Fuzzy Control of HVAC Systems Optimized by Genetic Algorithms

Transcription

1 Appled Intellgence 18, , 2003 c 2003 Kluwer Academc Publshers. Manufactured n The Netherlands. Fuzzy Control of HVAC Systems Optmzed by Genetc Algorthms RAFAEL ALCALÁ Department of Computer Scence, Unversty of Jaén, Jaén, Span alcala@ujaen.es JOSE M. BENÍTEZ, JORGE CASILLAS, OSCAR CORDÓN AND RAÚL PÉREZ Department of Computer Scence and Artfcal Intellgence, Unversty of Granada, Granada, Span jmbs@decsa.ugr.es casllas@decsa.ugr.es ocordon@decsa.ugr.es fgr@decsa.ugr.es Abstract. Ths paper presents the use of genetc algorthms to develop smartly tuned fuzzy logc controllers dedcated to the control of heatng, ventlatng and ar condtonng systems concernng energy performance and ndoor comfort requrements. Ths problem has some specfc restrctons that make t very partcular and complex because of the large tme requrements exstng due to the need of consderng multple crtera (whch enlarges the soluton search space) and to the long computaton tme models requre to assess the accuracy of each ndvdual. To solve these restrctons, a genetc tunng strategy consderng an effcent multcrtera approach has been proposed. Several fuzzy logc controllers have been produced and tested n laboratory experments n order to check the adequacy of such control and tunng technque. To do so, accurate models of the controlled buldngs (two real test stes) have been provded by experts. Fnally, smulatons and real experments were compared determnng the effectveness of the proposed strategy. Keywords: HVAC systems, fuzzy logc controllers, genetc tunng, multple crtera 1. Introducton In EU countres, prmary energy consumpton n buldngs represents about 40% of total energy consumpton and t has grown from 1974 over 13% overall. Ths energy consumpton s hghly dependent on weather condtons. Moreover, dependng on the countres, more than a half of ths energy s used for ndoor clmate condtons. On a technologcal pont of vew, t s estmated that the consderaton of specfc technologes lke Buldng Energy Management Systems (BEMSs) can save up to 20% of the energy consumpton of the buldng sector,.e., 8% of the overall Communty consumpton. BEMSs are generally appled only to the control of actve systems,.e., Heatng, Ventlatng, and Ar Condtonng (HVAC) systems. HVAC systems are equpments usually mplemented for mantanng satsfactory comfort condtons n buldngs. The energy consumpton as well as ndoor comfort aspects of ventlated and ar condtoned buldngs are hghly dependent on the desgn, performance and control of ther HVAC systems and equpments. On the other hand, a study performed n the frame of the ALTENER 1 project has shown that the use of automatc control for passve systems (e.g., shadng or free coolng) and ts ntegraton nto a BEMS could result n mportant energy savngs when compared to manual control [1]. Therefore, the role of automatc control s thus of major mportance. However, control systems n buldngs are often desgned and tuned usng rules of thumb not always compatble wth the controlled equpment requrements, energy

2 156 Alcaláetal. performance and users expectatons and demand. Therefore, an optmum operaton of these systems s a necessary condton for mnmzng energy consumptons and optmzng ndoor comfort. Moreover, n current systems, varous crtera are consdered and optmzed ndependently one from another: varable ar flows are used for Indoor Ar Qualty control, controlled ar temperature s used for thermal comfort management, and temperature set ponts are modfed for energy consumpton control. No global strategy for a coupled and ntegrated management of all these crtera has been yet effcently mplemented at an ndustral level. The use of rule-based controllers, specally Fuzzy Logc Controllers (FLCs) [2 4], would enable the mplementaton of multcrtera control strateges ncorporatng expert knowledge. However, a ratonal operaton and mproved performance of FLCs s requred for mplementng complex control technques. The use of smart settng and tunng technques for these controllers could mprove the energy savngs and the ndoor comfort by fttng prevously obtaned Knowledge Bases (KBs) provded by experts [5]. Genetc Algorthms (GAs) [6, 7] present the deal framework to tune these FLCs [8] when multple crtera are consdered. In ths paper, the use of GAs to develop smartly tuned FLCs to control HVAC systems concernng energy performance and ndoor comfort requrements s presented. To evaluate the goodness of the proposed technque, several FLCs ncorporatng the sad nnovatons have been produced and tested n laboratory experments n order to check the adequacy of such control and tunng technques. To run the proposed tunng technque, accurate models of the controlled buldngs (two real test stes) were provded by experts n order to assess the ftness functon. Ths paper s set up n the followng way. In the next secton, the bascs of HVAC systems and FLCs are presented, explanng how these knds of controllers can be appled to HVAC systems. In Secton 3, the HVAC systems tunng restrctons are ntroduced, proposng a partcular genetc tunng technque to solve ths problem. Secton 4 shows the experments performed n the two test stes. Frst, several experments are set up, showng the oddtes from each system to be controlled. Later, smulated and expermental results are analyzed. In Secton 5, some concludng remarks are ponted out, showng how ths methodology could be appled to other systems and progressvely mplemented at ndustral level. Fnally, a table wth the used acronyms s presented n Appendx A. 2. HVAC Systems and ther Control wth FLCs Nowadays, there are a lot of real-world applcatons of FLCs lke ntellgent suspenson systems, moble robot navgaton, wnd energy converter control, ar condtonng controllers, vdeo and photograph camera autofocus and magng stablzer, ant-sway control for cranes, and many ndustral automaton applcatons. In the specfc case of HVAC systems, most works apply FLCs to solve smple problems such as thermal regulaton, mantanng a temperature setpont [9 11]. However, n ths work varous dfferent crtera must be consdered n order to reduce the energy consumpton mantanng a desred comfort level. Therefore, many varables have to be consdered from the controlled system, whch makes t very complex. In the followng we wll see how we can solve ths complex problem by the applcaton of FLCs Heatng, Ventlatng, and Ar Condtonng Systems An HVAC system s comprsed by all the components of the applance used to condton the nteror ar of a buldng. The HVAC system s needed to provde the occupants wth a comfortable and productve workng envronment whch satsfes ther physologcal needs. Temperature and relatve humdty are essental factors n meetng physologcal requrements. When temperature s above or below the comfort range, the envronment dsrupts person s metabolc processes and dsturbs hs actvtes. Therefore, an HVAC system s essental to a buldng n order to keep occupants comfortable. A welldesgned operated, and mantaned HVAC system s essental for a habtable and functonal buldng envronment. Outdated, napproprate, or msappled systems result n comfort complants, Indoor Ar Qualty ssues, control problems, and exorbtant utlty costs. Moreover, many HVAC systems do not mantan a unform temperature throughout the structure because those systems employ unsophstcated control algorthms. In a modern ntellgent buldng, a sophstcated control system should provde excellent envronmental control [9].

3 Fuzzy Control of HVAC Systems 157 Outsde Ar A B C D E F G +/- Supply Ar Return Ar h H h -/+ Exhaust Ar J I Room Room 1 n Fgure 1. Generc structure of an offce buldng HVAC system. In Fg. 1, a typcal offce buldng HVAC system s presented. Ths HVAC system would comprse the followng components to be able to rase and lower the temperature and relatve humdty of the supply ar: A. Ths module mxes the return ar and the outsde ar to provde supply ar, and also closes outsde ar damper and opens return ar damper when fan stops. B. It s a flter to reduce the outsde ar emssons to supply ar. C. The preheater/heat recovery unt preheats the supply ar and recovers energy from the exhaust ar. D. A humdfer rasng the relatve humdty n wnter. E. Ths s a cooler to reduce the supply ar temperature and/or humdty. F. An after-heater unt to rase the supply ar temperature after humdfer or to rase the supply ar temperature after latent coolng (dehumdfer). G. The supply ar fan. H. The dampers to demand controlled supply ar flow to rooms. I. It s a heat recovery unt for energy recovery from exhaust ar. J. The exhaust ar fan. There are no statstcal data collected on types and szes of HVAC systems delvered to each type of buldng n dfferent European countres. Therefore, to provde an HVAC system compatble wth the ambance s a task of the BEMS desgner dependng on ts own experence Fuzzy Logc Controllers FLCs [2 4] are sutable for engneerng because ther nputs and outputs are real-valued varables, mapped wth a non-lnear functon. These knds of systems acheve an alternatve for those applcatons where classcal control strateges do not acheve good results. In many cases, these systems have two characterstcs: the need for human operator experence, and a strong non lnearty, where t s not possble to obtan a mathematcal model. Expert Control s a feld of Artfcal Intellgence that has become a research topc n the doman of system control, wth the purpose of avodng the aforementoned drawbacks wth respect to classcal control strateges. Fuzzy Logc Control s one of the topcs wthn Expert Control. Moreover, FLCs, as ntated by Mamdan and Asslan [3, 4], are now consdered as one of the most mportant applcatons of Fuzzy Set Theory proposed by Zadeh [12] n Ths theory s based on the noton of fuzzy set as a generalzaton of the ordnary set characterzed by a membershp functon µ that takes values n the nterval [0, 1] representng degrees of membershp to the set. FLCs typcally defne a non-lnear mappng from the system s state space to the control space. Thus, t s possble to consder the output of an FLC as a non-lnear control surface reflectng the process of the operator s pror knowledge. An FLC s a knd of Fuzzy Rule-Based System whch s composed of a KB that comprses the nformaton used by the expert operator n the form of lngustc control rules, a Fuzzfcaton Interface, that transforms the crsp values of the nput varables nto fuzzy sets that wll be used n the fuzzy nference process, an Inference System that uses the fuzzy values from the

