Comfort-based fuzzy control optimization for energy conservationin HVAC systems

Sajid Hussain b, Hossam A. Gabbar a,b,n, Daniel Bondarenko b,Farayi Musharavati c, Shaligram Pokharel c

a Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa, Ontario, Canada L1H7K4b Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa, Ontario, Canada L1H7K4c Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

a r t i c l e i n f o

Article history:Received 9 February 2014Accepted 13 August 2014Available online 15 September 2014

Keywords:Energy conservationFuzzy logic controllersGenetic algorithmsHVAC systemsCo-simulations

a b s t r a c t

The work presented herein illustrates the use of computational intelligence and optimization approachesfor improving the fuzzy controller's performance in architectural heating, ventilation, and air condition-ing system (HVAC). The primary purpose of the performed research is to find a method to moderate theenergy use without compromising the comforts of the inhabitants. The control design used to meet thispurpose includes the predicted mean vote (PMV) and predicted percentage dissatisfied (PPD) indices.The software of choice for evaluating PMV and PPD is EnergyPlus. Whereas, for the fuzzy controller andthe evolutionary optimization framework, the co-simulation tool with building controls virtual test bed(BCVTB) is used in conjunction with Simulink. The ensuing comparison between EnergyPlus's thermalcontrol of HVAC and our fuzzy approach is the outcome of the present research.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Over 40% of the energy in large cities is used for heating orcooling the buildings’ environment (Siddharth, 2011). However,with the use of advanced building energy management systems(BEMS), it is possible to reduce architectural energy consumptionin a building by about 20% (Jiru, 2014). Such systems can manageenergy in three ways:

1. Effective control strategy for energy-related resources inside abuilding such as HVAC, lighting, electrical equipment, lifts, andescalators (Hussain & Gabbar, 2013),

2. Improvement in efficiency for energy-related resources (Yu &Chan, 2008), and

3. Energy efficiency of construction material used in buildings(Chung & Rhee, 2014).

For the efficient control of energy-related resources in a building,the use of a more suitable control strategy tactics is necessary. Overthe past, the different control strategies have been implemented,starting from classical mechanized controllers (Preglej, Rehrl,

Schwingshackl, Steiner & Igor Skrjanc, 2014) to Proportional–Inte-grate–Derivative (PID) controllers (Qu & Zaheeruddin, 2004), andpredictive and optimal controllers (Chen, 2001). Due to continuousimprovement in the control strategy, the adaptive controllers (Kumar,Aggarwal, & Sharma, 2013; Zaheer-uddin & Zheng, 2000) have beenincreasingly used for architectural energy conservation. In designingcurrent adaptive controller, various criteria like thermal regulation,energy consumption or comfort management are considered inde-pendently and in many cases only thermal regulation and comfortmanagement are given the importance. However, the advantage ofadaptive controllers is the ability to self-generate and adapt to thechanging climate conditions of the buildings (Holland, 1975). Thisaspect can be further improved by combining the adaptive controllerswith the fuzzy logic or rule-based algorithms, and thereby achieving asuperior performancewith respect to the classical or conventional PIDcontrollers (Bi et al., 2000; Taleghani, Tenpierik, Kurvers, & van denDobbelsteen, 2013).

The incorporation of expert knowledge in fuzzy logic control-lers makes them very robust tools for implementation. A fuzzycontroller uses non-linear mapping to transform the systems statespace to control space. Thereby, the output of a fuzzy controller isa non-linear control fuzzy surface that replicates expert's knowl-edge. However, the experts in the field regularly use the rules ofthumb to design the fuzzy logic controllers. As a result, theoutcomes of this method are not always compatible with system'sdynamics, energy performance measures, and user expectations.Therefore, there is a need to optimize the different objectives at

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journal homepage: www.elsevier.com/locate/conengprac

Control Engineering Practice

http://dx.doi.org/10.1016/j.conengprac.2014.08.0070967-0661/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: University of Ontario Institute of Technology, EnergySystems and Nuclear Science, Faculty of Engineering and Applied Science, 2000Simcoe Street North, FESNS-ERC-UOIT, Oshawa, Ontario, Canada L1H7K4.Tel.: þ1 905 721 8668x5497; fax: þ1 905 721 3046.

E-mail address: Hossam.gabbar@uoit.ca (H.A. Gabbar).

