ACTIVE CONTROL ANALYSIS OF MINING VEHICLE CABIN NOISE USING FINITE ELEMENT MODELLING

Transcription

1 ACTIVE CONTROL ANALYSIS OF MINING VEHICLE CABIN NOISE USING FINITE ELEMENT MODELLING D.A. Stanef, C.H. Hansen and R.C. Morgans Actve Nose and Vbraton Contro Group, Department of Mechanca Engneerng, The Unversty of Adeade, South Austraa 5005, Austraa Document statstcs: 8 Pages 7 Fgures Tabes Posta Address: (a authors) Professor Con H. Hansen con.hansen@adeade.edu.au Fax: Head, Department of Mechanca Engneerng The Unversty of Adeade South Austraa 5005 Austraa Correspondng author. E-ma address:con.hansen@adeade.edu.au 1

2 Numerca smuaton has been used to predct the reducton of acoustc potenta energy n a mobe mnng vehce cabn as a resut of actve nose contro. Resonance frequences and mode shapes of both the structura and cavty modes were cacuated usng a fnte eement mode. Moda coupng anayss was used to determne the couped response of the mode to an nteror acoustc source, and the resuts were compared to measurements taken nsde the cabn. Correaton between the fnte eement mode and physca measurements was mproved to the extent that the mode coud be used to predct the effect of actve nose contro n the cabn for dfferent confguratons of contro sources and error sensors. As expected from prevous work, t was found that the acoustc potenta energy nsde the cabn coud be sgnfcanty reduced f a contro source s paced n cose proxmty to the prmary voume veocty source. However, ncreasng the number of sensors and/or ncreasng the number of contro sources ocated remotey from the prmary source had tte mpact on the achevabe reducton n the overa acoustc potenta energy n the cabn. Ths supported resuts obtaned n off-ne experments usng contro source to error sensor transfer functon measurements and quadratc optmsaton theory, where t was found that good reducton at the error sensors was possbe nsde the mnng vehce cabn but that goba contro was not feasbe usng sources remotey ocated from the prmary source. 1. INTRODUCTION Low frequency nose n the cabns of heavy machnery such as dese-drven mnng vehces resut n drvers experencng fatgue and hgh eves of dstracton. Here, the effectveness of appyng an actve nose contro (ANC) system to a Caterpar mnng vehce cabn s nvestgated usng fnte eement modeng.

3 Prevous work on appyng ANC to encosures has ncuded anaytca, numerca and expermenta nvestgatons. In genera, resuts from these studes have ndcated that ANC w work n encosed spaces, provded that the condtons dscussed n the foowng paragraphs are met. Neson et a. [1] nvestgated theoretcay the feasbty of goba contro n an arbtrary encosure excted at a snge frequency under steady state condtons. They concuded that the reducton of acoustc potenta energy (PE) n an envronment of hgh moda densty s ony possbe f the contro source s ocated wthn haf a waveength of the prmary source. Bumore et a. [] showed that n an acoustca envronment of ow moda densty, goba attenuaton of sound wth a secondary source ocated further than haf a waveength from the prmary source s achevabe provded that the secondary source s paced at an antnode of the prmary fed. Pacng sensors n encosure corners and mnmsng the responses there has the greatest effect on reducng acoustc PE n an encosure when more than one mode domnates. However, for these cases to work, the prmary exctaton must be at an acoustc resonance. Eott et a. [3] attempted an expermenta verfcaton of the prevous two studes usng a smpe rectanguar encosure. As predcted by the computer smuaton of Bumore et a. [], good reductons were acheved ony when the encosure was excted on resonance. Very good correatons between the predcted and measured mpedance transfer functons were observed; however, correatons between predcted and observed nose reductons were not accurate. The spata dstrbutons of the predcted and measured controed sound feds n the encosure of nterest were smar, but the amptude of each was not. The average amptudes of the two feds were manuay set equa ony to ad comparson. A predcton of the achevabe acoustc PE reducton over a narrow frequency range showed that n most cases the acoustc PE woud be reduced, but there was a chance of ncreasng the energy at some frequences. Appcaton of ANC to a more compex encosure was reported by Bumore et a. [4]. In ths paper, a BAe 748 twn turbo-prop arcraft fuseage was modeed theoretcay as a thn cyndrca 3

4 she and a cyndrca room (wth foor). The dampng of the arcraft cabn n ths case was estmated by matchng predcted and expermenta resuts, and found to be approxmatey 30% across a modes. It was not suggested that the dampng for the fuseage was actuay as hgh as 0.3, but that ths was the parameter vaue that must be used n order to obtan reasonabe agreement between expermenta and theoretca resuts. The smuaton resuts by Bumore et a. [4] showed that for a contro system comprsed of 3 error sensors and 16 contro sources, the achevabe average sum of squared pressure reductons over a pane representatve of the heght of seated passengers was 14 db for the frst propeer bade passage frequency (BPF) of 88 Hz, and 4 db for the second harmonc. Eott et a. [5,6] vadated the study by Bumore et a. [4], achevng broad agreement wth the theoretca predctons. Aternatve confguratons of contro sources were tested, wth mproved contro at the second and thrd harmoncs obtaned by concentratng the majorty of the oudspeakers n the pane of the propeers. The reducton n the tone at the fundamenta frequency was a maxmum when a fuy dstrbuted contro source arrangement throughout the cabn was used. When a three harmoncs were controed smutaneousy, a ess than optma reducton was recorded at some mcrophones and an ncrease n sound eve recorded at others. Aso of nterest n the paper by Eott et a. [6] were the resuts from testng a two-mcrophone, two-contro source ANC system on a passenger seat. A grd was set up that enabed the sound pressure around the mcrophones to be measured. As woud be expected, reducton down to the nose foor was acheved at the two mcrophones. Reasonabe reductons were aso recorded around the controed mcrophones up to about 70mm away. Ths corresponded to resuts presented by Eott et a. [7], where t was shown that, on average, the resut of drvng the pressure to zero at an error sensor w be a spherca zone of quet wth a dameter about one tenth of the waveength of the exctaton frequency. The sound eve wthn ths zone s expected to be at east 10 db ess than the prmary eve at that ocaton. 4

