New Algorithms for Daylight Harvesting in a Private Office

Transcription

1 18th Intenational Confeence on Infomation Fusion Washington, DC - July 6-9, 2015 New Algoithms fo Daylight Havesting in a Pivate Office Rohit Kuma Lighting Solutions and Sevices Philips Reseach Noth Ameica Biacliff Mano, NY Rohit.Kuma@Philips.com Abstact A daylight havesting system can poduce almost 60% enegy saving by using daylight to satisfy illumination equiements. In this pape we study the poblem of daylight havesting fo an indoo office which has adjustable electic lights and blinds. Thee ae two main poblems with such a system namely; a) photo senso should ideally be placed on the wok desk to measue illumination. Howeve such a senso can be accidently coveed by pape o occluded by use leading inaccuate measuements b) changing daylight distibution inside the oom due to movement of sun and window blinds. New data fusion algoithms ae poposed in this pape that employ machine leaning and adiosity theoy to compute the electic light and daylight component (hence total illuminance) on the wok plane using ceiling mounted senso. Expeimental esults fom a eal test bed ae povided at the end to highlight the pefomance of each algoithm. Keywods: Daylight Havesting, Intelligent Lighting Systems, Enegy Savings. 1 Intoduction The poblem of daylight havesting is well-known and well-eseached in lighting community [1, 2, 3, 4]. The goal of the poblem is to maximize the use of daylight to satisfy illumination demands and theeby minimize the use of electicity. In this pape we study the daylight havesting poblem fo an office envionment as shown in Fig. 1(a) whee the goal is to maintain constant illumination on the wok desk (a.k.a. wok plane). A geneal daylight havesting system consists of photo senso which measues the illumination, and a contolle which uses the measuements fom photo senso to adjust the electic light. One can basically have two types of contolles in this set up: a) Open-loop contolle: In case of an open-loop contolle, the system adjusts the luminance inside the oom based on some extenal paametes o sensos. Geneally, a senso is placed outside the oom (such as on the window) which measues the daylight falling on the window. The contolle adjusts the atificial (electic) light based on luminance on the window and it does not have any infomation about the illuminance inside the oom, and b) Closed-loop contolle: In case of closed-loop contolle, a senso is placed inside the oom. As expected, the pesence of the senso inside the oom povide illuminance inside the oom and is moe accuate to contol the atificial light [5, 6]. Ideally, in case of a closed-loop contolle, the senso should be placed on the wok desk to measue the tue illumination. This infomation can then be fed to the contolle to adjust the atificial light to meet the illuminance demand. Howeve a senso on the wok desk can be accidently coveed by files, pape, o use himself leading to inaccuate measuement [8]. These measuements ae fed to the contolle which adjust the atificial light incoectly esulting in a failed system. Hence, as lagely accepted by the lighting community, senso should be mounted on the ceiling o on the wall. With the senso mounted on the oof and not on the aea of inteest (wok desk), it equies advanced algoithms to estimate the illumination on the wok plane based on these ceiling/wall mounted sensos. Fig. 1(b) shows a office set up with ceiling mounted senso. The senso measues the illumination due to daylight and atificial light in the oom. While atificial light is elatively static and can be computed accuately, daylight is moe dynamic and vaies a lot. The amount of light falling on the wok plane is not only dependent on the outside light but also on the status of blinds, i.e., blind