Broadband implementation of coprime linear microphone arrays for direction of arrival estimation

Acoustic-Based Rolling Bearing Fault Diagnosis Using a Co-Prime Circular Microphone Array

This study proposes a high-efficiency method using a co-prime circular microphone array (CPCMA) for the bearing fault diagnosis, and discusses the acoustic characteristics of three fault-type signals at different rotation speeds. Due to the close positions of various bearing components, radiation sounds are seriously mixed, and it is challenging to separate the fault features. Direction-of-arrival (DOA) estimation can be used to suppress noise and directionally enhance sound sources of interest; however, classical array configurations usually require a large number of microphones to achieve high accuracy. To address this, a CPCMA is introduced to raise the array's degrees of freedom in order to reduce the dependence on the microphone numbers and computation complexity. The estimation of signal parameters via rotational invariance techniques (ESPRIT) applied to a CPCMA can quickly figure out the DOA estimation without any prior knowledge. By using the techniques above, a sound source motion-tracking diagnosis method is proposed according to the movement characteristics of impact sound sources for each fault type. Additionally, more precise frequency spectra are obtained, which are used in combination to determine the fault types and locations.

Sparse planar arrays for azimuth and elevation using experimental data

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

Model-based Bayesian analysis in acoustics-A tutorial

Bayesian analysis has been increasingly applied in many acoustical applications. In these applications, prediction models are often involved to better understand the process under investigation by purposely learning from the experimental observations. When involving the model-based data analysis within a Bayesian framework, issues related to incorporating the experimental data and assigning probabilities into the inferential learning procedure need fundamental consideration. This paper introduces Bayesian probability theory on a tutorial level, including fundamental rules for manipulating the probabilities, and the principle of maximum entropy for assignment of necessary probabilities prior to the data analysis. This paper also employs a number of examples recently published in this journal to explain detailed steps on how to apply the model-based Bayesian inference to solving acoustical problems.

Sparse Bayesian learning for beamforming using sparse linear arrays

Sparse linear arrays such as co-prime and nested arrays can resolve more sources than the number of sensors. In contrast, uniform linear arrays (ULA) cannot resolve more sources than the number of sensors. This paper demonstrates this using Sparse Bayesian learning (SBL) and co-array MUSIC for single frequency beamforming. For approximately the same number of sensors, co-prime and nested arrays are shown to outperform ULA in root mean squared error. This paper shows that multi-frequency SBL can significantly reduce spatial aliasing. The effects of different sparse sub-arrays on SBL performance are compared qualitatively using the Noise Correlation 2009 experimental data set.

A model-based Bayesian framework for sound source enumeration and direction of arrival estimation using a coprime microphone array

Coprime microphone arrays use sparse sensing to achieve greater degrees of freedom, while the coprimality of the microphone subarrays help resolve grating lobe ambiguities. The result is a narrow beam at frequencies higher than the spatial Nyquist limit allows, with residual side lobes arising from aliasing. These side lobes can be mitigated when observing broadband sources, as shown by Bush and Xiang [J. Acoust. Soc. Am. 138, 447-456 (2015)]. Peak positions may indicate directions of arrival in this case; however, one must first ask how many sources are present. In answering this question, this work employs a model describing scenes with potentially multiple concurrent sound sources. Bayesian inference is used to first select which model the data prefer from competing models before estimating model parameters, including the particular source locations. The model is a linear combination of Laplace distribution functions (one per sound source). The likelihood function is explored by a Markov Chain Monte Carlo method called nested sampling in order to evaluate Bayesian evidence for each model. These values increase monotonically with model complexity; however, diminished returns are penalized via an implementation of Occam's razor.

n-tuple coprime sensor arrays

Until now, coprime sensor arrays have used two sparsely spaced subarrays to emulate the performance of a single uniform array with many more sensors (generally on the order of the product of each subarrays' number of sensors). This allows for similar results with fewer sensors, or the observation of higher frequencies (above the Nyquist limit) with a similar number of sensors. The theory rests on the cross-referencing (using directional filter banks) or cancellation (using product processing) of the M grating lobes in one subarray's beampattern and N grating lobes in the other, where M and N are coprime integers. Sets of coprime integers can consist of more than two integers, however, and introducing another coprime factor theoretically multiplies observable frequency (or further decreases the number of array elements needed for the same frequency). Any amount, n, of coprime integers and corresponding subarrays may be used. In this work, "n-tuple coprime sensor array" theory is expounded and implemented. Experimentally measured beampattern results of a triple coprime sensor array (with three subarrays) are shown, using an extension of the authors' previously established product processing. Results also confirm that the usable range of an n-tuple coprime array extends below its design frequency.

Localization and separation of acoustic sources by using a 2.5-dimensional circular microphone array

Circular microphone arrays (CMAs) are sufficient in many immersive audio applications because azimuthal angles of sources are considered more important than the elevation angles in those occasions. However, the fact that CMAs do not resolve the elevation angle well can be a limitation for some applications which involves three-dimensional sound images. This paper proposes a 2.5-dimensional (2.5-D) CMA comprised of a CMA and a vertical logarithmic-spacing linear array (LLA) on the top. In the localization stage, two delay-and-sum beamformers are applied to the CMA and the LLA, respectively. The direction of arrival (DOA) is estimated from the product of two array output signals. In the separation stage, Tikhonov regularization and convex optimization are employed to extract the source amplitudes on the basis of the estimated DOA. The extracted signals from two arrays are further processed by the normalized least-mean-square algorithm with the internal iteration to yield the source signal with improved quality. To validate the 2.5-D CMA experimentally, a three-dimensionally printed circular array comprised of a 24-element CMA and an eight-element LLA is constructed. Objective perceptual evaluation of speech quality test and a subjective listening test are also undertaken.

A reconfigurable all-optical ultrasound transducer array for 3D endoscopic imaging

A miniature all-optical ultrasound imaging system is presented that generates three-dimensional images using a stationary, real acoustic source aperture. Discrete acoustic sources were sequentially addressed by scanning a focussed optical beam across the proximal end of a coherent fibre bundle; high-frequency ultrasound (156% fractional bandwidth centred around 13.5 MHz) was generated photoacoustically in the corresponding regions of an optically absorbing coating deposited at the distal end. Paired with a single fibre-optic ultrasound detector, the imaging probe (3.5 mm outer diameter) achieved high on-axis resolutions of 97 μm, 179 μm and 110 μm in the x, y and z directions, respectively. Furthermore, the optical scan pattern, and thus the acoustic source array geometry, was readily reconfigured. Implementing four different array geometries revealed a strong dependency of the image quality on the source location pattern. Thus, by employing optical technology, a miniature ultrasound probe was fabricated that allows for arbitrary source array geometries, which is suitable for three-dimensional endoscopic and laparoscopic imaging, as was demonstrated on ex vivo porcine cardiac tissue.