Energy xxx (2011) 1e10. Contents lists available at ScienceDirect. Energy. journal homepage:

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1 Eergy xxx (2011) 1e10 Ctets lists available at ScieceDirect Eergy jural hmepage: Multi-bjective ptimizati f HVAC system with a evlutiary cmputati algrithm Adrew Kusiak *, Fa Tag, Guagli Xu Departmet f Mechaical ad Idustrial Egieerig, 3131 Seamas Ceter, The Uiversity f Iwa, Iwa City, IA , USA article if abstract Article histry: Received 24 July 2010 Received i revised frm 15 Jauary 2011 Accepted 20 Jauary 2011 Available lie xxx Keywrds: Data-drive mdels Evlutiary cmputati algrithm HVAC system ptimizati Eergy savigs A data-miig apprach fr the ptimizati f a HVAC (heatig, vetilati, ad air cditiig) system is preseted. A predictive mdel f the HVAC system is derived by data-miig algrithms, usig a dataset cllected frm a experimet cducted at a research facility. T miimize the eergy while maitaiig the crrespdig IAQ (idr air quality) withi a user-defied rage, a multi-bjective ptimizati mdel is develped. The slutis f this mdel are set pits f the ctrl system derived with a evlutiary cmputati algrithm. The ctrllable iput variables d supply air temperature ad supply air duct static pressure set pits d are geerated t reduce the eergy use. The results prduced by the evlutiary cmputati algrithm shw that the ctrl strategy saves eergy by ptimizig peratis f a HVAC system. Ó 2011 Elsevier Ltd. All rights reserved. 1. Itrducti Reducig the eergy csumpti f HVAC (heatig, vetilatig ad air cditiig) systems is essetial, as it cstitutes ver 50% f the buildig eergy csumed i the US [1]. The perati f HVAC system is a critical activity i terms f ptimizig the ctrl settigs t reduce the eergy csumpti, imprvig the system efficiecy, ad preservig the thermal cmfrt fr the ccupats. The perfrmace f the existig HVAC system ca be largely imprved by adjustig the ctrl set pits t maximize the verall system capacity ad efficiecy. This has itesified the research i mdelig ad ptimizati f eergy use by HVAC systems. Aalytical appraches [2] ad simulati-based methds [3] were studied t mdel thermal behavir f buildigs. Differet ctrl strategies, icludig experimetal determiati ad itelliget ctrl were applied [4,5]. Zheg ad Zaheer-Uddi [6] frmulated the thermal prcess i a VAV (variable air vlume) bx with cstraits ze humidity. This prvided daily peratig strategies achievig ptimal utdr air-flw rates ad eergy savigs. Wag ad Ji [7] prpsed a ctrl strategy based a geetic algrithm t search fr the ptimal settigs f multiple variable prcesses. Differig frm the data-drive mdels, the ptimizati algrithm was applied the icremetal mdels, * Crrespdig authr. Tel.: þ ; fax: þ address: adrew-kusiak@uiwa.edu (A. Kusiak). with self-tuig esurig the accuracy f the mdels. Fg et al. [8] discussed eergy reducti by usig a evlutiary prgrammig apprach t suggest ptimal settigs i respse t the dyamic clig lads ad chagig weather cditis. Ke ad Mumma [9] studied the impact f tuig the supply air temperature set pit i a VAV eergy csumpti. Based the steady-state mdels, Nassif et al. [10,11] applied evlutiary algrithms t e- ad twbjective ptimizati f a HVAC system, ad the supervisry ctrl strategies resulted i eergy savigs. Msslly et al. [12] examied three ctrl strategies develped by a geetic algrithm. Sigificat eergy savig were achieved by varyig system parameters. Kusiak ad Li [13] applied a evlutiary strategy algrithm t slve a bi-bjective ptimizati mdel t miimize the clig utput while maitaiig the crrespdig thermal prperties. A HVAC system is a cmplex, liear, discrete system ctaiig umerus variables ad cstraits. Therefre, the mdelig ad ptimizati f a HVAC system is a challege fr traditial mathematical mdels [14] ad simulati appraches [15]. I this study, several data-miig algrithms are applied t build the predictive mdels. A multi-bjective evlutiary cmputati algrithm is prpsed fr geeratig ptimal ctrl strategies f a existig HVAC system. Extesive test rus have bee perfrmed t determie the accuracy f the mdels. The ptimized set pits are used t miimize the eergy csumpti by maximizig the HVAC system efficiecy. Differet ctrl strategies are give by weightig the bjective fuctis t satisfy /$ e see frt matter Ó 2011 Elsevier Ltd. All rights reserved. di: /j.eergy

