CMF Signal Processing Method Based on Feedback Corrected ANF and Hilbert Transformation

Transcription

1 .478/ms-4-7 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 CMF Sigal Pocssig Mthod Basd o Fdbac Coctd NF ad Hilbt Tasfomatio Yaqig Tu, Huiyu Yag, Haitao Zhag, Xiagyu Liu Logistical Egiig Uivsity, Chogqig 43, P.R.C addss:yq.tu@63.com; huiyu_yag@63.com I this pap, w focus o CMF sigal pocssig ad aim to solv th poblms of pcisio shap-dcli occuc wh usig adaptiv otch filts (NFs) fo tacig th sigal fqucy fo a log tim ad phas diffc calculatio dpdig o fqucy by th slidig Gotzl algoithm (SG) o th cusiv DTFT algoithm with gativ fqucy cotibutio. ovl mthod is poposd basd o fdbac coctd NF ad Hilbt tasfomatio. W dsig a idx to valuat whth th NF loss th sigal fqucy o ot, accodig to th colatio btw th output ad iput sigals. If th sigal fqucy is lost, th NF paamts will b adjustd duly. t th sam tim, sigula valu dcompositio (SVD) algoithm is itoducd to duc ois. d th, phas diffc btw th two sigals is dtctd though tigoomty ad Hilbt tasfomatio. With th fqucy ad phas diffc obtaid, tim itval of th two sigals is calculatd. ccodigly, th mass flow at is divd. Simulatio ad xpimtal sults show that th poposd mthod always psvs a costat high pcisio of fqucy tacig ad a btt pfomac of phas diffc masumt compad with th SG o th cusiv DTFT algoithm with gativ fqucy cotibutio. Kywods: Coiolis mass flow mt, adaptiv otch filt, Hilbt tasfom, fqucy tac, phas diffc.. INTRODUCTION URING THE last dcads, itst i Coiolis mass D flow mts (CMFs) has b icasig stadily. aso is that CMFs dictly masu th mass flow, whas oth istumts masu volumtic flow []. High pcisio, wid tolac of masuabl fluids ad multi-paamt masumt also justify thi fast gowth ad accptac i idusty. Mass flow at is obtaid i CMF by masuig th tim itval, which is dpdt o th fqucy ad th phas diffc btw two vibatio sigals dtctd by lctomagtic ssos. Thfo, th pcis masumts of th sigal fqucy ad th phas diffc a th cos of CMF sigal pocssig. Taditioal aalogu mthods fo CMF sigal pocssig a of poo itfc sistac ad masud sults a phas diffcs of sultat wavs []. Vaious digital mthods hav b ctly itoducd ito CMF so as to impov th pcisio [3]. Romao [4] itoducd th disct Foui tasfom (DFT) ito CMF sigal pocssig fo th fist tim i 99. Th sigal fqucy was calculatd by DFT, ad th phas diffc was obtaid by subtactig two DFT phass at th maximum spctal li. This mthod is of good sistac to hamoic itfc but calls fo a ufasibl tchiqu of itgal piod samplig which limits its pacticality. Fma ad shvillc [5] adoptd digital phas-locd loop (PLL) to tac th vibatig fqucy of flow tubs. Dis [6] pstd a mthod fo CMF sigal pocssig basd o othogoal dmodulatio. Howv, pcisio of th mthod dpdd o th pfomac of low-pass filts. slidig Gotzl algoithm (SG) was itoducd to masu th phas diffc btw CMF sigals. Th SG gats phas diffc cotiuously, but th is a slow covgc at ad a umical ovflow. What is mo, th SG ds fqucy wh th phas diffc is calculatd. I [8], a mthod was