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Fuzzy logic model to classify effectiveness of daylighting in an office with a movable blind system
Building and Environment 69 (2013) 22e34
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Fuzzy logic model to classify effectiveness of daylighting in an office with a movable blind system çe Kazanasmaz* Tug _ Department of Architecture, Izmir Institute of Architecture, Urla 35430, Izmir, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2013 Received in revised form 13 July 2013 Accepted 16 July 2013
This study estimated daylight illuminance and classified its effectiveness in an office with a movable blind system. First, measurements were carried out to validate and apply a simulation model using DIALux. Second, the simulation model was constructed utilizing physical properties similar to those of the case office. Third, the simulation model provided the daylighting calculations in terms of the slat angles of the movable blind system. A fuzzy model was later employed using the Mamdani fuzzy inference 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 daylighting standards and design norms. Regarding the movable blind system, slat angles of 30 and 45 provided more uniformly distributed daylight than other angles throughout standard working hours. Thus, according to the degree of match between the simulated and fuzzy models, the majority of the uniformity outcomes of the fuzzy model fully fit the simulation outcomes. Because the fuzzy model successfully estimated the daylight illuminance and its distribution (uniformity), it could be easily employed to examine early architectural design schemes. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Daylighting Fuzzy logic Uniformity Building Movable blind
1. Introduction Daylight penetration and its even distribution throughout a space are basic considerations made in building design. Both define the effectiveness of daylighting. A sufficient amount of daylight reduces the demand for electrical lighting and provides a healthy visual environment. Moreover, daylighting results in enhanced energy efficiency and visual acuity [1e5]. Apart from the benefit provided by daylight’s intensity, uniformly distributed daylight does not give rise to glaring surfaces and enhances visual quality and comfort [6e9,10]. Consequently, the primary physical measure use to quantify this phenomenon is illuminance. The estimation of uniformly distributed daylight is necessary, both in early architectural design processes and in daylighting performance evaluation studies [5,11e13]. Foreseeing further deficiencies regarding daylighting, i.e., incorrect window dimensions or misuse of a blind system, can be avoided in the early design stage. While evaluating the daylighting performance of an existing interior, any visual
* Tel.: þ90 232 7507063. E-mail addresses: [email protected], [email protected]. 0360-1323/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.buildenv.2013.07.011
comfort problems related to daylight may be assessed straightforwardly and rapidly. The literature reveals several techniques for predicting daylight illuminance. Contemporary techniques that have been used over the years include the construction of scale models and the use of analytical formulas and simulation tools. An overview of these methods was presented in previous studies by the author [14,15]. The strengths and weaknesses of these techniques were explained by reviewing selected studies. Recent methodologies, such as artificial intelligence [14], simulation tools such as Radiance, DIALux, etc. [12,16e18] and a trial simulation tool named Codyrun [19], have been introduced to predict indoor illuminance by accepting the irrefutable nature of daylighting and by simplifying its complexity for the ease of design. Several studies of daylighting metrics and rules of thumb have also been proposed to overcome initial design problems [1,2,20]. Gagne et al. [10] suggested an interactive design expert system for daylighting design, which might be used in the early design phase. This system was developed as an alternative to simulation tools to guide users in making design modifications. This tool was defined as a “virtual daylighting consultant”, including a daylighting knowledge-base and a fuzzy rule-based decision-making logic. The former involved information
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about the impact of design conditions on daylighting, while the latter is for the decision on the main effect on design actions to improve daylighting conditions [10]. Reinhart and Wienold [5] proposed a new method for conducting integrated daylighting design analysis and thereby examine annual daylight availability, visual comfort and energy use together with dynamic simulation potentials. The authors named this tool ‘the daylighting dashboard’. It is known that there are many variables affecting daylight illuminance in a space [8,9,14]. In consideration of the all of the factors outlined above, this study aimed to estimate daylight illuminance simply by utilizing fewer variables, relative to the number of variables typically used in other methods, obtained from architectural drawings and using time data and to classify the distribution of illuminance (the daylighting effectiveness) in an office with a movable blind system by fuzzy logic modeling. The implementation of movable blind systems has been extensively recommended due to the systems’ ability to provide visual comfort and daylight for user’s appraisal and to meet peak electric demand. Movable blind systems are reliable and economical devices in satisfying energy-saving requirements and total energy use [3e8]. Several studies have been conducted on the design and performance of these devices in terms of visual comfort and their effect on thermal comfort and energy performance [12,13,18,21]. Specifically, Hu and Olbina focused on automated blind systems and aimed to construct an illuminance-based ANN model to select the optimal slat angles [18]. Additionally, the literature reveals various studies on the use of a fuzzy logic approach in automated blind control in the daylighting sector. In this context, fuzzy controllers have been proposed to achieve optimum daylight intensity and energy savings [22e25]. If properly integrated into a fenestration system, movable blind systems prevent unwanted heat gain during the cooling period and allow heat gain during the heating period. In particular, the applications of
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movable blind systems in buildings located in hot-humid regions with mostly clear-sky conditions are favorable for improving daylighting uniformity and visual comfort. Movable blind systems are composed of different materials and are designed in various sizes [6e8]. In view of their common use in hot-humid regions and their design alternatives, the estimation of the effectiveness of movable blind systems with respect to daylight distribution in interiors has become a major research issue, particularly regarding how a movable blind system performs in terms of daylighting or what slat angle leads uniform illuminance. Such inquiries should be addressed during the very early stages of design by simple and straightforward examination of architectural drawings. Thus, a fuzzy model was developed to evaluate daylight distribution, and its effectiveness was assessed. 2. Background of fuzzy logic 2.1. Fuzzy logic concept The practice of fuzzy logic derives from the transformation of verbal expressions into analytical information for use in computing processes. This mathematical tool then categorizes variables into certain degrees of subsets based on the theory that “an event occurs with a relative graded membership” [26]. Thus, a fuzzy inference system (FIS) constructs a model that provides outcomes with meaningful decision-making implications as a result of these categories of imprecise data and vague statements of verbal information [26,27]. This model helps to categorize the complexity of real-world tasks into simple units. The prediction of daylight illuminance is one such task. This methodology was applied in a previous study by the author in the field of architecture [28]; however, the problem in this study depends on the optimum estimation and classification of fuzzy sets with respect to the effectiveness of daylighting.
Fig. 1. An example of fuzzy rule system with defuzzification.
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There are generally four steps that must be followed to construct a fuzzy model. First, fuzzification transforms input data into grades of membership through membership functions of a fuzzy set. The membership function matches a degree (grade) to a linguistic term such as “low” or “medium”. There may be one or more membership functions. Each input value is associated with a value (an infinite number in the interval [0 1]) between 0 and 1. Fuzzy membership functions may be triangular or trapezoidal in form for the ease of application [26e30]. Second, fuzzy rules are constructed to determine all possible relations between input and output data in the fuzzy knowledge (rule) base. These IF/THEN rules with AND/OR connectors determine the uncertainties, nonlinear relationships and/or model complexity of the descriptive fuzzy inference process. The fuzzy concept does not involve numerical equations and model parameters. Therefore, Mamdani, a type of rule system in which the result of a fuzzy rule is expressed verbally, was applied in this study. In detail, “the fuzzy numbers of the antecedent of the rule are combined according to the AND/OR operators that may be used in the syntax of the rule, respectively, to produce a new fuzzy number” [26]. An example of this process specific to this study is summarized in Fig. 1. Third, a fuzzy inference engine operates with fuzzy rules to diagram the outputs through deduction based on inputs. The engine performs mathematical computations such as applying min or prod activation operators. Finally, defuzzification displays the fuzzy output as a meaningful crisp value (a number).
The literature on fuzzy logic offers more detailed information [26e 34]. In this study, to evaluate the prediction accuracy of the proposed model, the measured illuminance outputs were compared with the estimated ones and the illumination divergence error was calculated. 3. The case office The case office is located in a three-story educational building _ of the Faculty of Architecture (Izmir Institute of Technology) on a hilly site (latitude 38.19 ; longitude 26.37 ). The offers measure 4.5 m in length and 5.5 m in width, as schematically shown in Fig. 2a. The story height is 3.8 m. This office has one exterior wall with two identical double-glazed windows (1.9 m 2.0 m) facing east. The fenestration is composed of white aluminum profiles. The floor covering material is white marble, the walls are painted in acrylic light beige and the ceiling is white. The glass hemisphericalehemispherical transmittance, normalenormal transmittance and wall surface hemisphericalehemispherical reflectance values in the office were measured on-site according to the daylighting performance evaluation method mentioned by Fontoynont [35]. The first transmittance was 94%, the second transmittance was 90% and the reflectance of the wall material was 89%. According to the literature, non-specular surfaces for floors with 20e50% reflectance, for walls with 40e70% reflectance
Fig. 2. A schematic layout of the case office (a) and photos of the blind system (b).
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
and for ceilings with 70e90% reflectance are recommended by the IESNA lighting standards [36]. The exterior movable blind system is composed of white horizontal slats placed 10 cm apart as shown in Fig. 2b. The slats are able to move within two guiding profiles. 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 solar altitude 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.
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4. Method 4.1. Field measurements All measurements of daylight illuminance were conducted at 15 reference points by following certain practical guidance offered by the Chartered Institution of Building Services Engineers (CIBSE). The number of measurement points and their locations were also determined according to the CIBSE by considering the ratio between room size and height. Reference
Fig. 3. Fuzzy membership functions for (a) hour, (b) angle, (c) distance, (d) location and (e) illuminance.