height and blind angle. Fo instance, even if thee is lot of daylight falling on the window and blinds ae positioned to block sunlight, the amount of daylight in the oom will be minimal and vicevesa. In initial wok, eseaches tied to develop an illumination atio to coelate extenal daylight to the illumination on the wok plane [2, 3]. Howeve, one coelation atio was unable to model changing dynamics of the sunlight in the oom. Theefoe, othe eseaches in [7] developed multiple illumination atios fo diffeent blind angles (30, 40, 50 and 60 degees). The discete limits imposed by these authos pevents the system fom exploiting oveall ange of blinds. This dawback was addessed in [8] wheein authos have developed a clusteing technique to model the daylight ISIF 383

2 inside the oom moe accuately. Consequently, the numbe of atios developed in this case is not detemined a pioi but is dependent on the location of the window and status of the blinds. We shall employ thei clusteing technique and develop new data fusion algoithms to bette estimate the illuminance falling on the wok plane. The pape is oganized as follows: Section 2 details the expeimental set and the poblem statement fo this eseach. Section 3 develops elation between the illumination between wok plane and measuements by the sensos. These elations ae employed to develop seveal data fusion algoithms in Section 4. Section 5 has expeimental esults to highlight the pefomance of diffeent algoithms and the pape ends with conclusion and diections fo futue wok in Section 6. 2 Poblem Set Up In this section, we shall descibe the expeimental set up fo ou daylight havesting system and then fomulate the estimation poblem. 2.1 Expeiment Set Up The expeimental set up fo a pivate office is shown in Figue 2. The set up consists of the following components: 1. Sensos: We shall employ thee sensos in this system to measue illumination. Two sensos (C 0 and C 1 ) ae mounted on ceiling inside the oom while one senso (C 2 ) is placed on the window facing outwad (towads the sky). Note that ceiling sensos ae not necessaily located diectly ove the wok plane. It only measues the illumination in the oom while window senso only measues daylight falling on the window and cannot measue illumination in the oom. 2. Light Fixtues: Thee ae two light fixtues (L 0,L 1 ) with adjustable ballast. Ballast level fo each light fixtue can be vaied between 0 to Blinds: Room has one lage window that is fitted with moveable blinds. Height (b h ) and tilt (angle)(b θ ) of the blinds can be adjusted to maximize the amount of light falling in the oom without causing glae to the use. Theefoe, the light falling on the window as measued by window senso may not be equal to daylight illumination on the wok plane. 4. Contolle: In ou cuent set up, we have one openloop and one closed-loop contolle unning. The open-loop contolle adjusts the blind height (b h ) and blind angle (b θ ) based on diection of the window and movement of sun. The open-loop contolle adjusts the blinds to maximize the daylight in the oom without causing discomfot (glae) to the use [9, 8]. The closed-loop contolle adjusts the ballast level fo light fixtues (L 0,L 1 ) to satisfy the illumination equiements. Since contolle is not the focus of this pape, we shall not delve into details of contolle. We shall conside it as a black box which outputs the adjustable ballast levels given the senso measuements. Notation: In ode to eliminate excessive notations, we shall abuse the notation slightly. We shall use C i to indicate i th senso (i {0,1}). It will also be used to indicate its measuements. The efeence will be clea fom the context. We shall use a simila stategy fo atificial lighting (L j, j {0,1}). C i (L 1,L 2 ) indicates measuement of i th ceiling senso in pesence