基于HELS法的多源相干声场重建研究

STUDY ON RECONSTRUCTION OF COHERENT ACOUSTIC FIELD WITH MULTI-SOURCE BASED ON HELMHOLTZ EQUATION AND LEAST SQUARE METHOD

针对Helmholtz方程最小二乘法(HELS)对多源相干声场进行重建无法得到满意的结果这一问题,提出一种改进的HELS方法。其基本思想是,辐射声场由多个相干声源产生的一系列声场叠加而成,每个声源产生的声压可以用球面波函数构成的正交函数的线性组合表达。组合系数可通过测点的声压来确定。采用预估基函数展开项数和循环迭代法相结合的优化方法确定基函数的最佳项数,提高了计算效率。在求解系数向量的过程中采用奇异值分解和正则化方法,减轻了逆问题求解过程中产生的不适定问题。数值仿真表明,改进的HELS方法能有效地重建多源相干声场,并可估计每个声源对声场的贡献,具有声场分离的作用。

A modified Helmholtz Equation Least Square(HELS) method is suggested to reconstruct a coherent acoustic field which is reconstructed badly by the original HELS method.The modified HELS method is based on the assumption that the stimulant sound field is the superposition of the sound fields induced by multiple coherent acoustic sources and the pressure produced by the sources can be expressed as an expansion of the particular solutions to Helmholtz equation.The related coefficients can be determined by the measurement of pressure in the field.A loop iteration method is proposed to optimize the number of expansion ferms.The singular value decomposition and regularization are suggested to alleviate the illposed nature in the inverse problem.The contribution of each source can be evaluated and the exterior field can be predicted by the modified HELS method.The simulation shows the validity of the modified HELS method for the coherent acoustic field with multiple sources.