A novel configuration method of the acoustic random beamforming array for multiple wideband moving sound source localization

Transcription

1 INTER-NOISE 6 A novel configuration ethod of the acoustic rando beaforing array for ultiple wideband oving sound source localization Zhihong LIU ; Huichao LI ;Chujie YI 3 Qingdao Technological University, China Qingdao Energy and Environental Equipent Center, China 3 Qingdao Technological University, China ABSTRACT A new generating approach of the rando beaforing array configuration is proposed for localization of ultiple wideband oving sources. The target rando beaforing array generation is on the basis of beaforing technique and the perforance of rando sparse array. Firstly according to the principle of the beaforing technique for oving sound source identification, the array angular resolution of ultiple sources, array plane grid spacing and non-equidistance rings radius based on coaxial circular ring array in the polar coordinates are deduced. The candidate rando arrays are generated by array plane segenting schees and array structural filter conditions. Secondly the target rando beaforing array can be obtained fro candidate rando arrays by the perforance evaluation and condition filtering in the polar coordinates. Finally nuerical siulation and ultiple wideband oving source identification test have been done. The results show that using the ethod to generate rando beaforing array is effective.copared with the traditional regular array which are suitable for oving sound source location, target rando sparse array can save ore tie for array configuration and has ore accurate ultiple wideband oving sound source identification perforance. Keywords: Rando Beaforing Array, Array Configuration, Moving Sound Sources I-INCE Classification of Subjects Nuber(s): 5.3. INTRODUCTION Traffic noise is one of the ost iportant environental noise source in countries. With the increased traffic intensity and extended road networ, traffic noise levels have been enhanced. The characteristics of traffic noise, such as ultiple sources, broadband and soe sound source exist only if the vehicle oves, which are strongly coupled with the speed of the vehicle. More and ore attentions have been focused on the ethods for vehicle noise easureent. Beaforing is an iportant ethod which has been applied to the easureent of the noise source identification during the pass-by of a car and the characterization of those noise sources (,, 3). Beaforing is an array-based easureent technique. The perforance of a beaforing array is to a very large extent deterined by the array geoetry because this defines the bea forer response through the array pattern. Basically, the source location is perfored by estiating the aplitudes of plane (or spherical) wave incident towards the array fro the directions. The pea in the array pattern which is called the ain lobe depicts the actual incident direction of plane (or spherical) waves, i.e. the actual sources. A pea in the array pattern different fro ain lobe is naed side lobe which is focused in a specific direction not equal to the actual incident wave direction, i.e. the ghost sources. The beaforing array geoetry has crucial effect on the noise easureent. At present any researchers have done lots of studies on the design and optiization of beaforing array for easureent the oving noise source(, 4).Microphone arrays have proven to be useful for identifying noise sources on oving as well as stationary sources(5, 6).Many types of array configurations have been used. Aong the are linear arrays, regular two-diensional arrays, non-redundant arrays and crossed arrays(7, 8, 9).Non-unifor array configurations have been lzhqingdao@63.co lihuicha@63.co 3 chuijieyi@vip.63.co 45

2 INTER-NOISE 6 used to reduce the aount of redundant inforation gathered by the array at the expense of increasing sidelobe levels in the array directivity pattern(, ). To deal with this proble, Rando sparse arrays have been proposed for reducing sidelobe levels based on the segent schee of the array surface(). A sparsely optiized ethod has been applied to the linear, planar, cylindrical or spherical array geoetry by Legendre Fraction Transfor. A fast rando array generation ethod which is suitable for identify the oving sound source has been introduced by partitioning, condition filtering and siulation evaluation(3, 4). This overview shows that, to identify and characterize the oving sound source, the following conditions should be taen into consideration: ) To avoid the spatial aliasing, the distance between two adjacent icrophones should be at least the half-wavelength of the incident wave.) Array aperture should be large enough to distinguish ultiple wideband oving sound sources, because of the angular resolution is inversely proportional to the array diaeter easured in units of wavelength. Especially at low frequencies, this requireent is usually too difficult to be et, so the resolution will be poor. 3) Configuration of array is vital for suppression the sidelobe influence at high frequency. If an array is to eet conditions, the nuber of icrophones and the aperture will be increased which will increase the easureent cost and add tie of signal processing. This paper is focused on the array layouts that can be used to identify the noise sources when the sources is oving and get ore insight to the rando sparse array setup of localization ultiple wideband oving sound source. In the approach described here, the array configuration is rando and two-diensionally sparse which generate rapidly and efficiently by segent schee, geoetry constraints and array perforance optiization. The sound field is generated by a oving car with two wide-band sources and easured on the basis of the vehicle passby tests. In addition, array icrophone outputs are processed in the frequency doain.. BEAMFORMING of MOVING SOUND SOURCE The easureent of oving sound sources by beaforing array describes as Figure.Where the fixed coordinate syste Oxyz depicts the array plane A, and the reconstruction plane B is oving with the car. The distance fro the ground to the botto of array is h and the focused distance is Z. Figure Measureent of oving sound sources with beaforing array On the basis of the beaforing processing of pressure signals fro the icrophones on the array plane A, let F, be the sound field features function at the rando points, of the reconstruction plane B s during the period of tie and given as F s t, b t,, dt () t All points on the plane B can be calculated by forula (). The three-diensional sound pressure distribution graph will be obtained. Based on the relative intensity of the nuerical value of feature function on the point of graph and the ain source position can be identified. Hereb t,, is the delay-and-su beaforer output in the tie doain. The FFT of it can be express as: M j r B, w p e, N () N th Where p is the easured pressure signals of the icrophone, w is a set of weighting factor that are 46

