optimization of luminaire reflector design using genetic

Revisiting the Role of Architecture for 'Surviving’ Development. 53rd International Conference of the Architectural Science Association 2019, Avlokita Agrawal and Rajat Gupta (eds), pp. 733–742. © 2019 and published by the Architectural Science Association (ANZAScA).

Optimization of luminaire reflector design using genetic algorithm method for highway lighting

Revantino1,2, Rizki Armanto Mangkuto1, Adhe Khresna Pustiadi1 and Bagas Aulia Kautsar1 1 Institut Teknologi Bandung, Bandung, Republic of Indonesia

[email protected], [email protected], [email protected] 2 Ministry of Industry, Bandung, Republic of Indonesia

[email protected]

Abstract: In this study, the genetic algorithm method is adopted to optimise the ellipsoid parameters of faceted reflector; i.e. solid angles of θ and ϕ, semi-latus rectum (d), and eccentricity (e). There are two types of reflector which designed in this study, those are divergent and convergent. Both designs are verified through simulation with the target of illuminance (Eav) and uniformity (Ul) values, which conform to the national standard for highway lighting. The approach of one-to-one mapping is used in optimisation, thus one facet illuminates one target point precisely. From the optimisation stage, it is yielded the ranges of θ angles from 0° to 36° (for divergent type) and 0° to 43° (for convergent). Meanwhile for ϕ angles, it gave the ranges of 0° to 58° (divergent) and 0° to 85° (convergent). The d values are ranged between 0.52 m to 0.66 m (for divergent type) and 0.53 m to 0.65 m (for convergent), while the eccentricities have ranges from 0.95 to 0.98 (divergent) and 0.95 to 0.99 (convergent). From final simulation, the values of Eav are varied from 22.2 lx to 70.3 lx with Ul = 0.4; which fulfilled the standard requirements of minimal 20 lx and Ul = 0.2.

Keywords: Faceted reflector; solid angles; semi-latus rectum; eccentricity.

1. Introduction

Several methods have been used in designing reflector of lighting units (luminaires), among of them are tailored freeform surface (Ries and Winston, 1994) and simultaneous multiple surfaces (Gimenez-Benitez et al., 2004). Some approaches also have been adopted to optimise the reflector designs, e.g. numerical (Prins et al., 2013), analytical (Kloos, 2007), and differential evolution (Yang et al., 2008). However, those optimisation methods are not easy to carry out, because of the limited computational resources and highly cost to access the compatible software. Therefore, it needs to find the optimisation method with more adequate and affordable resources. In this study, the algorithm of genetic evolution is adopted to optimise the ellipsoid parameters of faceted reflector. This method ever had been used by Ashdown (1994) in designing general reflectors and lenses for non-imaging optics.

In case of highway lighting, reflectors have function to spread the light (that emitted from a source), so it can be distributed until the farthest area between two luminaires. An optimal reflector design can

734 Revantino, R.A. Mangkuto, A.K. Pustiadi and B.A. Kautsar

contribute to improve the energy efficiency; on contrary, the improper designs may lead to produce light pollution, beside can interfere with driving safety factor. In Indonesia, the highway lighting system (luminaires and its supporting construction) should meet the requirements of SNI (abbreviation of “Indonesian National Standard”) No. 7391 (BSN, 2008). One of the standard criteria is minimum illuminance (Eav) of 20 lx with longitudinal uniformity (Ul) values = 0.2. Hence, the output values which yielded of this study also should meet those standard criteria (through lighting simulation).

The objective of this study is to determine the optimum design of faceted reflector; which focuses on parametric values of solid angles (θ and ϕ), semi-latus rectum (d) i.e. distance between focus point and ellipsoid surface which parallel to semi-minor axis, and eccentricity (e). The scope and assumptions which used in this study are as follows:

The light source is considered as point source with Lambertian light spreading. Light losses because of scattering are ignored. The configuration of luminaire follows the actual highway conditions, i.e. the stakes are placed on

the roadside (with two main lanes) and the same distance between the stakes. Luminaires become the only light sources on the highway.

2. Methodology

This study is conducted into three consecutive steps; i.e. identification, design optimisation, and testing.

In identification step; it is conducted the characterisation of reference luminaire (based on technical sheets), configuration of luminaires on the highway, specification of the highway, and simulation of initial (reference) condition.

The step of design and optimisation covers determination of illuminance target from each measuring point, structure of ellipsoid reflector, parameters of each facet ellipse, and modelling the reflector (including polar distribution of luminous intensity). The optimisation is carried out (using genetic algorithm method) in determining the parameters of facet ellipse.