5 Dorng et a. [8] aso performed expermenta work n the BAe 748 twn turbo-prop arcraft. They predcted and verfed the contro of the 88 Hz fundamenta exctaton frequency n the cabn usng a 7-mcrophone, 4-contro source ANC system. Reducton of sound pressure at over 50 ponts n the cabn was measured and compared to reductons predcted usng quadratc optmsaton theory. Reasonabe agreement between predcted and expermenta data was acheved. Johansson et a. [9] expermentay nvestgated the performance of a contro system that used two reference sgnas to attenuate the nose of two propeers enterng an arcraft fuseage. In one case two prmary sources generated the same frequency and n another the prmary nose fed comprsed of two frequences separated by 0.5 Hz such that beatng occurred. Attenuaton of the order of 3-5 db was acheved at the BPF n the presence of beatng, and 18 db n ts absence. In Thomas et a. [10] a cyndrca she mode of an arcraft fuseage was used to nvestgate the effectveness of usng structura contro sources to attenuate the nose eve nsde the cabn. The rada component of the knetc energy n the structure was mnmsed for contro and produced predctons of poor goba attenuaton nsde the cavty. Consequenty, Thomas et a. [10] attempted usng structura forces to mnmse the acoustc PE of the cavty nstead. The resuts from ths approach were much more encouragng. Thomas et a. [11] showed that good goba reductons of acoustc PE are possbe at the two harmoncs of nterest usng reatvey few structura sources. In fact, t seemed that better reducton of acoustc PE was acheved usng structura force nputs than acoustc sources. Snyder and Hansen [1] presented a theoretca desgn methodoogy for an ANC system n encosed spaces. The mportance of optmsng both the physca and eectronc parts of the contro system was dscussed. In Snyder and Hansen [13] t was shown that the mechansm by whch the acoustc PE s reduced n an encosure wth acoustc contro sources s by source unoadng, and that n optma condtons, the sources shoud never cause an ncrease n the acoustc PE. Zander [14] nvestgated the effect of contro source and error sensor confguratons for a smpfed ght arcraft fuseage. He found that the eve of acoustc PE reducton n the arcraft 5

6 structure was much more a functon of the ocatons of the contro sources reatve to the prmary source, and that as the number of contro sources ncreases, so too dd the eve of reducton. Aso, a hgher reducton n acoustc PE was acheved when the prmary exctaton of the structure was at an acoustc resonance. In addton to the theoretca methods mentoned above, fnte eement (FE) modeng has emerged as a too that can be used for anaysng an encosure targeted for ANC. Aved [15] nvestgated how a FE mode coud be used for smuatng the performance of an ANC system on an arcraft structure. He used the mode to cacuate the reducton possbe by mnmsng the sum of the quadratc pressures over the cabn usng an optmsaton agorthm. However, no deta was gven as to how the mode was verfed. Carett et a. [16] deveoped a smpstc FE mode of an earth-movng cab and used t to predct the tme averaged acoustc PE reducton possbe at three frequences reated to engne and coong system nose. They verfed ther mode by comparng the magntude of sound eve measurements taken n the cab wth eves predcted by the mode, and acheved good agreement at two out of the three frequences. Da and Fuer [17] showed the mportance of contro source ocatons n an ANC system paced n an arcraft fuseage. Optma postons were cacuated to reduce the tota acoustc PE n the nteror cavty at a snge frequency. These ocatons were entered nto a FE mode and sound pressure eve resuts were obtaned wth and wthout contro. Resuts were then obtaned wth contro sources ocated n random postons and compared to those obtaned wth the optma source ocatons. Resuts showed that the optma ocatons acheved greater goba and oca contro than ocatons seected randomy. Appyng moda coupng theory to a FE mode was reported by Cazzoato [18], and Cazzoato and Hansen [19]; for a curved pane wth smpe rectanguar backng cavty. By appyng moda coupng theory to cacuate the couped structura-cavty response, they acheved good correaton 6

7 between smuated and measured data for the actve contro of sound transmsson nto the encosure over a range of frequences. Cases where more compex structures have been modeed over a range of frequences have aso been reported. Unruh and Dobosz [0] modeed an arcraft fuseage wth FE methods, and expermentay verfed ther mode over a frequency range of Hz. Usng an externa shaker as the prmary source, they measured the nteror nose eves n the fuseage and acheved at worst a 10 db error between ther mode and expermenta data. Lke Bumore et a. [4], they beeved the use of average acoustc moda dampng for nteror nose predcton worked we. Sung and Nefske [1] nvestgated the characterstcs of a GM van wth the ad of FE toos to determne whch panes contrbuted most to nose nsde the vehce. Incorporatng moda coupng, ther mode acheved broad agreement wth expermenta resuts over a Hz frequency range, athough at some frequences there were dscrepances of more than 0 db. The oss n accuracy was attrbuted to ncreasng moda densty at hgher frequences. Foowng the terature revew, t appears that tte work has been done on anaysng compex encosures wth hgh dampng and hgh moda densty wth the ad of FE modeng. Attempts to anayse the contro of sound over a broad frequency range are aso mted. Bumore et a. [4] targeted the constant operatng frequency 88 Hz (and ts harmoncs) whch corresponded to the BPF of the arcraft n queston. The operatng frequency of a mnng vehce cabn, however, s tme varant. Therefore any anayss of a mnng vehce cabn shoud take a range of frequences nto account. The prmary focus of the work descrbed here was to deveop an accurate FE mode of a mnng vehce cabn that coud be used for desgnng an optmum ANC system and nvestgatng the possbtes for both goba and oca nose reductons. An attempt has been made to mode the cabn so that the sound eve response wth and wthout actve contro can be accuratey predcted over a frequency range up to 300 Hz. Usng a nove representaton of moda dampng, accurate FE modes of the cabn and ts encosure are deveoped usng ANSYS and then the acoustc and structura modes are 7