Control Engineering Practice 32 (2014) 172–182

the same time and simultaneously tune the fuzzy logic controllers. Bytuning the fuzzy rules and membership functions it is possible to finda better set of required parameters. A fuzzy logic controller (FLC)involving seven variables is optimized in (Hamdy, Hasan, & Siren,2011; Lukasse et al., 2009) to decrease energy consumption andmaintain a temperature set point. In (He, Zhang, & Kusiak, 2014),genetic algorithm (GA) is used to optimize thermal comfort, indoor airquality, energy consumption and system stability (Michalewicz, 1994).In Halawa and van Hoof (2012), a combination of FLC and GA is usedto optimize predicted mean vote (PMV) index for thermal comfortonly. In Navale and Nelson (2010), GA and FLC approach is used todevelop an adaptive FLC for a cooling coil. An FLC by GA is used forcontrolling greenhouse micro climate in Hahn (2011).

EnergyPlus is a popular tool used by many architects, civil andHVAC engineers, and construction contractors to control theheating and cooling set points for HVAC. However, EnergyPluslacks coordinated energy-saving control strategy. An ideal thermalcomfort control strategy would be to combine the energy-savingpotential of HVAC controls, based on thermal comfort model, withcomfort satisfactions of people inside a building.

Two main contributions of this research are as follows. The useof real-coded genetic algorithm (GA), restriction on FLC's member-ship functions (MFs) variation interval boundaries, and penaltymultiplier approach in objective function reduces the solutionsearch space for the GA and makes the GA to converge faster. Asdiscussed above, EnergyPlus is well-known and widely used soft-ware for evaluation of different mechanical systems in a building.A comparison and an improvement are given in control logic bycombining FLC with GA. Many existing approaches either discussthe EnergyPlus simulations or design their own controllers but donot make comparisons and evaluations with the widely usedEnergyPlus control strategies.

In Section 1.1, the basics of combining GAwith FLC are discussed.The co-simulation methodology is explained in Section 2. Section 3presents the case study used in this paper followed by the FLCdesign in Section 4 and simulations in Section 5. Finally, Section 6concludes the paper.

1.1. GA–FLC

We propose the combination of real codes GA with FLC in thefollowing ways. GA can evolve the fuzzy controller knowledge baseand fuzzy rule matrices (FRMs) to form a solution as explained inNavale and Nelson (2010). The GA method produces a multitude ofpossible FRMs. A fitness value is calculated based on multipleobjectives for each FRM and the best FRM is selected for imple-mentation in FLC. Fuzzy membership functions (MFs) shapes andpositions can also be tuned through GAs as demonstrated in He et al.(2014), Jiru (2014) and Lukasse et al. (2009). During the fuzzy MFstuning the different shapes (trapezoid, triangular, Gaussian etc.) andpositions are chosen arbitrarily and evaluated with their fitnessvalues. The MFs that have the best FLC performance are adaptedfurther by GA to evolve into the improved MFs population. In eithercase, the focus of GA is to provide the best FLC with the high fitnessvalue. In Fig. 1, the concept of using GAs with FLCs is shown.

The current work shows the evolution of the MFs through the GAfor architectural energy conservation. An initial FLC is designedbased on data returned by EnergyPlus (see Section 4) and the MFs ofthe FLC are evolved through GA in order to minimize certainobjective. The GA used in this study is real coded GA to decreasethe computational complexity and hence, increase the convergencespeed. To evolve the MFs of the FLC, the vertices of the MFs areconstructed into strings of chromosomes and the chromosomes arerandomly varied in order to construct an initial population for GAoptimization. The chromosomes contain the original floating pointvalues of MFs vertices for example the chromosome encoding for

output temperature input variable (Fig. 10) is constructed as follows:

OT : ½�30�30�20�15�20�15�10�15�10�5�10�50�50þ50þ5þ10þ5þ10þ15þ10þ15þ20þ15þ20þ25þ20þ25þ30þ25þ30þ40þ40�

Here each point inside is called a gene. The random variationsof the genes in chromosome are restricted within genes variationsintervals. These intervals are computed from the initially designedFLC's MFs. Thus, the variation intervals of each definition point ofthe jthlabel membership function of the ithvariable, (aij,b

ij,c

ij), are

calculated as (Fig. 2)

fl1a ; l2ag ¼ f maxðcij�3; bij�2; a

ij�1Þ; minðcij�2; b

ij�1; b

ijÞg

fr1a ; r2ag ¼ fmaxðcij�2; bij�1; a

ijÞ; minðcij�1; b

ij; b

ijþ1Þg

½Laij ;Raij� ¼ l2a�

l2a� l1a2

; r1aþr2a�r1a

2

" #;

fl1b ; l2bg ¼ fmaxðcij�2; bij�1; a

ijÞ; minðcij�1; b

ij; a

ijþ1Þg

fr1b ; r2bg ¼ fmaxðcij�1; bij; a

ijþ1Þ; minðcij; bijþ1; a

ijþ2Þg

½Lbij ;Rbij� ¼ l2b�

l2b� l1b2

; r1bþr2b�r1b

2

" #;

fl1c ; l2c ;g ¼ fmaxðcij�1;bij; a

ijþ1Þ; minðcij; bijþ1; a

ijþ2Þg

fr1c ; r2c ;g ¼ f maxðcij;bijþ1; aijþ2Þ; minðcijþ1; b

ijþ2; a

ijþ3Þg

½Lcij ;Rcij� ¼ l2c �

l2c � l1c2

; r1c þr2c �r1c

2

" #;

Notice that the associated variation intervals of the correspond-ing extreme values, aij and cij, are calculated exactly as the intervalsfor bij�1 and bijþ1, respectively. In a strong fuzzy partition (those inwhich the membership degree within the variable domain is keptto 1.0), the vertex of each label (bij) coincides with the nearestextreme points of its neighbor labels, cij�1 ¼ bij ¼ aijþ1. In this case,only the vertex of the labels has to be considered and the same

Fig. 1. GA tuning of fuzzy logic controller.

Fig. 2. Variation intervals of MFs.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182 173

variation interval can be defined for coincident points. Thus, thevariation intervals are usually defined by the middle pointsbetween the correspondent vertex and the vertex of the previousand the next label.

Different other concepts used in the implementation of the GAare as follows.

1.1.1. SelectionWe use a very simple selection approach called roulette-wheel

selection, also named as stochastic sampling with replacement.The individuals are mapped to contiguous segments of a line, suchthat each individual's segment is equal in size to its fitness. Arandom number is generated and the individual whose segmentspans the random number is selected. The process is repeateduntil the desired number of individuals is obtained (called matingpopulation).

1.1.2. Arithmetic crossoverReproduction involves creation of new offspring from themating of

two selected parents or mating pairs. It is thought that the crossover

operator is mainly responsible for the global search property of the GA.We used an arithmetic crossover operator that defines a linearcombination of two chromosomes. Two chromosomes, selectedrandomly for crossover, CGen

i and CGenj may produce two offspring,

CGenþ1i andCGenþ1

j , which is a linear combination of their parents as

CGenþ1i ¼ αCGen

i þð1�αÞCGenj

CGenþ1j ¼ αCGen

j þð1�αÞCGeni : ð1Þ

here CGenand CGenþ1are the individuals from old and new genera-tions respectively and α is a weighting factor, which governsdominant individual in the reproduction process. The value of αranges from 0 to 1.

1.1.3. Arithmetic mutationThe mutation operator is used to inject new genetic material

into the population and it is applied to each new structureindividually. A given mutation involves randomly altering eachgene with a small probability. We generate a random real valuewhich makes a random change in the Kth element selected

Fig. 3. Co-simulation in optimization framework. (a) The coupling mechanism and (b) the ptolemy environment.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182174

randomly of the chromosome. In arithmetic mutation, we againinvolve two chromosomes but mutate only one according to somemutation probability. The two chromosomes CGen

i and CGenj selected

for crossover in the previous section can undergo mutation andany one of them has equal probability of selection for mutation.Let say, two offspring, CGenþ1

i and CGenþ1j have been produced in

crossover operation and Kth element of CGenþ1i is selected for

mutation. The mutation will occur as follows:

CGenþ1i ¼ Ci1;Ci2; :::Ciðk�1Þ; αC

Genþ1jk þð1�αÞCGenþ1

ik ; :::;Ciðn�1Þ;Cin

D E:

ð2Þ

1.1.4. ElitismElitism is the process of selecting the better individuals, or

more to the point, selecting individual with a bias towards the

better ones. Elitism is important since it allows the solutions to getbetter over time.