4 158 Alcaláetal. Knowledge Base Fuzzfcaton Interface Inference System Defuzzfcaton Interface State Varables Controlled System Control Varables Fgure 2. Generc structure of a fuzzy logc controller. Fuzzfcaton Interface and the nformaton from the KB to perform the reasonng process, and the Defuzzfcaton Interface, whch takes the fuzzy acton from the nference process and translates t nto crsp values for the control varables. Fgure 2 shows the generc structure of an FLC. The KB encodes the expert knowledge by means of a set of fuzzy control rules. A fuzzy control rule s a condtonal statement n whch the antecedent s a condton n ts applcaton doman, the consequent s a control acton to be appled n the controlled system and both, antecedent and consequent, are assocated wth fuzzy concepts, that s, lngustc terms. The KB s comprsed by two components: the Data Base (DB) and the Rule Base (RB). The DB contans the defntons of the lngustc labels, that s, the membershp functons for the fuzzy sets. The RB s a collecton of fuzzy control rules, comprsed by the lngustc labels, representng the expert knowledge of the controlled system. Accordng to the form of the consequents of the fuzzy control rules, we can usually dstngush two man dfferent types of FLCs n the specalzed lterature, Mamdan FLCs [4] and Takag-Sugeno-Kang FLCs [13, 14]: Mamdan-type rules are composed of nput and output lngustc varables takng values on a lngustc term set wth a real-world meanng: R : If X 1 s A 1 and... and X n s A n then Y s B, Takag-Sugeno-Kang-type rules are based on the dvson of the nput space nto several fuzzy subspaces n whch each rule defnes a lnear nputoutput relatonshp by means of the real-valued coeffcents p j : R : If X 1 s A 1 and... and X n s A n then Y = p 1 X p n X n + p 0, where X and Y are the nput and output lngustc varables and the A j and B are lngustc labels wth fuzzy sets assocated specfyng ther meanng. Wthout lack of generalty, n the followng we consder an RB consttuted by m Mamdan-type fuzzy control rules R, = 1,...,m. The Fuzzfcaton Interface establshes a mappng between each crsp value of the nput varable and a fuzzy set defned n the unverse of the correspondng varable. Beng x 0 a crsp value defned n the nput unverse U, A a fuzzy set defned n the same unverse and F a fuzzfer operator, t works as follows: A = F(x 0 ). There are two man types of fuzzfcaton, the frst one beng the most usual: a Sngleton Fuzzfcaton: A s bult lke a sngleton fuzzy set wth support x 0 : { 1, f x = A x0 (x) = 0, otherwse. b Non-Sngleton or Approxmate Fuzzfcaton: In ths case, when x = x 0, A (x 0 ) = 1, and the membershp of the rest of the values for U decreases whle movng away from x 0. The Inference System s based on the applcaton of the Generalzed Modus Ponens, an extenson of the

5 Fuzzy Control of HVAC Systems 159 classcal Modus Ponens, proposed by Zadeh n the way: If X s A then Y s B XsA YsB The fuzzy condtonal statement If X s A then Y s B (wth X, Y beng lngustc varables and A, B fuzzy sets) represents a fuzzy relaton between A and B defned n U V, wth U and V beng the unverses of the varables X and Y, respectvely. The fuzzy relaton s expressed by a fuzzy set R whose membershp functon µ R (x, y) s gven by: x U, y V: µ R (x, y) = I (µ A (x),µ B (y)), wth µ A (x) and µ B (y) beng the membershp functons of the fuzzy sets A and B, respectvely and I beng a fuzzy mplcaton operator (rule connectve) modelng the fuzzy relaton. The consequent B, obtaned from the Generalzed Modus Ponens, s deduced by projecton on V by means of the Compostonal Rule of Inference, gven by the followng expresson n whch T s a connectve: µ B (y) = Sup x U {T (µ A (x), I (µ A (x),µ B (y)))}. When Sngleton Fuzzfcaton s consdered, the fuzzy set A s a sngleton. Thus, the Compostonal Rule of Inference s reduced to the followng expresson: µ B (y) = I (µ A (x 0 ),µ B (y)). As sad, the calculaton of µ A (x 0 ) conssts of the applcaton of a conjunctve operator T on µ A (x ): µ A (x 0 ) = T ( µ A1 (x 1 ),µ A2 (x 2 ),...,µ An (x n ) ). The Inference System produces the same amount of output fuzzy sets as the number of rules collected n the KB. These groups of fuzzy sets are aggregated by the also connectve, whch s modeled by an operator G. However, they must be transformed nto crsp values for the control varables. Ths s the goal of the Defuzzfcaton Interface. To descrbe ts operaton mode, we denote by B the fuzzy set obtaned as output when performng nference on rule R, and by y 0 the global output of the FLC for an nput x 0. There are two types of defuzzfcaton methods [15 17] accordng to the way n whch the ndvdual fuzzy sets B are aggregated through the also connectve, G: Mode A: Aggregaton Frst, Defuzzfcaton After. The Defuzzfcaton Interface performs the aggregaton of the ndvdual fuzzy sets nferred, B,to obtan the fnal output fuzzy set B : µ B (y) = G { µ B 1 (y),µ B 2 (y),...,µ B n (y) }. Usually, the aggregaton operator modelng G s the mnmum or the maxmum. After that, the fuzzy set B s defuzzfed usng any strategy D, lke the Mean of Maxma, or the Center of Gravty mostly: µ 0 = D(µ B (y)). Mode B: Defuzzfcaton Frst, Aggregaton After. It avods the computaton of the fnal fuzzy set B by consderng the contrbuton of each rule output ndvdually, obtanng the fnal control acton by takng a calculaton (an average, a weghted sum or a selecton of one of them) of a concrete crsp characterstc value assocated to each of them. More complete nformaton on FLCs can be found n [2, 18, 19] Applyng Fuzzy Logc Controllers to Heatng, Ventlatng, and Ar Condtonng Systems In buldng automaton, the objectve of a global controller would be to mantan the ndoor envronment wthn the desred (or stpulated) lmts. In our case, to mantan envronmental condtons wthn the comfort zone and to control the Indoor Ar Qualty. Furthermore, other mportant objectves could be requred, e.g, energy savngs, system stablty, etc. In any case, numerous factors have to be consdered n order to acheve these objectves. It makes the system beng controlled very complex and present a strong non lnearty. In these cases, FLCs are very robust tools whch would enable the mplementaton of multple crtera control strateges ncorporatng expert knowledge. As t s known, the desgn of an FLC s focused on the followng parameters and characterstcs: Control and controlled parameter selecton. Controlled parameters are varables whch are affected by the acton of a controlled devce recevng sgnals from a controller, whlst control parameters are varables whch may be used as nputs or outputs for a control strategy.

6 160 Alcaláetal. The composton of the FLC KB, that s, the set of fuzzy control rules formng the RB, and the set of lngustc terms n the fuzzy parttons of the nput and output spaces formng the DB. FLC archtecture and operators,.e., the rule type and archtecture of the FLC, the membershp functon type, the conjunctve operator and, the mplcaton functon, the defuzzfcaton mode, the characterstc value and the control crsp value. In ths way, after the BEMS desgner has defned the system to be controlled (buldng and HVAC specfcaton), the constructon of the correspondng FLC can be performed. Ths task can be subdvded n the followng subtasks: 1. Knowledge extracton method selecton. 2. Identfcaton of the controlled and the control parameters. 3. Identfcaton of global ndces for assessment of the ndoor buldng envronment. 4. Descrpton of number and archtecture of fuzzy controllers. 5. KB dervaton method selecton. 6. Selecton of the nference system operators. 7. KB dervaton. In the followng, several of these desgn tasks are analyzed more deeply The Composton of the FLC KB. As sad, the KB encodes the expert knowledge of the controlled system. Therefore, t depends on the concrete applcaton makng the accuracy of the desgned FLC drectly depend on ts composton. There are four modes of dervaton of fuzzy control rules, that are not mutually exclusve [19]. These modes are the followng: a Expert experence and control engneerng knowledge: It s the most wdely used, beng effectve when the human operator s able to lngustcally express the control rules he uses to control the system. Snce they present an adequate form to represent expert knowledge, these rules are usually of Mamdan type. b Modelng of the operator s control actons: The control acton s formed makng a model of the operator actons wthout ntervewng hm. c Based on the fuzzy model of a process: It s based on developng a fuzzy model of the system and constructng the fuzzy rules of the KB from t. Ths approach s smlar to that tradtonally used n Control Theory. Hence, structure and parameter dentfcaton are needed [20]. d Based on learnng and self-organzaton: Ths method s based on the ablty for creatng and modfyng the fuzzy control rules n order to mprove the controller performance by means of automatc methods. In these knds of problems (HVAC system controller desgn), the KB s usually constructed by usng the frst method,.e., based on the operator s experence. However, FLCs sometmes fal to obtan satsfactory results wth the ntal rule set drawn from the expert s experence [11]. Ths s because of: the gatherng and structurng of expertse s not easy, the settng up of the KB s an extensve task, and although a lot of knowledge s generc, the structure of the system to whch t wll apply vares substantally. Moreover, n our case the system beng controlled s too complex and optmal controllers are requred. Therefore, ths approach needs of a modfcaton of the ntal KB to obtan an optmal controller. To do so, a tunng on the semantc of an FLC prevously obtaned from human experence could be performed by modfcaton of the DB components. Other possblty s to perform the rule learnng together wth the dervaton of the DB components [21]. In ths work, FLCs wll be obtaned from human experence to subsequently be tuned by the applcaton of automatc tunng technques. Thus, the learnng method s a combnaton of the frst and fourth dervaton modes. On the other hand, to evaluate the FLC performance, physcal modelzaton of the controlled buldngs and equpments s needed. These models wll be developed by BEMS desgners usng buldng smulaton tools, and they wll have to be able to account for all the parameters consdered n the control process. The models wll be valdated usng expermental data correspondng to the real stes beng smulated. Many data correspondng to varous operaton condtons and heat or coolng load wll be prepared and compared wth smulatons. Thus, we wll have the chance to evaluate the FLCs desgned n the smulated system wth the desred envronmental condtons. In the same way, these system models can be used by the experts to valdate the ntal KB before the tunng process. On the other hand, t s