8 combned usng moda coupng anayss to determne the couped structura and acoustc response of the cabn to exctaton by an nteror acoustc source. The numerca mode s then verfed expermentay for some smpe cases. Then, the achevabe reducton n both oca and goba cabn nteror nose s nvestgated numercay. The prmary source used for the nta nvestgaton was a oudspeaker ocated n the rear of the cabn. Ths s a smpfcaton of how the actua sound n the cabn s generated as, n practce, the engne exctes the cabn structure, whch n turn radates sound nto the nteror. However, for the purposes of nvestgatng the accuracy of fnte eement modeng and the potenta effectveness of oca actve nose canceaton, the oudspeaker prmary source was consdered to be adequate.. ANALYTICAL MODELLING The mode of the mnng vehce cabn was deveoped usng ANSYS wth the fna mode comprsng 3484 eements and 856 nodes. The cabn s ustrated n Fgure 1 and the FE mode s ustrated n Fgure. The frst 100 acoustc and 500 structura modes were cacuated usng the bock Lanczos sover and couped, to obtan the response to a gven exctaton, usng moda coupng theory ([1], [18], [] and [3]) mpemented n MATLAB. As the resonance frequences of these modes spanned the frequency range up to 600 Hz, t was consdered that the response n the frequency range up to 300Hz was not sgnfcanty nfuenced by modes not consdered..1. SUMMARY OF MODAL COUPLING ANALYSIS Fahy [Error! Bookmark not defned.] showed that the couped moda equatons of moton for the structure and the cavty are: 8

9 9 = + Φ = + 1, 0 M F B M S w w & && ρ ω (1) = Λ Λ = Φ + Φ 1 0, 0 Q c w B S c & & & ω () where w s the moda dspacement, ω s the moda resonance frequency, F s the generased force, and M s the moda mass of the th structura mode. Φ s the potenta, Q the generased voume veocty, ω s the resonance frequency and Λ the moda mass of the th acoustc mode. S s the tota surface area of the structure, and B, s the non-dmensona coupng coeffcent between the th acoustc mode and th structura mode: = S da S B ) ( ) ( ) ( 1, r r r ψ φ (3) where φ and ψ are the respectve mode shape functons of the uncouped acoustc and structura modes. Upon rearrangng and sovng equatons (1) and () for arbtrary frequency ω, the equaton for pressure n the cavty arsng from both structura and acoustc sources wrtten n terms of the acoustc wavenumber wth the ncuson of a dampng term, ω ω η a j, for the cavty s: + + Λ = = s n a Q B v S k k k j k j p 1, 0 ) ( η ω ρ (4) and the equaton for veocty of the structure arsng from both structura and acoustc sources wth the ncuson of a dampng term, s j ω η, for the structure s: + + = = a n s F B p S j M j v 1, ) ( ω ω η ω ω (5) Fnay, to arrve at the couped acoustc response of the system to acoustc sources ony, the force term n equaton (5) s set to zero and v s substtuted nto equaton (4) to yed the resutant pressure of the th acoustc mode:

10 Λ = = = s a n n s a r Q B B p S j M j S k k k j k j p 1, 1, 0 ) ( ) ( ω ω η ω ω η ω ρ (6) whch smpfes to: = = + = + Λ s a n n r a Q p Z M B B S j p k k k j k j 1 1,, 0 ) ( ω ω ρ η (7) Summarsed n matrx form, the couped acoustc response of a system (resutant pressure) n whch acoustc sources but no structura forces act, s: Q Z p 1 q = (8) where p s a (n a x 1) vector, the eements of whch represent the pressure amptude of each acoustc mode, Q s an (n a x 1) vector, the eements of whch represent the reatve contrbuton of the acoustc voume veocty sources to each acoustc mode, and Z q s the (n a x n a ) acoustc moda nput mpedance matrx, the eements of whch are: = + Λ = s u n u a u u u u q k k k j k j Z M B B S j u u Z 1 0,, ) ( ), ( ω ρ η ω (dagona terms) (9) = = n s v u q Z M B B S j v u Z 1,, ), ( ω (off-dagona terms) (10) where the ndces u and v are the uth and vth acoustc modes from 1 to n a. Of mportant note here s the way n whch vaues for structura and acoustc dampng were defned. In prevous work, Cazzoato [18] arbtrary specfed a constant % dampng across a structura and acoustc resonant frequences for hs curved pane wth backng cavty mode. However, here measured transfer functons between a oudspeaker sound source (P1-P5) (rato of the acoustc pressure to the source voume veocty) and a mcrophone n the cabn (M1-M8) were used to estmate both acoustc and structura dampng n the foowng way. The response n the cabn was frst smuated at a number of ocatons (P1-P5) assumng a constant % dampng across a modes. Then

11 the dampng for each mode was manuay adjusted so that the numerca predctons matched the measured transfer functons as best as possbe through a tra and error process... SUMMARY OF QUADRATIC OPTIMISATION THEORY Quadratc optmsaton theory (QOT) [4] was used to determne the unque contro source sgna amptudes and phases for mnmsng the cost functon at a number of error sensor ocatons and subsequenty to predct the optma eve of contro achevabe n the cabn. The cost functon to be mnmsed s: e H H J p = pt = p t pt = ( p p + Zq s ) ( p p + Zq s ) (11) = 1 where p t s the vector of tota sound pressures at the error sensor ocatons, made up of the combned prmary, p p, and controed, p s, pressure feds at the same ocatons. The vector, q s, represents the contro source voume veoctes and the transfer mpedance matrx, Z, s defned as: z11 z1 L z1 c = z 1 z L z c Z (1) M M M M z e1 z e L z ec where the eements of Z are found by measurng the transfer functon between each error sensor and each contro source nput sgna n turn, wth the prmary source turned off, such that: Expanded and represented n quadratc form, the cost functon becomes: p s = Zq s (13) H H H J p q Aq + q b + b q + c (14) = s s s s where A, b, and c are the coeffcents of a quadratc equaton, gven by: 11