of atificial lights which ae set at level L 1 and L 2. C i (L j ) indicates measuement of i th ceiling senso in pesence of j th light fixtue which is set at level L j. The othe light is assumed to be tuned off. C i (C 2,b h,b θ ) indicates measuements of i th ceiling senso in pesence of daylight whee daylight falling on window is C 2, and blind status is (b h,b θ ). C i (C 2,b h,b θ,l 1,L 2 ) indicates measuements of i th ceiling senso in pesence of atificial light and daylight. We wish to emphasize that C i (x) is not a function. It only indicates ceiling senso measuements in pesence of x (x can be daylight paametes (C 2,b h,b θ ) o ballast levels fo atificial lights (L 1,L 2 )). 2.2 Poblem Fomulation The total illuminance (I W ) on wok plane is given as: I W = f(l 0,L 1,C 2,b h,b θ ) (1) whee f is some unknown function. Howeve fom theoy of adiosity [8], we know that total illumination on the plane is linea combination of light emitted fom diffeent light souces. Theefoe, I W = f e (L 0,L 1 )+ f d (C 2,b h,b θ ) = I E + I D (2) whee f e is a function that maps the given ballast levels to illumination (I E, i.e., electic light component) on wok plane, and f d is a function that maps the outside light and status of blinds to illumination (I D, i.e., daylight component) on wok plane. The oveall five dimensional function appoximation poblem educes to two function appoximation poblem of smalle size. The dimension eduction is citical not only fo educing computation load but also povides bette undestanding of the system fo fault detection and diagnosis. Hence, the goal of this estimation poblem is to estimate daylight ( f d ) and electic light ( f e ) component based on the available senso measuements. 3 Relationship between wok plane illumination and senso measuements In this section we shall define elationships (to be employed in next section) to addess the challenge of estimating the illuminance on the wok plane without placing a senso on it. In paticula, we shall we place an auxiliay senso (called as hobo senso and shall be denoted by h) on the 384

3 (a) (b) Figue 1: Wokplane illumination estimation set up (a) using a senso on the desk (b) using ceiling mounted sensos Figue 2: Expeiment Set Up. wok plane duing data collection phase and then pefom supevised leaning [10, 11] to estimate the elation between illuminance falling on the wok plane (as measued by hobo) and measued by the ceiling sensos. As mentioned ealie, the illuminance falling on the wok plane is a combination of daylight and electic light. Theefoe, we shall estimate the afoementioned elationships fo both. We wish to highlight that hobo senso is only used duing the leaning phase of the set up and is not foeseen to be pat of the final poduct. Fo hobo senso, we shall the notation simila to ceiling senso whee h(x) will indicate eading by hobo senso in pesence of x (x can be daylight paametes (C 2,b h,b θ ) o ballast levels fo atificial lights (L 0,L 1 )). 3.1 Relationship fo atificial light Fist, we shall deive elationships fo atificial light, i.e., electic lights. In paticula, given the status of ballast levels fo each light fixtues, we shall develop its elationship to tue illumination on the wok plane (as measued by hobo senso) and measuement by ceiling sensos. Befoe we define the expeimental details, we shall outline some elationships that ae used in computations late. Note that total illuminance on the wok plane as measued by hobo senso will be given as: f e (L 0,L 1 )=h(l 0,L 1 ) Again using adiosity theoy, we futhe educe twodimensional function to one-dimensional as follows: h(l 0,L 1 )=h(l 0 )+h(l 1 ) (3) i.e., the total illumination on the wok plane (as measued by hobo) fo given ballast levels of light fixtues is equal additive in natue. Hence, it is