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points were located at the center of equal divisions of the floor area [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 in November and clear skies in June. The external illuminances were measured according to the method mentioned by Fontoynont [35]. They ranged from 4.8 klux to 6 klux, and from 16 klux to 20 klux, respectively. The cloudy-sky condition resembles the weakest external condition experienced, which leads to the minimum level of daylight inside the room. By utilizing this type of sky condition, the model tested the worstcase scenario in terms of daylight level. The clear-sky condition was also taken into account because it represents the case in which a blind system is used to control sunlight. A digital lightmeter with a silicon photodiode detector was used for field measurements. The constant height for each reading was set to 0.8 m from the floor to define the working plane. Measurements were taken 0.5 m away from walls/columns/partitions, and grid points were positioned with equal spacings (Fig. 2). Moreover, a luminance meter was required to determine the transmittance of the glazing and the brightness of finishing surfaces as observed within the field of view. To evaluate these measurements, literature regarding certain lighting standards was reviewed. According to DIN 5034 [38], the uniformity values for daylit interiors should satisfy the following equations;
Dmin =Dmax > 0:67
Table 1 An example of 20 fuzzy rule sets randomly selected from the total 108 sets. Hour
Distance
Angle
Location
Illuminance
L L H L M M VL M L L H L M H M VL H VL H H
L L H M M L H M H H L M M M M H L H M H
L L L L L L M H M H M L L H M L L H L H
L H M H L H L M L H L H M H H H H H M L
VVL VL H L H M VL VL M L VVL VVH VVH VVL L M L VVL M VVL
(1)
and
Dmin =Davg > 0:5
(2)
In addition, several recommendations regarding daylighting illuminance vary among various countries because standardization of daylighting is a complex task that has yet to be resolved. The predictable and unpredictable characteristics and dynamic nature of daylight in terms of its intensity and color are the drivers for its complexity. It is widely accepted that the characteristics and quality of daylight are superior to those of electric lighting. Although minimum illuminance is defined as 300 lux for offices according to the CIBSE standards [37], the recommended daylight levels in the German DIN 5034-4 standard range from 250 lux to 500 lux for normal tasks and from 750 lux to 1000 lux for difficult tasks [38]. Daylight requirements are cited explicitly by Boubekri [39] and Licht [38].
4.2. DIALux modeling DIALux is a simulation tool that is used for electric lighting design practice and energy research, mainly to estimate power consumption. The tool operates using technical data for a wide range of lamps. It calculates illuminance with the necessary power load. However, although the program calculates and evaluates energy consumption, it should be noted that the operation of electric lighting systems is not independent of daylighting systems and shading components. The schedule of daylight availability and penetration time reduce the operating time of artificial lighting, which is why both daylighting and artificial lighting should be designed collectively. Furthermore, a design tooldpreferably a simulation tool to meet today’s demandsdshould be used to test these factors in the early design phase. This tool would make it easy to determine the dimensions and the form of shading components or daylighting systems or window apertures required. Other variable conditions or daylighting complications such as insufficient
Fig. 4. Comparison of measured and simulated results; (a) under cloudy-sky condition, (b) under clear-sky condition.
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Fig. 5. Schematic sections of slat angles.
illuminance, glare or an excessive amount of direct sunlight (sunpatch) at any time during the year [4e6,11e13] can be estimated correctly by comparing DIALux outputs with the values recommended by common standards. To date, DIALux has been a useful tool for analyzing and designing daylighting. Its advantage lies in the integration of the use of real electric lighting fixtures from the market (for real applications) with daylighting analysis. The sky models of DIALux, i.e., clear, overcast and partially overcast sky, are in accordance with CIE 110-1994 “Spatial Distribution of Daylight e Luminance Distributions of Various Reference Skies” [40]. The program performs calculations according to DIN 5034 and CIE publication 110 by considering location, time, orientation and daylight obstruction [41]. Geographical location is defined by latitude and longitude, and time is determined according to GMT. In this study, measurements and simulations were carried out under clear-sky conditions in summer and cloudy (overcast)-sky conditions in winter. 4.3. Fuzzy logic modeling A fuzzy model was constructed by employing the original data obtained from DIALux modeling and considering the recommended illuminance for offices mentioned in the CIBSE standards [37]. The fuzzy rules and their membership functions were constructed by considering expert opinion and the data set gathered from the sample. MATLAB software was used to execute mathematical algorithms to construct the model. The input parameters hour, angle, distance and location were fuzzified in fuzzy subsets to obtain the degree of illuminance effectiveness. Hour, which determines the position of the sun, was the most significant variable [36]. The slat angle was the key indicator of the movable blind
system’s performance. The blind position defined the amount of daylight penetration [8]. The remaining two parameters identified each reference point. The illuminance measured at these points defined the pattern of light distribution. The hour range was 9 a.m.e3 p.m., and the four subsets into which it was subdivideddvery low (VL), low (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3a. However, angle was considered to have a maximum value of 7, and the three subsets into which it was subdivideddlow (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3b. Similarly, the maximum values of distance and location were 5 and 3, respectively. The three subsets into which they were divideddlow (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3c, d. Finally, the maximum illuminance was determined to be 2000 lux, and the then subsets into which it was subdivided were considered to have triangular membership functions, as shown in Fig. 3e. The subdivisions of the input variables were defined explicitly depending on the nature of the data and the existing literature. Similarly, the subsets of fuzzy variations in illuminance resemble the values of relevant norms and guidelines. They represent basic classifications that capture detailed deviations in any illuminance distribution. The fuzzy rule base, representing the relationships between the inputs, i.e., hour, angle, distance and location, and the output, i.e., illuminance, was then constructed. Fuzzy rules were intuitively applied by taking into account the measured and simulated data. They were also inferred from general knowledge presented in the literature [8,37e39]. The commonly used Mamdani rule system was employed in this study. The system is used to relate
Fig. 6. 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. (cloudy-sky condition in winter).
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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 constructing fuzzy rules [13e16]. The antecedent part of a ruledthe part beginning with IF, up to THENdincluded a statement on hour, angle, distance and location, whereas the consequent partdthe part beginning with THEN, up to the enddincluded a statement on illuminance. For example, ‘IF the hour is ‘Low’, the angle is ‘Low’, the distance is ‘Medium’ and the location is ‘Low’, THEN the illuminance is ‘Low’. There were a total of 108 fuzzy rule sets, 20 of which were randomly selected and summarized in Table 1. The following fuzzy inferencing engine operators were used: the min operator was employed to determine the firing strength of each rule, the max composition operator was used to combine fuzzy output sets from each fired rule into a single fuzzy output set; and the centroid method 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. The actual locations of furniture and window openings were modeled as shown in Fig. 2. The color and reflectance of surface materials were selected carefully to resemble the actual materials correctly. A set of simulation outputs was then compared with the measurements to validate and finalize the DIALux model. Then, the corrected simulations were carried out. The field measurements conducted in November and June were incorporated into this process. The error rate was determined and the model validated according to the method applied by Kim and Chung [17]. First, the relative errors at each measurement point were determined separately. Second, the minimum, maximum and mean RE values for all
Fig. 8. Distribution of illuminance for a slat angle of 45 at (a) 9 a.m., (b) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (cloudy sky condition in winter).
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slat positions were determined. Third, regression lines created for scatter plots of the gathered data represented the degree of relationship between the measurement and simulation results. Specifically, the Relative Error (RE) between the two results was calculated 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 SE is the matching simulated illuminance determined by DIALux. Based on this calculation, the minimum RE value was 3% at point C4, and the maximum RE value was 43% at point B1 for all slat positions. The mean value of RE at the measurement points for all angles ranged from 5% to 30%. The simulated results closely matched the measurement results. In the linear regression analysis performed to estimate the relationship between the measured and simulated results, the coefficient of determination (R2) values ranged from 96% to 97%. To correct the simulated findings, a correction factor (CF) and corrected simulation (CS) value were recalculated at each point. The value of CF was the average value of the relative errors at each point. The value of CS was the simulated illuminance obtained by placing CF instead of RE in Eq. (3). In other words, each measured illuminance was multiplied by the mean value 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 the measurement results. This comparison showed that the RE value ranged from 1% to 24%. Moreover, the R2 values ranged from 96% to 98% for the corrected simulation values (Fig. 4). Because the DIALux model was calibrated and finalized with relative errors of 2e4%, trial models were applied for fuzzy model construction. Simulation results at 9 a.m., 11 a.m., 1 p.m. and 3 p.m. were obtained for overcast-sky conditions on December 21st and clearsky conditions on June 21st. The daylight calculations were iterated for each slat angle of the movable blind, i.e., 60, 45, 30 , 0 , 30 , 45 and 60 ; schematic sections of the blind angles are shown in Fig. 5 and the distribution of illuminance in Figs. 6e9. The total number of data sets obtained from DIALux was 375.
Fig. 10. Fuzzy results versus simulation results for (a) cloudy-sky condition in winter and (b) clear-sky condition in summer.
5.2. Fuzzy model application A fuzzy logic algorithm was applied to predict daylight illuminance in an office with a movable blind system as mentioned previously. The objective of the study was to classify the degree of
Fig. 9. Distribution of illuminance for a slat angle of 45 at (a) 9 a.m., (b) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (clear sky condition in summer).
