Strategies to control daylight in a responsive skylight system

Automation in Construction 28 (2012) 91–105

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Strategies to control daylight in a responsive skylight system Gonçalo Castro Henriques a,⁎, José Pinto Duarte b, Vitor Leal c a b c

TU Lisbon Faculty of Architecture, X-Ref Architectural Research & Development, Portugal TU Lisbon Faculty of Architecture, Researcher at TU Lisbon ICIST (IST Construction Institute), Portugal FEUP, Faculty of Engineering of the University of Porto Institute for Mechanical Engineering, Portugal

a r t i c l e

i n f o

Article history: Received 11 September 2011 Accepted 7 June 2012 Available online 15 August 2012 Keywords: Responsive system Daylight simulation Illuminance and visual contrast Heuristics Multi-criteria decision

a b s t r a c t This research aims to develop a skylight system that responds to both external, environmental conditions and adjustable internal functional demands. The system adapts to different geometries, uses, locations, times and sky conditions. In the design process, the disposition and size of skylights are customized to the context. After construction, the apertures of the skylights control interior conditions. This paper focuses on the dynamic process to control daylight using a case study. The goal is to assure adequate illuminance and low visual contrast. Parametric and environmental software analysis is used to generate and assess solutions. Heuristics strategies are developed to find adequate configurations, given that optimization methods are time and resource consuming. The performance of such configurations is evaluated in specific conditions. An interpolation method is proposed to find configurations adequate to other conditions. A friendly-interface allows selecting the best configuration in real-time using multi-criteria. © 2012 Elsevier B.V. All rights reserved.

1. Introduction

1.1. Biological influences: natural evolution and behavior

The current research is part of a larger research concerned with the use of digital technologies in the Architecture, Engineering and Construction (AEC) sector. The ultimate goal is to improve the ability of buildings to respond to the context, by enabling local adaptation and customization. To study the use such technologies in different stages of the building's life cycle, namely, design, production, and operation, current research is focused on the development of a system of responsive skylights. The idea is to use generation, simulation, fabrication, and automation techniques to conceive skylight systems adapted to different geometries, uses, locations and weather conditions. The process of finding an adequate configuration involves two form-finding processes: first, manipulating the skylight shape and tessellation according to the input geometry at the design stage, and then altering the aperture of its skylights at the operation stage. These processes are called static and dynamic customization, respectively. A simplified pavilion structure, called TetraScript, is used as a case study to guide the development of the system. The present article focuses on the identification of the design requirements to ensure good response to daylight requirements through dynamic customization.

The current research was inspired at several levels on features of biological systems. The static and dynamic customization processes referred to above have a parallel in natural systems. In nature, organisms evolve adapting to the environment in the long run, using the process of natural selection. This is the case of certain vegetables whose shape and surface texture enable them to control their inner temperature in hot climates (Fig. 1). The process of finding an adequate configuration for a building using static adaptation can be compared to natural selection over time. Some organisms have behavior mechanism and respond to changes in local conditions, in real-time. Some plants, like the snow buttercup follow the sunlight direction to receive more sun, in a heliotropic response. Other plants like the King Protea, open more to get sunlight, reacting to the quantity of light, responding to non-directional stimuli in a photonasty response. The process of changing the apertures of the skylights can be compared to such responses (Fig. 1). The goal is to propose responsive system, using the principles of existing natural systems, in order to improve performance according to local conditions. A parametric system is proposed to generate multiple skylight configurations, as it will be described in Section 1.2. For the current study the TetraScript pavilion (Fig. 2) is used as a case study. 1.2. Static and dynamic customization

⁎ Corresponding author. E-mail addresses: [email protected] (G.C. Henriques), [email protected] (J.P. Duarte), [email protected] (V. Leal). 0926-5805/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2012.06.002

The problem of adapting the pavilion to the context is a matter of manipulating its shape in response to internal and external conditions (both long-term as short-term conditions). In the context of the current

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Fig. 1. Examples of vegetal customization to environmental conditions in the tropics: skin texture of Durian and Jackfruit (above) resulting from natural adaptation; behavior mechanism of the king Protea that reacts to the presence of daylight by opening (below).

study, this problem was simplified by means of using a case study — the design of a small pavilion. The internal conditions depend on the particular use intended for the pavilion; several different uses are possible such as leisure, exhibition, office-type or even greenhouse. Obviously the use has an important impact on spatial and daylighting requirements. The relevant external conditions for lighting analysis are mainly the geographical location, time of the day and year, and weather conditions, which impact on the direction and amount of available sunlight. So, the problem becomes one of finding an adequate configuration for the pavilion, i.e., the set of values for the shape control variables that yield adequate indoor lighting conditions. The configuration of the pavilion is determined by a small set of variables including basic form, tessellation and texture in what regards static adaptation, and the degree of aperture of the skylight panels in what regards dynamic customization. The adequate values for these variables can be determined through two processes in two different stages described next. Static customization is used in the design phase to adapt the shape of the building to its particular use and location at the moment of construction. The variables that can be controlled at this stage are basic form, tessellation, and texture and the corresponding values are found at the design stage. To control the universe of possibilities and focus the study on lighting aspects, the basic form was limited to closed elliptical domes and the manipulation of the correspondent variables determines the specific shape and dimensions of the pavilion. Tessellation is then used to decompose the dome's shape surface into discrete elements for fabrication and to define the orientation and size of the skylights. The surface's texture is created by the pyramidal shape of the

skylights. The case study considers a dome solution with 6 × 4 × 3 m at a 41.2°N, −8.62°W. The process of finding the shape of the pavilion following a static adaptation process is described elsewhere [1]. Dynamic customization is used to adapt the shape of the building to changing internal and external conditions in its daily operation after built. At this phase the only shape variable that can be controlled is the degree of aperture of the skylights, which therefore determines the pavilion configuration. This process of dynamic customization for the pavilion concept will be developed in Section 2. Besides the inspiration in biological systems referred in Section 1.1, static and dynamic customization find also significant background in the vernacular architecture. To a certain extent, vernacular architecture can be seen as the result of a static adaptation process in which spatial and formal solutions were fine-tuned after hundreds or even millennia of years of evolution. Vernacular architecture has examples of static adaptation in which ornamentation is used to solve multi-task problems and qualify space with attributes. An example can be found in Islamic Architecture with the use of mashrabiya screen walls [2]. Such screens enable ventilation, provide shade and modulate the luminous environment of the interior. There are also examples of dynamic customization, for instance, in the use of movable shading devices such as lattices and shutters [3]. However, even if the desire of a responsive architecture is an old human aspiration, the advent of digital technologies brings an increased opportunity in this regard. With the development of computation, more powerful tools are now available for designing spaces that respond to the users and the environment following static and dynamic processes. Computational media can be used to simulate processes of

Fig. 2. The TetraScript pavilion concept and prototype, presented at the Beyond Media Festival, Florence 2009.

