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The acoustic beamforming has been widely applied in the imaging of flow-induced aeroacoustic sound sources. However, the measured signals of the rotor blades often accompanied with the unwanted interference from other components of the experimental setup in the wind tunnel test (for example, the rotor shaft and the stand), which results in the undistinguished sources in the beamforming result. In this paper, the signals of rotor blades are defined first as the cyclostationary process based on the Ffowcs Williams-Hawkings (FW-H) equation in the form of Wold-Cramer decomposition, which connects the statistical definition of rotor blades signals with the wave propagation model of moving sources. Then the developed cyclostationary signal processing tools of a second order, specifically the reduced-rank cyclic Wiener filter, can be applied in the wind tunnel test of rotor blades. The rotor blades signals can be extracted from the noisy measurements with other interferences, which aide to purify the image results of beamforming in the final experiment of wind tunnel test. [ABSTRACT FROM AUTHOR]

The measurements of aero-engine fan noise are crucial to engine-noise reduction and silent-turbofan design. The duct mode identification is adpoted to decompose inner duct noises into spinning modes from acoustic pressure measured by a microphone array. However, modes identification of the aero-engine fan are difficult cause the number of modes is usually much larger than the number of microphones and leading to an ill-posed problem during the inverse process. A mode identification method based on Iterative Bayesian Focusing is used to solve this problem. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The sparsity of the target acoustic modes is applied as a priori condition, and a Mode Aperture Function (MAF) is developed. The aperture width of the MAFis automatically updated and contracted through iterations, after which mode coefficients are contracted to a sparsest solution. The used mode identification method is firstly validated through numerical simulations, and the effects of the number of microphones and SNR on mode identification results are discussed. Then the Iterative Bayesian Focusing-based mode identification method is experimentally verified through a well designed Spinning Mode Synthesizer. Both numerical and experimentalresults indicate that target modes can be accurately identified when the number of microphones are much less than the number of all propagating modes. [ABSTRACT FROM AUTHOR]

• Acoustic inverse problems in the framework of ADMM are investigated. • The iteration algorithms of ADMM in the complex domain have been derived. • ADMM has been systematically compared with the sparse holography. • Both simulation and experimentation have verified the performance of ADMM. Acoustic imaging is an important technique for sound source identification which is widely used in noise control and fault detection. It can be described as a method for reconstructing the amplitude and phase distribution of an acoustic field in a given plane. When the size of radiating object is huge and measurement environment is noisy, accuracy and efficiency of acoustic imaging algorithm deteriorate easily. In this paper, a novel computational framework is investigated to simplify the algorithm and balance computation speed with accuracy. It converts acoustic imaging into an inverse problem and then divides this problem into two parts including forward model and denoising model. This computation framework is based on the alternating direction method of multipliers, which makes parallel implementation and distributed optimization possible, especially for large scale measurements. It is assumed that the acoustic field is composed of a cluster of monopole sources and the equivalent source method is taken to solve the acoustic inverse problem. Both L 2 -norm penalization based on the minimal energy assumption and L p -norm (0 < p ⩽ 1) penalization based on the sparsity hypothesis are taken in this framework. Thus, the regularization parameter in the algorithm, which balances the standard least square error and the norm of the source solution, can be coupled with some pre-existing methods incluing L-curve, GCV and Bayesian strategies. Different regularization parameters are proposed and the comparison is made in this paper. The proposed method provides a general and convenient method for different type of sound source priors and it is validated with an experiment. [ABSTRACT FROM AUTHOR]