poposd fo CMF sigal pocssig basd o cusiv DTFT algoithm with gativ fqucy cotibutio. Wh th Foui cofficits a calculatd, th mthod acclats th covgc at ad impovs th accuacy gatly. But th sigal fqucy is also dd. I [9], adaptiv otch filt (NF) was itoducd to CMF sigal fqucy tacig. Th NF s stuctual paamts w adjustd automatically accodig to sigal chaactistics ad th vibatig fqucy of flow tubs is gatd cotiually. Thas to th fqucy tacig ability ad good sistac to ois, th NF has gaid a lot of atttio ctly. lattic NF (LNF) was bought i CMF sigal pocssig i []. [] ad [] itoducd a ovl IIR-typ NF volvd fom th Stiglitz-McBid mthod (SMM-NF) [3] fo CMF sigal fqucy tacig. Th ovl NF has ubiasd thoy sults, high pcisio ad fast covgc at compad with LNF. Howv, ths NFs icludig th ovl NF caot supply costatly high-accuacy sults. It has limitd thi applicatios i CMF sigal pocssig. To impov th pcisio of CMFs, a w mthod is poposd i this pap basd o fdbac coctd NF ad Hilbt tasfomatio [4]. Th mthod is xpctd to supply costatly high-accuacy sults ad limiat th dpdc o fqucy wh calculatig phas diffc. This pap is ogaizd ito six sctios. Sctio itoducs th poposd mthod pocss. I Sctio 3, a fdbac coctd NF is poposd fo fqucy stimatio. Sctio 4 psts a phas diffc masumt mthod basd o th Hilbt tasfomatio. Th poposd mthod fo sigal fqucy stimatio ad phas diffc masumt is validatd by simulatios ad xpimts i Sctio 5 ad Sctio 6, spctivly. Coclusios a daw i th last sctio. 4

2 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4. METHOD PROCESS Pocss of th poposd mthod is xpoudd i Fig.., fom which w ca s that th fqucy stimatio ad th phas diffc masumt a caid out i paalll, diffig fom th xistig mthods. O th o had, SVD algoithm is fistly usd to duc th ois cotaid i CMF sigals. d th phas diffc is calculatd by tigoomty opatio btw th oisducd sigals ad thos aft th Hilbt tasfomatio. O th oth had, sigal fqucy is stimatd cotiually by th fdbac coctd SMM-basd NF. Th, tim itval of th two sigals is figud out as th fqucy ad th phas diffc is obtaid. ccodigly, th mass flow at is divd. Fig.. Th sigal pocssig flow chat. 3. FREQUENCY ESTIMTION BSED ON FEEDBCK CORRECTED NF statgy of fdbac coctio fo NF is poposd so as to impov th stability of its accuacy. ccodig to th colativity btw th output ad iput sigals, w dsig a idx fo al-tim valuatio of th fqucy stimatio pcisio. If th idx ovus its limit, NF paamts will b adjustd adhig to th fdbac. Th SMM-NF is ta as a xamiatio fo th fasibility of th poposd statgy.. Th SMM-NF Stuctu of th NF basd o Stiglitz-McBid mthod is show i Fig., ad its tasf fuctio is giv by: ˆ ( ) ˆ z + α z + z H ( z) = = ˆ () ( ρ ) m z = + ρ ˆ α z + ρ z t covgt stag, th pol cotactio facto coms to o ad th badwidth appoximatly quals to zo (). Howv, du to th NF iht stuctu, th is a icomplt covgc stag spcially wh th sigal fqucy is vy low o vy high (clos to Nyquist fqucy). t this stag, th NF s o-quadatic o sts o a local miimum, ad th th sigal fqucy will b lost soo. y( ) z ˆ ( ) ρ z