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effectiveness according to the slat angles of the movable blind, where effectiveness is the indicator of daylight distribution in a space; thus, predicting the illuminance at each reference point was the essential step. Taking the simulated illuminance of the reference points into consideration, the daylight illuminance values were predicted by the fuzzy model. An example of this Mamdani fuzzy inference system based on three rules was illustrated in the previous section (Fig. 1). The fuzzy subsets for the input and output variables are shown in Fig. 3. The total number of data sets that were used to test the model was 375. The model was executed in the fuzzy logic toolbox in MATLAB. The prod and centroid methods were employed as the inference operator and for defuzzification, respectively. The predicted illuminance that falls into any subset is shown in Fig. 3d.
The relative error obtained by the model was 11%. The model predicted the simulation values with a high rate of accuracy, nearly 87% for randomly selected data sets (Fig. 10). The fuzzy outcomes fit the simulation outcomes very well. However, the uniformity values deviated extremely. Overall, the findings obtained under cloudy- and clear-sky conditions showed similarities. Here, the focus will be on the results obtained for the clear-sky condition and their differences from the other findings obtained for the cloudy-sky condition. The distributions of Emin, Emax and Eavg determined from the simulated and fuzzy models as a function of slat angle are shown in Fig. 10 (cloudy-sky condition in winter) and Fig. 11 (clear-sky condition in summer). Whereas the fuzzy model constructed under the cloudy-sky condition estimated the Emin, Emax and Eavg values more accurately at slat angles of 0 , 30 and 45 than the values at other
Fig. 11. Distribution of Emin, Emax and Eavg values determined yielded by simulated and fuzzy models as a function of slat angle (cloudy-sky condition in winter).
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
angles, the model under the clear-sky condition yielded more accurate results at slat angles of 30 , 45 and 60 . Even the Emax values deviated for the most part. Another distinctive finding is that the majority of the Eavg values yielded by the fuzzy model closely matched the average illuminance calculated by simulation. Indeed, under the clear-sky condition, the average daylight illuminance satisfied the daylighting standards and norms for normal tasks for most of the standard working period (starting at 9 a.m. until 3 p.m.) at all angles, unlike that determined by the model under the cloudy-sky condition. Regarding the Emax values at points near the window zone, most of the slat angles provided a daylight illuminance above 1200e1600 lux. In general, the majority of the slat angles were successful in avoiding sunpatches during working hours. 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
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hours, as obtained in the simulation model. Thus, this situation affected the illuminance at nearby points in the room. The fuzzy model failed to capture such deviations in illuminance (Figs. 6e8). The points displaying sunpatches were eliminated in analyzing the uniformity values (Fig. 12). The uniformity values of the simulated and fuzzy models implied that none of the U1 (uniformity 1 ¼ Emin/Emax) values were in overall agreement with current daylighting requirements and design criteria mentioned in the literature [8,35,38]. However, with only a few exceptions, all U2 (uniformity 2 ¼ Emin/Eavg) values were relevant. Thus, three uniformity effectiveness classes were proposed with respect to the standard uniformity ratios mentioned in the literature [8,35,38]. Uniformity ratios that ranged from 0.30 to 0.49 defined the poorly effective class, those that ranged from 0.50 to 0.59 defined the moderately effective
Fig. 12. Distribution of Emin, Emax and Eavg values yielded by simulated and fuzzy models as a function of slat angle (clear-sky condition in summer).
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class and those that ranged from 0.60 to 0.70 defined the highly effective class. Table 3 summarizes all of the uniformity classes for all slat angles. The fuzzy model was able to successfully predict the uniformity classes for slat angles of 30 and 45 . When the blind’s slat angle was 0 , the model was also successful under the cloudy-sky condition (Table 2). Concerning the simulation model, when slat angles of 0 , 30 , 45 and 60 were used, daylight was distributed both poorly and highly inside the office throughout the working period. The fuzzy model results were lower or higher than but similar to the simulated results at specific hours. Even the U2 values nearly fell into the satisfying and preferred uniformity class. The lowest matching uniformity values were obtained by the fuzzy model at a slat angle of 0 . Thus, according to the degree of match for the simulated and fuzzy models, the majority of the uniformity outcomes of the fuzzy model fully fit the simulation outcomes. The majority of the uniformity values for the resting slat angles did not fully match the simulation results because of the deviation in U2 values at 0 and 60 and the deviation in U1 values at 60 , 45 and 30 . In general, a higher degree of matching among uniformity values was achieved under the cloudy-sky condition than under the clear-sky condition. This result can be attributed to the difficulty in controlling direct sunlight versus diffuse light. It is necessary to reconsider
the design of the blind system in terms of its form and its size. Further analysis is recommended for developing a new blind system design that tracks sun angles. Slat angles of 30 and 45 provided a more uniform daylighting distribution than the other angles did throughout the working period. Thus, it was concluded that these angles represented the most suitable design alternatives that would be preferred in the architectural design of offices that are located in similar areas and exhibit similar climate and orientation characteristics. The data sets used in this fuzzy model included data gathered under both the cloudy-sky and clear-sky conditions. The former allowed for the elimination of extreme deviations in daylight illuminance during winter. Thus, the illuminance was close to the minimum levels considered valid for the design process. However, as because the main function of a blind is to control sunlight under clear skies, the findings focused on the latter condition. Additionally, the illuminances complied with the recommended levels under this condition, although the U1 values did not. 6. Discussion To summarize, the DIALux and fuzzy logic models developed in this study were used to estimate the daylight illuminance and classify the uniformity rates in an existing office with a movable
Table 2 Uniformity values yielded by the simulated and fuzzy models as a function of slat angle (cloudy-sky condition in winter). Angle
Degree of match
U1
U2
0.57 0.59 0.63
Fully Fully Half
Poorly Poorly Poorly
0.30
0.45
Half
Poorly
0.54
0.50
0.68
No
0.24
0.54
0.38
0.60
Half
Poorly in simulation; moderate in fuzzy Poorly
13.00 15.00
0.24 0.24
0.54 0.54
0.38 0.40
0.57 0.65
Fully Half
Poorly Poorly
9.00 11.00
0.29 0.29
0.58 0.58
0.40 0.44
0.58 0.67
Fully Half
Poorly Poorly
13.00
0.29
0.58
0.44
0.66
Half
Poorly
15.00
0.29
0.58
0.33
0.48
Half
Poorly
9.00 11.00 13.00 15.00 9.00 11.00 13.00 15.00
0.42 0.41 0.41 0.41 0.46 0.46 0.46 0.46
0.69 0.69 0.69 0.69 0.72 0.71 0.72 0.71
0.44 0.41 0.47 0.33 0.44 0.40 0.43 0.35
0.61 0.64 0.67 0.49 0.63 0.60 0.61 0.55
Fully Fully Fully Fully Fully Fully Fully Half
Poorly Poorly Poorly Poorly Poorly Poorly Poorly Poorly
45
9.00
0.44
0.70
0.32
0.57
Half
Poorly
60
11.00 13.00 15.00 9.00
0.44 0.44 0.44 0.42
0.70 0.70 0.70 0.69
0.44 0.50 0.47 0.25
0.60 0.67 0.74 0.50
Fully Fully Fully Half
Poorly Poorly Poorly Poorly
11.00
0.42
0.69
0.60
0.61
Half
13.00
0.42
0.69
0.60
0.76
Half
15.00
0.42
0.70
0.49
0.69
Fully
Poorly in simulation; high in fuzzy Poorly in simulation; high in fuzzy Poorly
Moderate Moderate Moderate in simulation; high in fuzzy Moderate in simulation; poorly in fuzzy Moderate in simulation; high in fuzzy Moderate in simulation; high in fuzzy moderate Moderate in simulation; high in fuzzy moderate Moderate in simulation; high in fuzzy Moderate in simulation; high in fuzzy Moderate in simulation; poorly in fuzzy High High High High High High High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High High High in simulation; moderate in fuzzy High
60
45
30
0
30
Hour
Simulation model
Fuzzy model
Emin/Emax U1
Emin/Eavg U2
Emin/Emax U1
Emin/Eavg U2
9.00 11.00 13.00
0.23 0.23 0.23
0.53 0.53 0.53
0.39 0.42 0.46
15.00
0.23
0.53
9.00
0.24
11.00
High High
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Table 3 Uniformity values yielded by simulated and fuzzy models as a function of slat angle (clear-sky condition in summer). Angle
60
45
30
0
30
45
60
Hour
Simulation model
Fuzzy model
Emin/Emax U1
Emin/Eavg U2
Emin/Emax U1
Emin/Eavg U2
Degree of match
U1
U2
9.00
0.33
0.65
0.58
0.74
Half
High
0.54
0.73
Half
0.70 0.56
0.45 0.16
0.65 0.30
Fully Half
Poorly in simulation; moderate in fuzzy Poorly in simulation; moderate in fuzzy Poorly Poorly
11.00
0.35
0.65
13.00 15.00
0.39 0.25
9.00
0.31
0.63
0.57
0.74
Half
11.00
0.39
0.69
0.62
0.77
Half
13.00 15.00 9.00
0.39 0.28 0.50
0.70 0.59 0.71
0.43 0.26 0.62
0.65 0.42 0.77
Fully Fully Half
11.00 13.00 15.00
0.43 0.43 0.32
0.71 0.72 0.59
0.38 0.38 0.29
0.60 0.60 0.45
Fully Fully Half
Poorly in simulation; moderate in fuzzy Poorly in simulation; high in fuzzy Poorly Poorly Moderate in simulation; high in fuzzy Poorly Poorly Poorly
9.00 11.00
0.40 0.40
0.66 0.67
0.54 0.33
0.70 0.56
Fully Half
Poorly Poorly
13.00
0.43
0.70
0.33
0.54
Half
Poorly
15.00
0.44
0.68
0.30
0.50
Half
Poorly
9.00
0.37
0.66
0.60
0.77
Half
11.00
0.39
0.69
0.32
0.48
Half
Poorly in simulation; high in fuzzy Poorly
13.00 15.00 9.00 11.00 13.00 15.00 9.00
0.39 0.44 0.37 0.37 0.41 0.41 0.39
0.67 0.73 0.69 0.68 0.71 0.72 0.72
0.45 0.35 0.42 0.43 0.46 0.33 0.33
0.65 0.65 0.65 0.63 0.64 0.63 0.57
Fully Fully Fully Fully Fully Fully Half
Poorly Poorly Poorly Poorly Poorly Poorly Poorly
11.00
0.39
0.70
0.50
0.42
Half
Poorly
13.00 15.00
0.40 0.38
0.71 0.69
0.50 0.31
0.68 0.52
Fully Half
Poorly Poorly
blind system. A fuzzy logic approach was employed to assess the effect of the slat angles on the daylight distribution in this room. The fuzzy model was validated by comparing simulations run in DIALux for a large number of alternatives. Before doing so, the simulations were validated and corrected based on a series of field measurements performed in the office. The findings are summarized in Section 5. A number of limitations regarding the methodology and its relationship to daylight illuminance and the distribution thereof were considered noteworthy. One limitation concerns the selection of the DIALux tool. DIALux has been implemented as a tool for analyzing and designing electric lighting and daylighting collectively. Only CIE skies are used, although site locations may be defined by various inputs, namely, latitude and altitude and GMT time, and selected in advance according to location. However, not every type of weather file can be uploaded in the simulation. Indeed, there may be variations between the sky of the considered site and the CIE sky because CIE skies are standardized and rely on average conditions. The literature shows that there are many models that use these sky conditions to estimate daylight illuminance and its performance. However, it was realized that every model may not be suitable for
