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Pl1206340061687-4846 Print, 1687-4854 Online, 1687-4862 CD-ROM"ANfIS MODEL FOR THE TIME SERIES PREDICTION OF INTERIORDAYLIGHT ILLUMINANCE"September, 2006, Volume (6), Issue (3), Pages (35--40)Ciji Pearl Kurian, VI.George, Jayadev Bhat & Radhakrishna S AithalManipal Institute of Technology Manipal- 576104, [email protected] [email protected]!!!Q/ /\'V\vw. manipaJ. edu

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AIML Journal, Volume (6), Issue (3), September, 2006

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ANFIS MODEL FOR THE TIME SERIES PREDICTION OF

INTERIOR DAYLJGHT ILLUMINANCECiji Pearl Kurian, -V.I.George, Jayadev Bhat & Radhakrishna S Aithal

Manipallnstitute of Technology <'0Manipal -.576104, India

cpkOO [email protected], vier rect(rvvahoo.colllhit r:/ /lVwlV.n i~111illill.o:du

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Abstract c-

The increasing need for more energy sensitive andadap~ive systems for bJlilding lighting controlf'hasencouraged the use of more precise and delicatecomputational models. This paper presents a til1Jeseries prediction model for daylight interiorilluminance obtained u ing Adaptive neuro fuzzyinference system (ANFIS). Here the training data iscollected by simulation, using the globally acceptedlighting software Desktop Radiance. The modeldeveloped is suitable for adaptive predictive controlof daylight - artificial

clight integrated schemes

incorporating dimming and window shading control.Matlab's Fuzzy logic Tool box is used for thesimulations.

Keywords: ANFfS, Time series prediction, Daylightinterior illuminance, Aula regression model, daylight

factor, Automatic control, daylight artificial lightintegrated scheme, desktop radiance.

1. Introduction

To develop, automatic control strategies in additionto evaluate the visual and energy performanceprovided by daylight requires an accurate predictionof daylight entering a building. Daylight Factor' (DF),Daylight Coefficient' (DC), Useful DaylightIlluminance' (UDI), computer simulations", Averagedaylight factor'": .etc. are the various methodsadopted for the estimation of interior daylightilluminance. The OF approach has been in practicefor the last 50 years. The OF approach has gainedfavour owing to its simplicity, but it is not flexibleenough to predict the dynamic variations in daylightilluminance as the sun's position and sky conditionchange. OF is defined as the ratio horizontal internaldaylight illuminance to the exterior horizontalilluminance under CIE overcast sky. Overcast skiesare considered to provide the worst daylightingconditions and the sunlight is completely impeded

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c without any direct component. So DF approachcannot provide sufficient accuracy for automatedbuilding control schemes, it can be considered asdesigner's tool just in ·the planning stage.The DC concept developed by Tregenza PR5, whichconsiders the changes in the luminance of the skyelements, offers more effective way" of computingindoor daylight illuminance. As the sky is treated asan array of point sources, the daylight coefficientapproach can be used to calculate the reflectedsunlight, and is particularly appropriate for innovativedaylighting system with complex optical properties.In most daylighting computations the time consumingpart is the calculation of inter reflected light. Inconventional calculation, a single inter reflectedsimulation is carried out, but this process needs to berepeated for each change in sky luminancedistribution. In a DC based approach, aninterreflection calculation is carried out once for eachelement of sky, the process need not be repeated forchange in sky luminance distribution. This approachis even suitable for interiors with static shadingdevices with reflecting or refracting components.However, daylight coefficients are less suitable to usewith movable devices such as Venetian blinds or suntracking mirrors". This is' because a separate set ofcoefficients need to be found for each position of theshading system.The UDI approach, a new concept the useful daylightilluminance metrics are based on absolute values oftime varying daylight illuminance for a period of fullyear. But it is doubtful about the assessment of thecharacteristics of daylighting, with averaged hourly.irradiance or test reference years (TRY) data sets,when owing to rapid cloud movements and skyluminance patterns. It is certainly a valuablecontribution for computer simulations of annualdaylight changes and energy consumption predictions.But it will be more complex when taking intoconsideration automated blind system. Computersimulations, available in many varieties, are

