Research on Soft Sensing Modeling Method Based on the Algorithm of Adaptive Affinity Propagation Clustering and Bayesian Theory

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1 Sensors & Transducers 13 by IFSA hp:// Research on Sof Sensng Modelng Mehod Based on he Algorh of Adapve Affny Propagaon Cluserng and Bayesan Theory 12 LIU Ranran 1* LI Zhengng 1 PAN Tanhong 1 School of Elecrcal and Inforaon Engneerng Jangsu Unversy Zhenang 2113 Chna 2 Changzhou Lu Guoun Vocaonal Technology College Changzhou 2104 Chna 1 Tel.: fa: E-al: lzng@us.edu.cn Receved: 9 Aprl 13 /Acceped: 14 May 13 /Publshed: May 13 Absrac: The ndusral daa has he characersc of cluserng and grang wh he operang pon. The accuracy and generalzaon ably of he sngle-odel predcon are poor because of he large aoun of nforaon los n sngle-odel odelng. In order o overcoe hese probles a odelng ehod of ulodel sof sensor was proposed based on adapve affny propagaon cluserng (ADAP) and Bayesan flerng. ADAP algorh was ulzed n hs ehod o realze he cluserng and rackng of ulple operang pons. The sub-odels of varous ypes of saples were esablshed ulzng Bayesan flerng ehod and he on oupu and esaon were carred ou based on he odel of he subclass of curren workng pon. The sof sensor odels of CO and CO 2 n odaon sde reacon were ulzed n he ehod. The sulaon resuls show ha he esaon and generalzaon ably of sof sensng odel s sgnfcanly proved by he ehod. Copyrgh 13 IFSA. Keywords: Adapve affny propagaon cluserng algorh Bayesan flerng Sof sensor Mul-odel. 1. Inroducon In praccal producon process he anpulaed varables of each devce are conrolled around he gven values. These gven values of he operang pon ofen need o be changed o ee he producon requreen whch leads o a proble ha he producon daa cluser and grae wh he workng pon. Sngle odel has probles lke long sudyng e low accuracy poor process characersc ach and poor generalzaon ably. Therefore he ulodel odelng ehod was proposed [1-3]. The basc dea of hs odelng ehod s o cluser he ranng saples by cluserng algorh and esablsh he sof sensor sub-odel for dfferen ypes of saples. When he process operang pon changes n a wde range he odel can denfy hs change and he predcon and oupu could be conduced n accordance wh he odel of he correspondng operang pon. The coon cluserng algorhs are K-eans cluserng and fuzzy cluserng ec. The nal cluser ceners and he nuber of clusers are deerned based on pror knowledge. However pror knowledge s generally unknown for he operaon daa of acual producon. Affny propagaon cluserng algorh a new cluserng algorh [4] proposed n recen years could deerne he ceners and he nuber of clusers accordng o he characerscs of he daa. Ths ehod has been wdely appled so far Arcle nuber P_SI_