7 Fuzzy Control of HVAC Systems 161 of major mportance to assess the ftness functon n tunng Control and Controlled Parameter Selecton. Control and controlled parameters have to be chosen regardng the control strategy beng mplemented, the techncal feasblty of the measurements as well as economc consderatons. Fortunately, the BEMS desgner s usually able to determne these parameters. However, our ntenton s to develop both controllers and tunng strateges. Ths requres the use of explct parameters (drectly used as fuzzy controller s nputs or outputs) as well as mplct parameters used n the ftness functon developed n order to evaluate the performance of each controller. To dentfy the FLC s varables, varous parameters (control or explct parameters) may be consdered dependng on the HVAC system, sensors and actuators. We propose the followng parameters: Predcted Mean Vote (PMV) ndex for thermal comfort: Instead of only usng ar temperature as a thermal comfort ndex, we could consder the more global PMV ndex selected by nternatonal standard ISO 7730 (ncorporatng relatve humdty and mean radant temperature). Dfference between supply and room temperatures: Possble dsturbances can be related to the dfference between supply and mean ar temperature. When ventlaton systems are used for ar condtonng, such a crteron can be mportant. CO 2 concentraton: Indoor Ar Qualty was found to be crtcal. As CO 2 concentraton s a relable ndex of the polluton emtted by occupants, t can be selected as Indoor Ar Qualty ndex. It s therefore supposed that the buldng and HVAC system have been properly desgned and that occupants actually are the man source of polluton. Outdoor temperature also needed to be accounted for, snce durng md-season perods (or even mornngs n summer perods) ts coolng (or heatng) potental through ventlaton can be mportant and can reduce the necessty of applyng mechancal coolng (or heatng). HVAC system actuators: It drectly depends on the concrete HVAC system, e.g., valve postons, operatng modes, fan speeds, etc. To dentfy global ndces for assessment of the ndoor buldng envronment, varous (controlled or mplct) parameters may be measured dependng on the objectves of the control strategy. In these knds of problems, these parameters could be selected among: Thermal comfort parameters: Indoor clmate control s one of the most mportant goals of ntellgent buldngs. Among ndoor clmate characterstcs, thermal comfort s of major mportance. Ths mght nclude both global and local comfort parameters. Indoor Ar Qualty parameters: Indoor Ar Qualty s also of major concern n modern buldngs. It s controlled ether at the desgn stage by reducng possble pollutants n the room and durng operaton thanks to the ventlaton system. As our work s dedcated to HVAC systems, Indoor Ar Qualty s also an mportant parameter to account for. Energy consumpton: If approprate Indoor Ar Qualty and thermal comfort levels have to be guaranteed n offces, ths has to be acheved at a mnmum energy cost. Therefore, energy consumpton parameters would need to be ncorporated. HVAC system status: A stable operaton of the controlled equpments s necessary n order to ncrease lfe cycle and thus reduce the mantenance cost. Informaton of the status of the equpments at the decson tme step or on a longer perod must thus be consdered. Outdoor clmate parameters: Indoor condtons are nfluenced by outdoor condtons (ar temperature, solar radaton, wnd). Moreover, n an ar dstrbuton HVAC system, the power requred to rase or lower the supply temperature s a functon of outdoor temperature and humdty. Some of these parameters would thus need to be selected. The selecton of these parameters s a task concerned to the BEMS desgner as well. In our case, several controller archtectures nvolvng dfferent varables (control or explct parameters) have been developed dependng on the concrete testng ste (buldng) consdered (see Fg. 8 n Secton 8 for a concrete FLC archtecture and ts respectve parameters) FLC Archtecture and Operators. Archtecture and nference operators are factors that have a sgnfcant nfluence on the FLC behavor. The nfluence of several of these factors s analyzed n [16, 22], takng as a bass several control applcatons. As we have already seen, there are dfferent alternatves to select these factors. In ths secton, we wll

8 162 Alcaláetal. propose one of them attendng to ther advantages and weaknesses n some aspects of the KB dervaton process. We wll strve to apply operators as smple as possble wthout loss n the system accuracy. If so, these operators wll be easer to mplement and faster to compute. A dstrbuted herarchcal archtecture [23, 24], whch allows us to dvde the control tasks among dfferent modules, s proposed for our FLC. Usng the expert knowledge of the system to partton the controller permts an adequate control wth much fewer rules. Moreover, wth ths approach, the subsequent control tunng becomes easer snce the modfcaton of one parameter nfluences a smaller number of rules. In addton, t s recommended that three controllers (rather than a sngle one) be developed for each testng ste (n our case, by only changng the correspondng KB and mantanng the FLC archtecture). The reason for ths les n the mportant clmate varatons all over the year and the varable expectatons from occupants accordng to season. Therefore, one controller per season wll be developed consderng fall and sprng as the same knd of season. These controllers could be swtched accordng to dates or by mxng the three controllers ncludng a new meta-level n the herarchcal FLC. On the other hand, the remanng factors to be consdered are the followng: rule type, type of membershp functons, conjunctve operator, mplcaton functon, defuzzfcaton mode, characterstc value and control crsp value. The selecton of all of them s presented below. We propose the Mamdan-type rules because they provde a natural framework to nclude expert knowledge n the form of lngustc rules whch s of major mportance n our problem. In the same way, we propose the trangular membershp functons nstead of the trapezodal or the gaussan ones beng the former two lnear functons and the latter a non-lnear functon. Snce we expect a KB dervaton from experts, lnear functons are more ntutve and easer to manage. Moreover, as all of them acheve smlar results [25], we wll use trangular membershp functons, whch are smpler. Ther formula s: x a b a, f a x < b µ A (x) = c x c b, f b x c 0, otherwse. Among all the assocatve functons, t-norms are the more sutable to be used to defne the connectve and [16]. Two basc t-norms have been usually consdered: mnmum (Mn(x, y) = mn(x, y)) and product ( (x, y) = x y). Mnmum operator acheves cooperatve rules whle product operator acheves compettve rules. Snce we have recommended trangular membershp functons and a good co-operaton among rules s nterestng n ths case, the mnmum operator s proposed. On the other hand, from the results reported n [16], we recommend the use of the mnmum t-norm (Mamdan mplcaton) also as mplcaton operator (rule connectve) because t yelded the best behavor among the 41 mplcaton operators tested. We use Mode B defuzzfcaton (see Secton 2.2) because the defuzzfcaton method workng n ths mode s more robust, quck and easer to compute than those used n Mode A [16]. As characterstc value and control crsp value, we propose the Mean of Maxma weghted by the rule antecedent matchng, h, snce accordng to the results reported n [16], t renders the best accuracy among the 17 dfferent defuzzfcaton methods tested. 3. Genetc Tunng of FLCs for HVAC Systems The tunng of FLCs for HVAC systems presents two specfc restrctons that make t very partcular and complex. The followng subsectons address these problems proposng an effcent genetc tunng technque to develop smartly tuned FLCs dedcated to the control of HVAC systems HVAC Systems Tunng Restrctons Tunng problems are usually based on the avalablty of a predefned RB and a prelmnary set of membershp functons assocated to the fuzzy parttons, DB. Ther man am s to fnd a better set of parameters by only changng the DB components, thus reducng the soluton search space. We have followed the same approach but, n our case, the problem has two specfc restrctons whch make t very partcular and complex: The evaluaton s based on multple objectves (energy consumpton, occupants thermal comfort, Indoor Ar Qualty, peak load electrcal demand,...). Ths fact adds complexty to the search because we must obtan the best trade-off among the dfferent crtera.