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AIML Journal, Volume (6), Issue (3). September. 2006

appropriate for the planning stage to building designphase, but none or them arc suitable for real timemeasurement and control. But to build an intelligentmodelling concept, these computer simulations,endow with better assistance.Recently, Kittler d. al(' have proposed a new rangeof 15 standard sky luminance di tributions includingfive clear, five partly cloudy and five overcast skytypes. OIIW l.i ct. al.4 have proposed averagedaylight factor concept suitable Ior all thc above ~5standard skies. This proposition may be a usefulparadigm for planning and design of dayl.ightingystcrns, but again uncertain about the effectiveness

or this method 1'01' automated control strategy a wecannot predict the type 01' sky ahead. Time varying

C illuminance predictions, as used for meteorologicaldata sets, offer a more realistic account of truedaylighting conditions, tRan the previously menti0~edOF, DC and UDI. ANFJS shows very good learningand prediction capabilities, which makes it anefficient tool Rl deal with uncertainties encountered inthis venture. A variety of computer design tools are

( available for colleoting the data required for trainingthe Adaptive Neuro Fuzzy Inference system. Here,the software Desktop Radiance is used f..()rcollectingone full year data with different sky conditions. Theinterior illuminance level is calculated for a givenenvironment at any time of the year. Instead of usingmeasured values of illuminance levels, here we usedthe simulated data from the model created using theappropriate design tool. The illuminance levelsobtained in this way are used as a training data forANFIS to predict the six step ahead values for themodel under consideration. Hence, these predictedvalues identify how the system is going to behaveahead of a particular time. This paper highlights howANFIS can be employed to predict future values ofthe daylight availability.

2. ANFIS an Overview

In 1'993 Roger Jang, suggested Adaptive NeuroFuzzy Inference system' (ANFIS). ANFIS can rerveas a basis for constructing a set of fuzzy 'if-then'rules with appropriate membership functions togenerate the stipulated input-output pairs. Here, themembership functions are tuned to the input-outputdata and excellent results are possible.Fundamentally, ANFIS is about taking an initialfuzzy inference (FrS) system and tuning it with aback propagation algorithm based on the collection ofinput-output data. The basic structure of a fuzzyinference system consists of three conceptualcomponents: A rule base, which contains a selectionof fuzzy rules; a database, which defines themembership functions used in the fuzzy rules; and areasoning mechanism, which performs the inferenceprocedure upon the rules and the given facts to derivea reasonable output or conclusion.

These intelligent systems combine knowledge,techniques and methodologies from various sources".They possess human-like expertise within a speci~cdomain - adapt themselves and learn to do better 111

changing environments. In ANFIS, neural n.etworksrecognize patterns, and help ndaptutiou toenvironments. Fuzzy inference systems incorporatehuman knowledge and perform interfacing anddecision-making. ANFIS is tuned with a backpropagation algorithm based on the collection orinput-output data.

3. Chaotic Time Series PredictionI [ere the training data is obtained by simulating t.hSroom model using the lighting sollwarc DesktopRadiance!". Desktop Radiance is a¢)owerful lightinganalysis program designed to accurately predict theinterior illuminar.ce in complex building spaces due

,to daylight and electric lighting schemes. Thisenables the user to model interior daylight levels forany sun and sky ~ondition in spaces having winduws,·skylights or other standard fenestration systems. Theprog;;111 calculates lighting levels on all interiorsurfaces, as well as planes that can be artificiallypositioned to represent work surfaces or otherlocations of interest to user. Model depend on roomdimensions, room position, building data windows,outdoor obstructions, sky definition and sitedefinition. Since it takes care of all the relevantinformation for the prediction of interior illuminance,the data collected for the training will be veryeffective. Data is collected for one full year for four 0