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adaptation that could otherwise take many years; it can also be used to make buildings that can automatically respond in real‐time to changes in contextual conditions. The literature already includes several examples of works using static and dynamic customization. Static customization has been used, for instance, to find adequate configurations in response to functional (Duarte [4]), structural (Shea and Cagan [5]), acoustic (Monks, [6]), and environmental (Caldas and Norford [7]) requirements. It also includes examples of dynamic customization. In fact, the evolution of mechanical devices and hardware gave new possibilities to program and control devices using software. In the 90's the Aegis Hyposurface reflects the increasing possibilities of human interaction with electromechanical devices using new media and pneumatic actuators to control a surface that responds to light and sound changes [8]. The work by Skavara [9] with adaptive cellular automata uses artificial neural networks, to control the position of façade elements. Roosegaarde uses hardware devices, as computer controlled fans, to respond to human presence, creating responsive environments [10]. Other approaches rely in the use of smart materials, as the heat sensitive system proposed by Vergara [11], which uses heat to change the aperture of components. Roosegaarde uses a set of components in metal foils that open with human proximity. This proposal uses a lotus shape, similar to the shape of the proposed skylights [12]. The examples of static customization mentioned above use optimization to pre-conceive the form, while the reactive examples do not use optimization. The system here proposed intents to bridge between these two strategies by proposing a heuristic search method to find an adequate form in real time while avoiding the long converging time that has made optimization methods unsuitable to dynamic customization. The literature mentioned some practical examples; however more general examples of digital design methodologies and methods should be referenced, namely [13–15]. The current approach can be identified with the compound model proposed by Oxman [14] as it uses digital generation, fabrication, simulation and evaluation in early stages of design. The proposed research extends Oxman's compound category and the digital process beyond the design stage, as the building configuration can change after construction using similar methods.

1.3. Requirements for visual comfort One of the most decisive factors in customizing space is the amount and type of daylight provided. The sunlight is important for health and well-being and if missing can promote health problems and diseases, as it controls the biological clock and activates body functions. Nevertheless, sunlight needs to be controlled and balanced in terms of sufficiency vs. excess in order to suit the occupant comfort requirements [16]. Visual comfort in work places has been traditionally associated with providing adequate illuminance levels for human tasks (Table 1), minimizing other stimuli from the environment [17]. If an office space requires an average illuminance of 500 lx and half of the space has shadows and the other half has high illuminance, even if the average result complies with recommendations, other factors need to be addressed. Therefore lighting design recommendations for office buildings discourage zones with simultaneous shadow and direct sunlight, thereby avoiding visual contrast and favouring uniform conditions. Visual contrast expresses the illuminance difference in a point of space, where a task is to be performed, with the surrounding space. Among others, Veitch and Newsham [17] recommend a ratio Illuminance task/surrounding of 0.20 to 0.80, which doesn't exclude zones with shadows. Some recent studies in environmental psychology and ergonomics have emphasized the need for a more interesting environment in the work place, with the benefit of improving productivity [18]. The current study aims to provide alternative light/shadow mix configurations, guaranteeing visual comfort with adequate illuminance levels and good visual contrast.

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Table 1 Illuminance requirements and categories for generic Indoor activities; A–C large area, D–F localized tasks, G–I extremely difficult visual tasks; source: Illuminating Engineering Society [16]. Visual tasks

Activity

Orientation Public spaces with dark surroundings Simple orientation for temporary visits Working spaces with occasional visual tasks Common Performance of visual tasks of high contrast/large size Performance of visual tasks of medium contrast/small size Performance of visual tasks of low contrast or very small size Special Performance of visual tasks low contrast/ prolonged periods Performance of visual tasks very prolonged and exact Performance of v. tasks special visual tasks ext. low cont.

Category Lux A B C D

20–50 50–100 100–200 200–500

E

500–1000

F

1000– 2000 2000– 5000 5000– 10,000 10,000– 20,000

G H I

1.4. Reference outdoor conditions Daylight (or natural light) is the solar radiation in the range of visible wavelengths, from 400 to 760 nm. Natural light comes from the sun (direct sunlight), from the sky dome (diffuse light), and from the outdoor environment surfaces (reflected light). The technique of bringing natural light into a building through openings is often referred as Daylighting [16]. Besides the building form and the characteristics of its transparent surfaces, the daylight perceived indoors depends on the location, time and weather conditions. Location and time determine the sun position and therefore affect not only the angle of incidence, but also the intensity of sunlight and the sky dome conditions. The intensity of sunlight is affected mainly by the latitude and decreases from the equator to the poles as the distance of atmosphere that the sunlight must cross increases. The sky dome produces diffuse light, which results from the scattering and reflection by the clouds and air humidity in the sky and depends in the atmospheric conditions. As clouds move through the sky, the distribution of light can change almost minute by minute. As a result, sky conditions are always changing and it is necessary to set reference conditions to perform studies. The Commission International de l'Éclairage (CIE) has developed a series of mathematical models of ideal luminous distributions under different sky conditions, from which CIE clear and CIE Overcast skies represent the two standard extreme conditions [16]. The CIE Overcast Sky distribution model is based on a completely clouded sky where the Sun is not visible, what results in Illuminance three times bigger at the zenith than at the horizon. The CIE clear sky assumes that the sky is visible without clouds, which results in a very nonuniform luminance distribution, where the area around the Sun is much brighter than any other area. The landscape-reflected light depends on the local environmental conditions, namely of the materials and geometry of the surrounding place. The study here developed to characterize the potential daylight inside the pavilion adopts these reference scenarios “CIE clear sky” and “CIE overcast sky” for studying the performance of the pavilion in a given geographical location. It is sub intended that by analyzing the extreme cases the range of indoor performance will be established. In terms of moments of the year, it was decided to consider the summer and winter solstices (21 June and 21 December), and for each three times of the day: 10 AM, 12 PM and 4 PM, solar time. In this way it will be possible to capture representative mid-morning, Mid-day and mid-afternoon conditions. Overall, the perspective adopted for the visual comfort assessment at this stage of the development of the pavilion concept was one of strategic assessment rather than specific assessment. This implied that the procedures adopted tried to avoid very specific conditions of choices

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Table 2 Calculation of diffuse illuminance on the horizontal surface (K Lux). Using the formulas: Overcast IES, Evd = 0.3 + 21.0 sinγs and Clear IES, Evd = 0.8 + 15.5 (sinγs)0.5. Evd — diffuse illuminance on horizontal surface (Lux), γs — solar angular elevation (degrees), obtained from [19].

CIE clear sky CIE overcast sky

Date

10 AM

12 PM

4 PM

21 June 21 December 21 June 21 December

15.22 9.86 18.49 7.48

15.92 11.06 20.27 9.51

12.82 5.38 12.94 2.13

of materials or position of occupants within the pavilion. In practice when designing a specific pavilion for a specific purpose, further analyses can consider specific data regarding the user, tasks to be performed and precise indoor location. Additional information about the diffuse illuminance on the horizontal surface is provided in Table 2.