equal to sum of illuminance contibuted by each luminaies. Futhe, one can develop simila elationship fo ceiling sensos as given below: C 0 (L 0,L 1 ) = C 0 (L 0 )+C 0 (L 1 ) (4) C 1 (L 0,L 1 ) = C 1 (L 0 )+C 1 (L 1 ) (5) We shall descibe the pocedue fo function appoximation h(l 0 ) and h(l 1 ), i.e, illuminance on the wok plane (as measued by hobo senso) fo given ballast level (L 1,L 2 ) of the light fixtues. Simila pocess can be epeated fo ceiling sensos as well (i.e., fo C i (L j ), i, j {0,1}). The function appoximation is pefomed in thee steps: 1. Data Collection: Data collection pocess is pefomed at night (in absence of daylight). Set L 1 = 0 (switch 385

4 off). Vay L 0 fom 0 to 255 in steps of 5 and collect measuements fo hobo senso fo each ballast level. Theefoe, we have {h m 0,Lm 0 }M m=1, M measuements whee L0 m indicates the ballast level and hm 0 indicates the coesponding illuminance on the wok plane as measued by hobo senso. Then epeat the expeiment fo L 1 with L 0 = 0 and collect {h m 1,Lm 1 }N m=1 N data points. 2. Clusteing: A manual eview of collected data shows that hobo measuements fom piecewise linea function of ballast levels. Thee will be thee linea links as shown in Fig 3) and shall be paameteized using following equations: whee h(l 0 )=u 00L 0 + v 00 (6) h(l 1 )=u 01L 1 + v 01 (7) = 1 if L 0 n 1 ; 2 if n 1 < L 0 n 2 ; 3 if L 0 > n 2. The paametes u 00,v 00,u 01,v 01 will be estimated using data collected in Step 1. We select n 1 = 30 and n 2 = 210. Although n 1 and n 2 ae selected manually, it can be easily automated. Based on the given thesholds (n 1 and n 2 ), the cluste the data into thee goups as follows: Figue 3: Example fo elation between tue illumination between on wok plane fo given ballast level {h m 0,Lm 0 }M 1 m=1 if Lm 0 < n 1 {h m 0,L m 0} M 2 m=1 if n 1 L m 0 n 2 {h m 0,Lm 0 }M 3 m=1 if n 2 L m 0 {h m 1,L m 1} N 1 m=1 if Lm 1 < n 1 {h m 1,Lm 1 }N 2 m=1 if n 1 L m 1 n 2 {h m 1,Lm 1 }N 3 m=1 if n 2 L m 1. whee M 1 + M 2 + M 3 = M and N 1 + N 2 + N 3 = N 3. Regession: Pefom linea egession to estimate the unknown paametes in Eqn. (6) and (7). (u 00,v 00)=agmin a,b (u 01,v 01)=agmin a,b M m=1 N m=1 {h m 0 (alm 0 + b)}2 {h m 1 (alm 1 + b)}2 Theefoe, Eqn. (6) and (7) maps the given ballast level of light fixtues to illumination on the wok desk. Additionally, one can also find elation between given ballast level and light measued by ceiling sensos, i.e., one can estimate following elationships: C 0 (L 0 ) = a 00L 0 + b 00 (8) C 0 (L 1 ) = a 01L 1 + b 01 (9) C 1 (L 0 ) = a 10L 0 + b 10 (10) C 1 (L 1 ) = a 11L 1 + b 11 (11) 3.2 Relationship fo daylight Simila to pevious subsection, we shall deive the elation between illumination on wok plane and ceiling senso fo daylight in the oom. The amount of daylight in the oom is detemined by daylight falling on the window (C 2 ) and blind status(b h,b θ ). 1. Data Collection: Lage numbe of measuements wee collected fo{c0 m,cm 1,Cm 2 and hm } M m=1 fo vaious combinations of (b h,b θ ). b h is vaied using sola position and b θ is some contol to maximize the amount of sunlight in the oom and yet avoiding glae. The electic lights wee switched off duing data collection. Subsequently we pefom clusteing and egession analysis. 2. Clusteing: Cluste the obseved data based on vaious combinations of (b h,b θ,c 2 ), i.e., { } K {C0 m,cm 1,Cm 2,hm } M c m=1 whee thee ae K clustes c=1 such that c th cluste has M c data points. Inteested eades ae efeed to wok of [9] fo details about clusteing. 3. Regession: We assume that thee exists a linea elationship between the following quantities: C 0 (C 2,b h,b θ ) = α0 c C 2+ β0 c (12) C 1 (C 2,b h,b θ ) = α1 c C 2+ β1 c (13) h(c 2,b h,b θ ) = αh c C 2+ βh c (14) h(c 2,b h,b θ ) = αmc c 0 (C 2,b h,b θ ) +βmc c 1 (C 2,b h,b θ ) (15) whee supescipt c indicates the cluste index. C 0 (C 2,b h,b θ ),C 1 (C 2,b h,b θ ),h(c 2,b h,b θ ) epesent the daylight measuement by ceiling senso and hobo senso espectively. Note that fo given cluste, 386