different sky conditions. Out of the collected data wehave used 500 for training and another 500 for thevalidation of the model. With a proper trainingscheme and fine filtered data-sets, ANFIS is capableof predicting indoor illuminance values quiteaccurately since it learns from the training data. Thismeasurement- free architecture also makes itimmediately available for operation once they aretrained.In time series prediction the past values of daylight

illuminance up to time't' are used to predict the valueat some point in the future 't + P '. The standard

method for this type of prediction is to create amapping from D points of the time series spaced 'D.'apart: that is [x(t-(D-l)D.]. ...x(t-t1),x(t) to predict afuture value xCI + p) , where D = 4 and

fl = P = 6 are used. For off-line learning data isupdated and predicted only after presentation ofentire data set, or only after an epoch. The number oftimes the entire data set is used to check and validatethe prediction is called the epoch number. Matlab'sFuzzy logic toolbox" is used for the entire process oftraining and evaluation of FIS.

co

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AIML Journal, Volume (6), Issue (3), September, 2006

4. Model training and validation

In order to build an I\NFIS that can predict xCI + 6)from the past values of daylight levels, the trainingdata formatis [x(t-18),x(t-12),x(t-6),x(t);x(t+6)] .Training and checking data are shown in Figure I andInput membership functions for training are shown inFigure 2. There are four inputs and three membershipfunctions and therefore the number of rules is31\4 = 81 rules. In the generated FIS matrix thenumber of fitting parameters is 441, including 36.non-linear parameters and 405 Jinear parameters.Obviously most of the fitting is done by the linearparameters while the non-linear parameters aremostly for fine- tuning for further improvement. Theerror curves for both checking and training data areshown in Figure 3. Note that the training error ishigher than the" checking error, which is a commonprocess in non- linear regression; it could indicatethat Ihe training process ~s not close to finished yet.Figure 4 s'hows the time series preddction of daylightinterior illuminance obtained using ANFIS. Here the

odirl'erence between predicted values and measuredvalues are impossible to differentiate.

Table I shows the performance of non-linear ANFISmodels with different training data set, number ofmembership functions and prediction mode. Theseresults are obtained with 20 epochs, and ANFIS with500 training data and 3 gbell membership functionsshow better performance with 6 step ahead and 10step ahead prediction. Membership function 'gbell' isselected because of their smoothness and concisenotation and these curves have the advantage of beingsmooth and non-zero at all points. Table 2 shows theperformance of linear auto regression (AR) modelsfor different prediction modes. It is clear that thisparticular application, non- linear ANFIS

. outperforms the linear AR models. Selection ofnumber of membership functions, training data andepochs are obtained by trial and error.

Table I Comparison of the performance of ANFIS models

Predictio Trainin No. RMSE" RMSE,. Predn g data of n k error

gbells

I step 500 3 0.56 1.12 1.6ahead6 step 500 3 0.32 0.24 0.03ahead6 step 500 2 66.01 64.44 0.83ahead6 step 300 3 0.47 0.33 3.5ahead10 step 500 3 0.18 0.13 0.01head

Table 2 Comparison of the performance of A R models

Prediction Tr:tininJ.! d.lIa Pn'derror

I step ahead 500 0.196 step ahead 500 0.766 step ahead 500 0.91

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0°O~--~200~---«n~--~~~--~eoo~--~'~OX>~--~'200

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Figure I Training & Checking data usC<!for ANFIS prediction

Figure 5 shows the prediction error, it is found thaterror is 'maximum of I lux' which does not result anychange in the control signals (very small varietion 0

will "not be considered as it results too muchfluctuation of lighting, is really a disturbingexperience). So we stopped at this level ofperformance instead gof going for more extensivetraining. Figure 6 shows the non-linear surface, of theSugeno Fuzzy model for the problem of time seriesprediction. We have <Used Fuzzy logic Toolbox ofMATLAB to develop the ANFIS model with 4 inputsand single output as given in Figure 8.

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E 0.6'00.4.~ 0.2'".; 0 c..,,'000=--=:2000::S===:=~

tnpul3Figure 2 lnitial membership functions on inputs.

