Journal of Theoretical and Computational Acoustics

In this work, an algorithm that combines deep-learning based dereverberation and beamforming is proposed for sound source localization in the reverberant environment. The contribution is combining deep-learning based dereverberation and beamforming together. Through deep learning, the proposed algorithm can directly achieve dereverberation of the cross-spectral matrix of microphone array measurement signals in the reverberant environment, which can overcome the challenge of requiring multiple measurements like average beamforming. In this way, the proposed algorithm can be applied to the reverberant environment that requires efficient sound source localization. At the same time, the network of deep-learning based dereverberation is trained directly using the cross-spectral matrix of signals collected by microphone arrays, which can overcome the challenge of requiring prior knowledge of reflective surfaces like empirical dereverberation beamforming. In this way, the proposed algorithm can be applied to the reverberant environment composed of walls with unknown sound reflection coefficients. Both specular reflections, diffuse reflections, and background noise are considered in the reverberant environment. The cross-spectral matrix of microphone array measurement signals in the reverberant environment is first fed into the U-net for dereverberation and then combined with beamforming for sound source localization. The results in the test set show that the proposed algorithm can eliminate the influence of reverberation on sound source localization. The applicability limitation results of the proposed algorithm show the proposed algorithm’s strong robustness to unseen sound reflection coefficient, unseen SNR, and expandability to some degree for unseen source location. However, the proposed algorithm cannot provide stable and accurate sound source localization results under unseen room geometry. The proposed algorithm has higher spatial resolution and smaller errors than the average beamforming and the empirical dereverberation beamforming.

Beamforming maps are often seriously impacted by background noise. Background Noise Subtraction (BNS), Eigenvalue Identification and Subtraction (EIS), and Eigenvalue Identification, Organization and Subtraction (EIOS) have been successively proposed and mainly used to reduce the influence of coherent background noise. In this work, an approach of Robust Principal Component Analysis (RPCA) combined with reference background noise is proposed to effectively suppress coherent background noise. The simulation results demonstrate that the most significant advantage of this method is its robustness to inaccuracies in reference background noise estimation, as it still exhibits good noise suppression performance through RPCA-based denoising. The experimental results also indicate that the Schatten-$p$ norm consistently outperforms BNS, EIS, EIOS, and nuclear norm-based RPCA in denoising performance, both when overestimating and underestimating the background noise.

In this work, the difference convex function based on capped nuclear norm minimization (CNNM-DC) method, a cross-spectral matrix (CSM) completion iterative algorithm with excellent noise immunity, is proposed to realize acoustic imaging of non-synchronous measurements (NSM) under the condition of low signal-to-noise ratio (SNR). Compared with the CSM completion algorithm based on the nuclear norm minimization (NNM) model, the truncated nuclear norm regularization (TNNR) model, and the weighted nuclear norm minimization (WNNM) model, the proposed method can obtain the acoustic image with narrow main lobes and no sidelobe under the condition of low SNR. The simulation results show that, under conditions of low SNR, the proposed method effectively reduces the width of the main lobe, suppresses the side lobes, and achieves more accurate imaging results than the previous method. Finally, experiments were conducted to verify the feasibility of CNNM-DC. The experimental results show that the proposed method is an accurate acoustic imaging algorithm for NSM under low SNR, which lays a foundation for acoustic imaging in industrial occasions with strong background noise interference.

The two-dimensional grid-free compressed sensing method with planar microphone arrays is expected to achieve super-resolution direction-of-arrival (DOA) estimation for acoustic sources in the hemispherical space in front of array. The existing methods are not yet well compatible with arbitrary planar array geometries. In this paper, we aim to break this limitation and explore a novel method applicable to arbitrary planar array geometries. First, the covariance between source-induced signals at arbitrary two microphones is formulated as related to the two-dimensional inverse Fourier transform of the source strength. Then, a mathematical model with a source sparsity constraint is built in the continuous domain to denoise the covariances of measured signals, which can be solved by decoupled positive semidefinite programming. Finally, the DOAs are extracted from the solution of the mathematical model via a matrix pencil and pairing method. Simulation and experimental results demonstrate the effectiveness of the proposed method.

When rotating noise sources, such as turbomachinery, are investigated using phased microphone array measurements and beamforming, sidelobes appear on the resulting beamforming maps. Sidelobes can be decreased by increasing the number of microphones. However, if the investigated phenomenon is steady, then there is a cost-effective alternative: performing asynchronous measurements using phased arrays having a limited number of microphones. The single beamforming maps can be combined in order to arrive at results that are superior in resolution and sidelobe levels. This technique has been investigated in the literature, but according to the authors’ best knowledge, has not yet been applied to turbomachinery. This article introduces a means for applying the asynchronous measurement technique and the combination methods for rotating noise sources. The combination methods are demonstrated on two rotating point sources (both in simulations and measurements), and then on an axial flow fan test case. In the case of the two rotating point sources, the achievable improvement in resolution, average-, and maximum sidelobe levels are shown as compared to the single results. In the case of the axial flow fan, it is demonstrated that the combination methods provide more reliable noise source locations and reveal further noise sources.

