Research On Theory And Algorithm Of Acoustic Source Identification Using Spherical Arrays Based On Sparse Representation

By virtue of excellent features of the completed acquisition on sound field information and the omni-directional source identification,the acoustic source identification technology using rigid spherical microphone arrays?spherical arrays?has played an important role in the interior/cabin noise source identification,such as aircrafts,high-speed trains,and automobiles.Equivalent source method and spherical harmonics beamforming are the classical methods for acoustic source identification with spherical arrays.However,the former has the shortcomings of the narrow frequency range and small hologram distances,while the latter suffers from some shortcomings,in terms of terrible high-frequency spurious sources,poor low-frequency spatial resolution,and defective ability to identify radial distance.Therefore,the explorations on acoustic source identification methods using spherical arrays have become hot and difficult points,aiming at wide frequency range,high identification accuracy,good robustness,high computational efficiency,and strong suppression on spurious sources.In view of this,this dissertation aims at improving the acoustic source identification performance using spherical arrays.Based on the mathematical models of the spherical equivalent source method and the spherical beamforming,the dissertation establishes the new theories and algorithms on the basis of sparse representation for acoustic source identification using spherical arrays,by utilizing the fact that the main sources usually have spatially sparse distributions.Firstly,the reconstruction performance is analyzed for the newly proposed Spherical Equivalent Source Method based on Tikhonov Regularization?TR-S-ESM?.The results indicate that TR-S-ESM has good performance of sound field reconstruction and acoustic source identification at low frequencies and small hologram distances,but it is difficult to achieve acoustic source identification at medium-high frequencies and large hologram distances.To improve the acoustic source identification of TR-S-ESM,a WBH-S-ESM method is proposed based on Wideband Holography?WBH?solution,which combines the sparse representation frameworks of the steepest descent method and the iterative hard thresholding.The performance of the proposed method is compared with that of TR-S-ESM.The results show that the upper limit and applicable distance of WBH-S-ESM are improved significantly.WBH-S-ESM can achieve good acoustic source identification at the hologram distance up to 5 times the array radius for the medium-high frequencies,but its low-frequency performance is still poor for acoustic source identification.To further improve the acoustic source identification of S-ESM at low frequencies and large hologram distances,IRLS-S-ESM and w-l₁-S-ESM are proposed based on the Iteratively Reweighted Least Squares?IRLS?and Iteratively Reweightedl₁-norm minimization?w-l₁-norm?solutions,which are also formulated in the framework of sparse representation.The effects of source frequency,hologram distance and signal-to-noise ratio?SNR?on the acoustic source identification are investigated.The results indicate that the proposed methods enjoy better identification accuracy,spatial resolution,applicable frequency and hologram distance.They can achieve good acoustic source identification in the wide frequency range and large hologram distances.Hence,the application scopes of the four S-ESM methods are ascertained.For low frequencies and small hologram distances,w-l₁-S-ESM and IRLS-S-ESM are better than TR-S-ESM,and WBH-S-ESM is the worst.For low frequencies and large hologram distances,w-l₁-S-ESM and IRLS-S-ESM are significantly better than TR-S-ESM and WBH-S-ESM.For medium-high frequencies,w-l₁-S-ESM,IRLS-S-ESM and WBH-S-ESM have similar overall performance,while TR-ESM fails.To improve the accuracy of the acoustic source identification using spherical beamforming,a two-dimensional Compressive Spherical Beamforming?2D CSB?method is proposed based on spherical wave propagation,compressive sensing theory,and 2D spherical focusing grid model.Pressure contribution is introduced as its beamforming output,and the three sparse recovery algorithms are employed to solve 2D CSB,namely,Orthogonal Matching Pursuit?OMP?,generalized Orthogonal Matching Pursuit?gOMP?,and w-l₁-norm.The numerical and experimental results show that 2D CSB can quantify the pressure contribution accurately,and overcome the adverse effects caused by the inconsistency between the focus distance and the radial distance.Compared with spherical harmonics beamforming,the 2D CSB method based on spherical imaging has higher identification accuracy,better spatial resolution,strong sidelobes and noise suppression.gOMP circumvents biased localization?compared to OMP?,although the adaptability to noise is inferior to OMP.w-l₁-norm outperforms the other solution algorithms at low SNR of 10 dB,but the computational efficiency is far less than OMP and gOMP.On this basis,a three-dimensional compression spherical beamforming?3D CSB?is proposed by developing a 3D volumetric focusing grid model.Source strength is directly employed as the beamforming output.Then,the influence of the sensing matrix coherence on the acoustic source identification is investigated.The 3D CSB method based on volumetric imaging can realize 3D localization at some cases,and quantify the source strength directly.However,the robustness of the source localization is significantly affected by the source locations,noise interference,and sensing matrix coherence.Finally,to enhance the robustness of 3D CSB,a high-dimensional and highly coherent mathematical model is established for 3D CSB in full three-dimensional space domains covering the spherical harmonics and radial distances domains,which is on the basis of the multi-snapshots observation signals and the principal component analysis pretreatment.With high tolerance to the high coherence in the columns of the sensing matrix,Sparse Bayesian Learning?SBL?is developed to solve that troublesome mathematical model.Multi-snapshots 3D CSB method using SBL is hereby proposed for 3D acoustic source identification.Then,the effects of SNR,snapshot numbers,nearby sources,and radial distances on the acoustic source identification are analyzed.The results indicate that the proposed multi-snapshots 3D CSB using SBL achieves robust acoustic source identification,and improves the accuracy of the source localization and quantization in three-dimensional spaces significantly.