37

AIML Journal, Volume (6), Issue (3), September, 2006

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10 12 14 16 19 20Epochs

r, Eigurc 3 Error ,'iJrves; training crror(solid line) and checking

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Figure 4 Illuminance Predicted using ANFIS model

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~40~--~2OO~--~<Ol~--~600=---~ano~--~,OOO=---~'2OOTIme(stc:)

Figure 5 prediction errors

Figure 6 Input - Output SURFVIEW of A FIS scheme

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Figure 7 ANFI~ Structure

5. Matlab functions used for time series Ccc

prediction

GE FISt - It generates an initial Sugeno-type FISfor ANFIS training using a grid partition method. FIS= GENFIS 1 (DATA) generates a single-outputSugeno-type FIS using a grid partition on the data (noclustering). FIS is used to provide initial conditionsfor ANFIS training. DATA is a rnatrsc with N + Icolumns where the first N columns contain data foreach FIS input, and the last column contains theoutput data. By default, GENFIS] uses two ·'g-bell' C

type membership functions for each inputmembership function .Each rule generated byGENFIS 1 has one output membership function,which is of type 'linear' by default.ANFIS - ANFIS uses a hybrid learning algorithm toidentify the membership function parameters of c

single-output, Sugeno type FIS. A combination of. . c

least-squares and back propagation gradient descentmethods are used for training FIS membershipfunction parameters to model a given set ofinput/output data.EVALFIS This performs fuzzy inferencecalculations. Y = EVALFIS(U,FIS) simulates the FISfor the input data 'U' and returns the output data 'Y'.For a system with N input variables and outputvariables, 'U' is Mvby-N matrix, each row being aparticular input vector and Y is M-by-L matrix, eachrow being a particular output vector,

6. Significance of the schemeIn recent decades, technological development hasincreasingly automated switching/dimming andallowed integration of devices into, larger moreflexible systems. Model based predictive control is aninevitable part of automatic intelligent controls. Thiscomputational algorithm is developed as a part of theresearch towards robust control and optimization ofdaylight artificial light integrated schemes. A PCbased photo electrically controlled lighting scheme isgiven in Figure 8. The model discussed in this paper

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AIML Journal, Volume (6), Issue (3), September, 2006

helps to predict the future values of interiorilluminance and hence generate the control signals forthe dimming of lighting circuit in advance. This isactually a simplified form of ANFIS rnode!" for theprediction and control of light in integrated lightingschemes incorporating inverse control theory and softcomputing. In photo sensor based control strategy,sensors are located in .different zones of the room.Compared to individual photo sensor based controls,PC based intelligent scheme requires less number ofsensors and connections.

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PIIOTOSENSOR

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00

oElectric Main,

r01(tr to Lighting Circuito

Figure 8 photo electrically controlled lighting systemco

7. Conclusion

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The most important advantage of such a model is theability to predict natural system's behavior at a futuretime, which can be used for lighting econtrol, Theimplementation of ANFIS model is less complicatedthan that of sophisticated identification andoptimization procedures. Compared to fuzzy logicsystems, ANFIS has automated identificationalgorithm and easier design and compared to neuralnetworks it has less number of parameters and fasteradaptation. The non- linear characteristics of thedaylighting systems can be tolerably handled in theproposed system. This prediction could be utilized asinput for the artificial light and shading controls.Possibility to reduce the number of sensors andconnections improve the performance of controlstrategy. In the projects EDIFICO'o, NEUROBAT",DELTA 12 etc. deal about intelligent controllers basedon Fuzzy logic systems. In HISST01J neural networkprediction model is discussed. But ANFIS based timeseries prediction model for daylight interiorilllurninance is unique and novel as it is simple,reliable and easily accessible for different roomconditions.

8. References[I] A Nabil and .I Mardaljcvic , "Useful daylight

illuminance: a new paradigm for assessingdaylight in buildings.", Lighting Research &Technology, Volume 37, Number I, 2005, pp 41-59.

[2] DHW Li, CCS Lau and lC Lam, "Predictingdaylight Illuminance by computer simulation

techniques." , Lighting Research & Technology,Volume 36, Number 2, 2003, pp 113- 129.