ˆ ( ) ρ z g( ) h( ) ˆ ( z ) z ρ + ( ) s ˆ ˆ ( ρ z ) ( z ) z Fig.. Stuctu of th SMM-NF Wh m is th tap umb, amly th si wav umb i y( ) ; ρ is pol cotactio facto dtmiig th tap badwidth is usd to duc th colatio btw th ois i y ad y( ),. ˆ α is adaptiv adjustd though th Nwto-typ algoithm, ˆ α ( ) cos ˆ = ω, ˆ ω ( ) is otch fqucy cospodig to th siusoidal fqucy. -od NF with a sigl tap is usd i ou study as th CMF sigals hav oly o xpctat siusoidal. Th NF badwidth is oft iitializd with a big valu ad th dcass stp by stp so as to acqui th sigal fqucy. B. ssssmt of fqucy stimatio accuacy Th ois-ducd sigal cˆ( ) show i Fig.3. is obtaid by th output s( ) ad th iput y( ), xpssd as ( ρ ) ˆ α( ) z + ( ρ ) z cˆ( ) = y( ) + ραˆ ( ) z + ρ z Thas to th idpdc of ois o y( ), th sigalcˆ( ) appoximats to c( ) wh th NF wos wll. Othwis, th sigal cˆ( ) appoximats to ( ). Cosqutly, idx h is dsigd to valuat th accuacy of th NF. Th idx is calculatd oli i al tim by th -od LMS, as follows: (3) ρ( t) BW = cos + ρ ( t) () ε = cˆ h y h = h( ) + µ hε y (4) 4

3 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 wh, µ h is th stp siz, ad h is th solutio of Wi- Hopf quatio o th covgc coditio. { ( ) } { ( ) ˆ ( ) } h E y = E y c (5) E{ c( ) ( )} quals to zo as th sigal c is ulatd to ois ( ). Th, th (5) ca b witt: ( { ( )} { ( )]}) { ( ) ˆ( )} { ( )} { ˆ( )} h E c + E = E c c + E E c With { ( )}, σ ad as: E, E{ ( )} ad { ( )} y( t ) (6) E c qual to /, spctivly, th idx h ca b divd h( t) { ( ) ˆ( )} E c c h= / + σ ε( t ) cˆ( t ) ε( t ) Fig.3. Stuctu of th fdbac modifid SMM-NF. Th a two possibl situatios fo th idx h with ith good o bad pfomac of th NF. If th NF wos wll, cˆ( ) appoximats to c( ) ad th, th idx h= / ( + σ ). If th NF loss th sigal fqucy, th is o colatio btw cˆ ad c( ). Thfo, th xpctd valu E{ c( ) cˆ ( )} idx h coms to zo cosqutly. C. Fdbac coctio statgy (7) ca appoximat to zo, ad th, th compaativ paamt T h is iitializd with small valu so as to judg whth th NF loss th sigal fqucy o ot. If h is gat tha T h, w hav othig to do. Othwis, th NF s paamts will b adjustd accodig to a adom sach mthod, ath tha simply iitializatio, which will lad to aoth covgc pocss. Th coctio statgy of th two y paamtsλ adρ of th SMM- NF is giv by λ = λ + δλ, < δλ < λ λ() ρ = λ + δρ, < ρλ < ρ ρ() whλ adρ dot th fial valu ofλ adρ, spctivly, δλ adδ ρ a th stp siz. (8) 4. PHSE DIFFERENCE MESUREMENT BSED ON HILBERT TRNSFORMTION phas diffc masumt mthod basd o th Hilbt tasfomatio is poposd i this sctio, xpctig to limiat th dpdc o sigal fqucy. Th sigula valu dcompositio (SVD) algoithm is fistly usd to duc th oiss i CMF sigal. Th, th phas diffc is calculatd usig th ± π / phas-shift popty of th Hilbt tasfomatio.. SVD-basd ois ductio Th is a m -od othogoal matix U calld th lft sigula valu vcto ad a -od othogoal matix V calld th ight sigula valu vcto. Th two matics satisfy th quatio that = U T V.Wh, is th Ha matix composd of sigal x( t ), spcifid i (3) is a M N o-gativ diagoal matix withσ σ L σ N o its diagoal positios. σ i ( i N) a th sigula valus pstig th gy of matix. Nois-ducd sigal ca b costuctd by svig th fo sigula valus which cospod to sigal pow ad sttig th oths zo which dfi th ois compots. x() x( )... x( ) x( ) x( 3 )... x( + ) = M M M M x( N m+ ) x( N m+ )... x( N ) Th a is th y fo th bst spaatio of th sigal ad oiss. To choos a optimal a, sigula topy is dfid as E (9) E () i= = wh Ei is th sigula topy icmt at th a i, computd by / l / m Ei = i i i = ( σ ) σ σ () Th sigula topy E, which flcts th ifomatio cotaid i th sigal, icass apidly wh th a is low. Th icas of E dops off with th is of a, as th sigal compot cotibutio aivs at th maximum. Th, th a i ca guaat a good doisig pfomac. Th SVD-basd ois ductio algoithm is simpl i picipl, asy to implmt, but oly usful to statioay sigals. Thfo, a slidig ctagula widow is adoptd to cut th CMF sigal ito stady ovlap sgmts. 43

4 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 B. Phas diffc calculatio Hilbt tasfomatio joys a ± π / phas-shift popty. Hby, th phas diffc fuctio ca b divd by th tigoomtic opato btw th CMF sigal ad its Hilbt tasfomatio. CMF sigals dtctd by lctomagtic ssos ca b dscibd by y = si( ω + ϕ ) + σ y = si( ω + ϕ ) + σ () wh, is th amplitud, ϕ adϕ a iitial phass; ω is th sigula fqucy, ω = π f / fs. Ou goal is to valuat th phas diffc ϕ, ϕ = ϕ ϕ. Th Hilbt tasfomatios of th two CMF sigals a giv by yˆ = cos( ω + ϕ ) + σ 3 yˆ = cos( ω + ϕ ) + σ 4 Th phas diffc ϕ ca b divd: yˆ y yˆ y ac ta ϕ = y ˆ ˆ y + y y (3) (4) Th, phas diffc is masud at vy samplig poit i tim gio, dspit th sigal fqucy [4]. 5. SIMULTION RESULTS Comput simulatios ad actual xpimts hav b do to valuat th poposd mthod. Thi sults a pstd i th followig sctios, spctivly.. Simulatd sigals Th CMF sigal paamts vay fom tim to tim du to th ffct of fluid poptis, flow pulsatio, tc. timvayig sigal modl, i which th sigal fqucy, amplitud, ad phas vay ov tim basd o th adom wal modl, was pstd i [5] so as to mo closly dscib th CMF sigals. Howv, this modl faild to dscib th sigals i spcial coditios such as pulsatig flows. Hby, th tim-vayig sigal modl basd o adom wal is amdd, as follows: y = si[ ω + φ] + σ (5) = ( ) + δ σ (6) ω = ω( ) + δ σ (7) ω ω ω φ = φ( ) + δ σ (8) φ φ φ wh, ( ), ( ), ω, ad φ a whit oiss, with o colatio btw ach oth. σ, σ, σ ω ad σφ a th wal amplificatios, whil δ, δω adδ φ a wal factos followig - distibutio with th pobabilitis P, P ω ad P ϕ spctivly. Th pobabilitis a dtmid by th flow chaact ad viomt. Tabl. Iitializatios of simulatio paamts. Nam Iitial valu Nam Iitial valu mplitud () = mv Pobabilitis P = P = P =.5 Fqucy f = 98 Hz σ =, Stp siz.6 Sampl fqucy 3 =, σ ω 6 σ ω =, σ ϕ ϕ f = Hz s = 3 Fqucy [Hz] mplitud [mv] (a) (c) 98.4 Vayig fqucy Iitial fqucy mplitud X( jω ) 3 Phas diffc [ad] (b) Fqucy [Hz] (d) 6 Vayig phas diffc 4 Iitial phas diffc - Fig.4. Simulatd sigals Hz