High High Moderate in simulation; poorly in fuzzy High High High Moderate High High High Moderate in simulation; poorly in fuzzy High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High in simulation; moderate in fuzzy High High High High High High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High in simulation; moderate in fuzzy
every application. Simplified but accurate models are convenient for performing quick estimations but may be limited. DIALux is a powerful tool in this respect and especially convenient in the early design stage. Accordingly, there is another noteworthy consideration to be taken into account. A climate-based approach could be used to carry out the entire design process. This approach would involve applying the weather file of a given site and calculating the illuminance values throughout the year. Software such as Radiance, Ecotect and Daysim are suitable tools. However, these tools use similar sky conditions and require long calculation times. There are other drawbacks and limits to this approach as mentioned in previous studies, including limited material definitions, information management, output reports, not being user friendly and not being intuitive [5,10,14,15]. The objective of this study was to introduce a new and potentially useful tool for building designers and practitioners: the fuzzy logic approach. It should be noted that the application of fuzzy logic is not completely new to the daylighting sector. However, its application is limited in another specific area: daylight illuminance control using fuzzy logic. Automated blind control strategies have been developed to maximize daylight performance or indoor comfort levels by fuzzy
34
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
controllers in the field of electrical engineering [22e25]. However, the development of such strategies to estimate daylight illuminance in the field of architecture has not been extensively explored. 7. Conclusions In this study, a fuzzy logic model was developed to predict daylight illuminance simply and to classify its distribution in an office with a movable blind system. The input parameters of the fuzzy model were hour, angle, distance and point location, which may be easily employed and examined in early architectural design schemes. Compared with the ANN model developed in a previous study conducted to predict daylight illuminance [8], the fuzzy model developed in this work can estimate daylight luminance by utilizing fewer variables, which may be taken from architectural schemes and using time data. In addition, the model was constructed for an office with a movable blind system. Therefore, the fuzzy model also determined the appropriate slat angles of the blind system. The model successfully estimated the daylight illuminance and its distribution (uniformity). To construct and validate the fuzzy model, a simulation model was constructed for this office using DIALux. Field measurements were 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 model closely matched the daylight distributions obtained by the simulation model. Specifically, the uniformity was effective at slat angles of 30 and 45 . Among three uniformity classes, namely, poorly, moderately and highly effective, the fuzzy model could properly estimate the uniformity values for the majority of slat angles. This noteworthy finding implies that the proposed method may be a robust and easily implemented tool in the early architectural design phase when considering a blind system and predicting its daylighting performance. Other conclusions derived from this study concerned the methodology used. This study shows that, similar to ANN models, fuzzy logic models may be used in the field of architecture as they are widely applied in engineering. Researchers should be made aware of this model and employ it in daylighting performance studies. Architects and lighting designers would benefit from this model by using it as an assistive tool to determine illuminance and light distributions. Additionally, this model may be improved by testing other spatial parameters or climatic aspects. Further models could involve other location and orientation characteristics. Finally, designers would benefit from this model by employing it before constructing a simulation model, mostly for visualization purposes and for conducting detailed lighting analyses. Thus, timely decisions could easily be made and necessary precautions taken before performing simulations, and the number of simulations required to correct basic architectural issues would be minimized. An early sketch, even one created by hand, would be enough to predict the performance of a blind system in terms of daylighting. References [1] Leslie RP, Radetsky LC, Smith AM. Conceptual design metrics for daylighting. Lighting Res Technol 2012;44:277e90. [2] Mardaljevic J, Heschong L, Lee E. Daylight metrics and energy savings. Lighting Res Technol 2009;41:261e83. [3] Lim HS, Kim G. Predicted performance of shading devices for healthy visual environment. Indoor Built Environ 2010;19(4):486e96. [4] Konis K. Evaluating daylighting effectiveness and occupant visual comfort in a side-lit open-plan office building in San Francisco, California. Built Environ 2013;59:662e77. [5] Reinhart CF, Wienold J. The daylighting dashboard: a simulation-based design analysis for daylit spaces. Built Environ 2011;46:386e96.
[6] Fontoynont M. Perceived performance of daylighting systems: lighting efficacy and agreeableness. Sol Energ 2002;73:83e94. [7] Ruck NC. International Energy Agency’s solar heating and cooling task 31. IEA; 2006. [8] International Energy Agency (IEA). Daylight in buildings, a source book on daylighting systems and components, International energy Agency (IEA) solar heating and cooling programme, energy conservation in buildings & community systems. Berkeley, CA: The Lawrence Berkeley National Laboratory; 2000. [9] Leslie RP. Capturing the daylight dividend in buildings: why and how? Build Environ 2003;38:381e5. [10] Gagne JML, Andersen M, Norford LK. An interactive expert system for daylighting design exploration. Build Environ 2011;46:2351e64. [11] Li DHW, Tsang EKW. An analysis of daylighting performance for office buildings in Hong Kong. Build Environ 2008;43:1446e58. [12] Lim Y, Kandar MZ, Ahmad MH, Ossen DR, Abdullah AM. Building façade design for daylighting quality in typical government office building. Build Environ 2012;57:194e204. [13] Ko SY, Yeo MS, Kim KW. Automated blind control to maximize the benefits of daylight in buildings. Build Environ 2010;45:1508e20. [14] Kazanasmaz T, Gunaydin M, Binol S. Artificial neural networks to predict daylight illuminance in office buildings. Build Environ 2009;44:1751e7. [15] Kazanasmaz T, Fırat P. Comparison of simulation tools mostly used in daylighting performance studies. In: Proceedings of international congress of architecture I “architecture and technology” (ICONARCH). Konya, Turkey: Selcuk University; 2012. p. 79e84. [16] Li DHW, Tsang EKW. An analysis of measured and simulated daylight illuminance and lighting savings in a daylit corridor. Build Environ 2005;40: 973e82. [17] Kim C, Chung S. Daylighting simulation as an architectural design process in museums installed with toplights. Build Environ 2011;46:210e22. [18] Hu J, Olbina S. Illuminance-based slat angle selection model for automated control of split blinds. Build Environ 2011;46:786e96. [19] Fakra AH, Miranville F, Boyer H, Guichard S. Development of a new model to predict indoor daylighting: integration in CODYRUN software and validation. Energy Convers Manag 2011;52:2724e34. [20] Reinhart CF, LoVerso VRM. A rules of thumb-based design sequence for diffuse daylight. Lighting Res Technol 2010;42:7e31. [21] Tzempelikos A, Shen H. Comparative control strategies for roller shades with respect to daylighting and energy performance. Build Environ 2013. http:// dx.doi.org/10.1016/j.buildenv.2013.05.016. [22] Daum D, Morel N. Identifying important state variables for a blind controller. Build Environ 2010;45:887e900. [23] Kolokotsa D. Comparison of the performance of fuzzy controllers for the management of the indoor environment. Build Environ 2003;38:1439e50. [24] Lah MT, Zupancic B, Krainer A. Fuzzy control for the illumination and temperature comfort in a test chamber. Build Environ 2005;40:1626e37. [25] Görgülü S, Ekren N. Energy saving in lighting system with fuzzy logic controller which uses light-pipe and dimmable balast. Build Environ 2013;61: 172e6. [26] Gravani MN, Hadjileontiadou SJ, Nikolaidou GN, Hadjileontiadis LJ. Professional learning: a fuzzy logic-based modelling approach. Learn Instr 2007;17: 235e52. [27] Sivanandam SN, Sumathi S, Deepa SN. Introduction to fuzzy logic using MATLAB. Berlin, Heidelberg: Springer-Verlag; 2007. [28] Kazanasmaz T, Tayfur G. Classifications for planimetric efficiency of nursing units. METU J Fac Arch 2012;29(1):1e20. [29] TAYFUR G. Soft computing in water resources engineering. Southampton, United Kingdom: WIT Press; 2012. [30] Akkurt S, Tayfur G, Can S. Fuzzy logic model for the prediction of cement compressive strength. Cem Concr Res 2004;34:1429e33. [31] Vakili-ardebili A, Boussabaine AH. Application of fuzzy techniques to develop an assessment framework for building design eco-drivers. Build Environ 2007;42:3785e800. lu Ö. Design enhancement by fuzzy logic in architecture. In: [32] Çiftçiog Nasraoui O, Frigui H, Keller JM, editors. Proceedings of the 12th IEEE international conference on fuzzy systems. St. Louis Missouri, USA: Institute of Electrical and Electronics Engineers (IEEE); 2003. p. 79e84. [33] Tayfur G. Fuzzy, ANN, and regression models to predict longitudinal dispersion coefficient in natural streams. Nord Hydrol 2006;37:143e64. [34] Saltan M, Saltan S, Sahiner A. Fuzzy logic modeling of deflection behavior against dynamic loading in flexible pavements. Constr Build Mater 2007;21: 1406e14. [35] Fontoynont M. Daylight performance of buildings. London: Earthscan; 1999. [36] Rea MS. The IESNA lighting handbook. New York: Illuminating Engineering Society of North America; 2000. [37] Chartered Institution of Building Services Engineers CIBSE. Code for lighting. London: CIBSE; 2002. [38] Licht UB. Lighting design, detail practice. Munich: Birkhauser; 2006. [39] Boubekri MA. Overview of the current state of daylight legislation. J Human Environ Syst 2004;7:57e63. [40] CIE 110-1994. Spatial distribution of daylight e luminance distributions of various reference skies. [41] DIALux version 4.9. User manual. Software standard for calculating lighting layouts, Lüdenscheid; 2011.