12 H A = Z Z (15) b = Z H p p (16) H p p p p c = (17) The optma set of secondary contro source strengths that w mnmse J p s: q s(opt) 1 = A b (18) As the matrx, A, s not square, t s necessary to use the pseudo nverse, A 1 = ( A H A) 1 A H Note that f the same number of error sensors as contro sources s used, quadratc optmsaton w predct that zero sound pressure can be acheved at a error sensors. So n practce, ether a mt s set on the controer accuracy or more error sensors than contro sources are used. 3. EXPERIMENTAL WORK 3.1. PRIMARY SOURCE VOLUME VELOCITY MEASUREMENT The use of moda coupng theory assumes that both the prmary and contro acoustc sources are monopoe constant voume veocty sources. Therefore, for verfcaton wth the FE mode, t was necessary to measure the voume veocty output of the acoustc source, n ths case a oudspeaker backed by a sma encosure. Anthony and Eott [5] outne three technques for voume veocty measurement. They compare two methods wth aser veocmetry; namey, measurement of the nterna source pressure, and usng a movng-co oudspeaker as an output transducer (known as Saava s method). They concuded that Saava s method s superor n terms of measurement accuracy and harmonc dstorton. However, a three of these methods are dffcut to execute expermentay. Snyder and Hansen [6] descrbe a fourth method for measurng voume veocty. Usng ths method, the nterna pressure generated by a oudspeaker n a seaed backng encosure s measured and 1

13 converted nto voume veocty by usng the cacuated mpedance of the voume. Ths method s easer to mpement expermentay, and was the one chosen for the work descrbed here. 3.. EXPERIMENTAL WORK USING THE MINING VEHICLE CABIN Expermenta work was carred out nsde a Caterpar mobe mnng vehce cabn to gan further understandng of ts acoustc propertes, and more mportanty, to verfy the mode. Externay, the cabn was.4m ong, 1.5m wde, and 1.7m ta. The source and mcrophone postons referred to n the text to foow are dentfed n Fgure 3. Testng on the cabn was dvded nto two stages. In the frst stage, the objectve was to measure transfer functons that coud be used to confrm the accuracy of the FE and moda coupng modes n predctng the nteror sound pressure fed generated by a constant voume source, whch was approxmated usng a sma oudspeaker backed by a sma encosure. Ths requred the measurement of transfer functons between a mcrophone n the cabn and a mcrophone nsde the prmary source speaker encosure, and then convertng the resut to a rato of cabn pressure to source voume veocty [6] to make the measurements compatbe wth the ANSYS/MATLAB smuatons. A PULSE system generator (B&K mut-channe data acquston unt type 816 wth generator modue type 3107) ampfed va a Paymaster Pro Seres 3 power ampfer was used to drve an Exce Seas 110mm dameter speaker wth random nose up to 400 Hz. B&K type 4133 mcrophones connected to a B&K type 804 preampfer were used to measure the requred transfer functons, wth one mcrophone beng securey paced nsde the speaker housng, and the other strategcay ocated n the cabn. Varous randomy seected postons of sensors and sound sources were used to verfy the FE mode usng a constant voume veocty oudspeaker source. Eght cabn mcrophone postons and fve prmary source postons were tested. The resuts of the mode verfcaton procedure are presented n secton

14 For the second stage of testng, the objectve was to measure transfer functons that coud be used to predct the eve of oca contro and the extent of goba contro achevabe n the cabn for varous error sensor and contro source confguratons when squared pressure s mnmsed. Transfer functons between the acoustc pressure at 18 dfferent cabn mcrophone ocatons and the source voume veocty for sx dfferent source ocatons were measured. The source voume veocty was determned usng a mcrophone n the backng cavty of the oudspeaker encosure as descrbed by Snyder and Hansen [6]. QOT [4] was apped to these transfer functons to ascertan the optmum eve of contro achevabe nsde the cabn ( off-ne contro). Rea tme controers are usuay mted by how many channes they can contro smutaneousy. The EZANC II system used for the work descrbed here has a maxmum of ten nput and ten output channes aowng up to nne contro sources to be used to contro a maxmum of nne error sensors. For reastc resuts to be determned usng QOT, the number of error sensors shoud exceed the number of contro sources. If the number of error sensors s equa to the number of contro sources, t s theoretcay possbe to acheve zero sound pressure at each error sensor. If there are more contro sources than error sensors, the system s over determned and there s no unque souton for optma contro source strengths. For these reasons, eght error sensors and sx contro sources were used for reastc contro predctons. The eght mcrophone ocatons nearest the voume that surrounds the drver s head f he/she were sttng n the cabn were seected for ths purpose. Transfer functons were measured from the contro source voume veocty to other non-error mcrophone ocatons to ascertan the effect that controng nose eve at one ocaton has on other ocatons n the cabn. Transfer functons at four mcrophone ocatons, each wthn λ 6 (at 300 Hz) of one of the eght error sensors were measured, as we as sx more non-error mcrophone ocatons we away from the error mcrophones (mnmum separaton λ at 300 Hz), where λ s the waveength of sound. A of these 14

15 transfer functons were dupcated n the FE mode and correated wth the expermenta data. The resuts are presented n secton 4.. The sx dfferent contro source ocatons and prmary source ocaton used for the off-ne contro anayss were chosen based on ther practcaty and potenta mpact on the nteror sound fed. That s, the ocatons were chosen to be as cose as possbe to encosure corners where the sources are key to be abe to drve a acoustc modes excted n the encosure. Snce accuratey measurng the acoustc PE of a arge cavty requres a muttude of sensors, acoustc PE reducton predctons were performed soey usng the FE mode. A range of prmary dsturbance ocatons were aso seected for the acoustc PE reducton predctons of the FE mode. Ths was because t was found that the ocaton of the prmary source had a sgnfcant mpact on the controed response. Hence every combnaton of contro sources was used severa tmes n smuatons to contro a prmary source at each specfc ocaton. The acoustc PE reducton predctons are dscussed n secton DISCUSSION OF RESULTS 4.1. VERIFICATION OF THE FINITE ELEMENT MODEL The resuts of the correaton between cacuated and expermenta frequency responses n the cabn are presented n two forms. For each contro source and sensor combnaton shown, the response at the sensor ocaton s presented frst as a one thrd octave band average, and then as a spectrum up to 300 Hz. To cacuate the band averaged amptude eve, the tme averaged vaues of the pressure squared at each frequency n a one thrd octave band were averaged and then converted to decbes. 15

