Paulson MSreport

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PERSONALIZEDILLUMINANCEMODELINGUSINGINVERSE

MODELINGANDPIECEWISELINEARREGRESSION

By

RyanRobertPaulson

BS(MichiganTechnologicalUniversity)2008

AreportsubmittedinpartialsatisfactionoftheRequirementsforthedegreeof

MastersofScience,PlanII

in

MechanicalEngineering

atthe

UniversityofCaliforniaatBerkeley

CommitteeinCharge:

_______________________

ProfessorAliceM.Agogino,Chair

_______________________

ProfessorDuncanCallaway

Spring2012


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Abstract

Buildingsaccountfornearly40%ofthetotalenergyuseintheUnitedStates,morethan

eithertransportationorindustry.Ofthis,lightingaccountsfor11%ofenergyuseinresidential

buildings and 25% of the energy use in commercial buildings. Increased energy efficiency in

lightingsystemscouldhaveamajorimpactonenergyusageonaglobalscale.BuddingSmart

Grid research calls for more localized control and greater energy efficiency across multiple

independentbuildingsystems.InordertoensureafutureinwhichtheSmartGridcoverslarge-

scalefacilitiesandsmallresidentialandofficebuildingsalike,low-cost,easily-installedretrofit

energyefficiencysolutionsarerequired.

Thisreportdetailsaplug-and-playinversemodeldevelopmentpackagethattakesdatafrom

wireless light sensors and performs multiple linear regression to build a piecewise linear

functionthatpredictstheworkplaneilluminanceduetodaylightandasinglelinearfunction

thatpredictsworkplaneilluminanceduetoartificiallight.Theproposedmodelis intendedfor

useinpredictivelightingcontrollersandmayallowfortheoptimizationoflightlevelsacross

multiple workstations. Coefficients for artificial light contribution are time-invariant, while

differentcoefficientsareusedfordaylightcontributiondependingonsunposition.Thetests

wereperformedinareal-lifesetting,typicalofasharedresidentialspace.

Theartificiallightmodelwasfoundtobeverypromising,witharesidualmeanandstandard

deviationof-0.11812.5626lux.Thedaylightmodelwasfoundtohavedifficultywithdirect

sunlight,anerrorattributedmainlytolightsensorlimitations.Thedaylightmodelwasfound,

formultiplesimulationsthroughoutayear,tohavearesidualmeanandstandarddeviationof-

54.5229846.9855lux.However,byremovingtheerrorsfromhighluxdirectsunlightsensing,


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themodelsignificantlyimprovesandgivesaresidualmeanandstandarddeviationof-85.368

174.9429.


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Contents

Introduction.................................................................................................................................................1

ResearchGoal..........................................................................................................................................1

DescriptionofTechnology.......................................................................................................................3

Methodology...............................................................................................................................................4

Terminology.............................................................................................................................................4

IlluminanceduetoArtificialSources.......................................................................................................4

SolarIlluminance.....................................................................................................................................6

Sunposition...........................................................................................................................................10

InverseProblemTheory.........................................................................................................................11

MultipleLinearRegressionbyOrdinaryLeastSquares.........................................................................12Hardware...................................................................................................................................................14

LightSensor...........................................................................................................................................14

LightSensorCalibration.........................................................................................................................15

Software....................................................................................................................................................17

TestsandTestResults................................................................................................................................19

Testbeddescription...............................................................................................................................19

TestOverview........................................................................................................................................23

ArtificialLightSourceTest.....................................................................................................................23

PilotDaylightTests................................................................................................................................25

UpdatedDaylightTests..........................................................................................................................27

RadianceDaylightSimulation................................................................................................................29

CombinedDaylightandArtificialLightTest...........................................................................................32

Discussion..................................................................................................................................................34

Futurework...............................................................................................................................................35

Acknowledgements...................................................................................................................................37References.................................................................................................................................................38

Appendix....................................................................................................................................................42

AppendixA SourceCode..................................................................................................................42

AppendixB LightSensorCircuitDiagram.........................................................................................52

AppendixC TelosBBlockDiagram....................................................................................................53


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ListofFigures

Figure1Directsolarnormalilluminanceasafunctionofsolaraltitude[13]. 7

Figure2Clearskydiffuseilluminanceasafunctionofsolaraltitude[13]. 8

Figure3Predictedandsimulatedilluminancefordifferentroomscenarios.[14]. 9

Figure4Horizontalilluminancemappedtooutdoorverticalirradianceforafixedsunpositionatvarying

Perezskyclearnesscategories[14]. 10

Figure5RelativespectralsensitivityofOSRAMSHF5711illuminancesensor[22]. 15

Figure6Illuminancereadingsofmotesplottedagainstluxmeterreadings 16

Figure7Softwareflowchart. 18

Figure8Testbedoverview 20

Figure9Pilotandupdatedpositionofdeskmote1. 20

Figure10Pilotandproposedupdatedpositionofdeskmote2. 21

Figure11Positionofartificialmote51. 21

Figure12Positionofartificialmote52. 22

Figure13Positionofwindowmote101. 22

Figure14February14dataofartificiallightsourcecontributionondesktop1inabsenceofdaylight. 24

Figure15February14Mote1dataandPredictionfordesktop1. 24

Figure16March8DataandPredictionsfromApril3. 25Figure17March20DataandPredictionsfromApril3. 26

Figure18April3DataandPredictionsfromApril3. 26

Figure19April15DataandPredictionsfromApril15andMay5. 27



Figure22May5DataandPredictionsfromApril15andMay5. 29

Figure23RadiancemodeloftestbedforNovember10,16:00. 30

Figure24SimulatedRadiancedataofdesktop1forJune20. 31

Figure25SimulatedRadiancedataofdesktop1forNovember10. 32

Figure26April7Combinedartificialanddaylighttest. 33

Figure27April7Combinedartificialanddaylighttest,Mote1andpredictedvalue. 33


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Introduction

ResearchGoal

Buildingsaccountfornearly40%ofthetotalenergyuseintheUnitedStates,morethan

eithertransportationorindustry[1].Over$369billionarespentonenergyacrossthenation

eachyear.Ofthis,lightingaccountsfor11%ofenergyuseinresidentialbuildingsand25%of

the energy use in commercial buildings [2]. The numbers indicate that increased energy

efficiencyinlightingsystemscouldhaveamajorimpactonenergyusageonaglobalscale.

