Sub-wavelength focusing for low-frequency sound sources using an iterative time reversal method

Abstract

Microphone array measurement processed with the image algorithm is commonly performed to identify and quantify noise sources of machines, which is the premise of noise control. However, due to the limitation of the half-wavelength theory, Beamforming and Time Reversal (TR) methods are difficult to separate multiple low-frequency sources. Although near-field acoustic holography can overcome the diffraction limit, it will encounter the ill-posed problem. To avoid solving the inverse problem, iterative time reversal processing (Iterative-TR) is proposed to obtain the sub-wavelength focusing and improve the spatial resolution at low-frequency. The focusing result is corrected step by step with iteration implemented until the result reaches the convergence threshold. The propagation matrix between microphones and focusing points is reconstructed by singular-value normalization to ensure the convergence of the iteration. Numerical simulation results show that Iterative-TR method is able to break through diffraction limit below 1000 Hz within a measurement distance of 0.5 m and reach convergence within 105 iterations that is less than 10 s. The experimental results in indoors with significant reverberation show that Iterative-TR has the ability to stably give the multiple source positions with 0.11 m spacing even at 100 Hz, that is, the spatial resolution reaches 1/31 wavelength. Detailed analysis shows that the overall performance of Iterative-TR outperforms other methods capable of subwavelength focusing for signals below 1000 Hz. The identification of two loudspeakers in the car shows the practicality of the proposed method.

Resolution-Enhanced and Accurate Cascade Time-Reversal Operator Decomposition (C-DORT) Approach for Positioning Radiated Passive Intermodulation Sources

“…Due to its good spatiotemporal focusing property in complicated environments, the time reversal (TR) technique has been widely used in detecting and imaging applications, such as medical imaging [10,11], microwave imaging [12], radar imaging [13,14], and damage detection [15]. For the fundamental TR imaging technique, iterative time-reversal mirror (ITRM) imaging method works by iteratively retransmitting the back-scatterer signals and realizes the scatterer's positioning in the medium [16]. However, the ITRM method is exposed to overwhelm from the weak-amplitude target and cannot distinguish between a far target and a near target.…”