Research Article Optimization of Fixed Microphone Array in High Speed Train Noises Identification Based on Far-Field Acoustic Holography

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1 Hindawi Advances in Acousics and Vibraion Volume 7, Aricle ID 89498, pages hps://doi.org/.55/7/89498 Research Aricle Opimizaion of Fixed Microphone Array in High Speed Train Noises Idenificaion Based on Far-Field Acousic Holography Rujia Wang and Shaoyi Bei School of Auomoive and Transporaion, Jiangsu Universiy of Technology, Changzhou, Jiangsu, China Correspondence should be addressed o Rujia Wang; rujia.wang@jsu.edu.cn Received July 6; Revised 4 December 6; Acceped 4 January 7; Published February 7 Academic Edior: Marc Asselineau Copyrigh 7 Rujia Wang and Shaoyi Bei. This is an open access aricle disribued under he Creaive Commons Aribuion License, which permis unresriced use, disribuion, and reproducion in any medium, provided he original work is properly cied. Acousical holography has been widely applied for noise sources locaion and sound field measuremen. Performance of he microphones array direcly deermines he sound source recogniion mehod. Therefore, research is very imporan o he performance of he microphone array, is array of applicaions, selecion, and how o design insrucive. In his paper, based on acousic holography moving sound source idenificaion heory, he opimizaion mehod is applied in design of he microphone array, we selec he main side lobe raio and he main lobe area as he opimizaion objecive funcion and hen pu he opimizaion mehod use in he sound source idenificaion based on holography, and finally we designed his paper o opimize microphone array and compare he original array of equally spaced array wih opimizaion resuls; by analyzing he opimizaion resuls and objecives, we ge ha he array can be achieved which is opimized no only o reduce he microphone bu also o change objecive funcion resuls, while improving he far-field acousic holography resolving effec. Validaion experimens have showed ha he opimizaion mehod is suiable for high speed rains sound source idenificaion microphone array opimizaion.. Inroducion The noise of high speed vehicles such as high speed rains is one of he severes noise polluion sources [, ]. Based on sudies in he reconsrucion of he sound field microphone array, predecessors o build a grid array cross array have inheren defecs; namely, in order o ensure a small main lobe widhofhesoundfieldreconsrucionoimproveresoluion, he need o mainain a larger size of he array, such ha he spacing beween adjacen array elemens, is increased and causes he emergence of graing lobes, which grealy weakened he abiliy of he sound field reconsrucion array. Compared wih beamforming, acousic holography mehod can achieve a quaniaive measure of moving sound source, so in recen years i has been widely sudied and applied. Acousic holography heory in he 98s by he Williams and Maynard e al. [3 5] pu forward he sric acousic radiaion based on he heory. In he 99s, Tanaka e al. [6] were firs used he far-field acousic holography mehod o measure a vehicle noise source and in 4 by using wo-dimensional arrays based on far-field acousic holography mehod of analyzing ire/road noise and ire noise successfully. From 998 o 8, Park e al. [7, 8] esablished a framework for holographic mobile, using sound field space ransformaion mehod o eliminae he Doppler effec and measure and analyze a low-speed rain noise. Yang e al. [9 ] firs proposed he inernaional far-field diffracion acousic holography mehod and in proposed eliminaing he ime-domain mehod Doppler effec, for he firs ime o achieve a speed of 7 km/h, vehicle quaniaive idenificaion of noise sources ouside he vehicle. In his paper, based on formaion simulae annealing opimizaion mehod o opimize he unequal a fixed spacing array, raher han a random array, for obaining a more accurae resul of he sound source idenificaion, i can