16 For the smuated response curves up to 300 Hz, spata averagng was used. The response was averaged over the cosest 50 nodes to the sensor coordnates seected; ths represented an effectve voume of the approxmate sze of a 10cm cube. Ths had the effect of averagng out any probems caused by sght modeng naccuraces and coud be justfed n a smar way that 1/3 octave band data are used for frequency averagng purposes. Modeng naccuraces are a resut of assumptons and approxmatons made regardng the dmensons of the cabn, ts matera propertes, connectons, seas, boundary condtons, and dampng. Measured and predcted transfer functons between severa contro source ocatons and one mcrophone ocaton are shown n Fgure 4. These ocatons are dfferent to those used to optmse the moda dampng vaues for the numerca mode. Consderng the compex nature of the envronment modeed, the correaton between the measured transfer functons and smuated responses s consdered acceptabe for ANC predctons. The mode predcts the basc shape of the measured transfer functon, and the amptude predcton s reasonabe. The mode s aso robust to aternatve combnatons of contro source and sensor ocatons, wth the mode predctng the changes that dfferent combnatons cause. Errors were ony sgnfcant at ant-resonant frequences where the coherence between the two sgnas used to derve the transfer functon was poor. The mode and measurements concur that the acoustc cavty modes domnate the overa system response. Many of the smaer bumps observed n the measured transfer functons are due to the presence of the weaker structura modes. However, these had mnma mpact on the overa shape of the transfer functon curve, and are not evdent n the smuated mode resuts. However, t s mportant to ncude the structura response n the mode as that w aow future nvestgaton of actve contro when the unwanted sound resuts from vbraton of the cabn was. Presentaton of the data n band averaged form shows that the mode s reasonaby consstent wth the rea structure. In the majorty of frequency bands, an amptude error of ess than 5 db was acheved. In bands where there was a greater dfference t was usuay due to the smuated eve beng 16

17 much ower than the measured response over that frequency band (partcuary n the 5 Hz and 31.5 Hz bands). The coherence between the two sgnas makng up the transfer functon measurement at frequences n these bands was poor, so as for the narrow band comparsons, poor agreement between measured and predcted resuts can be expected for these bands. 4.. OFF-LINE CONTROL Fgures 5(a)-(c) show the measured and predcted prmary sound fed at a mcrophone, and the off-ne contro predcton usng QOT wth sx contro sources for both measured and smuated transfer functons. The controed sound fed predcton curves usng the cabn measurements have been passed through a functon that averaged the orgna curve over Hz bands and then ftted the resutant ponts wth a poynoma of degree 50. Ths was done because the orgna predcted controed sound feds cacuated usng QOT were hghy scattered n nature. Ths effect s most key to be a resut of poor condtonng n the matrces nvoved n the QOT dervaton of optma contro source strengths. Aternatng the order of error sensors n the Z matrx was attempted to emnate the probem, but wth no success. Broadband reducton up to 30 db s predcted usng off-ne contro at the error mcrophones and there s even some reducton at the mcrophones cose to those beng controed. However, tte or no reducton s seen at the mcrophones furthest away from the error mcrophones. Ony the resuts of a snge mcrophone from each of the three ocaton types are shown here. As wth the resuts n secton 4.1, reasonabe agreement was acheved between the measured and smuated transfer functons n Fgures 5 (a)-(c). Over the 300 Hz frequency range of nterest, the FE mode broady estmates the amptude of the prmary fed transfer functon n the mnng vehce cabn, and then predcts wth accuracy the eve of reducton that occurs at each of the 18 mcrophone ocatons measured when the eght error mcrophones near the drver s head are controed wth sx contro sources. 17

18 Wth poynoma fttng, the controed sound fed transfer functon derved from cabn measurements s reatvey smar to that of the optmsed FE mode transfer functon. Furthermore, the trend over the three genera categores of mcrophone ocatons tested (error sensors, non-error sensors near the error sensors, and non-error sensors we away from the error sensors) s the same for the two sets of data. Both data sets show arge reductons at the error sensors, moderate reducton at the nonerror sensors nearby, and tte reducton or even an ncrease n nose eve at the non-error sensors we away from the error sensors. Ths agrees wth the resuts obtaned by Eott et a. [7]. It aso hghghts the potenta for oca contro and the mpractcaty of goba contro n the mnng vehce cabn usng oudspeaker contro sources. There s evdence suggested by Cazzoato [18], and aso by Keste et a. [7] that the areas of oca contro can be expanded nto arger zones by usng energy densty sensng. An energy densty sensor suggested by Cazzoato [18], comprses of four mcrophones, three of whch are ocated aong the three orthogona cartesan axes and the fourth n an arbtrary pane. In theory, f an energy densty sensor can be used n pace of a mcrophone and arranged n a contro system such that the pressure at the four mcrophones of the energy densty sensor are a drven to zero (ths coud be acheved wth four contro sources), then t woud be possbe to create a zone of quet arge enough to encose the head of the drver up to frequences around 300 Hz, snce energy densty strateges are expected to produce arge epsod shaped zones of quet (wth the arger radus equa to λ 4 ) around the error sensor (Eott and Garca-Bonto [8]). The EZANC II controer coud then be fuy utsed wth a second energy densty probe for the passenger and four more contro sources. Ths concept s the subject of on gong work PREDICTION OF THE EFFECT OF ACTIVE NOISE CONTROL USING THE MODEL 18