5 Eqn. (12)-(15) maps the window senso measuements to ceiling sensos, Eqn. (14) maps it to illumination on wok plane. Eqn. (15) maps the ceiling senso measuements to tue illumination on the wok plane. The egession paametes fo the above equation can be computed using simple linea least squae. Fo instance, Eqn. (12) paametes can be computed using equation below: (α c 0,β c 0 )=agmin a,b M c m=1 {C m 0 (acm 2 + b)}2 Simila optimization can be pefomed fo Eqns.(13)- (15). Next, we ewite Eqn. (15) in matix fom whee k c 2 = [ α c m β c m 4 Algoithms h(c 2,b h,b θ )=I D = k c 2 T C D (16) ] [ C0 (C and C D = 2,b h,b θ ) C 1 (C 2,b h,b θ ) Unde the nomal woking conditions, the ceiling senso measuements will be a combination of contibution due to atificial light and daylight, i.e C i (C 2,b h,b θ,l 0,L 1 )= C i (C 2,b h,b θ )+C i (L 0,L 1 ) (17) whee i {0, 1}. Now we shall employ diffeent elationships developed in ealie section to fuse infomation fom diffeent senso and estimate the illumination on the wok plane. 4.1 Algoithm I In this algoithm, we detemine illumination due to electic light (I E ) using elation in Eqn. (6)-(7). The daylight component (I D ) is a two step pocess: fist we compute the daylight component in ceiling senso measuement using Eqn. (17), then Eqn. (15) is used to compute daylight illumination on wok plane. Since atificial light estimation is based on taining, thee is no feedback mechanism to detemine a faulty bulb (in which case thee is zeo illuminance fo any ballast level). This is the main dawback of this algoithm. The steps fo Algoithm I ae given in Table Algoithm II In Algoithm II, we compute the electic light component using elation in (6), (7) and employ window senso to compute the daylight component as in (14). The main advantage of this algoithm is that daylight and electic light component ae computed independently. Hence the estimation eo in one is not popagated. Thee ae two dawbacks on this algoithm, i.e., simila to Algoithm 1, it is unable to detemine a faulty bulb in the oom and since this algoithms is not using ceiling senso at all, tue illuminance of oom is unknown. The steps fo Algoithm II ae given in Table 2. ] 1. Given C i (C 2,b h,b θ,l 0,L 1 ),L i,c 2,b h,b θ,i {0,1}. 2. Compute I E using (6), (7) and (3). 3. Compute C 0 (L 0,L 1 ) using Eqns.(8), (9), (4), and C 1 (L 0,L 1 ) using Eqns.(10), (11), (5). 4. Compute C 0 (C 2,b h,b θ )= C 0 (C 2,b h,b θ,l 0,L 1 ) C 0 (L 0,L 1 ) C 1 (C 2,b h,b θ )= C 1 (C 2,b h,b θ,l 0,L 1 ) C 1 (L 0,L 1 ) 5. If C i (C 2,b h,b θ )<0 then set it equal to zeo i {0,1}. 6. Compute cuent cluste index c using C 2,b h,b θ. 7. Compute I D using Eqn. (15). 8. I W = I E + I D. Table 1: Steps fo Algoithm I 1. Given L 0,L 1,C 2,b h,b θ. 2. Compute I E using Eqns.(6), (7) and (3). 3. Compute cuent cluste index c using C 2,b h,b θ. 4. Compute I D using Eqn I W = I E + I D. Table 2: Steps fo Algoithm II 4.3 Algoithm III Befoe we go into details of this algoithm, we ewite Equations (6)-(11) using matix notations: [ ] [ C0 (L 0,L 1 ) a = 00 a ][ ] 01 L0 b +[ 00 + b ] C 0 (L 0,L 1 ) a 10 a L 1 b 10 + b 11 [ h(l 0,L 1 )= a 0 a ] [ ] L [ b L 0 + ] b 1 1 Define C E = [ C0 (L 0,L 1 ) C 0 (L 0,L 1 ) p=[ b 00 + b 01 b 10 + b 11 ] [ L0,L= L 1 ] a= [ a 0 a 1 ],V s =[ a 00 a 01 a 10 a 11 ] T,b= [ b 0 + b 1 Theefoe ewiting the ealie equation we get, C E = V s L+p h(l 0,L 1 ) = a T L+b = a T V s 1 (C E p)+b = k T (C E p)+b = k T C E k T p+k T b Theefoe, the electic light illuminance on the wok plane can be expessed in tems of ceiling senso values. Fo the given expeiment, we find the k T p+k T b is vey small and hence will be neglected. Theefoe, h(l 0,L 1 )=I E = k T C E (18) In this algoithm, the daylight component is computed using the window senso. The electic light computation is a thee step pocess: fist compute the daylight sensed by the ceiling senso, next compute the electic component of the ceiling ] ] 387