2 Advances in Acousics and Vibraion P P P P P 3 P P (c) (d) Figure : Schemaic diagram of beamforming sound field reconsrucion. furher improve he accuracy of idenificaion of he sound source.. Acousical Holography Far-Field Sound Source Idenificaion Mehod for he Moving Sound Source.. Shor-Time Beamforming. Shor beamforming mehod is based on he delay accumulae beamforming signal superimposed principle [, 3]. For he reconsrucion of he surface a poins, he period of is reconsrucion [, ] sound pressure signal wihin he principle is shown in Figure. Firs, calculae he ime period o be analyzed according o he respecive microphone receiving he segmen signal period, as shown in Figure ; secondly exraced sound for each signal segmens he desired pressure, as shown in Figure ; hen, any delay ime based on acousic wave propagaion, such as he signal, is p(), provided ha i emissoundwavesaimepoins(ε, η) o he microphone i, he propagaion ime of r i (, ε, η)/c, andhenasignaldelay processingasshowninfigure(c): p i =p i (+ r i (, ε, η) ). () c Finally, he superimposed signals of each delay processing, o obain he reconsrucion resul of he analysis period, are shown in Figure (d). According o his principle, he sound field characerisic funcion reconsrucion formula a any poin s(ε, η) on he reconsrucion side R is shown as follows: W s (ε, η) = P (, ε, η) d, P(,ε,η)= N N i= p i ( + r i (, ε, η) ), c ()

3 Advances in Acousics and Vibraion 3 y x Σ U y x z Σ U z s(ε, η) P s(ε, η) r n θ A R r A θ n Figure : Schemaic diffracion of acousic holography. where W s (ε, η) is he sound field characerisic funcion for any poin on he surface of he sound source s(ε, η) a ime wihin, P(,ε,η) is he sound source esimaed characerisic funcion applied of beamforming mehod, p i () is he received sound source pressure signals of i h microphone a ime, c is he sound velociy, N is he number of microphones, r i (, ε, η) is he physical disance beween he poin s(ε, η) inhesoundsourcesurfaceandi h microphone a ime. Based on his principle, across he enire surface of he sound source, sound field characerisic funcion of he disribuion of he enire surface of he sound source can be obained inside in ime [, ]... Far-Field Acousic Holography Mehod. NAH (Nearfield AcousicalHolography)mehodisproposedbyWilliamse al. [4, 5] in he 98s, and hen he mehod and heory of NAH s applicaions exend o he far-field condiions. ProfessorYangfromTsinghuaUniversiyhasproposedand esablished he heory of diffracion acousic holography based on far-field acousic holography heory. The principle is shown in Figure. In Figure, N is he ouward normal o he direcion of he hologram surface, r is he radius vecor, θ is he angle beween he hologram surface r and ouward normal direcion n, Σ is he posiion in he measuring surface of infinie plane in space, he measuremen par of he surface A is Σ, andr is assumed source poin s o he plane, known as he sound source surface. As i is showed in Figure U canbeviewedashe poin sound source, which assumed ha spherical wave a a spaial sound field disribuion, H(x, y, f), is U. In Σ plane componen, in he case of U which is known, he wave propagaion direcion of he space of passive can be calculaed by he using of Kirchhoff diffracion inegral calculaion mehod. Any poin P of he sound field formula is obained in U (P) = 4π [( ejkr H r ) U U n (ejkr n r )] dσ. (3) Figure S canbeviewedasavirualsoundsource space.soundfieldinhedisribuionins,asonicconvergein S,sphericalwave,andS sen ou acually muually conjugae wave. According o he principle of acousic holography reconsrucionasshownin(4)iisobainedbasedonhe principle of conjugae wave convergence: U(ε,η,f)= Ck j H (x,y,f) H [+( jkr ) z r ] e jkr dx dy. r k=f/cis he wave number, c is he sound velociy, C is a hologram consan, and r is he reconsrucion of he surface poin Q(ε, η) beween he hologram surface poins (x, y) disance. Equaion (4) is calculaed according o he resuls of a single frequency f, coninuous several frequencies. Calculaing according o he energy superposiion can be obained wihin a frequency range of he sound pressure ampliude calculaion, as shown in (4) f P(ε,η)= U(ε,η,f) df. (5) f Reconsrucing by he above mehod assumes ha he sound pressure of he sound source Q value, as we can see in Figure 3, supposes he poin raverse plane of reconsrucion