Fig. 4. Nomenclature, relevant angles used to calculate the aperture of the skylight panels. Ap — Aperture value in degrees, α — angle of opening, β — complementary angle α, Δ — angle light vector/panel, Θ — angle of incidence, angle light vector/normal sub-surface.

2. Research methods 2.1. Heuristics specification Different combinations of the pavilion skylight panels can provide different type and quantity of daylight, but can also produce different light-shadow patterns with aesthetic interest. In any case the indoor conditions must be adequate to the activities to perform, and therefore a process is needed to choose the arrangement of skylight panels that ensures such adequate conditions, taking into account also aesthetic aspects, such as regular patterns of shadow and light. Given that each panel can be controlled independently in terms of its aperture angle (ranging from 0° to 72°), the number of potential states is enormous and it is not possible to characterize them all. A process is therefore needed to guide the definition of the skylight arrangements. The process that is proposed in this work is based on pre-assessing five different configurations, each corresponding to a rationale of control or heuristic. Heuristics are rationales used to identify good solutions in a short time, rather than optimal solutions which would consume much more time to identify. This is achieved by typifying solutions, therefore reducing the search space [20]. Optimization search could potentially provide better solutions, but needs too much time to converge into it, as the search space of all possible configurations is very large — often too large to be analyzed. The proposed heuristic search method encompasses quantitative and qualitative daylight qualities that will be described in detail. The 5 heuristics used, schematically represented in Fig. 3, are:

As the heuristics are defined by parametric equations, aperture values must be provided to determine the skylight panels' apertures. For instance, if H0 is chosen, after an aperture is provided all skylights will have that value, according to the definition of the heuristic H0. So the aperture is an open parameter for all heuristics that will be tested with apertures of 0°, 12°, 36°, 60°. Daylight simulation is used to analyze the results of these skylight panels' dispositions and their performance. Heuristics nomenclature is diagrammed in Fig. 4 and described next. H0. Uniform aperture Ap ¼ α with α ¼ 90°−β and 0 ¼< β < 90° In this heuristic, all the skylight panels open the same angle value α, regardless of their relative position and the location of the sun. The generative process that precedes the use of the heuristics determines the maximum allowable aperture of the skylights' shading panels depending on the position of the adjacent skylights to avoid collisions between their shading panels. The first input is a convex surface that is divided in a diagrid, composed of quadrilaterals that are the geometric base surface of each skylight — a tetrahedral pyramid. Therefore if a non-convex surface is used, the restrictions to avoid the collision of each skylight panels with the adjacent is determined by the complementary angle of β, the angle formed between the base of the pyramid and their closed faces. In this case study, β= 28° so using H1, the skylight panels can open from 0° to the maximum of 72°. H1. Maximum direct sunlight

H0 H1 H2 H3 H4

Uniform aperture Maximum direct sunlight Diffuse light (excludes direct sunlight) Incident sunlight Hybrid: low incidence + diffuse daylight (inverse H3 + H2).

Ap ¼ Δ; angle light vector=panel This heuristic, which can also be designated as “follow the sun”, seeks to maximize sunlight and minimize the shadow effect. To determine

Fig. 3. Heuristics rendered preview (above) and schematic representation (bellow). From left to right : H0 uniform aperture, H1 maximum direct light, H2 maximum diffuse light, H3 incident sunlight and H4 Hybrid low incident + diffuse light.

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the angle that every skylight panel has to rotate it is necessary to find the angle Δ between the skylight panels and the light vector. By aligning the panels with the sun direction, it is obtained maximum direct sunlight indoors, thereby minimizing the shadow area. To compare the illuminance values with other heuristics it's necessary to introduce other intermediate skylight apertures, in addition the one that provides maximum direct sunlight. For that purpose the measurement scales are normalized. H2. Maximum diffuse light Ap ¼ α; if angle Θ > 90°; else Ap ¼ 0 This heuristic provides diffuse light, avoiding direct sunlight. To ensure only diffuse light, it's necessary to calculate the angle Θ between the normal to the base of each pyramid and the light vector. Only if this angle is greater than 90° the skylight panels open; otherwise they are closed to avoid direct sunlight. To obtain a more harmonious disposition, when Θ > 90 all the skylight panels have the same angle α. H3. Incident sunlight Ap ¼ cos Θ x Ap; ifΘ < 90°; Ap ¼ 0 if Θ >¼ 90° The goal of this heuristic is to provide incident sunlight, that is more light where the sun shines directly, and less where it is less incident. So, as the angle Θ — or the angle of the sun with the perpendicular line of each skylight's base — increases the skylight's aperture diminishes. It provides non-uniform light-shadow patterns by taking into account the position of each pyramidal skylight of the pavilion, in relation to the sunlight direction. It differs from H1 that aligns every panel to the sunlight direction, regardless of its position (for a better comparison see Fig. 3). To obtain a more harmonious disposition every pyramidal skylight and its four panels have the same aperture angle (cos Θ). To determine the aperture of the skylight panels of every pyramid is necessary to calculate the angle Θ between the sunlight direction and the base of each pyramidal skylight's. The skylight panels aperture is maximum when the sunlight is secant (i.e. angle Θ is 0°, incident light) and decreases linearly until it reaches the minimum when the sunlight is tangent (i.e. angle Θ is 90°, grazing light ), and closes if the angle is greater than 90°. Synthesizing, this heuristic introduces a light graduation producing a non-uniform light-shadow pattern indoors that is based on the geometry of the pavilion. H4. Hybrid, low incidence + diffuse Ap ¼ sin Θ x Ap; if Θ < 90°; Ap ¼ Ap if Θ >¼ 90° This heuristic provides low incidence angle sunlight combined with diffuse light, generating non-uniform light-shadow patterns. These non-uniform patterns are the result of taking into account the position of each pyramidal skylight of the pavilion, in relation to the sunlight direction. To obtain a more harmonious disposition every pyramidal skylight and its four panels have the same aperture angle (sin Θ). To determine the aperture of the skylight panels of every pyramid is necessary to calculate the angle Θ between the sunlight direction and the base of each pyramidal skylight's. In this case the skylight panels aperture is maximum when the sunlight is tangent (i.e. angle Θ is 90°, grazing light) and decreases linearly until it reaches the minimum when the sunlight is secant (i.e. when the angle Θ is 0°, incident light). When there is no incident daylight, or Θ > 90°, the panels open to receive diffuse light. If only diffuse light would be considered excluding direct sunlight, as in H2, the pattern would be more uniform.

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3. Parametric analysis 3.1. General framework As previously stated, the indoor lighting conditions in the pavilion will depend essentially on the time of year, outdoor sky conditions, and position of the skylight panels. Since the complexity of the phenomena does not allow deriving an analytical solution of the problem, it is necessary to perform a parametric analysis to understand how the several variables impact on the indoor daylighting results. The framework established for this parametric analysis is as follows: − − − −

Weather conditions: CIE overcast sky and CIE clear sky. Time of year: 21 June and 21 December. Time of day: 10 AM, 12 PM and 4 PM solar time. Skylight control heuristic: H0, H1, H2, H3 and H4 as described in Section 2.1. − Skylight panel maximum aperture: 00°, 12°, 36° and 60°.