• Non-synchronous measurements beamforming is investigated. • ALM and ADMM based fast implementation are presented. • Simulations and an industrial application are given. Acoustic beamforming is a technique to measure the sound field and then achieve the localization of the sound sources. It usually works at a high frequency because the size and density of the microphone array are limited. Differing from the traditional beamforming, non-synchronous measurements beamforming can widen the working frequency bandwidth with a movable microphone array. It generates a cross-spectral matrix of all the microphones in the sequential positions of measurements, and this matrix is incomplete due to the missing phase relationships between non-synchronous measurements. Thus the non-synchronous measurements beamforming can be regarded as a cross-spectral matrix completion problem. One application of the non-synchronous measurements beamforming is that it can immediately obtain a completed noise image by scanning a large sound source; then the primary sound sources are expected to be identified by the global image. However, it is still a challenge for the current non-synchronous measurements beamforming algorithm since the computation time is long when more numbers of measurements are involved. In this paper, two algorithms based on the augmented Lagrange multiplier method and alternating direction method of multipliers are proposed for achieving fast implementation. The proposed algorithms can improve the iteration speed of the non-synchronous measurements beamforming which is proved first in the simulation, and they are further applied in the on-site measurement of the vehicle engine compartment (the data missing cross-spectral matrix of 15 non-synchronous measurements for a given frequency can be completed only in a few seconds). This industrial application has shown the potential of the proposed methods to be further applied for the sound source imaging of large mechanical systems. [ABSTRACT FROM AUTHOR]

The localization of cyclostationary sound sources is important for rotating machinery noise source identification and fault diagnosis. Cyclostationary sound sources are a special class of nonstationary sound sources, which exhibit periodic changes in statistics. Most of the conventional sound source identification methods are based on the stationary sound source assumption, which do not consider the cyclostationarity of the radiated sound field by rotating machinery. Thus, they are hard to localize the acoustic sources with different cyclic frequencies. In this paper, a novel technique of localizing the cyclostationary acoustic sources with different cyclic frequencies is proposed. First, the cyclostationary conventional beamforming (CSCBF) method is deviated. In CSCBF, the cyclic-cross-spectral matrix (CCSM) is defined considering all the cross cyclic spectral correlation (CSC) between different microphones in the array. The left steering vector and right steering vector are constructed to focus the CCSM on each scanning grid point at a given combination of cyclic frequency and spectral frequency. Then, the high resolution cyclostationary beamforming (HR-CSBF) is further developed to improve the spatial resolution of CSCBF. In HR-CSBF, two linear equations according to the property of CSC is established as the acoustic inverse problems. With the sparse distribution of the cyclostationary sources in the space as the prior knowledge, the iterated Bayesian focusing (IBF) is utilized to obtain a robust and sparse solution in HR-CSBF. Numerical simulations and experiments are conducted to validate the proposed methods. To explore the potential applications of the proposed methods, the localization of high pressure pump (HPP) and rolling bearing with outer-race failure are also used to evaluate the effectiveness of the proposed methods. It turns out that both CSCBF and HR-CSBF can localize the cyclostationary sources with different cyclic frequencies. Compared with CSCBF, HR-CSBF can achieve a higher spatial resolution in the obtained acoustic map. [ABSTRACT FROM AUTHOR]

• A Kalman filter-based time domain plane wave superposition method is proposed. • The proposed KF-TDPWSM performs a forward process to improve the solving stability. • The superiority of the proposed KF-TDPWSM is proved by comparing with the TDPWSM. A Kalman-filter-based time-domain plane wave superposition method (KF-TDPWSM) is proposed for reconstructing the instantaneous sound field generated by a source. In the KF-TDPWSM, a discrete state formulation is first acquired using the superposition formula of time-varying pressure on a hologram plane, which forms a multiple-input and multiple-output acoustical system. Then, an eigensystem realization algorithm is implemented to obtain the minimum realization of this system. The process and measurement equations of the KF-TDPWSM are established by combining the equation of the first-order smoothness condition with the minimum realization. Finally, the forward iteration calculation of the Kalman filter is used to estimate the state vector, including the pressure time–wavenumber spectra on a virtual source plane. The spectra estimated at all times are employed to calculate the time-varying pressure on a reconstruction plane. The KF-TDPWSM utilizes a forward iteration calculation and does not use the inverse calculation with the time-marching characteristic to improve the reconstruction stability of the instantaneous sound field. A numerical simulation is designed to investigate the reconstruction performance of the KF-TDPWSM. Simulation results confirm that the KF-TDPWSM effectively reconstructs the instantaneous sound field of a source in the time and space domains. The effects of certain parameters of the KF-TDPWSM are examined through simulations, and it is shown that its reconstruction accuracy is superior to that of the time-domain plane wave superposition method. An experiment is conducted to further validate the KF-TDPWSM. [ABSTRACT FROM AUTHOR]