Beacon-Aided Adaptive Localization of Sound-Sources aboard a Pass-By Rail-Car Using a Track-Side Acoustic Microphone-Array Yue Ivan Wu1, Kainam Thomas Wong1,a, Siu-kit Lau2,b 1

Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2 Department of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

ABSTRACT A new adaptive “beamforming” signal-processing algorithm is developed to locate noisesources aboard a pass-by rail-car, using an immobile track-side microphone-array. The microphone-array’s beamforming is aided by two narrowband acoustic beacons abroad the rail-car aid to track the rail-car’s spatial movement and thus to locate the noise-sources with respect to the rail-car. No other auxiliary hardware (e.g., no radar nor video-camera) is needed. 1

INTRODUCTION

Railway noise-pollution degrades the public health of neighborhoods near the rail-tracks. These noise-sources’ exact locations on the rail-car, their relative strengths, and their signals’ time-frequency structures depend on the train speed, the roughness of the wheel/rail, and the aerodynamic contours of the rail-car’s carriage. Cost-effective reduction of such annoying and health-hazardous noise-pollution could be facilitated by an accurate estimation of the individual offending noise-sources’ locations on the rail-car and their power levels. However, this estimation needs to be achieved in the presence of the rail-car’s variable and a priori unknown movements. The use of an array of multiple microphones, instead of a single microphone, allows azimuth (or azimuth-elevation) directional beam-forming. c A common beamforming approach is the “delay-and-sum” (DAS) beamformer, which forms a spatial filter matched towards a pre-set direction-of-arrival. This pre-set direction-of-arrival focus would vary over time with the pass-by train’s movement. That is, the microphone-array’s “delay-and-sum” beamformer would “sweep” its focus to track the mobile train [3], [4]. Wayside emissions (from acoustic sources aboard a pass-by train) have been measured by an immobile microphone-array placed along the trackside, since at least the late 1970s in [2] – [4] and [7] – [18]. However, [2], [7] – [11], [13] and [15] – [17] explain little or nothing of the beamforming algorithm used. Nonetheless, they appear to be using the sum-and-delay algorithm or the sweeping-focus algorithm in [3], [4]. To address this rail-car tracking problem, this paper proposes a new but simple measurement-system consisting of: a

Email address: [email protected] Email address: [email protected] c Such rail-car noise-sources would lie in the microphone-array’s near-field, with the radial distance between the microphone-array and the track (which may be curved and has varying elevation) approximately known, from off-line field measurements. b

(I)

one microphone-array placed at a calibrated location besides a railway track, to collect data of a pass-by train’s airborne wayside acoustic pressure as a function of space, time and frequency. (II) two narrowband acoustic beacons (placed near the rail-car’s two ends outside the rail-car carriage) to help track the rail-car’s a priori unknown movements and to facilitate the subsequent beamformer sweeping over the carriage’s entire length. The proposed microphone-array receiver will track the train’s on-board beacons via recursive-least-squares (RLS) “reference-signal distortionless-response minimum-variance beam-forming”, by exploiting the beacon’s time-frequency structure a priori known to the microphone-array receiver. These beacons will transmit at an intensity inaudible to humans, on or off the train. Theses beacons will be placed away from the likely locations of the dominant noise-sourcesd, but near the rail-car carriage’s two ends to facilitate interpolative scanning of the carriage’s middle sections. Each beacon’s acoustic emittance is narrowband, so that each beacon-signal may be isolated, with minimal “contamination” from the noise-sources, using after narrowband bandpass filtering ― This means that much of the noise-sources’ power (which lies outside this narrow passband) would be rejected. The two beacon-signals would occupy distinct bands to minimize interference with each other. These bands will reside at the high end of the microphone-array’s operational spectrum, to maximize the array’s effective spatial aperture (in terms of wavelengths) for better spatial localization of the beacons. These beacon-signals will serve as reference-signals a priori known to the microphone-array’s receiver to track the rail-car’s movement (which may vary over time and is a priori unknown to the microphone-array receiver). No other track-side auxiliary hardware (such as radar, photo cells, or video cameras needed in many existing systems) will be required in the proposed scheme to track the moving train’s motion. This hardware simplification will enhance system affordability, operational simplicity, and measurement accuracy. This work is possibly the first in the open literature to propose the use of on-board acoustic beacon signals to track the rail-car. Beacon sources are graphically indicated in a Bruel & Kjaer Powerpoint file, entitled “Pass-By Beamforming”, which, however, does not explicitly specify each reference-signal’s waveform, how the reference-sources are used, nor for what purpose. 2

THE NEW ALGORITHM

2.1

The Data Model

An array of L identical and omni-directional microphones is placed horizontally and in parallel to a straight section of the rail-track. Traveling down this rail-track is a rail-car, equipped with two acoustic beacons, each continually emitting a pure-tone at a distinct frequency that is a priori known to the track-side microphone-array receiver. These two beacons are placed at the rail-car’s two ends. In between are located I number of polluting noise-sources aboard the rail-car. Figures 1 and 2 show the spatial geometry between the passing rail-car and this microphone-array. These figures also define the mathematical notation to be subsequently used. At time t, the microphone-array collects an L × 1 vector-measurement, I +1

x(t ) = b(t )a(φb ) + ∑ pi (t )a(φi ) + n(t ) i =1

d

Prior train-noise studies show that the rail-car’s dominant wayside noises come from the rail wheels.