9 Fuzzy Control of HVAC Systems 163 The controller accuracy s assessed by means of smulatons whch usually take a long tme. Ths causes the run tme of the algorthms to be extremely long. Although there are many genetc tunng technques [26 28], nether of them n ther orgnal proposed forms can be satsfactorly used because they do not properly address these restrctons. On the one hand, nether of them s ntally prepared to tackle wth multobjectve optmzaton (of course, they could be adapted to do so). On the other hand, the choces consdered for the GA components n these proposals (generatonal replacement, codng scheme, etc.) would make the optmzaton process extremely slow f appled drectly to a problem lke ours where the smulaton performed to evaluate each chromosome could take approxmately 200 seconds. Therefore, n order to solve these two problems, effcent tunng approaches consderng both restrctons should be developed. GAs can represent any type of fuzzy rules, present flexblty to work wth dfferent FLC archtectures and have a good capablty to nclude expert knowledge [8]. Furthermore, the ablty to handle complex problems, nvolvng features such as dscontnutes, multmodalty, dsjont feasble spaces and nosy functon evaluatons, renforces the potental effectveness of GAs n multcrtera search and optmzaton. For these reasons, GAs have been recognzed to be possbly wellsuted to multcrtera optmzaton [29]. From ths pont of vew, the frst restrcton wll be solved by usng multcrtera genetc optmzaton technques that wll allow us to work wth ftness functons comprsed by compettve objectves. In these cases, we could obtan not only an optmal soluton, but a possble soluton set. Dependng on the number of solutons obtaned, we can dstngush between those multcrtera approaches based and not based on aggregaton of the objectves. All classcal multcrtera aggregaton-based methods scalarze the objectve vector reducng t to a scalar optmzaton problem. Probably, the smplest of all these classcal technques s the objectve weghtng method. In ths case, multple objectve functons are combned nto one overall objectve functon by means of a vector of weghts. Ths technque has much senstvty and dependency toward weghts. However, when trustworthy weghts are avalable, ths approach reduces the search space provdng the adequate drecton nto the soluton space and ts use s hghly recommended. Therefore, the man queston to be consdered n ths approach s: have we trusted weghts to estmate the mportance of each objectve? In our case, trustworthy weghts were provded by the BEMS desgner. Therefore, the ftness functon wll be based on objectve weghtng. Furthermore, the use of fuzzy goals for dynamcally adaptng the search drecton n the space of solutons wll be consdered. It wll make the method robust and more ndependent from the weght selecton for the ftness functon. In order to solve the second restrcton, the use of effcent tunng methods s necessary. There are some approaches that ncrease the convergence speed of GAs: An objectve weghtng technque would reduce the search space when trustworthy weghts are used. A steady-state GA [30], that nvolves selectng two of the best ndvduals n the populaton and combnng them to obtan two offsprng. Ths approach mproves the convergence and smultaneously decreases the number of evaluatons. Reducng the populaton sze, the number of evaluatons s sgnfcantly decreased. However, ths sze must be large enough n order to mantan the dversty n the genetc populaton. Both, the multcrtera and the effcent tunng approaches wll be consdered n the proposed tunng method Genetc Tunng Proposal Takng nto account the exstence of trusted weghts and n order to beneft from them, we propose a smple steady-state GA wth the classcal real codng [31] and wth a ftness functon based on objectve weghtng, the so called Weghted Mult-Crtera Steady-State Genetc Algorthm (WMC-SSGA). In the followng subsectons, GAs and multcrtera genetc plan aggregaton approaches are brefly ntroduced to subsequently present the proposed WMC- SSGA Genetc Algorthms: The Steady-State Approach. GAs are general-purpose global search algorthms that use prncples nspred by natural populaton genetcs to evolve solutons to problems. The basc prncples of the GAs were frst lad down rgorously by Holland [32] and are well descrbed n many texts such as [7].

10 164 Alcaláetal. The basc dea s to mantan a populaton of knowledge structures that evolves over tme through a process of competton and controlled varaton. Each structure n the populaton represents a canddate soluton to the specfc problem and has an assocated ftness to determne whch structures are used to form new ones n the process of competton. Hence, a subset of relatvely good solutons are selected for reproducton to gve offsprng that replace the relatvely bad solutons whch de. Usually, offsprng replace ther parents for the next generaton (generatonal approach). These new ndvduals are created by usng genetc operators such as crossover and mutaton. The crossover operator combnes the nformaton contaned nto the parents ncreasng the average qualty of the populaton (explotaton), whle the mutaton operator randomly changes the new ndvduals helpng the algorthm to avod local optma (exploraton). On the other hand, the steady-state approach [30] conssts of selectng two of the best ndvduals n the populaton and combnng them to obtan two offsprng. Then, these two new ndvduals are ncluded n the populaton replacng the two worst ndvduals f the former are better adapted than the latter. An advantage of ths technque s that good solutons are used as soon as they are avalable. Therefore, the convergence s accelerated whle the number of evaluatons needed s decreased Multcrtera Genetc Optmzaton. Generally, multcrtera GAs only dffer from the rest of GAs n the ftness functon and/or n the selecton operator. The evolutonary approaches n multcrtera optmzaton can be classfed nto three groups [29]: plan aggregatng approaches, populaton-based non-pareto approaches, and pareto-based approaches. The method of objectve weghtng belongs to the former approach. Wthn ths approach, as conventonal GAs requre scalar ftness nformaton to work on, a scalarzaton of the objectve vectors s always necessary. In most problems, where no global crteron drectly emerges from the problem formulaton, objectves are often artfcally combned, or aggregated, nto a scalar functon accordng to some understandng of the problem, and then the GA s appled. Practcally, all the classcal aggregaton approaches can be used wth GAs. Optmzng a combnaton of the objectves has the advantage of producng a sngle compromse soluton, requrng no further nteracton wth the decsonmaker. The problem s that, f the optmal soluton can not be accepted, new runs of the optmzer may be requred untl a sutable soluton s found. However, when trustworthy weghts are avalable ths problem dsappears Weghted Mult-Crtera Steady-State Genetc Algorthm. WMC-SSGA conssts of a GA based on the well-known steady-state approach [30]. Its man characterstc s the fact that good solutons are used as soon as they are avalable, thus acceleratng the convergence and decreasng the number of evaluatons needed. Fgure 3 presents the flowchart of the proposed method, whle ts man components are ntroduced as follows Codng Scheme. WMC-SSGA uses a real codng scheme [31]. A soluton s drectly encoded nto a chromosome by jonng the representaton of the l labels of each one of the m varables composng the DB. For example: C = ( a1, b 1, c 1,...,a l, bl, cl ), C = C 1 C 2...C m. Begn = 1,...,m, t t+1 Fgure 3. no Varaton Intervals Defnton Intal Populaton Generaton Evaluaton t 0 Varaton Intervals Adaptng Converge no Selecton of the two parents Crossover Mutaton t > t max yes End Flowchart of the GA process. yes Restart Evaluaton

