The optimization design of microphone array layout for wideband noise sources

Transcription

1 PROCEEDINGS of the 22 nd International Congress on Acoustics Acoustic Array Systes: Paper ICA The optiization design of icrophone array layout for wideband noise sources Pengxiao Teng (a), Jun LV (b) (a) Institute of Acoustics, Chinese Acadey of Sciences, China, (b) Institute of Acoustics, Chinese Acadey of Sciences, China, Abstract Microphone array syste has been an iportant tool to identify ain noise sources fro ixed acoustic field eitted fro running achines. The perforance of localization is affected by several paraeters such as the icrophone array layout, the nuber of icrophone, weights and the array aperture. Usually the array aperture and the nuber of icrophone are restricted in practical applications, and therefore array layout design and weights are the ost crucial paraeters to iprove localization perforance characterized by the array bea pattern. Array layout optiization design is highly related to frequency bandwidth. Therefore, a new array layout optiization ethod is presented in this paper for wideband noise sources to generate low side-lobe level bea patterns based on particle swar optiization (PSO) which has proven to be very efficient in optial layout design. In this paper, we present a general fraework to consider the overall perforance based on the narrow ain-lobe width and low side-lobe level criterion using the particle swar optiization ethod. In low frequency band we place ore ephasis on the ain-lobe width, and place ore ephasis on the side-lobe level within high frequency band. In the presented paper, both weights and layout can be optiized siultaneously. Finally, siulations and experients are carried out to deonstrate that the proposed schee can iproved localization perforance of wideband noise sources. Keywords: icrophone array layout, optiization design, wide band, localization.

2 The optiization design of icrophone array layout for wideband noise sources 1 Introduction Microphone array has been an iportant research field in acoustic source localization and source separation for acoustic caera in the last decades. The perforance of localization is deterined by the array bea pattern characterized by ain-lobe width (MLW) and low sidelobe level (SLL), which is affected by several paraeters such as the icrophone array layout, the nuber of icrophone, weights and the array aperture. The larger array aperture can lead to narrower ain-lobe width which eans higher spatial resolution, and the ore icrophones can allow low side-lobe level in higher frequency band, which eans high iaging dynaic range. However, the array aperture size and the nuber of icrophone are usually restricted in practical application or by product cost. Therefore, array layout design and weight are two crucial paraeters which we can eploy to iprove localization perforance. Recently, ost of work in the literature has focused on optial design of sparse linear or planar array [1-6]. Although statistical analysis ethod was used to suggest the possible perforance of sparse arrays [5], it can not represent a design ethodology to optiize the array geoetry. Hol analyzed two optiization ethods of weights and both the layout and weights [6]. The optiization algorith is based on linear prograing and iniizes the peak side-lobe level lower than the ean of side-lobe of the array. However, only a single frequency is assued in this paper and array layout optiization design is highly related to noise frequency bandwidth. In [3], the design of wideband array based on siulated annealing was proposed by suing the frequency band. As a general result, the side-lobe level increases with frequency bandwidth and a fraction of frequency bandwidth was used in the paper. In this paper, we present a general fraework to consider the overall perforance based on the narrow ain-lobe width and low side-lobe level criterion using the particle swar optiization ethod [7]. In low frequency band we place ore ephasis on the ain-lobe width, and place ore ephasis on the side-lobe level within high frequency band. Thereafter, the array geoetry is optiized by the criterion of narrow ain-lobe width for low frequency and that of low side-lobe level for high frequency band based on the particle swar optiization ethod. In the presented paper, both weights and layout can be optiized siultaneously. An alternate PSO is proposed to iprove the optiization process. This paper is organized as follows. In Sect.2, we give the array configuration odel. A odified PSO ethod is proposed to optiize the array layout. In Sect.3, an optiization design fraework of icrophone array layout for wideband sources is proposed, which ipleents the geoetry optiization for low frequency band and for high frequency band respectively. Then weights optiization is also further optiized to balance the ain-lobe and side-lobe level. Siulations are carried out and results are deonstrated in Sect.4. The conclusions are drawn in Sect.5. 2

