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Acoustic source reconstruction techniques are an essential technical basis for noise source identification and fault diagnosis. How to computationally efficiently obtain the accurate estimation of acoustic source location and strength remains a fundamental challenge for acoustic source reconstruction techniques. To accommodate the needs of processing complex-valued signals, complex approximate message passing algorithm (CAMP) is considered. Benefiting from the Onsager correction term, the reconstruction performance and convergence speed of CAMP are enhanced. The computational complexity of CAMP is significantly reduced by avoiding matrix inversion in each iteration. Therefore, a sparse Equivalent Source Method (ESM) based on CAMP is proposed in this paper and named CAMP-ESM for achieving acoustic source reconstruction with increased accuracy and computational efficiency. Simulation results show in the mid-high frequency range, CAMP-ESM achieves the best reconstruction results in the shortest time compared to other ℓ 1 -based ESM. In addition, the proposed method achieves a good balance between reconstruction accuracy and computational efficiency compared to other state-of-the-art ESM methods. Two experiments verified that CAMP-ESM can accurately localize the acoustic source and quantify the acoustic power. [ABSTRACT FROM AUTHOR]

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]

Helicopter detection is an important part of the safety and security during flight. Most of the aerodynamic noise of modern helicopters comes from the main rotor, the main rotor aerodynamic noise thus can be used for helicopter detection. However, the Signal-to-Noise Ratio (SNR) of the measurement noise has always been quite small while the helicopter is flying over long distance away from the microphone. The current passive detection methods are not robust enough in the presence of substantial interference. A robust passive sound detection method is proposed to detect the far-field helicopter based on the cyclostationarity of the main rotor noise. The Sparsity-Enhanced Spectral Coherence (SESC) is derived from the spectral coherence decomposition to improve the detection robustness at far distances and low SNR. Furthermore, a global detector is constructed to detect helicopters adaptively by fusing the detection of multiple orders of BPF, which can be performed on the calculated SESC. More accurate and robust detection of the far-field helicopter can be obtained by the proposed SESC detector. The effectiveness of the proposed detection approach is demonstrated and contrasted by using simulation and far-field flight test measurements of the ROBINSON R22 helicopter. [ABSTRACT FROM AUTHOR]

Helicopter rotor aerodynamic noise research has become essential as helicopters' reliability and comfort requirements have increased. Significant progress has been made in modeling the aerodynamically generated sound of helicopter rotors. The cyclostationary signal processing methods have been widely used for machine fault diagnosis, machinery system identification and mechanical source separation. However, the lack of a generally accepted formal definition of cyclostationarity based on the basic aerodynamic theory and wave propagation model limits cyclostationary methods' application to the helicopter rotor aerodynamic noise. A formal cyclostationary modeling process to the helicopter rotor aerodynamic noise based on aerodynamic and wave propagation theory is proposed in this paper for subsequent cyclostationary signal processing. The rotor blade noise is mathematically formulated as a cyclostationary process by imposing the periodic Green's function based on the Wold–Cramer decomposition form of the Ffowcs Williams–Hawkings (FW–H) equation, and the formal definition of the rotor blade noise cyclostationary process is derived. Then, the cyclostationarity is defined for both the tonal noise and the broadband noise of rotor aerodynamic noise, respectively. Furthermore, a periodic amplitude modulation (PAM) signal model is proposed to approximate the measured rotor aerodynamic noise signal. The proposed signal model is validated by the measurement in the wind tunnel test. • Cyclostationarity of the aerodynamically generated sound of helicopter rotors is proved. • A cyclostationary signal model is proposed for helicopter rotor aerodynamic noise. • The theory and signal model is validated by the measurement in the wind tunnel test. [ABSTRACT FROM AUTHOR]

• Space-snapshot representation for acoustic imaging in a complex, noisy environment is investigated. • Low rank and Mixture of Gaussian modeling are proposed to achieve significant denoising performance. • Comparisons with other methods are made in simulations and experiments to verify the effect of the state-of-the-art methods. The microphone array can simultaneously obtain the multi-dimensional information (space-time-frequency) of sound sources, which is recognized as a fundamental and powerful tool in acoustic imaging. Acoustic Beamforming is one of the widely used methods in acoustic imaging. However, most of the applications of beamforming are based on the Gaussian noise assumption, which is not always accurate in on-site measurements. For example, shock noise with a skewed probability density function (PDF) may appear on the signal record when the turbulent eddies are not controlled. Thus, in this paper, the conventional Gaussian noise model is extended to a Gaussian mixture noise model, which can approximate any probability distribution of the noise in theory. The space-snapshot representation of microphone array measurements is further modeled as a combination of the low-rank matrix part (measurements from the sound sources) and a Gaussian mixture matrix part (measurement noise). The signal from the sources of interest is finally recovered by the Expectation–maximization algorithm, which iterates between the low-rank approximation of the sound sources and the estimation of the parameter of the Gaussian mixture model. The proposed method is further investigated with simulations and compared with robust principal component analysis (RPCA) and Gaussian-based probabilistic factor analysis (PFA). It is concluded that the proposed method outperforms the state-of-the-art denoising methods. [ABSTRACT FROM AUTHOR]