3 INTER-NOISE 6 applied to each individual icrophone, is a unit vector and f c is the wave nuber vector of a plane wave incident fro the direction which the array is focused, wheref andc represent the incident frequency and the propagation speed of the acoustic wave in the ediu respectively. Now assue a plane wave incident with a wave nuber vector different fro the preferred direction. The pressure easured by the array can be written as p j r p e According to Eq. (),array output can be represented as (3) B (4) M j r, p w e p W HereW function is the so-called array pattern W M K w jk r e Where r is the array icrophones position vector. The array pattern deterines the perforance of a beaforing array and that is largely influenced by array geoetry. 3. RANDOM ARRAYS FORMATION 3. Segent Schees The principle of segent schees of basic array plane is that can be ensure the icrophone arrangeents as unifor as possible. For this ai, firstly, the array plane is divided into several equally areas, i.e., unifor subsections, by grid point spacing. Secondly, the alternative grid points can be generated randoly in subsections. Every one of alternative grid points has a possible to be selected to place icrophone. 3.. Grid Point Spacing The grid spacing of basic array is the vital factor for localization the oving sound sources. On the assuption of plane phase plane, to avoid spatial aliasing, the iniu grid distance can be calculated as: d c f sin (6) in ax Wheref ax is the highest frequency that contributes significantly to the sound field incident on the array, and is the incident angle. However in reality, the noise source lie within the near field of the icrophone array, i.e., spherical spreading effects are significant. An analysis perfored assuing spherical phase surfaces would result in a decrease in the allowable icrophone spacing. So, in this paper, the grid point spacing in arc length is equal or greater than which is given by the below forula: d c f ax (7) Considering the frequency range of the sound source and the array geoetry, the polar radius of the first ring is selected to be: c (8) f ax The radius difference of two adjacent rings is assued as.in order to reduce utual coupling and side lobe effect, the space of ring radius should be:.5 (9) Where is the wavelength. 3.. Alternative Grid Point The icrophone position will be selected fro the alternative grid points in each subsection. For the unifority of icrophone layout, in the approach presented here, the sae nuber alternative grid points and icrophones are placed in each subsection, and the phase reference icrophone need to be set on the center of the array. Based on the principle of aperture, the nuber of alternative grid point sets ten and the nuber of icrophone is two. The ten alternative grid points polar angle can be generated randoly in each subsection. They are set on the rings fro inner to outer a ccording to the order of polar angle fro large to sall. The nuber of alternative grid point on the rings is (5) 47