2 2 A. Kusiak et al. / Eergy xxx (2011) 1e10 the preferece f maagemet peratis. The eergy use required fr actual peratis, alg with the predictive results btaied frm the traied ad validated mdels, is cmpared t the e attaied thrugh the ptimizati ctrller set pits. The resultig eergy savigs are preseted. 2. HVAC system structure ad descripti The HVAC system beig ivestigated is perated by the ERS (Eergy Resurce Stati) i Akey, Iwa. It csists f tw idepedet AHUs (air hadlig uits) with the same ze lads ad utside weather cditis. Each AHU servig fur differet thermal zes is set as a test area. Fig. 1 prvides a schematic diagram f the existig AHU. Fr each thermal ze, a VAV bx is cected t the AHU t maitai the cmfrt temperature f the thermal ze. The structure f the VAV bx is shw i Fig. 2. The experimet cducted i ERS was desiged t ivestigate the impacts f AHU set pits the ttal eergy csumpti, sice the HVAC system csumes a majrity f the eergy i a particular ffice buildig. Tw set pits, amely, AHU supply air temperature set pit ad static pressure set pit, were adjusted fr bth air hadlig uits, AHU-A ad AHU-B. The supply air temperature set pit varied frm 52 F(11.11 C) t 63 F (17.22 C) with 1 F(0.56 C) icremets. The supply air static pressure varied frm 1.2 WG (0.3 kpa) t 1.8 WG (0.45 kpa) with 0.2 WG (0.05 kpa) icremets. T simulate the impact f peple ad the lightig i the thermal zes, the iteral lad was divided it fur stages reflectig the differet thermal states at differet time. The purpse f this experimet was t fid the ptimal set pits miimizig the eergy csumpti while maitaiig a acceptable level f IAQ. The ttal eergy csumed by the HVAC system icludes tw parts: the AHU ad the VAV bx. Fr the eergy csumed i the AHU, three majr categries, amely heat eergy, fa eergy, ad pump eergy, accut fr the ttal eergy csumpti. Sice all three categries cme frm electricity, they ca be calibrated by the meters rigially istalled i the system. I the VAV bx, the reheat lad accuts fr the maximum csumed eergy. The VAV bx supplies the cditied air fr a specific thermal ze t meet the cmfrt temperature f the ze evelpe. By tuig the valve psiti ad the dampers i the VAV bx, the ht water flws thrugh the cils adjustig t the actual requiremets f the ze cmfrt. The reheat lad is cmputed frm equati (1) [16]. Fig. 2. The schematic diagram f a sigle-rm VAV bx. Q Reheat ¼ cm T VAVEAT T VAVDAT where c is the heat capacity f the ht water, m is the mass flw rate f the ht water, ad T VAV EAT ad T VAV DAT represet the eterig ad leavig water temperatures f the hydric reheat cil, respectively. The ttal eergy csumed by the system is expressed i equati (2). E Ttal ¼ E Heat þ E Fa þ E Pump þ Q Reheat (2) (1) Exhaust air Outside air Damper Damper Damper Mixed air Supply water Valve Retur water Valve Supply water Retur water Fig. 1. The schematic diagram f the AHU system. Retur air Supply air Retur fa Supply fa where E Heat is the eergy csumed by the heat cil, E Fa is the eergy csumed by the fa, E Pump represets fr the eergy use f water pump, ad Q Reheat is the eergy csumed durig the reheat prcess i the VAV bx. The iheret liearity ad cmplexity f a typical HVAC system is difficult t accurately represet by a mathematical r a physics-based mdel. Hwever, it ca be easily captured by the empirical mdels develped frm the prcess data. The data-drive mdels fte utperfrm the traditial mdels f dyamic prcesses ad predicti f perfrmace metrics [17e19]. I this study, differet data-miig algrithms are applied t derive the tempral prcess mdels. T miimize the ttal eergy E Ttal, the fucti y Eergy ðtþ ¼ f ðx 1 ; x 2 Þ shuld be established betwee the utput E Ttal ad the iput variables f the HVAC system. The fucti f() represets the AHU prcess, x 1 is a vectr f m ctrllable variables, x 2 is a vectr f uctrllable variables, ad y is the utput variable. Bth ctrllable ad uctrllable variables are used t represet the uderlyig dyamic prcess. T maitai the desired IAQ level, bth rm humidity ad rm cmfrt temperature are csidered.