5 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 Wh th pobabilitis appoximatly qual to zo, th amdd tim-vayig sigal modl dgats to th siusoidal with supposd whit ois, dscibig th CMF sigal ud th cicumstac of stady flow. Wh th pobabilitis com to o, it is th oigial tim-vayig modl, dscibig th CMF sigal ud th cicumstac of gal fluctuat flow. Th CMF sigals ud th cicumstac of mutatio flow ca also b dscibd by ducig th pobabilitis ad icasig th wal amplificatio. Sigals usd i simulatios a gatd accodig to th tim-vayig sigal modl amdd abov. Paamts of th sigal modl a iitializd as Tabl. Fig.4. shows th simulatd sigal, th fqucy spctum, th vayig fqucy ad th vayig phas diffc. B. Fqucy stimatio sults Th sigal fqucy is stimatd by th fdbac coctd SMM-NF, whil th lattic NF ad th oigial SMM-NF a usd as cotol xpimts. Th sults a show i Fig.5. It ca b cocludd fom th sults that th fdbac coctd SMM-NF covgs fast tha th LNF, slightly slow tha th oigial SMM-NF. Th fdbac coctd SMM-NF has a high pcisio compad with th LNF ad th oigial SMM-NF, spcially wh thy wo fo a log tim. Th aso is that th fdbac coctd SMM-NF utilizs a dsigd idx fo obsvig th accuacy cotiuously ad adjusts its ow o-ffctiv paamts duly. Fqucy [Hz] ctual fqucy LNF SMM-NF Fdbac adjustmt SMM-NF Fig.5. Pfomacs of fqucy tacig. To dscib th pcisio advatag of th fdbac coctd SMM-NF i dtail, Mot Calo simulatios hav b do fo tims idpdtly ad th ma squa os (MSEs) w calculatd by MSE = N ˆ N - m f(i)- f(i) (9) i=m wh f(i) ad ˆf(i) a th actual fqucy ad th stimatd fqucy, spctivly. m is th bgiig of th computig sigal, whil N is th d. Th stimatd fqucy i th covgc pocss has ot b compad i this sach so as to guaat th justic. m quals to 4,, ad N is 4,, th lgth of th simulatd sigal. Fig.6. shows th MSEs of fqucy stimatio. Fom Fig.6., it ca b s that th MSEs of th fdbac coctd SMM-NF a th stadist ad th lowst, compad with th LNF ad th SMM-NF. Th MSEs ma of th fdbac coctd SMM-NF is.6 % of th LNF,.58 % of th oigial SMM-NF. MSE [Hz ] x -3 LNF SMM-NF Fdbac adjustmt SMM-NF Simulatio tims Fig.6. MSEs of fqucy stimatio. C. Phas diffc masumt sults Th poptis of th poposd phas diffc masumt mthod a aalyzd with th SG ad th cusiv DTFT algoithm with gativ fqucy cotibutio (th algoithm i [8] fo shot) as compaisos. Th phas diffc masumt sults a pstd i Fig.7. Phas diffc [ad] x ctual phas diffc SG lgoithm i [8] Hilbt tasfom basd mthod Fig.7. Pfomac of phas diffc masumt. It ca b s fom Fig.7. that th poposd mthod basd o th Hilbt tasfomatio has o covgc pocss ad outputs th sults fom th bgiig, whil th SG ad th algoithm i [8] d a tim to covg. Th aso of this phomo is that th poposd mthod ds o itatios ad calculats th phas diffc though th tigoomty opato btw th oigial CMF sigals ad thos aft thi Hilbt tasfomatios, vy difft fom th SG ad th algoithm i [8] dpdig o DFT itativ calculatio. Obsvig th local sults of phas diffc masumt, w ca also s that th SG has a tim dlay ad caot flct th dtails. This is du to th quimt fo a log slidig widow i th SG (4 poits i th xpimt with 35 poits ovlappd). With th gativ fqucy cotibutio big cosidd, th 45