3 2 Array odel As is known that acoustic source localization is highly related to the array bea pattern. The bea pattern forula is given for the planar array, and then an odified PSO ethod is proposed to iprove optiization process in array configuration both according to MLW and SLL in this section. Assue that a source signal propagates fro the direction ( θϕ, ) and the coordinate of icrophone p is [ r cos φ, r sin φ ] illustrated in Fig.1. The tie delay of th icrophone is represented as: r τ( ) = ( cosφ sinθ cosϕ + sinφ sinθsinϕ ) (1) c Using Eqation (1), one ay obtain the bea pattern as: ω r B w j M = 1 c (2) ( θϕ, ) = exp ( cosφ sinθcosϕ+ sinφ sinθsinϕ) Z Plane wave ϕ θ Y X Figure 1. Planar array odel The MLW is defined as Θ which is the angular interval of the first pair nulls of B ( θϕ) given ϕ and the side-lobe level is represented as:, for a Θ ( θϕ, ) ( θϕ, ) B SSL = 20log (3) 10 B where Θeans side-lobe which is the angular interval outside the ain-lobe. Based on the narrow MLW and low SLL criterion, an array configuration can be optiized by ax 3

4 in {MLW, ax{sll}} st.. r r r in ax (4) where [ r in, r ax ] being the range of array eleents. In this paper, we eploy PSO ethod to ipleent the optiization. In order to ipleent optiization, a fitness value is designed to evaluate the updated particles. where the integral lower liit 0 θ π ( Θ (, ) (, )) (, ) θϕ ξ θϕ δ θϕ θ ϕ (5) li F = B d d θ0 π θ is the first null of (, ) upper liit θ is the angle boundary liit. [ θ, ] li 0 θli to side-lobe. In Equation(5), δ( θϕ, ) is defined as: B θϕ outside the ain-lobe and the integral is angle volue where we pay ore attention ( θϕ) > ξ( θϕ) ( θϕ) ξ( θϕ) 1, B Θ,, δ( θϕ, ) = 0, B Θ,, (6) 3 The odified particle swar optiization The ai of eploying PSO ethod [7] to ipleent equation (4) is to exploit possible icrophone positions in order to find a set of optial position which obtains both narrow MLW and low SLL. Consider a swar with N particles, each of which represents an array configuration. where each particle can be denoted as [ ] T X = x1, x2, xn x N (7) x = [ x, x, x, x ] (8) n n1 n2 nd nd where D is the diension of optiization. We represent the best individual solution for each particle in the iteration process as: [ ] T P = p1, p2, pn p N (9) where p n = [ pn 1, pn2, pnd, pnd ] is the best individual solution for the nth particle, and the best swar solution is represented as: g = [ g, g, g, g ] (10) 1 2 With Equation(7)through (10), the particles are updated according to the following equations: d D 4

5 v ( nd ) ( d ) t t 1 t 1 t 1 = w v + cr p x + cr g x nd nd 11 nd 2 2 nd x = x + v t t 1 t nd nd nd (11) where c1 and c 2 are two positive constants (typically c 1 = c 2 = 2 ), r 1 and r2 are two rando variables, and w is inertia weight. The t and t 1 represent newly updated variable and previous one, respectively. Fro Equation (11), we can see that the new velocity is deterined by three ters. The first ter represents how uch the previous velocity is kept. The second ter related to the distance between the best individual solution and its current one allows each particle to approach closely to best individual solution. Last ter related to the distance between the best global swar solution and its current one allows each particle to approach closely to best swar solution. A large inertia weight w tends to explore global area while a sall one tends to search local area. Shi [8]suggested a way to deterine the inertia weight written in Equation(12) to ake a balance in exploring global and local area. w w = (12) T ax in w w t t ax where w and w are axiu and iniu weight respectively, and T is the total iteration ax in nuber, t is current iteration index.in this paper, we proposed a odified PSO procedure which alternately optiizes the ain-lobe and side-lobe level. As a result, the can be suarized as follows: STEP1. Initialize PSO paraeters including the nuber of particle N, the optiization diension D, particles X, best individual solution P, and best global solution g, inertia weight w in, w ax. Set a preliinary SLL and MLW θ 0. STEP2. All particles are updated using Equation (11) through (12). STEP3. Calculate the fitness value using Equation (5) to evaluate new particles, and judge if P and g are replaced by newly updated particles. STEP4. Judge if the fitness value is zero. If so, decrease the θ 0 in a sall aount and go to step2, and then repeat step2 through step 4. Otherwise, go to step5. STEP5. Judge if the iteration nuber reaches the axiu T. If not, repeat step2 through step4. Otherwise, go to step6. STEP6. Terinate and obtain the final result g. 5