19 Havng estabshed that the FE mode s a suffcent representaton of ts rea counterpart, the mode was used to run smuatons to predct the reducton of tota acoustc PE achevabe n the mnng vehce cabn. In a smuaton envronment, physca parameters such as ocaton and number of contro sensors and contro sources can be modfed easy, savng expermenta tme. Trends can aso be obtaned much faster, as the effects of changes n the physca parameters on the frequency responses can be seen mmedatey. Workng n a smuaton envronment has the addtona advantage of aowng one to tra deas that at the tme are not practcay feasbe, to determne f they are worthy of expendng the effort on mpementaton at a ater date (for exampe, the use of 3 error sensors and 16 contro sources n a mnng vehce cabn contro system, as w be detaed shorty). The smuatons used the ocatons of the prmary and contro sources specfed n secton 3 to cacuate the response at each of the 856 nodes n the mode before and after secondary sources were ntroduced. The average of the squared pressures at a of these nodes was used as a good approxmaton to the acoustc PE n the cabn and the quantty mnmsed was the sum of the cacuated squared pressures at the 856 noda ocatons. Orgnay t was ntended to optmse the number and ocaton of the contro sources by usng a genetc search agorthm. However, the estmated ength of tme to do such a search and the computer power requred to do t rendered the approach mpractca. Hence the contro sources were ocated n the corners of the cabn, where they were best abe to excte most of the cabn modes. For each prmary source poston, the optmay controed response usng one to eght contro sources and the 856 error sensors (one for each node n the mode) was cacuated. In Fgure 6 the response when usng one contro source and a eght contro sources s shown for each of the three prmary source postons. The use of any number of contro sources between one and eght resuted n a performance that was wthn the two extremes shown. The resuts n Fgure 6 concde wth the concusons of Zander [14]. Inspecton of these resuts reveas that the effect of the ocaton of the contro source wth respect to the prmary source s more 19

20 mportant than the number of contro sources n terms of achevabe reducton n the acoustc PE. However t can be seen that n a cases, eght contro sources provde greater reducton n acoustc PE than one source and ths s more notceabe at hgher frequences. The ack of contro at hgher frequences s a resut of the hgh moda overap, whch s controed by the number of modes and the moda dampng, both of whch are hgh. The acoustc and structura moda dampng, moda densty, and moda overap are shown as a functon of frequency n Tabe 1 and Tabe. The dfference n contro performance for the three prmary source ocatons consdered s due to the reatve ocatons of the prmary source and contro sources. Consderng the hghest frequency n the frequency range of nterest (300 Hz), for the resuts shown n Fgures 6(a) and 6(b), the prmary source s never coser than 3λ 5 to any contro source. For the resuts shown n Fgures 6(c) and 6(d), the prmary source s wthn 7λ 10 of a contro source, and for the resuts shown n Fgures 6(e) and 6(f), the prmary source s wthn 3λ 100 of one of the contro sources. Ths agrees wth the resuts obtaned by Neson et a. [1] for an acoustca envronment of hgh moda densty. In Fgure 7, possbe reductons n acoustc potenta energy usng 1, 8 or 16 contro sources and 8, 16, 3 and 856 error sensors are shown for one prmary source ocaton that s reatvey far (0.6λ at 30 Hz and 6λ at 300 Hz) from any of the contro sources. The cost functon was the sum of the squared sound pressures at the error sensors and the contro sources were ocated n the corners of the cabn, where they were best abe to excte most of the cabn modes. It can be seen from Fgure 7 that as the number of error sensors are reduced, there s more of an ncrease n the overa cabn acoustc potenta energy at hgher frequences, even though the sum of the squared pressures s mnmsed. Restrctng the error sensors to a sma voume resuts n more effectve goba contro (Fgure 7(d)), than acheved wth the same number unformy dstrbuted. It s 0

21 aso seen that ncreasng the number of contro sources above a mnmum number can aso have an adverse effect on the acoustc potenta energy at hgher frequences. 5. CONCLUSIONS By ntroducng ndvdua moda dampng vaues and matchng them wth many dfferent transfer functon measurements, an accurate FE mode of a mnng vehce cabn has been deveoped. The mode has been shown to accuratey predct both structura and acoustc resonance frequences and mode shapes. The FE mode was used wth moda coupng anayss to accuratey predct frequency response functons between acoustc source voume veoctes and sound pressures at mcrophones n the cabn over a frequency range up to 300 Hz. The measured transfer functons used for verfyng the numerca mode were aso used n offne contro experments. Quadratc optmsaton theory was apped to the measurements and FE mode smuatons to predct the optma contro achevabe usng sx contro sources and eght error mcrophones. Good agreement was agan obtaned, wth the two sets of resuts ndcatng that a sgnfcant nose reducton at the error sensors was possbe but goba contro was not feasbe for contro sources paced a reatvey arge dstance (>λ/) from the prmary source. Ths confrmed the nta assumpton that goba contro s dffcut to acheve n a compex three-dmensona encosure by usng sma acoustc sources to mnmse the squared sound pressure, as suggested by Eott et a. [7] for encosures of hgh moda densty. Numerca smuatons that predcted the reducton of acoustc PE across the cavty were aso performed. The FE mode and accompanyng MATLAB code used for post-processng assumed a prmary voume veocty source. As expected from prevous work by Neson et a. [1], t was found that the acoustc PE nsde the cabn can be sgnfcanty reduced f a contro source s paced n cose 1

22 proxmty to the prmary source. Ths s vabe for expermenta purposes, but may not be appcabe to a rea vehce where the prmary nose orgnates from the engne and s radated nto the cabn by vbraton of the was. However, for ths more practca case, t may be possbe to use dstrbuted acoustc sources that cover the entre nteror sod was, roof and foor of the cabn to provde an effectve canceng sound fed [9]. Ths s the subject of future work. Increasng the number of sensors and/or ncreasng the number of contro sources ocated remotey from the prmary source had tte mpact on the overa acoustc PE n the cabn because the moda overap was too hgh. Contro at ower frequences was margnay mproved wth the use of more contro sources, whch was prevousy demonstrated by Zander [14], but the tendency for the energy eve to ncrease rather than decrease at other frequences was aso observed. Ths supported the resuts obtaned prevousy n off-ne experments usng quadratc optmsaton theory. Areas of oca contro can be expanded nto arger zones usng an energy densty sensng strategy and ths s the subject of ongong work. ACKNOWLEDGEMENTS The authors gratefuy acknowedge the Austraan Research Counc for ts fnanca support of the work undertaken here and Dr Ben Cazzoato for provson of the moda coupng MATLAB code requred for evauatng the FE mode.