6 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 algoithm i [8] ca dtct a small phas diffc chag with a vy shot widow (8 poits i this xpimt with 7 poits ovlappd). Th ability of dyamic phas diffc masumt is also sigificatly impovd. s fo th poposd mthod basd o th Hilbt tasfomatio, th phas diffc is dictly calculatd by th CMF sigals ad thos aft thi Hilbt tasfomatio, with o DFT. ccodigly, th a o subsctios ad o itatio opatios i th poposd mthod. Thfo, th dyamic masuig pfomac is futh impovd. 6. EXPERIMENTL RESULTS ND DISCUSSION. Expimtal systm s show i Fig.8., th xpimtal systm fo CMF sigal pocssig cosists of two CMFs (FS with a 7R tasmitt, ad TQ-884 with a ERE tasmitt), a PLC usd to chag flow, a pump, a batch ta ad a sigal acquisitio subsystm. Th sigal acquisitio subsystm cosists of two data acquisitio dvics (NI 934 ad USB47), a lctic scal (FS398-), ad a comput. Supply ta Bloc Valu Pump Batch ta FLOW Scal Bloc Valu CMF(FS) CMF(TQ-884) Flow Cotol 7R USB47 NI USB934 CMF Sigals Flow at ERE Fig.8. Bloc of th xpimtal systm. PLC Flow at is cotolld by comput though th PLC ad a cotol valv. CMF oscillatio sigals a acquid by th 4- chal dyamic sigal acquisitio NI 934. Istataous mass flow at masud by th CMFs is collctd by th USB47. Mass flow masud by th scal is dmd as th actual valu. Th tst of th poposd sigal pocssig mthod is caid out by th comput. Th oscillatio sigals usd i th xpimts com fom th FS CMF with its high pcisio ad stabl pfomac compad with th TQ-884 CMF. B. Rsults ccodig to CMF s picipl, th is a lia latioship btw th mass flow at q m ad th tim itval t, that is qm = t+ b () Wh, th paamt b is costat. Th tim itval t dpds o th fqucy ad th phas diffc. Th cofficit is dcidd by th CMF typ, tmpatu, pssu ad so o, but is fixd at th sam situatio. Fo th FS CMF, w w ifomd of = ad b=.47 fom th maufactus. Display valus of FS CMF a dmd as actual mass flow. Th SG ad th algoithm i [8] a ta as compaisos. s w ow, th SG ad th algoithm i [8] d sigal fqucy to coclud th phas diffc. To guaat th justic, fqucy stimatd by th fdbac coctd SMM-NF is usd idtically. Sigals at i ids of stady flow a collctd ad pocssd. Mass flow is computd ad show i Tabl. It ca b s that th sults cocludd by th th mthods ag with ach oth. Th poposd mthod ows th highst pcisio, whos lativ o is blow.5 %. Th, w com to th coclusio that th poposd mthod is ffctiv ad pactical. Tabl. Expimtal sults. Mass flow (g/mi) Estimatd fqucy(hz) SG (g/mi) lgoithm i[8] (g/mi) Th poposd mthod (g/mi) CONCLUSION Th co of CMF sigal pocssig is th fqucy stimatio ad th phas diffc masumt. Howv, th is a dpdc o fqucy wh th SG o th algoithm i [8] is usd to calculat th phas diffc. It is a quimt that th sigal fqucy is timly tacd with a high-pcisio, du to its timvayig chaact. comphsiv ovl mthod fo CMF sigal pocssig is poposd basd o th fdbac coctd SMM-NF ad th Hilbt tasfomatio. Simulatio ad xpimtal sults validat th poposd mthod ad idicat som of its advatags, icludig: 46

