Global optimal solution for active noise control problem

Transcription

1 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: Global otmal soluton for actve nose control roblem Syed Faz Ahmed 1, Abdul Rehman Memon 1, Ch Fahad Azm and Hazry Desa 3 1 Faculty of Engneerng Scences & Technology, Hamdard Unversty, Pakstan School of EEE, Nanyang Technologcal Unversty, Sngaore 3 Engneerng dvson, Unversty Malaysa Perls, Malaysa syed0011@ntuedusg; abdulrahman@hamdardedu; fahadazm@hamdardedu; hazry@unmaedumy Abstract Ths aer resents the global otmal soluton for actve nose cancellaton usng Genetc algorthm technque The conventonal actve nose control methods such as FXLMS have roblem of local mnma The roosed global otmal soluton based on Genetc algorthm can handle ths roblem very well and gve batter results Comuter smulaton results demonstrate that Genetc algorthm based actve nose control system gve more otmal results Keywords: Actve nose control, otmal soluton, genetc algorthm Introducton Acoustc nose s comosed of a mxture of sound that has no benefcal effect on human bengs snce t s ncomrehensble In fact, t s a source of rrtaton that dsruts mental concentraton Generally, t s regarded as a tye of envronmental olluton that can have adverse effects on human lfe n varous ways In recent years, acoustc nose roblems are becomng more evdent wth the ncrease n the use of ndustral equment such as engnes, fans, transformers and comressors The growth of hgh-densty housng ncreases the oulaton's exosure to a wder sectrum of nose source In addton, manufacturers have the tendency to use lghter materals for buldngs and transortaton that further add to the envronmental nose Hearng loss s robably the most sgnfcant and serous health roblem caused by excessve nose Contnuous exosure can lead to varyng levels of hearng loss rangng from a mld rngng n the ears to total deafness due to the damaged audtory recetors n the ear Researchers have shown that f a erson s subected to a sound level of over 85 db for several hours a day, ermanent damage wll occur The greater the amount of sound, the longer the exosure and the hgher the ntensty, the greater wll be the ossblty of deafness occurrng Nose can also mask mortant sounds and dsrut communcaton between ndvduals n a varety of settngs Ths rocess can cause anythng from a slght rrtaton to a serous safety hazard nvolvng an accdent or even a fatalty because of the falure to hear the warnng sounds of mmnent danger Such warnng sounds can nclude the aroach of a radly movng motor vehcle, or the sound of malfunctonng machnery Nose-nduced slee nterference s one of the crtcal comonents of communty annoyance It can roduce short-term adverse effects, such as mood changes and decrements n task erformance the next day, wth the ossblty of more serous effects on health and well beng f t contnues over long erods In an effort to overcome these roblems, actve nose control has receved consderable nterest and has shown sgnfcant romse It works on the rncle of destructve nterference between the sound felds generated by the rmary sound source and that due to the secondary antsources Fg1 shows the rmary unwanted nose sgnal, ant-nose sgnal, and resdual orgnal sgnal that result when they are suermosed To acheve the otmal erformance of nose cancellaton, t s requred that the ant-nose sgnal s of the same amltude but nverse hase as that of the nose to be canceled Ths aer resent a global otmal soluton usng genetc algorthm based FIR (fnte-mulse resonse) flter to mnmze the unwanted nose sgnal n actve nose control system Genetc algorthm search globally and udate the coeffcents of FIR flter otmally Actve nose control (ANC) s an old concet that has receved attenton for more than 50 years Tradtonal aroach to acoustc nose control uses assve technques such as enclosures, barrers, and slencers to attenuate the undesred nose Besdes, the tradtonal nose control aroach often nvolves the rearrangement of the nose source, the hyscal structure and Fg1Actve nose control system Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol

2 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: FgBlock dagram of actve nose control system Unwanted nose sgnal Nosy Area Sensor Controlled sgnal Actve Nose Controller Nose Free Area Error Sensor Nose free resultant sgnal surroundng envronment The develoment of adatve dgtal sgnal rocessng theory and hardware resolve these roblems Consderable research works had been done n actve nose control area and now the ANC adatve control system classfcaton structure, shown n systems are commercally mlemented n arcondtonng ducts, actve headsets, transformer nose, unknown lant (z) Fg 3; where adatve flter w (z) s used to redct an engne nose n certan arcraft cabns and cars (Dehandschutter et al, 1995; Smth et al, 1996; Crawford When adatve flter converged, then w (z) = (z) and & Stewart, 1997) In medcal scences ANC also lay very error sgnal wll become zero and the outut of the mortant role, Hrayama and Kda (008) worked on adatve flter y (n) wll become equal to d (n) whch s actve nose control system use for reducng nose n MRI unwanted sgnal and resultant error sgnal wll be machne; ths ANC system used otcal mcrohone and ezo-electrc loudseaker for ANC system Blnear e ( n) d ( n) y( n) 0 (1) FXLMS algorthm s roosed by Kuo and Wu (005) for Fg3 ANC control system n adatve flter confguraton nonlnear adatve flters to solve the roblems of sgnal saturaton and other nonlnear dstortons that occur n ANC systems A sub-band adatve flterng (SAF) x(n) technque s used by Mlan & Panah (009) n desgnng of actve nose control (ANC) systems They reduce the comutatonal comlexty of ANC algorthms, artcularly, when the acoustc nose s a broadband sgnal Artfcal Neural Networks (ANN) had been aled to the ANC due to the lmtaton of resently emloyed lnear control strategy Sutton and Ellot (1991) develoed a non-lnear adatve harmonc controller by usng the ANN Ma and Snha (1996) wrote on the develoment of a neural network based otmal system to control vbraton n flexble structures subected to determnstc and erodc exctaton They used large numbers of actuators on structures to control sound Unknown Plant P(z) Adatve Dgtal Flter W(z) d(n) y(n) e(n) 1016 transmsson through structures In an attemt to further smlfy the control rocess Delemotte and Montasser (1995) suggested usng herarchcal bo control n whch a small number of sgnals are sent from an advanced, centralzed controller and are then dstrbuted by local smle rules to multle control actuators Actve nose control system The basc block dagram of Actve Nose Control system s shown n Fg The unwanted nose sgnal s detected by sensor and fed n to the actve nose controller The controller generates control sgnal whose amltude s same but nverse n hase from unwanted nose sgnal The ANC controller manulates the control sgnal accordng to the nut sgnal and the feedback sgnal comng from the error sensor The effcency of unwanted nose cancellaton deends uon the effectveness of the ANC controller algorthm Actve nose control system can also be realzed n an Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol

3 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: Fg4 Genetc algorthm based ANC system x(k) Unknown Plant G(z) d(k) y(k) Dgtal Flter W(z) S(z) y(k) Relacement Genetc Oeraton Selecton Genetc Algorthm Block Well-known Least Mean Square (LMS) algorthm as adatve flter algorthm has been wdely studed and aled to nose cancellaton (Clarkson & Whte, 1989) Besde LMS, the FXLMS algorthm s also very famous algorthm for the ANC system It s n essence a method searchng local otmum wth a gradent followng technque These conventonal aroaches are easy to converge to a local otmal soluton f the ntal condton s not arorate To solve the roblem of local mnma, genetc algorthm can be use as an alternatve and more effcent methodology n the ANC Proosed global otmal soluton The alcaton of GA n the ANC s demonstrated n Fg4, whch shows the block dagram of the Genetc Algorthm based Actve Nose Control system The adatve flter used here s a Fnte Imulse Resonse (FIR) flter wth order of L-1 FIR flter ncororates only zeros Hence, t s always stable and can rovde a lnear hase resonse In ths dagram x(k) s the unwanted nose sensed by the rmary sensor, d(k) s the acoustc sgnal at the error sensor, y(k ) s the ant-hase sgnal that s generated by the adatve flter, y (k ) s the sgnal fltered through the secondary ath, e(k) s the resdual nose sgnal after cancellaton S (z) denotes the acoustc ath from the secondary source to the error mcrohone, G(z) denotes acoustc ath from the rmary nose source to the error sensor and W(z) s FIR flter whose coeffcents are udated by usng GA algorthm Snce the unwanted nose date vector sgnal s: k xk, xk 1, xk, xk L x 1 () And adatve flter weght vector s: w( k) [ w 0, k, w 1, k, w, k, w L 1, k (3) ] wth 1 Where s the grous of oulaton for Genetc algorthm Then sgnal y(k ) that s generated by the adatve flter n vector form wll be: T Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol

4 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: y1 y y k k k w1 w w 0, k w1 1, k w1 L1, k 0, k w1, k wl1, k 0, k w1, k wl1, k xk 1 xk xk L1 And the sgnal y (k ) that s fltered through the secondary ath y1 y y' ' k ' k k y1 y y k y1 K1 y1 kl1 k y k1 y kl1 s1 s sl 1 k w k1 y kl 1 Therefore the resdual nose sgnal e(k) after cancellaton of unwanted nose can be calculated by equaton: e ( k) d( k) y '( k) (6) Genetc algorthm n actve nose control system Genetc Algorthm conssts of three oeratons: Selecton, Genetc Oeraton, and Relacement The oulaton s bascally a grou of chromosomes from whch canddates can be selected for the soluton of a roblem Intally, a oulaton s generated randomly The ftness values of the all chromosomes are evaluated by calculatng the obectve functon (Omar Al Beg & Val uddn, 009) a) Ftness evaluaton To evaluate the goodness of chromosomes, an obectve functon s needed to calculate the ftness value The results of ths evaluaton wll rovde an ndcaton on the ftness level of the ndvdual chromosome A 'wndowed mean-square-error' functon s roosed here for the ftness evaluaton n 0 z 1 1 C ( e) e ( k) (7) z nn0 (4) (5) Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol 1018 Where: C (e) = ftness value of th chromosome n the oulaton e (k) = calculated error sgnal at k tme = 1,,3, z = wndow sze b) Selectng Parentng Poulaton The reroducton oerator determnes how the arents are selected to generate the offsrng Ths oerator s a rocess n whch chromosomes are coed accordng to ther obectve functon values (Rahman, 001) A chromosome wth the lowest value has the greatest robablty of matng The cost weghtng technque can be use for the selecton Cost weghtng In cost weghtng method, the robablty s calculated accordng to the cost of the chromosomes b n C C 1 n 1 C (8) Where: C = Ftness value of th chromosome C = Ftness value of th chromosome wth lowest cost weght b = Probablty of th chromosome beng selected as a arent Ths aroach weghts the to chromosome more when there s a large cost dfference between the best and worst chromosomes c) Crossover oerator Crossover s the core oerator of the GA It creates a grou of chldren from the arents by exchangng genes among them A new offsrng contans mxed nformaton from both the arents Gene exchange For the bnary codng, the crossover s based on bt exchange It selects one or more onts n the chromosome randomly The genes among these onts are swaed between the two arents To acheve better chromosomes, the gene values from both the arents are combned nto new arameter values n the chldren usng followng equaton (9) C new 1 C new (10)

5 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: Fg 5 Orgnal sgnal Fg 6 Nose sgnal cked by error sensor Fg 7Desred sgnal for the adatve flter Fg 8 Orgnal sgnal recovered by ANC system Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol

6 Indan Journal of Scence and Technology Vol 4 No 9 (Se 011) ISSN: Where: 1 & = Values of two arent genes; C new1 & C new =Values of two chld genes; =Random value between [-06, 06] d) Mutaton oerator Even though the reroducton and crossover come u wth many new chromosomes, they do not ntroduce any new nformaton nto the oulaton at a gene level (Erguo L, 004) Mutaton oerator solves ths roblem by randomly dsturbng the genetc nformaton e) Relacement of oulaton The relacement s the last stage of any breedng cycle It determnes how new chromosomes wll be ut nto the oulaton, and how chromosomes are to be elmnated Through one GA cycle, two arents are drawn from a oulaton They breed two chldren But not all of them can return to the oulaton, two have to be dscarded Two of the weakest ndvduals n the oulaton are relaced by the two chldren, so long as the chldren are ftter f) Termnaton crteron After Reroducton, Crossover, Mutaton, and Relacement, the new generaton of the offsrng forms a new oulaton wth art of the revous generaton Ths new generaton wll undergo further round of the GA oeraton untl a redefned Termnaton Crteron s met Ths crteron can be a gven mnmum acoustc energy e k The GA wll sto searchng when the mnmum ftness value n the oulaton dros below the convergence value It can brng the search to a seedy concluson whle ensure to reduce nose to a low level Smulaton and results At the begnnng of the smulaton, GA arameters are ntalzed as oulaton sze s 30 chromosomes, crossover rate s 075, mutaton rate s 01 and the order of the flter s 3 The chromosome values are gven randomly and are evaluated accordng to an obectve functon Then a arentng oulaton s selected The whole GA cycle wll consst of Crossover, Mutaton, Ftness re-evaluaton, and Relacement The best chromosome wll be chosen to generate the ant-nose sgnal In smulaton results Fg5 shows the orgnal sgnal, the sgnal cked by the error sensor s shown n Fg6 The desred sgnal for the adatve flter whch s the combnaton of orgnal sgnal and fltered nose sgnal (Fg7) and the recovered orgnal sgnal s llustrated n Fg8 From these results, t has been observed that the error between the two sgnals reduces gradually It s notced that the nose can be reduced sgnfcantly n frst 50 teratons and after around 100 teratons the nose sgnal s almost vanshed and orgnal sgnal s recovered Concluson We have roosed and mlement the global otmal soluton for actve nose cancellaton roblem by usng genetc algorthms From the smulated results we can concluded that genetc algorthm s feasble soluton for actve nose control system roblem, t search globally and fnd otmal soluton Ths technque s smle, effectve and can generate batter results wth hgh stablty References 1 Delemotte Ch Carme V and Montasser A (1995) ANR (actve nose reducton) n turbo-ro arcraft Actve Clarkson PM and Whte PR (1989) Smlfed analyss of the LMS adatve flter usng a transfer functon aroxmaton IEEE Trans ASSP, 35 (7), Crawford DH and Stewart RW (1997) Adatve IK fltered-v algorthms for actve noe control, J Acoust Soc Am 101(4) Dehandschutter W et al, (1995) Actve structural acoustc control of structure borne road nose: theory, smulatons, and exerments Actve Erguo L (004) A genetc neural fuzzy system and ts alcaton n qualty redcton n the necton rocess Chem Engg Commun 191(3) Hrayama R, Kda M Kakawa (008) An actve nose control system for MR nose: A study on an avalable ANC system n magnetc feld Intl Conf on Sgnal Processng, Beng, ICSP (9) Kuo SM and Hsen-Tsa Wu (005) Nonlnear adatve blnear flters for actve nose control systems IEEE Transactons on Crcuts and Systems I Regular Paers 5, Ma RP and Snha A (1996) A neural network based actve vbraton absorber wth state feedback control Letters to Edtor J Sound & Vbraton 190(1), Mlan AA and Panah IMS Lozou (009) A new delayless subband adatve flterng algorthm for actve nose control systems, audo, seech, and language rocessng IEEE Transact 17, Omar Al Beg and Val uddn (009) Imlementaton of genetc algorthms for arameter estmaton of LTI systems nd IEEE Intl Conf Comuter Control and Communcaton Karach, IEEE- IC-4 () Rahman MA (001) A flexble way to generate PWM- SHE swtchng atterns usng genetc algorthm Sxteenth Annual IEEE Aled Power Electroncs Conference and Exoston (Cat No 01CH37181) APEC Smth SP et al (1996) Actve control of low-frequency broadband et engne exhaust nose, Nose Control Eng J 44(1), Sutton TJ, Ellot SJ and Moore I (1991) Use of nonlnear controllers n the actve attenuaton of road nose nsde cars Proc Recent Advances n Actve Control of Sound and Vbraton Technomc Publ Inc, Pennsylvana : 93 Research artcle Global soluton for nose control SFAhmed et al Indan Socety for Educaton and Envronment (See) htt://wwwndstorg Indan JScTechnol