Sensors & Transducers Published by IFSA Publishing, S. L.,

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1 Sesors & rsducers Pulshed y IFSA Pulshg, S. L., 06 Reserch of Eergy Cosupto Ptter Clssfcto sed o Fuzzy Logc d RF etworks Hydrulc Systes Xgyu He, Shghog He College of Autoole d Mechcl Egeerg, Chgsh Uversty of Scece d echology, Chgsh, Hu, 40004, Ch E-l: hexgyu04@63.co Receved: 3 Octoer 06 /Accepted: 8 Octoer 06 /Pulshed: 3 Octoer 06 Astrct: sed o fuzzy logc theory d RF etworks, eergy cosupto ptter clssfcto pproch for the hydrulc systes ws proposed ths pper. Frst, the eergy cosupto ptter fetures re extrcted fro fuzzy uto-regressve wth extr outputs (FARX odel. Secod, RF etworks serve s clssfer d the work codto d eergy cosupto ptters of the hydrulc systes re detfed. Severl typcl eergy cosupto ptters of hydrulc systes were used to verfy the clssfcto pproch. Keywords: Hydrulc syste, Eergy cosupto ptter, Fuzzy logc, Auto-regressve wth extr outputs (ARX odel.. Itroducto he theory of fuzzy logc forulted y Zdeh hs ee cosdered s pproprte presetto ethod for ucertty, precso d copleteess. Fuzzy systes hve ee successfully used y pplctos cludg recogto of hdwrtg, dgoss [-3], d other stces. echques sed o fuzzy logc hve dvtge over covetol techques sgfctly provg the ccurcy of eergy cosupto ptters. hese ttrutes ke fuzzy delly suted for provdg hgh ccurcy eergy cosupto ptter lyss uder wde vrety of systes d codtos. Rdl ss fucto (RF etworks eerged s vrt of As the lte 980 s. However, the roots re etreched old ptter recogto techques, such s potetl fuctos, clusterg, fuctol pproxto, sple terpolto, d xture odels []. RFs re eedded two-lyer eurl etwork where ech hdde ut pleets rdl ctvted fucto. he output uts pleet weghted su of hdde ut outputs. he put for the RF etwork s oler wheres the output s ler. he excellet pproxto cpltes hve ee studed [4, 5]. RF etworks, whch hve oler pproxto propertes, re cple of odelg coplex ppgs, wheres perceptro eurl etworks c oly odel coplex ppgs y ultple teredry lyers. RF etworks hve ee successfully ppled to vrous felds, such s terpolto, chotc teseres odelg, syste detfcto, cotrol egeerg, electroc devce preter odelg, chel equlzto, speech recogto, ge restorto, shpe fro shdg, 3D oect odelg, oto estto, ovg oect segetto, d dt fuso [6-8]. I ths study, eergy cosupto ptter clssfcto pproch sed o fuzzy logc d RF etworks ws proposed. Frst, fuzzy uto-regressve wth extr outputs (FARX odel ws used to extrct 58