Withgrowingenergycostsandaspreadingawarenessofthemassiveenergyconsumption

plaguingsocietyhereandabroad,supportforresearchintoSmartGridtechnologiesisgrowing

rapidly.ThebuddingSmartGridcallsformorelocalizedcontrolandgreaterenergyefficiency

acrossmultipleindependentbuildingsystems[3].Thissuggeststhatsoonbuildingsystemswill

becommunicatingwitheachotherto balanceenergyconsumptionacrosstheentirebuilding,

takingintoaccountpeakloadtimesandpricesaswellasuserpreferences.Thislevelofcontrol

requiresaccurateandefficientsystems,ofcourse,buttheSmartGridwillnotjustincludelarge

office complexes with plenty of money to spend on new systems. The Smart Grid will also

encompasssmallofficespacesandresidentialsystems,whichwouldrequirelow-cost,easily-

installedretrofitenergyefficiencysolutionsandthetoolstohelpbuildthem.

Energyefficientautomatedlightingsystemsarenowcommerciallyavailable,buttheyhave

limitations. Careful calibrations must be performed by a technician for each space. Daylight

controlis achievedthroughsensorsthatcomparelightlevelstopredeterminedset-points[4].


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Light levels are gradually adjusted to achieve the set-points. This method is convenient for

single workstations, but does not lend itself to predictive control or to energy usage

optimizationacrossmultipleworkstations.

Inverse modeling packages for building systems control are not new; researchers are

developingthemforlighting[5]andHVAC[6]control.Thesemodelsarerobust,butrequirethe

usertoleavelightsensorsontheirdesksorneartheirworkstationsindefinitely.Manymodels

opt instead to use simulation packages that take into account building geometry and

reflectanceofallsurfacesintheroom[7-9].Thesecalculationsareusuallyperformedthrough

theuseofRadiance,aspecializedlightingprogram[10].Thedownsidetotheseprogramsisthat

theyrequiredetailedknowledgeofthebuildingstructureandfurnituredimensions,aswellas

thetechnicalexpertisetoputtheinformationintoaCADprogram.Thislevelofaccuracyalso

requires significant computing power that could take several minutes to several hours of

processingtoachieveanaccuratemodel.

Thegoalofthisprojectistoinvestigatethepotentialforaportableplug-and-playinverse

modeling package that models light based on multiple linear regression by ordinary least

squares. By plug-and-play we mean that the package can easily be set up with minimal

instructionorinfrastructure.Thatis,thepackageshouldnotrequiretasksthatwouldbetaxing

for an inexperienced user, such as modeling room geometry, complex programming, or

expensiveandcomplicatedinstallationprocedures.Inaddition,themodelshouldbereasonably

accuratethroughoutthedayandyear.Themodelshouldbeabletoaccommodateanygiven

number of sensor inputs. The use of multiple linear regression decreases the required


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computingpowertocreateamodel.Thephysicsofilluminationsuggeststhatalinearmodelis

possibleandthisresearchinvestigatesthevalidityofthisassumption.

DescriptionofTechnology

A novel software program has been developed for the generation of a plug-and-play,

predictive,personalizedmodelofroomlightingusingawirelesssensornetwork.Theinputsto

the modelare illuminance levelsmeasuredateach user workstationwith both artificial and

naturallightsources.Apiecewiselinearmodelisgeneratedforeachworkstationsuchthatthe

illuminanceduetodaylightcanbepredictedbasedonvaluesfrommeasurementstakenata

nearbywindow.Likewise,asinglelinearfunctionisgeneratedforeachworkstationsuchthat

the illuminance due to artificial light sources can be predicted based on values from

measurementstakenincloseproximitytonearbyartificiallights.Inthismodel,coefficientsfor

artificiallightcontributionsaretime-invariant,whiledifferentcoefficientsareusedfordaylight

contributiondependingonsunposition.Duetotheextremelyhighspeedoflight,thesystem

canbeassumedtorequirenearlyinstantaneousresponse.Forthisreason,anopen-loopsystem

wasimplementedtominimizeresponsetime.

It is also important that this tool can be used in energy optimization of lighting across

multiple users in a shared space. In this research, the predicted effect of proposed lighting

scenarioscanbefoundandcomparedtothedesiredresults.Withthistool,anoptimallighting

scenarioshould befound that satisfies all userswhilereducing the energy consumedby the

luminaries.


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Methodology

Terminology

Radiantflux is theflow rate of radiantlightenergy,measured in wattspersquaremeter.

Luminousfluxistheperceivedpoweroflight,adjustedtoreflectthevariablesensitivityofthe

humaneyetodifferentwavelengths.TheSIunitofluminousfluxisthelumen,whichisdefined

intermsofluminousfluxofmonochromatic555nmradiation.Illuminanceisameasureofthe

luminousfluxperunitarea.TheSIunitofilluminanceisthelux,whichisequivalentto1lumen

persquaremeter[11].

IlluminanceduetoArtificialSources

The illuminance due to an artificial source is fairly straightforward. We assume that the

effectoflightreflectedoffofotherobjectsontothemeasurementsurfaceisminimalandthe

majorityoflightincidentonthemeasurementsurfaceisduetodirectirradiation.Evenso,any

lightthatisreflectedissimilarlygovernedbythesameprincipleasdirectirradiance,withsome

lossduetodiffusion.Forthesereasonswewillinvestigateonlydirectirradiance.Theequation

formeasurableirradiancethathasbeenemittedfromapointsourceincidentonanarea

withsurfacenormalangleofandsolidanglesubtendedbythemeasurementisasfollows

[12]:

=!

cos Equation1 Whereis the irradiance andis the total radiant flux emitted by the source. For small

angles,theequationsimplifiesto:


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cos Equation2 If the sourceof radiant flux andtheobservation area do not change with respect to one

anotherovertime,thetermsinthedenominatorareallconstantsandcanbecollectedintoa

singleconstant,,whichdescribeslocationandangleoftheobservationarea.Inaddition,ifthe

spectrum of the light does not vary then it is a linear transformation from radiant flux to

luminousfluxandlikewiseirradiancetoilluminance.Combiningthelineartransformationinto

thelinearconstantgivesus:

! = ! Equation3

Whereis illuminance. Sinceis constant for a given location and orientation, we can

describeasecondobservationareaassuch:

! = ! Equation4

Fromherewecanusesubstitutionandsolvefor!:

! =!