(1)

where φb and φi symbolize the azimuth angles respectively of the to-be-tracked beacon and the interference pi(t), b(t) denotes the φb-beacon’s transmitted signal waveform, a(φ) represents the microphone-array’s steering-vector due to a point-source located at the azimuth-angle φ ∈ [−π/2, π/2], and n(t) denotes an L × 1 vector of thermal noises. The I + 1 summation includes I onboard noise-sources plus the other beacon (with at a pure-tone frequency different from that of the φb-beacon).

Figure 1: Geometry of the railway and the sensor array.

Figure 2: The sources on the train carriage and the sensor array.

2.2

Beacon-Aided Rail-Car Tracking

With a priori knowledge of the pure-tone beacons’ frequencies, the microphone-array can use reference-signal beamforming [1], [5] to focus separately on each of the two beacons. For the beamformer tracking the φb-beacon, the peak of this beamformer output’s azimuthspectrum would reveal the respective beacon’s instantaneous azimuth-angle with regard to the microphone-array. This azimuth-angle estimate φˆb along with the a priori known spatial geometry in Figures 1 and 2, locates the concerned beacon’s instantaneous spatial location.

1) Reference-Signal Beamforming: If the L × 1 microphone-array data x(t) and the beacon’s reference signal b(t) were jointly stationary over time, the L × 1 reference-signal beamforming weight vector would equal: arg max

w opt

{

= w E w H x(t ) − b(t )

2

}

(2)

= R x,−1x rx ,b

(3)

where the superscript H denotes the Hermitian operator, Rx,x = E{x(t)xH(t)}, and rx,b = E{x(t)b(t)}. In the present application, {pi(t), ∀i} and {x(t), ∀t}$ are actually non-stationary. Moreover, Rx,x and rx,b are a priori unknown. Hence, for any t = nTs (where Ts represents the time-sampling period), replace (3) by:

[ ] rˆ

n) ˆ (n) w (opt = R x,x

−1 ( n ) x ,b

(4)

where

( ) (b )

ˆ (n) = Γ ⊗ 1 • X(n) X( n) R x,x L ,1

rˆx(,nb) = Γ ⊗ 1L ,1 • X ( n )

H

(5)

( n) H

(6)

X ( n ) = [x(n), x(n − 1), K , x(n − N s + 1)]

b ( n ) = [b(n), b(n − 1), K , b(n − N s + 1)]

and • denotes an element-by-element matrix-product, ⊗ refers to the Kronecker product, 1L,1 symbolizes an L × 1 vector of all ones, and Γ = γ N s −1 , γ N s −2 , K , γ 0 is related to the “forgetting factor” 0 < γ ≤ 1 to emphasize the more recent data. A computationally efficient method to update (5) and (6) for (4) is the “recursive least squares” (RLS) algorithm [6] and is summarized in Table 1.

[

]

2) Adaptive Localization of Beacons Aboard the Moving Rail-Car in the MicrophoneArray’s Near Field: As the rail-car may pass in front of the microphone-array as close as only a few meters, e near-field considerations hold in the subsequent analysis. That is, the microphone array manifold depends implicitly on both the azimuth angle and the radial distance between any onboard noise-source and any microphone. However, these two geometric parameters (i.e., the azimuth angle and the radial distance) are geometrically interdependent, given the (a priori known) spatial relationships between the rail-track and the microphone array in Figures 1 and 2. Denoting as Si,j the separation between the ith onboard noise-source and the jth microphone, application of the Cosine Law to Figure 2 gives: Si , j = Si2,1 + 2Si ,1 ( j − 1)∆ sin φi + ( j − 1) 2 ∆2

e

(7)

Given 2L2 / λ as the demarcation between the far field and the near field, the onboard noise-sources are in the near-field of the microphone-array.