The testing is performed to verify the optimised reflector design against the reference parametric values using inverse approaching.

3. Results and discussion

3.1. Identification

The LED (light-emitting diode) luminaire is set as reference, with consideration of this type has widely used on several sections of toll road in Indonesia. The luminaire has nominal power of 124 W with maximum length of 102 cm. The input parameters for initial simulation are set as follows:

Configuration of luminaires consists the height of stake = 10 m and distance between stakes is 40 m, with the values of boom angle and boom length are 5° and 2 m.

The road properties have width per section of 3.6 m with pavement type of R3. The measuring grids consist of 14 points in x-axis and 6 points in y-axis.

3.2. Design and optimisation

3.2.1. Illuminance target of measuring points

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The simulation is performed using Dialux evo and visualisation of polar diagram by open source software of IES Viewer. There are three identical luminaires are set in initial simulation, which performed in two scenarios. The first scenario is the three luminaires are turned on, while the second one is only the middle (as reference) is light on. Those scenarios are conducted to obtain the illuminance contribution of one luminaire on each measuring point (through calculation). Total of 84 measuring points (from grid multiplication of x and y axis) are set, as can be seen in Figure 1; with the blue-coloured point is the position of reference luminaire (x = 20 m and y = 2 m from the road axis). After contribution of reference luminaire was obtained (as can be seen in Figure 2), the illuminance targets (which should fulfilled by the luminaire) are calculated on each measuring point from differences against the standard value.

Figure 1: The mapping of measuring points in simulation.

Figure 2: The illuminance contribution of reference luminaire.

3.2.2. The structure of ellipsoid reflector

The reflector is made from aluminium material, with the assumption of reflection coefficient = 0.9. There are two types of reflector based on the direction of reflected light, i.e. crossing and non-crossing. In this study, it is decided to design the crossing reflector which also distinguished into two types, following the geometry of light spreading. Those are convergent type and divergent type (see Figure 3).


Figure 3: The types of crossing reflector design based on the geometry of light spreading. (source: Pustiadi and Kautsar, 2018)

The structure of reflector consists of 84 facets (according to the number of measuring points), which designed with the approach of one-to-one mapping; i.e. one target point is exactly illuminated by one facet. Because of symmetrical behaviour against the y-axis of mapping, the design process can be simplified on half side of the reflector (only 42 facets) and then identically mirrored to the other half. Each facet is numbered according to its target point, which distinguished based on the values of θ and ϕ angles (see Figure 4). The facets are also grouped by the same value of ϕ angle and the reference facet is set for both types of design; i.e. facet #3 for the divergent type and #39 for the convergent (as displayed in Figure 5).

Figure 4: The facets partition based on the values of θ and ϕ angles.

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Figure 5: The numbering, grouping, and the reference facet from both types of reflector design.

3.2.3. Optimisation of facet parameters

The values of solid angles (θ and ϕ) are optimised by genetic algorithm method, using the feature of GA Optimization from Ms. Excel software. This method was developed by Holland (1992) which inspired from biological evolution mechanism of living creatures. It is often used to find the solution of multi-objectives problem like optimisation (McCall, 2005). The algorithm works in a population of artificial chromosomes, which each of them is representing one solution. The chromosomes are taken randomly and selected (crossover) according to its accuracy (quality of solution); then it generates new population of child chromosomes from recombination of the parents. After several iterations (until certain convergence value), the ultimate solutions from optimisation are obtained.

In this study, it is set 16 (24) of parent chromosomes in population and crossover probability 0.9; with amount of iterations = 100 and convergence value until 10-5. The first iteration is performed on reference facet from both types of reflector design. Thereafter, iterations on each type of reflector are continued to the other facets in same area of ϕ; so on to the other facet areas. Before optimisation of solid angles is conducted, the luminous intensity values (Iθ,ϕ in Candela) are calculated from illuminance target of corresponding measuring point (for each facet).

The optimisation for parameters of semi-latus rectum (d) and eccentricity (e) is also performed with the same procedure. The position of d parameter is as shown in Figure 6 and the value of e is calculated by equation (1). The results from optimisation step are as shown in Table 1 (for divergent type) and Table 2 (the convergent type). In order to shorten the presented table, the data in each column are separated by semicolons.


Figure 6: Geometrical parameters of an ellipse.

||||1

2

2

v

d

v

de (1)

Where:

v = Connecting vector between two focus points of F1 and F2.

Table 1: The optimised values of solid angles and ellipsoid parameters from the divergent type.

