Journal of Engineering Science and Technology Review 7 (3) (2014) Research Article

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1 Jestr Joural of Egeerg Scece ad Techology Revew 7 (3) (04) Research Artcle JOURA OF Egeerg Scece ad Techology Revew Estmato of Bodesel Yeld usg Fast Deelated eural etwork Esemble Hogya Sh,, *, B, Xu Wag, Yg Wag ad Dresutsky Wog 3 Dept. of Iformato Egeerg, Sheyag Uversty of Chemcal Techology, Sheyag 04, aog, Cha Sheyag Isttute of Automato, Chese Academy of Sceces, Sheyag 006, aog, Cha 3 Rga Vocatoal College of Scece&Techology, Galuge Str.00, Rga V-98, atva Receved February 04; Accepted 9 July 04 Abstract The accurate ad relable ole measuremet of the product yeld s very essetal for the cotrol ad optmzato of the bodesel process. A bodesel yeld predcto model based o the fast deelated eural etwork esembles (FDE) was establshed to ehace the estmated performace. The radom vector fuctoal lk (RVF) etworks were serted to the fast deelated eural etwork esemble frame as the base model sce t could provde better geeralzed performace ad faster speed. The FDE product yeld predcto model talzes the hdde layer parameters of base models radomly, ad calculates the output layer parameters usg the least square method wth egatve elato learg. Smulato results show that the proposed method has relatvely hgher accuracy ad relablty compared wth the sgle RVF model. Keywords: Bodesel Yeld, egatve Correlato earg, Fast Deelated eural etwork Esembles, RVF. Itroducto Due to the cotuous decle of lmted petroleum reserves ad the growg evrometal cocers, the use of bodesel recet years as a fuel the exstg desel eges has gaed much mportace [], [], [3]. Although there are may researches o the sythess techology of bodesel, o the expermetal data processg of bodesel yeld ad aalyss of the teracto betwee factors s stll less. I the bodesel reacto, the yeld as ma qualty dex s affected by dfferet parameters [4]. However, four ma factors have bee cosdered by researchers as follows: molar rato betwee alcohol ad ol, reacto tme, catalyst, ad reacto temperature [5], [6]. agetc resoace detecto method s ofte used to measure the yeld of bodesel whle o-le hardware sesors are dffcult to meet the requremets of o-ste motorg ad cotrol due to bg vestmets, poor relablty, ad log respose tme. Recetly, esemble methods have receved cosderable attetos because t ca effectvely mprove the valdty ad credblty of the regresso model through buldg a set of models [7], [8], [9]. ay ovel mache learg techques are proposed to tra a esemble model dvdually or collectvely such as baggg, boostg ad radom forests [0], [], [], [3]. Alhamdoosh ad Wag [4] proposed a effcet algorthm to buld esemble models a very short tme amed fast deelated eural etwork esembles (FDE) whch employed the radom vector fuctoal lk (RVF) etworks as base compoets * E-mal address: shhogya@sa.c ISS: Kavala Isttute of Techology. All rghts reserved. ad corporated wth the C strategy for buldg eural etwork esembles. egatve elato learg (C) [5] s a algorthm for trag eural etwork esemble wth soud geeralzato capablty through cotrollg the dsagreemet of base model. I ths paper, a fast bodesel yeld esemble model usg fast deelated eural etwork esemble was establshed, whch radomly talzed the hdde layer parameters of base RVF etworks, ad the employed the least square method wth egatve elato learg scheme to aalytcally calculate the output weghts of these base etworks. The proposed method was the verfed by the expermetal data of bodesel product. The expermetal results of the testg datasets demostrated that the producto yeld esemble model had the capacty of strog geeralzato ad low computato load. Ths paper s orgazed as follows: secto presets bascs o RVF eural etworks, egatve elato learg ad fast deelated eural etwork esembles, secto 3 focuses o the aalyss of expermet results ad secto 4 presets the coclusos.. Bodesel yeld esemble model based o FDE algorthm. The Descrpto of the Bodesel Process The expermetal devce used for cotuous process of bodesel sythess uder supercrtcal methaol s show Fg.. Soybea ol was placed vessel ad heated to 35 ~ 50 C, the sold catalyst was packed to fx bed reacto tubes usg pressurzed gas aalyzer. The ol ad methaol were pumped to the ppele by a hgh pressure pump,