11 Fuzzy Control of HVAC Systems Intal Gene Pool. To make use of the exstng knowledge, the DB prevously obtaned from expert knowledge s ncluded n the populaton as an ntal soluton. The remanng ndvduals are randomly generated mantanng ther genes wthn ther respectve varaton ntervals. These ntervals are computed from the ntal soluton. Thus, the varaton ntervals of each defnton pont of the j-th label membershp functon of the -th varable, (a j, b j, c j ), are calculated as { l 1 a, la} 2 { ( = max c j 3, b j 2, a ) ( j 1, mn c j 2, b j 1, a )} j { r 1 a, ra 2 } { ( = max c j 2, b j 1, a ) ( j, mn c j 1, b j, a )} j+1 [ La, R ] j a j = [la 2 l2 a l1 a, ra r a 2 r a 1 ], 2 { l 1 b, lb} 2 { ( ) ( )} = max c, mn c j 2, b j 1, a j { r 1 b, rb 2 } { ( = max c j 1, b j, a j+1 [ Lb, R ] j b j = [lb 2 l2 b l1 b j 1, b j, a j+1 ) (, mn c j, b j+1, a )} j+2, rb r b 2 r b 1 2 { l 1 c, lc 2 } { ( = max c j 1, b j, a ) ( j+1, mn c j, b j+1, a )} j+2 { r 1 c, rc 2 } { ( = max c j, b j+1, a ) ( j+2, mn c j+1, b j+2, a )} j+3 [ Lc, R ] j c j = [lc 2 l2 c l1 c, rc r c 2 r c 1 ], 2 Notce that the assocated varaton ntervals of the correspondng extreme values, a j and c j, are calculated exactly as the ntervals for b j 1 and b j+1, respectvely. In a strong fuzzy partton (those n whch the membershp degree wthn the varable doman s kept to 1.0), the vertex of each label (b j ) concdes wth the nearest extreme ponts of ts neghbor labels, c j 1 = b j = a j+1. In ths case, only the vertex of the labels has to be consdered and the same varaton nterval can be defned for concdent ponts. Thus, the varaton ntervals are usually defned by the mddle ponts between the correspondent vertex and the vertex of the prevous and the next label. In our case, a more flexble approach s consdered and the vertex of the labels does not have to concde wth the nearest extreme ponts of ts neghbor labels (see Fg. 4). However, consderng these three ponts as a smple set for each label B j ={c j 1, b j, a j+1 } and takng nto account that they have the same varaton nterval, the same approach can be followed. In ths way, the mddle pont between two sets can be computed consderng the maxmum pont of the frst set and the mnmum pont of the second set. Therefore, to calculate the left extreme of the varaton nterval ], a j Label j-1 Label j Label j+1 L c j-1 c j-2 L b j L a j+1 R c j-1 R b j b b j-1 j b j+1 R a j a c j+1 j-1 a j+2 B j-1 B j B j+1 Fgure 4. Varaton nterval of b j, c j 1 and a j+1. for a concrete defnton pont x B j, we should consder the maxmum pont of B j 1 (lx 1 ) and the mnmum pont of the correspondng set B j (lx 2 ). And for the correspondng rght extreme, we should consder the maxmum pont of B j (rx 1 ) and the mnmum pont of B j+1 (rx 2). Fgure 4 graphcally depcts the varaton ntervals for those ponts contaned n B j followng the proposed approach. We have consdered that the vertex of the labels at the edges of the varables doman must concde wth the extreme ponts. These labels wll be symmetrcal wth respect to ther vertexes. Fnally, these ntervals are dynamcally adapted from the best ndvdual for each generaton, avodng the restrctons of fxng them from the begnnng of the GA run. Once these ntervals have been calculated, the genes out of range are randomly generated wthn them Evaluatng the Chromosome. The ftness functon was fnally selected wth the followng typcal components: O 1 Upper thermal comfort lmt: f PMV > 0.5, O 1 = O 1 + (PMV 0.5). O 2 Lower thermal comfort lmt: f PMV < 0.5, O 2 = O 2 + ( PMV 0.5). O 3 Indoor Ar Qualty requrement: f CO 2 conc. > 800 ppm, O 3 = O 3 + (CO 2 800). O 4 Energy consumpton: O 4 = O 4 + Power at tme t. O 5 System stablty: O 5 = O 5 + System change from tme t to (t 1), where system change states for a change n the system operaton,.e., t counts the system operaton changes (a change n the fan speed or valve poston). c j

12 166 Alcaláetal. Ths ftness functon s based on objectve weghtng. However, t has been modfed n order to consder the use of fuzzy goals for dynamcally adaptng the search drecton n the space of solutons, decreasng the mprovement possblty of those objectves whch approach ther goals n the frst place. Thus, a functon modfer parameter, δ (x), s used to penalze each objectve (takng values over 1.0) whenever ts value gets worse wth respect to the ntal soluton or to decrement the mportance of each ndvdual ftness value whenever t comes to ts respectve goal (takng values close to 0.0). Moreover, a penalzaton rate has been ncluded n δ (x), allowng the user to set up prortes n the objectves. Ths penalzaton rate, p, for each objectve s a real number from 0.7 to practcally 1, although the user specfes ths penalzaton from 0 to 1 (less and more prorty, respectvely), whch s more nterpretable. Therefore, the global ftness s evaluated as: F = 5 w δ (O ) O, =1 wth w beng the weghtng coeffcents to be set for each specfc problem. Two cases can happen n the correspondng ndvdual accordng to the value of the goal, g, and the value of the ntal soluton,. Dependng on these values, two dfferent δ functons wll be appled: The frst case s when the value of g s lesser than the value of, presentng the followng behavor (see Fg. 5): 0, f x g x g, f g δ (x) = < x < g x + 1, f x. x x p 1 In ths case, the objectve s not consdered f the goal s met and penalzed f the ntal results are worsen. The second case happens when the ntal value,, s lesser than the goal value, g (see Fg. 6): 0, f x < g δ (x) = x g + 1, x x p f g x. Fgure 6. δ (x) when g >. Now, the ntal results can be worsen whle the goal s met, and t s penalzed otherwse. Notce that the penalzaton functon allows the search to slghtly worsen the goal, mprovng other objectves to subsequently met the goal agan Genetc Operators. Snce WMC-SSGA uses the real codng scheme, the crossover and mutaton operators have been selected accordng to ths aspect: the Max-Mn-Arthmetcal crossover [33] and Mchalewcz s non-unform mutaton [7]. Let C v = (c 1,...,c k,...,c H ) and C w = (c 1,..., c k,...,c H ) be the two parents selected for crossover. Usng the max-mn-arthmetcal crossover, the resultng descendents are the two best of the next four offsprng: g C 1 = ac w + (1 a)c v C 2 = ac v + (1 a)c w C 3 wth c 3k = mn{c k, c k } C 4 wth c 4k = max{c k, c k }, 1 0 g Fgure 5. δ (x) when g. 0 wth a beng a constant parameter chosen by the GA desgner, and H beng the number of genes. In the case of the Mchalewcz s non-unform mutaton, a gene c k, wth a varaton nterval [L ck, R ck ], can be mutated as c k = c k + (t, R ck c k ) wth probablty 0.5, or as c k = c k (t, c k L ck ), otherwse. Wth t

13 Fuzzy Control of HVAC Systems 167 beng the current generaton, functon (t, y) returns a value n the range [0, y] such that the probablty of (t, y) beng close to 0 ncreases as the number of generatons ncreases. Ths functon s formulated as (t, y) = y(1 r (1 t T )b ), wth r beng a random number n [0, 1], T the total number of generatons, and b beng selected by the user to determne the dependency wth t. On the other hand, the selecton s based on the Baker s stochastc unversal samplng [34] together wth the eltst selecton Restart. Fnally, to get away from local optma, ths algorthm uses a restart approach [35]. Thus, when the populaton of solutons converges to very smlar results, the entre populaton but the best ndvdual s randomly generated wthn the varaton ntervals. Ths allows the algorthm to perform a better exploraton n the search space and to avod gettng stuck at local optma. 4. Experments and Results Obtaned To evaluate the goodness of the proposed technque, several experments have been carred out wthn the framework of the JOULE-THERMIE programme under the GENESYS 2 project. Two real test stes were avalable for the experments. The frst one s provded by both Centre Natonal de la Recherche Scentfque (CNRS) and the Ecole Natonale des Travaux Publcs de l Etat (ENTPE) from France, whlst the second belongs to a French prvate enterprse whose name must reman anonymous. From now on, the latter wll be called ATC test cells from Anonymous Test Cell. In both cases, the man objectve was the energy performance but mantanng the requred ndoor comfort levels. To run the proposed tunng technque, accurate models of these controlled buldngs were provded by experts for each season. These models assess the tunng algorthm for ftness computaton (see Secton and Secton 3). The results obtaned were very satsfactory, specally for the ATC summer-season model. However, due to the large number of results, we wll work only wth a cross-secton of the models, the CNRS ENTPE md-season and summer-season models, and the ATC summer-season model. In ths secton, the experments performed wth the sad models are presented. After the experments are set up showng the oddtes from each system to be controlled, smulated and expermental results wll be analyzed. Results wll be compared to the performance of the ntal expert FLC and to a classcal control technque, an On-Off controller Expermental Set-Up The frst task was to develop the thermal models of the two test stes that would be used n the complete learnng process. These test stes have dfferent characterstcs, specally regardng the composton of ther HVAC system. The man aspects of these stes are the followng: CNRS ENTPE test ste: Two sngle zone twn cells wth low thermal mass located n a large hall whose clmatc condtons can be controlled. The clmatc control of the large hall temperature make t possble to create artfcal clmate wth at least 8 C ampltude per day (e.g. from 23 to 31 C n summer condtons). The HVAC system s based on an ar supply ventlaton system wth a maxmum ar flow rate of 2000 m 3 /h (test cells volume s 80 m 3 ), wth drect expanson coolng and an electrc col controlled through a trac. Three fan speeds make t possble to slghtly control suppled ar flow rates (Fg. 7 llustrates these test cells). ATC test ste: Also located n France, ths test envronment conssts of two adjacent twn cells. Around these test cells walls, an artfcal clmate can be created at any tme (wnter condtons can be smulated n summer and vce-versa). These test cells are medum weght constructons. The HVAC system tested s a fan col unt suppled by a reverse-cycle heat pump, and a varable fan speed mechancal extract for ventlaton. These test cells were equpped wth all sensors requred accordng to the selected control and controlled parameter. The man achevement was the development of a full monozone buldng model. Ths model was bult from scratch wthn the Matlab-Smulnk envronment, beng developed as a general purpose model whch could be used for any other condtons, projects or applcatons n the future. However, n order to mprove ts performance, t was later customzed to sut each testng faclty (dfferent test stes and seasons). Ths customzaton (such as ncludng HVAC systems models)