2 eergy cosupto ptter fetures. he FARX odel ots ore ccurte eergy cosupto ptter of oler chrcterztos th covetol uto-regressve wth extr outputs (ARX odel. RF etworks were tred wth dt uder vrety of eergy cosupto codtos d the used for eergy cosupto ptter clssfcto o the hydrulc syste. hs pproch ws effectvely ppled o excvtor hydrulc syste d could ccurtely detere eergy cosupto ptter.. RF etworks RFs re eedded to two-lyer feedforwrd eurl etwork, whch s chrcterzed y set of puts d set of outputs. A lyer of processg uts clled hdde uts s locted etwee the puts d outputs. Ech of these hdde uts pleets RF. he er whch the etwork s used for dt odelg s dfferet whe esttg te-seres d ptter clssfcto. he structure of RF etworks cludes three lyers, ely, the put lyer, hdde lyer, d output lyer (Fg.. p where k s the uer of ss fucto, x R s the put vector, ϕ s the ss fucto, h s the sooth coeffcet, c s the cetrod of cluster, ω s the weght d s the Euclde or. We chose Guss for s the ss fucto y usg followg equto: ( z exp( z φ ( We c costruct coplete RF etwork y deterg the ceter posto d the weghts. o detere the ceter posto, the oectve fucto could e defed s follows k, J u d d x c (3 where x represet the th oservto sple pot, d u c detere whether x elogs to the th eershp fucto. o ze crtero J, ely ( J, terto lgorth s pleeted y the followg steps: Rdoly tlze the c-prtto trx ccordg to C u,,..., (4 ( 0 d geerte U. Clculte the cetrods of clusters y usg Fg.. Structure of RF etworks. o use RF etworks, we eed to specfy the hdde ut ctvto fucto, the uer of processg uts, crtero for odelg gve tsk, d trg lgorth for fdg the etwork preters. Fdg the RF weghts s clled etwork trg. If we hve set of put-output prs clled trg set, we c optze the etwork preters to ft the etwork outputs fro the gve puts. he ft ws evluted y es of cost fucto, whch s usully ssued to e the e squre error. After trg, the RF etwork could e used wth dt tht hve uderlyg sttstcs slr to tht of the trg set. Ole trg lgorths dpt the etwork preters to the chgg dt sttstcs. A RF etwork could e expressed s follows: c u x u (5 3 Copute the dsslrty etwee cetrods d dt pots y u C x c x c k k 4 Stop terto whe ( k+ ( k (6 U U ε (7 ( g x k ωϕ x c h ( ( k 5 Updte U d go to Step (. 6 Costruct k-deso spce vector 59

3 x c exp h y (8 x ck exp h where the vrces re detfed, d g( x ω y (9 7 y pleetg the lest e squre error (LMSE ethod, the trx of the weght c e estted s follows: ωˆ 3. FARX Model ˆ ω ˆ ω ˆ ω ˆ ˆ ˆ ω ω ω ˆ ω ˆ ˆ k ωk ωk (0 Cosder sgle-put-sgle-output oler syste tht c e cofgured s the followg fuzzy reltol equtos: R : IF x s A, HE y s r r r R : IF x s A, HE y s ( he syste could e descred y syste of dsuctve rules, d we could decopose these rules to sgle ggregted fuzzy reltol equto s follows: ( ( AD r AD ( x R y xr xr AD ( Aove equtos c e represeted ggregted fuzzy reltol equto s follows where ( φ( ( ( ( y t y t Θ t + e t φ ( t y( t,, (,, ( u t u t,,,,, θ Θ,,,,, θ ( y( t μ ( y( t,, μ ( y( t Eq. (4 could the e splfed s follows: where y( t ( ( + ( (4 y t φ t θ e t, (5 ( θ Θ. he eergy cosupto ptter extrcto pproch could e gve s followg steps: Defe eershp fuctos. Fve Guss eershp fuctos were used to represet the output y s show Fg.. or y x R Fg.. Meershp fucto of the output y. r where, R R R. he ARX odel could e corported to fuzzy reltol equtos. he FARX odel could e wrtte s the followg equtos: ( y( t y( t ( ( ( : IF y t s, HE + u t + + u t + e t : IF y t s, HE + u t + + u t + e t ( y( t y( t ( ( ( (3 Defe the fuzzy reltol rules. Fuzzy reltol rules were cossted of fve equtos whch c e gve y ( y( t y( t ( ( ( : IF y t s, HE + u t + + u t + e t 5 5 : IF y( t s, 5 5 HE y t y t y t u t + + u t + e t ( ( ( ( ( ( (6 60