The near-field steering-vector for the ith narrowband source would then be a(φi ) = a near (φi ) S −S ⎡ − j 2π S i , 2 − Si , 1 − j 2 π Si , 3 − Si , 1 − j 2 π i , L i ,1 ⎤ λ λ λ = ⎢1, e ,e ,K, e ⎥ ⎢⎣ ⎥⎦

T

(8)

D 2 + ( j − 1)∆D sin 2φi + ( j − 1) 2 ∆2 cos 2 φi − D , ∀j = 2, 3, … , L. Also, the cos φi microphone-array parameters of L and ∆ are a priori known. This work will assume the railtrack/array separation D to have been measured off-line. where Si , j − Si ,1 =

Table 1: RLS Algorithm Summary.

For each discrete-time index n, initialize the algorithm by setting w(n)(0) = 0 and P(0) = δ −1I, where δ is a small positive constant. For the iteration-index m = 1, 2, ... M, do: π ( m) κ ( m) k ( m)

α ( m)

= x H (n − M + m)P(m − 1) = γ + π ( m) x( n − M + m) P(m − 1)x(n − M + m) = κ ( m)

[

]

H

= b(n − M + m) − w ( n ) (m − 1) x(n − M + m)

w ( n ) (m) = w ( n ) (m − 1) + k (m)α * (m) P' (m − 1) = k (m) π(m) 1 P ( m) = [P(m − 1) − P ' (m − 1)]

γ

n) After the above iteration, set w (opt = w (n) (M ) .

n) With w (opt computed from (4) via the RLS algorithm in Table 1, the beacon’s azimuthangle at time t = nTs is estimated as: arg max

φˆb( n ) = φ

(w )

a near (φ ) 1442443 (n) H opt

=B

2.3

(n)

(9)

(φ )

Localization of Noise-Sources w.r.t. the Moving Rail-Car’s Carriage

The two beacons’ above-estimated locations define a straight line segment on which all onboard noise-sources must lie. Any position on this line segment corresponds to a unique azimuth-angle with respect to the microphone array. Hence, spatial match-filtering (i.e., delay-and-sum beamforming) may next be employed to scan along the rail-car’s entire length to locate acoustic noise-sources. The resulting azimuth power-spectrum equals:

(

P φˆ

3

(n) b

)

1 +φ = M

n

∑

a

m = n − M +1

H near

(φˆ

(n) b

2

)

+ φ γ x( m) 1424 3 n −m

(10)

weighted data

SIMULATIONS

Monte Carlo simulations verify the proposed scheme’s efficacy. A rail-car moves with constant speed along a straight rail-track in parallel to and D = 2000λ ≈ 34.4 meters away from a uniform linear array of L = 20 identical omni-directional microphones spaced apart by ∆ = 0.5λ, where λ =0.0172 meter corresponding to a 20kHz frequency. One beacon is placed on each end of a rail-car carriage of length ( 3 +1)D ≈ 5464 ≈ 93.98 meters. The beacons emit pure-tone sinusoids at 20kHz and 19kHz, both at a power level of 2 from the left end and the right end respectively of the carriage, and with statistically independent initial temporal phases that are randomly distributed over [0, 2π). Two dominant noise-sources are aboard the rail-car carriage, located at ( 3 − 1)D ≈ 1464λ and 3 D ≈ 3464λ, and each with power 104. There also exist I − 2 = 5 number of weak noise-sources aboard the rail-car carriage, uniformly spaced along the train carriage between the two beacons and each at a power level of 103. These give a signal-to-interference-plus-noise ratio (SINR) slightly below −40 dB, for data pre-filtered by a narrow passband centered around the φb-beacon’s pure-tone frequency. Hence, the actual raw data’s SINR is still much lower and much more adverse. The noise-sources as a group emit a spatio-temporally white Gaussian time-series. The timesampling frequency is 80 kHz. All simulations below (unless otherwise stated) have an RLS window length of M = 12 and a forgetting-factor of γ = 0.9. Figure 3 shows the beacon-aided adaptive reference-signal near-field beamformer output’s magnitude-response B(n)(φ) at n = 6000, normalized to give a unity peak amplitude. The tracked beacon’s true location, marked by the vertical solid line, coincides well with the peak of the beamformer-output’s azimuth-spectrum. The two dominant onboard noisesources’ true locations, marked by the vertical dashed lines, are very close to the nulls of the azimuth-spectrum. All these verify the efficacy of the proposed tracking of the pass-by railcar via adaptive beacon-aided ``reference signal" beamforming. 0 −5

Normalized B(φ), in dB

−10 −15 −20 −25 −30 −35 −40

−80

−60

−40

−20

0 20 φ (in degrees)

40

60

80

Figure 3: Normalized beam pattern versus azimuth angle φ, 6000 samples are captured, γ = 0.9, SNIR = −40dB.