!

! Equation5

From Equation 5, wecan see that illuminance due to a point source measured from one

location is directly proportional to the illuminance measured at another location. This is

important for estimating the contribution of artificial light sources to the workstation

illuminance.Whiletheidealsetupusesdimmableluminariesthattransmittheirpowerlevelsas

apercentageofthetotalpower,itmaynotbefeasibletoretrofitallluminariesinaspace.If

this is the case, the contribution of artificial light to the workstation illuminance can be

estimatedbyplacinganilluminancesensorincloseproximitytoeachluminaryandusingthis


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reading in the linear regression model as a direct replacement for power level, with the

assumptionthateachindividualluminaryisthemajorcontributortotheilluminancereadingfor

thecorrespondingilluminance.Thismethoddoesintroducesomeerrorintothesystem,asthe

illuminancereadingsmaybeduetoacombinationofunaccounted-forlightsources.However,

ifthelinearityassumptionholds,theerrorshouldberelativelysmall.

SolarIlluminance

Solar illuminance is generally described as a linear combination of direct normal solar

illuminance (also called beam illuminance) and diffuse illuminance, which is the illuminance

thathasbeenscatteredbypassingthroughair.Thedirectnormalsolarilluminancehasbeen

foundtocloselyfollowafunctionoftheform[13]:

!" = !" 1+ 0.0333 360

365

!!

!"# ! Equation6

Where!"isthedirectnormalsolarilluminance,!"isthemeanextraterrestrial solar

illuminance (127.5 klux),is the Julian calendar date between 1 and 365, is the optical

atmosphericextinctioncoefficient(empiricallyestimatedtobe0.210forcleardays),and is

thesolaraltitude.DatatakenfromseverallocationsintheUnitedStatesthroughouttheyear

canbefoundinFigure1.


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Figure1Directsolarnormalilluminanceasafunctionofsolaraltitude[13].

Diffusesolarilluminancehasbeenfoundtobeoftheform:

! = + sin !

Equation7

Where!ishorizontaldirectilluminance,and,,andareempiricallyderivedconstants

that vary depending on the clarity of the sky. Data for diffuse solar illuminance taken

throughout the year at different locations around the world on clear days can be found in

Figure2.Whiledirectsolarilluminancecanbeeasilyestimatedusingjustthetimeofday,the

diffuse solar illuminance can be much harder to estimate without an irradiance meter and

accesstoweatherdata.


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Figure2Clearskydiffuseilluminanceasafunctionofsolaraltitude[13].

To avoid this dependence on weather data, a different estimation can be used. A very

accurateapproximationofilluminanceduetodaylightwithinaroomforafixedsunposition

[14]canbedescribedas:

!"!!" = !"#!!" + !"##!!" Equation8

Where !"!!" is indoor horizontal illuminance, !"#!!" is outdoor horizontal directirradiance, !"##!!" is horizontal diffuse irradiance, and and are model-dependent

coefficients.[14]utilizedRadiancesimulationstotesthisequationforsouth-facingandwest-

facing rooms. The relationship between predicted and simulated illuminances was found to


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haveverysmallresidualsandthecorrelationcurvesasshowninFigure3.Itisworthittopoint

outthatthealgorithmrequiredmonthsofdatatoperformatthislevelofaccuracy.

Figure3Predictedandsimulatedilluminancefordifferentroomscenarios.Thepredictionmodelwasa

linearcombinationofdirectanddiffuseirradianceforagivensunposition[14].

If solar irradiance is not accessible and a reasonably clear sky can be assumed, a good

approximationcanalsobefoundusingoutdoorverticalilluminance,accordingtoboth[14]and

[15]:

!"!!" = !!"#$ Equation9 Where!!"#$ is the vertical faade illuminance and is a model-dependent coefficient.

Guillemins test resulted in standard deviations of 416 lux. [14] tested this relationship and


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foundapromisingnearly-linearcorrelationbetweenverticalfaadeirradianceandhorizontal

illuminanceforarangeofPerezskyclearnessvalues,andtheresultscanbefoundinFigure4.

Perezskyclearnessisadiscretizedmeasurementofcloudcoverandrangesfromcloudy(values

oflessthan3)toveryclear(valuesgreaterthanorequalto8)[16].

Figure4Horizontalilluminancemappedtooutdoorverticalirradianceforafixedsunpositionatvarying

Perezskyclearnesscategories[14].

Sunposition

An accurate daylight illuminance prediction algorithm needs to take into account the

positionofthesun.Themostaccurateofsevenreviewedby[17]istheAstronomicalAlmanacs

algorithm,implementedby[18].Ofthesevenalgorithmsreviewed,theAstronomicalAlmanacs

algorithmhadthesmallestaverageerrorsforzenithangle(-0.121),azimuth(-0.042)andthe


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smallestaveragesunvectordeviation(0.201).Blanco-Murieletal.[17]alsodevelopedanovel

algorithmthatismoreaccuratethanthe AstronomicalAlmanacsalgorithm,butweprefera

computationallylightalgorithmandthustheAstronomicalAlmanacsalgorithmwasselectedto

determinethesunposition.

InverseProblemTheory

Inverseproblemtheorydescribesmethodsbywhicha modelofa system isdevelopedby:

(1) parameterizing the system in terms of a set of model parameters that adequately

characterizethesysteminthedesiredpointofview,(2)makingpredictionsontheactualvalues

basedonphysicallawsandgivenvaluesofthemodelparameters,and(3)usingactualresults

frommeasurementstodeterminethemodelparameters[19].

