用于水声参量阵广角声场计算的改进轴向近似模型
An improved axial approximation model for wide-angle sound field calculation of the underwater acoustic parametric array
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摘要: 随着水声参量阵产生差频频率的降低, 波束宽度将逐步增大, 现有轴向近似模型可简化参量阵声场计算, 但受限于模型中对几何距离的轴向近似方程式, 无法在全频段保障广角计算精度。针对该问题, 提出了一种用于水声参量阵广角声场计算的改进轴向近似模型。该模型基于瑞利积分非近轴近似和虚源积分, 并应用高斯波束展开法降低积分维度。通过讨论各轴向近似模型的近似假设、计算误差, 分析参量阵广角声场计算精度。结果表明: 现有轴向近似模型的广角计算精度显著依赖于高频指向性、差频频率, 应结合应用频段选择合适模型计算广角声场; 改进轴向近似模型在任意应用频段下均可保障广角计算精度, 但计算量较大, 可作为水声参量阵广角声场的通用计算模型。实验数据验证了改进模型及广角计算精度分析结果的有效性。Abstract: As the difference-frequency of an underwater acoustic parametric array decreases, the beamwidth gradually increases. Although existing axial approximation models can simplify the calculation of the sound field of the parametric array, they are restricted by the axial approximation equation of geometric distance and cannot ensure the accuracy of wide-angle calculations in the entire frequency band. This paper proposes an improved axial approximation model to calculate the wide-angle sound field of the underwater acoustic parametric array. The model is based on the non-paraxial approximation of the Rayleigh integral and the virtual source integration. Furthermore, the Gaussian beam expansion method is applied to reduce the integration dimension. The accuracy of the wide-angle sound field calculation of the parametric array is analyzed by discussing the approximate assumptions and the calculation errors of each axis approximation model. The analysis results show that the accuracy of the wide-angle calculation of the existing axial approximation models is significantly dependent on the high-frequency directivity and the difference-frequency. A suitable model should be selected for calculating the wide-angle sound field depending on the application frequency band. The improved axial approximation model ensures accurate wide-angle calculations in any application frequency band. However, this model requires a large amount of computation and can therefore be used as a general calculation model for the wide-angle sound field of an underwater acoustic parametric array. Experimental data validate the effectiveness of the improved model and the accuracy of the wide-angle calculation analysis.