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Fuzzy logic model to classify effectiveness of daylighting in an office with a movable blind system çe Kazanasmaz* Tug _ Department of Architecture, Izmir Institute of Architecture, Urla 35430, Izmir, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 April 2013 Received in revised form 13 July 2013 Accepted 16 July 2013
This study estimated daylight illuminance and classified its effectiveness in an office with a movable blind system. First, measurements were carried out to validate and apply a simulation model using DIALux. Second, the simulation model was constructed utilizing physical properties similar to those of the case office. Third, the simulation model provided the daylighting calculations in terms of the slat angles of the movable blind system. A fuzzy model was later employed using the Mamdani fuzzy inference 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 daylighting standards and design norms. Regarding the movable blind system, slat angles of 30 and 45 provided more uniformly distributed daylight than other angles throughout standard working hours. Thus, according to the degree of match between the simulated and fuzzy models, the majority of the uniformity outcomes of the fuzzy model fully fit the simulation outcomes. Because the fuzzy model successfully estimated the daylight illuminance and its distribution (uniformity), it could be easily employed to examine early architectural design schemes. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Daylighting Fuzzy logic Uniformity Building Movable blind
1. Introduction Daylight penetration and its even distribution throughout a space are basic considerations made in building design. Both define the effectiveness of daylighting. A sufficient amount of daylight reduces the demand for electrical lighting and provides a healthy visual environment. Moreover, daylighting results in enhanced energy efficiency and visual acuity [1e5]. Apart from the benefit provided by daylight’s intensity, uniformly distributed daylight does not give rise to glaring surfaces and enhances visual quality and comfort [6e9,10]. Consequently, the primary physical measure use to quantify this phenomenon is illuminance. The estimation of uniformly distributed daylight is necessary, both in early architectural design processes and in daylighting performance evaluation studies [5,11e13]. Foreseeing further deficiencies regarding daylighting, i.e., incorrect window dimensions or misuse of a blind system, can be avoided in the early design stage. While evaluating the daylighting performance of an existing interior, any visual
* Tel.: þ90 232 7507063. E-mail addresses: [email protected], [email protected]. 0360-1323/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.buildenv.2013.07.011
comfort problems related to daylight may be assessed straightforwardly and rapidly. The literature reveals several techniques for predicting daylight illuminance. Contemporary techniques that have been used over the years include the construction of scale models and the use of analytical formulas and simulation tools. An overview of these methods was presented in previous studies by the author [14,15]. The strengths and weaknesses of these techniques were explained by reviewing selected studies. Recent methodologies, such as artificial intelligence [14], simulation tools such as Radiance, DIALux, etc. [12,16e18] and a trial simulation tool named Codyrun [19], have been introduced to predict indoor illuminance by accepting the irrefutable nature of daylighting and by simplifying its complexity for the ease of design. Several studies of daylighting metrics and rules of thumb have also been proposed to overcome initial design problems [1,2,20]. Gagne et al. [10] suggested an interactive design expert system for daylighting design, which might be used in the early design phase. This system was developed as an alternative to simulation tools to guide users in making design modifications. This tool was defined as a “virtual daylighting consultant”, including a daylighting knowledge-base and a fuzzy rule-based decision-making logic. The former involved information
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
about the impact of design conditions on daylighting, while the latter is for the decision on the main effect on design actions to improve daylighting conditions [10]. Reinhart and Wienold [5] proposed a new method for conducting integrated daylighting design analysis and thereby examine annual daylight availability, visual comfort and energy use together with dynamic simulation potentials. The authors named this tool ‘the daylighting dashboard’. It is known that there are many variables affecting daylight illuminance in a space [8,9,14]. In consideration of the all of the factors outlined above, this study aimed to estimate daylight illuminance simply by utilizing fewer variables, relative to the number of variables typically used in other methods, obtained from architectural drawings and using time data and to classify the distribution of illuminance (the daylighting effectiveness) in an office with a movable blind system by fuzzy logic modeling. The implementation of movable blind systems has been extensively recommended due to the systems’ ability to provide visual comfort and daylight for user’s appraisal and to meet peak electric demand. Movable blind systems are reliable and economical devices in satisfying energy-saving requirements and total energy use [3e8]. Several studies have been conducted on the design and performance of these devices in terms of visual comfort and their effect on thermal comfort and energy performance [12,13,18,21]. Specifically, Hu and Olbina focused on automated blind systems and aimed to construct an illuminance-based ANN model to select the optimal slat angles [18]. Additionally, the literature reveals various studies on the use of a fuzzy logic approach in automated blind control in the daylighting sector. In this context, fuzzy controllers have been proposed to achieve optimum daylight intensity and energy savings [22e25]. If properly integrated into a fenestration system, movable blind systems prevent unwanted heat gain during the cooling period and allow heat gain during the heating period. In particular, the applications of
23
movable blind systems in buildings located in hot-humid regions with mostly clear-sky conditions are favorable for improving daylighting uniformity and visual comfort. Movable blind systems are composed of different materials and are designed in various sizes [6e8]. In view of their common use in hot-humid regions and their design alternatives, the estimation of the effectiveness of movable blind systems with respect to daylight distribution in interiors has become a major research issue, particularly regarding how a movable blind system performs in terms of daylighting or what slat angle leads uniform illuminance. Such inquiries should be addressed during the very early stages of design by simple and straightforward examination of architectural drawings. Thus, a fuzzy model was developed to evaluate daylight distribution, and its effectiveness was assessed. 2. Background of fuzzy logic 2.1. Fuzzy logic concept The practice of fuzzy logic derives from the transformation of verbal expressions into analytical information for use in computing processes. This mathematical tool then categorizes variables into certain degrees of subsets based on the theory that “an event occurs with a relative graded membership” [26]. Thus, a fuzzy inference system (FIS) constructs a model that provides outcomes with meaningful decision-making implications as a result of these categories of imprecise data and vague statements of verbal information [26,27]. This model helps to categorize the complexity of real-world tasks into simple units. The prediction of daylight illuminance is one such task. This methodology was applied in a previous study by the author in the field of architecture [28]; however, the problem in this study depends on the optimum estimation and classification of fuzzy sets with respect to the effectiveness of daylighting.
Fig. 1. An example of fuzzy rule system with defuzzification.