2. Co-simulation methodology

In order to simulate under realistic conditions this prototype ofadaptive thermal comfort control, a building simulation tool wasrequired (Crawley et al., 2005). Such tool should be able to modelthe dynamical physical phenomena and environmental parametervariations in a building with a short time step (few minutes). Also,it would have to offer the possibility and flexibility to integrate acomplex control algorithm, to simulate the dynamic individualperceptions of thermal comfort for several occupants simulta-neously, and their interaction with the user interfaces. Presently,no single building performance simulation (BPS) tool, nor a system

Fig. 4. Large hotel (a) lobby layout and (b) large hotel 3D sketchup.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182 175

simulation tool, offers sufficient capabilities to tackle this type oftask. Therefore, co-simulation, that is, integration of, two simula-tors, a BPS tool and a system simulation tool may be adopted asone of the options. For this study, we have used EnergyPlus (thatprovides designs to use less energy and water), SketchUp (thathelps in the design of control areas of the building), Matlab (modelbased design software for computing) and the Building ControlsVirtual Test Bed (BCVTB, a co-simulation software that allowsintegration of different simulation programs and to link simulationprograms with hardware components). The BPS tool EnergyPlus iscoupled with Matlabs, through the middleware BCVTB based onPtolemy II environment. Although other BPS tools like TRNSYS17or ESP-r allow a similar coupling process, we selected EnergyPlusbecause of its building physics model, which is considered to bethe most sophisticated and realistic (Crawley, Hand, Kummert, &Griffth, 2005). EnergyPlus also integrates a recent module calledEnergy Management System (EMS), which allows developingcontrol algorithms which are able to drive controlled parametersdynamically as a function of feedback parameters. Meanwhile thepossibilities of this module are limited in comparison with puresystem simulation tools like Matlabs or Simulinks. One of thedrawbacks of EMS is its textual based language that limits itsusability and makes it tedious to develop or write complexalgorithms. On the contrary, Matlabs and Simulinks give moreflexibility and graphical methods for controller design. A couplinghas been used, for data exchange between EnergyPlus andMatlabs. In this coupling EnergyPlus sends the ambient tempera-ture, mean radiant temperature, and relative humidity at a timestep (assumed as 15 min) to Matlabs. Matlabs in turn will use thefuzzy algorithm to use these data to provide dynamical heatingand cooling set-point temperatures and then sends them back toEnergyPlus at the start of the next time step. The couplingmechanism is shown in Fig. 3.

In Fig. 3(a), the middleware BCVTB is symbolized by the twoarrows. Concerning the simulation platform Matlabs, it constitu-tes the fuzzy logic controller and evolutionary optimization basedon GA. In Fig. 3(b), the Ptolemy environment is shown withEnergyPlus and Simulinks, integrated. According to Trcka,Wetter, and Hensen (2009), this type of coupling methods givean excellent balance between calculation speed and accuracy.

3. Case study

The building model used in this study is a large hotel located inToronto, Canada where employees worked Monday to Sunday for24 h and there is always people activity in the hotel. Energyconsumption equipment is switched ON and OFF according tothe time of the day and weather conditions. The building has ninestories above the ground level, faces north, and has a total floorarea of 4448.42 m2. The building layout and 3D model (obtainedusing Google SketchUp) are shown in Fig. 4. The building is

divided into eight energy zones. The building zone types containsuper market, hotel lobby, hotel corridor, and hotel guest rooms asshown in Table 1.

All of the zones contain the HVAC system in the building. TheHVAC system is comprised of variable fan air flow with fanefficiency of 60.45% and motor efficiency of 93%. The electricchiller used in HVAC has chilled water temperature leaving HVACas 6.67 1C. The hot water boiler used has nominal thermalefficiency of 80%, design water outlet temperature at 82 1C withupper limit of 99oC. The cooling design supply air temperature forthe zones is 14 1C and heating design supply air temperature is40 1C. Zones heating and cooling supply air humidity ratios are0.0085 and 0.0080 kgWater/kgDryAir, respectively. The followingparameters of the building are used:

Exterior walls: Construction sequence: 100 mm Brick –

200 mm Heavyweight concrete – 50 mm Insulation board –

Wall air space resistance – 19 mm Gypsum board.Exterior windows: Construction sequence: 3 mm Glass clear –13 mm Air gap – 3 mm Glass clear.Exterior door: Construction sequence: Metal surface – 25 mmInsulation board.Exterior floor: Construction sequence: 50 mm Insulation board– 200 mm Heavyweight concrete.Exterior roof and Interior ceiling: Construction sequence:100 mm Lightweight concrete – Ceiling air space resistance –

Acoustic tile.Interior doors: Construction sequence: 25 mm Wood.