3 A. Kusiak et al. / Eergy xxx (2011) 1e10 3 Let y Eergy ðtþ ¼f ðx 1 ; x 2 Þ be a bjective fucti reflectig the eergy csumpti t be ptimized with a evlutiary cmputati algrithm. The same parameters are used fr mdelig the idr rm temperature y 2 ðtþ ¼f ðx 1 ; x 2 Þ ad humidity y 3 ðtþ ¼f ðx 1 ; x 2 Þ, represetig the IAQ at a acceptable level. The glbal ptimal settigs are achieved by miimizig the eergy bjective y Eergy while esurig y 2 (t) ad y 3 (t) vary withi their cstrait rage. The ptimizati mdel prpsed i this research is preseted ext. Mi y Eergy ðtþ subject t: y 2 ðtþ ¼f ðx 1 ; x 2 Þ (3) y 3 ðtþ ¼f ðx 1 ; x 2 Þ x 1 R 1 y j R j j ¼ 2; 3 A evlutiary cmputati algrithm has bee mdified t search fr the ptimal ctrl settigs f the HVAC system. The tw ctrllable variables, the AHU supply air temperature ad the supply air static pressure, are csidered t vary i a restricted rage meetig the requiremets f HVAC system. The rm temperature ad humidity are treated as cstraits with their values chagig i a certai rage, s as t t sacrifice the evirmetal cmfrt while the utput is miimized t reduce the eergy csumpti. 3. HVAC system mdelig The mdel prpsed i this study has bee tested the data cllected frm February 4 t 15, 2010 at ERS. Mre tha 300 variables have bee captured reflectig the differet characteristics f the HVAC system. The frequecy f the rigial dataset is 1 mi. T reduce the errr prduced by time delay ad system errr, the rigial 1 mi data has bee aggregated t 1 h iterval data by calculatig the mea value. I ttal, there are 576 bservatis (2 variables, twelve days f 1 h iterval data) recrded i this dataset. Because f the existece f system ad sesr errrs, sme abrmal data exist ad will affect the accuracy f the experimet. After the pre-prcessig f the whle data, the dataset with 500 bservatis was radmly sampled ad rughly divided it a traiig set (85% f dataset) ad a testig set (15% f dataset). The dataset descripti is preseted i Table Parameter selecti ad data dimesiality reducti Sme f the parameters cllected are irrelevat r redudat i the mdelig prcess. Therefre, parameter selecti is essetial befre buildig the predictive mdel. The presece f irrelevat r redudat parameters i data miig may mask primary patters. Redudat parameters als duplicate much r all f the ifrmati ctaied i e r mre ther parameters, makig the mdelig task much mre difficult tha it shuld be. Elimiatig parameters that are less imprtat r related may imprve the accuracy, scalability, ad cmprehesibility f the resultig mdels ad decrease the dimesiality which may greatly reduce the cmplexity f a mdel [20]. Fr example, the mixed air temperature was imprtat i this experimet fr predicti, as it directly reflected hw much eergy Table 1 Data descripti. Dataset Descripti N. f istaces 1 Mdel traiig; A radm sample f 85% f the data Mdel test; The remaiig 15% f the data 73 shuld be csumed t reheat the air up t the cmfrt temperature. Hwever, it had almst the same distributi f the supply air temperature, ad thus it culd be discarded as duplicate ifrmati. Wrapper algrithms [21,22] that use iducti learig as evaluati fuctis were applied t select the mst imprtat parameters. A wrapper algrithm searches the space f all the pssible parameters ad evaluates each subset f parameters by buildig a mdel each subset. The subset f parameters prvidig highest predicti accuracy is selected. Csiderig high cmputatial cst, three widely used search methds, amely geetic algrithm, greedy, ad liear frward, were used i the wrapper apprach. Fur differet classifiers, amely liear regressi, pace regressi, SVM (supprt vectr machie) regressi, ad MLP (multi-layer perceptr), were als used. Sice a sigle wrapper algrithm might dmiate the features i sme aspects, a vte methd that is mre rbust t select the apprpriate parameters tha a sigle methd, was applied t balace the selecti f parameters by cmbiig five differet wrapper evaluati fuctis (Table 2) with 10-fld crss-validati. Fr each wrapper evaluatr, the umber f each cadidate selected withi the 10-fld iterative crss-validati was summed up. The the results f the five differet wrapper evaluatrs were aggregated t determie the imprtace f each parameter by cutig the ttal umber f times selected. The parameter gettig the mre vtes idicates the larger impact the utput f the HVAC system. The results f the five differet cmbiatis f wrapper evaluatrs are preseted i Table 3. Based bth dmai kwledge ad the results f the wrapper algrithm, the tp 12 variables were selected