Research On Near-Field Acoustical Holography Based On Sparse Sampling And Fast Wave Superposition Spectrum

Near field acoustic holography is a powerful technique for identifying and locating noise sources and visualizing sound field.By measuring the relative acoustic quantities(complex sound pressure,sound intensity or particle velocity)of the near-field region of the vibrator,and then using the sound field reconstruction algorithm,the relative acoustic quantities of the vibrator surface and any point in the whole sound field can be obtained,which has great application potential and development space in the field of noise control.In recent decades,after in-depth research,scholars at home and abroad have proposed the near-field acoustic holography based on spatial Fourier transform,the near-field acoustic holography based on boundary element method,and the near-field acoustic holography based on equivalent source method.Among them,the equivalent source method has been widely used in recent years because of its advantages of simple calculation and strong adaptability.However,the equivalent source method is ill posed in the inverse problem of sound field reconstruction,and the minimum measurement noise will lead to complete distortion of reconstruction results.In order to solve this problem,a regularization method based on least squares is used to get a stable approximate solution.In the near-field acoustic holography based on the equivalent source method,the virtual source intensity is usually discretized in the form of element values,which will have a certain impact on the reconstruction results,especially in the high-frequency acoustic field reconstruction.Therefore,in order to ensure the reconstruction accuracy of this method,there must be enough measurement points and equivalent source points.However,the number of measurement points is usually limited by the measurement conditions,the actual measurement cost and other factors,so it is difficult to get the overdetermined equations with the number of measurement points larger than the number of source strength points.At this time,it is difficult to get ideal results if the least square method is used to solve the above equations.In order to solve this problem,the equivalent source intensity and integral kernel function are expanded by bidirectional Fourier series on the axisymmetric virtual plane,so that the source intensity vector is transformed into sparse Fourier expansion coefficient vector.Combined with the compressed sensing reconstruction algorithm,a semi analytical and semi numerical equivalent source near-field acoustic holography method based on compressed sensing and fast wave superposition spectrum is established.Compared with the traditional method,this method can also ensure high reconstruction accuracy and good anti-noise performance under the condition of less measurement points.The main research work and chapters are as follows(1)Firstly,the background and research status of near-field acoustic holography are introduced,and the related problems in practical application are analyzed.Then,the theory of compressed sensing and its application in near-field acoustic holography are introduced.At the same time,the problems in practical application are discussed.In view of the above problems,the main research direction and content of this paper are determined.(2)A near-field acoustic holography based on sparse sampling and fast wave superposition spectrum method is proposed.In this method,the equivalent source intensity and the integral kernel function are expanded by Fourier series along the circumferential and meridian directions on the axisymmetric virtual plane,and the sound pressure expression in the form of Fourier series is obtained.Because this method is a semi analytical and semi numerical method,it has higher accuracy than the traditional method.At the same time,the unknown source intensity vector is transformed into sparse Fourier expansion coefficient vector,which can be combined with the reconstruction algorithm of compressed sensing theory to reconstruct the sound field.Numerical simulation shows the effectiveness and superiority of the method.(3)A planar near-field acoustic holography based on sparse sampling and fast wave superposition spectrum method is proposed.In this method,the source intensity of the equivalent source method is expanded by the bidirectional Fourier series on the rectangular virtual surface,so that the source intensity vector to be solved is transformed into the sparse Fourier expansion coefficient vector,which is solved by the compressed sensing reconstruction algorithm.The effectiveness and superiority of the proposed method are analyzed and verified by numerical simulation.The results show that the proposed method has higher accuracy than the traditional compressed equivalent source method in the whole analysis frequency band.(4)On the basis of the previous paper,a series of "acoustic mode" sparse bases obtained by singular value decomposition(SVD)of the transfer matrix are introduced into this method,and then a sparse sampling sound field reconstruction method based on SVD and fast wave superposition spectrum is established.The effectiveness and superiority of the improved method are verified by numerical simulation.The results show that the reconstruction result of the improved method is more robust than that of the proposed method without sparse basis.(5)The main research work of this paper is summarized,and the future research direction is put forward.