Table 2 shows the properties of the different materials used in theconstruction of the building. The wall air space thermal resistance andceiling air space thermal resistance are 0.15 m2 K/W and 0.15 m2 K/W,respectively. Thermal absorbance and solar absorbance for all thematerials used are 0.90 and 0.70, respectively. The conductivity of3 mm glass clear is 0.90W/m K, the solar transmittance at normal and

Table 1Large hotel zones and electric loads.

Zone Type Area (m2) Lights (W/m2) Elec. equipment (W/m2)

Zone 1 Banquet hall/Large café Total: 746.76 12.59 Banquet: 32.29Large café: 2.79Banquet: 446.71

Café: 301.27Zone 2 Kitchen 305.70 11.625 260.05Zone 3 Corridor 288.03 4.84 NoneZone 4 Super market/Office 744.47 11.62 5.164Zone 5 Lobby 697.99 10.65 4.09Zone 6 Guest rooms 5115.228 10.65 7.31Zone 7 Guest rooms 5237.96 10.65 7.31Zone 8 Store room 153.32 8.71 1.399

Table 2Properties of materials.

Material types Conductivity(W/m K)

Density(kg/m3)

Specificheat(J/kg K)

100 mm Brick 0.89 1920 790200 mm Heavyweightconcrete

1.95 2240 900

25/50 mm Insulation board 0.03 43 121019 mm Gypsum board 0.16 800 1090Metal surface (0.0008 m) 45.28 7824 500100 mm Lightweight concrete 0.53 1280 840Acoustic tile 0.060 368 59025 mm Wood 0.15 608 1630

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182176

solar reflectance at normal are 0.837 and 0.075, respectively. Otherproperties for the different loads in the building are as follows:

Lights load: Super Market Area: 16.4687 W/m2, HotelCorridor: 4.8437 W/m2, and Hotel Lobby and Guest Rooms:10.6562 W/m2.People load: Super Market Dry Storage: 0.035 persons/m2,Super Market Office: 0.053820 persons/m2, Super Market Sales:0.086111 persons/m2, Hotel Corridor: 0.010764 persons/m2,Hotel Lobby: 0.322917 persons/m2 and Hotel Guest Rooms:0.038427 persons/m2.

4. Design of initial fuzzy logic controller

For the sake of simplicity and computational complexityreduction, zone 5 or lobby (Fig. 5(a)) is used in this section.EnergyPlus is setup to run the simulation for zone 5 and toimplement a comfort control criteria to calculate the HVAC'sheating and cooling set-points. The set-points are calculated to

maintain the required thermal comfort. Thermal comfort inbuildings is usually evaluated using the operative temperature,which is, in a simplest way, defined as the average of the airtemperature and the mean radiant temperature (area weightedmean temperature of the surrounding surfaces). However, thethermal comfort is a more complicated quantity and, in accor-dance with ISO7730 (ISO7730:2005, 2005) and ASHRAE 55 (ANSI/ASHRAE Standard 55-2004, 2004) international standards, it canbe defined in a more general way, “The condition of mind whichexpresses satisfaction with the thermal environment”, pointing outthat it is a cognitive process influenced by various quantities,physical activity, physiological, and psychological factors. Therehave been a lot of studies on the calculation of the thermalcomfort conditions and the most widely used thermal comfortindex is the Predicted Mean Vote (PMV) index developed byFanger in the seventies (Fanger, 1970) who introduced a set ofequations which includes parameters that influence thermalcomfort of a person. Even if it was originally developed in climatechambers with steady-state environmental conditions, the PMVmodel was proved to remain a viable and accurate thermalsensation index in non-steady-state indoor environment like ours,