The Non-Synchronous Measurements is particularly effective at expanding the operating frequency range of a single microphone array. The completed cross-spectral matrix of the synthetic array, when combined with high-resolution imaging algorithms, can yield accurate sound source identification results. However, when matrix completion algorithms are applied to large synthetic arrays, their computational complexity increases significantly. Furthermore, existing integrations with high-resolution imaging algorithms often encounter difficulties in the presence of coherent sound sources. To address this problem, this paper introduces the accelerated gradient descent algorithm for the covariance matrix fitting by orthogonal least squares. The matrix completion model for non-synchronous measurements is initially simplified through matrix decomposition, thereby enabling the rapid completion of the cross-spectral matrix using the accelerated gradient descent algorithm. This is then followed by the application of the covariance matrix fitting by orthogonal least squares to achieve quick and precise identification of coherent sound sources employing the completed cross-spectral matrix. The performance of the algorithm is evaluated using numerical simulations and validated through loudspeaker experiments in an anechoic chamber. The results from these simulations and experiments reveal that the proposed algorithm not only improves matrix completion performance on large synthetic arrays but also accurately identifies the locations and correlation coefficients of coherent sound sources. [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]

Noise source localization is considered a key technology for the low-noise design of machinery and equipment. The spatial resolution of conventional beamforming localization methods is effectively improved by the fast iterative shrinkage thresholding algorithm(FISTA). The application of FISTA for sound source localization in reverberant environments is limited by the selection of reflection parameters. In this paper, FISTA extends to FISTA-Net and is proposed to solve the problem of adaptive fitting of reflection parameters to improve the performance of sound source localization in a reverberant environment. In FISTA-Net, the network model can be established by expanding and truncating the FISTA algorithm based on a fixed number of iterations. The parameter iteration steps, shrinkage thresholds and update operators are updated in the FISTA-Net model by training. A series of simulations are conducted for various frequencies, reverberation times, and signal-to-noise ratios and compared to several de-reverberation algorithms to evaluate the performance of the proposed algorithm. The loudspeaker source localization experiment was conducted in a closed room to verify the effectiveness of FISTA-Net in real-world scenarios. [ABSTRACT FROM AUTHOR]

Transfer learning techniques have been extensively developed for the intelligent diagnosis of rotating machinery as a critical and valuable tool dedicated to minimizing the distributional discrepancies between different working conditions of the machine. However, conditional probability information about fault classes and the geometric features of data distribution is rarely considered in traditional distance metrics, invalidating cross-domain diagnostic models when faced with significant distributional discrepancies. To address these issues, a new cross-domain diagnostic algorithm is proposed via joint conditional Wasserstein distance matching. First, the conditional Bures–Wasserstein distance is constructed based on the second-order statistic cross-covariance operator, approximating the distributions in the source and target domains while constraining the geometry. Then, to avoid losing first-order fault data information, the conditional probability 1-Wasserstein distance is embedded to construct a joint distance adaptation. The entropy loss is introduced into the training process to build reliable pseudo labels for the target domain samples. In the proposed method, the samples and label features of different domains are mapped to the reproducing kernel Hilbert space (RKHS), and the Feature Extractor and Classifier modules of the model are jointly optimized to obtain a more robust diagnostic model. The proposed cross-domain diagnostic model is experimentally validated on bearing and gearbox datasets under variable loads and speeds with significant diagnostic performance compared to existing transfer models. [ABSTRACT FROM AUTHOR]