6 1. Given C i (C 2,b h,b θ,l 0,L 1 ),L i,c 2,b h,b θ,i {0,1}. 2. Compute cuent cluste index c using C 2,b h,b θ. 3. Compute I D using (14). 4. Compute C 0 (C 2,b h,b θ ) using Eqn. (12) and C 1 (C 2,b h,b θ ) using Eqn. (13). 5. Compute C 0 (L 0,L 1 )= C 0 (C 2,b h,b θ,l 0,L 1 ) C 0 (C 2,b h,b θ ) C 1 (L 0,L 1 )= C 1 (C 2,b h,b θ,l 0,L 1 ) C 1 (C 2,b h,b θ ) 6. Compute I E using (18). 7. I W = I E + I D. Table 3: Steps fo Algoithm III 1-5. The Step 1 to 5 ae simila to Algoithm III as given in Table Compute C 0 (L 0,L 1 ) and C 1 (L 0,L 1 ) using (4) and (5), espectively. 7. { C C 0 (L 0,L 1 )= 0 (L 0,L 1 ) if X is satisfied; C 0 (L 0,L 1 ) othewise. X = 0.8 C 0 (L 0,L 1 ) C 0 (L 0,L 1 ) 1.1 C 0 (L 0,L 1 ). Similaly fo C 1 (L 0,L 1 ). 8. Compute I E using (18). 9. I W = I E + I D. Table 4: Steps fo Algoithm IV senso measuement and use (18) to compute I E. The main advantage of this algoithm is that ceiling sensos povide feedback about the tue illuminance in the oom. Hence, it is able to esolve the issue of faulty bulb. The steps fo Algoithm III ae given in Table Algoithm IV The last algoithm is simila to Algoithm III but with the additional featue of outlie ejection. Algoithm III is highly pone to eo in ceiling senso measuements especially aound noon on the sunny day. The steps fo Algoithm IV is given in Table 4. 5 Expeiments In this section, we shall pesent expeimental esults fo the theoy poposed fo atificial light elationship in Section III A, daylight elationship in Section III B, and estimation algoithms in Section IV. 5.1 Atificial Light Expeiments Fig. 4(a), (b) and (c) show pefomance of egession analysis fo the data collected at night fo C 0, C 1 and hobo senso (h) espectively. In these plots, fo time instants T = 40 to 240, L 1 = 0 and L 0 is vaied while fo time instants T = 260 to 460, L 0 = 0 and L 1 is vaied and coesponding ceiling sensos and hobo senso measuements ae ecoded. As shown, the data was collected on 1, 5, 7 and 12 Decembe and egession coefficients wee estimated. We then applied the egession coefficients of each day and to the last day (12 Decembe) data. The egession functions matches tue data with mino vaiations. Hence, one can select any data paametes fo electic light illuminance. The coefficients ae tabulated in Table 5. An impotant point to note in all thee figues is the piecewise linea elation of ballast levels to the illumination. The thee linea links ae as follows: 1. = 1 indicates the low ballast level egion. In this egion, illumination is almost zeo fo zeo ballast level and emain constant fo ballast levels less than n 1, i.e., even though ballast level is inceased fom 0 to n 1, thee is no incease in illumination. The low illuminance in this egion can be attibuted to eithe ambient light in the oom o esidual eading of senso. 2. = 2 indicates the egion between n 1 and n 2 wheein illumination on wok plane is diectly popotional to the ballast levels, i.e., thee is incease in illumination with incease in ballast level and vice vesa. This is the most impotant egion fo opeation of light fixtues. 3. = 3 indicates the high ballast egion and simila to egion 1 (= 1), the illumination is constant even though thee is incease is ballast level beyond n 2. Hence fo most pactical puposes, Region 2 (=2) is most impotant. 