2 Hogya Sh, B, Xu Wag, Yg Wag ad Dresutsky Wog /Joural of Egeerg Scece ad Techology Revew 7 (3) (04) uder the codtos of a total volume flow rate of ~ 4ml/m, after mxed the ppele to the reacto tube. The reacto temperature, pressure ad the molar rato of methaol to ol were cotrolled accurately by the reacto apparatus. The reactor temperature could be cotrolled betwee 60 ~ 400 C ad the ter pressure was regulated betwee 3~4Pa by back pressure valve. The product effluet from the reacto tube was sampled after codeser ppe codesate. where f( x ) s the predctve value of sample( x, y ), y s the expected output of x..3 egatve Correlato earg egatve elato learg (C) s proposed to reduce the covarace amog esemble dvduals whle the varace ad bas terms are ot creased. Ulke tradtoal esemble learg approaches, C s troduced to tra base models smultaeously a cooperatve maer that deelates dvdual errors e [6]. athematcally, the learg error of the th sub-model gve Eq. (3) s modfed to clude a pealty term p as follows: e f x y p x (3) = [ ( ( ) ) + λ ( )] Where λ [0,] s a regularzg factor. Set a trag dataset D t wth sze, Dt = {( x, y),( x, y)...( x, y)}, where x s the put of the eural etwork, y s the expected output of x. The mportat steps of egatve elato learg lst as follows: Step: Calculatg the output of each sub-model f (), ad the compute the output of the whole esemble f( x ) Fg.. Bodesel Supercrtcal Sythess Devce. RVF eural etwork For arbtrary dstct samples ( x, y ), =,...,, where T T m x = [ x, x,..., x] R, y = [ y, y,..., ym] R, RVF eural etwork as sgle-layer feed-forward etworks (SFs) s mathematcally defed as: T f( x; β) = βkg( ωk x+ bk) () k = d d where x R s put vector, ωk R ad b k Rare put weghts ad hdde layer bases, β = [ β, β,... β ] R s the output layer weghts, d s the umber of put layer, G() s the bass fucto, f () s the output of eural etwork. I RVF etwork, the parameters of the hdde layer are assged radomly ad depedetly of the trag data; whle the lear parameters β of the output layer ca be tued usg the least squares method. Testg dataset wth sze ʹ ca be deoted D = {( x y ),( x, y )...( x, y )}, the geeralzato by t, ʹ ʹ error E( D)of the RVF etwork model s defed as the f t mea squares error (SE) averaged over all possble realzatos of D f t = t ʹ E ( D) = ( f( x ) y ) () ʹ k f( x ) = f ( x ) (4) = where s the umber of sub-model. Step: Usg the output of sub-model ad the output of whole model to decde the pealty term p p = ( f( x) f( x)) ( f ( x) f( x)) (5) Step3: Addg the pealty term p to the error fucto, so the learg error of the th sub- model could be defed as follows: e f x y p x (6) = [ ( ( ) ) + λ ( )] Step4: Applyg the ew learg error to the update the weghts..4 Fast Deelated eural etwork Esembles Due to the ucertates the learg process that are caused by the radom talzatos of bass fuctos, a sgle RVF etwork ca ot guaratee the accuracy of the forecasts. A ew esemble learg approach, whch uses RVF etworks as esemble compoet s adopted ad t s ftted egatve elato learg framework. Sce RVF etworks are used to populate the esemble, the output of the th base etwork s stmulated wth a stace x, whch s gve by 59