The analysis will consider all the possible combinations of these parameters, thus resulting in (2 × 2 × 3 × 5 × 4 =) 240 combinations to be considered. The results are presented in Section 3.3. 3.2. Simulation tools In the last decade there has been an increasing emphasis on environmental and energy issues, including the overall energy Implications of daylighting and solar gains. Examples of this reality are the energy rating systems that have been introduced to manage energy consumption and improve environmental efficiency (e.g.: North America: ASRA and LEED Green, U.K. BREEEAM), which introduced standard definitions, in project and construction. However, while for thermal evaluation there are standard procedures and tools already established, the same is not true for daylighting evaluation. Ibarra and Reinhart made daylighting comparative studies with the programs Ecotect, Daysim and Radiance, concluding that the results obtained by the third one are more reliable than the others [18]. Radiance was therefore selected as the tool to use in the study of the scenarios presented in Section 3.1. A short description of the use and calibration of software will be done, starting with software to draw the form (generative software) and then addressing the Daylighting evaluation software (Radiance). A geometry modelling program is used to set the configurations according to the different heuristics, in our case is Rhinoceros. To facilitate the study of the performance of such a high number of configurations, it was necessary to write algorithms to automate shape generation. The programming language Vb.Net is thus used together with RhinoScript and the plug-in Grasshopper. For each heuristic, an algorithm is used to calculate the position of the sun, and another to determine the respective configuration for the system of skylights in each scenario. The algorithm to determine the sun's position is based on the one developed by Ted Ngai [22], which uses the Solar Position Calculator and available data from the U.S. National Oceanic and Atmospheric Administration. The algorithm developed to set the various configurations uses a substantial number of variables in order to define the aperture values for all the 140 skylight panels, which are used in the pavilion of this case study. To evaluate the performance of the different configurations the software used was Radiance [23]. It has been reported that, although this tool has the potential for high accuracy, it is common to be misused and to produce poor results if the settings for the simulation are not properly defined. Ibarra and Reinhart (2009) performed tests with expert users concluding that the program has an error margin around 20%, which is considered acceptable. The same authors conducted a study, with students without previous experience in simulation, and identified the beginner's most common errors using this software. They summarized the most important errors in three

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categories: geometric modelling, materials, and simulation settings. The modelling in the current study therefore learned from this lesson to ensure high quality. As a particularly important point, Ibarra and Reinhart study produced recommendations regarding the parameters to be used if high accuracy is needed. These recommendations, correspond to a scene of “high complexity, where fully adopted for this study: ambient bounces (ab = 6), ambient divisions (ad = 1500), ambient sampling (as = 100), ambient accuracy (aa = 0.05) and ambient resolution (ar = 300). Considering the material properties, it was decided to consider as reference the materials of a prototype pavilion that has been built in real scale [1]. The prototype was built using the same material as the final pavilion system, namely a composite material called OSB (oriented strand board). OSB was used both as the main structural material and the cladding material for the shading panels of the skylights panels. To connect the structure, metal connectors are used. The chosen material enabled shape customization, fast fabrication and easy assemblage. The diffuse reflectance was therefore set to 80% for the OSB structure and panels and to 8% and for the ground floor, based on the material properties of OSB (white painted reference) and previous recommendations of reflectance [21]. To collect the illuminance values on the ground it was necessary to set a virtual grid of sensors. However the pavilion has an ellipse floor and the program requires that the sensor grid be rectangular. It was therefore decided to use the most approximate rectangular grid to overcome such a limitation. After testing different numbers and positions for the light sensors, it was decided to use a grid of 200 × 150 sensors, which corresponds to a matrix of 30,000 points, occupying an area of 4.00 × 3.00 m. The results of the daylight simulation are therefore collected in a matrix of illuminance values on the ground inside the pavilion, which can be visualized using different representation, as Lux-isolines and renderings (Fig. 5). The analysis and discussion of results is presented in the following section.

maximum allowed aperture (degrees). The values of the minimum, maximum and average indoor illuminance were retrieved for each situation. Fig. 6 shows graphics summarizing the results for Heuristic 1. By analyzing these graphics it can be noted that as expected there is a great difference in illuminance between clear and overcast sky conditions. For the strategy maximum direct sunlight (H1), the minimum values in June, with clear sky, is 3 times higher than with the overcast sky, the average value is 12 times greater, and the maximum 7 times (Table 3). The same study was done for the other heuristics but is not presented graphically here because of space limitations. The results are however summarized in Table 2. The illuminance variation between summer and winter, with the same type of sky, is less significant than the variation between different sky types. If considering H1 in the summer (clear sky) the minimum value 4 times higher than in the winter, and the maximum 2 times higher. The results with clear skies present a larger range of illuminance variation, from maximum to minimum, than overcast skies. Conversely, overcast skies have a smaller range of illuminance variation in June, and even smaller in December. This variation tendency according to the sky type and the situation in summer and winter occurs in other heuristics, although with different magnitudes. To compare the illuminance results per heuristic strategy, a more detailed representation of the scenarios results per heuristic is presented in Fig. 7. It displays 5 graphs with aperture/illuminance results, for every heuristic strategy. As the majority of tasks only need up to 2000 lx (Table 1), the maximum scale of illuminance is set to this value. The graphics confirms that there are significant differences in the results per heuristic in the situations analyzed. Comparing the individual behavior of the different heuristic strategies, it can be noticed that H0 and H1 can ensure an illuminance of up to 2000 lx even with a small degree of aperture, while that is not possible with H2. Heuristic strategies H3 and H4 can ensure 2000 lx in most scenarios.

3.3. Results per heuristic 3.3.1. Illuminance Simulations were performed for each heuristic in the scenarios described in Section 1.4. The goal was to determine the indoor illuminance (Lux) achieved for each combination of heuristic and skylight

3.3.2. Contrast The visual contrast is, after illuminance, the second parameter adopted to evaluate the visual quality of a room. For most activities, a high visual contrast can be disturbing or indicative of conditions favourable to glare. Recommendations for office-type spaces are to

Fig. 5. Heuristic H3 Daylight simulations with iso-lux contour isolines, at the 21th June 2010, at 4 PM, with CIE clear sky. Interior view (first row) and section view (second row), from left to right with aperture value of 12°, 36°, 60°.

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Fig. 6. Simulation results for Heuristic H1 relating Illuminance (Lux) and aperture (Degrees) in the several scenarios: with clear sky in June and December (top row) and with overcast sky (bottom row), each considering three times of the day (10 am, 12 pm, and 16 pm). Key: MIN = minimum, MAX = maximum, Avr = average, JN = June, DC = December.

limit the contrast to a value of 4 [14]. For this work, it was decided to evaluate the contrast as being the ratio between the 80% percentile and the 20% percentile of the frequency curve of illuminance distribution in the room. In this way the disturbance caused by exceptional events, such as a single sunlight ray, is contained. While this procedure of evaluating contrast in the horizontal plane and with illuminances rather than with luminances, it is in line with the considerations at the end of Section 1.4 regarding the preference on a strategic analysis that overcomes specific conditions of materials or occupant positions and view directions. The results of the glare evaluation are shown in Fig. 8. Considering the heuristics H0, H1 and H3, it can be verified that until a 12° opening of the skylights there is an acceptable contrast, but when the apertures approach 36°, it becomes excessive. As the aperture value increases, the contrast decreases again in some cases, as with overcast skies, to acceptable values. Conversely, the contrast values H0 and H4 are satisfactory with all aperture degrees tested. H4 may thus be used as an alternative to H2, if high levels of illuminance with low contrast are required.