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There are generally four steps that must be followed to construct a fuzzy model. First, fuzzification transforms input data into grades of membership through membership functions of a fuzzy set. The membership function matches a degree (grade) to a linguistic term such as “low” or “medium”. There may be one or more membership functions. Each input value is associated with a value (an infinite number in the interval [0 1]) between 0 and 1. Fuzzy membership functions may be triangular or trapezoidal in form for the ease of application [26e30]. Second, fuzzy rules are constructed to determine all possible relations between input and output data in the fuzzy knowledge (rule) base. These IF/THEN rules with AND/OR connectors determine the uncertainties, nonlinear relationships and/or model complexity of the descriptive fuzzy inference process. The fuzzy concept does not involve numerical equations and model parameters. Therefore, Mamdani, a type of rule system in which the result of a fuzzy rule is expressed verbally, was applied in this study. In detail, “the fuzzy numbers of the antecedent of the rule are combined according to the AND/OR operators that may be used in the syntax of the rule, respectively, to produce a new fuzzy number” [26]. An example of this process specific to this study is summarized in Fig. 1. Third, a fuzzy inference engine operates with fuzzy rules to diagram the outputs through deduction based on inputs. The engine performs mathematical computations such as applying min or prod activation operators. Finally, defuzzification displays the fuzzy output as a meaningful crisp value (a number).
The literature on fuzzy logic offers more detailed information [26e 34]. In this study, to evaluate the prediction accuracy of the proposed model, the measured illuminance outputs were compared with the estimated ones and the illumination divergence error was calculated. 3. The case office The case office is located in a three-story educational building _ of the Faculty of Architecture (Izmir Institute of Technology) on a hilly site (latitude 38.19 ; longitude 26.37 ). The offers measure 4.5 m in length and 5.5 m in width, as schematically shown in Fig. 2a. The story height is 3.8 m. This office has one exterior wall with two identical double-glazed windows (1.9 m 2.0 m) facing east. The fenestration is composed of white aluminum profiles. The floor covering material is white marble, the walls are painted in acrylic light beige and the ceiling is white. The glass hemisphericalehemispherical transmittance, normalenormal transmittance and wall surface hemisphericalehemispherical reflectance values in the office were measured on-site according to the daylighting performance evaluation method mentioned by Fontoynont [35]. The first transmittance was 94%, the second transmittance was 90% and the reflectance of the wall material was 89%. According to the literature, non-specular surfaces for floors with 20e50% reflectance, for walls with 40e70% reflectance
Fig. 2. A schematic layout of the case office (a) and photos of the blind system (b).
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
and for ceilings with 70e90% reflectance are recommended by the IESNA lighting standards [36]. The exterior movable blind system is composed of white horizontal slats placed 10 cm apart as shown in Fig. 2b. The slats are able to move within two guiding profiles. 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 solar altitude 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.
25
4. Method 4.1. Field measurements All measurements of daylight illuminance were conducted at 15 reference points by following certain practical guidance offered by the Chartered Institution of Building Services Engineers (CIBSE). The number of measurement points and their locations were also determined according to the CIBSE by considering the ratio between room size and height. Reference
Fig. 3. Fuzzy membership functions for (a) hour, (b) angle, (c) distance, (d) location and (e) illuminance.
26
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
points were located at the center of equal divisions of the floor area [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 in November and clear skies in June. The external illuminances were measured according to the method mentioned by Fontoynont [35]. They ranged from 4.8 klux to 6 klux, and from 16 klux to 20 klux, respectively. The cloudy-sky condition resembles the weakest external condition experienced, which leads to the minimum level of daylight inside the room. By utilizing this type of sky condition, the model tested the worstcase scenario in terms of daylight level. The clear-sky condition was also taken into account because it represents the case in which a blind system is used to control sunlight. A digital lightmeter with a silicon photodiode detector was used for field measurements. The constant height for each reading was set to 0.8 m from the floor to define the working plane. Measurements were taken 0.5 m away from walls/columns/partitions, and grid points were positioned with equal spacings (Fig. 2). Moreover, a luminance meter was required to determine the transmittance of the glazing and the brightness of finishing surfaces as observed within the field of view. To evaluate these measurements, literature regarding certain lighting standards was reviewed. According to DIN 5034 [38], the uniformity values for daylit interiors should satisfy the following equations;
Dmin =Dmax > 0:67
Table 1 An example of 20 fuzzy rule sets randomly selected from the total 108 sets. Hour
Distance
Angle
Location
Illuminance
L L H L M M VL M L L H L M H M VL H VL H H
L L H M M L H M H H L M M M M H L H M H
L L L L L L M H M H M L L H M L L H L H
L H M H L H L M L H L H M H H H H H M L
VVL VL H L H M VL VL M L VVL VVH VVH VVL L M L VVL M VVL
(1)
and
Dmin =Davg > 0:5
(2)
In addition, several recommendations regarding daylighting illuminance vary among various countries because standardization of daylighting is a complex task that has yet to be resolved. The predictable and unpredictable characteristics and dynamic nature of daylight in terms of its intensity and color are the drivers for its complexity. It is widely accepted that the characteristics and quality of daylight are superior to those of electric lighting. Although minimum illuminance is defined as 300 lux for offices according to the CIBSE standards [37], the recommended daylight levels in the German DIN 5034-4 standard range from 250 lux to 500 lux for normal tasks and from 750 lux to 1000 lux for difficult tasks [38]. Daylight requirements are cited explicitly by Boubekri [39] and Licht [38].
4.2. DIALux modeling DIALux is a simulation tool that is used for electric lighting design practice and energy research, mainly to estimate power consumption. The tool operates using technical data for a wide range of lamps. It calculates illuminance with the necessary power load. However, although the program calculates and evaluates energy consumption, it should be noted that the operation of electric lighting systems is not independent of daylighting systems and shading components. The schedule of daylight availability and penetration time reduce the operating time of artificial lighting, which is why both daylighting and artificial lighting should be designed collectively. Furthermore, a design tooldpreferably a simulation tool to meet today’s demandsdshould be used to test these factors in the early design phase. This tool would make it easy to determine the dimensions and the form of shading components or daylighting systems or window apertures required. Other variable conditions or daylighting complications such as insufficient
Fig. 4. Comparison of measured and simulated results; (a) under cloudy-sky condition, (b) under clear-sky condition.
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
27
Fig. 5. Schematic sections of slat angles.
illuminance, glare or an excessive amount of direct sunlight (sunpatch) at any time during the year [4e6,11e13] can be estimated correctly by comparing DIALux outputs with the values recommended by common standards. To date, DIALux has been a useful tool for analyzing and designing daylighting. Its advantage lies in the integration of the use of real electric lighting fixtures from the market (for real applications) with daylighting analysis. The sky models of DIALux, i.e., clear, overcast and partially overcast sky, are in accordance with CIE 110-1994 “Spatial Distribution of Daylight e Luminance Distributions of Various Reference Skies” [40]. The program performs calculations according to DIN 5034 and CIE publication 110 by considering location, time, orientation and daylight obstruction [41]. Geographical location is defined by latitude and longitude, and time is determined according to GMT. In this study, measurements and simulations were carried out under clear-sky conditions in summer and cloudy (overcast)-sky conditions in winter. 4.3. Fuzzy logic modeling A fuzzy model was constructed by employing the original data obtained from DIALux modeling and considering the recommended illuminance for offices mentioned in the CIBSE standards [37]. The fuzzy rules and their membership functions were constructed by considering expert opinion and the data set gathered from the sample. MATLAB software was used to execute mathematical algorithms to construct the model. The input parameters hour, angle, distance and location were fuzzified in fuzzy subsets to obtain the degree of illuminance effectiveness. Hour, which determines the position of the sun, was the most significant variable [36]. The slat angle was the key indicator of the movable blind
system’s performance. The blind position defined the amount of daylight penetration [8]. The remaining two parameters identified each reference point. The illuminance measured at these points defined the pattern of light distribution. The hour range was 9 a.m.e3 p.m., and the four subsets into which it was subdivideddvery low (VL), low (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3a. However, angle was considered to have a maximum value of 7, and the three subsets into which it was subdivideddlow (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3b. Similarly, the maximum values of distance and location were 5 and 3, respectively. The three subsets into which they were divideddlow (L), medium (M) and high (H)dwere considered to have triangular membership functions, as shown in Fig. 3c, d. Finally, the maximum illuminance was determined to be 2000 lux, and the then subsets into which it was subdivided were considered to have triangular membership functions, as shown in Fig. 3e. The subdivisions of the input variables were defined explicitly depending on the nature of the data and the existing literature. Similarly, the subsets of fuzzy variations in illuminance resemble the values of relevant norms and guidelines. They represent basic classifications that capture detailed deviations in any illuminance distribution. The fuzzy rule base, representing the relationships between the inputs, i.e., hour, angle, distance and location, and the output, i.e., illuminance, was then constructed. Fuzzy rules were intuitively applied by taking into account the measured and simulated data. They were also inferred from general knowledge presented in the literature [8,37e39]. The commonly used Mamdani rule system was employed in this study. The system is used to relate
Fig. 6. 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. (cloudy-sky condition in winter).
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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 constructing fuzzy rules [13e16]. The antecedent part of a ruledthe part beginning with IF, up to THENdincluded a statement on hour, angle, distance and location, whereas the consequent partdthe part beginning with THEN, up to the enddincluded a statement on illuminance. For example, ‘IF the hour is ‘Low’, the angle is ‘Low’, the distance is ‘Medium’ and the location is ‘Low’, THEN the illuminance is ‘Low’. There were a total of 108 fuzzy rule sets, 20 of which were randomly selected and summarized in Table 1. The following fuzzy inferencing engine operators were used: the min operator was employed to determine the firing strength of each rule, the max composition operator was used to combine fuzzy output sets from each fired rule into a single fuzzy output set; and the centroid method 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. The actual locations of furniture and window openings were modeled as shown in Fig. 2. The color and reflectance of surface materials were selected carefully to resemble the actual materials correctly. A set of simulation outputs was then compared with the measurements to validate and finalize the DIALux model. Then, the corrected simulations were carried out. The field measurements conducted in November and June were incorporated into this process. The error rate was determined and the model validated according to the method applied by Kim and Chung [17]. First, the relative errors at each measurement point were determined separately. Second, the minimum, maximum and mean RE values for all
Fig. 8. Distribution of illuminance for a slat angle of 45 at (a) 9 a.m., (b) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (cloudy sky condition in winter).