14 168 Alcaláetal. AIR CONDITIONER Tsupply Ar duct 27 Tf Ar vent Ar vent Tr CO 2 T, HR Tout SUPERVISOR Acquston devce 184,5 Fgure 7. Representaton of the CNRS ENTPE test cells. mght be slghtly changed n the future n order to account for further experments and calbraton. The thermal smulaton was based on fntedfferences methods for the conducton model. The maxmum value for the tme-step of the smulaton was calculated usng the stablty condton accordng to the dscretzaton scheme. Smulaton tme step could be reduced to 60 seconds for these test cells. Due to the relatvely small thckness and large thermal conductve of wndows, the heat conducton model for the wndows was consdered constant. Convectve heat exchanges were based on constant heat convecton coeffcents. Radant temperature s calculated as a functon of surface temperature, weghted by ther relatve area. The HVAC system models were based on manufacturers data and modules developed n the frame of IEA task 22 provded by the Royal Techncal Insttute of Stockholm. Ftness functon and fuzzy nference algorthms (see Secton 2.3.3) were also added wthn these models. Data were avalable and used for models calbraton. The man problems n the calbraton concerned the modelzaton of the HVAC equpments as well as solar radaton effects on nternal heat gans. For each of the two testng stes, a dfferent herarchcal FLC archtecture was selected, regardless of the season consdered n each case. They are very slghtly dfferent n ther structure but all of them nclude at least PMV,CO 2 concentraton, prevous HVAC system status and outdoor temperature. In addton, the archtecture developed for the ATC FLC ncluded measures of thermal dscomfort, Indoor Ar Qualty dscomfort and energy consumpton for a 30 mnutes to 1 hour perod pror to the control decson. The ATC FLC archtecture s presented n Fg. 8. Another mportant outcome was the development of the ftness functon amng to characterze the performance of each tested controller towards thermal comfort, Indoor Ar Qualty, energy consumpton and system stablty crtera. Ths was presented n Secton However, n order to compare the dfferent solutons obtaned, the fuzzy goals wll not be consdered to compute the ftness value of the results presented n tables. Ths ftness functon was comprsed of fve crtera. The man problem was then to assgn approprate weghts to each crteron. The basc dea n ths weght defnton was to fnd fnancal equvalents for all of them. Such equvalences are dffcult to defne and there s a lack of confdent data on ths topc. Whereas energy consumpton cost s easy to set, comfort crtera are more dffcult. Recent studes have shown that an 18% mprovement n people s satsfacton about ndoor clmate corresponds to a 3% productvty mprovement for offce workers. Based on typcal salares and due to the fact that PMV and CO 2 concentratons are related to people s satsfacton, such equvalences can be defned. The same strategy can be appled to the systems stablty crteron, lfe-cycle of varous systems beng related to number of operatons. Based on ths, weghts can be obtaned for each specfc offce (or test cell n our case). Thus, trusted weghts for both test cells were obtaned. For CNRS ENTPE model the chosen values

15 Fuzzy Control of HVAC Systems 169 Fgure 8. Intal rule base and generc structure of the ATC summer-season fuzzy logc controller. were: w 1 = ,w 2 = ,w 3 = ,w 4 = and w 5 = For ATC model: w 1 = ,w 2 = ,w 3 = ,w 4 = and w 5 = Fnally, ntal KBs were obtaned from BEMS desgners for each model and season. Fgures 8 and 9 show the ntal RB and DB of the ATC FLC for summer-season. Ths ntal RB s fxed for all the tunng process. As ntal DB, we consdered symmetrcal fuzzy parttons of trangular-shaped membershp functons for each one of the m varables. These membershp functons were labeled from L1 toll, wth l beng the number of membershp functons of the -th varable. Notce that n Fg. 8 we represent the decson tables of each module of the herarchcal FLC consdered n terms of these labels. When the RB consders more than two varables (as n the case of modules M-2 n layer 2 and M-3a and M-3b n layer 3 where three nput varables are nvolved), the three-dmensonal table s decomposed nto three twodmensonal decson tables (one for each possble label of the frst varable) n order to clearly show ts composton. Therefore, each cell of the table represents a fuzzy subspace and contans ts assocated output consequent(s),.e., the correspondng label(s). The output varables are denoted n the top left square for each module. Notce that, when there are two consequents they are placed n the same cell (dvded by a dagonal lne) Experments Developed on Smulated Systems Three dfferent models were mplemented, the CNRS ENTPE md-season and summer-season models, and the ATC summer-season model. The FLCs obtaned

16 170 Alcaláetal. V3: Thermal preferance V1: PMV V13: Valve old poston V4: Tout-Tn V5: Requred heat V2: PMV t-1 V11: Thermal/Energy prorty V3: Thermal preferance V5: Requred heat V4: Tout-Tn V14: Valve new poston Intal fuzzy sets Tuned fuzzy sets V9: Integral of PMV V15: Fan col speed V6: CO V7: dco2/dt V10: Integral of energy consumpton V11: Thermal/Energy prorty V12: Ventlaton/Energy prorty V8: Ar qualty preference V16: Old extract fan speed V8: Ar qualty preference V12: Ventlaton/Energy prorty V17: New extract fan speed Fgure 9. Intal and tuned DB of the ATC fuzzy logc controller. from the proposed technque wll be compared among them, to the orgnal FLC wthout tunng and to a classcal On-Off controller for all of these models (the goals and mprovements wll be computed wth respect to ths classcal controller). The tunng strategy was assessed wth smulatons of 10 days wth the correspondent clmatc condtons. The results obtaned by the tunng method for each model are presented n the followng and they are pcked up from the last populaton obtaned from each strategy CNRS ENTPE Md-Season Model. In ths case, WMC-SSGA was run two tmes, frst from the ntal DB and then from the best DB obtaned n the prevous run. Each run had 500 teratons. Snce the tme requred for each model evaluaton was approxmately 200 seconds, the estmated run tme was four days for 500 teratons (computed as the product of the number of evaluatons per generaton, the evaluaton tme and the number of generatons). Our goal from experts was to acheve up to 15% energy savng wth a system stablty at least equal to

17 Fuzzy Control of HVAC Systems 171 Table 1. Results obtaned wth the CNRS ENTPE Md-Season model. Ftness PMV > 0.5 PMV < 0.5 CO 2 Energy Stablty ENTPE model Val. % Val. % Val. % Val. % Val. % Val. % On-Off Int. FLC Goals WMC WMC WMC WMC the On-Off controller stablty (2730) and PMV nferor crtera no more than 10% hgher than for On-Off (PMVnf < 105) see Table 1. However, the values mposed to the method were the followng: 0, 108, 0, and 2800, respectvely for ftness, PMV superor, PMV nferor, CO 2, energy and stablty. The penalzaton rates consdered were 0.0, 0.0, 0.0, 0.5 and 0.7, respectvely. From Table 1, and takng nto account the requested goals, experts consdered as the best soluton the frst obtaned by WMC-SSGA, that practcally meets the energy goal wth a 12%, and completely meets the remanng ones. On the other hand, the thrd soluton wth only an 8% of loss n stablty gets notorous mprovements n energy. It shows that even n the case of consderng an objectve-weghtng ftness functon, dverse ndvduals could be obtaned. Moreover, all these ndvduals ncrease the global ftness n more than 10% showng that all of them are very acceptable solutons CNRS ENTPE Summer-Season Model. In ths case, WMC-SSGA was run three tmes from the best DB obtaned n the prevous run. Each run had 500 teratons. The tme requred for each model evaluaton was approxmately 220 seconds. Therefore, the computaton tme was smlar to that of the md-season model. Our goal was to reduce PMV superor to 0 and to mantan HVAC stablty as close as possble to the On-Off controller (1160), wth energy not greater than (see Table 2). In ths way, the values mposed to WMC-SSGA were the followng ones: 0, 13.7, 0, 9000 and 1477, wth penalzaton rates of 1, 1, 1, 0.9 and 0.99, respectvely. In vew of the results shown n Table 2, all the goals but the stablty were practcally met. In ths case, the soluton presentng the best stablty value ( 25.1%) s the frst from WMC-SSGA, due to whch t was consdered the best one by the experts. However, ths soluton does not meet the PMV goal, thus makng the fourth soluton a good alternatve. In any case, values n stablty were mproved 100% from the ntal FLC results, and all the remanng goals have been practcally met; hence t s a very good result for ths tunng method. Table 2. Results obtaned wth the CNRS ENTPE Summer-Season model. Ftness PMV > 0.5 PMV < 0.5 CO 2 Energy Stablty ENTPE model Val. % Val. % Val. % Val. % Val. % Val. % On-Off Int. FLC Goals WMC WMC WMC WMC