3.3.3. Trade-off analyses between illuminance and contrast Fig. 9 displays the results of every heuristic on June 21th with clear Sky, showing simultaneously the average illuminance and the contrast achieved. From left to right, the first graph displays the illuminance vs. aperture results; the second the contrast vs. aperture results, and the third one shows the illuminance vs. contrast. Observing the first graph, it can be concluded that with an aperture of 24°, all heuristic strategies, except the H0, can provide an illuminance up to 5000 lx. The heuristic H1 (maximum direct light) is the one that requires a smaller aperture to have higher illuminance values, followed by H0 (uniform aperture), H3 (incident light), H4 (Hybrid), and H2 (diffuse light only). The last one reaches a maximum of 3000 lx with an aperture of 60°. The maximum illuminance that can be attained is about 70,000 lx, with an opening of 60° at 12 pm with H1 (Fig. 9, third graph). Generally, the time of the day that has the highest illuminance with the smallest aperture is 12 pm, except for H2, which receives more light at 16 pm and at 10 pm than at 12 pm.

Table 3 Indoor illuminance values (Lux), summary for the different heuristics in the analyzed scenarios. Key: jn = June, dc = December.

CIE clear sky

H0 jn

H0 dc

H1 jn

H1 dc

H2 jn

H2 dc

H3 jn

H3 dc

H4 jn

H4 dc

min avr 10am (12,36,60°) avr 12pm (12,36,60°) avr 4 pm (12,36,60°) max

235 19,506 23,191 18,945 85,115

67 10,705 12,577 3,471 37,754

235 29,807 38,136 25,791 90,051

67 11,471 16,156 4,678 46,743

235 1,089 516 1,439 73,029

67 1,082 787 787 27,548

235 14,711 16,599 13,225 79,715

67 6,355 9,174 2,396 36,445

235 8,199 10,761 7,928 83,458

67 3,980 5,109 1,927 35,332

CIE overcast sky min avr 10am (12,36,60°) avr 12pm (12,36,60°) avr 4 pm (12,36,60°) max

H0 jn 73 4,697 5,540 4,113 11,412

H0 dc 19 1,722 2,527 1,923 5,143

H1 jn 73 6,684 8,190 6,777 13,608

H1 dc 19 2,609 3,846 1,598 5,608

H2 jn 73 837 324 1,026 5,984

H2 dc 19 623 698 345 3,102

H3 jn 73 2,134 2,580 1,755 7,104

H3 dc 19 484 774 266 2,684

H4 jn 73 2,778 3,339 2,566 9,281

H4 dc 19 1,207 1,209 728 3,387

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Fig. 7. Simulation results of the five proposed heuristics relating Illuminance (Lux) and aperture (degrees) in the analyzed scenarios (clear and overcast skies, summer and winter solstices, at 10 am, 12 pm, and 16 pm). Key: Jn — June, DC — December, SN — clear sky, CL — overcast sky.

The second graphic in Fig. 9, displays the results for visual contrast and aperture. Until 18° all heuristics present an acceptable contrast value, lower than 4. With an aperture of about 36°, H0 and H1, have a large amount of contrast, which is three times higher than the maximum recommended, while H2, H4, and H3 continue to present adequate values, inside the range proposed in Section 3.3.2. When the aperture approaches 60°, the contrast decreases in H0 and H1, remains adequate in H2 and H4 and grows substantially in H3. As illuminance and contrast do not follow the same pattern of variation with the aperture, another graphic was used to analyze these two factors together (Fig. 9, graph 3); the plot points have the apertures (12°, 36°, or 60°) displayed close to them. The graphic shows that the high contrast values occur with an illuminance higher than 15,000 lx, which is much higher than required in typical conditions (Table 1 in Section 1.3). In Fig. 10 the average illuminance and visual contrast are comparatively analyzed in range of scenarios studied (clear and overcast sky, summer and winter solstices, at 10 am, 12 pm, and 16 pm). With clear skies, most of the heuristics allow to obtain good illuminance values with low contrast. So, in clear skies in the summer it is possible to obtain more than 5000 lx with all heuristics, except with H2. With this last one a value of 3000 lx is reached, which is a value still more than sufficient for most tasks as was seen in Section 1.3. Moreover, during winter the majority of the strategies can reach 5000 lx, except for H2 and H3. On the other hand, while considering overcast sky, it is also possible to obtain good illuminance with low contrast; Strategies H0, H1, and H3can provide plenty of illuminance with low contrast in overcast skies in the summer, but are more limited in the winter. Contrast values are

higher in the summer than in the winter, but the variation between overcast and clear sky is not conclusive, and it depends on the heuristic used. Fig. 10 shows that good solutions, those having high illuminance and low contrast, can be found for every heuristic in the considered situation. The good solutions in every graphic are situated on the lower right corner, close to the illuminance axis. Poor solutions are either at the upper right or left corners, or at the lower left corner. So, there are several good solutions in all scenarios of season, sky type and hour of day, which can be identified from the graphic. An automated process will be proposed in the next chapter to facilitate the decision process and also to expand these analyses to other sky types, days and times of the day. 3.3.4. Analyses of the daylight results The illuminance results of every heuristic strategy, in frame of scenarios analyzed, with the apertures of 0°, 12°, 36°, and 60° are collected in a database matrix. Some conclusions can be draw by comparing the illuminance results collected in this database: as expected, H1 (maximum direct light) has the maximum illuminance values in 91.7% of the analyzed scenarios. In the remaining 8.3% situations, H0 (uniform aperture) has the best illuminance. Another matrix with the visual contrast results has been prepared with the same structure. Taking into account visual contrast, the best results are obtained in 52.8% of the cases with H0, in 27.8% with H4 (Hybrid, low incidence+ diffuse light), and in 19.4% with H1. Even if results demonstrate that a uniform aperture (H0) has better visual contrast in the majority of the situation (53.8%), this occurs with overcast sky. In fact, with a clear sky H4, the

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Fig. 8. Results of visual contrast for the all the proposed heuristics in the several scenarios analyzed (clear and overcast sky, summer and winter solstices, at 10, 12, 16 pm). Key: JN — June, DC — December, SN — clear sky, CL — overcast sky.