23 REFERENCES 1. P.A. Neson, A.R.D. Curts, S.J. Eott and A.J. Bumore 1987 Journa of Sound and Vbraton 117(1), The actve mnmzaton of harmonc encosed sound feds, Part I: Theory.. A.J. Bumore, P.A. Neson, A.R.D. Curts and S.J. Eott 1987 Journa of Sound and Vbraton 117(1), The actve mnmzaton of harmonc encosed sound feds, Part II: Computer smuaton. 3. S.J. Eott, A.R.D. Curts, A.J. Bumore and P.A. Neson 1987 Journa of Sound and Vbraton 117(1), The actve mnmzaton of harmonc encosed sound feds, Part III: Expermenta verfcaton. 4. A.J. Bumore, P.A. Neson and S.J. Eott 1990 Journa of Sound and Vbraton 140(), Theoretca studes of the actve contro of propeer-nduced cabn nose. 5. S.J. Eott, P.A. Neson, I.M. Stothers and C.C. Boucher 1989 Journa of Sound and Vbraton 18(), Premnary resuts of n-fght experments on the actve contro of propeer-nduced cabn nose. 6. S.J. Eott, P.A. Neson, I.M. Stothers and C.C. Boucher 1990 Journa of Sound and Vbraton 140(), In-fght experments on the actve contro of propeer-nduced cabn nose. 7. S.J. Eott, P. Joseph, A.J. Bumore and P.A. Neson 1988 Journa of Sound and Vbraton 10(1), Actve canceaton at a pont n a pure tone dffuse sound fed. 8. C.M. Dorng, G.P. Eatwe, S.M. Hutchns, C.F. Ross and S.G.C. Sutcffe 1989 Journa of Sound and Vbraton 18(), A demonstraton of actve nose reducton n an arcraft cabn. 9. S. Johansson, P. Persson and I. Caesson 1999 Proceedngs of Actve 99, Actve contro of propeer-nduced nose n an arcraft mock-up. 3

24 10. D.R. Thomas, P.A. Neson and S.J. Eott 1993 Journa of Sound and Vbraton 167(1), Actve contro of the transmsson of sound through a thn cyndrca she, Part I: The mnmzaton of vbratona energy. 11. D.R. Thomas, P.A. Neson and S.J. Eott 1993 Journa of Sound and Vbraton 167(1), Actve contro of the transmsson of sound through a thn cyndrca she, Part II: The mnmzaton of acoustc potenta energy. 1. S.D. Snyder and C.H. Hansen 1994 Journa of Sound and Vbraton 170(4), The desgn of systems to actvey contro perodc sound transmsson nto encosed spaces, Part I: Anaytca modes. 13. S.D. Snyder and C.H. Hansen 1994 Journa of Sound and Vbraton 170(4), The desgn of systems to actvey contro perodc sound transmsson nto encosed spaces, Part II: Mechansms and trends. 14. A.C. Zander 1994 Ph.D. Dssertaton. The Unversty of Adeade, Adeade, Austraa. Infuence of error sensor and contro source confguraton and type upon the performance of actve nose contro systems. 15. M. Aved 1993 Proceedngs of Inter Nose 93, Optmsaton of secondary sources for actve nose contro n a FE-mode of an arcraft cabn. 16. E. Carett, G. Mcco and I. Vecch 1996 Proceedngs of Inter Nose 96, Earth-movng cab encosed sound fed actve contro smuaton. 17. Y. Da and C. Fuer 1995 Proceedngs of Inter Nose 95, Numerca smuaton of actve contro of nteror nose n a busness jet wth pont force actuators optmzaton of transducers. 18. B.S. Cazzoato 1999 Ph.D. Dssertaton. The Unversty of Adeade, Adeade, Austraa. Sensng systems for actve contro of sound transmsson nto cavtes. 19. B.S. Cazzoato and C.H. Hansen 1998 Journa of the Acoustca Socety of Amerca 104(5), Actve contro of sound transmsson usng structura error sensng. 4

25 0. Unruh, J.F. & Dobosz, S.A Journa of Vbraton, Acoustcs, Stress, and Reabty n Desgn, 110, Fuseage structura-acoustc modeng for structure-borne nteror nose transmsson. 1. S.H. Sung and D.J. Nefske, D.J Journa of Vbraton, Acoustcs, Stress, and Reabty n Desgn, 106, A couped structura-acoustc fnte eement mode for vehce nteror nose anayss.. L. Pope 1971 Journa of the Acoustca Socety of Amerca 50(3), On the transmsson of sound through fnte cosed shes: Statstca energy anayss, moda coupng, and non-resonant transmsson. 3. F. Fahy 1985 Sound and Structura Vbraton: Radaton, Transmsson, and Response. London: Academc Press. 4. C.H. Hansen 001 Understandng Actve Nose Canceaton. London: Spon Press. 5. D.K. Anthony and S.J. Eott 1991 Journa of the Audo Engneerng Socety 39(5), A comparson of three methods of measurng the voume veocty of an acoustc source. 6. S. Snyder and C. Hansen 1989 Journa of the Acoustca Socety of Amerca 86, Actve nose contro n ducts; Some physca nsghts. 7. C.D. Keste, B.S. Cazzoato and C.H. Hansen 001 Journa of the Acoustca Socety of Amerca 109(1), Actve nose contro n a free fed wth vrtua sensors. 8. S. Eott and J. Garca-Bonto 1995 Journa of Sound and Vbraton 186(4), Actve canceaton of pressure and pressure gradent n a dffuse sound fed. 9. Fuer, C.R. Johnson, M.E. and Grffn, J.R. 000 Actve-passve contro of arcraft nteror boundary ayer nose usng smart foam. AIAA Paper No

