Noise induced by incipient-propeller tip vortex cavitation (TVC) has a few sources near the propeller tips, which radiate a broadband signal. This article describes a compressive sensing (CS)-based TVC localization technique for coherent multiple-frequency processing, which jointly processes the measured data at multiple frequencies. Block-sparse CS, which groups several single-frequency measurements into blocks, is adopted for coherent multiple-frequency processing. The coherent multiple-frequency processing improves localization performance over that of single-frequency processing. Unlike single-frequency processing using conventional CS, which combines independent single-frequency measurement treatments by averaging, coherent multiple-frequency processing produces accurate localization without requiring a sufficient number of treated frequencies, long-time-sampled data with a time-invariant signal assumption, or even a single cavitation event. The approach is demonstrated on experimental data from a transducer source experiment and a cavitation source experiment.

The propeller tip vortex cavitation (TVC) localization problem involves the separation of noise sources in proximity. This work describes a sparse localization method for off-grid cavitations to estimates their precise locations while keeping reasonable computational efficiency. It adopts two different grid (pairwise off-grid) sets with a moderate grid interval and provides redundant representations for adjacent noise sources. To estimate the position of the off-grid cavitations, a block-sparse Bayesian learning-based method is adopted for the pairwise off-grid scheme (pairwise off-grid BSBL), which iteratively updates the grid points using Bayesian inference. Subsequently, simulation and experimental results demonstrate that the proposed method achieves the separation of adjacent off-grid cavitations with reduced computational cost, while the other scheme suffers from a heavy computational burden; for the separation of adjacent off-grid cavitations, the pairwise off-grid BSBL took significantly less time (29 s) compared with the time taken by the conventional off-grid BSBL (2923 s).

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Marine propeller cavitation is a dominant noise source of ships. Thus, localizing the cavitation noise source is essential for subsequent remedy. Given that incipient tip vortex cavitation (TVC) noise radiates in all directions as a monopole source and a few noise sources exist in the vicinity of the propeller, the localization problem can be considered as a sparse signal reconstruction problem. Compressive sensing (CS) based localization technique utilizes a sparsity promoting constraint and solves the localization problem efficiently with high resolution. Block-sparse CS, based on block-sparsity, is adopted to process multiple frequency components of the sources coherently. Block-sparse CS localization of TVC shows superior performance with high resolution compared to the conventional CS based incoherent multiple frequency processing. To demonstrate the performance of the block-sparse CS localization, both synthetic and real cavitation tunnel experiment data are used.

Acoustic channel impulse responses (CIRs) consisting of multiple arrivals are extracted from the measured data during SAVEX15 experiment (conducted in the northern East China Sea during May 2015) using compressive sensing, providing high-resolution results due to sparsity promoting objective function. Performance of grid-based compressive channel estimation degrades when basis mismatch occurs because delays of the arrivals do not correspond to delays on the grid. To overcome this, grid-free compressive channel estimation is derived from the formulation of grid-free compressive beamforming [J. Acoust. Soc. Am. 137, 1923-1935 (2015)]. The grid-free compressive channel estimation is applied to signals from SAVEX15; the signals were transmitted from a towed source and received at two separate vertical line arrays (16 elements each); they are used to measure the signals traveling through waveguides. Acoustic structures are observed clearly due to high-resolution CIRs along depth, which are varied by the moving source and internal wave activities.