• A multistep acoustic method is extended to suppress the reconstruction instability of instantaneous vibration of a structure. • The more serious time-domain instability of the reconstruction between the pressure and acceleration is proved. • The superiority of the extended M-TDPWSM is demonstrated by comparing with the S-TDPWSM. A multistep acoustic method is extended to suppress the more serious instability in the inverse process between the time-evolving pressure on the hologram plane and the time-wavenumber acceleration spectrum on the virtual source plane, and further stabilizes the reconstruction of the instantaneous vibration of an exciting planar structure. In the extended method, the solving equation relating the time-evolving pressure to the time-wavenumber acceleration spectrum at each time step is first established. Then, the established equations at several time steps are combined to constitute a new large solving equation. Finally, after one-time solving inverse calculation of the new equation, the time-wavenumber acceleration spectra at these several time steps are solved simultaneously. The multistep calculation in the expanded method not only can reduce the total number of solving the time-wavenumber acceleration spectra for reducing the accumulation errors in the time domain, but also can expand the dimension of the solving inverse matrix to add the number of the nonzero element for improving the filtering effect. A planar plate excited by a steel ball is designed as the numerical simulation to test the ability of the extended method in suppressing the instability of the inverse process of reconstructing the structural surface acceleration. In the simulation, some important parameters, such as the position of the virtual source plane, the sampling number in the wavenumber domain, the noise and the multistep number, are discussed. The simulation results demonstrate that in the reconstruction of the instantaneous vibration, the single-step time domain plane wave superposition method is more sensitive to these parameters and the divergence problem of its solution is more serious, but the extended method has a stronger adaptation ability in the changes of these parameters and can effectively suppress the reconstruction instability of the instantaneous vibration of an exciting structure for providing a more stable solution. An experiment with a steel plate excited by a steel ball is further employed to verify the superiority of the expanded method in suppressing the serious instability of the inverse process of reconstructing the instantaneous vibration. [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 fan noise is the primary component of aero-engine noise. Duct acoustic modal identification is essential for analyzing the mechanism of fan noise generation and propagation. The acoustic modal in the duct can be identified by the measurement of the microphone array mounted on the duct wall. It is generally assumed in the conventional modal identification methods that the modal coefficients are independent of each other. However, the realistic duct acoustic modal coefficients exhibit significant statistical dependence. A Boltzmann machine(BM) model considering the statistical dependence between modal coefficients is proposed for recovering the modal coefficients in this paper. The modal coefficients are estimated using a block coordinate optimization method in a Bayesian framework. Moreover, the modal Boltzmann parameters can be learned iteratively by the BM. The effectiveness of the proposed method is verified by numerical simulations and experimental tests. It turns out that the modal coefficients can be accurately identified by the proposed method, and a more significant sparsity is shown by the results. In addition, the statistical dependence between the modal coefficients can be captured by the BM. • A Boltzmann machine modeling method that considers the statistical dependence between the modal coefficients is proposed. • The modal coefficients and the modal Boltzmann parameters can be estimated adaptively and iteratively. • The accuracy and robustness of the modal identification results are analyzed. • The proposed method is evaluated in Spinning Mode Synthesizer experiments. [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]

Intelligent mechanical fault diagnosis techniques have been extensively developed in recent years. Owing to the advantage of data privacy protection, federated learning has recently received increasing attention; this approach can utilize monitoring data from multiple local clients to train an optimal global diagnosis model. However, low-quality data are often present for some clients, including mislabeled data and incomplete data that lack some health states. Furthermore, the data distributions are usually different across different clients owing to variations in machine operating conditions. Therefore, the performance of the federated diagnostic model may be limited by low-quality data and data distribution discrepancies. To address this issue, a federated transfer learning method with low-quality knowledge filtering and dynamic model aggregation is proposed. First, a dynamic filter is designed by filtering out low label probabilities predicted by low-quality source domain models to construct high-confidence pseudo-labels for the target domain data. Then, the batch normalized maximum mean discrepancy (BN-MMD) distance metric is introduced into the training loss function to reduce the data distribution discrepancy between the source clients and the target client without private data leakage. While building the global model in each training round, a dynamic model aggregation algorithm is proposed to mitigate the influence of low-quality clients. This algorithm evaluates the weight of each client according to its contribution to the total consensus diagnostic knowledge and then aggregates the local models with adaptive weights. Consequently, it can overcome the drawback of the classical federated averaging (FedAvg) algorithm, where all local clients are assigned the same weight when constructing the global model. Experiments are conducted on three bearing datasets under various loads and speeds. Compared with some existing diagnostic methods, the proposed federated transfer learning method can reduce the impact of low-quality data and achieve higher diagnostic accuracy while preserving data privacy. • A novel federated transfer learning method is proposed for bearing fault diagnosis. • Low-quality knowledge of some source clients is eliminated by a dynamic filter. • A dynamic model aggregation algorithm is derived to obtain an optimal global model. [ABSTRACT FROM AUTHOR]

