Acoustic sources in supersonic motion

Supersonic source localization: inverse time-reversal problem and supersonic field synthesis

Supervised student : Guillaume Mahenc

Supervision : Éric Bavu , Manuel Melon , Pascal Hamery and Sébastien Hengy ( ISL )

Project duration : 3 years (2014 - 2017)

Funding : 100% funding from the Saint Louis Institute

Abstract : This project is part of a joint work between ISL and LMSSC are interested in the use of the information carried by the Mach wave generated by a supersonic projectile, in order to achieve sniper localization in urban environment.

Indeed, current sniper localization techniques only exploit the muzzle wave generated by the weapon. These techniques are not robust to field situations where snipers use silenced weapons.

Based on this observation, we developed new techniques, which aimed to reconstruct the trajectory of a supersonic projectile in a reverberant environment using the inverse problem. This project therefore required the development of two different aspects:

• the reproducible physical synthesis of a conical wavefront reproducing the behavior of a Mach cone in the laboratory without firing a projectile
• the inverse problem of source trajectory reconstruction using distributed acoustic measurements

Supersonic field synthesis

To recreate the geometrical structure and the typical temporal trace of a Mach wave, we have developed an electroacoustic device consisting of 256 miniaturized loudspeakers, allowing to physically simulate the propagation of a Mach cone, using inverse filtering methods and a multi-channel control device with a large number of audio channels of MADI type.

Figure : Modular line of 256 loudspeakers developed jointly with ISL in this project. Each module contains 4 miniature loudspeakers on its external faces, and the whole is fed by a MADI card with 64 channels and 64 independent amplification stages, and controlled by an optical fiber computer managing the signals to be emitted. This line can then be placed in any environment simulating an urban or reverberant environment.

This method requires a first phase of “learning” of the electrical signals to be fed to each of the loudspeakers of the line array, thus allowing to carry out the inverse filtering procedure correcting the response curves of each of the loudspeakers in order to create, by 3D synthesis, a wavefront with a typical temporal signature of an N-wave corresponding to a weapon shot. This approach is in itself a technological and numerical challenge, since the signal to be reconstituted must be extremely short (which represents hardly more than a dozen samples for devices sampled at 44100 Hz.), and it is necessary to control in amplitude and phase the 256 loudspeakers (grouped by 4 on modules designed at the ISL) precisely so that the Mach cone is physically well synthesized.

Vidéo : Measurement of the field synthesized by the line of loudspeakers after apprenttising the supply signals by inverse filtering. The structure of the Mach cone is well reconstructed by electro-acoustic method, and the temporal signature of the signals is well respected.

Figure : Time signature of a Mach wave, simulated by the speaker line.

Inverse problem: reconstruction of the projectile trajectory

Once this field synthesis was achieved, the project consisted in developing a method to reconstruct the trajectory of the supersonic projectile. To do this, we have focused on time reversal techniques, particularly suited to the impulse characteristics of this type of source. For this purpose, we have developed a method that exploits pressure field measurements on a discrete (and if possible parsimonious) distribution of microphones on the ground of an urban corridor.

The inverse problem is solved by numerically computing the back-propagated field from the microphone positions to vertical slices along the street. The use of a fourth-order spatiotemporal statistical criterion (kurtosis) allowed us to reduce the contribution of the source terms in the back-propagated field, which causes a divergence of the pressure field around the microphone positions. The axis of the Mach cone can then be located with a good angular accuracy, by combining the Kurtosis analysis of the back-propagated field with a RANSAC (random sample consensus) method allowing to keep automatically only the unbiased estimates of the points of the trajectory axis.

Figure : Reconstruction of the supersonic projectile trajectory: experiment in a reverberant urban corridor in the laboratory, 3D field synthesis and inverse problem). The blue walls represent the reflecting walls during the experiment, the grey area on the ground represents the area where the microphones are placed. The black line represents the real trajectory of the source, the purple dotted line represents the trajectory determined by the inverse problem algorithm. Here, the absolute error on the determination of the Mach cone axis is 0.53 degrees and 0.28 cm from the real axis.

These methods have been tested and validated both numerically and experimentally (in laboratory, using the loudspeaker line synthesizing the Mach cone), and in real life shooting between two reflecting walls on the experimental field of the ISL, in Baldersheim.

Publications and communications related to the project

• G. Mahenc, É. Bavu, P. Hamery, S. Hengy, M. Melon, Axis retrieval of a supersonic source in a reverberant space using time reversal, Journal of Sound and Vibration, 402, 185–202, 2017. doi
• G. Mahenc, É. Bavu, P. Hamery, S. Hengy, M. Melon. Le retournement temporel en milieu réverbérant pour localiser une source supersonique. Actes du 13ème Congrès Français d’Acoustique joint avec le 20ème colloque VIbrations, SHocks and NOise, CFA/VISHNO 2016, Le Mans, Sarthe, France, 11-15 avril 2016.
• G. Mahenc, É. Bavu, P. Hamery, S. Hengy, M. Melon. Synthesis of a Mach cone using a loudspeaker array. Proceedings of the 7th Forum Acusticum, Krakow, Poland, September 7-12, 2014.
• G. Mahenc, É. Bavu, P. Hamery, S. Hengy. Synthesis of a Mach cone using a loudspeaker array. The 5th Workshop on Battlefield Acoustics, Saint Louis, France, October 11-12, 2016.