4 INTER-NOISE 6 proportional to the rings nuerical order, i.e., the nuber of alternative grid point on the rings fro first to fourth is ::3:4 in each subsection. The eight partition of a four rings coaxial circular array with eighty alternative grid points are showed in Figure. 3-8 subsection index nuber alternative grid point Figure The partition of basic coaxial circular ring array 3. Candidate Rando Arrays The partition layout can be resolving the unifor distribution of icrophone on the array plane as a whole. However, the nuber of the generating rando arrays is very larger. In order to iprove the seeing of the reliable rando array layout, soe structural constraint conditions have been applied for producing candidate rando array. The rando array can be described with atrix of icrophone position s radius and angle in the polar coordinates. The row of atrixes depicts the distribution of the radius and angle and the colun represents the subsections. AssuingC and J depicts the nuber of the subsections and alternative grid point in each subsection. Here the polar radius atrix R and the polar angle atrixφ of the basic coaxial circular array are described as: R J J J J C Φ () J J J Assuing the candidate rando array is coposed of N icrophones. The th ring has a nuber of icrophones N, polar angle Q and alternative grid pointw.the nuber of alternative grid point and icrophones position of each subsection describes as Sa and S. The structural constraint conditions are described as: Condition: The rando array can be generated by choosing two icrophone positions, and ten alternative grid point set in each subsection: S, Sa () Condition: Ensure the distribution of icrophones on each ring of the candidate rando array eets the unifority and avoiding the periodicity. In practice: Sa N C N W W N, Q W W Q (,3, M ) Condition3: In order to resolve the cluping proble and considering the predefined position couldn t be placed by other icrophones, the constraint can be expressed as: Here, C p q p,, C ; q, C pq (3) ( Sa C ) p q pq represents the eleent of row p and colun q of the angle difference atrixψ.this J C () 48

5 INTER-NOISE 6 atrix shows the angle difference of icrophone position in the sae or different subsection fro the polar axis along counterclocwise direction. When a randoly generated array satisfied the above conditions, the rando array is called a candidate rando array which has been depicted by generated polar radius atrix R and the polar angle atrix Φ which are described as: R J Φ J J J C J J C (4) if not, it has to produce the icrophone position atrix including the polar radius and polar angle atrix again. Then, it will re-search until creating candidate rando arrays. Figure3shows one of the candidate rando arrays generated by structural constraint conditions. icrophone Figure 3 One of the candidate rando arrays The target rando array will be selected fro the above candidate rando array by array perforance paraeter sidelobe suppression ratio r sp and ainlobe width MW. In array pattern, the level of the side lobe relative to the ain lobe defines the ability of the beaforer to suppress ghost iages. Based on the three-diensional rando array response pattern r sp is defined as: r sp log h p hv (5) Aplitude of array response function(pa ) Where h p and hv represent the pea of ainlobe and the highest sidelobe pea respectively, as shown in Figure h p 4 3 hv Ele vati on ang l e( rad ) ngle uth a Azi ( rad ) Figure 4 Three-diensional candidate rando array response pattern 49

6 INTER-NOISE 6 A good array design can be characterized with having a side lobe suppression ratio which eets the criterion. The paraeter s quantitative criterion has been acquired by statistics analysis of the nuerical results. Defining as 5 6 N 4 r sp (6) N 4 In candidate rando arrays, the one eeting the above criterion becoes a target rando array, i.e., the rando beaforing array. The flow diagra of the generating process is shown as Figure5. Segent Schees Generate atrixes of radius R and polar angleφ No Conditions Yes Candidate Rando Arrays Generate atrixes of radius R and polar angleφ Figure 5 Flow diagra of the generating process Excepting sidelobe suppression ratio as a ey perforance factor, ainlobe width is also r sp considered. The trade-off between the has been discussed through nuerical siulation. 4. VERIFICATION No Perforance 4. Nuerical Siulation In order to prove the validity of the generating ethod for testing ulti oving sound source, two types of sources are discussed. The ain paraeters depict in Table. Table. The ain paraeters of siulation Factors Aziuth angle,rad Elevation Angle,rad Frequency, Hz Source pi/4 pi/4 5- Source -pi/4 -pi/4 8- Candidate arrays are the four rings concentric circular ring array with 5 icrophones. One icrophone is place on the center of array and another 4 icrophones are positioned randoly on the rings. The array configuration is the sae as that in Figure3.To aes sure that the target rando array perforance is optial. In addition to sidelobe suppression ratio r sp, the trade-off of 3dB down ainlobe width and the sidelobe suppression ratio have been given through statistical analysis of two-thousand array layouts. The trade-off curves are plotted which is shown in Figure6. Yes Target Rando Array 5