7 MESUREMENT SCIENCE REVIEW, Volum 4, No., 4 Th poposd mthod cais out fqucy tacig ad phas diffc masumt idpdtly. W ca obtai th fqucy ad th phas diffc at th sam tim. Thus, th ability of al-tim masumt is impovd accodigly. Fo fqucy tacig, th pstd fdbac coctd SMM-NF joys a costatly high accuacy, whil oths udgo a shap dcli i accuacy wh woig fo a log tim. Th MSE s ma of th fdbac coctd SMM-NF is.6 % of th LNF,.58 % of th oigial SMM-NF. What is mo, th statgy of th fdbac coctio is also applicabl fo oth NFs. Fo phas diffc masumt, th pstd mthod basd o th Hilbt tasfomatio calculats th sults dictly, with o itativ opatio ad o covgc stag, ad pfoms btt i accuacy, compad with th SG ad th algoithm i [8]. To impov th pcisio ad shot th calculatio tim of th CMF sigal pocssig, this pap suggsts cayig out th fqucy tacig ad th phas diffc masumt idpdtly. Th ida has plimiaily b validatd by th mthods poposd i Sctio 3 ad Sctio 4, ad futh sach is ud discussio. CKNOWLEDGMENT This wo is suppotd by Natioal Natual Scic Foudatio of Chia (67449, 6375), ad Natual Scic Foudatio of Chogqig, Chia (CSTC, B5, cstc3jcyj43). REFERENCES [] Shamugavalli, M., Umapathy, M., Uma, G. (). Smat Coiolis mass flowmt. Masumt, 43 (4), [] Matt, Ch. (). Mthod fo dtmiig th mass flow though a coiolis mass flowmt. Uitd Stats Patt [3] Kitami, H., Shimada, H. (). Sigal pocssig mthod, sigal pocssig appaatus, ad coiolis flowmt. Uitd Stats Patt [4] Romao, P. (99). Coiolis mass flow at mt havig a substatially icasd ois immuity. Uitd Stats Patt [5] Fma, B.S. (998). Digital phas locd loop sigal pocssig fo coiolis mass flow mt. Uitd Stats Patt [6] Hot, D. (). Multi-at digital sigal pocsso fo vibatig coduit sso sigals. WIPO Patt 83. [7] Xu, K.-J., Xu, W.-F. (7). sigal pocssig mthod basd o FF ad SG fo coiolis mass flowmts. cta Mtologica Siica, 8 (), [8] Tu, Y., Zhag, H. (8). Mthod fo CMF sigal pocssig basd o th cusiv DTFT algoithm with gativ fqucy cotibutio. IEEE Tasactios o Istumtatio ad Masumt, 57 (), [9] Bos, T, Dby, H.V., Raja, S. (996). Mthod ad appaatus fo adaptiv li hacmt i Coiolis mass flow mt masumt. Uitd Stats Patt [] Xu, K.-J., Ni, W. (5). lattic otch filt basd sigal pocssig mthod fo coiolis mass flowmt. cta Mtologica Siica, 6 (), [] Tu, Y.-Q., Su, F.-H., Sh, T.-., Zhag, H.-T. (). Nw adaptiv otch filt basd a timvayig fqucy tacig mthod ad simulatio fo coiolis mass flowmt. Joual of Chogqig Uivsity, 34 (), [] Yag, H., Tu, Y., Zhag, H. (). fqucy tacig mthod basd o impovd adaptiv otch filt fo coiolis mass flowmt. pplid Mchaics ad Matials, 8-9, [3] Chg, M.-H., Tsai, J.-L. (6). w IIR adaptiv otch filt. Sigal Pocssig, 86 (7), [4] Vucija, N.M., Saaovac, L.V. (). simpl algoithm fo th stimatio of phas diffc btw two siusoidal voltags. IEEE Tasactios o Istumtatio ad Masumt, 59 (), [5] Li, Y., Xu, K., Zhu, Z., Hou, Q. (). Study ad implmtatio of pocssig mthod fo timvayig sigal of oiolis mass flowmt. Chis Joual of Scitific Istumt,, 8-4. Rcivd pil 6, 3. ccptd Fbuay 6, 4. 47