[3] P.1 Littlefair, "Daylight coefficients for practicalcomputation of internal illuminances.", LightingResearch & Technology, Volume 24, Number 3,1992, pp 127-135.

[4) DHW Li and GHW Cheung, "Average daylightfactor for the 15 CIE standard skies.", LightingResearch & Technology, Volume 38, Number 2,2006, pp 137-152.

[5] Tregenza PR, Waters 1M, "Daylightcoefficients.", Lighting Research & Technology,Volume 15, 1983, pp 65-71. . .

[6] Kittler R, Darula S and Perez R, "A set ofstandard skies characterising daylight conditionsfor computer and energy conscious design.",Bratislava, Slovakia, 1998.

[7J .I.S.T Jang, C.T Sun and E.Mizutani, NCUfOFuzzy and Soil computing, Prentice HallInternational, Inc., 1997.

[8] Chin-Teng Li2? C.S.George Lee, Neural Fuzz~Systems, Pren~ce - Hall International, Inc. 1996.

[9) Mathworks. MATLAB Fuzzy Logic Tool box(

2.1 Manual, 2nd edition, 2000.o

[10] ED! FICI O.http://www.leso.cptl.ch/anglais/technit/edificio.pdf

[11]Mario El-Khoury, .lens Krauss, CSEM Neuchatel,Manuel Bauer, Nicolas, Morel, NEUROBA T,Predictive Neuro-fuzzy Building Control System,LESO, EPFb.-, 1%98.

[121 M. Bauer, J.Gcigingcr, W. l lcgctschwcilcr,G.Seikora, N. Morel, P.Wurmsdombler, DELTA,A blind controller using Fuzzy Logic, FinalOFEN report LESO, EPFL,1996.

r i31Scongju Chang. A lIybrid Computational Modelfor Building Systems Control. PhD thesis,School of Architecture, Carnegie MellonUniversity, 2000.

[14] Radiance reference manual, hltp://radsite.lbl.gov.[15] C P Kurian, S Kuriachan, J Bhat and R S Aithal ,

" An Adaptive neuro-fuzzy model for theprediction and control or light in integratedlighting schemes", Lighting Research &.Technology, Volume 37, Number 4, 2005, pp343-352.

Author Biography

Mrs. ClJI PEARL KURIAN is currentlyREADER in the Department or Electrical &Electronics l.nginccring, Manipal institute

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AIML Journal, Volume (6), Issue (3), September, 2006

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or Technology, Manipal. She obtained !3. Tech inElectrical Engineering, M. Tech in IlluminationTechnology and postgraduate diploma in informationTechnology and has 20 years of teaching experience.She is currently doing research work in the field ofRobust Control of Daylight - Artificial lightIntegrated Schemes. Her research interest includesIllumination Technology, Control Systems, SoftComputing and Computer simulations and systemidentification & control

e Dr. V.I .George, was born in Kerala,India 1961. He received ~raduatedegree in Electrical Engineering fromuniversity of Mysore, M.Tech degreein Instrumentation and Control

engineering from NIT. Calicut and received Ph Dfrom Bharathidasan University, in COQJrol systems.He i~ currently 'Prof: and Head, in the Department ofInstrumentation and Control engineering at MITManipal. His research interest are Instrumentation,Gontrol systems, H 00 csntrol, Robust control,MATLAB programming., Multivariable robust

( control, Optimization,« Guidance and control ofAero~pace vehicles.

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oDr. Jayadev Bhat, is a senior professorin the department of ChemicalEngineering, Manipal Institute ofTechnology, Manipal. He reccived Phl)

from lIT Mumbai. His research specializationincludes Process control, Chemical Reaction Engg,and Modelling & simulation.

Dr. Radhakrishna S. Aithal, Professorin Illumination Engineering, Departmentof Electrical & Electronics Engg. atManipal Institute of Technology, Manipal,

is serving in this institution since 1988. Having a totalteaching experience of 20 years at U.G.& P.G. level,he has published more than 27 research / reviewpapers in National/International Journals /Conferences.

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