Research On Three-dimensional Sound Field Reconstruction Method Based On Bayesian Theory

As a main tool for identifying and locating noise sources,near-field acoustic holography plays an important role in industrial production,machining of mechanical equipment and components,and product quality evaluation.The spherical equivalent source method,which combines the traditional equivalent source method with a spherical array and achieves three-dimensional acoustic field reconstruction through a spatial transformation algorithm,is currently widely used in near-field acoustic holography.In order to further improve the accuracy of spherical equivalent source method for three-dimensional acoustic field reconstruction,this paper established a theoretical model of acoustic field reconstruction based on Bayesian theory to address the ill posed problems in its acoustic field reconstruction process.The optimal Bayesian regularization parameter selection method was deeply studied and developed.The effectiveness and feasibility of the proposed method were verified by MATLAB simulation and anechoic chamber experiments.The main research work of this dissertation is as follows:(1)A theoretical model of sound field reconstruction based on Bayesian theory is established.Firstly,the acoustic radiation theory of vibrating bodies is introduced,and a theoretical framework for acoustic field reconstruction is constructed.The equivalent source method is used to reconstruct the acoustic field;The relationship between sound source surface,holographic surface,and reconstruction surface is described.The ill conditioned problems in the process of sound field reconstruction are pointed out,and the regularization methods are introduced.Using Bayesian theory and its basic ideas,theoretical derivation of sound field reconstruction is carried out,and it is further proposed that the Bayesian regularization parameter selection method can be used as the optimal parameter selection method.By constructing a cost function and using marginal likelihood maximization,the optimal regularization parameters are obtained,successfully solving the pathological problems in the process of sound field reconstruction,and achieving high-precision sound field reconstruction.(2)The numerical simulation of the Bayesian regularization parameter selection method in the spherical equivalent source method was carried out.By using Tikhonov regularization and damped singular value decomposition methods,Bayesian regularization is applied as the optimal regularization parameter selection method to the two regularization methods,respectively,to verify their effectiveness;The numerical simulation is compared with the commonly used generalized cross validation method under different sound source frequencies and distances.The results show that the Bayesian regularization parameter selection method has more advantages than the generalized cross validation method.By changing the signal-to-noise ratio,it is verified that the combination of Bayesian regularization parameter selection method and Tikhonov regularization has the best robustness in three-dimensional sound field reconstruction.(3)Using a hollow sphere array as the measurement array,the acoustic field reconstruction experiment was conducted.The real-time sound pressure measured in a fully anechoic room is converted into complex sound pressure through Fourier transform.The theoretical sound pressure levels at sound source frequencies of 100 Hz,500 Hz,and 800 Hz,corresponding to sound source distances of 0.36 m and 0.41 m,were compared with the reconstructed sound pressure levels,verifying the effectiveness,superiority,and robustness of the Bayesian regularization parameter selection method in three-dimensional sound field reconstruction.