Fig. 5. Grid partitioning in fuzzy rule selection.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182 177

where fast environmental parameter changes are ordered by thecontrol algorithm. Thus, in our test building and for othernumerous centrally controlled HVAC buildings, this model is themore adapted tool for a personalized thermal comfort control, andeven more if we give the occupant the possibility to indicate hisown thermal sensation and consequently to act on the evaluationof his personal parameters. PMV model calculates in an indoorenvironment, a statistical thermal sensation and a statisticalcomfort acceptability rate (called predicted percentage of dissa-tisfied or PPD), according to four measurable environmentalparameters (ambient air temperature, mean radiant temperature,relative air velocity, and relative humidity), and two personalparameters (clothing insulation and metabolic rate). The PPD isdirectly calculated from the PMV according to the following

formula:

PPD¼ 100�95e�0:03353PMV4 �0:2179PMV2 ð3Þ

Numeric values of PMV are linked with thermal sensations accordingwith a seven-point thermal sensation scale (Table 3). Based on thisPMV/PPD model, three classes of thermal comfort have been definedin the international standard ISO7730 (Table 4). Class “A” is veryrestrictive and defines a comfort zone with PMVA �0:2;0:2½ �corresponding to PPDo6%. Class “B”, generally recommended,defines a comfort zone with PMVA �0:5;0:5½ �corresponding toPPDo10%. Class “C” is less restrictive with its comfort zone definedwithPMVA �0:7;0:7½ �, which corresponds to PPDo15% (Table 4).Simulations for a whole year with Toronto weather are performedwith parameters values in Table 3 and EnergyPlus is set toautomatically control HVAC's heating and cooling set-points in orderto maintain the PMV in class B, PMVA �0:5;0:5½ �. Results returnedby EnergyPlus are used to design initial fuzzy controller in Fig. 5. Theinitial fuzzy logic controller is designed using a grid-type fuzzypartitioning of the input space. In grid-type fuzzy portioningapproach, the domain interval of each input is divided into ante-cedent fuzzy sets with labels as shown in Fig. 5. Here, we representnumbers as labels. The advantage of grid based approach is thatfuzzy rule-based systems with high interpretability can be generatedfrom this type of fuzzy partitions. As discussed in Suzuki andFuruhashi (2001), homogeneous fuzzy partitions are more interpre-table than adjusted ones. Thus we use homogeneous fuzzy partitionsas shown in Fig. 5. Usually we do not know an appropriate fuzzypartition for each input. In general, each input may have a differentfuzzy partition as depicted in Fig. 5.

In Fig. 5, we use “Humidity Ratio”, “Ambient Temperature” and“Mean Radiant Temperature” returned by EnergyPlus as threeinputs for our fuzzy logic controller. The outputs are heating andcooling set-points. Initially, the fuzzy rules are constructedthrough the parameters and set-points calculated and returnedby EnergyPlus. Later on the rules and fuzzy membership functions(MFs) are evolved through GA in order to minimize a certain

Fig. 6. Linear fuzzy rules matrix.

Table 3Seven point thermal sensation scale ISO7730.

Thermal sensations PMV PPD

Hot þ3 100%Warm þ2 76.8%Slightly warm þ1 26.1%Neutral 0 5%Slightly cool �1 26.1%Cool �2 76.8%Cold �3 100%

Table 4Individual comfort classes: ISO7730.

ISO 7730 Operative temperature range PMV range PPD [%]

Class A 2271 070.2 o6Class B 2271.5 070.5 o10Class C 2272.5 070.7 o15

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182178

objective function. The heating and cooling set-points returned byEnergyPlus have equal values in this case. Also the end points ofthe membership functions are kept open or comparatively large inorder to cater for unseen and abrupt transients in the systemdynamics.