The microphone array is widely used in acoustics as a non-contact measurement tool, which can obtain multi-dimensional information about the sound source, such as spatial, time, and frequency. The microphone array is not always used in an ideal anechoic chamber environment, making the sound source signal contaminated with the background interference. The separation of the sound source signal from the complex background interference is very challenging, especially when arrays are used in wind tunnel measurements. A probability model on the time–frequency matrix is constructed in this paper to address this issue. The background interference is constructed by the Gaussian mixture model to fit its complex probability distributions adaptively. The sound source signal is constructed as a low-rank model according to its correlation characteristics on the microphones. The distributions of parameters involved in the low-rank and Gaussian mixture model are estimated through variational Bayesian inference, which can realize the separation of the sound source signal from the complex background interference. The performance of the proposed method is evaluated by the numerical simulation and the DLR closed wind tunnel experimental. The robustness and the effectiveness of extracting the sound source signal from the complex background interference are also verified. • Complex interference suppression in the microphone array measurement is investigated. • A hierarchical parametric framework is constructed based on the low-rank and Gaussian mixture model. • The optimal model parameters are adaptively determined by the Variational Bayesian inference. • The proposed method can effectively remove the interference for acoustic imaging in the DLR wind tunnel test. [ABSTRACT FROM AUTHOR]

The Non-Synchronous Measurements is an efficient technique to improve the acoustic image of conventional beamforming for sound source localization. It is unable to quickly reveal the sound sources of the large machinery which requires a large synthetic array with many microphones to capture enough sound pressure data. In this paper, four Non-Synchronous Measurement algorithms with improved computational efficiency are demonstrated. They are implemented by combining the Alternative Direction Method of Multipliers (ADMM) method with different randomization-based acceleration strategies. The new algorithms are developed firstly by (1) using Randomized Singular Value Decomposition (RSVD) to construct the projection basis, and then by (2) migrating the computation platform from the Central Processing Unit to the Graphics Processing Unit for the Cross-Spectral Matrix completion steps, (3) accelerating the soft threshold shrinkage operator with RSVD, or (4) replacing the soft threshold shrinkage with RSVD-enhanced optimal shrinkage in the Cross-Spectral Matrix completion steps. Numerical simulations are carried out under different conditions, including the number of sequential measurement positions, the step length between two sequential measurement positions, the frequency of the sound sources, and the Signal-to-Noise Ratio of the sound pressure signals measured by the microphones. The sound source localization performance of the improved algorithms is assessed by examining their acoustic maps, and the computational performance of these algorithms is compared through their Cross-Spectral Matrix reconstruction errors and time consumption. • Four accelerated Non-Synchronous Measurement algorithms are proposed. • Proposed algorithms are based on the Randomized Singular Value Decomposition. • The matrix completion accuracy of the original algorithm are optimized. [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]

Fan noise is a predominant noise component of the aero-engine, which consists of tonal noise and broadband noise. Duct mode calculation of random broadband noise is more complex than that of tonal noise. A probabilistic approach for duct acoustic mode identification is proposed to identify duct modes of broadband fan noise with high efficiency and accuracy. The inverse problem of mode identification is represented by a Bayesian framework based on a Gaussian-scale mixture prior model. Computational complexity and consuming time are remarkably decreased by approximating the Gaussian likelihood through a surrogate function. The block coordinate descent algorithm in the majorization–minimization framework is adopted for the indirect and iterative calculation of the mode coefficients. Simulations and experiments have verified the high computational efficiency afforded by the method, which provides more accurate results for duct mode identification of broadband noise, removes the influence of interfering modes on the recognition results, and allows better observation of the characteristics of the mode in a wide range of frequencies and rotating speeds. [ABSTRACT FROM AUTHOR]

The Modal Composition Beamforming (MCB) method can quickly achieve the localization of fast-rotating sound sources; however, its low resolution and unclear applied conditions severely limit its industrial application. This study aims to investigate the MCB-based high-resolution localization method for multiple rotating sound sources and apply it to the localization and identification of axial-fan blade-noise. In this paper, the Variational Bayesian Approximation (VBA) and the Subspace Variational Bayesian Approximation (SVB) methods are used to solve the MCB-based rotating sound power propagation (RSP) model, denoted as RSP-VBA and RSP-SVB, respectively. The effectiveness of the proposed RSP-VBA and RSP-SVB are experimentally validated for the first time. Compared to the conventional MCB method, the resolution is significantly improved, and the proposed high-resolution methods are even faster than the classical Rotating Source Identifier (ROSI) method in most conditions. More importantly, the applied condition of the MCB, RSP-VBA, and RSP-SVB methods is given and verified by using three evaluation indicators. Then a schematic of the applied condition with examples is provided. With the guide of the applied conditions, the RSP-VBA and RSP-SVB methods are applied to the blade-noise localization of various multiblade high-speed axial fans. [ABSTRACT FROM AUTHOR]