18 172 Alcaláetal. It s notceable that energy savngs were about 15% for all the solutons, ths beng the man objectve n the project. Moreover, the mprovement of the ftness functon was about 13% whch show a good general behavor of the obtaned FLCs ATC Summer-Season Model. The tuned DBs presented n Table 3 for the Summer ATC model correspond to three ndvduals from the populaton at generaton 500 wth WMC-SSGA. The tme requred for each model evaluaton s approxmately 215 seconds. Therefore, once agan the algorthm was n the known tmes. The goals determned by the experts were to try to have 15% energy savng and global ftness reduced by 10% compared to On-Off control. Comfort parameters could be slghtly ncreased f necessary (no more than 1 pont for objectves 1 and 2). In ths way, the goal values mposed to WMC-SSGA were the followng ones: 1, 1, 7, and 1000, wth penalzaton rates of 1, 1, 1, 0.9, and 0.97, respectvely. Notce that these goals mposed to the algorthm are hgher than the ones ntally requred snce the ntal goals were easly met. In ths case, the goals have been easly met by WMC- SSGA. Moreover, the solutons present a desrable dversty that allowed us to select dfferent and nterestng FLCs. From the results n Table 3, experts selected the thrd DB from WMC-SSGA as the most promsng one. In ths case, the solutons obtaned present mprovement rates of about 20% n energy and ftness. Fgure 9 represents the ntal and the fnal DBs for the ATC FLC takng as fnal DB the thrd soluton from WMC-SSGA n Table 3. It shows that small varatons n the membershp functon parameters cause large mprovements n the FLC performance Method Analyss. The proposed technque has yelded much better results than the classcal On-Off controller, showng the good behavor that FLCs can acheve on these knds of complex multcrtera problems. The good results obtaned by WMC-SSGA can be attrbuted to the use of a method of objectve weghtng that can drectly gude to the best soluton, to the use of fuzzy goals for dynamcally adaptng the search drecton n the space of solutons, and to the restart approach gettng away from local optma. In the followng, a convergence analyss on WMC-SSGA wll be made n order to see the way n whch these factors affect to the ftness functon. Fgure 10 llustrates the evoluton chart of the ftness (orgnal expresson wthout consderng goals) and performance values obtaned by the WMC-SSGA method when tunng the ATC summer model. The chart has been generated obtanng the values of the best ndvdual (accordng to the ftness wth goals) n each generaton. The mprovement attaned by the tunng process wth respect to the On-Off controller soluton s represented n vertcal axs, where 0% stands for no mprovement, a negatve value for a worsened result, and a postve value for an mproved result. Analyzng the chart, we can observe how, after some ntal generatons where the algorthm s beng stablzed, the energy consumpton s gradually decreased untl the generaton 131 where almost 16% of mprovement s acheved. Stablty and hence ftness are also mproved durng ths perod. After that, a sgnfcant mprovement of the energy causes a worse stablty to be obtaned and the algorthm les n a local optmum Table 3. Results obtaned wth the ATC Summer-Season model. Ftness PMV > 0.5 PMV < 0.5 CO 2 Energy Stablty ENTPE model Val. % Val. % Val. % Val. % Val. % Val. % On-Off Int. FLC Goals WMC WMC WMC

19 Fuzzy Control of HVAC Systems 173 Ftness Improvement (%) (0.81,131) (-15.86,131) (11.48,250) (-19.44,250) (-12.13,402) (-17.79,402) PMVsup/nf/CO2 Energy Stablty (-1.88,500) (-19.66,500) Generaton Fgure 10. Evoluton of the WMC-SSGA n the ATC summer season model. where an mprovement of 19.4% for energy s obtaned at the expense of stablty, 11.5% worse than that of the On-Off controller. Ths s kept untl the generaton 402 where makng the energy slghtly worse nvolves fndng a good stablty result 12.1% better than the On-Off controller. Ths fact s derved from the restart acton performed some generatons before and t allows the algorthm to get away from the local optmum. From ths generaton to the end of the run, the energy s gradually mproved wth an acceptable stablty that entals decreasng the ftness functon value. The obtaned chart leads us to notce the convergence degree of the WMC-SSGA algorthm and analyze the tunng process from the effcency (tme-consumng) pont of vew. From ths angle, t s nterestng to verfy that a good soluton where the energy consumpton s mproved n a 15.9% wth the rest of performance values smlar to the On-Off controller s obtaned n less than 100 generatons. Ths means that good solutons are quckly obtaned and the process could be stopped n ths state f severe tme constrants are mposed Experments on the CNRS ENTPE and ATC Real Test-Cells Results are presented only for both CNRS ENTPE and ATC summer-season experments. From now on, experments s referred to the tests n the real stes. These experments were performed usng an FLC wth the best DB selected by experts for each model. At ATC (see Table 4), expermental results show that energy savngs are nterestng (12.5%). However, the stablty crteron s far more mportant than ntally expected. Ths could also be observed when new Table 4. ATC Summer-Season model: Smulaton results vs. test results (two days perod only). Ftness PMV > 0.5 PMV < 0.5 CO 2 Energy Stablty Smulaton On-Off Fuzzy Dfference (%) Experment On-Off Fuzzy Dfference (%)

20 174 Alcaláetal. Table 5. CNRS ENTPE Summer-Season model: Test results (four days perod only). Experment Ftness PMV > 0.5 PMV< 0.5 CO 2 Energy Stablty On-Off Fuzzy Dfference (%) smulatons have been performed wth the same clmatc condtons. The reason for ths s partly due to the CO 2 concentraton model. In the model, mxng s supposed perfect, whch s not the case n the real test cells. Despte the sensor beng located close to extract fan, CO 2 concentraton proved to be measured at much hgher values than expected. Fan operaton has therefore been more mportant and so dd stablty. For CNRS ENTPE (Table 5), excellent results have been obtaned wth up to 30% energy savngs. Expermental condtons created outdoor condtons from 21 C at nght up to 31 C durng the day. Outdoor ar coolng potental n the mornng s therefore qute mportant for these experments, whch explans these excellent results. On the other hand, stablty proved to be very bad. A possble reason for ths s a roundng problem wthn the controller. Actuator s operated wth a small number of postons (4 for fan speed and 3 for mode) and roundng s requred between fuzzy output and actuator sgnal, thus creatng unstabltes. Summarzng, t has been proved that energy consumpton s greatly reduced durng expermentaton n real tests cells. Moreover, comparsons between smulatons and experments are n good agreement for the BEMSs desgners. Therefore, the proposed technque has been demonstrated to be effectve to solve ths problem. 5. Concludng Remarks In ths paper, a GA has been consdered to develop smartly tuned FLCs dedcated to the control of HVAC systems concernng energy performance and ndoor comfort requrements. To evaluate the goodness of the proposed technque, several FLCs have been produced and tested n laboratory experments n order to check the adequacy of such control and tunng technques. To run the proposed tunng technque, accurate models of the controlled buldngs (two real test cells) were provded by experts. The proposed technque has yelded much better results than the classcal On-Off controller showng the good behavor that FLCs can acheve on these knds of complex multcrtera problems. Regardng the expermentaton n real test cells, comparsons between smulatons and experments are n good agreement for the BEMSs desgners, presentng sgnfcant energy savngs n both cases. It shows the effectveness of the proposed technque to solve ths problem. The proposed tunng algorthm has an nterestng advantage for ndustral applcaton: the consderaton of fuzzy goals to perform the multcrtera optmzaton. These fuzzy goals sgnfcantly mprove the tunng performance and make easer the expert s knowledge nterpretaton snce the specfcaton of goals,.e., when each objectve has been properly mproved, seems to be easy to gve. Furthermore, the use of these goals together wth the penalzaton factor nternally changes the ntal proposed weghts durng the evoluton of the WMC-SSGA algorthm, dynamcally adaptng the search drecton n the space of solutons. It makes ths method robust and more ndependent from the weght selecton for the ftness functon. The results of ths work should be ready for mplementaton n real buldngs for the specfc studed systems. An extended test of our prototypes wll however be necessary before product marketng. Moreover, approprate nterfaces wll have to be developed. Frst ndustral applcatons of our results could therefore start approxmately n two years. Ths methodology could then be appled to other systems and progressvely mplemented at ndustral level. However, the marketng potental should be partcularly studed as well as the way by whch they could be effcently extended to other equpments and buldngs.