4 3 Estlsh the Fuzzy ARX odel. We c estlsh correspodg ARX odel for ech fuzzy rule. he preters of the FARX odel were estted y pplyg the lest squre ethod: t ( μ ( y( t ( t ( t ˆ θ φ φ t μ ( y( t φ( t y( t (7 were used to tr the RF etwork clssfer, he the RF etwork clssfer ws used to clssfy the eergy cosupto ptters. he clssfcto result shows tht ll eergy cosupto ptters were correctly clssfed. d ˆ θ ˆ Θ (8 ˆ 5 θ 4 Extrct the eergy cosupto ptter vector. he deso of the preter trx ws lrge; thus, the eergy cosupto ptter clssfer could ot properly detere the eergy cosupto ptter codto. o prove the effcecy, we used the weghted vector s the eergy cosupto ptter feture vector: where λ+ + λ5. f λθˆ + + λ θˆ (9 5 5 Fg. 3. Experetl pltfor of the.7 to excvtor. 4. Experet I ths secto,.7 to excvtor hydrulc syste ws developed s the experetl pltfor for testg the proposed eergy cosupto ptter clssfcto pproch. hs excvtor ws produced y Suwrd Equpet Group (Fg. 3. hs experetl excvtor cossts of oo, stck, d ucket d oves v trcks or wheels. he oto of the oo, stck, d ucket re drve y correspodg hydrulc cylders. A sc opertg cycle volves dggg pss through the k, loded swg to dup posto, dup to hul truck, epty swg ck to dggg, d repostog or spottg of the ucket t the fce. o fulfll these coplex opertos, excvtor s usully equpped wth vrous hydrulc copoets, cludg vrle pup, proportol vlves d cylders. he vrle pup coverts echcl eergy to hydrulc eergy d proportol vlves dstrute hydrulc eergy to cylders to drve the oo, stck, d ucket. Hece, we c splfy the hydrulc syste of excvtor to severl slr sc hydrulc loops despte of the fuctol dfferece (Fg. 4. Severl test sples were troduced to verfy the clssfcto perforce of the RF etwork clssfer. eergy cosupto ptter feture vectors Fg. 4. sc hydrulc loop of the excvtor. 5. Sury A eergy cosupto ptter clssfcto pproch y usg RF etworks ws proposed ths pper for hydrulc syste. FARX odels were developed y usg sple dt for trget eergy cosupto ptters. Eergy cosupto ptter feture vector ws extrcted fro the FARX odels. 6

5 RF etwork clssfer ws used s the Eergy cosupto ptter clssfer to sort the test sple to the trget ptters. he hydrulc syste of.7 to experetl excvtor ws developed to verfy the eergy cosupto ptter clssfcto pproch. Ackowledgeet hs work s proect fuded y Hu Provce Scece d techology proect uder Grt o. 05JC3058 d the Key Lortory of Lghtweght d Rellty echology for Egeerg Vehcle, Educto Deprtet of Hu Provce (Chgsh Uversty of Scece & echology uder Grt o. 03KFJJ07. he uthors re would lso lke to express ther scerest grttude to Yg Jg for helpful dscussos o ths topc, d vlule coets o erler drfts of ths pper. Refereces []. Qghu He, Dqg Zhg, Peg Ho, d Jx Zhu. Model d experetl reserch o cotrol of hydrulc excvtor's pultor, Jourl of Cetrl South Uversty (Scece d echology, Vol. 37, Issue 7, 006, pp [].. Mrcu,. Köppe-Selger, R. Stücher. Desg of fult detecto for hydrulc looper usg dyc eurl etworks, Cotrol Egeerg Prctce, Vol. 6, Issue, 008, pp [3]. A. E. e-kh, M. A. Mhoud, Coolg lod predcto for uldgs usg geerl regresso eurl etworks, Eergy Coverso d Mgeet, Vol. 45, 004, pp [4]. W. Y. Lee, J. M. House,. H. Kyog, Susyste level fult dgoss of uldg's r-hdlg ut usg geerl regresso eurl etworks, Appled Eergy, Vol. 77, Issue, 004, pp [5]. H. K. Cgzoglu, M. Alp, Geerlzed regresso eurl etwork odelg rver sedet yeld, Advces Egeerg Softwre, Vol. 37, 006, pp [6]. R Iser, Fult-Dgoss Systes: A Itroducto fro Fult Detecto to Fult olerce. erl, Sprger erl Hedelerg, Gery, 006. [7]. Achd Wdodo d o-suk Yg, Applcto of oler feture extrcto d support vector ches for fult dgoss of ducto otors. Expert Systes wth Applctos, Vol. 33, Issue, 007, pp [8]. D. Zogg, E. Shf, d H. P. Geerg, Fult dgoss for het pups wth preter detfcto d clusterg, Cotrol Egeerg Prctce, Vol. 4, Issue, 006, pp [9]. he MthWorks Ic., Mtl ( Pulshed y Itertol Frequecy Sesor Assocto (IFSA Pulshg, S. L., 06 ( 6