REAL-TIME DETERMINATION OF INDOOR CONTAMINANT SOURCE LOCATION AND STRENGTH, PART II: WITH TWO SENSORS. Beijing , China,

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1 REAL-TIME DETERMIATIO OF IDOOR COTAMIAT SOURCE LOCATIO AD STREGTH, PART II: WITH TWO SESORS Hao Ca,, Xantng L, Wedng Long 3 Department of Buldng Scence, School of Archtecture, Tsnghua Unversty Bejng 84, Chna, cahaohvac@63.com Engneerng Insttuton of Engneerng Corps, PLA Unversty of Scence & Technology, anjng 7, Chna, cahaohvac@63.com 3 Sno-German College of Appled Scences, Tongj Unversty, Shangha 84, Chna, wednglong63@63.com ABSTRACT In the precedng companon paper (Part I), a method wth one sensor that could dentfy the ndoor contamnant source locaton strength n short tme was presented. On the bass of further theoretcal study, a method wth two sensors s presented n ths paper to dentfy contamnant source wth hgher accuracy. Ths paper demonstrates how to use the method wth two sensors to fnd the locaton of contamnant source n a threedmensonal room. In addton, the accuracy of two types of methods was compared. The correctness probablty, whch are used to evaluate the accuracy of source locatng, of the method wth two sensors the method wth one sensor are 83.3% 94.8% respectvely. The results show that the method wth two sensors wors better for locatng contamnant source than that wth one sensor. In practce, the method wth two sensors may be more applcable for the stuatons where the accuracy of source dentfcaton s crucal whle the costs of sensors are not of great concern. KEYWORDS Contamnant source, Identfcaton method, Computatonal flud dynamcs (CFD), Sensor, Indoor envronment ITRODUCTIO In Part I of ths companon papers, we presents a method wth one sensor (Method I for short) to dentfy the contamnant source locaton strength n real tme. The results of case study show that Method I could dentfy the contamnant source locatons wth acceptable accuracy. Although the dentfcatons of source strength are not very accurate, the predctons actual values are n the same order of magntude (Ca et al, 7). One major purpose of the above study s to explore whether we could dentfy the contamnant source wth mnmum sensors. If the answer s postve, the costs of sensors wll be saved sgnfcantly, so that the technque of source dentfcaton wll be more applcable for the stuatons where the costs of sensors are of great concern. Fortunately, we get the postve answer. evertheless, problems are stll far from settled. Let us consder another nd of stuatons where the accuracy of source dentfcaton s crucal whle the costs of sensors are not of great concern. Under such crcumstances, t may be of sgnfcance to explore the problem that whether we can mprove the accuracy of dentfcaton wth more sensors. Ths paper ams to presents a new method wth two sensors (Method II for short) to mprove the accuracy of Method I. For the purpose of demonstraton comparson, ths new method wll be appled to the dentcal room presented n the prevous paper (Part I). METHODOLOGY The premses of present method are same wth that of Method I. They are brefly summarzed n the followng,. Indoor arflow s nown s n steady state;. Only one pont source s released at a steady rate n the room; 3. The sensors employed can measure the contamant under any condtons; 4. The release the measurements tae place smultaneously. Suppose that two sensors are placed n the room at ponts β. Unnowns to the problem nclude locaton α strength S of the source CS. The overall framewor of Method II s dvded nto two stages just as Method I. In the pre-event stage, we dvde the room nto control volumes form a set A = { α, α, L, α } wth ther centers, construct a vector X ( ) composed of ndex X, ) whch represents the closeness degree between α α, run CFD

