Research On Sound Field Reconstruction Algorithm Of Plane Microphone Array Sparse Equivalent Source

Acoustic imaging based on microphone arrays plays an effective role in noise control in engineering fields such as vehicles,aircrafts,high-speed rails,and ships,thanks to its ability to identify noise sources and visualize the sound field.As one of the mainstream acoustic imaging tools,Near-field Acoustical Holography（NAH）is able to perform sound pressure measurements,locate sound sources,and reconstruct sound field information in the near-field domain;the Equivalent Source Method（ESM）,a typical NAH solver,can be used to solvel₂ norm and thel₁ norm regularization inverse problem,but it is limited by practical experimental scenarios and conditions as it requires a large number of measurements to determine the sound field model parameters.With the motivation of reducing the number of microphone measurements required and the goal of improving the performance of planar acoustic array sound field reconstruction,the thesis put forward the theory and algorithm of sound field reconstruction of planar acoustic arrays characterized by underdetermined systems in the framework ofl₁ norm andl_p norm（0<p<1）.The three types of sparse equivalent source algorithms,namely thel₁ norm regularization minimization,l₁/l₂ norm scaling model,and thel_p norm minimization,are investigated.The effects of factors such as holographic distance and signal-to-noise ratio on the reconstruction performance of the sound field are analyzed,and finally the application of the sparse equivalent source method for planar acoustic arrays is extended and numerical algorithms are developed,and their correctness and effectiveness are verified by experiments.To reduce the sidelobe"ghosting"of the identification results and to focus on the acoustic center,a functional beamforming modified improved fast iterative shrinkage threshold acoustic field reconstruction algorithm（m IFISTESM-v）is proposed,that is,combining the modified improved fast iterative shrinkage/threshold equivalent source method m IFISTESM with the functional beamforming method FB,using the coefficient matrix obtained by the FB method to adjust the reconstructed sound pressure output values derived from m IFISTESM.The practicality of the proposed method is verified by numerical simulations,resolution quality analysis and experiments on monopole source localization and double source localization,showing that the proposed method can better achieve the effect of sound field reconstruction and localization and enhanced the resolution quality.To improve the resolution quality of the conventional equivalent source method in the middle-and high-frequency ranges,a fast iterative shrinkage thresholding sound field reconstruction algorithm LFISTA is proposed,using the threshold function introduced by Laplace’s law is applied to replace the threshold function of the fast iterative shrinkage thresholding algorithm（FISTA）,and then solved using FISTA;the performance of the proposed method is compared with that of the Tikhonov regularization method,the monotonic two-step iterative The performance of the proposed method is compared with the Tikhonov regularization method,the monotonic two-step iterative shrinkage thresholding method（MTw IST）,and FISTA,showing that the proposed method identifies the target sound source more accurately in the interested frequency range compared with the traditional Tikhonov regularization method;it is more adaptable than the MTw IST method in the low frequency range.In the field of sound field reconstruction,most existing methods require the selection of regularization parameters during the solution process,and the values of the regularization parameters directly affect the accuracy of the sound field reconstruction.Thel₁/l₂ norm scaling model is introduced into the sound source identification and sound field reconstruction,and the alternating direction multiplier method is used for the solution to robustly locate the sound source in the low-and middle-frequency ranges,avoiding the selection of the regularization parameters.Monte Carlo analysis shows that the proposedl₁/l₂ norm scaling model has stable sound pressure reconstruction results in the low-and middle-frequency ranges compared to three other approaches using classical penalty functions,including the Tikhonov regularization method,the iterative zoom-out shrinkage thresholding algorithm and the fast iterative shrinkage thresholding algorithm.To achieve robust sound field reconstruction and source localization in the middle-and low-frequency ranges,the fast iterative Cauchy thresholding algorithm FICTA is proposed based on the idea of Cauchy penalty model,i.e.,using the Cauchy penalty term instead ofl₁ norm penalty term to construct sound field reconstruction model.Through Monte Carlo analysis,the proposed method achieves stable sound pressure reconstruction results in the middle-and low-frequency ranges with good distance adaptation and signal-to-noise ratio adaptation for the inverse sound field reconstruction problem compared to three classical penalty function methods（Tikhonov regularization method,wideband acoustical holography and interior point method）.However,in the case of introducing thel₁norm penalty term separately:on the one hand,the sound field reconstruction results are susceptible to the interference;on the other hand,thel₁norm penalty term may underestimate the high amplitude components of the signal to be estimated,and the accuracy of the sound field reconstruction results cannot be guaranteed.To address this problem,a sound field reconstruction method based onl₁norm penalty term and Cauchy penalties（l₁-Cauchy）is proposed,i.e.,retaining both Cauchy penalty term andl₁norm penalty term when constructing the sound field reconstruction model.It fully combines thel₁norm and Cauchy penalty functions;the method can improve the sparsity of the sound source signal and better handle the parametric artifacts to avoid false detection based on ensuring the robustness of the sound field reconstruction results.Through Monte Carlo analysis,compared with three typical penalty function methods,namely Tikhonov regularization method,wideband acoustical holography（WBH）and fast iterative Cauchy threshold algorithm（FICTA）,this method obtains stable sound pressure reconstruction results in the middle-and low-frequency ranges with good distance adaptation and signal-to-noise ratio adaptation in the inverse problem of sound field reconstruction.