sky condition in winter).

Degree of match U1 U2

Fully Poorly ModerateFully Poorly ModerateHalf Poorly Moderate in simulation;

high in fuzzyHalf Poorly Moderate in simulation;

poorly in fuzzyNo Poorly in simulation;

moderate in fuzzyModerate in simulation;high in fuzzy

Half Poorly Moderate in simulation;high in fuzzy

Fully Poorly moderateHalf Poorly Moderate in simulation;

high in fuzzyFully Poorly moderateHalf Poorly Moderate in simulation;



poorly in fuzzyFully Poorly HighFully Poorly HighFully Poorly HighFully Poorly HighFully Poorly HighFully Poorly HighFully Poorly HighHalf Poorly High in simulation;

moderate in fuzzyHalf Poorly High in simulation;

moderate in fuzzyFully Poorly HighFully Poorly HighFully Poorly HighHalf Poorly High in simulation;

moderate in fuzzyHalf Poorly in simulation;

high in fuzzyHigh

Half Poorly in simulation;high in fuzzy

High

Fully Poorly High

Table 3Uniformity values yielded by simulated and fuzzy models as a function of slat angle (clear-sky condition in summer).

Angle Hour Simulation model Fuzzy model Degree of match U1 U2

Emin/Emax

U1Emin/EavgU2

Emin/Emax

U1Emin/EavgU2

�60 9.00 0.33 0.65 0.58 0.74 Half Poorly in simulation;moderate in fuzzy

High

11.00 0.35 0.65 0.54 0.73 Half Poorly in simulation;moderate in fuzzy

High

13.00 0.39 0.70 0.45 0.65 Fully Poorly High15.00 0.25 0.56 0.16 0.30 Half Poorly Moderate in simulation;

poorly in fuzzy�45 9.00 0.31 0.63 0.57 0.74 Half Poorly in simulation;

moderate in fuzzyHigh

11.00 0.39 0.69 0.62 0.77 Half Poorly in simulation;high in fuzzy

High

13.00 0.39 0.70 0.43 0.65 Fully Poorly High15.00 0.28 0.59 0.26 0.42 Fully Poorly Moderate

�30 9.00 0.50 0.71 0.62 0.77 Half Moderate in simulation;high in fuzzy

High

11.00 0.43 0.71 0.38 0.60 Fully Poorly High13.00 0.43 0.72 0.38 0.60 Fully Poorly High15.00 0.32 0.59 0.29 0.45 Half Poorly Moderate in simulation;

poorly in fuzzy0 9.00 0.40 0.66 0.54 0.70 Fully Poorly High

11.00 0.40 0.67 0.33 0.56 Half Poorly High in simulation;moderate in fuzzy



30 9.00 0.37 0.66 0.60 0.77 Half Poorly in simulation;high in fuzzy

High


13.00 0.39 0.67 0.45 0.65 Fully Poorly High15.00 0.44 0.73 0.35 0.65 Fully Poorly High

45 9.00 0.37 0.69 0.42 0.65 Fully Poorly High11.00 0.37 0.68 0.43 0.63 Fully Poorly High13.00 0.41 0.71 0.46 0.64 Fully Poorly High15.00 0.41 0.72 0.33 0.63 Fully Poorly High

60 9.00 0.39 0.72 0.33 0.57 Half Poorly High in simulation;moderate in fuzzy


13.00 0.40 0.71 0.50 0.68 Fully Poorly High15.00 0.38 0.69 0.31 0.52 Half Poorly High in simulation;

moderate in fuzzy


blind system. A fuzzy logic approach was employed to assess theeffect of the slat angles on the daylight distribution in this room.The fuzzy model was validated by comparing simulations run inDIALux for a large number of alternatives. Before doing so, thesimulations were validated and corrected based on a series of fieldmeasurements performed in the office. The findings are summa-rized in Section 5.