2 smulatons to get the concentraton of contamnant at ponts β for every possble scenaros, store the smulatons n the database for next stage. As dscrbed n Part I, ths stage s not tme-crtcal not dffcult to acheve by vrtue of fast personal computers nexpensve data storage devces. In the second stage, we solve the vector X ( ) wth the smulatons stored n the database the measurements from the two sensors, fnd the closest pont α to α n the set A usng the vector X ( ). As dscussed n Part I, ths stage s mathematcally smple can be executed n real tme durng a release event. Although the premses overall framewor of Method II s smlar to that of Method I, Method II s dstnct from Method I n one mportant feature, that s, the specfc form of ndex X, ). In order to mae full use of the measurements from two sensors mprove the accuracy of dentfcaton, we should develop a new ndex n ths paper. In the followng, we wll present how to derve ths new ndex. Frst, we redefne the smlarty characterstc ndex as follows, SC, ) = log C, t)d t C ( β, t)dt C, t)d t C, t)dt () where SC (, ) α s a non-dmensonal parameter, whch ndcates the smlarty characterstc of α α at tme ; C, t) C, t) are the measurements from two sensors at tme t, at pont β, respectvely, when the unnown source CS s released n the room; C, t) C, t) are the contamnant concentratons at tme t, at pont β, respectvely, when the source CS s released at pont α wth steady strength S, whch are obtaned by smulatons stored n the database; the subscrpt represents that two sensors are employed. Snce the ndoor flow feld s nown, the equaton of contamnant transport s a lner equaton, where Superposton Theorem can be appled. Thus f S S are constant, when α, we get C, t)dt S C (, )d S β t t α () From Eqs. () (), we obtan that (, ) log SC α = as α α, n other words, the varaton curve of SC (, ) α wth approaches a horzontal lne f ( ) =. Based on SC (, ) α, we rewrtten the absolute smlarty ndex n the followng, { } ASD ( α, ) = SC ( α, t)dt (3) where ASD (, ) α s a non-dmensonal parameter whle ASD (, ) α n Part I s dmensonal. From the Eq. (3), we can see that ASD (, ) α s characterzed by the followng propertes: ) ASD (, ) α ; ) The more the curve of g( ) = SC, ) approaches the horzontal lne f ( ) =, the greater the value of ASD (, ) α ; 3) As α α, ASD (, ) α. Accordng to ASD (, ) α, the relatve smlarty nex s gven further, MGS ( α, ) = ASD ( α, ) ASD ( α, ) (4) = where MGS (, ) α s a non-dmensonal ndex has major propertes as follows: ) MGS, ) ; ) MGS, ) = ; = 3) As α α, (, ) MGS α. Wth the above propertes, MGS (, ) α s employed here to represent the closeness degree between α α. As there are control volumes, we construct a vector as, MGS ( ) = [ MGS( α, ), MGS( α, ), L, MGS ( α, )] T (5) In the above vector, the value of each element represents the probablty or menbershp grade of whch α s at pont α. The larger the dffferences between these elements, the easer more accurate the dentfcaton wll be, vce versa. If we fnd the center α whch s correspondng to the bggest element n MGS ( ), then the contamnant source locaton could be dentfed

3 After we have clarfed how to locate the contamnant source wth Method II the major dfferences between two methods, t s nessecary to determne whether Method II can locate source wth hgher accuracy than Method I. Therefore, an evaluaton system s needed. The correctness probablty ndex η correspondng evaluaton stard, whch are proposed n Part I, wll be adopted n the next secton for the purpose of comparson between two methods. Based on the dentfcaton of source locaton, we move on to dscuss how to fnd ts strength further. In ths paper, we stll use the method presented n the Part I to dentfy the source strength, although ths method needs to be mproved. Despte ths, f source locatng s more accuracte wth Method II, we can also dentfy the strength of source more accurately. For example, f the source locatng s proved to be wrong wth Method I, we could hardly solve the source strength wth hgh accuracy. However, f the souce locatng s rght wth Method II, the soluton of strength may be easer more accurate. CASE STUDY In the followng, we apply Method II to the room, whch s dentcal wth that presented n Part I, for the purpose of demonstraton comparson. Case descrpton The room s 5 m long(x), 3m hgh(y) 5m wde (Z) as shown n Fg.. Detals of t can be referred to that n Part I. SA S Fgure Schematc of the room (SA supply ar dffuser, RA return ar grll, S Contamnant source locatons to be dentfed) Sxteen possble locatons of source are set up n the example (see Fg. ), whch constuct the set A = { α, α, L, α6} to be determnated. These unnown locatons correspond wth the volume centers one by one, that s α = α ( =,, K,6). Two sensor are placed at the pont β, X, Y, Z =.5,.,.5 m,, X, Y, Z = 3.75,., 3.5 RA m. The plan of unnown sources, sensors, control volumes are shown n Fgure n whch sources zones at lower level n Y drecton are labeled n the bracet. Fgure Plan of the locatons of sources two sensors, the volumes Results dscusson Snce two nds of methods presented n ths companon papers decouple the pre-event smulatons from source dentfcaton durng the event stage, we can qucly obtan the results wth Method II, need not re-execute the tmeconsumng pre-event stage of the smulatons. The decoupled nature of these methods together wth the correctness problty ndex also allow easy quc evaluaton of alternatve dentfcaton methods samplng plans wthout repeatng the computatonally ntensve CFD smulatons. In the precedng paper (Part I), we solved the concentraton feld of contamnant by Arpa (Fluent Inc. ) n order to obtan the measures from the sensor durng the event. In each smulaton, the contamnant source to be dentfed was placed at the locatons, α ( =,, L,6), released n steady strength, S =. g/s. In ths study, what we only need to do s to read the samples of C, t) C, t) wth a constant tme step s from the solved concentraton feld. By calculatng MGS ( ), we dentfy the source locatons qucly n the second stage. Table summarzes the results of the dentfcatons by two methods. The samplng duraton of sensors was = 3s, that s, the samplng of sensor ended after 3s from the release. From Table, t s shown that Method II s more accurate than Method I for source locatng. In ths case, all the sxteen locatons are dentfed correctly by vrtue of the new method, whch mproves the accuracy of source locatng by - 8 -