Area (ϕ) Facet No. θ Iθ,ϕ (Cd) d (m) e

1 (13°) #3; #9 6°; 9.6° 3,734; 3,742 0.53; 0.56 0.98; 0.97 #15; #21 12.6°; 15.6° 4,141; 4,329 0.59; 0.62 0.97; 0.96 #27; #33 18.8°; 22.8° 4,258; 4,256 0.63; 0.64 0.96; 0.95 #39 30.5° 4,329 0.64 0.95

2 (22°) #4; #10 7°; 11.2° 3,808; 3,879 0.52; 0.55 0.98; 0.97 #16; #22 15°; 19° 3,998; 3,772 0.58; 0.61 0.97; 0.96 #28; 34 23.1°; 27.9° 3,943; 3,880 0.63 0.96; 0.95 #40 35° 3,951 0.63 0.95

3 (34°) #5; #11 6°; 9.6° 3,796; 3,855 0.53; 0.56 0.98; 0.97 #17; #23 13°; 16° 3,833; 4,360 0.59; 0.62 0.97; 0.96 #29; #35 19.1°; 23° 4,459; 3,901 0.64; 0.65 0.96; 0.95 #41 28° 3,739 0.65 0.95

4 (50°) #6; #12 4.1°; 7.5° 3,849; 3,879 0.53; 0.56 0.98; 0.97 #18; #24 10.5°; 13° 3,900; 3,880 0.59; 0.62 0.96; 0.96 #30; #36 16.2°; 19.2° 4,232; 3,983 0.64; 0.66 0.96; 0.95 #42 22.8° 3,690 0.66 0.95

5 (48°) #2; #8 3.2°; 4.8° 3,643; 4,475 0.53; 0.55 0.98; 0.97 #14; #20 6.6°; 8.1° 3,763; 4,370 0.58; 0.61 0.97; 0.96 #26; #32 10°; 11.9° 3,743; 4,521 0.63; 0.65 0.96; 0.95 #38 17° 3,698 0.65 0.95

6 (58°) #1; #7 7°; 10.9° 3,643; 3,789 0.52; 0.54 0.98; 0.97 #13; #19 14.6°; 18.3° 3,928; 3,881 0.57; 0.6 0.97; 0.96 #25; #31 22.1°; 26.9° 4,093; 3,811 0.62; 0.63 0.96; 0.95 #37 36° 3,612 0.63 0.95

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Table 2: The optimised values of solid angles and ellipsoid parameters from the convergent type.

Area (ϕ) Facet No. θ Iθ,ϕ (Cd) d (m) e

1 (23°) #3; #9 23.6°; 23.2° 4,157; 4,912 0.61 0.99 #15; #21 22.7°; 21.8° 3,987; 4,329 0.61 0.99; 0.98 #27; #33 20.6°; 19.1° 4,325; 3,743 0.61 0.98; 0.97 #39 16.1 3,803 0.6 0.95

2 (45.1°) #4; #10 22°; 21.5° 3,643; 4,218 0.59 0.99 #16; #22 20.8°; 19.8° 4,281; 4.392 0.59 0.99; 0.98 #28; 34 18.6°; 16.6° 4,012; 3,913 0.59 0.98; 0.97 #40 13.4° 3,812 0.58 0.95

3 (60.9°) #5; #11 22.5°; 22° 4,689; 5,707 0.58; 0.57 0.99 #17; #23 21.3°; 20.4° 5,718; 5,210 0.57 0.99; 0.98 #29; #35 19°; 17° 5,209; 3,959 0.57 0.98; 0.97 #41 12.9° 4,219 0.57 0.95

4 (85°) #6; #12 18.4°; 17.9° 3,922; 4,262 0.54 0.99 #18; #24 17.4°; 16.4° 4,193; 4,075 0.54 0.99; 0.98 #30; #36 15°; 13° 4,076; 4,070 0.53 0.98; 0.97 #42 10° 3,647 0.53 0.95

5 (20.3°) #2; #8 28.1°; 27° 1,530; 3,261 0.63; 0.62 0.99 #14; #20 26.2°; 25.4° 4,303; 3,699 0.62 0.99; 0.98 #26; #32 24.1°; 22.1° 3,391; 3,692 0.62 0.98; 0.97 #38 19° 3,538 0.61 0.95

6 (27.9°) #1; #7 43.1°; 42.6° 5,933; 4,656 0.65 0.99 #13; #19 41.7°; 40° 3,861; 4,233 0.65 0.98 #25; #31 38°; 36.1° 6,086; 1,784 0.64 0.98; 0.97 #37 25° 4,200 0.63 0.95

3.2.4. The model of ellipsoid reflector and polar diagram

After the objective parameters were optimised, the model of both reflector designs are built; as shown in Figure 7 (for divergent type), Figure 8 (the convergent type), and Figure 9 (polarity diagram of luminous intensity).