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
29
slat positions were determined. Third, regression lines created for scatter plots of the gathered data represented the degree of relationship between the measurement and simulation results. Specifically, the Relative Error (RE) between the two results was calculated 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 SE is the matching simulated illuminance determined by DIALux. Based on this calculation, the minimum RE value was 3% at point C4, and the maximum RE value was 43% at point B1 for all slat positions. The mean value of RE at the measurement points for all angles ranged from 5% to 30%. The simulated results closely matched the measurement results. In the linear regression analysis performed to estimate the relationship between the measured and simulated results, the coefficient of determination (R2) values ranged from 96% to 97%. To correct the simulated findings, a correction factor (CF) and corrected simulation (CS) value were recalculated at each point. The value of CF was the average value of the relative errors at each point. The value of CS was the simulated illuminance obtained by placing CF instead of RE in Eq. (3). In other words, each measured illuminance was multiplied by the mean value 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 the measurement results. This comparison showed that the RE value ranged from 1% to 24%. Moreover, the R2 values ranged from 96% to 98% for the corrected simulation values (Fig. 4). Because the DIALux model was calibrated and finalized with relative errors of 2e4%, trial models were applied for fuzzy model construction. Simulation results at 9 a.m., 11 a.m., 1 p.m. and 3 p.m. were obtained for overcast-sky conditions on December 21st and clearsky conditions on June 21st. The daylight calculations were iterated for each slat angle of the movable blind, i.e., 60, 45, 30 , 0 , 30 , 45 and 60 ; schematic sections of the blind angles are shown in Fig. 5 and the distribution of illuminance in Figs. 6e9. The total number of data sets obtained from DIALux was 375.
Fig. 10. Fuzzy results versus simulation results for (a) cloudy-sky condition in winter and (b) clear-sky condition in summer.
5.2. Fuzzy model application A fuzzy logic algorithm was applied to predict daylight illuminance in an office with a movable blind system as mentioned previously. The objective of the study was to classify the degree of
Fig. 9. Distribution of illuminance for a slat angle of 45 at (a) 9 a.m., (b) 11 a.m., (c) 1 p.m. and (d) 3 p.m. (clear sky condition in summer).
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T. Kazanasmaz / Building and Environment 69 (2013) 22e34
effectiveness according to the slat angles of the movable blind, where effectiveness is the indicator of daylight distribution in a space; thus, predicting the illuminance at each reference point was the essential step. Taking the simulated illuminance of the reference points into consideration, the daylight illuminance values were predicted by the fuzzy model. An example of this Mamdani fuzzy inference system based on three rules was illustrated in the previous section (Fig. 1). The fuzzy subsets for the input and output variables are shown in Fig. 3. The total number of data sets that were used to test the model was 375. The model was executed in the fuzzy logic toolbox in MATLAB. The prod and centroid methods were employed as the inference operator and for defuzzification, respectively. The predicted illuminance that falls into any subset is shown in Fig. 3d.
The relative error obtained by the model was 11%. The model predicted the simulation values with a high rate of accuracy, nearly 87% for randomly selected data sets (Fig. 10). The fuzzy outcomes fit the simulation outcomes very well. However, the uniformity values deviated extremely. Overall, the findings obtained under cloudy- and clear-sky conditions showed similarities. Here, the focus will be on the results obtained for the clear-sky condition and their differences from the other findings obtained for the cloudy-sky condition. The distributions of Emin, Emax and Eavg determined from the simulated and fuzzy models as a function of slat angle are shown in Fig. 10 (cloudy-sky condition in winter) and Fig. 11 (clear-sky condition in summer). Whereas the fuzzy model constructed under the cloudy-sky condition estimated the Emin, Emax and Eavg values more accurately at slat angles of 0 , 30 and 45 than the values at other
Fig. 11. Distribution of Emin, Emax and Eavg values determined yielded by simulated and fuzzy models as a function of slat angle (cloudy-sky condition in winter).
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
angles, the model under the clear-sky condition yielded more accurate results at slat angles of 30 , 45 and 60 . Even the Emax values deviated for the most part. Another distinctive finding is that the majority of the Eavg values yielded by the fuzzy model closely matched the average illuminance calculated by simulation. Indeed, under the clear-sky condition, the average daylight illuminance satisfied the daylighting standards and norms for normal tasks for most of the standard working period (starting at 9 a.m. until 3 p.m.) at all angles, unlike that determined by the model under the cloudy-sky condition. Regarding the Emax values at points near the window zone, most of the slat angles provided a daylight illuminance above 1200e1600 lux. In general, the majority of the slat angles were successful in avoiding sunpatches during working hours. 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
31
hours, as obtained in the simulation model. Thus, this situation affected the illuminance at nearby points in the room. The fuzzy model failed to capture such deviations in illuminance (Figs. 6e8). The points displaying sunpatches were eliminated in analyzing the uniformity values (Fig. 12). The uniformity values of the simulated and fuzzy models implied that none of the U1 (uniformity 1 ¼ Emin/Emax) values were in overall agreement with current daylighting requirements and design criteria mentioned in the literature [8,35,38]. However, with only a few exceptions, all U2 (uniformity 2 ¼ Emin/Eavg) values were relevant. Thus, three uniformity effectiveness classes were proposed with respect to the standard uniformity ratios mentioned in the literature [8,35,38]. Uniformity ratios that ranged from 0.30 to 0.49 defined the poorly effective class, those that ranged from 0.50 to 0.59 defined the moderately effective
Fig. 12. Distribution of Emin, Emax and Eavg values yielded by simulated and fuzzy models as a function of slat angle (clear-sky condition in summer).
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T. Kazanasmaz / Building and Environment 69 (2013) 22e34
class and those that ranged from 0.60 to 0.70 defined the highly effective class. Table 3 summarizes all of the uniformity classes for all slat angles. The fuzzy model was able to successfully predict the uniformity classes for slat angles of 30 and 45 . When the blind’s slat angle was 0 , the model was also successful under the cloudy-sky condition (Table 2). Concerning the simulation model, when slat angles of 0 , 30 , 45 and 60 were used, daylight was distributed both poorly and highly inside the office throughout the working period. The fuzzy model results were lower or higher than but similar to the simulated results at specific hours. Even the U2 values nearly fell into the satisfying and preferred uniformity class. The lowest matching uniformity values were obtained by the fuzzy model at a slat angle of 0 . Thus, according to the degree of match for the simulated and fuzzy models, the majority of the uniformity outcomes of the fuzzy model fully fit the simulation outcomes. The majority of the uniformity values for the resting slat angles did not fully match the simulation results because of the deviation in U2 values at 0 and 60 and the deviation in U1 values at 60 , 45 and 30 . In general, a higher degree of matching among uniformity values was achieved under the cloudy-sky condition than under the clear-sky condition. This result can be attributed to the difficulty in controlling direct sunlight versus diffuse light. It is necessary to reconsider
the design of the blind system in terms of its form and its size. Further analysis is recommended for developing a new blind system design that tracks sun angles. Slat angles of 30 and 45 provided a more uniform daylighting distribution than the other angles did throughout the working period. Thus, it was concluded that these angles represented the most suitable design alternatives that would be preferred in the architectural design of offices that are located in similar areas and exhibit similar climate and orientation characteristics. The data sets used in this fuzzy model included data gathered under both the cloudy-sky and clear-sky conditions. The former allowed for the elimination of extreme deviations in daylight illuminance during winter. Thus, the illuminance was close to the minimum levels considered valid for the design process. However, as because the main function of a blind is to control sunlight under clear skies, the findings focused on the latter condition. Additionally, the illuminances complied with the recommended levels under this condition, although the U1 values did not. 6. Discussion To summarize, the DIALux and fuzzy logic models developed in this study were used to estimate the daylight illuminance and classify the uniformity rates in an existing office with a movable
Table 2 Uniformity values yielded by the simulated and fuzzy models as a function of slat angle (cloudy-sky condition in winter). Angle
Degree of match
U1
U2
0.57 0.59 0.63
Fully Fully Half
Poorly Poorly Poorly
0.30
0.45
Half
Poorly
0.54
0.50
0.68
No
0.24
0.54
0.38
0.60
Half
Poorly in simulation; moderate in fuzzy Poorly
13.00 15.00
0.24 0.24
0.54 0.54
0.38 0.40