2 [5-7]. A ul-odel odelng algorh of suppor vecor achne based on affny propagaon cluserng algorh (ADAP) was proposed for he odelng of arachdonc acd ferenaon process n leraure [5]. A ul-odel sof-sensng odelng ehod based on onlne cluserng and assocaon vecor achne was proposed n leraure [8] whch has acheved good resuls n he fnal-bolng-pon predcon syse of lgh naphha n hydrocrackng un fraconaor. A ul-odel algorh of affny propagaon cluserng wh supervson was proposed n leraure [6] o crcularly adus he cluserng based on he oupu errors and hs ehod was beer han radonal ul-odelng ehods n er of odelng effec. Affny propagaon cluserng algorh however s dffcul n deernng he values of key paraeers for he opal cluserng resuls and he concusson of he cluser nuber generaed n he erave process does no auoacally dsappear o ake algorh converged [9-13]. In alluson o hese probles a sof-sensng odelng ehod based on Bayesan flerng and adapve affny propagaon cluserng was proposed n he sudy. The ADAP algorh was ulzed for he classfcaon of ranng saples n hs ehod; Bayesan esaon ehod was ulzed o creae he sub-odels of he sall classfed saple and carry ou global oupu n accordance wh he odel of he belongng subclass of curren operang pon. The effecveness of hs ehod was proved by he CO and CO2 sof-sensng odel n odaon sde reacon. 2. Algorh of Adapve Affny Propagaon Cluserng 2.1. Affny Propagaon Cluserng Algorh Affny propagaon cluserng s a new fas and effecve cluserng ehod proposed n leraure [4]. Frs all saple pons are regarded as poenal cluser ceners and each saple pon copees for he cluser cener n he eraon loop. So here s no need o deerne he nuber of clusers n advance. A gven saple se y N R s he npu of -denson saple; y R s he oupu of he saple. Negave Eucldean dsance s ulzed o easure he slary of and whch s S. Saples are sandardzed before solvng he slary o elnae he effec of denson. Rk s defned as he aracon degree ha k s su for he cluser cener of ; Ak s defned as he ebershp degree ha k s chosen as he cluser cener of. AP algorh connuously collecs he evdences ( Rk and Ak ) fro daa saples. The eraon forula Rk s shown n forula 1: of R k Rk a (1 ) new new R k S k A S R k R k R k The eraon forula of Ak forula 2: A k Ak a0 new A kk R k (1) s shown n n(0 a0 (1 ) new A k A k A k new A k R kk R k (2) If R k Ak a R A n daa pon k s he cluser cener of. The updae speed of he eraon could be changed by he adusen of dapng facor λ λ=0~1. The eleen on he dagonal of slary ar s a bas paraeer P whch ees. ( ) a R kk pk Ak S k The bgger ( ) k pk s he bgger R kk and A k are. So cluser head k has he bgges chance of becong he cluser cener. The ore and bgger pk ( ) eans ha he ore cluser heads could fnally becoe he cluser cener. Thus he change of P could affec he cluser nuber of AP. When pror knowledge s unknown he value of pk ( ) s he edan of S whch s n S ( ) 1 (3) pk ( ) p k1... n 2 n An ndcaor Slhouee nroduced o acheve he effec of evaluaon cluser ndcaes he nner-cluser ghness and ner-cluser separably of cluser srucure. Assue ha he daa se s dvded no k cluser subse C ( k) he ndcaor Slhouee of a saple s n dc ( ) a ( ) Sl() a a ( ) n dc ( ) (4) 212

3 where n dc ( ) s he average Eucldean dsance fro o anoher cluser C ; a() s he average Eucldean dsance fro o he cluser C. The average value of he ndcaor Slhouee of all he saples n a saple se s Slav eansu( Sl( )). Sl can reflec he qualy of all he daa and clusers. A bgger Sl av av eans beer cluser effec and he correspondng cluser nuber of he au s he opal cluser nuber. If Sl av s bgger han 0.5 each cluser could be apparenly separaed; f Sl av s saller han 0.2 hen a relevan cluser srucure s needed Cluserng Algorh of Adapve Affny Propagaon AP algorh can deerne he cluserng resuls based on he characerscs of he daa wh a fas arhec rae. Bu he algorh has he followng probles: he ncrease or decrease of he bas paraeer p can ncrease or decrease he cluser nuber of AP algorh so s dffcul o deerne he value of P o generae he opal cluserng resuls of algorh; algorh canno auoacally elnae he concusson and converge. In order o solve he above probles he cluserng algorh of adapve affne propagaon was proposed n leraure [9]. The eraon seps of he cluserng algorh of adapve affne propagaon are: Sep 1: nalze S and P and sar he algorh wh a relave bg P. The nal value of P n hs paper s p=0.5p (he eleen n S s negave so p s negave); Sep 2: eecue AP algorh once hen K cluser heads and he ypes of each saple are generaed wheren λ=0.5; Sep 3: eane wheher he K cluser heads are converged (he convergence condon s o ee he prese connuous consan frequency ω=0.5); f hey are converged evaluae he cluserng resuls wh effecveness ndcaor S l-av and reduce P wh a sep of 0.01p psep 0.1 K 50 f hey are no converged ncrease λ wh a sep of sep = 0.05; f hey are no converged when a ( a s 0.85) he concusson of P s obsnae and a relavely bg λ could no resran he concusson. Ths P needs o be abandoned. Reduce P wh a sep of 0.01p psep 0.1 K 50. Sep 4: deerne wheher he algorh ees he ernaon condon whch s o ee ha he au nuber of loop eraon or he nuber of clusers reaches 2. Ternae he eraon f he condon s e; oherwse go o sep 2. ADAP algorh searches for he nuber of clusers space o fnd he opal cluserng resuls by adapve scannng bas paraeer space. Adapvely adus he dapng facor o elnae he concusson n he erave process and reduce he value of P o ge rd of he concusson when he dapng facor adusen ehod fals. 3. Esablshen of Sof Sensng Mul-odel In order o overcoe he probles of sngleodel odelng he srucure of sof sensng ulodel based on Bayesan heory s shown n Fg. 1. Frsly cluser he ranng saples and fnd he opal cluserng resuls ulzng ADAP algorh. Secondly esablsh he sub-odels of each saple ulzng Bayesan heory. Lasly predc he oupu based on he correspondng sub-odel of curren operang pon n he process. Is srucure s shown n Fg. 1. Fg. 1. Srucure of ulple odels sof-sensng ehod. 213