21 Fuzzy Control of HVAC Systems 175 Appendx A. Acronyms Acronym BEMS HVAC FLC KB GA DB RB PMV WMC-SSGA CNRS ENTPE ATC Acknowledgments Meanng Buldng Energy Management System Heatng, Ventlatng, and Ar Condtonng Fuzzy Logc Controller Knowledge Base Genetc Algorthm Data Base Rule Base Predcted Mean Vote ndex for thermal comfort Weghted Mult-Crteron Steady-State Genetc Algorthm Centre Natonal de la Recherche Scentfque Ecole Natonale des Travaux Publcs de l Etat The Anonymous Test Cell from a French prvate enterprse Ths research has been supported by the European Commsson under the Genesys Project JOE-CT Ths work has been carred out wthn the framework of the JOULE-THERMIE programme under the GENESYS 2 Project sponsored by the European Commsson, Drectorate-General XII for Energy. We would lke to thank the GENESYS 2 project partners for ther careful mplementaton of the presented models and for ther valuable assstance. Notes 1. ALTENER Project: Promotng the use of renewable energy sources, European Commsson, Drectorate-General XVII for Energy. 2. GENESYS Project: Fuzzy controllers and smart tunng technques for energy effcency and overall performance of HVAC systems n buldngs, European Commsson, Drectorate-General XII for Energy (contract JOE-CT ). References 1. M. Bruant, G. Guarracno, P. Mchel, A. Voeltzel, and M. Santamours, Impact of a global control of boclmatc buldngs n terms of energy consumpton and buldng s performance, n Proc. of the 4th European Conference on Solar Archtecture and Urban Plannng, Berln, pp , D. Drankov, H. Hellendoorn, and M. Renfrank, An Introducton to Fuzzy Control, Sprnger-Verlag, E.H. Mamdan, Applcatons of fuzzy algorthms for control a smple dynamc plant, n Proc. of the IEEE, vol. 121, no. 12, pp , E.H. Mamdan and S.Asslan, An experment n lngustc synthess wth a fuzzy logc controller, Internatonal Journal of Man-Machne Studes, vol. 7, pp. 1 13, R. Alcalá, J. Casllas, J.L. Castro, A. González, and F. Herrera, A multcrtera genetc tunng for fuzzy logc controllers, Mathware and Soft Computng, vol. 8, no. 2, pp , D.E. Goldberg, Genetc Algorthms n Search, Optmzaton, and Machne Learnng, Addson-Wesley, Z. Mchalewcz, Genetc Algorthms + Data Structures = Evoluton Programs, Sprnger-Verlag, O. Cordón, F. Herrera, F. Hoffmann, and L. Magdalena, Genetc Fuzzy Systems: Evolutonary Tunng and Learnng of Fuzzy Knowledge Bases, World Scentfc: Sngapore, M. Arma, E.H. Hara, and J.D. Katzberg, A fuzzy logc and rough sets controller for HVAC systems, n Proc. of the IEEE WESCANEX 95, vol. 1, NY, 1995, pp P.Y. Glorennec, Applcaton of fuzzy control for buldng energy management, n Buldng Smulaton: Internatonal Buldng Performance Smulaton Assocaton 1, Sopha Antpols: France, 1991, pp S. Huang, and R.M. Nelson, Rule development and adjustment strateges of a fuzzy logc controller for an HVAC system Parts I and II (analyss and experment), ASHRAE Transactons, vol. 100, no. 1, pp , , L.A. Zadeh, Fuzzy sets, Informaton and Control, vol. 8, pp , M. Sugeno and G.T. Kang, Structure dentfcaton of fuzzy model, Fuzzy Sets and Systems, vol. 28, pp , T. Takag and M. Sugeno, Fuzzy dentfcaton of systems and ts applcaton to modelng and control, IEEE Transactons on Systems, Man, and Cybernetcs, vol. 15, no. 1, pp , A. Bardossy and L. Ducksten, Fuzzy Rule-Based Modelng wth Applcaton to Geophyscal, Bologcal and Engneerng Systems, CRC Press, O. Cordón, F. Herrera, and A. Peregrín, Applcablty of the fuzzy operators n the desgn of fuzzy logc controllers, Fuzzy Sets and Systems, vol. 86, pp , L.X. Wang, Adaptve Fuzzy Systems and Control. Desgn and Stablty Analyss, Prentce-Hall, P.P. Bonssone, Fuzzy logc controllers: An ntroducton realty, n Computatonal Intellgence: Imtatng Lfe, edted by J.M. Zurada, R.J. Marks II, and C.J. Robnson, IEEE Press, 1994, pp C.C. Lee, Fuzzy logc n control systems: Fuzzy logc controller Parts I and II, IEEE Transactons on Systems, Man, and Cybernetcs, vol. 20, pp , , R. Palm, D. Drankov, and H. Hellendoorn, Model Based Fuzzy Control, Sprnger-Verlag, L.A. Sánchez and J.A. Corrales, Nchng scheme for steady state GA-P and ts applcaton to fuzzy rule based classfers nducton, Mathware and Soft Computng, vol. 7, nos. 2/3, pp , J. Kszka, M. Kochanska, and D. Slwnska, The nfluence of some fuzzy mplcaton operators on the accuracy of a fuzzy

22 176 Alcaláetal. model Parts I and II, Fuzzy Sets and Systems, vol. 15, pp , , A.E. Gegov and P.M. Frank, Herarchcal fuzzy control of multvarable systems, Fuzzy Sets and Systems, vol. 72, pp , R.R. Yager, On the constructon of herarchcal fuzzy systems model, IEEE Transactons on Systems, Man, and Cybernetcs, vol. 22, pp , M. Delgado, M.A. Vla, and W. Voxman, On a canoncal representaton of fuzzy numbers, Fuzzy Sets and Systems, vol. 93, no. 1, pp , O. Cordón and F. Herrera, A three-stage evolutonary process for learnng descrptve and approxmatve fuzzy logc controller knowledge bases from examples, Internatonal Journal of Approxmate Reasonng, vol. 17, no. 4, pp , F. Herrera, M. Lozano, and J.L. Verdegay, Tunng fuzzy controllers by genetc algorthms, Internatonal Journal of Approxmate Reasonng, vol. 12, pp , C. Karr, Genetc algorthms for fuzzy controllers, AI Expert, pp , C.M. Fonseca and P.J. Flemng, An overvew of evolutonary algorthms n multobjectve optmzaton, Evolutonary Computaton, vol. 3, pp. 1 16, D. Whtley and J. Kauth, GENITOR: A dfferent genetc algorthm, n Proc. of the Rocky Mountan Conference on Artfcal Intellgence, Denver, 1988, pp ,. 31. F. Herrera, M. Lozano, and J.L. Verdegay, Tacklng real-coded genetc algorthms: Operators and tools for the behavour analyss, Artfcal Intellgence Revew, vol. 12, pp , J.H. Holland, Adaptaton n Natural and Artfcal Systems, The Unversty of Mchgan Press: Ann Arbor, 1975 (The MIT Press, London, 1992). 33. F. Herrera, M. Lozano, and J.L. Verdegay, Fuzzy connectves based crossover operators to model genetc algorthms populaton dversty, Fuzzy Sets and Systems, vol. 92, no. 1, pp , J.E. Baker, Reducng bas and neffcency n the selecton algorthm, n Proc. of the 2nd Internatonal Conference on Genetc Algorthms, edted by J.J. Grefenstette, Lawrence Erlbaum: Hllsdale, NJ, 1987, pp L.J. Eshelman, The CHC Adaptve Search Algorthm: How to Have Safe Search when Engagng n Nontradtonal Genetc Recombnaton, Morgan Kauffman: San Mateo, CA, José M. Benítez receved the M.S. Degree n 1994 and the Ph.D. Degree n 1998, both n Computer Scence and from the Unversty of Granada, Span. Currently, he s a Tenured Professor at the Department of Computer Scence and Artfcal Intellgence (DECSAI) of the Unversty of Granada. He s a member of the Research Group n Intellgent Systems. Along wth Dr. Castro and Dr. Mantas, he s a co-ordnator of the EUSFLAT Workng Group on Neuro-Fuzzy Systems. Hs research nterests nclude neural networks, fuzzy rule-based systems, neuro-fuzzy systems, cluster computng and e-commerce. He s a member of IEEE, IEEE Computer Socety, ACM and EUSFLAT. Jorge Casllas was born n Granada, Span, n He receved the M.Sc. degree n Computer Engneerng n 1998 and the Ph.D. n Computer Scence n 2001, both from the Unversty of Granada, Span. He s an Assstant Professor wth the Department of Computer Scence and Artfcal Intellgence, Unversty of Granada. Hs research nterests nclude fuzzy modelng, and learnng/tunng fuzzy systems for modelng, control, and classfcaton wth dfferent metaheurstcs. Rafael Alcalá receved the M.Sc. degree n Computer Scence n 1998 from the Unversty of Granada, Span. He s an Assstant Professor wth the Department of Computer Scence, Unversty of Jaén, Span. Hs research nterests relate to fuzzy modelng. Oscar Cordón receved the M.Sc. degree n Computer Scence n 1994 and the Ph.D. n Computer Scence n 1997, both from the Unversty of Granada, Span. He s an Assocate Professor wth the Department of Computer Scence and Artfcal Intellgence at the Unversty of Granada. He has publshed about 30 papers n nternatonal journals and he s

23 Fuzzy Control of HVAC Systems 177 co-author of the book Genetc Fuzzy Systems: Evolutonary Tunng and Learnng of Fuzzy Knowledge Bases (World Scentfc, 2001). As edted actvtes, he has co-organzed several specal sessons n nternatonal conferences and co-edted some specal ssues n nternatonal journals on Genetc Fuzzy Systems and Informaton Retreval. Hs current man research nterests are n the felds of: fuzzy rule-based systems, fuzzy and lngustc modelng, fuzzy classfcaton, genetc fuzzy systems, evolutonary algorthms, ant colony optmzaton, and nformaton retreval. He s currently an Assocate Professor n the Department of Computer Scence and Artfcal Intellgence, Unversty of Granada, Span. Hs doctoral dssertaton was n learnng fuzzy rules usng genetc algorthms. Hs research nterests nclude fuzzy logc, learnng systems, search algorthms, control and related applcatons. Dr. Pérez s a member of the Intellgence Systems Group. Raúl Pérez was born n He receved the M.S. (Computer Scence) and Ph.D. degrees from the Unversty of Granada, Span, n 1992 and 1997, respectvely.