hybrid strategy that provides a gradient light-shadow patterns, is a good choice in 27.8% of the situations. H4 provides low incidence and diffuse sunlight combination. H1 provides the best (lower) visual contrast values in 19.4% of the cases, which correspond to situations with clear skies and low aperture values (12°). Combining illuminance and visual contrast best values and giving the same importance (i.e. same weight in the multi-criteria decision) to both factors, it comes out that H1 is the best choice in 55.6% of the

analyzed scenarios, followed by H0 in 30.6% and by H4 in 13,9%. Nevertheless, results may promote other heuristics as the more adequate solution, by introducing weights in this two-criteria selection. A similar analysis has been made to detect the heuristics that lead to the worst results, which are characterized by low illuminance and high visual contrast. The heuristic strategy that leads to lower illuminances is H2 in 91.7% of the cases, which matches the expectation, as this configuration only provides diffuse light. H3 presents the lowest

Fig. 9. Comparative analysis relating aperture with illuminance and visual contrast for all the heuristics at the summer solstice with clear sky. The first graph considers aperture (degrees) and illuminance (Lux), the second aperture (degrees) and contrast (percentile 80/20), and finally the dispersion chart considers illuminance (Lux) and contrast (percentile 80/20). The labels “12”, “36” and “60” in the last graph are the aperture values of the skylight panels in degrees.

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Fig. 10. Comparative analyses relating illuminance (Lux) with visual contrast (percentile 80/20) and aperture (degrees) for the 5 proposed heuristics in the studied scenarios (clear and overcast sky, summer and winter solstices, at 10 am, 12 pm, and 16 pm).

illuminance in December with an overcast sky that corresponds to 8.2% of the cases. The least favourable contrast results are obtained with H3 in 55.6% of the cases, which can be explained by the different aperture values that this configuration uses, being the highest where the sun is incident and decreasing to zero when the sun light is tangent. This configuration can be used to provide direct sunlight for a given object, but is not a good choice for an office space. Surprisingly, H2 presents high contrast in 25% of the cases, but that only occurs with a overcast sky and with aperture values higher than 12°. Finally, H4 is the worst in 8.3% of the cases (aperture 12° at 12 pm) and H0 also in 8.3% (aperture 36° in June, with clear sky). 4. Real-time selection of heuristic and aperture The daylight simulations presented in Section 3 calculated the illuminance and visual contrast in the scenarios of season, sky type, time of day, heuristic and skylight panels' apertures considered. The subsequent objective is to determine the apertures required to guarantee a certain illuminance. This is an inversion of the reasoning used so far (where the aperture was an input and the illuminance an output), but it represents the actual challenge of managing the system in its real operation. Each simulation in Section 3, took on average 3 h to finish; so it is unfeasible to make accurate daylight simulations in real-time. It is therefore necessary to use the results of Section 3 to assist in this process of finding the right aperture for a certain target conditions of indoor illuminance and contrast. It is possible to determine graphically the aperture value for a certain illuminance using the graphics in Fig. 7. In order to determine the

aperture, it is necessary to know which aperture patterns might provide the closest results. For example, to guarantee 500 lx using heuristic search H0 at the June 21 t at 12 pm, is it necessary to find out which apertures provide the closest illuminance, which can be done by interpolation. The natural way of using the results of Section 3 to find combinations of heuristic and aperture that yield a certain illuminance is to interpolate the results there obtained. For that an algorithm is proposed to interpolate the results based on the geometrical intersection just described. The algorithm interpolates between existing illuminances and apertures, determining the skylights' apertures, to set a certain illuminance. This process uses a sequential search and so the existing database with daylight results must be organized in a table (Table 4). The matrix relates certain conditions (rows) with degrees of aperture (columns) which results in average illuminance values. The rows are arranged sequentially, separately for each heuristic, i.e. the H0 with all scenarios is followed by H1 in all scenarios and so on. Each heuristic strategy is organized by sky type (clear or overcast), the type of sky is subdivided into summer and winter (June/December), and these into 3 h of the day (10 am, 12 pm, and 16 pm). The resulting average illuminance with apertures of 0°, 12°, 36°, and 60° is displayed in columns. The proposed search algorithm uses sequential procedures to progressively limit the search space by decreasing the number of rows to consider. To identify the aperture that leads to a given intended illuminance, in a defined location and time, the algorithm uses the following steps: 1) Select the heuristic strategy (Example H0, Table 1); 2) Set the intended illuminance;

G.C. Henriques et al. / Automation in Construction 28 (2012) 91–105 Table 4 Matrix of daylight results, aperture/scenario and resulting average illuminance (Lux). H0 uniform aperture

21 June

Ap 00

Ap 12

Ap 36

Ap 60

CIE clear sky

10 pm 12 pm 16 pm 21 December 10 pm 12 pm 16 pm 21 June 10 pm 12 pm 16 pm 21 December 10 pm 12 pm 16 pm

369 341 401 Ap 00 256 161 292 Ap 00 147 173 128 Ap 00 53 81 33

4,444 4,444 6,492 Ap 12 2,391 3,074 1,183 Ap 12 1,079 1,273 947 Ap 12 398 580 236

19,157 22,236 18,790 Ap 36 15,546 12,383 3,589 Ap 36 4,585 5,391 4,014 Ap 36 1,680 2,470 1,002

34,917 42,892 31,554 Ap 60 14,179 22,273 5,642 Ap 60 8,427 9,956 7,378 Ap 60 3,089 4,533 4,533

CIE overcast sky

3) Select the type of sky that is more close to the situation, CIE clear or CIE overcast. 4) Calculation of apertures. To have the desired illuminance of 500 lx (for example) for the selected sky, the aperture is calculated for June and December at 10 am, 12 pm, and 16 pm, thereby finding the necessary apertures to have the desired illuminance in each situation (row). The algorithm looks for the upper and lower bound in each row to know between which apertures that illuminance can be obtained. For example, using H0, clear sky, at 10 pm, to have 500 lx, the algorithm looks for the upper bound in the first row. Ap00 results in 369 lx and Ap12 results in 4444, so an interpolation is made to determine the skylight aperture to have 500 lx, in this case should be 0.38°; 5) The aperture that provides the required illuminance is calculated through interpolation for 10 am, 12 pm, and 4 pm for the 21th June and 21th December. 6) Month and day input. Using this data the day of the year is calculated. To have the results for that day an interpolation is made using the necessary apertures for June 21th and December 21th; 7) Hour input. If the requested hour is 10 am, 12 pm, or 16 pm, the interpolation between the hours of the days is direct. Otherwise a further interpolation, between illuminance and apertures, is necessary to determine the necessary aperture for the desired hour. A similar algorithm uses a matrix with contrast values, knowing the aperture and interpolating the value using upper and lower bounds of previous calculated skylight panel apertures.