fr the ptetial cadidates t cstruct the eergy csumpti mdel. The crrelati cefficiet [23] matrix was the applied t the selected parameters t reduce the liearity relatiships amg these variables, sice sme parameters may ctai similar ifrmati ad prduce the same impact the utputs. The results f the crrelati cefficiet are preseted i Table 4. Frm the matrix shw abve, if we set the value f the liear relatiship as 0.8, the parameter MA-Temp has a highly liear relatiship with SA set pit, ad SA-Temp ad OA-Temp are als highly crrelated. Therefre, SA set pit ad OA-Temp are selected t represet the characteristic f the tw parameters, respectively. Te sigificat parameters have bee ultimately selected as iputs f the mdel f the HVAC system icludig bth ctrllable variables, i.e., the supply air temperature ad supply air duct static pressure set pits, ad uctrllable variables such as iteral lad, supply air humidity ad all the weather patters. Table 5 lists all the fial iputs f the mdel. The iteral lad (t) has fur basic states determied by the HVAC system itself t simulate the actual activity i the test rms. The system delay is imprtat i mdelig the AHU system; therefre, the parameter iteral lad (t 1) was selected. Fr istace, past values f the system iteral lad may have mre impact the utput f the HVAC system tha its curret value. The ther uctrllable parameters reflectig the utside weather cditis shuld als be take it csiderati. The perati f the AHU system is Table 2 Five differet algrithms f the wrapper evaluatr. Evaluatr Classifier Search methd Wrapper Liear regressi Geetic Pace regressi Liear frward Liear regressi Greedy SVM regressi Geetic MLP Geetic

4 4 A. Kusiak et al. / Eergy xxx (2011) 1e10 Table 3 The results f parameter selecti by vtig-based wrapper algrithm. Wrapper ¼ Liear regressi þ Geetic search Wrapper ¼ Pace regressi þ Liear frward Wrapper ¼ Liear regressi þ Greedy Wrapper ¼ SVM regressi þ Geetic search Wrapper ¼ MLP þ Geetic search Rak N. f times selected N. f times selected N. f times selected N. f times selected N. f times selected Ttal Iteral lad (t 1) SA set pit MA-Temp OA-Hum SPSP set pit BAR-Pres OA-Temp SOL-Beam Iteral Lad (t) SA-Hum IR-Rad SOL-Hr WIND-Dir WIND-Vel OA-CO impacted by the weather patters. The tw ctrllable parameters, the AHU supply air temperature ad the supply air duct static pressure set pits, directly accut fr the system eergy csumpti. They are ptimized i the ext secti, ad the ctrl strategy t geerate them is discussed Cstructi ad validati f the eergy csumpti mdel After parameter selecti ad dimesiality reducti, the eergy csumpti mdel f the HVAC system is expressed i equati (4). y Eergy ðtþ ¼f x SAT Spt ; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x SA Humd ; x SOL Hrz ; x IR Radia ; x Bar Pres ; x OA TEMP ; x SOL Beam where y Eergy (t) is the eergy t be ptimized; x represets all the iputs f this predictive mdel. Five data-miig algrithms were used t extract the mappig betwee iputs ad utputs: Exhaustive Geeral CHAID (Chi-square Autmatic Iteracti Detectr) [24], Bstig Tree [26], Radm Frest [27], SVM (Supprt Vectr Machies) [28], ad MLP [29]. The Exhaustive CHAID algrithm is derived frm the stadard CHAID [25], which is a type f decisi tree allwig multiple splits f des ad ca be used fr detecti f iteracti betwee variables i regressi ad classificati aalysis. It allws fr mre cmprehesive mergig tha stadard CHAID. Bstig tree is a typical machie learig meta-algrithm fr perfrmig supervised learig. Bstig is a iterative prcedure ð4þ used t adaptively mdify the distributi f traiig examples s that the base predictrs will mstly ccetrate learig istaces misclassified by the previus biased examples. Radm Frest is a class f esemble methds csistig f multiple decisi trees, where each tree is geerated based the values f a idepedet set f radm variables. Ulike the adaptive apprach used i Bstig, the radm variables are geerated frm a fixed prbability distributi. SVM is a supervised learig algrithm based kerel fuctis, ad it is applied t biary classificati ad regressi. Usig specific kerel fuctis, the rigial vectr space is trasfrmed it a higher-dimesial space where a separated hyperplae is cstructed with the maximum margi. The MLP Esemble methd presets a cmbiati f multiple mdels t leverage the stregth f multiple MLP mdels i achievig better predicti accuracy tha ay idividual mdel des. The five differet data-miig algrithms have bee tested fr the cstructi f predictive mdels. I rder t evaluate the perfrmace f differet algrithms, the fllwig fur metrics (see equatis (5)e(10)) have bee used t measure the predicti accuracy f the mdel: the MAE (mea abslute errr), the Std_AE (stadard deviati f abslute errr), the MAOE (mea abslute percetage errr) ad the Std_APE (stadard deviati f abslute percetage errr) [30]: AE ¼ y ~ y (5) P i ¼ 1 MAE ¼ AE i (6) N Table 4 The results f the crrelati cefficiet matrix. Iteral lad (t) Iteral lad (t 1) SA set pit SASP set pit MA-temp SA-Hum BAR-Pres IR-Rad OA-Hum OA-Temp SOL-beam SOL-Hr Iteral lad (t) Iteral lad (t 1) SA set pit SP set pit MA-Temp SA-Hum BAR-Pres IR-Rad OA-Hum OA-Temp SOL-Beam SOL-Hr