Figure 7: The 2-dimensions view of ellipsoid reflector model from the divergent type.


Figure 8: The 2-dimensions view of ellipsoid reflector model from the convergent type.

Figure 9: The polar diagram of luminous intensity from both types of reflector design.

3.3. Testing

Final simulation is performed using the optimised values from both types of reflector design; with the results of Eav as shown in Table 3 and the position of measuring points is same with Figure 1. It can be seen that the results of both types are almost similar. It is shown that the testing results are increasing significantly (> 50%) on measuring points of #1 to #6, #9 to #12, and #15; with Ul value of the whole points = 0.42. In order to shorten the presented table, the data in each column are separated by semicolons.

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Table 3: Comparison of Eav (in lx) between initial values and the testing results.

Measuring points Initial values Divergent type Convergent type

#1; #7; #13 12.4; 19.8; 28 22.7; 27.9; 34.8 22.7; 27.9; 34.8 #19; #25; #31; #37 35.5; 41.3; 44.5; 49 41.5; 49; 56.2; 70.3 41.5; 49; 56.2; 70.3

#2; #8; #14; #20 12.5; 20; 28.2; 35.5 23; 28.4; 34.3; 40.6 23; 28.5; 34.3; 40.5 #26; #32; #38 41.5; 44.7; 46.9 47; 53.3; 58.6 47; 53.4; 58.6

#3; #9; #15 12.2; 20; 27.6 37.1; 39.2; 41.8 37.1; 39.2; 42.3 #21; #27; #33 35.4; 41.3; 44.4 44.8; 48; 52 44.8; 47.9; 52 #39 49.3 50.3 50.4

#4; #10; #16 11.8; 19.3; 27.5 30.1; 34.2; 38.3 30.1; 34.1; 38.3 #22; #28; #34 34.9; 41.1; 44.4 42.3; 47.3; 48.6 42.3; 47.3; 48.6 #40 48.4 49.4 49.4

#5; #11; #17 11.4; 19.1; 26.8 25.6; 30.8; 36 25.6; 30.7; 36.2 #23; #29; #35 34.4; 40.3; 43.7 41.6; 44.3; 46.8 41.6 44.2; 46.8 #41 47.9 49.2 49.2

#6; #12; #18 10.6; 18; 25.6 21.6; 28.7; 35.2 22.8; 28.7; 34.8 #24; #30; #36 33.3; 39.3; 42.4 38.8; 42.4; 46.5 38.9; 42.5; 46.7 #42 46.7 48.9 48.9

3.4. Discussion

This study is conducted by adopting genetic algorithm method in optimisation of faceted reflector design. The method generated detail of optimised parameters with the approach of one-to-one mapping, thus each facet of reflector illuminates corresponding target point precisely. As comparisons; the study of Gitin (2013) has designed faceted reflectors which consist of elementary plane mirrors, using graphical method (unfolding technique) in optimisation. Meanwhile Yang et al. (2008) have investigated the possibility combination of NURBS (non-uniform rational basis spline) and differential evolution method in optimising freeform reflector design. Nevertheless, both studies did not verify yet to the impact of optimised design through lighting simulation. This study also needs further verification in real construction of optimised reflector design.

4. Conclusions

This study has optimised the faceted reflector design in two types of divergent and convergent, with optimisation parameters i.e. solid angles (θ and ϕ), semi-latus rectum (d), and eccentricity (e). It is yielded the optimal values of θ angles in range of 0° to 36° for divergent type and 0° to 43° for the convergent. Meanwhile the ϕ angles have optimised range in 0° to 58° (for divergent type) and 0° to 85° (the convergent type). For the semi-latus rectum values, it gave the optimised range of 0.52 m to 0.66 m (divergent type) and 0.53 m to 0.65 (the convergent); with the eccentricity ranges are 0.95 to 0.98 (divergent) and 0.95 to 0.99 (convergent). All of the optimised parameters are verified through simulation to the illuminance of target points. Both types of optimised design gave the similar results of the Eav values between 22.2 lx to 70.3 lx with Ul = 0.4, which conform to the national standard values of minimal 20 lx and Ul = 0.2.


Acknowledgements

This research was supported by the Ministry of Research, Technology, and Higher Education of the Republic of Indonesia, through the Fundamental Research Program 2019; and by the Institute of Research and Community Services of Institut Teknologi Bandung (LPPM ITB), through the ITB Multidisciplinary Research Program 2019.

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