• A nonconvex GMC penalty is introduced into ESM for acoustic source reconstruction. • The GMC penalty-regularized ESM is solved by an efficient ADMM framework. • The proposed method can improve the reconstruction accuracy and spatial resolution. • The feasibility of the sparsity-enhanced ESM in real scenarios is validated. The Equivalent Source Method (ESM) is a powerful technique for acoustic source reconstruction, which has been widely used in noise control and machinery fault detection. Because the inverse acoustic source reconstruction problem is typically ill-conditioned, regularization techniques are often adopted in ESM to achieve meaningful solutions. Based on the sparse distribution assumption of acoustic sources, sparse regularization can be utilized in ESM to promote the spatial resolution of reconstructed results. Existing sparse ESMs often adopt convex l 1 norm or nonconvex l p norm as the regularization terms. However, l 1 norm-regularized ESM suffers from an insufficient sparsity-inducing problem, which decreases the spatial resolution and reconstruction accuracy. Meanwhile, reconstructed results of l p norm-regularized ESM are often unstable due to multiple local minimas. In this paper, a sparsity-enhanced ESM is proposed, which introduces a nonconvex Generalized Minimax-Concave (GMC) penalty into ESM as the regularization term. The GMC penalty can enhance the sparsity of solutions and simultaneously maintain the convexity of the overall objective function in acoustic source reconstruction. Consequently, the GMC penalty-regularized ESM can improve the spatial resolution and reconstruction accuracy of the reconstructed results. To solve the acoustic source reconstruction problem rapidly, a computation framework based on Alternating Direction Method of Multipliers (ADMM) is derived. Simulation studies indicate that the proposed method can improve the acoustic source reconstruction accuracy in a wide frequency band, compared with existing l 1 and l p norm-regularized ESMs. Two experimental cases further verify that the proposed sparsity-enhanced ESM can effectively reconstruct the acoustic sources with high spatial resolution and reconstruction accuracy at higher frequencies. [ABSTRACT FROM AUTHOR]

Fault characteristic extraction of rolling bearings is essential for fault diagnosis. Rolling bearings are usually operated at changing speeds, and the nonstationary signals of the bearings are covered by the heavy background noise, making the extraction task of fault features very difficult. To address this issue, a robust fault characteristic extraction approach based on the time–frequency analysis under variable speed conditions is proposed in this paper. Firstly, the sparse property of the time-variant fault characteristics and low-rankness of background noise are explored and utilized in the time–frequency representation (TFR). Then, the sparse and the low-rank components are integrated into a hierarchical Bayesian model, and a random error term is considered to make the Bayesian model more robust. The Gibbs sampler is applied to extract the desired sparsity-enhanced component of the TFR in the Bayesian framework. Eventually, the time–frequency reassignment technique is adopted further to optimize the time–frequency resolution of the sparse component. Two simulated scenarios and a real-data experiment are used to evaluate the suggested approach's performance. It turns out that the proposed approach is robust to noise and can extract the bearing time-varying fault features effectively. • A sparsity enforced time–frequency decomposition model is constructed for bearing fault feature extraction. • The optimal model parameters can be adaptively determined by Gibbs sampler under the Bayesian framework. • The proposed method can effectively denoise and improve the time–frequency resolution of time-varying fault features. • The efficacy and superiority of the proposed method are investigated using simulated and experimental data. [ABSTRACT FROM AUTHOR]

• The proposed MR based pseudo negative stiffness control approach is one of the most practical and efficiency semi-active vibration control for stay cable. • Clarify the gain role of pseudo-negative stiffness force in stay cable vibration control in the theoretical asymptotic solution. • Establish a real-time simulation model of the stay cable coupled with time-varying control system. Stay cables are prone to large amplitude vibrations, due to their low inherent damping and high lateral flexibility. In this study, one magnetorheological (MR) damper based programmable intelligent control device is developed to control the vibration of the stay cable more practically and efficiently. The proposed programmable scheme possesses the advantages of low energy consumption, less real time calculation and dynamic input. Its control oriented dynamic model integrated with programmable pseudo negative stiffness (PNS) strategy is built. And its beneficial role in the vibration control is explained in the complex eigenvalue theory analysis of stay cable with MR damper based programmable PNS force. Finally, the simulation of dynamic response of stay cable shows the superiority of programmable control scheme. Its realization demonstrates the feasibility of the single-input programmable PNS scheme experimentally. The dynamic response simulation of stay cable shows that MR damper based PNS scheme can offer better damping performance than conventional control method and its additional damping ratio is 1.63 times higher than that of optimal MR damper passive-on control. [ABSTRACT FROM AUTHOR]