Page 26 - Acoustics Today Summer 2011

Fig. 10. Similar to Fig. 9 but for the ballistic model-based method which uses both the muzzle blast and shock wave information.
sn /c) and arrival angles 􏰀n of the muzzle blast and shock waves at a sensor node n (a small baseline sensor array) enables the range r to be estimated—see Fig. 7. For a bullet travelling with a constant velocity (V), the range is,25 r=c∆τn/(1-cos􏰀n). In practice, range estimates based on the constant bullet velocity assumption can have significant errors (especially at long source ranges), necessitating the development of a ballistic model-based approach that accounts for the deceleration of the bullet along its trajecto- ry. The shock wavefront is better represented (visualized) as a half prolate spheroid (pointed oval shape like an American football) for a decelerating bullet, rather than as a conical surface for a bullet travelling with a constant velocity. The ballistic parameters, which must be known a priori or esti- mated in situ, are the bullet’s initial velocity and the ballistic constant (which depends on the bullet’s mass, cross-section- al area and aerodynamic drag). The results of applying this method to the passive ranging of real gunshot data from the five different firing positions are shown in Fig. 10. When compared with the passive ranging by wavefront curvature method (Fig. 9), the variances of the ranges of the firing posi- tions are reduced when estimated using the ballistic model- based method, most notably at the longer source ranges. The converse is true for the bearings of the source positions
because of the shorter baseline of the sensor array used with the ballistic model-based method. Additionally, when the source ranges are estimated using the conventional method which assumes a constant bullet velocity, they are found to have significant bias errors especially at the longer firing ranges. Also, the radial error, which is defined as the separa- tion distance between the estimated and actual firing posi- tions, is found to be dependent on the caliber of the bullet— the conventional method’s radial errors are much larger for 5.56 mm rounds than for 7.62 mm caliber ammunition.
Currently under development is a third localization method26 that relies only on the ballistic shock wave informa- tion, which is advantageous when the received muzzle blast is absent due to the use of a sound suppressor (silencer) or weak due to the high transmission loss (spreading loss plus absorp- tion loss) suffered by the acoustic signal when its propagation path from source to sensor is long. Another advantage of this method occurs when there is simultaneous fire from differ- ent firing positions as each shock wave signal is not required to be associated with a corresponding muzzle blast signal as is the case with the ballistic model-based method. A new method proposed by the authors is simultaneous localization and classification, which uses both the muzzle blast and shock wave information received by a next-generation network of spatially-distributed unattended ground sensors comprising “low-cost sensor nodes operating on shoestring power budgets for years at a time in potentially hostile environments without hope of human intervention.”
Summary
In this article we have presented three examples of signal processing approaches in physical and engineering acoustics. In time reversal, we exploit a principle in physical acoustics to enhance the detection of flaws in plates and structures. In gearbox monitoring we show how sophisticated statistical techniques such as principle component analysis and blind source separation can be employed to solve a difficult and important problem in structural and machine monitoring. Finally, in point of fire localization we see how both wave- front curvature and shock front propagation can be com- bined to improve estimates of the origin of a bullet fired from a gun. We hope this gives a flavor of the variety of approach- es and applications of signal processing to physical and engi- neering acoustics.AT
Acknowledgments
Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.
References
1 For more information contact author B.E.A. Electronic mail: bea@byu.edu
2 M. Fink, “Time reversed acoustics,” Physics Today 50, 34–40 (1997). 3 B. E. Anderson, M. Griffa, C. Larmat, T. J. Ulrich, and P. A.
Johnson, “Time reversal,” Acoustics Today 4(1), 5–16 (2008).
4 A. Parvulescu and C. S. Clay, “Reproducibility of signal trans-
22 Acoustics Today, July 2011