6 Figure 2. Modified PSO flow chart 4 Array geoetry and weights optiization In this paper, we present a general fraework to optiize array layout considering narrow ainlobe width and low side-lobe level criterion. On one hand, in low frequency band we use odified particle swar optiization presented in Sect.3 to optiize soe icrophones to obtain higher spatial resolution according to narrow ain-lobe criterion. On the other hand, we eploy odified particle swar optiization to optiize the left part of icrophones to obtain lower side-lobe level in higher frequency band according to low side-lobe level criterion. Therefore, we place ore ephasis on the ain-lobe width within low frequency band and place ore ephasis on the side-lobe level within high frequency band when optiizing array geoetry. Afterward, once the array geoetry is deterined, weights are optiized to balance the ain-lobe and side-lobe at each frequency bin. When the array geoetry and weights are deterined, the bea pattern can be calculated. 6

7 Figure3-Figure5 show the siulation results of array optiization. The nuber of icrophone is 128 and array radius is 0.5. We copare three typical array layouts: optiized array, rando array and circle array. The circle array represents an extree case which has very narrow ain-lobe and high side-lobe level. Fig.3 shows the position of array eleents. In Fig.4, it can be shown that circle array has narrowest ain-lobe but has highest side-lobe level. The optiized array has narrower ain-lobe and lower side-lobe level. Fig.5 shows the siilar results at the frequency of 9000Hz. Therefore, the proposed ethod allows to have ability to balance the ain-lobe and side-lobe level flexibly by adjusting the weights when the array geoetry is fixed. Figure 3. Optiized array layout Figure 4. Beapatterns of three arrays at 1000Hz (Optiized Array,Rando Array,Circle Array) 7

8 Figure 5. Beapatterns of three arrays at 9000Hz (Optiized Array,Rando Array,Circle Array) 5 Conclusions In this paper, we present a general fraework to control the narrow ain-lobe width and low side-lobe level based on the particle swar optiization ethod. In low frequency band we place ore ephasis on the ain-lobe width, and place ore ephasis on the side-lobe level within high frequency band. In the presented paper, both weights and layout can be optiized siultaneously. Siulations are carried out to deonstrate that the proposed schee can iproved localization perforance of wideband noise sources. References [1] Wilson, M.J. Sparse-periodic Hybrid Array Beaforer, IET Radar Sonar Navig.,15(2), 2007, [2] Kirkebo,J.E.; Austeng,A. Sparse Cylindrical Sonar Arrays. IEEE Journal of Oceanic Engineering, 33(2), 2008, pp [3] Cardone,G; Cincotti, G. Design of Wideband Arrays for Low Sidelobe Level Bea Patterns by Siulated Annealing. IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control, 49(8), 2002,pp [4] Teng, P.; Chen, R. A Hybrid Schee for Localization and Separation for Multiple Noise Sources using a Microphone array. International Congress and Exposition on Noise Control Engineering, New York, USA, August 19-22, [5] Steinberg,B. The Peak Sidelobe of the Phased Array Having Randoly Located Eleents: Antennas and Propagation. IEEE Trans.Antenna.Propag., 20(2), 1972,pp [6] Hol.S; Elgetun,B.;Dahl.G. Properties of the Beapattern of Weight- and Layout-Optiized Sparse Array. IEEE Trans. Ultrason.,Ferroelect.Contr. 44(5),1997, pp

9 [7] Kennedy.J. The PSO: Social Adaptation of Knowledge. Proc IEEE Int. Conf. on Evolutionary Coputation, 1997, pp [8] Shi.Y; Eberhart.R. Paraeter Selection in Particle Swar Optiization. Proceedings of the 7th International Conference on Evolutionary Prograing,