Research On Meshless Wave Function Equivalent Source Method For Near-field Acoustic Holography

Near-field acoustic holography is a very effective sound field visualization technology for sound source identification and localization,and is widely used in noise identification and sound field reconstruction in machinery,ships and aviation.After decades of research and development,various algorithms applied to near-field acoustic holography have been proposed,which play an important role in the promotion and application of near-field acoustic holography.Among them,the near-field acoustic holography algorithm based on the equivalent source method has received extensive attention in recent years because of its great advantages in numerical calculation and applicability over other algorithms.The equivalent source method,also known as source intensity simulation technology,is based on the principle that a series of virtual sources are arranged outside the solution domain to equivalent or simulate the sound field radiated by the real sound source.However,the selection of virtual source type in the equivalent source method has a significant impact on its calculation accuracy and efficiency.At present,there are three types of virtual sources:(1)The surface source is used as the virtual source,which is generally called the wave superposition method.This method requires element interpolation processing and numerical integration calculation,and the calculation efficiency is low.(2)The surface source is simplified into a simple source(monopole,dipole,etc.)as a virtual source.This method avoids element interpolation and numerical integration,and effectively improves the computational efficiency.However,due to the existence of integral approximation error,the calculation accuracy is lost.(3)Orthogonal spherical wave sources are used as virtual sources(single-point multi-pole method,multi-point multi-pole method,etc.).This method also does not require numerical integration,and because the spherical wave source has orthogonality,its coefficient matrix has good solution characteristics.However,the single-point multipole method has poor convergence for the calculation of sound sources with large length-width ratio,which affects the calculation accuracy and stability.The selection of the position and order of the spherical wave source in the multi-point multipole method is cumbersome,which increases the application cost of the method.In this paper,the theoretical analysis and comparative study of the common algorithms of the near-field acoustic holography of the above three commonly used equivalent source methods are carried out.Then,from the perspective of both calculation accuracy and calculation efficiency,a unit wave function superposition method is proposed by combining the advantages of the three methods.The idea of this method is to construct a wave function equivalent to the element integral sound pressure field instead of the element integral,so that the calculation accuracy equivalent to the element integral can be obtained efficiently without numerical integration calculation for each element.In this paper,the triangular constant element and rectangular constant element commonly used in near-field acoustic holography are taken as examples.The orthogonal spherical wave is used to construct the element extrapolation wave function based on the free-field Green ’s function.In order to further improve the efficiency of the wave function solution,a more efficient extrapolation wave function is constructed by using the far-field analytical formula of the unit radiation sound field.The sound field calculation of a single element is compared.The results show that the calculation accuracy of the element extrapolation wave function is equivalent to the extrapolation wave function,and the calculation efficiency is higher than the extrapolation wave function method and direct integration calculation.In the near-field acoustic holography based on the wave superposition method,the influence on the sound field reconstruction is mainly concentrated in the main directivity range of the virtual surface source.Therefore,the triangular constant element and the rectangular constant element can be approximated as an equivalent circular surface source with the same area to calculate the radiated sound field within the main directivity range of the element.Based on the wave function of the circular surface source,a meshless wave function method is proposed by combining the meshless characteristics of the monopole equivalent source method,so that the wave function construction is no longer dependent on the discrete elements on the virtual boundary.Finally,the meshless wave function method is applied to the numerical simulation of near-field acoustic holography.The calculation results show that the meshless wave function method takes into account the advantages of the calculation accuracy of the traditional wave superposition method and the calculation efficiency of the monopole equivalent method.It is a wider and more efficient sound field calculation method.