A model that takes into account location would require the input of accurate building

dimensions,oratleastthemotepositionswithrespecttothelightsources.Themodelwould

thenestimatethelightingasasummationoftheluminariesatanyoreverypositioninthe

room. This system would be very accurate and robust, but the user input and computation

requiredwouldbesignificant.Unlessanextremelysimplifiedinterfacewascreated,alocation-

basedmodeldevelopmentsystemwouldrequireatechniciantosetup.

Aninversemodelwouldnotrequireluminaryorworkstationpositionstofunction.Instead,

thesystemwouldmeasurelightingdataatworkstationsabouttheroom.Thedatawouldbe

mappedtothecontrollableluminarylevelsandtothelightlevelsfromthedaylightmeasured

atthewindowsviaaregressionmodel.Themodelthereforewillbetreatedasablackboxof

sorts,withinputsofdaylightandcontrollablelightlevelsandoutputsofthelightlevelatthe


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workstations.Thissystemwouldnotbeasaccurateorasextensibleasafullsimulationmodel

thattakesintoaccountthelocationofthemotesthesystemcannotdeterminethelightlevels

ofeveryspaceintheroom,onlythoseattheworkstationsbutthesystemcouldberelatively

easytosetup.Properlydesigned,thesystemwouldbeabletobedeployedwithminimaleffort

ontheendoftheuser.Forthesereasons,aninversemodelisapromisingchoiceforaplug-

and-playlightingsystemdesignedforease-of-use.

MultipleLinearRegressionbyOrdinaryLeastSquares

Multiplelinearregressionisanefficientandrelativelysimpleprocedurethatcanfindalinear

relationship between multiple regressors anda regressand. The ordinary least squares (OLS)

method functions tocreatea bestlinearfit toa givendata set byminimizing the sum ofthe

squaredresiduals[20].

For this project, a linear relationship between the illuminance measured at artificial and

naturallightsourcesandtheilluminancemeasuredataworkstationareassumedoftheform:

!= !!! + !!! ++ !!! + !!! ++ Equation10

Where!

,!

,and!

areilluminancereadingsattheworkstation,anartificiallightsource,

andanaturallightsource,respectively,whileandareconstantsdefinedbythemodeland

israndomerror.Ifwehavesamples,theequationbecomes:

!!

!!

= !!!!

!!!

+ !

!!!

!!!

++ !

!!!

!!!

+ !

!!!

!!!

++ Equation11


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Tosolvethisequation,themethodofordinaryleast-squaresleadsustofindthevaluesof

andthatminimizethesumofthesquaredresiduals.Asimplewaytodothisistofirstarrange

thedataintotheform:

!!

!!

=

!!!

!!!

!!!

!!!

! !

!!!

!!!

!!!

!

!

!!

+ Equation12

SimplifyingEquation12forclarity:

= + Equation13

From therewe assume strict exogeneity,or that the error hasa mean of zero and is not

correlated to the regressors. We also assume linear independence. This assumption is valid

because,whilethereissomeriskofmulticollinearityifthereisonlyonelightsourceandthe

sensormotesarepositionedveryclosetogether,thisriskismediatedsimplybyensuringthe

motes are spaced well apart at varying distances from the light source. Using these

assumptions,wecanthenuselinearalgebratoarrangetheequationintheform:

= ! !!Equation14

Theequationcanalsobewrittenas:

=1

!

!

!!!

!

!

!!

1

!!!

!!!

Equation15

ThisequationistheOrdinaryLeastSquaresEstimator,andgivesusthebestfitlinearmodel

forthedata.


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Hardware

A wireless light sensor network was utilized for inverse modeling. The network was

comprisedofTelosBmoteplatformsrunningonAA-batteries[21].Themoteswereconfigured

withanambientlightsensorthatwassampledatregularintervals.Themotescommunicated

eachsamplereadingoverthe802.15.4layertoanothermoteconnectedtoabasecomputer.

LightSensor

ThelightsensorusedwasanOSRAMSFH5711ambientlightsensor[22].Thesensorisa

photodiodethatoutputsacurrentthatisreadbythemoteplatform.Thesensorwaschosen

becauseofitssensitivitytothenakedeyeandforthelogarithmiccalibrationcurveassociated

withit.Thiscurveallowedforawiderangeofluxvaluestobesampledwhilemaintaininga

smalldatapacketsize.Thesensorsweresensitivetoilluminancesbetween3-80kluxatnormal

operating temperatures. The spectral sensitivity range, shown in Figure 5, was between

wavelengthsof475and650nm,slightlywithinthespectralsensitivityrangeofthehumaneye,

whichisbetweenwavelengthsofroughly400-700nm.Thepeaksensitivityisbetween540and

570nanometers,dependingonthesensor.Thetypicalvalueis555nm,whichisverycloseto

thehumaneyespeaksensitivityof550nmduringtheday.


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Figure5RelativespectralsensitivityofOSRAMSHF5711illuminancesensor[22].

LightSensorCalibration

Thecalibrationcurveasdefinedbythemanufacturerisasfollows:

!"# = log !!

Equation16

Where!"# is the output current, is a sensitivity constant of 10 A,! is a constant

conversionfactorof1lux,and!

istheincidentilluminance.Thisequationwastestedacross

multiplesensorssimultaneouslyandtheresultscanbeseeninFigure6.Themotenumbering

forthistestdoesnotreflectposition.


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Figure6Illuminancereadingsofmotesplottedagainstluxmeterreadings,withoutdirectsunlight.

Itisapparentthatthemotesarequiteaccurateuntilaround2000lux,whentheyappearto

becomesaturated.Below2000lux,theresidualsmeansandstandarddeviationsofthedataare

46.5759 36.4637, -9.3955 69.4646, and 11.6397 37.1833 for motes 1, 2, and 3,

respectively. Above 2000 lux the residuals with become -442.7070 454.6512, -912.2821

554.1084, and -744.8797 427.1665 for motes 1, 2, and 3, respectively. The motes have

difficultymeasuringdirectsunlightwithmuchaccuracy.Therearesomedifferencesbetween

themotemeasurementswhichmaybeduetominorcalibrationerrorsor,morelikely,dueto

variations in illuminance throughout the test space. While the motes and lux meter were

situated in as close proximity to each other as possible, there are variations in illuminance

betweenthe1-2inchesthatseparatedtheminthetest.Inaddition,slightvariationsinsensor

anglearepresentbetweenthemotesduetoassembly.Theresidualsfoundforluxlevelsbelow


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2000 lux arenearor within human perception limits for differentiating between illuminance

levels.Becausetheaveragehumancannotdistinguishbetweentwoilluminancelevelsthatare

separatedby30luxdifferenceatlowluxlevels[23]themotesarewellcalibratedbelow2000

lux.

