Research On Fast Iterative Shrinkage Thresholding Algorithm Based Beamforming Sound Source Identification Method

Beamforming is an array-based measurement technology and has become indispensable in the acoustic source identification in some fields such as aviation aircraft,express train,wind turbine and automobile over the last decades,for its advantages of fast measuring speed,high calculation efficiency and being suitable for middle and long distance measurement.Its basic idea is that beamforming uses spatially distributed microphones to receive acoustic source pressure signal,forms focus grid points by making the target signal discrete and post-processing the data by focusing each mesh point reversely based on a specific algorithm.So that the true source of focus point is strengthening,formed the main lobe,and the other focal point of the output is attenuated to form the sidelobe.Due to the finiteness and dispersion of the array microphone sampling,the output of the conventional beamforming cannot be equal to the ideal ? function.The width of the main lobe affects the spatial resolution of the sound source identification,and the side lobes appear to contaminate the sound source imaging map.And in the actual non-ideal measurement environment,in addition to receiving the acoustic signal radiated by the target sound source,the array microphones are inevitably subject to some external interference,and the output of each focused grid point contains both the target of interest.The information of the sound source also contains external interference information,which increases the uncertainty of the target sound source identification and reduces the accuracy and applicability of the sound source identification.Therefore,extending the application scenarios of the conventional beamforming sound source identification method,reducing the main lobe width,improving the spatial resolution,enhancing the suppression of ghosting and antiinterference ability have become the hot and difficult points of the current sound source identification research.In view of this,this paper aims to improve the sound source recognition performance of beamforming sound source identification method.Based on the deconvolution beamforming sound source identification method and the iterative shrinkage threshold theory,considering the sparseness of sound source,three fast iterative shrinkage threshold sound source identification methods are proposed.The reflection of acoustic source signals coming from the ground is a very signification aspect to the experiment measurement and it may affect the identification accuracy of conventional beamforming algorithm.In order to eliminate the influence of ground reflection on beamforming acoustic source identification results,a mirror ground beamforming method is provided.Furthermore,in order to improve the sound source identification performance of beamforming when there is reflection on the ground,the array point propagation function of the mirror image beamforming is derived,and the mirroring deconvolution beamforming method of mirror ground beamforming is given.The DAMAS and NNLS deconvolution beamforming algorithms can effectively solve the defects of conventional beamforming main lobe width,low resolution and wide range of side lobe coverage.The fast deconvolution algorithm based on the assumption of invariance of space transfer of point propagation function,the time domain convolution is transformed into the wavenumber domain product,can improve the computational efficiency of the deconvolution algorithm by reducing the operation of large dimension matrix.and the computation efficiency can be improved.According to the defects caused by the space transfer invariance assumption of point spread function,combined with the irregular focus point mesh,the theoretical and simulation analysis of the fast deconvolution beamforming recognition performance is carried out.Simulation and experimental results show that the performace of FFT-NNLS is slightly better than that of DAMAS2.In addition,in order to improve the acoustic source identification performance of beamforming when ground reflection exists,the array point spread function of mirror ground beamforming was derived and the corresponding deconvolution method based on non-negative least squares was given.In order to further improve the computational efficiency and resolution of deconvolution beamforming method,based on the theory of fast iterative shrinkage threshold,the theoretical formulas of zero boundary condition and periodic boundary condition are deduced,and the FFT-FISTA deconvolution beamforming algorithm based on zero boundary condition and periodic boundary condition is proposed.From the perspective of sound source identification,when the sound source is far away from the acoustic imaging center,the proposed FFT-FISTA sound source identification performance based on periodic boundary conditions is optimal.Compared with the calculation time of DAMAS2 and FFT-NNLS,the proposed FFT-FISTA based on periodic boundary conditions is the most efficient.On the basis of conventional beamforming theory and IFISTA deconvolution theory,,the Fourier transform theory formula based on periodic boundary conditions is deduced,and a FFT-IFISTA method with higher computational efficiency and better convergence characteristics is proposed.Compared with other deconvolution methods such as DAMAS2,FFT-NNLS,FFT-FISTA,FFT-IFISTA has higher computational efficiency,better convergence,faster convergence speed and better comprehensive performance of sound source identification.With the increase of weight coefficient,the less iterations needed to stabilize,the narrower the main lobe width obtained by FFT-IFISTA method and the better convergence,but the ghost shadow also increases.Increasing the weight coefficient can improve the convergence of FFT-IFISTA,but if the weight coefficient is too large,the convergence will become worse.Furthermore,considering that the main noise sources usually have sparse spatial distribution,SFISTA is applied to the beamforming sound source identification,and a new SFISTA deconvolution sound source recognition algorithm with better convergence and higher amplitude accuracy is proposed.The influence of smoothing parameter ? and regularization parameter ? on the performance of sound source identification is analyzed,and the recommended values are given.The influence of signal-to-noise ratio(SNR)on the identification performance of sound source is analyzed,and the accuracy of amplitude quantization is compared with SC-DAMAS,FISTA and IFISTA.The results show that the proposed SFISTA deconvolution method has the best comprehensive performance of sound source identification.In addition,comparisons between convergence and computational efficiency are made with FISTA and IFISTA.The results show that the standard deviation of SFISTA declines fastest,and the standard deviation of timeconsuming and stable is similar to that of IFISTA,which is higher than FISTA.