Applied Study of Hilbert-huang Transform and Elman Neural Network on Flow Regime Identification for Gas-liquid Two-phase Flow
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- Όφελος Αντωνόπουλος
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1 7 Vol.7 No. Apr Proceedgs of the CSEE 7 Ch.Soc.for Elec.Eg (7) O359 A 47 Elma ( 3 574) Appled Study of Hlbert-huag Trasform ad Elma Neural Network o Flow Regme Idetfcato for Gas-lqud Two-phase Flow ZHOU Yu-log, WANG Qag, SUN B, Zhag Yog-gag (. School of Eergy Resource ad Mechacal Egeerg, Northeast Dal Uversty, Jl 3, Jl Provce, Cha;. Shadog Phoex Pharmaceutcal co Ltd, Dogyg 574, Shadog Provce, Cha) ABSTRACT Flow ad heat trasfer characterstc of gas-lqud two-phase flow are strogly affected by ts flow patter. Therefore, the study o flow patter s always a mportat subject of two-phase flow. However, as exstg multfarous terphase boudary amog the medum of two-phase flow, t leads to varous of two-phase flow patter, ad the chages are radom. So t s dffcult to detfy the flow patter. Ad t s seldom to apply study of Hlbert-Huag trasform (HHT) ad eural etwork o flow regme detfcato for gas-lqud two-phase flow. I ths artcle a flow regme detfcato method usg Hlbert-Huag trasformato combed wth Elma eural etwork s put forward. Frstly the method aalyzes the trsc mode fucto (IMF) obtaed after the emprcal mode decomposto (EMD), the extracts IMF eergy feature as the put feature vectors of the Elma eural etwork, lastly flow regme detfcato of the gas-lqud two-phase flow a horzotal ppe ca be performed. The expermetal result shows that ths method ca detfy the four flow regmes of gas-lqud two-phase flow horzotal ppe. Ths method develops a ew drecto for the flow regme detfcato. I addto, the expermetal result shows that ths method s superor to BP eural etwork, ad t s stable ad hgher detfcato. Result also proves that the method s feasble. KEY WORDS: gas-lqud two-phase flow; flow regme detfcato; Hlbert-Huag trasform; emprcal mode decomposto; trsc mode fucto; Elma eural etwork (453), (HHT) Elma (EMD) (IMF) IMF Elma 4 BP Elma [] [] EMD(emprcal mode
2 Elma 5 decomposto) HHT(Hlbert-Huag trasform) [3-] EMD IMF EMD IMF (trsc mode fucto) IMF [3-3] BP BP [4] BP Elma, HHTElma HHT. EMD HHT [5] IMF s() t v () t v () t m= [ v ( t ) + v ( t )] () s() t m h s() t m= h () h s() t h IMF = h (3) c c IMF s() t c = r (4) r s() t c, c 3,..., rt () rt () st () = c + r (5) = IMF c, c,..., c r (5)EMD. Hlbert (HT) Xt HT () + X ( τ ) Yt () = dτ π (6) t τ + Y ( τ ) Xt () = dτ π (7) t τ θ ( ) Zt () = Xt () + Yt () = at ()e t (8) / at () = [ X() t + Yt ()] (9) θ () t θ ( t) = arcta Y( t) / X( t) () d θ ( t) f() t = () π dt at ().3 Hlbert IMF Hlbert j φ ( ) j ( )d t w t t () = = s() t = Re a ()e t = Re a ()e t r Re () HlbertHlbert j w ( t)dt H( w, t) = Re a ( t)e (3) = EMD Hlbert EMD HlbertHHT. HHT = E = a () t (4) PD-4
3 5 7 IMP Hz 48.~.5 MPa3~ 4 ~5 m 3 /s ~4.5m 3 /s 4 Fg. Expermet system of flow regmes P/kPa Fg. Dfferetal pressure sgals 3 IMF EMD HHT 3 4 HHT r a 8 HHT IMF (c ) d FFT 5 HHT HHT EMD EMD IMF EMD IMF 8 EMD 8 IMF r EMD IMF 8 r r 9 Hlbert (4) IMF r r r c8 c7 c6 c5 c4 c3 c c EMD Fg. 3 EMD decomposto of bubble flow a8 d8 d7 d6 d5 d4 d3 d d Fg. 4 Wavelet decomposto of bubble flow
4 Elma 53 Tab. 4 Test sample data ad classfcato result of four flow regmes c c c 3 c 4 c 5 c 6 c 7 c 8 r Elma BP B B B B B B I I I I I A I I I A A A S S S S S A A A A B I S A Tab. Eergy table of each layer c c c 3 c 4 c 5 c 6 c 7 c 8 r B B I I S S A A c9 c8 c7 c6 c5 c4 c3 c c 4 8 f/hz (a) d f/hz (b) c 5 FFT Fg. 5 FFT trasform EMD Fg. 6 EMD decomposto of termttg flow 4 Elma 4. Elma Elma 4 () 7 W 3 X W y(k) X W X c X c u(k ) 7 Elma Fg. 7 Model of Elma eural etwork
5 54 7 IMF r () () () () Elma 4 tasg logsg tasg logsg 8 9 Elma y x y.5 8 tasg Fg. 8 Tasg fucto 5 5 x 9 logsg Fg. 9 Logsg fucto 4. Elma 7 Elma 3 y( k) = g( w x ( k)) (5) x( k) = f( w xc ( k) + w ( u ( k ))) (6) x ( k) = x ( k ) (7) c y x u x c m l w 3 w w g() f () s Elma BP Ew ( ) = yk( w) y k( w) (8) k = [ ] y ( w) k 5,, 4 ( 4 6 ) 34 6 ( 4 ) 95.7% BP 3 ( ) 78.6% 4 Elma BP Elma Elma Fg. Error curve of Elma eutral etwork 6 Hlbert-Huag Elma EMD EMD IMFr IMF 4 3 Elma 4, BP
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