Software

The wireless sensor network was programmed in TinyOS, an open-source platform

developedatUCBerkeley[26].Themotesusedasimilarstructureasapreviousiterationused

inthesamelab[23-25].AflowchartforthesoftwarestructurecanbeseeninFigure7.The

motes,eachwiththeirownuniqueIDs,communicateddatapackagestoabasestationmote

which forwarded its data via a serial connection a computer that ran an initial data-parsing

programthatsavedtherawdatalocally.Thisprogramsimplytranslatedanysignalsitreceived

intotheproperluxandinternalvoltagereadingsaccordingtothecalibrationcurveforthelight

sensorandsavedthedataincomma-separatedvalueformatwithfilenamesthatcorrespondto

theuniquemoteIDs.


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From here,a Java-based program was developed toperformseveraltasks. First, the data

wereparsedtofillinanygapscausedbylostpackages.Second,thedatafromeachmotewere

thendivideddependingontheangleofthesunateachtimestep.Thenextstepdependedon

thetypeofmodelgenerated.Ifadaylightmodelwasbeinggenerated,linearregressionwas

performed as described above to create a piecewise linear function for each workstation,

dividedby angleof inclinationofthe sun.In sucha case,a linear functionwasestimatedfor

every0.5sunelevationforpilottestsor0.25forupdatedtests,whichhadahighersampling

rate.For theseinitial tests, the effect ofthe sun azimuth changingthroughoutthe year was

neglectedtosimplifythemodelfurther.Ifanartificiallightmodelwasbeinggenerated,asingle

Figure7Softwareflowchart.Dashedlinesrepresentflowofdatainmodelgenerationphaseonly,

solidlinesrepresentflowofdatainbothmodelgenerationandpredictionphases.Dash-double-dot

linesre resentfuturework.

Workstation

Sensors

External

Database

BaseStation(Addstimestamp)

Natural

Source

Artificial

Source

SunPosition

Estimator

PredictionUsing

RegressionModel

Regression

Model

LocalStorage


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linear function was estimated for the entire data set. These models were then used to

interpolatethevaluesoftheworkplaneilluminancesforeachprevioustimestepsothatthe

goodnessoffitcouldbedetermined.

TestsandTestResults

Testbeddescription

Thetestbedwasa450sq.ft.rectangularstudioapartmentwithawest-facingfloor-to-ceiling

window. The apartment was located on the 16th story of an apartment complex in San

Francisco,California.Thecontrollablelightsourceswere:akitchenceilingfixtureandabedside

lampnearthewindow.Throughoutthetest,thespacewasoccupiedbytworesidents(andtwo

cats) on a daily basis. This testbed was chosen as a real-life setting, typical of a shared

residentialspace.Figure8showsanoverviewoftheapartment.Figures9and10showthe

locationofdeskmotes1and2,respectively.Figures11and12showthelocationofartificial

sourcemotes51and52,respectively.Figure13showsthelocationofdaylightmote101.


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Figure8Testbedoverview

Figure9Pilotandupdatedpositionofdeskmote1.


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Figure10Pilotandproposedupdatedpositionofdeskmote2.

Figure11Positionofartificialmote51.


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Figure12Positionofartificialmote52.

Figure13Positionofwindowmote101.


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TestOverview

Thefollowingtestswereundertaken:

1.

Testoftwoartificiallightsourceswithoutdaylight

2. Testsofdaylightwithoutartificiallightsourcesa. Pilotdaylighttestsb. Updateddaylighttestsc. Radiancedaylightsimulations

3. TestofcombineddaylightandtwoartificiallightsourcesArtificialLightSourceTest

Atestwasperformedtoevaluatethevalidityoftheassumptionthatthecontributionoflight

emittedfromanartificialsourcefallingonanarbitrarypointinaroomcanbeestimatedusinga

linear transformation. Two artificial light sources at different points in the room were

controlledintheabsenceofdaylight.ThedatacanbefoundinFigure14.Theresultswerefed

intothelinearregressionmodelandtheresultingpredictioncanbeseeninFigure15.


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Figure14February14dataofartificiallightsourcecontributionondesktop1inabsenceofdaylight.

Figure15February14Mote1dataandpredictionfordesktop1.Meanandstandarddeviationof

residuals:-0.11812.5626.

Theresultantpredictionisverypromisingandsupportstheassumptionthatthecontribution

ofartificiallightsourcescanbemodeledasdirectilluminancethatcanbelinearlymappedtoan

arbitrarypointinthespace.


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PilotDaylightTests

An initial series of daylight testswere undertaken. At the time the tests were taken, the

effect of the sun position was not fully realized, therefore these data are not as full as the

updatedtest.Thedatafromonewindowmoteweremappedtoapiecewiselinearmodelfor

eachoftwodeskmotes.Thepredictedvalueswerecomputedusingthedatafromthesingle

daywiththewidestrangeofsuninclinationrecorded,thatofApril3.Themeansandstandard

deviationsoftheresidualsareshownforeachday.Figure16showsdatafromMarch8,Figure

17showsdatafromMarch20,andFigure18showsdatafromApril3.Ineachplot,aprediction

curveisplottedthatwascreatedusingdatafromApril3.

Figure16March8DataandPredictionsfromApril3.Meanandstandarddeviationofresiduals:

Desk1146.505368.0668,Desk2424.8409386.4171.


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Figure17March20DataandPredictionsfromApril3.Meanandstandarddeviationofresiduals:Desk1-85.771109.8475,Desk259.1792374.1701.