Figure 4 show that the rail-car tracking accuracy holds up even for a post-bandpassed SINR of −40 dB. This verify that the beacon signals can indeed be very small in power levels, thus inaudible to humans on or off the train. Figure 5 plots P(φ) (normalized to have a unity peak), obtained assuming perfect tracking of the two beacons. Figure 5 shows the correct localization of all dominant onboard noisesources, thereby verifying the efficacy of the proposed near-field carriage-sweeping algorithm. 90 mean of estiamtion error standard deviation of estimation error

Azimuth−Angle Estimation Error, in degrees

80 70 60 50 40 30 20 10 0 −10 −20

−80

−70

−60

−50

−40 −30 SINR, in dB

−20

−10

0

Figure 4: The beacon’s azimuth-angle estimation error versus SINR with respect to strong interference.

0

Normalized P(φ), in dB

−5

−10

−15

−20

−25

−30

Dominant noise−source

0

5

10

Weak noise−source

15 20 25 30 35 Onboard Source Location, in meter

40

45

Figure 5: Normalized delay-and-sum (DAS) beamformer output versus azimuth angle φ, γ = 0.9, SNIR = −40 dB.

4

ACKNOWLEDGEMENTS

The authors were supported by the Internal Competitive Research Grant number G-YF22 from the Hong Kong Polytechnic University.

5

[1] [2] [3]

[4]

[5] [6] [7]

[8] [9]

[10] [11] [12]

[13] [14] [15]

[16]

[17]

[18]

REFERENCES

B. Widrow, P. E. Mantey, L. J. Griffiths and B. B. Goode, “Adaptive Antenna Systems,” Proceedings of the IEEE, no. 12, vol. 55, pp. 2143-2159, December 1967. W. F. King III and D. Bechert, “On the Sources of Wayside Noise Generated by HighSpeed Trains,” Journal of Sound and Vibration, 66, 311-332 (1979). B. Barsikow, W.F. King III and E. Pfizenmaier, “Wheel/Rail Noise Generated by a High-Speed Train Investigated with a Line Array of Microphones,” Journal of Sound and Vibration, 118, 99-122 (1987). B. Barsikow and W. F. King III, “On Removing the Doppler Frequency Shift from Array Measurements of Railway Noise,” Journal of Sound and Vibration, 120, 190-196 (1988). B. D. Van Veen and K. M. Buckley, “Beamforming: A Versatile Approach to Spatial Filtering,” IEEE Acoustics, Speech and Signal Processing Magazine, 5(2), 4-24 (1988). S. Haykin, Adaptive Filter Theory, 2nd edition, (Prentice-Hall, U.S.A., 1991). S. Bruhl and K. P. Schmitz, “Noise Source Localization on High Speed Trains Using Different Array Types,” Proceeding of Inter-Noise Conference, Leuven, Belgium, pp. 1311-1314, 1993. J. D. van der Toorn, H. Hendriks and T. C. van den Dool, “Measuring TGV Source Strength with Syntacan,” Journal of Sound and Vibration, 193, 113-121 (1996). B. Barsikow, “Experiences with Various Configurations of Microphone Arrays Used to Locate Sound Sources on Railway Trains Operated by the DB AG,” Journal of Sound and Vibration, 193, 283-293 (1996). Y. Moritoh, Y. Zenda, and K. Nagakura, “Noise Control of High Speed Shinkansen,” Journal of Sound \& Vibration, 193, 319-334 (1996). G. Holzl, “Low Noise Goods Wagons,” Journal of Sound and Vibration, 193, 359-366 (1996). W. M. To and S. M. Yung, “Power Estimation of Sound Sources on Low-Speed Electric Trains Using a Deconvolution Approach,” Journal of Acoustical Society of America 104(4), 2350-2358 (1999). M. G. Dittrich and M. H. A. Janssens, “Improved Measurement Methods for Railway Rolling Noise,” Journal of Sound and Vibration, 231, 595-609 (2000). S. Bruhl and A. Roder, “Acoustic Noise Source Modelling Based on Microphone Array Measurements,” Journal of Sound and Vibration, 231, 611-617 (2000). B. Schulte-Werning, K. J.ager, R. Strube and L. Willenbrink, “Recent Developments in Noise Research at Deutsche Bahn (Noise Assessment, Noise Source Localization and Specially Monitored Track),” Journal of Sound and Vibration, 267, 689-699 (2003). T. Kitagawa and D.J. Tohmpson, “Comparison of Wheel/Rail Noise Radiation on Japanese Railways Using the TWINS Model and Microphone Array Measurement,” Journal of Sound and Vibration, 293, 496-509 (2006). C. Mellet, F. Letourneaux, F. Poisson, and C. Talotte, “High Speed Train Noise Emission: Latest Investigation of the Aerodynamic/Rolling Noise Contribution,” Journal of Sound and Vibration, 293, 535-546 (2006). T. F. Brooks and W. M. Humphreys, “A Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS) Determined from Phased Microphone Arrays,” Journal of Sound and Vibration, 294, 856-879 (2006).