3 Hogya Sh, B, Xu Wag, Yg Wag ad Dresutsky Wog /Joural of Egeerg Scece ad Techology Revew 7 (3) (04) f ( x ) = β g ( x ) = (7) where s the umber of hdde euros the th dvdual RVF etwork, β s the output weght coectg the th hdde euro wth the output euro the th base model, g ( x ) = ( w, b, x ) s the output of the th hdde euro the th base model, ad G ca be ay squashg bass fucto. The parameters ( w, b ) of the bass fuctos g are radomly set whle the oly parameters to be tued are the output weghts β. I order to get the best performace of model, e = 0, for=,..., should be satsfed, whch leads to e e( x) = = 0 for =,... (8) β β All base etworks are assumed to have smlar archtecture ad the same dataset s used to tra all of them. It ca get that ad the l th hdde euro of the k th dvdual RVF etwork, ad ϕ (, ) represets the elato betwee the th hdde euro of the th base etwork ad the target value. To facltate ths computatoal task, ths lear system a matrx form ca be desged by equato (4). HBes = Th (4) where H s called the hdde elato matrx, Bes s the global output weghts matrx ad T h s the hdde-target matrx. H H s defed by equato (5) or (6). ( p, q) Cϕ( m,, k, l) f m= k Cϕ( m,, k, l) otherwse = (6) where p m =, q k = (7) (( p ) mod ) + (8) l = (( q ) mod ) + (9) pq, =,..., Cϕ(,,, k) β + Cϕ(,,, l k) β = ϕ(, ) k k= l= k= l where ( ) C = λ (0) C = λ () ϕ(,,, k) = g ( x ) g ( x ) () kl ϕ(, ) = g ( x ) y (3) =,...,, =,... where s the umber of sub-model, s the umber of hdde euro,λ s a regularzg factor, ad C, C are two costats. ϕ(,,, l k) represets the elato betwee the th hdde euro of the th dvdual RVF etwork lk (9 ) Ad mod s the modulo operato. defed as follows: B es h = [ β! β β! β β! β ] T ϕ(,)! ϕ(, )]! T = [ ϕ(,)! ϕ(, ) ϕ(,)! ϕ(, )! T The output weghts β ca be got by equato () es h Bes ad T h are (0) () B = H T () The the output of th base etwork, smulated wth a sample x ca be got by equato (7). Uform averagg weghts are used to combe esemble base RVF etwork, ad the output of the esemble ca be obtaed as follows: f( x ) = f ( x ) (3) = Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) H = Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) Cϕ(,,, ) Cϕ(,,,) C ϕ (,,, ) ( ) (5) 60

4 Hogya Sh, B, Xu Wag, Yg Wag ad Dresutsky Wog /Joural of Egeerg Scece ad Techology Revew 7 (3) (04) FDE Algorthm Requre: Trag dataset D t, a bass fucto G : R R ; default s Sgmod, scalg coeffcet λ [.0], the sze of base model, ad the umber of base models. Esure: Traed DE model. ) Italze the archtecture of SFs to be the esemble base models. ) Italze the bass fuctos of base models radomly.e. w, b are radomly set. 3) Calculate the outputs of the hdde layers of base models for all examples D.e., calculate g ( x ) t 4) Calculate the costatsc ad C. 5) for p to do p 6) m 7) (( p ) mod ) + 8) for q to do q 9) k 0) l (( q ) mod ) + ) f m = k the ) H [, ] (,,, ) p q Cϕ m k l 3) else 4) H [, ] (,,, ) p q Cϕ m k l 5) ed f 6) ed for 7) ed for 8) k 9) for to do 0) for to do ) Th [ k] ϕ(, ) ) k k + 3) ed for 4) ed for 5) Calculate H, the pseudo-verse verse of H. 6) Calculate the estmated global output weghts matrx Bes from Eq. (). 7) for to do 8) Output weghts of base model: Bes [( ) + : ] 9) ed for 30) retur Esemble model (DE). etwork, three parameters wth hdde odes, submodels ad the regularzg factor λ are chose. Takg the mpact that the umber of hdde odes to the performace of the esemble to accout, a umber of expermets ca be coducted by chagg the umber of from 0 to 0 wth the terval of 0 ad keepg the other parameters same. Here s 8 ad λ s 0.6, 50 tmes are fshed for every. I ths paper, the root mea squares error () ad elato coeffcet ( R ) are calculated to reflect the performace of the models. metrc s defed by Equato (4), whch represets the smaller the, the better performace of the etwork. = ( f( x) y) = (4) R s calculated by Equato (5), ad R [0,]. If t s closer to oe, the model wll have better performace. R f ( x ) y f ( x ) y = = = = f x f x y y = = = = ( ( ) ( ( )) )( ( ) ) (5) Performace comparso of dfferet umber of hdde odes s show Fg.. Fg.3 llustrates how the umber of the sub-model affects the accuracy of the model. et chage (, 0) wth the terval of ad keepg ad λ same. ot oly does the umber of hdde odes mpact the performace of the esemble but also the sze of the esemble. Set =00, λ =0.6, for every stuato, t has fshed 50 tmes, ad the average ad R are obtaed. From Fg.3, t ca be cocluded that the best sze of our esemble s sx R the umber of hdde odes Fg.. Performace Comparso of Dfferet umber of Hdde odes R 3. Results ad dscusso I ths secto, the performace of FDE wth sgle RVF etwork was compared by the aalyss of bodesel dataset, the yeld dex was predcted by aalyzg temperature, pressure ad volume rato. All the expermets were carred out a ATAB evromet rug wth CPU.55GHz ad GB RA. For RVF etworks, there s oly oe parameter wth hdde odes eeds to be determed. For the FDE the umber of sub model 0.95 R R 6