A number of limitations regarding the methodology and itsrelationship to daylight illuminance and the distribution thereofwere considered noteworthy. One limitation concerns the selectionof the DIALux tool. DIALux has been implemented as a tool foranalyzing and designing electric lighting and daylighting collectively.Only CIE skies are used, although site locations may be defined byvarious inputs, namely, latitude and altitude and GMT time, andselected in advance according to location. However, not every type ofweather file can be uploaded in the simulation. Indeed, there may bevariations between the sky of the considered site and the CIE skybecause CIE skies are standardized and rely on average conditions.The literature shows that there are many models that use these skyconditions to estimate daylight illuminance and its performance.However, it was realized that every model may not be suitable for

every application. Simplified but accurate models are convenient forperforming quick estimations but may be limited. DIALux is apowerful tool in this respect and especially convenient in the earlydesign stage. Accordingly, there is another noteworthy considerationto be taken into account. A climate-based approach could be used tocarry out the entire design process. This approach would involveapplying the weather file of a given site and calculating the illumi-nance values throughout the year. Software such as Radiance, Ecotectand Daysim are suitable tools. However, these tools use similar skyconditions and require long calculation times. There are otherdrawbacks and limits to this approach as mentioned in previousstudies, including limited material definitions, information man-agement, output reports, not being user friendly and not beingintuitive [5,10,14,15].

The objective of this study was to introduce a new and potentiallyuseful tool for building designers and practitioners: the fuzzy logicapproach. It should be noted that the application of fuzzy logic is notcompletely new to the daylighting sector. However, its application islimited in another specific area: daylight illuminance control usingfuzzy logic. Automated blind control strategies have been developedto maximize daylight performance or indoor comfort levels by fuzzy


controllers in the field of electrical engineering [22e25]. However,the development of such strategies to estimate daylight illuminancein the field of architecture has not been extensively explored.

7. Conclusions

In this study, a fuzzy logic model was developed to predictdaylight illuminance simply and to classify its distribution in anoffice with a movable blind system. The input parameters of thefuzzy model were hour, angle, distance and point location, whichmay be easily employed and examined in early architectural designschemes. Compared with the ANN model developed in a previousstudy conducted to predict daylight illuminance [8], the fuzzymodel developed in this work can estimate daylight luminance byutilizing fewer variables, which may be taken from architecturalschemes and using time data. In addition, the model was con-structed for an office with a movable blind system. Therefore, thefuzzy model also determined the appropriate slat angles of theblind system. The model successfully estimated the daylight illu-minance and its distribution (uniformity).

To construct and validate the fuzzy model, a simulation modelwas constructed for this office using DIALux. Field measurementswere used to validate and calibrate this simulation model. Finally,the simulation model was finalized with relative errors of 2e4%.The daylight illuminance and uniformity classes of the fuzzy modelclosely matched the daylight distributions obtained by the simu-lationmodel. Specifically, the uniformity was effective at slat anglesof 30� and 45�. Among three uniformity classes, namely, poorly,moderately and highly effective, the fuzzy model could properlyestimate the uniformity values for the majority of slat angles. Thisnoteworthy finding implies that the proposed method may be arobust and easily implemented tool in the early architectural de-sign phase when considering a blind system and predicting itsdaylighting performance.

Other conclusions derived from this study concerned themethodology used. This study shows that, similar to ANN models,fuzzy logic models may be used in the field of architecture as theyare widely applied in engineering. Researchers should be madeaware of this model and employ it in daylighting performancestudies. Architects and lighting designers would benefit from thismodel by using it as an assistive tool to determine illuminance andlight distributions. Additionally, this model may be improved bytesting other spatial parameters or climatic aspects. Furthermodels could involve other location and orientation characteris-tics. Finally, designers would benefit from this model by employingit before constructing a simulation model, mostly for visualizationpurposes and for conducting detailed lighting analyses. Thus,timely decisions could easily be made and necessary precautionstaken before performing simulations, and the number of simula-tions required to correct basic architectural issues would beminimized. An early sketch, even one created by hand, would beenough to predict the performance of a blind system in terms ofdaylighting.

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fuzzy logic model to classify effectiveness of daylighting in an office with a movable blind system

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