4 4 Advances in Acousics and Vibraion O P i Poin Microphone array O y x η S(ε, η) ε m i H Z s Z m Microphone array Figure 3: Hologram surface srucure. z Sound source S(α, r) Y Cener of he array Microphone r r sin α r n Δd α n M/ M/ + M X d n r cos α Figure 4: Model of uniform linear array. and repeas his calculaion; we can calculae he enire plane of he sound pressure disribuion. In acual measuremen, he coninuous sound pressure poins in hologram surface canno be measured; herefore, (4) is discreized; as shown in Figure 3 for rules discree arrays can be reconsruced by direcly formula, as shown in U(ε,η,f)= Ck j M m= N H (m, n, f) n= [+( jkr ) z r ] e jkr dx dy, r where M and N, respecively,aremicrophonerowsand columns, H (m, n, f) is he mh row and he nh column of he holographic informaion of he microphone, r is he reconsrucion surface poins S(ε, η) mh row and he nh column from he microphone, and Δx and Δy are, respecively, microphone spacing and row disance. (6) 3. Compared Simulaion 3.. Applicaion in Microphones Array Sound Sources Discriminaion. The microphones array s performance mainly refleced he resul of spaial resoluion and idenificaion precision of source of noises; we used a microphone array of regular arrangemen wih equal disance as compared wih an array of opimizaion displacemen of microphones posiions; in boh simulaions, he number of microphones is he same; bu he size of he array may be differen in he simulaionresul.inhispaper,wesudiedheinfluenceof parameers on he performance of he array of arrays. We usedafixedcrossx-ypemicrophonearrayasanexample o describe he plane array performance and hen analyzes he simulaion and discusses he impac of microphones array displacemen on he resuls of he idenificaion. In his paper, we propose a word fixed array ; i means ha he microphones array is o adjus or opimize he X direcion han random microphone array displacemen.

5 Advances in Acousics and Vibraion 5 Table : Simulaion resul of equal disance array and opimizaion array. SLR (side lobe raio) MLA (main lobe area) Equal disance Opimizaion array Performance of he array is mainly refleced in he spaial resoluion, such as an array of irregular random arrangemen of he microphone as compared wih a regular grid array having he same number of microphones, and hen how o idenify he source of noise a higher frequencies is very imporan, due o he performance of he microphone array, is array of applicaions, selecion, and design insrucive. Figure 4 shows he model of uniform linear array. This aricle sudies he influence of parameers on he performance of he array of arrays. A fixed cross X-ype microphone array as an example describes he plane array performance analysis and process simulaion and discusses he impac of microphones arranged in he form of is properies. Based simulaed annealing opimizaion mehod, he MLA (main lobe area and main lobe energy/sidelobe energy) and SLR (side lobe raio) were chosen as objecive funcions, wheher i is feasible o ge a beer resul by he means of reducing he numbers of microphones. 3.. Simulaion. Based simulaed annealing opimizaion mehod,weselecedwoobjecivefuncions,mla(main lobe area) and SLR (side lobe raio), which are he parameers of measuremen crieria for evaluaion of idenificaion resuls, and we end o ge he value of MLA, he smaller he beer,andhevalueofslr,hebiggerhebeer,oroge he balance beween hem. The purpose of he simulaion is o compare he microphones array fore-and-af opimizaion andhenoidenifyifherewouldbehepossibiliyof reducionofhenumbersofmicrophonesbucanachieve a beer idenificaion resoluion. The simulaion resul can be seen in Figure 5; in he simulaion, he parameers of he sound source are as follows: he speed of sound source is km/h, he numbers of microphones are 9 in one fixed X array, and he disance beween microphone array and he sound source is m. Calculaionmehodsofhemainlobearea(m)andhe main sidelobe raio (main lobe energy/sidelobe energy) are shown in Table. As we can ge from Figure 5, he resul of he simulaion is lised in Table. From Table, i can be seen ha, as a resul of opimizaion array,hevalueofslris.684,andhevalueofmla is.3, boh of he resuls are beer han he resuls of equal disances microphones array, and he resul is in accordance wih he objecives and resuls of opimizaion we proposed a firs. Then we ge he 9 opimizaion microphones coordinaes as shown in Figure 5, hen we Table : Resul of opimizaion microphones array coordinae. Number of microphones X Y will analyze he ways of easibiliy of reducing he number of microphones. The 9 opimizaion microphones coordinaes are shown in Table. And from Table, he coordinae numbers 5 and coordinae numbers 5 are very near o he coordinae [.]; he error is.% which can be considered as he microphones which are in he same posiions; we use coordinae numbers 6 9 o replace he coordinae numbers 5 and coordinae numbers 5, and hen 8 microphones can be reduced. And coordinae numbers 3 are he same asnumber[.],whichisinhesameposiions,and hen 4 microphones can be reduced. There were only 7 microphones lef. The res of 7 microphons simulaion is carriedoubyusinghesamemehod,henwegeheresul of MLA and SLR, and here are no changes in he value of boh of hem. In he above simulaion, he resuls show he opimizaion mehod which can be achieved o opimize and improve he resoluion of he objecive funcion, while achieving he purpose of reducing he number of microphones.