5 A. Kusiak et al. / Eergy xxx (2011) 1e10 5 Table 5 Parameter descripti. Parameter Type Parameter ame Descripti Uit Ctrllable SAT set pit AHU supply air C variables temperature set pit SASP set pit Supply air duct static kpa pressure set pit Uctrllable Iteral lad (t) System iteral lad / variables Iteral lad (t 1) The previus state f / system iteral lad SA-Hum Supply air humidity % RH SOL-Hr Slar rmal flux B/HFt2 IR-Rad Ifrared radiati B/HFt2 BAR-Pres Barmetric pressure mbar (rmalized t sea level) OA-Temp Outside air temperature C SOL-Beam Slar beam itesity B/HFt2 ~y y APE ¼ y P i MAPE ¼ ¼ 1 APE i N sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P i Std AE ¼ ¼ 1 ðae i MAEÞ 2 N 1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P i Std APE ¼ ¼ 1 ðape i MAPEÞ 2 N 1 (7) (8) (9) (10) where AE i equati (2) represets the abslute errr, ~ y is the predicted value btaied frm the mdel, y is the actual target value measured, ad N is the umber f data pits used fr traiig r testig. Table 6 presets the predicti perfrmace f the eergy csumpti mdels derived by five data-miig algrithms by presetig the respective traiig ad testig errrs. The cmputatial results listed i Table 3 demstrate that the MLP eural etwrk perfrms best the fur evaluati criteria. Therefre it is selected as the algrithm fr cstructig the eergy csumpti mdel. The test results f the MLP eural etwrk fr this mdel are shw i Fig. 3. The chart shws that the predicted values clsely track the bserved es at mst f the pits. Table 6 Predicti perfrmace f the eergy csumpti mdels built by five differetmiig algrithms. Dataset Algrithm MAE Std_AE MAPE (%) Std_MAPE (%) Traiig MLP esemble Testig Traiig MLP Testig Traiig SVM Testig Traiig Bstig tree Testig Traiig Radm frest Testig Traiig Exhaustive CHAID Testig y Humidity ðtþ¼f x SAT Spt ;x SASP Spt ;x LadðtÞ ;x Ladðt 1Þ ;x SA Humd ; x SOL Hrz ;x IR Radia ;x Bar Pres ;x OA TEMP ;x SOL Beam ð12þ where y Temp (t) ad y Humidity (t) are cstraits t meet the IAQ f HVAC system; x represets all the iputs f this predictive mdel. The MLP algrithm ad the same dataset are used t cstruct the tw mdels. The test results ca be see i Fig. 4 ad Optimizati algrithm 4.1. Mdel frmulati The ptimizati prcess seeks the set pit values miimizig the ttal eergy csumpti f the HVAC system. This is de by applyig the evlutiary cmputati algrithm [31]; the set pits were ptimized t maximize the eergy savigs. The ptimizati mdel is frmed thrugh the idetificati f the prblem parameters, the bjective fuctis, ad the cstraits Mdel parameters The mdel parameters f the HVAC system have bee determied by the wrapper algrithm described i Secti 3.1. Table 5 lists each parameter used fr the ptimizati prcess. The tw ctrllable parameters, the AHU supply air temperature ad the supply air duct static pressure set pits, are t be varied t btai the ptimal slutis. As uctrllable iput parameters are essetially idepedet f the ctrllable es, the values f uctrllable variables, such as supply air humidity, utside air 3.3. Cstructi ad validati f the IAQ mdels I this HVAC system examied, the value f rm temperature is maitaied frm 69 Ft73 F ad the rm humidity is ctrlled belw 30% t esure the thermal cmfrt. As the supply air temperature ad the supply air static pressure set pits chage, the rm temperature ad humidity are als affected by the implemetati f chageable settigs. Mdels f rm temperature ad humidity shuld be cstructed s as t cfrm t the idr air quality while miimizig the eergy csumpti. Usig the same methdlgy itrduced i Secti 3.2, the IAQ mdel ca be described as fllws: y Temp ðtþ ¼ f x SAT-Spt; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x SA-Humd; x SOL-Hrz ; x IR-Radia ; x Bar-Pres ; x OA-TEMP ; x SOL-Beam ð11þ Eergy csumpti [kj] Time [h] Observed eergy csumpti Predicted eergy csumpti Fig. 3. Test results prduced by the mdel.