0.57 0.65
Fully Half
Poorly Poorly
9.00 11.00
0.29 0.29
0.58 0.58
0.40 0.44
0.58 0.67
Fully Half
Poorly Poorly
13.00
0.29
0.58
0.44
0.66
Half
Poorly
15.00
0.29
0.58
0.33
0.48
Half
Poorly
9.00 11.00 13.00 15.00 9.00 11.00 13.00 15.00
0.42 0.41 0.41 0.41 0.46 0.46 0.46 0.46
0.69 0.69 0.69 0.69 0.72 0.71 0.72 0.71
0.44 0.41 0.47 0.33 0.44 0.40 0.43 0.35
0.61 0.64 0.67 0.49 0.63 0.60 0.61 0.55
Fully Fully Fully Fully Fully Fully Fully Half
Poorly Poorly Poorly Poorly Poorly Poorly Poorly Poorly
45
9.00
0.44
0.70
0.32
0.57
Half
Poorly
60
11.00 13.00 15.00 9.00
0.44 0.44 0.44 0.42
0.70 0.70 0.70 0.69
0.44 0.50 0.47 0.25
0.60 0.67 0.74 0.50
Fully Fully Fully Half
Poorly Poorly Poorly Poorly
11.00
0.42
0.69
0.60
0.61
Half
13.00
0.42
0.69
0.60
0.76
Half
15.00
0.42
0.70
0.49
0.69
Fully
Poorly in simulation; high in fuzzy Poorly in simulation; high in fuzzy Poorly
Moderate Moderate Moderate in simulation; high in fuzzy Moderate in simulation; poorly in fuzzy Moderate in simulation; high in fuzzy Moderate in simulation; high in fuzzy moderate Moderate in simulation; high in fuzzy moderate Moderate in simulation; high in fuzzy Moderate in simulation; high in fuzzy Moderate in simulation; poorly in fuzzy High High High High High High High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High High High in simulation; moderate in fuzzy High
60
45
30
0
30
Hour
Simulation model
Fuzzy model
Emin/Emax U1
Emin/Eavg U2
Emin/Emax U1
Emin/Eavg U2
9.00 11.00 13.00
0.23 0.23 0.23
0.53 0.53 0.53
0.39 0.42 0.46
15.00
0.23
0.53
9.00
0.24
11.00
High High
T. Kazanasmaz / Building and Environment 69 (2013) 22e34
33
Table 3 Uniformity values yielded by simulated and fuzzy models as a function of slat angle (clear-sky condition in summer). Angle
60
45
30
0
30
45
60
Hour
Simulation model
Fuzzy model
Emin/Emax U1
Emin/Eavg U2
Emin/Emax U1
Emin/Eavg U2
Degree of match
U1
U2
9.00
0.33
0.65
0.58
0.74
Half
High
0.54
0.73
Half
0.70 0.56
0.45 0.16
0.65 0.30
Fully Half
Poorly in simulation; moderate in fuzzy Poorly in simulation; moderate in fuzzy Poorly Poorly
11.00
0.35
0.65
13.00 15.00
0.39 0.25
9.00
0.31
0.63
0.57
0.74
Half
11.00
0.39
0.69
0.62
0.77
Half
13.00 15.00 9.00
0.39 0.28 0.50
0.70 0.59 0.71
0.43 0.26 0.62
0.65 0.42 0.77
Fully Fully Half
11.00 13.00 15.00
0.43 0.43 0.32
0.71 0.72 0.59
0.38 0.38 0.29
0.60 0.60 0.45
Fully Fully Half
Poorly in simulation; moderate in fuzzy Poorly in simulation; high in fuzzy Poorly Poorly Moderate in simulation; high in fuzzy Poorly Poorly Poorly
9.00 11.00
0.40 0.40
0.66 0.67
0.54 0.33
0.70 0.56
Fully Half
Poorly Poorly
13.00
0.43
0.70
0.33
0.54
Half
Poorly
15.00
0.44
0.68
0.30
0.50
Half
Poorly
9.00
0.37
0.66
0.60
0.77
Half
11.00
0.39
0.69
0.32
0.48
Half
Poorly in simulation; high in fuzzy Poorly
13.00 15.00 9.00 11.00 13.00 15.00 9.00
0.39 0.44 0.37 0.37 0.41 0.41 0.39
0.67 0.73 0.69 0.68 0.71 0.72 0.72
0.45 0.35 0.42 0.43 0.46 0.33 0.33
0.65 0.65 0.65 0.63 0.64 0.63 0.57
Fully Fully Fully Fully Fully Fully Half
Poorly Poorly Poorly Poorly Poorly Poorly Poorly
11.00
0.39
0.70
0.50
0.42
Half
Poorly
13.00 15.00
0.40 0.38
0.71 0.69
0.50 0.31
0.68 0.52
Fully Half
Poorly Poorly
blind system. A fuzzy logic approach was employed to assess the effect of the slat angles on the daylight distribution in this room. The fuzzy model was validated by comparing simulations run in DIALux for a large number of alternatives. Before doing so, the simulations were validated and corrected based on a series of field measurements performed in the office. The findings are summarized in Section 5. A number of limitations regarding the methodology and its relationship to daylight illuminance and the distribution thereof were considered noteworthy. One limitation concerns the selection of the DIALux tool. DIALux has been implemented as a tool for analyzing and designing electric lighting and daylighting collectively. Only CIE skies are used, although site locations may be defined by various inputs, namely, latitude and altitude and GMT time, and selected in advance according to location. However, not every type of weather file can be uploaded in the simulation. Indeed, there may be variations between the sky of the considered site and the CIE sky because CIE skies are standardized and rely on average conditions. The literature shows that there are many models that use these sky conditions to estimate daylight illuminance and its performance. However, it was realized that every model may not be suitable for
High High Moderate in simulation; poorly in fuzzy High High High Moderate High High High Moderate in simulation; poorly in fuzzy High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High in simulation; moderate in fuzzy High High High High High High High in simulation; moderate in fuzzy High in simulation; moderate in fuzzy High High in simulation; moderate in fuzzy
every application. Simplified but accurate models are convenient for performing quick estimations but may be limited. DIALux is a powerful tool in this respect and especially convenient in the early design stage. Accordingly, there is another noteworthy consideration to be taken into account. A climate-based approach could be used to carry out the entire design process. This approach would involve applying the weather file of a given site and calculating the illuminance values throughout the year. Software such as Radiance, Ecotect and Daysim are suitable tools. However, these tools use similar sky conditions and require long calculation times. There are other drawbacks and limits to this approach as mentioned in previous studies, including limited material definitions, information management, output reports, not being user friendly and not being intuitive [5,10,14,15]. The objective of this study was to introduce a new and potentially useful tool for building designers and practitioners: the fuzzy logic approach. It should be noted that the application of fuzzy logic is not completely new to the daylighting sector. However, its application is limited in another specific area: daylight illuminance control using fuzzy logic. Automated blind control strategies have been developed to maximize daylight performance or indoor comfort levels by fuzzy
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controllers in the field of electrical engineering [22e25]. However, the development of such strategies to estimate daylight illuminance in the field of architecture has not been extensively explored. 7. Conclusions In this study, a fuzzy logic model was developed to predict daylight illuminance simply and to classify its distribution in an office with a movable blind system. The input parameters of the fuzzy model were hour, angle, distance and point location, which may be easily employed and examined in early architectural design schemes. Compared with the ANN model developed in a previous study conducted to predict daylight illuminance [8], the fuzzy model developed in this work can estimate daylight luminance by utilizing fewer variables, which may be taken from architectural schemes and using time data. In addition, the model was constructed for an office with a movable blind system. Therefore, the fuzzy model also determined the appropriate slat angles of the blind system. The model successfully estimated the daylight illuminance and its distribution (uniformity). To construct and validate the fuzzy model, a simulation model was constructed for this office using DIALux. Field measurements were 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 model closely matched the daylight distributions obtained by the simulation model. Specifically, the uniformity was effective at slat angles of 30 and 45 . Among three uniformity classes, namely, poorly, moderately and highly effective, the fuzzy model could properly estimate the uniformity values for the majority of slat angles. This noteworthy finding implies that the proposed method may be a robust and easily implemented tool in the early architectural design phase when considering a blind system and predicting its daylighting performance. Other conclusions derived from this study concerned the methodology used. This study shows that, similar to ANN models, fuzzy logic models may be used in the field of architecture as they are widely applied in engineering. Researchers should be made aware of this model and employ it in daylighting performance studies. Architects and lighting designers would benefit from this model by using it as an assistive tool to determine illuminance and light distributions. Additionally, this model may be improved by testing other spatial parameters or climatic aspects. Further models could involve other location and orientation characteristics. Finally, designers would benefit from this model by employing it before constructing a simulation model, mostly for visualization purposes and for conducting detailed lighting analyses. Thus, timely decisions could easily be made and necessary precautions taken before performing simulations, and the number of simulations required to correct basic architectural issues would be minimized. An early sketch, even one created by hand, would be enough to predict the performance of a blind system in terms of daylighting. References [1] Leslie RP, Radetsky LC, Smith AM. Conceptual design metrics for daylighting. Lighting Res Technol 2012;44:277e90. [2] Mardaljevic J, Heschong L, Lee E. Daylight metrics and energy savings. Lighting Res Technol 2009;41:261e83. [3] Lim HS, Kim G. Predicted performance of shading devices for healthy visual environment. Indoor Built Environ 2010;19(4):486e96. [4] Konis K. Evaluating daylighting effectiveness and occupant visual comfort in a side-lit open-plan office building in San Francisco, California. Built Environ 2013;59:662e77. [5] Reinhart CF, Wienold J. The daylighting dashboard: a simulation-based design analysis for daylit spaces. Built Environ 2011;46:386e96.
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