Figure18April3DataandPredictionsfromApril3.Meanandstandarddeviationofresiduals:Desk1-0.151318.5949,Desk21.377365.4952.


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UpdatedDaylightTests

A second series of testswere undertaken with anupdated workstationmote location on

April 15, 22, and 26, and May 5. The desktop mote 1 was moved to the top of a computer

monitor,ratherthanonthedeskitself.Thisdecreasedthelikelihoodofinadvertentshading.

Thecomputermonitor,beingdirectlybelowthemote,didnothaveameasurableeffectonthe

illuminancereading.Inaddition,sensorreadingsweretakenevery5seconds,ratherthanevery

2minutesasintheprevioustest.Forthisreason,thepartitionsizeforthepiecewiselinear

functionwaschangedto0.25toreflecttheincreasedgranularity.Forthistestthefocuswas

onjustonedesktopmote.Twomodelsweremadetodeterminethebestfit,usingdatafrom

April 15 and May 5. The data can be found below with the two model predictions plotted

againsttheactualdata.Figure19showsdata for April15,Figure20showsdata for April22,

Figure21showsdataforApril26,andFigure22showsdataforMay5.

Figure19April15DataandPredictionsfromApril15andMay5.Meanandstandarddeviationof

residuals:April15Model0.5924109.8859,May5Model134.9063285.4182.


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Figure22May5DataandPredictionsfromApril15andMay5.Meanandstandarddeviationof

residuals:April15Model-84.6475169.0901,May5Model0.872463.5481.

RadianceDaylightSimulation

Radianceilluminancesimulationsformultipledaysthroughouttheyearwereperformedto

testtheeffectoftimeofyearonthemodel.AnexampleRadianceimagecanbefoundinFigure

23.TestswereperformedforFebruary10,March20,April22,May10,June20,August10,

September22,November10,andDecember21atdiscreteintervalsof2hoursbetween06:00

and 18:00, resulting in 56 simulations, or 7 simulations per day. Illuminance levels at the

locationsofsensormotesweretakenandcomparedtovaluespredictedfromtheApril15data

atthegivensuninclinationsandilluminanceatthelocationofthewindowmote.


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Figure23RadiancemodeloftestbedforNovember10,16:00.

Sample graph from the data can be found in Figures 24 and 25, which show Radiance

simulationsofdesktop1andwindowmotesforJune20andNovember10,respectively.The

figures also display predicted values generated by the model using daylight coefficients

generatedbythedatacollectedonApril15andthesimulatedvaluesfordesktopmote1and

thewindowmote101.Themeanandstandarddeviationoftheresidualsforthedatacanbe

foundinTable1.Themodelappearstohavedifficultywhenoneormoreofthemotesare

subjecttodirectsunlight,asdiscussedinthecalibrationsectionandthateffectisseenifthe

corresponding residuals are neglected. It is valuable to point out that the illuminance levels


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simulated for the window are at times much higher than the light sensors are capable of

measuring accurately. The lightsensors would report a smaller lux value if experiencing the

samelevelofilluminance,sothepredictedmodeloverestimatestheilluminanceincidenton

thedeskwhenthesimulationreportssuchhighluxlevelsatthewindow.

Figure24SimulatedRadiancedataofdesktop1forJune20withpredictedvaluesgeneratedusingdata

fromApril15.


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Figure25SimulatedRadiancedataofdesktop1forNovember10withpredictedvaluesgeneratedusing

datafromApril15.

Table1ResidualanalysisoffullRadiancedata(56teststotal)

Fulldata Onlydiffusesunlight

Residualmeanandstandarddeviation -54.5229846.9855 -85.368174.9429

Relativeresidualmeanandstandarddeviation

0.74882.3735 0.34511.7704

CombinedDaylightandArtificialLightTest

UsingdaylightcoefficientsfromtheApril15daylighttestandartificiallightcoefficientsfrom

the artificial lighttest onFebruary 14, a test was performed ondata that had contributions

frombothdaylightandartificiallight.TheresultscanbefoundinFigure26,withacloserlookat

thedesktopmoteandthepredictedvaluesinFigure27.


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Figure26April7Combinedartificialanddaylighttest.

Figure27April7Combinedartificialanddaylighttest,Mote1andpredictedvalue.Meanandstandard

deviationofresiduals:-93.0469254.1348.


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Whiletheresultsarenotperfect,itisapparentfromthegraphthatthemajorityoferrorlies

inthehighluxlevelsofthedaylightregime,whenartificiallightwouldnotbenecessary.Inthe

absenceofhighluxdaylight,theresultissignificantlymoreaccurate,whichfollowsfromthe

previoustests.

Discussion

Theartificiallightsourcepredictionmodelisverypromisingandappearstohaveahighlevel

ofaccuracy.Theproposeddaylightmodelseemstohavedifficultywiththehighluxlevelsof

direct sunlight, which could be offset by careful mote placement and/or mote enclosure

constructiontoavoiddirectsunlightoraswitchtomorerobustlightsensorsthatcanhandlea

wider range of illuminance levels. On the other hand, this error could easily be taken into

accountwiththelightingcontrolalgorithm,as inmostapplicationsnoartificiallightwouldbe

needediftheluxiswithinthehighluxrange.Ifthehurdleofdirectsunlightisovercome,then

theresidualstandarddeviationassuggestedintheRadiancedaylighttestsdropstoabout175

lux,lessthanhalfoftheresidualstandarddeviationof416reportedin[15].Thisvalidatesthe

piecewise linear approach, as the model created in [15] assumed a time-invariant linear

transformationbetweenverticalfaadeilluminanceandhorizontalindoorilluminance.

Theimplicationsofarapidlydevelopedpredictivelightmodelonlightingcontrolsystems

would be significant. One major advantage is that this package has the ability to evaluate

controlschemesacrossmultipleusers.Byassigningapiecewiselinearfunctiontoeachuser,it

is a relatively simple task to evaluate the effect of different control schemes on workplane

illuminance throughout a large room. A simple method could be to iterate between several


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proposed control schemes and evaluate each in terms of user satisfaction and energy

efficiency.Fromtherethecontrollercanchoosetheoptimallightingscheme.