There are two outputs of the fuzzy controller, “Heating SetPoint” and “Cooling Set Point”. Based on information presented inFig. 5, fuzzy rule matrix is formulated. Since, there are almostlinear relationships depicted in Fig. 5, we will construct a linearFRM at initial stage as shown in Fig. 6. The control action (heating

Fig. 7. PMVs comparison – EnergyPlus vs GA FLC.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182 179

and cooling set-points) is divided into six membership functions,“25, 26, 27, 28, 29, and 30”. The control action is same for heatingand cooling set-points in this case. The initial rule selection is ofthe form

IF “Outdoor” is �20 AND “Humidity” is 0, AND “MRT” is 23THEN “Heating Set Point” is 30 AND “Cooling Set Point” is 30

The aim of a fuzzy logic system (or model) is the acquisition ofa knowledge (rule) base that represents the input–output functionof the real system or problem that we want to model. Theobjective of the learning process is to create and then fine tunethe fuzzy sets and rules so as to meet user specified performancecriteria of the system, in our case, overall energy consumptionkeeping in view the comfort conditions in certain range. In thiscontext the training/learning of the rules base can be consideredas parameters optimization problem. The parameters to be opti-mized are the centers and deviations of the fuzzy membershipfunctions and the consequence part coefficients of each fuzzy rule.To achieve the above mentioned goal, the FRM and MFs of the FLCare evolved by GA and a certain objective is optimized and theresult is called genetic fuzzy system.

4.1. Objective function formulation

A multi-objective problem consists of optimizing (i.e. minimiz-ing or maximizing) several objectives simultaneously, with anumber of inequality or equality constraints. The problem can beformally written as follows:

Find x¼ xið Þ 8 i¼ 1;2;…;Nparam such as f i xð Þ is a minimum ormaximum 8 i¼ 1;2;…;Nobj subject to gj xð Þ ¼ 0 8 j¼ 1;2;…;M andhk xð Þr0 8k¼ 1;2;…;K , where x is a vector containing the Nparam

design parameters, ðf iÞi ¼ 1;…:;Nobj, the objective functions and Nobj

the number of objectives. The objective function ðf iÞi ¼ 1;…:;Nobj

returns a vector containing the set of Nobj values associated withthe elementary objective to be optimized simultaneously. In ourcase, the objective function is formulated such a way that the totalenergy cost is lowered and at the same time the thermal comfort issatisfied. The thermal comfort is represented by PMV or PPD inthis study, which can be obtained from EnergyPlus as an output.The objective function or fitness function used for this study is asfollows:

min FObj ¼ ncECoolþnhEHeatð Þþμ max2 0; PMVj j�0:7f g� �; ð4Þ

where,ECoolis energy consumption for the HVAC when cooling isON and EHeat is energy consumption for the HVAC when heating isON. The terms nc and nh are cooling and heating normalizationfactors, respectively. PMV is predicted mean vote and is restrictedwithin PMVj jr0:7 for class C. The term μ max2 0; PMVj j�0:7f g� �

is

a penalty method to convert constrained non-linear objectivefunction to unconstrained one. Here, we do not want to deviatefrom the limits PMVj jr0:7. Penalty methods drop constraint ofnon-linear objective functions and substitute new term in theobjective functions penalizing infeasibility in the form

max or min FðxÞ ¼ f ðxÞ7μ∑ipiðxÞ ð5Þ

here, “þ” for minimize problems and “–” for maximize problems,μis a positive penalty multiplier and pi are functions satisfying

piðxÞ¼ 0 ifxsatisfiesconstrainti40 otherwise

�: ð6Þ

As an example, if the constraint PMVj jr0:7gets satisfied, the μpartin Eq. (4) becomes zero and if the constraints are not satisfied, asquared penalty need to be included in the objective function. Thisstep also makes unfit chromosomes in the population worse sothat they can be replaced or die soon and the population convergesoon. In Eq. (4) we presented a linear scalarization or weightedsum of a multi-objective optimization problem. The most commonapproach in multi-objective optimization problem is to formulateit as a single-objective optimization problem such that optimalsolutions to the single-objective optimization problem are Paretooptimal solutions to the multi-objective optimization problem.

5. Simulations and discussions

Simulations are performed using the co-simulation frameworkas presented in Section 2. Matlabs starts with the initial fuzzycontroller designed in Section 4 and uses GA to evolve the FLC'sMFs and FRM. During the optimization process, the optimizationprogram (GA in Matlabs) passes several times through thesimulation program (EnergyPlus) for the different combinationsof the given parameters, calculating the total energy used and thethermal comfort for every combination of the parameters. Fig. 7shows a comparison between EnergyPlus controlled PMV forcomfort class “C” ( PMVj jr0:7) and GA evolved PMV for thesame class.