26 LIST OF TABLES Tabe 1. Acoustc moda propertes of the mnng vehce cabn mode Tabe. Structura moda propertes of the mnng vehce cabn mode 6

27 1/3 Octave Band Centre Frequency (Hz) Moda Densty of Band Average Moda Loss Factor of Modes n Band Band Moda Overap (Cavty) Tabe 1. Acoustc moda propertes of the mnng vehce cabn mode 1/3 Octave Band Centre Frequency (Hz) Moda Densty of Band Average Moda Loss Factor of Modes n Band Band Moda Overap (Structure) Tabe. Structura moda propertes of the mnng vehce cabn mode 7

28 LIST OF FIGURES Fgure 1. Photo of Caterpar mnng vehce cabn... 7 Fgure. Mnng vehce cabn fnte eement mode... 7 Fgure 3. Sde (a) and front (b) vew of the nteror of the mnng vehce cabn showng the mcrophone (M) prmary source (P) and contro source (S) ocatons referred to n the foowng text and fgures... 8 Fgure 4. Correaton between predcted and measured transfer functons. One-thrd octave resuts are shown on the eft and narrow band resuts on the rght. Transfer functons are the rato of the acoustc pressure at the mcrophone ocaton to the voume veocty of the oudspeaker source. (a) Source poston P1, mcrophone poston M (b) Source poston P, mcrophone poston M5 (c) Source poston P3, mcrophone poston M Fgure 5. Optma oca contro predcton and correaton between predcted and measured transfer functons usng sx sources and eght error sensors. Transfer functons represent the rato of the acoustc pressure at a mcrophone n the cabn and the voume veocty of the prmary oudspeaker source (P1). Dotted ne: Measured prmary sound fed n cabn. Dashed ne: Smuated prmary sound fed usng FE mode. Sod ne: Controed sound fed predcton usng cabn measurements. Dash-dot ne: Controed sound fed predcton usng FE mode. (a) Error mcrophone M5. (b) Mcrophone M9, wthn λ 6(at 300 Hz) of an error sensor (M5). (c) Mcrophone M13, mcrophone 5λ 7 (at 300 Hz) away from the cosest error sensor (M6) Fgure 6. Predcted prmary and controed acoustc PE eves n the mnng vehce cabn. (a) Prmary source ocaton P1, contro source ocaton S1 (b) Prmary source ocaton P1, a eght contro sources (c) Prmary source ocaton P, contro source S1 (d) Prmary source ocaton P, a eght contro sources (e) Prmary source ocaton P3, contro source S1 (f) Prmary source ocaton S3, a eght contro sources

29 Fgure 7. Predcted prmary and controed acoustc PE eves n the mnng vehce cabn wth the prmary source reatvey far from any contro source. (a) 1 contro source, 856 error sensors (b) 8 contro sources, 856 error sensors (c) 8 contro sources, 8 error sensors unformy dstrbuted (d) 8 contro sources, 8 error sensors n a spherca voume of radus 0.3 m (e) 8 contro sources, 16 error sensors unformy dstrbuted (f) 8 contro sources, 3 error sensors unformy dstrbuted (g) 16 contro sources, 3 error sensors unformy dstrbuted

30 Fgure 1. Photo of Caterpar mnng vehce cabn Fgure. Mnng vehce cabn fnte eement mode. 30

31 (a) Fgure 3. Sde (a) and front (b) vew of the nteror of the mnng vehce cabn showng the mcrophone (M) prmary source (P) and contro source (S) ocatons referred to n the foowng text and fgures. (b) 31

32 (a) (b) (c) Fgure 4. Correaton between predcted and measured transfer functons. One-thrd octave resuts are shown on the eft and narrow band resuts on the rght. Transfer functons are the rato of the acoustc pressure at the mcrophone ocaton to the voume veocty of the oudspeaker source. (a) Source poston P1, mcrophone poston M (b) Source poston P, mcrophone poston M5 (c) Source poston P3, mcrophone poston M3. 3

33 (a) (b) (c) Fgure 5. Optma oca contro predcton and correaton between predcted and measured transfer functons usng sx sources and eght error sensors. Transfer functons represent the rato of the acoustc pressure at a mcrophone n the cabn and the voume veocty of the prmary oudspeaker source (P1). Thck, grey ne: Measured prmary sound fed n cabn. Thck, dashed ne: Smuated prmary sound fed usng FE mode. Sod ne: Controed sound fed predcton usng cabn measurements. Thn, dash-dot ne: Controed sound fed predcton usng FE mode. (a) Error mcrophone M5. (b) Mcrophone M9, wthn λ 6 (at 300 Hz) of an error sensor (M5). (c) Mcrophone M13, mcrophone 5λ 7 (at 300 Hz) away from the cosest error sensor (M6) 33

34 (a) (b) (c) (d) 34

35 (e) (f) Fgure 6. Predcted prmary and controed acoustc PE eves n the mnng vehce cabn. (a) Prmary source ocaton P1, contro source ocaton S1 (b) Prmary source ocaton P1, a eght contro sources (c) Prmary source ocaton P, contro source S1 (d) Prmary source ocaton P, a eght contro sources (e) Prmary source ocaton P3, contro source S1 (f) Prmary source ocaton S3, a eght contro sources. 35

36 (a) (b) (c) (d) 36

37 (e) (f) (g) Fgure 7. Predcted prmary and controed acoustc PE eves n the mnng vehce cabn wth the prmary source reatvey far from any contro source. (a) 1 contro source, 856 error sensors (b) 8 contro sources, 856 error sensors (c) 8 contro sources, 8 error sensors unformy dstrbuted (d) 8 contro sources, 8 error sensors n a spherca voume of radus 0.3 m (e) 8 contro sources, 16 error sensors unformy dstrbuted (f) 8 contro sources, 3 error sensors unformy dstrbuted (g) 16 contro sources, 3 error sensors unformy dstrbuted. 37