4.1. Multi-criteria selection The actual challenge to control the skylight systems is, knowing the lighting conditions needed for a specific use foreseen inside the pavilion, to find a configuration of the skylights system that guarantees

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such conditions (or the closest possible in case they cannot be fully achieved with daylight only). The requirements for different building uses are reported in many daylight studies [19]. The results of Section 3 enabled to characterize the indoor conditions with particular skylight configurations under certain time-weather conditions. They actually showed that there may be multiple skylight panels' configurations (heuristic strategies) that can assure good illuminance with low contrast (Fig. 10). After the use for the pavilion is defined and the minimum illuminance threshold is found, the visual contrast can be determined by using a matrix similar to Table 4. In principle, it also must be possible to find the solutions that yield the best combinations of indoor illuminance and contrast. Since there are two different viewpoints involved, it becomes a multi-criteria choice problem. 4.1.1. Measurement scale normalization Since the human perception of Illuminance is not linear [17], it is necessary to normalize the measurement scale for evaluating illuminance in the multi-criteria decision procedure. A decrease in illuminance when the values are very low is far worse than when they are very high. The value of illuminance is therefore better represented with a logarithmic scale. If the maximum illuminance provided by a heuristic is greater than the one provided by the others heuristics (or is the greatest) it should be more valuated. Conversely the heuristic that has the smallest maximum should be devalued or negatively valued. So the maximum illuminance provided by each heuristic can be ordered from the one that provides the greatest value, to the one that provides the smallest (Table 5). Regarding the valuation of contrast, it is considered that the most favourable ratio is 1 and that the less favourable is 4. Therefore in the normalized value scale, a contrast of 4 is valued with zero and a contrast of 1 is valued with 1. All other contrast values are valued by linear interpolation or extrapolation of this scale. Therefore if the contrast is higher than 4, its value in the MCDM scale is negative. After the scale for both factors is normalized, weights can be applied to favour one criterion or the other. 4.1.2 . Identifying the most adequate solutions The process proposed to identify the best solutions within the range of calculated solutions (combination of heuristic and aperture) follows the following sequential steps: 1) The heuristics that cannot provide the minimum illuminance intended should be excluded. 2) Then, of the all heuristic strategies that can satisfy the minimum illuminance, the one that can provide lower contrast should be found, and all the values should be ordered. 3) Then the heuristic that provides the maximum illuminance should be found, and the values that each heuristic provides should be ordered as proposed before. So the maximum illuminance values provided by each heuristic, and the maximum visual contrast values, divide the search space in a smaller subset of solutions.

Table 5 Selection of the most adequate solution considering Illuminance and visual contrast, per heuristic on June 21st at 10 am with clear sky, with the minimum illuminance set to 15,000 lx; The table on the left‐hand side presents the illuminance and contrast results on a normalized scale (illuminance uses a logarithmic scale). In the table on the right‐ hand side, different weights are applied to illuminance and contrast, resulting in different heuristic solutions. Heuristic

Max

log

Search H0 H1 H1 H3 H4 Max Min

Ilum 46,271 63,038 2626 35,817 21,902 63,038 15,000

Ilum 4.7 4.8 3.4 4.6 4.3 4.8 4.2

cont 7.76 3.60 2.83 3.11 1.15 1.00 4.00

The best heuristics according to the given weights are in bold.

Ilum

cont

Illuminance + contrast weights

0-1 0.8 1.0 − 1.2 0.6 0.3

0-1 − 1.3 0.1 0.4 0.3 0.9

1+0 0.78 1.00 − 1.21 0.61 0.26 H1

0.8 + 0.2 0.38 0.83 − 0.89 0.54 0.40 H1

0.5 + 0.5 − 0.23 0.57 − 0.41 0.45 0.61 H4

0.2 + 0.8 − 0.84 0.31 0.07 0.36 0.81 H4

0+1 − 1.25 0.13 0.39 0.30 0.95 H4

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The best solution is chosen automatically but this process can be done using the information in the graphic in Fig. 10; by defining the bounds that limits the solutions — maximum contrast and minimum illuminance allowed — a sub-area of the graphic, or a sub-set of solutions can be found. Then it is possible to choose manually the heuristic that has the best solution in this area. To automate the selection of the most adequate solution, a set of procedures was defined. First, the maximum illuminance that each heuristic strategy can provide must be compared (Table 5, table on the left, second column). The heuristic strategy that can provide the maximum illuminance is considered the global maximum (maximum = 1, 5th column), whereas the one that provides the lowest (of the maximum), is considered the minimum in the scale, as long as it provides the minimum desired illuminance (in this case, Table 5, the minimum = 15000 lx). H2, in this case, cannot provide the minimum desired illuminance value and, therefore, is penalized with a negative value in the scale. The next step is to make the same comparison between the contrast values that each solution can provide, in a scale from 0 to 1. After the scales are normalized different weights can be applied to select the solution. By consulting Table 4 it can be concluded that if only the maximum illuminance was considered, or if it was considered with a weight of 40%(result = illuminance × 0.4 + contrast × 0.6)), the most adequate solution would be H1. If the maximum illuminance and contrast were equally considered (50–50%), or if only contrast was considered, the most adequate solution would be H4. In this case, all strategies except H2, can guarantee the minimum desired illuminance. Therefore, any solution except H2 could be chosen. To select among the possible solutions other criterion can be taken into account, like aesthetics, for instance. 4.2. Customized selection interface To test the robustness of the weights and select the most adequate solutions other values have been tested. Alternatively, instead of having fix weights, it is proposed that they can be changed using an interface in real-time (Fig. 11). The proposed interface is developed in Grasshopper, and can be used by someone without coding abilities, as it relies on an intuitive interface that uses slide bars. The values in the slide bars are the inputs for the code components that enclose instructions written in vb.net language to perform a task and generate an output. The slide bars generate inputs that are transmitted to the left-hand side of the components. The components generate outputs on their right-hand side that can then serve as input to other components. The component “day of the Year” (1), in the far left, needs as inputs the month, day, and hour (alternatively the “now” moment can

be selected.) This component calculates the day of the year and hour, and transmits these outputs to the second component “interpolation aperture” (2). Then it is necessary to set the minimum illuminance, depending on the activity inside the pavilion, and the actual type of sky using a Boolean variable, in which a “true” value means a clear sky and “false” overcast). With this inputs, the component “interpolation aperture” (2) calculates de illuminance and contrast per heuristic strategy and the output feeds the yellow panel on the right-hand side, where the details of the results per heuristic strategy can be read. The results per heuristic strategy are transmitted to the last component “IlumCont” (3), where the selection of the most adequate configuration solution is done. To obtain such a solution, the user can choose to have an automated selection or a manual selection. If the automated option is selected, it is necessary to assign weights to illuminance and visual contrast, as it was done in 4.1. The slider Ilum-Fact (Fig. 11) controls the weight criteria of illuminance, from 0 to 1, and defines the complementary value for visual contrast, that is 1-illuminance. The result of the chosen criteria is calculated automatically using a script. By changing the weights, different solutions might be tested, as the best solution, and respective data, will be displayed on the right-hand side, in the text panels: in red, the selected heuristic strategy; and, in green, the maximum illuminance that can be obtained and the visual contrast that is compatible with the required illuminance. The solution is then transmitted to the skylights, changing their aperture in real‐time (Fig. 11, image on the left). Alternatively, if manual selection is activated, any heuristic strategy can be chosen, but the data results will be displayed on the markers on the right-hand side, providing additional information.