4 properly tang advantage of the measurements from two sensors. By the evaluaton method presented n the prevous companon paper, we got the correctness probablty of Method II s 94.8%. Snce the correctness probablty of method I s 83.3%. A comparson between Method II Method I shows that the mprovement s qute obvous. Fgure 3 shows the nfluence of sensor samplng duraton on the locatng of dfferent sources usng the Method II. The probablty of correctness η decreases wth the ncrease of samplng duraton as shown, whch s just smlar to that of Method I. Ths smlar feature ndcates that t s possble for us to dentfy the soure wth hgh accuracy after short tme from the release usng Method II. The decoupled nature of the methods proposed n ths seres (Parts I II) together wth the evlauton stard smlar to the gradng method of shootng competton also allow easy quc evaluaton of alternatve dentfcaton methods samplng plans wthout repeatng the computatonally ntensve CFD smulatons. It could be helpful for us to further study the mprovement of dentfcaton methods the optmzaton of sensors layout n the future. ACKOWLEDGEMET Ths study s supported by atonal atural Scence Foundaton of Chna (Grant o ). REFERECES umber of Score s 6s s 8s Score Ca H., L X.T., Long W.D., et al. 7. Real-tme determnaton of ndoor contamnant source locaton strength, part I: wth one sensor, The th Internatonal Buldng Performance Smulaton Assocaton Conference Exhbton, Bejng (Submtted) Fluent Inc.. Arpa. User s Gude, Fluent Inc. Samplng Duraton, Fgure 3. Locatng results wth dfferent samplng duraton usng the method wth two sensors Moreover, snce all the sxteen locatons are dentfed correctly by Method II whle only thrteen locatons by Method I, the dentfcaton of strength may be more accurate by Method II. COCLUSIO Based on the prevous companon paper (Part I), ths paper presented a new method wth two sensors for dentfyng source locaton strength n real tme. Method II proposed n ths paper nhert the advantages of Method I mae full use of the measurements from two sensors. By applyng Method II to the room dentcal wth that presented n Part I, the followng conclusons could be drawn,. Method II could be more accurate than Method I for source locatng. As a result, Method II may be an alternatve way for mprovng the accuracy of the dentfcaton of source strength.. Method II also has the nature that the accuracy of source locatng decreases wth the ncrease of samplng duraton. 3. Method II may be more applcable for the stuatons where the accuracy of source dentfcaton s crucal whle the costs of sensors are not very mportant

5 Table Comparson of the contamnant source dentfcatons by two methods METHOD WITH OE SESOR METHOD WITH TWO SESORS (,3) DETERMIATIO MGS α OF LOCATIO DETERMIATIO MGS α O. OF LOCATIO VALUE RAKIG RIGHT? MARK VALUE RAKIG RIGHT? (Y/) (Y/) MARK.33 Y 5.69 Y 6.58 Y 6.78 Y Y Y Y 5.7 Y Y 6.3 Y Y 6.66 Y Y 6.6 Y Y 5.43 Y 5.75 Y 6.4 Y 5.4 Y 5.77 Y 6.83 Y Y 6.84 Y Y 6.8 Y Y 5.36 Y Y 6.77 Y 6 Correctness probablty η (%) 83.3 Correctness probablty η (%)