6 6 A. Kusiak et al. / Eergy xxx (2011) 1e10 temperature ad ther utside weather patters, ca be fixed i seekig the ptimal ctrl settigs at each time stamp Objective fuctis The ptimal ctrl strategy determies tw set pits t miimize the eergy use. The ttal eergy csumpti, icludig the fa, pump, ad reheat pwer, is cmputed frm equati (2). The iputeutput relatiship was expressed by the HVAC system mdel preseted abve i equatis (3), (11) ad (12). The eergy bjective fucti is t be miimized while the ther tw e temperature ad humidity bjective fuctis e are treated as cstraits t satisfy the idr air quality f the AHU system Cstraits The cstraits i the mdel are due t the upper ad lwer limits impsed the parameters f the HVAC system ad the IAQ mdels. The value f the supply air temperature set pit, the supply air duct static pressure set pit, idr rm temperature, ad rm humidity are restricted withi the limits: Supply air temperature must vary betwee 52 F(11.11 C) ad 63 F (17.22 C). Supply air duct static pressure must vary betwee 1.2 WG (0.3 kpa) ad 1.8 WG (0.45 kpa). Rm temperature must be maitaied betwee 70 F (21.11 C) ad 72 F (22.22 C). Rm humidity must be ctrlled belw 30%. Csequetly, the ptimizati mdel (13) is expressed as miimizig the bjective fucti (4) with ctrl parameters varyig withi their buds. Rm temperature [C] Observed rm temperature Time [h] Predicted rm temperature Fig. 5. Test results fr the rm temperature mdel. Slvig such a liear multi-bjective ptimizati prblem is a challege. Fr the typical HVAC system, the prcedure f cmputati is als cmplex ad time-csumig, resultig i the difficulty f gettig the results fr sme large datasets. I rder t simplify the prblem ad reduce the calculati time, the tw cstrait fuctis y Temp (t) ad y Humidity (t) are assiged it ebjective fucti shw i equati (14): y Cstraits ðtþ ¼max 0; 20:56 y Temp ðtþ þ max 0; y Temp ðtþ 22:78 þ max 0; 5 y Humidity ðtþ þ max 0; y Humidity ðtþ 25 ð14þ mi y Eergy ðtþ x SAT Spt;x SASP Spt subject t : y Eergy ðtþ ¼ f x SAT Spt ; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x SA Humd ; x SOL Hrz ; x IR Radia ; x Bar Pres ; x OA TEMP ; x SOL Beam y Temp ðtþ ¼ f x SAT Spt ; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x SA Humd ; x SOL Hrz ; x IR Radia ; x Bar Pres ; x OA TEMP ; x SOL Beam y Humidity ðtþ ¼ f x SAT Spt ; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x SA Humd ; x SOL Hrz ; x IR Radia ; x Bar Pres ; x OA TEMP ; x SOL Beam 11:11 x SAT Spt 17:22 0:3 x SASP Spt 0:45 20:56 y Temp ðtþ 22:78 5 y Humd ðtþ 25 (13) Rm humidity [%] Time [h] Observed rm humidity Predicted rm humidity Fig. 4. Test results fr the rm humidity mdel. csumpti [kj] Eergy IAQ cstraits Fig. 6. Feasible slutis btaied after 150 geeratis at sme time stamp.

7 A. Kusiak et al. / Eergy xxx (2011) 1e10 7 Table 7 Descripti f the eleve weight assigmet scearis. Sceari Weight assiged t eergy Weight assiged t IAQ cstraits Descripti 1 w 1 ¼ 1.0 w 2 ¼ 0 N IAQ cstraits 2 w 1 ¼ 0.9 w 2 ¼ 0.1 Preferece t eergy savig 3 w 1 ¼ 0.8 w 2 ¼ 0.2 Preferece t eergy savig 4 w 1 ¼ 0.7 w 2 ¼ 0.3 Preferece t eergy savig 5 w 1 ¼ 0.6 w 2 ¼ 0.4 Preferece t eergy savig 6 w 1 ¼ 0.5 w 2 ¼ 0.5 Equal imprtace t bth bjectives 7 w 1 ¼ 0.4 w 2 ¼ 0.6 Preferece t IAQ maiteace 8 w 1 ¼ 0.3 w 2 ¼ 0.7 Preferece t IAQ maiteace 9 w 1 ¼ 0.2 w 2 ¼ 0.8 Preferece t IAQ maiteace 10 w 1 ¼ 0.1 w 2 ¼ 0.9 Preferece t IAQ maiteace 11 w 1 ¼ 0 w 2 ¼ 1.0 Maximizati f thermal cmfrt As the cstraits are satisfied, each f the fur terms i equati (14) will remai 0 ad the sum equals 0. Hwever, sice rm humidity ad temperature are t at the same scale, the cstrait fucti may t accurately reflect the iflueces f them. It is pssible rm humidity may dmiate the result because f its high value. The values f rm humidity ad temperature are the rmalized t elimiate the deviati. The revised fucti is shw i equati (15). I the practical perati f HVAC system, it is pssible that sme cstrait is f mre imprtace r at least ver tha sme ther cstrait. I differet time perid f the year, maagers may emphasize differet bjectives. Fr example rm temperature shuld be paid mre atteti t rm humidity i witer sice the air humidity is really lw ad is t a big issue. Takig the effects f differet cstraits, weights shuld be assiged t each cstrait t meet the specific preferece f HVAC system. The fial cstrait fuctis are preseted i eqs. (16) ad (17).: y Cstraits ðtþ ¼w 1 * max 0; 20:56 y Temp ðtþ þ max 0; y Temp ðtþ 22:78 = y Temp upperbud y Temp lwerbud þ w 2 * max 0; 5 y Humidity ðtþ þ max 0; y Humidity ðtþ 25 = y Humidity upperbud y Humidity lwerbud ð16þ w 1 þ w 2 ¼ 1 (17) Based discussi abve, the ptimizati prblem was trasfrmed it a bi-bjective mdel. Fially the ptimizati ca be mdified t equati (18): mi y Eergy ðtþ x SAT Spt;x SASP Spt subject t : y Eergy ðtþ ¼f x SAT Spt ; x SASP Spt ;x LadðtÞ ; x Ladðt 1Þ ; x CHWC VLV ; x SA Humd ; x SOL Hrz ; x OA Humd ; x OA TEMP y Cstraits ðtþ ¼w 1 * max 0; 20:56 y Temp ðtþ þ max 0; y Temp ðtþ 22:78.y Temp upperbud y Temp lwerbud þ w 2 * max 0; 5 y Humidity ðtþ þ max 0; y Humidity ðtþ 25.y Humidity upperbud y Humidity lwerbud 11:11 x SAT Spt 17:22 0:3 x SASPSpt0:45 (18) y Cstraits ðtþ ¼ max 0; 20:56 y Temp ðtþ þ max 0; y Temp ðtþ 22:78 = y Temp upperbud y Temp lwerbud þ max 0; 5 y Humidity ðtþ þ max 0; y Humidity ðtþ 25 = y Humidity upperbud y Humidity lwerbud ð15þ 4.2. Evlutiary cmputati algrithm I this study, a mdified SPEA-LS (Stregth Paret Evlutiary Algrithm with Lcal Search) is used t slve the mdel (12). The algrithm is preseted belw: Step 1: Iitialize a ppulati P ad create a empty exteral ppulati P* t stre elite slutis. Step 2: Fid -dmiated slutis i P ad cpy them it P*. Step 3: Fid -dmiated slutis i P ad update the elite ppulati P*. Table 8 Weight assigmet f 11 scearis. Sceari Ttal eergy Recmmeded SA settig Recmmeded SASP settig Temperature Humidity IAQ vilati

8 8 A. Kusiak et al. / Eergy xxx (2011) 1e10 Temperature [ F] Origial SAT setpit Optimized SAT setpit (Sceari 11) Fig. 7. The bserved ad recmmeded supply air temperature settigs. Table 9 Cmparis f the slutis fr the weights f the 11 scearis. Sceari Average ptimized eergy used Average eergy savigs Average percetage eergy savigs (%) IAQ vilati Step 4: Assig fitess values t each idividual i P ad P*. Step 5: Select a set f P paret f size N paret frm P þ P* usig the biary turamet selecti scheme with replacemet. Step 6: Radmly select tw idividuals ad add a better e t P ffsprig. Apply recmbiati ad mutati peratrs t P ffsprig. Step 7: Lcal Search: Apply the mdified lcal search prcedure t all N ffsprig slutis i the curret ppulati. The curret ppulati is replaced with the N ffsprig slutis imprved by the lcal search. Step 8: Stppig Criteri: The maximum umber f geeratis. If t exceeded, retur t Step 2. The lcal search prcedure is as fllws: Step 1: Specify a iitial sluti x. Step 2: Examie eighbrhd slutis y ¼ {x 1, x 2,., x } f the curret sluti x. Step 3: Evaluate all the eighbrhd slutis i y ad fid the best e. If a sluti which is better tha x is fud, replace the curret sluti x with the better e. Step 4: Retur t Step 1 util all the idividuals are examied. I the prcess f assigig the fitess fr idividuals P ad P*, tw differet fuctis are applied t esure the elite sluti ad retai the variety f the ppulati. Fr idividuals i elite ppulati P*, the fitess fucti is: S i ¼ i (19) N þ 1 where S i is the fitess value f ith elite idividual i-dmiated ppulati P*, i is the umber f idividuals i P that sluti i dmiates, ad N is the ppulati size f P. Fr the idividuals i curret ppulati P, the fitess fucti is: S j ¼ 1 þ X i F S i (20) where S j is the fitess f jth idividual i the curret ppulati P, F is the elite set frm P*. The ctrl parameters f the evlutiary cmputati algrithm must be adjusted t prvide the best perfrmace, i.e., miimum eergy csumpti f the HVAC system with the least sacrifice f air quality. The mutati peratr i Step 6 is realized by addig ise Δx i (frm a Gaussia distributi with zer mea ad stadard deviati s) t the i th ctrllable variable x i. The ewly geerated sluti is x i * ¼ x i þ N(0,s). I glbal search, the ise value fr x 1 (t) ad x 2 (t) is set t 0.5 ad 0.05, respectively. I lcal search, the ise is set t 0.1 ad 0.01, respectively. The ppulati size is p z ¼ 100. The stppig criteri is set at 150 geeratis Optimizati results ad discussi The prpsed evlutiary cmputati algrithm was applied t slve the ptimizati mdel at each time stamp. Optimized ctrl settigs f the existig HVAC system, amely the supply air temperature ad the supply air duct static pressure set pits, were btaied. The perfrmace f the HVAC system mdel has bee validated. The buds set fr supply air temperature ad supply air static pressure may be slightly vilatig the cstraits durig the geeratis. Fig. 6 shws the values f the bjective fucti f mdel (18) geeratis f the evlutiary cmputati algrithm. A decrease i cstraits idicatig the better air quality requires a icrease i Static pressure [WG] [kj] Ttaleergy Origial SASP setpit Optimized SASP setpit (Sceari 11) Origial eergy use Optimized eergy use (Sceari 11) Fig. 8. The bserved ad recmmeded supply air static pressure settigs. Fig. 9. The bserved ad ptimized ttal eergy csumpti fr Sceari 11.