5.2 Daylight Expeiments Fig. (5) show plots fo elation between senso on the table (hobo) and window senso (C 2 ). This gives us elation between daylight falling on the wok plane (measued using hobo senso) and daylight on the window. As we see, data is divided into five clustes and linea egession is pefomed fo each cluste. Simila plots can be geneated fo C 0 and C 2 (see Fig. 6), and C 1 and C 2 (see Fig. 7) to undestand the elation between daylight falling on the window and sensed by the ceiling sensos. Note fom the plots that use of linea function is justified fo the daylight models. It pefoms well fo all the clustes. The daylight coefficients ae listed in Table 6. The expeimental esults fo daylight estimation ae povided fo completeness of the pape. Moe details can be found [8]. 5.3 Estimation Expeiments We an expeiment fo multiple days and show pefomance of algoithms fo Dec 6, 2012 and Dec 9, Fo each day, we show estimation esults, outside daylight, compaison between computed ceiling senso and estimated ceiling senso measuements, and changes in cluste ID. The gound tuth fo estimation is measued by placing a hobo senso on the wok plane. Fo Dec 6, all the algoithms have simila pefomance except Algoithm I as in Fig. 8(a). The pefomance of Algoithm I is mainly affected between 12:30-2:15pm. Duing this time, the algoithm is mainly in cluste 2 which has highe multiplie fo C 0. As esult, the lage eo measued in the C 0 fo atificial light gets popagated to computations of daylight and hence oveall lage estimation eo. One sees a small ise in the illumination on 388

7 Senso Paametes =1 =2 =3 ( ) ( ) ( ) ( ) a00 b C ( a 01 b 01 ) ( 0 6 ) ( ) ( ) a10 b C ( a 11 b 11 ) ( 0 10 ) ( ) ( ) u00 v h u 01 v Table 5: Relationship Coefficients fo vaious sensos with espect to ballast levels the wok plane aound 2pm even though outside daylight is educing. This is due to change in cluste index. The blinds ae fully aised in this cluste which causes some moe light to ente the oom. Notice in this case that this light was also sensed by ceiling sensos in Fig. 8(b). Simila behavio is obseved fo Algoithm I fo the expeiment on Dec 9 as seen in Fig. 9. As seen fom outside lux values, Dec 9 was a elatively sunnie day. Theefoe aound the lunch time, thee was lage amount of daylight in the coido of the set up. This exta daylight was ead by the ceiling senso (C 1 ) which is mounted nea the doo. Hence, this lage C 1 eading, affected the atificial light estimation (also seen in 9(b)). Hence, we see a lage spike in estimation with algoithm III. Howeve, this gets fixed in Algoithm IV as we have included a naive algoithm fo outlie ejection which accounts fo these lage deviations. Note that Algoithm II, which does not depend on ceiling senso measuement, has pefomed well in all the expeiments. Algoithm II is in some sense an open loop contolle and is completely dependent on the window senso. Hence it will not be able to adapt to the daylight changes in the oom. 6 Conclusion and Futue Wok In this pape we pesent a daylight havesting system that employs two ceiling mounted sensos inside the oom, one window mounted senso outside the oom, and adjustable light fixtues and blinds. The cuent system has two independent contolles unning, open loop contolle that contols the position of blinds dependent on the sola movement, and a closed-loop contolle that contols the atificial light to maintain equied illumination on the wok plane. We pesent many new algoithms to fuse infomation fom diffeent senso to estimation illumination on the wok plane. The poposed algoithms exploits the theoy of adiosity to educe the dimension of function appoximation which leads to educed computational demands and moe accuate estimations. The poposed algoithms eliminate the need of the senso on the wok plane and theefoe the senso measuements ae not affected by uses. Cuent eseach can be extended in many inteesting diections. Fist, most of the poposed