Anotherbenefitofthismodelissuchthat,whilenottothesamelevelofaccuracyasray-

tracingsoftware,themodelcanbedevelopedusingminimalinformation.Allofthemodelsin

this report were generated using just a days worth of data. An additional advantage this

package can provide to lighting control systems is accessibility and ease-of-use. Similar

predictivemodels,whilesuperiorinaccuracy,areseriouslylimitedinease-of-use.Mostexisting

predictivemodelsrequiresignificanthardwaresetupand/orroomgeometrymappingviaCAD

software,whichcanonlybedonebyprofessionals.Thesebothincreasecostofinstallationand

limitthemarketoftheproducts.Thispackageisplug-and-playtheusersimplyplacesmotesin

strategicplacesaroundtheroom,entersinthedesirednumberofmotestobefusedintoeach

workstation,and(optionally)inputsthenumberofinstalledlightingactuationmotes.Theuser

thenstartsthegenerationsoftware,whichthenrecordslightdataandmapsthecontrollable

anddaylightilluminancelevelstoeachworkstation.Althoughanelectricianwillberequiredfor

theinitialinstallationoftheactuationmotesinordertocontrolandtapintothelinepowerof

thelightingsystem,therestofthesystemcanbeinstalledbyanyonewithageneralknowledge

ofcomputers.

Futurework

The first major hurdle to overcome is the accuracy of the daylight model and the errors

presentinsensingdirectsunlight.Wewillnexttestwithappropriatecontrolalgorithmstoseeif

the accuracy achieved is sufficient for a personalized lighting system. If higher accuracy is


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requiredforhighluxlevels,wewillinvestigatenewlightsensorsorareconfiguredlightsensor

circuit that allows for sensing direct sunlight. In addition, research might be needed to

determine a set of placement rules that optimize performance of the sensors in a given

location.

Further testing is also required to determine the optimal partition size for the piecewise

linear function. In addition, creating the model over multiple days of data input will be

investigatedandcomparedtosingledayinput.

Testingneedsto beperformedtodetermine an easy-to-understanduser interface for the

modelgenerationpackage.Atthemoment,thesourcecodeisstrictlyformodelgenerationand

does not have a user-friendly interface. In addition, the code needs to be streamlined for

memorytoincreaseefficiency.

Additional research into the inclusion ofshadingcontrol orsimple shadeposition sensing

couldleadtoamorerobustmodel,asimplementedin[14]and[15].


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Acknowledgements

I would like to thank Alice Agogino, whose guidance and enthusiasm was crucial to the

performance of the group. I would like to thank Chandrayee Basu, whose diligence and

attentiontodetailwasinspiringaswellashelpful.I wouldliketothankAdrianaSeguradoand

SarahTeplitskyfortheirassistanceinRadiancetesting,whichcouldnothavebeencompleted

withouttheiraid.IwouldliketothanktheentireSmartLightingteamfortheirhelpandIhope

that this project can benefit their work. I would like to thank my parents, Jay and Sharon

Paulson,fortheirloveandsupportthroughoutmyacademiccareer.Lastbutcertainlynotleast

I wouldliketothank mybetter half,ChelseaEdwards; withouther encouragementand care

thisworkwouldnothavebeenpossible.


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References

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BuildingControlSystem,EnergyandBuildings,vol.33,pp.477-487,2001.

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AssociationConference,Beijing,China,2007,pp.1175-1181.

8) A.Mahdavi,M.Schuss,G.Suter,S.Metzger,S.Camara,andS.Dervishi,RecentAdvancesinSimulation-PoweredBuildingSystemsControl,EleventhInternational

IBPSAConference:BuildingSimulation2009,pp.760-766.


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9) M.Schuss,C.Prglhf,K.Orehounig,S.Dervishi,M.Mller,H.Wascher,andA.Mahdavi.PredictiveModel-BasedControlofVentilation,Lighting,andShadingSystems

inanOfficeBuilding,IBPSANews,2010,vol.20,pp.24-31.

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Taylor&FrancisGroup,2006.

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340.

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Lausanne,2003.Web.[AccessedApril26,2012].

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235-245,1993.

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[AccessedSeptember14,2011].

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Intelligence,W.Weber,J.M.Rabaey,andE.Aarts,Eds.NewYork:SpringerBerlin

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Appendix

AppendixA SourceCode

packagefusiontest;

/****@authorRyanPaulson*/importJama.Matrix;importjava.io.*;importjava.util.ArrayList;importjava.util.Arrays;importjava.sql.*;importjava.util.Calendar;publicclassFusionTest{

staticbooleanlastlineonly=false;//staticStringfileName="/home/ryan/test/";staticStringfileName="C:\\Users\\VooDoo\\Documents\\Berkeley\\Documents\\Lighting\\data\\test\\";staticintdelay=5000;//samplingrateinmilliseconds,usedforfillingingapsindatastaticStringthisLine;staticbooleanusewma=false;//booleansusedintestingvariousmethodsstaticbooleanusepreddata=false;staticbooleanlinearmodel=true;staticbooleanctrlswitching=false;staticbooleanwithconstterm=false;

staticbooleandeskmotespresent=true;staticdoublelatitude=37.777224;//latitudeandlongitude(SanFrancisco,CA)staticdoublelongitude=-122.417361;staticinttzoffset=8;//timezoneoffsetfromGreenwichMeanTimestaticintn=1;//numberofmotes/workstationstaticintworknum=1;//numberofworkstationsstaticintctrlnum=0;//numberofcontrollableinputsstaticintwinnum=1;//numberofmotesatwindowsstaticbooleandaylightonly=false;staticdoublepartitionsize=0.5;//definepartitionsizeforpiecewiselinearmodel

staticdoublemaxiterationang=151/partitionsize-1;staticStringampm;staticpublicvoidmain(String[]args){buildmodel();if(!daylightonly){for(intw=1;w


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}catch(IOExceptione){}}}for(intang=0;ang(136/partitionsize)/2){ampm="pm";

a=(136/partitionsize)-1/partitionsize-ang;}else{ampm="am";a=ang;}zone=0;if(a>-1000){if(a