6 6 Advances in Acousics and Vibraion Figure 5: Equal disance array simulaion resul; opimizaion array resul.

7 Advances in Acousics and Vibraion 7 Figure 6: The experimen lab and microphone array Figure 7: The experimen resuls of he saic speaker in he anechoic room. Resul from he acousic holography mehod; virual microphone array.

8 8 Advances in Acousics and Vibraion Figure 8: The measuremen sysem and esing high speed rain. z y Train Focal poin Traveling direcion x y a z a y dis Microphone array x a Microphone array Direcional microphone,5, 3,95, Train,5 4, Acousic barrier, R.L Figure 9: The measuremen sysem and esing high speed rain. 4. Validaion Experimens 4.. Saic Sound Sources Experimen. This experimen is done in anechoic chamber. The microphone array is made of microphones. The spacing beween each of he microphones is 6 mm. In his experimen, he sound source is a powered loud speaker, and he noise signal is a simple harmonic sound of khz. The experimen lab and experimen device are shown in Figure 6. AscanbeseenfromFigure7andhesimulaionresul in Table 3, comparing boh resuls, here is hardly a change in he value of MLA and SLR (also he resul of opimizaion of MLA (.45) is beer han equal disance microphones array) and no change in he relaive posiion; o some exen, he resul is nearly he same; i is concluded ha he9microphonesnearlyhavehesamesoluionwih microphones. 4.. High Speed Moving Sound Sources Experimen. The validaion experimen is done in circle es ground for high speed rain; we choose he high speed rain which was

9 Advances in Acousics and Vibraion Figure : Microphones array. The equal disance; he opimizaion array. Table3:Comparisonofheresuls. Table 4: Comparison of he resuls. Equal disance of microphones SLR MLA Equal disance of 9 microphones SLR MLA Opimizaion of 9 microphones SLR MLA Opimizaion of 7 microphones SLR MLA processing es o esify he simulaion resuls. We se he microphonesarraywhichismadeof9microphonesand hen use he 7 microphones opimizaion array o process he sound daa. The parameers in his experimen are as follows: he sound source is radiaed by one high speed rain, and he noise signal is a simple harmonic sound of 5 Hz khz. The experimen sysem is shown in Figures 8. The main validaion experimen device is as follows: convenional signal measuremen and analysis equipmen, B&K company s se of high-precision mulimicrophone se, 3 ses of high performance acousic sensors, and an array of developed measuremen sysems, X-ype array. The experimenal condiions are shown in Figure 9. In his experimen, he sound source daa analysis frequency is 5 7 Hz, he speed of esing rain is 5 km/h, he compare resuls are shown in Figure, one is he resul of idenificaion high speed rain sound sources wih 9 equal disance microphones array, and he oher is he resul of idenificaion high speed rain sound sources wih opimizaion microphones array. The resuls of experimen are shown in Figure and Table 4. Ascanbeseenfromheresul,bohFigureandTable4, compared wih he resuls, here is hardly change in he value of MLA and SLR (also he resul of opimizaion of MLA (.33) is beer han equal disance microphones array) and no change in he relaive posiion; o some exen, he resul is nearly he same; i is concluded ha he 7 microphones nearly have he same soluion wih 9 microphones. 5. Conclusion In his paper, based on he fixed X microphones array, selec he main SLR (side lobe raio) and he MLA (main lobe area) as he opimizaion objecive funcion, by using opimizaion mehod o opimize he microphone array. Compare simulaion resuls of equal disance microphones array wih opimizaion array found ha reduced he number of opimizaion microphones; here were no changes in he purpose funcion value. Also, validaion experimen has done o esify he simulaion resul; i is drawn from he resuls ha he experimen resul can be by reducing he number of microphones bu does no have changes in he purpose values. So he experimens wih limied condiions can be done, as o use fewer microphones o ge he similar resul. In he nex sudy, i will consider he angle beween surface reconsrucion of sound pressure and measuremen plane by furher opimizaion mehod. Compeing Ineress The auhors declare ha hey have no compeing ineress.