9 A. Kusiak et al. / Eergy xxx (2011) 1e Rm Temperature [ F] Origial rm temp Optimized rm temp (Sceari 11) Fig. 10. The bserved ad ptimized rm temperature fr Sceari 11. csumpti [kj] Eergy Sceari Average ptimized eergy use IAQ vilati Fig. 12. The ptimized eergy csumed versus IAQ vilati IAQ vilati eergy demad. Whe the cstraits are satisfied (the left pit the budary), the system csumes mre eergy tha at ther pits. If the decisi is t save mre eergy, the csequece must be the sacrifice f the thermal cmfrt ad air quality. Accrdig t the differet prefereces f maagemet, the results will largely differ if differet weights are assiged t each bjective fucti. A trade-ff must be csidered t meet the specific requiremets f differet systems. If we assig w 1 t bjective fucti e which csiders the eergy, ad w 2 fr bjective fucti tw represetig the vilati f air quality, the differet cmbiati f w 1 ad w 2 will give the differet prefereces. The ptimal sluti is selected frm the fial elite set by the weighted rmalized bjective fucti (17). The fllwig tw equatis shw the fllwig prcess. Objective ¼ w 2 * ðbjective1 bjective1 miþ ðbjective1 max bjective1 mi Þ þ w 2 * ðbjective2 bjective2 miþ ðbjective2 max bjective2 mi Þ (21) where w 1 ad w 2 represet the user-defied weights idicatig the imprtace f bjective 1 ad bjective 2, respectively; bjective 1 represets the eergy csumpti ad bjective 2 represets the vilati f air quality. Nte that w 1 þ w 2 ¼ 1. Let w 1 varies frm 1 t 0 with 0.1 decremet while w 2 varies frm 0 t 1 with 0.1 icremet. Eleve scearis represetig differet assigmets f weights t the bjectives have bee created i Table 7. Table 8 lists the ptimal slutis fr each f the 11 scearis at sme time stamp. After assigig differet weights t the bjectives, the bi-bjective ptimizati mdel is trasfrmed it a sigle bjective mdel t be miimized with the bjective fucti shw i (21). Sceari 1 has the lwest ttal eergy csumpti as the air quality is t csidered. As the weight assiged t the IAQ icreases, the ttal eergy savig is reduced. T cmpare the ptimal slutis with the actual eergy csumpti, Sceari 11 is selected. Figs. 7 ad 8 cmpare the rigial ad recmmeded ctrl settigs f the supply air temperature ad the static pressure. Based the ptimal ctrl settigs, the crrespdig ttal eergy ad the rm air quality metrics are estimated usig the eergy ad the IAQ mdels f Secti 3. Figs. 9e11 cmpare the rigial ad ptimized eergy as well as the IAQ idexes. Fig. 9 presets that the ttal eergy csumpti is reduced after the recmmeded ctrl settigs are implemeted. The crrespdig values f IAQ idexes are preseted i Figs. 10 ad 11. At times, miimizati f the eergy is cmprmised i rder t maitai the required IAQ idexes. The ttal eergy saved fr Sceari 11 is 21.4% cmpared t 22.6% Sceari 1 with IAQ cstraits icluded. The results discussed abve represet ly the tw extreme situatis f weights assigmets. Differet trade-ff ca be fud by chagig the weights t the crrespdig bjective. Table 9 presets the fial ptimal slutis after assigig differet weights t the bjectives. As the larger weight is assiged t IAQ cstraits, mre eergy is csumed while the air quality is imprved. Fig. 12 shws the gradiet tred f ptimized eergy use ad IAQ vilatis. Fig. 12 demstrates that whe the weight assciated with the eergy bjective decreases frm 0.6 t 0.4, the eergy csumpti icreases ad the adherece f IAQ idexes imprves. Bth, the eergy csumpti ad IAQ idexes are miimally affected whe the tw weights chage frm 1 t 0.6 ad 0 t 0.4, respectively. The sluti ze whe the values f the weights are clse t each ther is sesitive. By chagig the weights, the mdel allws fr icrprati f user s prefereces. Rm Humidity [RH%] Origial rm humidity Optimized rm humidity (Sceari 11) Fig. 11. The bserved ad ptimized rm humidity fr Sceari Cclusi The prpsed data-miig ad ptimizati apprach was applied t a existig HVAC system at the ERS. A predictive mdel f eergy csumpti, rm temperature, ad humidity were geerated by a MLP algrithm ad aggregated it a mdel ptimizig eergy csumpti. The mdel cstructed i the paper was slved with a evlutiary cmputati algrithm t prduce ptimized set pits f the supply air temperature ad the supply air static pressure f the HVAC system. The ptimized set pits determied by slvig a mdel with tw-bjectives resulted i

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