algoithms have an in-built causality, i.e., estimate daylight pio to atificial light and vice vesa. This leads to popagation of eo. Theefoe, new algoithms should be consideed to eliminate it. Second, the data fo daylight elationship is collected in a constained envionment (doo was closed). This leads to lage estimation eo aound noon. Theefoe, data collection should be pefomed in a moe geneal envionment to account fo vaious scenaios of daylight enteing the oom. Acknowledgment The autho would like to thank Dagnachew Biu and Maulin Patel fo thei guidance in conducting this eseach. Refeences [1] S. Selkowitz and E. Lee, Integating automated shading and smat glazings with daylight contols, Lawence Bekeley National Laboatoy, [2] F. Rubinstein, G. Wad, and R. Vedebe, Impoving the pefomance of photo-electically contolled lighting systems, Jounal of the Illuminating Engineeing Society of Noth Ameica (IESNA), vol. 18, pp , [3] D. L. DiBatolomeo, E. S. Lee, F. M. Rubinstein, and S. E. Selkowitz, Developing a dynamic envelope/lighting contol system with field measuements, Jounal of the Illuminating Engineeing Society, vol. 26, pp , May [4] J. Lu, D. Biy, and K. Whitehouse, Using simple light sensos to achieve smat daylight havesting, Poceeding of the 2nd ACM Woshop on Embedded Sensing Systems fo Enegy Efficiency in Buildings, pp , [5] S. Mukhejee, D. Biu, D. Cavalcanti, S. Das, M. Patel, E. Shen, and Y.-J. Wen, Closed loop integated lighting and daylighting contol fo low enegy buildings, In Poceedings of the 2010 ACEEE Summe Study on Enegy Efficiency in Buildings, Pacific Gove, CA, [6] E. Shen, M. Patel, and J. Hu, Compaison of enegy and visual comfot pefomance of independent and integated lighting and daylight contols stategies, ACEEE Summe Study on Enegy Efficiency in Industy,

8 (a) (b) (c) Figue 4: (a)(l 0,L 1 ) Vs C 0 (b)(l 0,L 1 ) Vs C 0 (c)(l 0,L 1 ) Vs h. n 1 = 30 and n 2 = 210 ae used fo taining. (a) (b) (c) (d) (e) Figue 5: Hobo vs C 2 Plots (a) Cluste 1 (b) Cluste 2 (c) Cluste 3 (d) Cluste 4 (e) Cluste 5 (a) (b) (c) (d) (e) Figue 6: C 0 (Light Only Senso) vs C 2 Plots (a) Cluste 1 (b) Cluste 2 (c) Cluste 3 (d) Cluste 4 (e) Cluste 5 390

9 Cluste Height (b h ) Angle (b θ ) Sunlight (C 2 ) h Vs C 2 C 0 Vs C 2 C 1 Vs C 2 h Vs (C 0,C 1 ) Index(c) (min,max) (min,max) (min,max) (β h,α h ) (β 0,α 0 ) (β 1,α 1 ) (β m,α m ) 1 (0, 0.3) ( 90, 90) (0, 3000) (7.16, ) (0, ) (0.930, 0.008) (0, ) 2 (0, 0.3) ( 90, 90) (3000, 15000) (13.16, ) (0.68, ) (2.67, ) (0, ) 3 (0.3, 0.8) ( 90, 90) (0, 15000) (0, ) (0, ) (1.64, ) (0.22, ) 4 (0.8, 1.0) ( 90, 55) (0, 15000) (0, ) (0, ) (0, ) (4.89, ) 5 (0.8, 1.0) (55, 90) (0, 15000) (0, ) (0, ) (0, ) (4.87, 0) Table 6: Table list the clusteing and elationship coefficients fo daylight estimation (a) (b) (c) (d) (e) Figue 7: C 1 (LightAndBlindSenso) Vs Window (C 2 ) elationship (a) Cluste 1 (b) Cluste 2 (c) Cluste 3 (d) Cluste 4 (e) Cluste 5 [7] K.-W. Pak and A. K. Athienitis, Wokplane illuminance pediction method fo daylighting contol systems, Sola Enegy, vol. 75, no. 4, pp , Octobe [8] S. Zhang and D. Biu, Wokplane illuminance estimation fo obust daylight havesting lighting contol, Octobe [9], An open-loop venetian blind contol to avoid glae and enhance daylight utilization, Sola Enegy, vol. 86, pp , Mach [10] T. Hastie, R. Tibshiani, and J. Fiedman, The Elements of Statistical Leaning. Spinge, [11] W. Hadle, M. Mulle, S. Spelich, and A. Wewatz, Nonpaametic and Semipaametic Models. Spinge Seies in Statistics,

10 (a) (b) (c) (d) Figue 8: Simulations fo 6th Decembe 2011 (a) Estimation Results (b) Senso Measuements (c) Window Senso Measuements (d) Cluste ID (a) (b) (c) (d) Figue 9: Simulations fo 9th Decembe 2011 (a) Estimation Results (b) Senso Measuements (c) Window Senso Measuements (d) Cluste ID 392