10 Advances in Acousics and Vibraion Figure : The comparison of validaion experimen resuls of he high speed rain wih equal disance microphones array and opimizaion array. References [] H. Pu and J. Weikang, Applicaion of sound inensiy echnique in idenify he noise sources of maglev rain, Journal of Railway Engineering Sociey,vol.5,pp.5 8,5. [] W.F.KingIIIandD.Becher, Onhesourcesofwaysidenoise generaed by high-speed rains, Journal of Sound and Vibraion, vol. 66, no. 3, pp. 3 33, 979. [3] Y.Takano,K.Terada,F.Aizawa,A.Iida,andH.Fujia, Developmen of a -dimensional microphone array measuremen sysem for noise sources of fas moving vehicles, in Proceedings of he Inernaional Congress on Noise Conrol Engineering (InerNoise 9), pp , Torono, Canada, July 99. [4] H. Kook, G. B. Moebs, P. Davies, and J. S. Bolon, Efficien procedure for visualizing he sound field radiaed by vehicles during sandardized passby ess, Journal of Sound and Vibraion,vol.33,no.,pp.37 56,. [5] Y. Takano, Developmen of visualizaion sysem for highspeed noise sources wih a microphone array and a visual sensor, in Proceedings of he Inernaional Congress on Noise Conrol Engineering (InerNoise 3), Seogwipo, Republic of Korea, Augus 3. [6] M. Genescà, J. Romeu, T. Pàmies, and A. Sánchez, Real ime aircraf fly-over noise discriminaion, Journal of Sound and Vibraion,vol.33,no.-,pp. 9,9. [7] S. Gade, J. Hald, and B. Ginn, Refined beamforming wih increased spaial resoluion, in Proceedings of he 4s Inernaional Congress and Exposiion on Noise Conrol Engineering (INTER-NOISE ), pp , New York, NY, USA, Augus.

11 Advances in Acousics and Vibraion [8] K. Saijyou and H. Uchida, Daa exrapolaion mehod for boundary elemen mehod-based near-field acousical holography, Journal of he Acousical Sociey of America, vol. 5, no., pp ,4. [9] Z. Wang and S. F. Wu, Helmholz equaion-leas-squares mehod for reconsrucing he acousic pressure field, Journal of he Acousical Sociey of America, vol.,no.4,pp. 3, 997. [] R. Seiner and A. N. Kaelin, Sound field reconsrucion of moving noise sources by means of acousical holography, in Proceedings of he InerNoise 998, Chrischurch, New Zealand, November 998. [] S.-H. Park and Y.-H. Kim, Visualizaion of pass-by noise by means of moving frame acousic holography, Journal of he Acousical Sociey of America,vol.,no.5,pp ,. [] C.-S. Park and Y.-H. Kim, Time domain visualizaion using acousic holography implemened by emporal and spaial complex envelope, JournalofheAcousicalSocieyofAmerica, vol. 6, no. 4, pp , 9. [3] D.G.Yang,S.F.Zheng,Y.K.Li,X.M.Lian,andX.Y.Jiang, Research on acousic holography mehod for he idenificaion of sound source, Aca Acusica, vol. 6, no., pp. 56 6,. [4] Y. Diange, Z. Sifa, L. Bing, L. Keqiang, and L. Xiaomin, Video visualizaion for moving sound sources based on binoculars sereo and acousic holography, Chinese Journal of Acousics, vol. 3, no., pp. 3 3,. [5]D.Yang,Z.Wang,B.Li,Y.Luo,andX.Lian, Quaniaive measuremen of pass-by noise radiaed by vehicles running a high speeds, Journal of Sound and Vibraion,vol.33,no.7,pp ,.

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