Note that in EnergyPlus PMV, there is a deviation of the PMVbelow the negative limit of �0:7 three times in Fig. 7(a) but this isnot the case in GA evolved PMV. Fig. 7(b) shows the Fanger PPDplots for EnergyPlus and GA evolved FLC. Most of the time,EnergyPlus PPD is less than 15% confirming the operation in class“C” but it goes higher than 15% four times as shown in Fig. 7(b).Whereas, GA evolved PPD exhibit more spread or standard deviationas shown in Fig. 7(c) but is always below 15%. GA evolved PPD orPMV exhibits more fluctuations as compared to EnergyPlus PPD andhence saves energy. Since, operation in comfort class “C” allowsfluctuations of PMVj jr0:7 and PPDj jr15%, GA optimized FLCtakes advantage of these limits. It introduces more fluctuations inPMV and PPD but at the same time inside the class “C” comfortlimits. On the contrary, EnergyPlus controller is more restricted andintroduces fewer fluctuations within class “C” comfort class limitsand consumes more energy. The GA–FLC optimization process isused with the parameters of the GA as listed in Table 5.

Fig. 8 shows the objective function evolution process for 500generations and for different reproduction plans of the GA. It isevident from Fig. 8 that the reproduction plan with “steady-statereplace worst” is more promising in this case and converges in lessthan 300 generations.

Fig. 9 shows a comparison between MFs of initial FLC and GAevolved FLC. Note that in initial FLC, we have set equal values forthe MFs of heating set-points and cooling set-points but the GAevolved FLC changes them accordingly in order to minimize theobjective function. This shows that the equal values of heating and

Table 5GA and objective function parameters used in optimization process.

GA parameter Value

Population size 50No. of generations 500Significant digits 6Crossover probability 0.85Mutation mode One point – fixed rateMutation rate 0.01Reproduction plan Full generational replacement steady-state replace

random steady-state replace worstElitism ON/OFFnc 10�8 (determined from cooling energy consumed by

EnergyPlus for full year simulations)nh 10�10(determined from heating energy consumed by

EnergyPlus for full year simulation)μ 1–5 (exponential increase with 500 steps)

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cooling set-points set by EnergyPlus are not suitable in this case. Interms of energy consumption, GA FLC exhibits 16.8% decrease incooling energy and 18.1% decrease in heating energy as comparedto EnergyPlus and shown in Table 6. In Table 6, mean PPD andPMV values for GA evolved FLC are approximately same as that ofEnergyPlus, but peak PPD and PMV is reduced in the case of GAevolved FLC. The reason is obvious as the GA FLC exhibitsmore variations while operating in Class “C” as compared toEnergyPlus.

6. Conclusion

The two main restrictions in approaching energy conservationproblems are optimization of multiple objectives and algorithmrun complexity. GA can solve both problems efficiently if itsparameters are carefully chosen. We used here a real codedgenetic algorithm to speed up the operation and avoid unneces-sary delays in encoding/decoding to/from binary strings. In thispaper, we tune a fuzzy logic controller (FLC) through genetic

Fig. 9. Membership functions – initial FLC vs GA evolved FLC.

Fig. 8. Objective function evolution process – GAFLC.

S. Hussain et al. / Control Engineering Practice 32 (2014) 172–182 181

algorithm and minimize certain energy related and comfortrelated objectives. As compared to the EnergyPlus in-built comfortcontrol mechanism, FLC evolved with the help of GA operates inclass “C” with the predicted mean vote (PMV) limits ofPMVj jr0:7. However, the average PMV is reduced as comparedto EnegyPlus, the overall energy consumption is decreased by16.1% in case of cooling and 18.1% in case of heating as comparedto EnergyPlus.

Acknowledgment

This paper was made possible by NPRP Grant# (NPRP 5-209-2-071) from the Qatar National Research Fund (a member of QatarFoundation). The statements made herein are solely the respon-sibility of the authors.

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Table 6Comparisons: GAFLC vs EnergyPlus.

Parameter GAFLC EnergyPlus

Mean PPD (%) 8.3310% 8.4748%Peak PPD (max %) 16.1074% 25.4877Mean PMV �0.3075 �0.3735Peak PMV (max/min) 0.6093/�0.7265 0.4665/�0.9849Heating energy (J) 3.942�1010(18.1% decrease) 4.8162�1010

Cooling energy (J) 1.658�108 (16.1 decrease) 1.994�108

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