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fw.close();}catch(IOExceptionerr){}}}if(!daylightonly){System.out.println("Ctrlfilespresent");break;}}System.out.println("End\n");

}staticpublicvoidprediction(intworkstation){Filectrlfile=newFile(fileName+"model/CtrlWinMatrix_total.csv");System.out.println("CtrlFileexists:"+ctrlfile.exists());if(!ctrlfile.exists()){return;}if(usepreddata){ctrlfile=newFile(fileName+"model/CtrlWinMatrix_"+workstation+".csv");}MatrixCtrlMatrix=newMatrix(1,1);try{BufferedReaderbr=newBufferedReader(newFileReader(ctrlfile));CtrlMatrix=Matrix.read(br);br.close();}catch(IOExceptione){System.out.println("Errorreading"+ctrlfile);}introw=CtrlMatrix.getRowDimension();intcol=CtrlMatrix.getColumnDimension();ArrayListpredlist=newArrayList();ArrayListanglist=newArrayList();ArrayListazilist=newArrayList();for(inth=0;h


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}catch(IOExceptione){}FileoutFile=newFile(fileName+"data/TimeSort_"+workstation+".csv");try{FileWriterfw=newFileWriter(outFile,false);for(inti=0;i


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packagefusiontest;

importJama.Matrix;

importJama.QRDecomposition;

importjava.io.*;

importjava.util.ArrayList;

importjava.util.Arrays;

publicclassMultRegModel{

publicstaticbooleanmatdata(intworknum,intctrlnum,intwinnum,doubleanglemin,Stringampm,StringfileName,booleanlinearmodel,booleanusewma,booleanctrlswitching,booleanwithconstterm,booleandeskmotespresent){

String[]linesplit=newString[4];

int[]maxdatalength=newint[worknum+ctrlnum+winnum];

StringthisLine;

ArrayListMoteReadings=newArrayList();

ArrayListControlReadings=newArrayList();

ArrayListControlReadingssq=newArrayList();

ArrayListWindowReadings=newArrayList();

ArrayListWindowReadingssq=newArrayList();

ArrayListWinTime=newArrayList();

if(deskmotespresent){

for(inti=0;i


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br.close();

}catch(IOExceptionerr){System.out.println("ErrorreadingControl"+(i+51)+""+anglemin+ampm);}

}}

for(inti=0;i


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}}

for(intk=0;k


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PrintWriterpw=newPrintWriter(Ctrlfullfile);

CtrlMatrix.print(pw,4,4);

pw.close();

}catch(IOExceptione){}

}else{CtrlMatrix=CtrlMatrixstart.getMatrix(0,ctrlrow-1,0,ctrlcol-2);}

QRDecompositionq=newQRDecomposition(CtrlMatrix);

System.out.println("CtrlMatrixfullrank?"+q.isFullRank());

System.out.println("WorkMatrix");

QRDecompositionq2=newQRDecomposition(WorkMatrix);

System.out.println("WorkMatrixfullrank?"+q2.isFullRank());

if(WorkMatrix.getRowDimension()!=CtrlMatrix.getRowDimension()){

System.out.println("Matrixdimensionsdonotmatch!");

double[][]b=newdouble[1][1];

MatrixB=newMatrix(b);

returnB;}

if(!q.isFullRank()||!q2.isFullRank()){

System.out.println("Matricesnotfullrank!\nVarycontrollableinputlevelsandtryagain");

MatrixB=newMatrix(1,1);

returnB;}

double[][]b=newdouble[1][CtrlMatrix.getRowDimension()];

MatrixB=newMatrix(b);

B=CtrlMatrix.solve(WorkMatrix);

introw=CtrlMatrix.getRowDimension();

intctrlcolumn=CtrlMatrix.getColumnDimension();

ArrayListQarraylist=newArrayList();

for(inti=0;i


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Filecoeffullfile=newFile(fileName+"model\\CoefCtrl_"+modelnum+".csv");

try{

BufferedReaderbr=newBufferedReader(newFileReader(coefwinfile));

CoefWin=Matrix.read(br);

br.close();


try{

BufferedReaderbr=newBufferedReader(newFileReader(coeffullfile));

Coef=Matrix.read(br);


intwinrow=CoefWin.getRowDimension();

intctrlrow=Coef.getRowDimension();

MatrixCoefAdj=CoefWin;

try{Predict=Ctrl.times(CoefAdj);

}catch(IllegalArgumentExceptione){System.out.println("Errorwithmatrixat:"+coefwinfile);

returnnull;}

returnPredict;

}

}


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packagefusiontest;importjava.lang.Math.*;importjava.sql.Timestamp;publicclassSunPos{publicstaticdouble[]getPos(longlongtime,inttzoffset,doublelatitude,doublelongitude){//sunpositionalgorithm

(AstronomicalAlmanac)Timestamptmstp=newTimestamp(longtime);Stringstr=tmstp.toString();String[]strarray=str.split("\\D");doubleyear=Integer.parseInt(strarray[0]);doublemonth=Integer.parseInt(strarray[1]);doubleday=Integer.parseInt(strarray[2]);doublehour=Integer.parseInt(strarray[3]);doubleminute=Integer.parseInt(strarray[4]);doublesec=Integer.parseInt(strarray[5]);doubledaysum=day;doubledeg2rad=Math.PI/180;//translatedate/timeintoastronomer'salmanactimeint[]m={0,31,28,31,30,31,30,31,31,30,31,30};

for(inti=0;i=60&&!(month==2&&day==60)){daysum+=1;}doubleh=hour+minute/60+sec/3600+tzoffset;doubledelta=year-1949;doublepastleap=Math.floor(delta/4);doublejd=2432916.5+delta*365+pastleap+daysum+h/24;doubletime=jd-2451545;

//Eclipticcoordinatesdoublemnlong=(280.46+0.9856474*time)%360;//meanlongitudeif(mnlong


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AppendixB LightSensorCircuitDiagram

C:100pFceramiccapacitor

R:68k0.25Wresistor


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AppendixC TelosBBlockDiagram[21]

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