4.3. Evaluation of the interpolation method's accuracy The validation of the proposed interpolation method could be achieved using two approaches, by digital simulation, or by field measuring in a real scale model. As the daylight software Radiance is a validated simulation program, and there were not enough funds to build a fully automated model, the digital simulation method was chosen. The interpolation method was used to estimate values of illuminance and visual contrast in new situations and these values were compared with the correspondent results done with the daylight simulation software Radiance. The following formula synthesizes the parameters considered (in brackets) and the total number of variations tested: H (5) × M (2) × h (3) × Ap (4) × S (2) = 5 × 3 × 3 × 4 × 2 = 249. These letterers represent H: heuristic (H0, H1, H2, H3, H4); M: month (February, April, August, October); h: time-of-the-day (11A.M and 2P.M.); Ap: aperture in degrees (24 and 36°); and S: sky.

Fig. 11. Automated selection of the most adequate heurist using Grasshopper. The application developed calculates the necessary aperture to have a certain minimum illuminance for all heuristics and calculates the contrast, the resulting light-shadow pattern, and suggests the best heuristic to use. The weight attributed to illuminance and contrast can be modified, and it's possible for the user to choose another solution (for example only diffuse light) in customized selection process.

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To test the method's accuracy, each parameter was changed individually one by one, while known values stored in the database (Section 3.2) were assigned to the remaining parameters. This procedure avoided an exponential increase in the number of calculations. The parameters that were tested individually were heuristic, month, time-of-the-day, aperture and sky. In addition, another 240 simulations were performed by randomly assigning values to all the parameters. The total number of simulations in this case was 480 which took around 1200 h or approximately 3 months to calculate. The accuracy of the calculated results, obtained using the daylight software, and those obtained using the interpolation method proposed here are presented in Fig. 12. The results calculated using the interpolation method are similar to those calculated with daylight software, namely with an approximation for illuminance of 95.7% (error of 4.3%), and for visual contrast of 107.3% (an error of 7.3%). Results suggest that the proposed method is an accurate forecast process, even if it can be further improved. Due to space limitations, the results of all the performed simulations are only briefly described here, but they will be detailed and published as part of PhD thesis.

4.4. Control algorithm, feedback, and improvement The user's decision regarding which weight to apply might result in a different solution. One of the goals of the research is to enable the customization and by using the proposed interface, the user has access to information that helps him to choose the most adequate solution in real-time. A control system, described in Fig. 12, is proposed to control the skylights' apertures. The system needs two types of inputs: from the user (manual) and from the computer (automated). The user can choose the activity thereby defining the minimal illuminance required. This information is transmitted to the algorithm that then computes all the possible configurations. The computer has instructions to get the time and-location information from the computer that is running the program, and both inputs — required illuminance and time-weather conditions — are fed to the heuristic search calculation, where values are interpolated. Then, the choice of the most adequate solution can be done automatically or manually. But the significance of this scheme is to add a feedback loop using light sensors to update the database. This process would enable the refinement of the expected values for each situation. Although this process is not yet implemented it is

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expected that its use would allow the system to correct values and, in a way, “learn with experience” (Fig. 13).

5. Conclusions The current research is part of the development of customized skylight systems that respond to both indoor requirements and outdoor environmental conditions. The research presented in this paper is focused on the development of strategies to control the daylight conditions inside a pavilion, in real‐time, through the operation of skylights that constitute the TetraScript pavilion. These strategies use heuristics to determine the apertures of the skylight panels, which have been tested using daylight simulation in a comprehensive range of scenarios, considering season, sky conditions and time of day, as explained in Section 3.1. By analyzing the results of such tests, in terms of illuminance and visual contrast, it can be concluded that the proposed heuristics succeed in providing a wide range of solutions with high illuminance and low visual contrast in each of the situations. The solutions obtained using the proposed heuristics take into account both functional, environmental, and aesthetic criteria in the control of daylighting. However, while functional and environmental criteria (use and lighting) were considered using heuristic search, aesthetic criteria were taken into account by constraining a priori the ranges of possible solutions to solutions that presented aesthetically pleasing configurations, for instance, by guaranteeing that all the shading panels in the same skylight presented the same degree of aperture. The proposed process works as follows. The results of the daylight simulations, including heuristics, apertures values, and best-case worst-case situations are stored in a data base. Using the database, a search algorithm called interpolated heuristic search is proposed to determine the apertures of the skylights that guarantee the required illuminance, and the resulting visual contrast value. The required illuminance is a function of the use set for the pavilion. The interpolation method looks up the data base in search for the situation that more closely matches the current situation and then uses interpolation to determine the corresponding solution, thereby discovering solutions for other days of the year, time of the day, and sky conditions other than those used to construct the date base. The database is used with the interpolation heuristic search to determine the panels' apertures needed to guarantee a certain illuminance. Nevertheless, in each situation it might found up to five solutions using the proposed heuristics. This means that one might obtain the same illuminance with

Fig. 12. Daylight forecast for other dates of illuminance (left) and visual contrast (right). Comparison between calculated results using daylight simulation software, and calculated values using the interpolation method proposed in this research.

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Fig. 13. Control system proposed, differentiating the user and computer inputs.

different skylight configurations resulting in different contrast values. To select the best of the solutions found and the most adequate heuristic, a multi-criteria weighted approach is used in an automated process. The sensitivity study of the weights applied suggested that different solutions can be found depending on the weights used as described in Section 4.1 (Table 5). To overcome this problem a visual interface is proposed that permits the user to change the weight of illuminance and visual contrast and select the solution in real-time. The interface also permits one to choose the heuristic based on other criterion like the type of lighting desired — diffuse, direct, and so on. In conclusion, an innovative process is proposed to associate skylight panels configurations with daylight performance so as to develop a responsive system to control skylights in real-time. The idea is to enable customization and control indoor daylight conditions. The research is based on a case study, but as a parametric design system is used both for the generation of skylight configurations and heuristics search, it can be applied to pavilions with other shapes, and other geometries, in other locations. For this research it was necessary to overcome pre-established disciplinary boundaries, involving areas like programming, parametric and algorithmic design, operations research, and daylighting. The use of programming supported a more inclusive approach in the development of a customizable responsive system. In this regard, the aim of future work will be twofold. First, it will seek to implement the control system and to refine and augment the database to guarantee a broader range of solutions from the lighting viewpoint. The Implementation of a feedback loop using local light sensors, could assure a more holistic system in this respect. Second, the next focus of future research will be on thermal comfort, with the expectation that this information may inform the choice of material and allow for more inclusive multi-criteria solutions. Acknowledgments The authors acknowledge the support of all participants in the project, including Carvalho Brito in programming languages, and Soeiro Ferreira in decision theory, both from the University of Porto, Faculty

of Engineering, Department Industrial Engineering and Management. Gonçalo Castro Henriques is funded by grant /BD/39034/2007 from Fundação para a Ciência e Tecnologia (FCT), Portugal.

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