AI 中文总结
研究利用心形麦克风对基于C-C方法估计声学强度，针对实际麦克风指向性误差问题提出基于球形紧框架配置的测量框架，通过多轴分量组合重构强度矢量，引入泄漏度量量化误差抑制能力，有效抑制误差实现准确宽带估计。
AI 中文摘要
本文基于心形-心形（C-C）方法研究使用心形麦克风对进行声学强度估计。与传统的压差技术不同，C-C方法对麦克风间距和声波长之间的关系本质上不太敏感。然而，实际麦克风不可避免地偏离理想心形指向性，产生方向依赖性估计误差。为提高对此类误差的鲁棒性，提出基于球形紧框架麦克风配置的测量框架。沿多个轴测量的方向强度分量被组合以重构三维声学强度矢量。此外，使用勒让德多项式和球谐展开表示指向性误差，并引入几何相关泄漏度量来量化不同麦克风布置抑制误差的能力。理论分析和数值模拟表明紧框架配置通过几何平均有效抑制方向依赖性误差。所提出的泄漏度量成功预测麦克风指向性缺陷对重构强度矢量的影响。结果还表明即使麦克风间距相对较大也能实现准确的宽带声学强度估计，这在传统压差方法中通常不实用。所提出的框架为使用定向麦克风阵列进行声学强度测量提供了一种具有物理可解释性和实际实用性的方法。
英文摘要
This paper investigates acoustic intensity estimation using pairs of cardioid microphones based on the cardioid-cardioid (C-C) method. Unlike conventional pressure-difference techniques, the C-C method is intrinsically less sensitive to the relationship between microphone spacing and acoustic wavelength. However, practical microphones inevitably deviate from ideal cardioid directivity, producing direction-dependent estimation errors. To improve robustness against such errors, a measurement framework based on spherical tight-frame microphone configurations is proposed. Directional intensity components measured along multiple axes are combined to reconstruct the three-dimensional acoustic intensity vector. Furthermore, directivity errors are represented using Legendre polynomial and spherical harmonic expansions, and a geometry-dependent leakage metric is introduced to quantify the error-suppression capability of different microphone arrangements. Theoretical analysis and numerical simulations demonstrate that tight-frame configurations effectively suppress direction-dependent errors through geometric averaging. The proposed leakage metric provides a qualitative indication of microphone directivity imperfections on the reconstructed intensity vector. The results further indicate that accurate wide-band acoustic-intensity estimation can be achieved even with relatively large microphone spacings, which are generally impractical in conventional pressure-difference approaches. The proposed framework provides a physically interpretable and practically useful approach for acoustic intensity measurement using directional microphone arrays.
CommentsAccepted for publication in Acoustical Science and Technology on August 22, 2026