The compressive-equivalent source method (C-ESM) has been developed for the sound field reconstruction by solving the $l_1$ minimization with the predetermined sparsity of the equivalent source strengths. However, the C-ESM would reconstruct the sound field with the error proportional to the measurement noise-related data fidelity constraint that increases with the decrease of the signal-to-noise ratio. Apart from that, the reconstruction stability of the C-ESM would not be guaranteed due to the existence of the measurement noise. To address such problem, the present paper proposes a compressed separable projection-based equivalent source method. In the method, the projections of the measured pressures in the predesigned basis that combines the priors of the sound radiation of the equivalent sources and the measurement noise are obtained by solving the $l_1$ minimization. This not only leads to the data fidelity constraint being small and unrelated to the measurement noise, but also separates the measurement noise from the measured sound field. Therefore, the proposed method can theoretically reconstruct the sound field more accurately and stably than the C-ESM. Numerical simulations and experiments are carried out to verify the effectiveness of the proposed method.

In this study, a more efficient time domain (TD) virtual rotating array (VRA) method is proposed that employs a zeroth-order interpolation scheme. The interpolation of sound fields in the receiver plane using only the nearest microphone at each time step improves the efficiency of the entire process. Additionally, the VRA method is demonstrated to function well with near-field acoustic holography for localizing rotating sound sources. The proposed methods are numerically and experimentally validated. The zeroth-order interpolation scheme is compared with linear, barycentric, and radial basis function schemes using either a circular array or an arbitrary array. The holographic reconstructions are compared for selected one-third octave band center frequencies. Compressive sensing-based holography is used for increasing the resolution of the numerical simulations at low frequencies. The source strength is calculated by integrating the holographic spectra in the source plane. A comparison of the predicted source strengths and locations suggests that the zeroth-order scheme yields a more accurate solution than higher-order schemes. The proposed zeroth-order scheme and the source reconstruction using VRA signals have the potential to visualize sound fields produced by compact rotating structures.

Uncertainties are significant in the early vibroacoustic development, e.g., of a car body, to prevent costly modifications close to the start of production. First, engineers must know which uncertain parameters are sensitive: Our previous work identified 170 uncertain parameters being sensitive out of a complex finite element model with 1,300 uncertain parameters – a parameter reduction of approximately 87%. Second, engineers aim to find reliable distributions of these sensitive input parameters for finite element simulations. Finding these distributions is very demanding in a large-scale vibroacoustic model with several connecting parameters, as research already acknowledges regarding simplified connections. In this paper, we address this challenge with neural networks. For this, we use data in the frequency domain. Due to the curse of dimensionality, it is difficult to determine the parameter set of 170 parameters with a neural network. Therefore, we examine the influence of the number of parameters on the performance of neural networks. Furthermore, we train a fully connected feed-forward neural network and compare this to a one-dimensional convolutional neural network. The latter exhibits a better performance. Finally, we show how to determine distributions of the analyzed parameters based on artificial measurement data. Due to this process, we can significantly improve our finite element simulations and show how to deal with the challenge of determining uncertain parameters in a large-scale vibroacoustic finite element model based on data in the frequency domain.

The vibration-based identification method has long been used as an alternative to mechanical tests for material characterization. Its non-destructive nature, high efficiency in parameter identification of anisotropic materials and its ability to achieve structure-level homogenization make it very attractive for both academic community and industry. Due to the absence of explicit mapping from the result of vibration test to elastic constants, conventional vibration-based identification approaches generally rely on the minimization of a cost function built on modal properties or Frequency Response Function (FRF) curve. In this paper, a direct relation from FRFs to mechanical properties is established by deep neural network, which offers a new perspective to solve the inverse identification problem. Specifically, this mapping is approximately built with Multilayer Perceptrons (MLPs) and the network’s weights are learned from massive training data. The training data-i.e., the FRF curves, is generated by a finite element model whose input parameters are selected by Latin Hypercube Sampling (LHS). After training, the obtained model is validated by dataset unseen during training process and will be further used to predict mechanical properties of materials from FRFs obtained by vibration test. The effectiveness and efficiency of the developed method are demonstrated on the case study of an aluminum plate. Both the Young’s modulus and Poisson’s ratio are retrieved with high accuracy.