Research On The Algorithm Improvements Of Near-field Acoustical Holography Based On Equivalent Source Method

The accurate identification and location of the source is the prerequisite for control noise.Near-field acoustic holography(NAH)based on microphone arrays is an effective tool for identifying sound sources and visualizing sound fields,and has been widely used in automobile and other fields.In the implementation algorithms of NAH,the equivalent source method(ESM)is appealing for its simplicity,computational efficiency,and the adaptability to arbitrarily shaped sources.The core of ESM is to solve the equivalent source strength,and different algorithms will bring different effects of sound field reconstruction.In this paper,three common algorithms of the ESM,named conventional ESM with Tikhonov regularization(TRESM),sparse equivalent source method based on CVX toolbox(ESM based on CVX)and Wideband acoustical holography(WBH),are compared and analyzed.The purpose of this paper is to improve the ESM,enhance the performance of sound field reconstruction and source identification,and broaden the application range of NAH based on ESM.Aiming at the application limitations of TRESM,ESM-based on CVX and WBH,an alternating iteration equivalent source method(AIESM)is proposed in the sparse framework to improve the performance of sound field reconstruction and source identification in a relatively wide frequency range,especially in low-medium frequencies.Meanwhile,combining the advantage of Functional beamforming(FB),AIESM-can possess a high dynamic range when detecting the source location.The validity of AIESM/AIESM-are verified by simulations and experiments with single and double coherent sources.For spatially extended sound source,a compressed singular value decomposition equivalent source method(CSVDESM)is proposed to reconstruct the sound field.A series of orthogonal basis of sound field are obtained by singular value decomposition(SVD),and accurate reconstruction of sound field is achieved by combining the equivalent source method with compressive sensing(CS)theory.A number of simulations and experiments are performed on structural plates.The results show that compared with CESM and TRESM,CSVDESM has higher accuracy of sound field reconstruction in a relatively wide frequency range.Compared with CMESM,the orthogonal basis constructed in CSVDESM contains more phase information and thus has more advantages in the sound field reconstruction of spatially extended sound source.Considering that in the practical acoustic applications,it is not easy to find the appropriate basis or dictionary due to the indeterminate characteristics of the source.In this paper,a new equivalent redundancy dictionary is constructed by combining the advantages of the CESM and the CSVDESM.Based on this quivalent redundant dictionary,the ERDCESM method is proposed to reconstruct the sound field of different types of sound sources.Finally,inspired by the idea of FB,a reformative method,named ERDCESM-is developed in this paper.In the measurements,a single source was selected to simulate the sparse source,and a simple supported plate was used as a type of spatially extended source.The results show that the reconstruction accuracy of ERDCESM is similar to that of CESM and significantly higher than that of TRESM and CMESM for spatially sparse sound sources.The application of ERDCESM-can further improve the location accuracy and dynamic range when detecting the source location.For spatially extended source(simply supported plate source),ERDCESM performs better reconstrction effects than the other three methods(TRESM,CESM,CMESM).With the order increasing,the coverage of the identified acoustic center was narrowed gradually.Therefore,the maximum area of sound pressure distribution can be located by increasing order,which provided direction for the optimization and improvement of structural panels.Finally,a series of experiments are carried out,and the results also verify the validity and practicability of ERDCESM for different types of sound sources.