4 3.1. Bayesan Esaon In hs research he conen of CO and CO2 was hough as a sae esaon proble. The saespace odel was ulzed o descrbe hs proble. Assue ha he poson sae of he arge s ( 1... ) N and he collecon for each oen observaon s ( 1... ) N. Then he sae of he arge can be descrbed by he oon equaon and observaon equaon n forula 5: F( 1) z H( ) (5) where F s he pac paraerc equaon descrbng he odel npu; H s he observaon odel whch descrbes he relaonshp beween he observed quany and odel oupu; s he nose whch s ulzed o descrbe he uncerany of oveen; s he observed nose whch s ulzed o descrbe he uncerany caused by ousde nerference and he nose of he deecng eleen. Bayesan esaon s a sae esaon ehod ulzng sae pror dsrbuon and he observaon of lkelhood funcon o deerne he poseror probably dsrbuon. For a frs-order Markov process assue ha he observaon of each oen s uually ndependen. If he poseror dsrbuon p( z ) a e -1 s 1 1 he pror dsrbuon a e can be epressed as shown n forula 6: p ( z ) p ( z ) p ( z ) d (6) p( where z 1) s he ranson probably densy funcon whch s deerned by F and he probably dsrbuon of he nose ( p( ) ) n oon equaon 5. The defnon s: p ( ) p( ) ( F ( )) d 1 1 (7) where n () s he Drac funcon. Afer he pror p( dsrbuon z 1) s obaned he sae poseror dsrbuon p( ) z could be epressed as: pz ( ) p ( z 1) p ( z) p( z ) p( z ) d 1 (8) p( z ) where s he observaon lkelhood funcon whch s deerned by H and he probably dsrbuon of he nose ( p( ) ). The defnon s: pz ( ) p( ) ( zh ( )) d (9) The above forula 6 and 7 consue he predcon process of Bayesan esaon; forula 8 and 9 consue he updae process of Bayesan esaon. The wo processes are deerned by he equaon and observaon equaon of sae space odel paraeers n forula 5 respecvely. The rackng of he poseror dsrbuon of sae could be acheved hrough he erave and recursve soluon of above predcon and updae process Sulaon Sudy S The source of our daa was he PTA producon process daa n a checal plan. The odel of paraylene () odaon sde reacon hrough sof sensor odel provded he bass for producon opzaon of operang paraeers and he ransforaon of he producon process. The an facors ha wll affec he cobuson sde reacon are: he reacon eperaure ( 1 C) solven rao ( 2 Kg. /Kg. ) he concenraon of cobal caalys ( 3 w%) he concenraon of anganese caalys ( 4 w%) he concenraon of brone acceleraor ( 5 w%) and he resdence e ( 6 S). Regard hese an facors afer daa preprocessng as he npu daa; he oal conen of CO and CO 2 (ФCOX) of he reacor ehaus gas as he oupu daa y. Generally 0 ses of daa were obaned. 170 ses of daa are he ranng daa and he reanng 80 ses of daa are he curren runnng daa n he process whch were ulzed o es he generalzaon capably of he odel. Fg. 2 s he cluser nuber of ADAP cluserng algorh and he correspondng ndcaor of effecveness l av. Fg. 2 shows he ADAP algorh was sared wh a large value of P o oban several cluserng resuls. The opal cluserng resuls S could be seleced accordng o he ndcaor l av. S The ndcaor l av was he larges when he ranng saples were dvded no wo clusers n ers of he daa ulzed n hs sudy. Therefore he ranng saples were dvded no wo clusers. Furher sulaon analyss on he ranng resuls and he lnear regresson analyss of he oupu and arge oupu of nework sulaon are shown n Fg. 3. The fgure shows ha he correlaon coeff- 214

