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

Abstract

Microphone array measurements processed with imaging algorithms are commonly performed to identify and quantify noise sources in machines, which is the premise of noise control. However, due to the limitations of the half-wavelength theory, beamforming and time reversal (TR) methods cannot effectively separate multiple low-frequency sources. Although near-field acoustic holography can overcome the diffraction limit, it will encounter an ill-posed problem. To avoid solving the inverse problem, iterative TR 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 it 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 the iterative-TR method is able to break through the diffraction limit below 1000 Hz within a measurement distance of 0.5 m and reach convergence within 105 iterations, which is less than 10 s. The experimental results 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 sub-wavelength focusing for signals below 1000 Hz. The identification of two loudspeakers in a car shows the practicality of the proposed method.