5 Hogya Sh, B, Xu Wag, Yg Wag ad Dresutsky Wog /Joural of Egeerg Scece ad Techology Revew 7 (3) (04) Fg.3. Performace Comparso of Dfferet umber of Sub-odels As show Fgure 4, t s the comparso of the expected value ad the predcted value of FDE. Fgure 5 shows the comparso of RVF etwork. I ths expermets, =00, =6, ad λ =0.6. After several expermets, t ca be foud that FDE perform better tha RVF etwork whe the same umbers of hdde odes are used. 00 comparo of Bodesel dataset (FDE) (rmse =.0507 R = ) expected value predcted value yeld comparo of Bodesel dataset (RVF) (rmse =.865 R = ) expected value predcted value yeld Sample umber Fg.4. Comparso of the Expected Value ad Predcted Value of FDE etwork Sample umber Fg.5. Comparso of the Expected Value ad Predcted Value of RVF etwork The average value of ad R of the trag data ad testg data after rug 00 tmes are preseted Table, whch FDE trag meas that the put s the trag dataset usg FDE model, ad FDE testg meas the put s the testg dataset dfferet from trag data. It s clear that the of FDE model s smaller tha RVF etworks model, ad R of FDE model s closer to oe. The performace of FDE model s better tha RVF etworks. Tab.. Comparso of testg FDE ad sgle RVF FDE trag RVF trag FDE testg RVF testg R Coclusos Although the RVF modelg method has mproved the geeralzed performace, t was dffcult to acheve better stablty. I ths work, a bodesel yeld model was bult usg fast deelated eural etwork esemble by buldg a set of models, rather tha a sgle model. The esemble model employed radom vector fuctoal lk (RVF) etworks as base model to talze the hdde layer parameters of base models radomly ad calculated the output aalytcal soluto usg the least square method wth egatve elato learg. The expermet results show that the proposed model has a hgher relatvely accuracy ad faster learg speed tha the sgle RVF model. I ths study, the results are lmted to the operatg codtos the laboratory ad more dustral expermets should be doe. Ackowledgmets The authors would lke to ackowledge the facal support provded by the atoal atural Scece Foudato of Cha (o.6030) ad Scece Research Foudato of aog Provcal Departmet of Educato (o.04 5) & (o.0358). Refereces. orad, G.R., Dehgha, S., Khosrava, F., ad Armadzadeh, A., The optmzed operatoal codtos for bodesel producto from soybea ol ad applcato of artfcal eural etworks for estmato of the bodesel yeld, Reewable Eergy 50(), 03, pp Jeog, G.T., Yag, H.S. et al., Optmzato of trasesterfcato of amal fat ester usg respose surface methodology, Boresourse Techology 00(), 009, pp Yusuf,., Kamarud, S., Overvew o the curret treds bodesel producto, Eergy Coverso ad aagemet 5(7), 0, pp Sharma, Y.C., Sgh B., ad Upadhyay S.., Advacemets developmet ad characterzato of bodesel: a revew, Fuel 87(), 008, pp Demrbas A. Bodesel fuels from vegetable ols va catalytc ad o-catalytc supercrtcal alcohol trasesterfcatos ad other methods: a survey, Eergy Coverso ad aagemet 44(3), 003, pp Baereea, A., Chakraborty, R., Parametrc sestvty trasesterfcato of waste cookg ol for bodesel producto a revew, Resource Coservato ad Recyclg 53(9), 009, pp Kouretzes,., Barrow, D. K., ad Croe, S. F., eural etwork esemble operators for tme seres forecastg, Expert Systems wth Applcatos 4 (9), 04, pp u, D. P, Wag, F.., Zhag,.., He, D. K., ad Ja,. X., eural etwork esemble modelg for osheptde fermetato process based o partal least squares regresso, Chemometrcs ad Itellget aboratory Systems 05(), 0, pp

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