cen s 0.99 whch eans ha he perforance of he nework s sasfyng. 0.76 0.74 0.72 0.70 0.68 0.66 0.64 0.62 0.6 0.58 2 4 6 8 10 12 14 16 The nuber of cluserng Fg. 2. The effecve nde of cluserng algorh.

5 cen s 0.99 whch eans ha he perforance of he nework s sasfyng The nuber of cluserng Fg. 2. The effecve nde of cluserng algorh. : he percenage of CO generaed by acec acd (%); CO : he percenage of CO accounng for he cobuson produc of acec acd sde reacon (%); gas : he flow of ehaus gas fro he reacor (f3/hr); CTA : CTA produc yeld (ons / Hr); The olecular wegh of acec acd: 60 (g / ol); consue : he aoun of acec acd loss (Kg / on. CTA); : he percenage of CO generaed by (%); CO : he percenage of CO accounng for he cobuson produc of sde reacon (%); The olecular wegh of : 106 (g / ol); consue : he aoun of loss (Kg / on CTA); Fro he above e he value CO and CO of are known as 60 % 75 % 40 % and 60 % respecvely; gas and CTA were obaned hrough he acual producon daa. 4. Analyss of he Effec on Process Operang Paraeers on Cobuson Loss Fg. 3. The analyss resul of nework oupu The Cobuson Loss Model of Acec Acd and Xylene Esablsh he cobuson loss odel of acec acd and based on he deerned generaon odel of CO. The cobuson loss odel of acec acd: Esablsh a odel o reflec he effec of operang paraeers on he and cobuson loss n odaon reacon process. Then analyze he effec of varous operang paraeers on and cobuson loss n he reacon process. Thereafer analyze he effec of resdence e reacon eperaure solven rao he concenraon of caalys lke cobal anganese brone and oher operang paraeers on he and cobuson loss hrough he odel respecvely. The resuls are shown n Fgs consue gas 60 CO CO 2 CTA 100 The cobuson loss odel of s: consue gas 106 CO CO 8 CTA 100 consue of --blue/--red(kg) COX : he oal conen of generaed CO and CO 2 of he ehaus gas; reacon e(s) Fg. 4. Effec of reacon e on odave sde-reacon. 215