7 Sidelobe suppression ratio(db) ainlobe width (deg) INTER-NOISE source source sidelobe suppression ratio(db) Figure 6 Trade-off curves of two sources The target rando array is selected with MW 6.degree and r sp 6dB, as shown in Figure7. The sidelobe suppression ratio curve of target rando array with the frequency range of 5-3Hz is presented in Figure8. icrophone Figure 7 Target rando array Frequency(Hz) Figure 8 The curve of sidelobe suppression ratio In case the two sources can be effectively identified. The three-diensional array response pattern of above target rando array shows in Figure9. 5

8 Aplitude of array response function(pa ) INTER-NOISE 6 7 source 6 5 source 4 3 Ele vat i on ang l e( r ad ) ngle uth a Azi ( rad ) Figure 9 Three-diensional array response pattern of above target rando array 4. Experiental Measureent The testing array layout is as the sae as that in Figure7. Two sources are placed on the oving car with the speed 4-8/h. The array plane aperture is. The focal distance is. The height fro floor to the botto of the array is.. The acoustic testing and iaging syste is the Acoustic Caera of Institute of Acoustics of Chinese Acadey of Sciences. The test-site picture is as Figure. Figure The test-site Figure Testing results picture The test results frofigure are as follow: when the car is in the testing doain, the recognition area of sound source identification is.4 and.3, the sound pressure dynaic characteristic is 66-7dB.The nuber of ghost source is zero. Fro results, it was obtained that the target rando array can effectively locate the two oving sound source with the difference wideband. 5. CONCLUSIONS In the present wor, a novel ethod was developed to generate a rando array in which a nuber of icrophones are randoly positioned on rings of coaxial circular ring array. The generated process was transfored to atrix operation in polar coordinates. Based on the oving sound source properties and array geoetry, the candidate arrays atrixes could be created effectively. Through selecting the positions of atrixes eleent eet the condition of the required array, the target array could be generated rapidly and reduce the screening blindness. Fro the siulated rando array configuration generated based on different sound sources, it was observed that the sidelobe suppression ratio was strongly related to the frequency of sources below thehz. The influence fro array layouts with the sae aperture on the ain lobe width was quite sall. To iprove the accuracy of the siulation, the testing was operated with a target array. The results of the oving sound source test verify the feasibility and availability of the generating procedure. 5

9 INTER-NOISE 6 ACKNOWLEDGEMENTS The authors gratefully acnowledge the support of the National Natural Science Foundation of China (Grant no.6445) and the National Natural Science Foundation of China (Grant no.67387). REFERENCES.Ballesteros JA, Sarradj E, Fernández MD, Geyer T, Ballesteros MJ. Noise source identification with Beaforing in the pass-by of a car. Applied Acoustics. 5;93:6-9..Fonseca WD, Gerges SN, Dougherty RP. Pass-By Noise Measureents Using Beaforing Technique. Inter-Noise Koo H, Moebs GB, Davies P. AN EFFICIENT PROCEDURE FOR VISUALIZING THE SOUND FIELD RADIATED BY VEHICLES DURING STANDARDIZED PASSBY TESTS. Journal of Sound and Vibration. ;33(): Christensen J, Hald J. Beaforing, Bruel & Kjaer. TECHNICAL REVIEW. N; 4. 5.Martellotta F. On the use of icrophone arrays to visualize spatial sound field inforation. Applied Acoustics. 3;74(8): Wan X, Wu Z. Sound source localization based on discriination of cross-correlation functions. Applied Acoustics. 3;74(): Gade S, Hald J. Array designs optiized for both low-frequency NAH and high-frequency Beaforing. SAE Technical Paper. 5(5-):44. 8.Johnson DH, Dudgeon DE. Array signal processing: concepts and techniques: Sion & Schuster; Steen KA, McClellan JH, Green O, Karstoft H. Acoustic source tracing in long baseline icrophone arrays. Applied Acoustics. 5;87: Kuar B, Branner G. Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geoetry. Antennas and Propagation, IEEE Transactions on. 5;53():6-34..Nongpiur RC. Design of iniax robust broadband beaforers with optiized icrophone positions. Digital Signal Processing. 4;3:-8..Koo H, Davies P, Bolton J. Statistical properties of rando sparse arrays. Journal of sound and vibration. ;55(5): Xu F, Lian X, Yang D, Luo Y, Zheng SA, University LK. Rando Array Generation Method for Identifying Noise Source of Moving Vehicles. Autootive Engineering. 6;8(3): Yan W, Zhihong L, Bobo W, Chuijie Y. A study on the rando array generation ethod for oving sound source identification. Chinese Journal of Acoustics. 5(3):