6 consue of --blue/--red(kg) Fg. 4-9: reacon resdence e has a grea effec on he cobuson loss; he effecs of reacon eperaure and he concenraon of Co Mn Br are sall bu he effec of reacon eperaure s slghly bgger. The effecs of each operang paraeer on he cobuson loss can be quanavely analyzed fro hese curves o provde gudance for he adusen and opzaon of operang paraeers n praccal producon process eperaure( ) Fg. 5. Effec of reacon eperaure on odave sde-reacon. consue of --blue/--red(kg) / Fg. 6. Effec of / on odave sde-reacon. consue of --blue/--red(kg) consue of --blue/--red(kg) Co(%) Fg. 7. Effec of Co concenraon on odave sde-reacon Mn(%) Fg. 8. Effec of Mn concenraon on odave sde-reacon. Fg. 9. Effec of Br concenraon on odave sde-reacon. 5. Conclusons Ulze he algorh of adapve affne propagaon cluserng o dvde he feld daa no wo caegores. The cobuson loss odel of and was esablshed based on Bayesan flerng. And hs neural nework odel regarded he an adusable process paraeers (resdence e he concenraon of Co Mn Br reacon eperaure and solven rao) as he ndependen varables and he oal conen of CO and CO2 as he dependen varable. The sulaon resuls show ha he nework s well perfored. The effecs of process operang paraeers on and cobuson loss are analyzed based on he odel. Wheren he effecs of resdence e reacon eperaure on he cobuson loss are bgger whle he effecs of oher facors are relavely sall. Acknowledgeen The auhors would lke o hank he fnancal suppor provded by Research and Innovaon Proec for College Graduaes of Jangsu Provnce of Chna under Gran CXLX12_0648 Naonal Naural Scence Foundaon under Gran and Prory Acadec Progra Developen of Jangsu Hgher Educaon Insuons (PAPD). 216

References [1]. L We Yang Yupu Wang Na LSSVM ul-odel regresson odelng based on he fuzzy kernel cluserng Conrol and Decson Vol. 23 Issue 5 08 pp. 560-562. [2].

7 References [1]. L We Yang Yupu Wang Na LSSVM ul-odel regresson odelng based on he fuzzy kernel cluserng Conrol and Decson Vol. 23 Issue 5 08 pp [2]. Suo Xngy Sh Hongbo The sof sensor odelng of sewage reaen process based on ul-odel fuzzy kernel cluserng algorh Eas Chna Unversy of Technology: Naural Scence Issue 5 10 pp [3]. Per K. Bogdan G. Sbylle S. Daa-drven sof sensors n he process ndusry Copuers and Checal Engneerng Vol. 33 Issue 4 09 pp [4]. Frey B. J. Dueck D. Cluserng by passng essages beween daa pons Scence Vol. 315 Issue pp [5]. L Luan Song Kun Zhao Yngka ARA ferenaon process odelng based on affny propagaon cluserng Journal of Checal Indusry and Engneerng Vol. 62 Issue 8 11 pp [6]. Deng Wewe Yang Hu A supervson ulodelng ehod of affny propagaon cluserng Shangha Jao Tong Unversy Vol. 45 Issue 8 11 pp [7]. L X. Su H. Chu J. Mulple Model Sof Sensor Based on Affny Propagaon Gaussan Process and Bayesan Coee Machne Chnese Journal of Checal Engneerng Vol. 17 Issue 1 09 pp [8]. Lu Xulang Su Hongye Chu Jan Mulple odel sof sensor based on onlne cluserng and relevance vecor achne Conrol and Insruens n Checal Indusry Vol. Issue 3 08 pp [9]. Wang KaJun Zhang Junyng L Dan Adapve Affny Propagaon Cluserng AAS Vol. 33 Issue 8 07 pp [10]. Shang F. Jao L. C. Sh J. e al. Fas affny cluserng: a ullevel approach Paern Recognon Vol. 45 Issue 1 12 pp [11]. Su Z. Wang P. Shen J. e al. Mul-odel sraegy based evdenal sof sensor odel for predcng evaluaon of varables wh uncerany Appled Sof Copung Vol. 11 Issue 2 11 pp [12]. Tan S. An effecve refneen sraegy for KNN e cluserfer Epor Syses wh Applcaons Vol. Issue 2 06 pp [13]. Ge Z. Song Z. A coparave sudy of us-n-elearnng based ehods for onlne sof sensor odelng Cheoercs and Inellgen Laboraory Syses Vol. 104 Issue 2 10 pp Copyrgh Inernaonal Frequency Sensor Assocaon (IFSA). All rghs reserved. (hp:// 217

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015 /4/ Learnng Objecves Self Organzaon Map Learnng whou Exaples. Inroducon. MAXNET 3. Cluserng 4. Feaure Map. Self-organzng Feaure Map 6. Concluson 38 Inroducon. Learnng whou exaples. Daa are npu o he syse