球面阵压缩波束形成声源识别理论及算法研究

The conventional algorithms of beamforming acoustic source identification technology with spherical arrays suffer from poor spatial resolution and severe sidelobe contaminations, which make it difficult to identify sources definitely. Some remedial algorithms have been proposed, but they present some new intrinsic drawbacks, specifically poor availability for coherent sources and low robustness for non-stationary sources. Consequently, the application of this technology is limited. The existing researches on beamforming with one-dimensional linear and two-dimensional planar arrays give out an inspiration that the compressive sensing based beamforming promises to solve the problem. Therefore, this project will focus on building a complete compressive beamforming theory for acoustic source identification with spherical arrays and forming a numerical algorithm. First, the sensing matrix of spherical arrays is deduced. Then, a mathematic model is built for compressive beamforming acoustic source identification. Next, fast, accurate and robust methods are explored to solve the mathematic model. Subsequently, the influence rules and mechanisms of typical geometrical and testing factors on the identification performance are revealed. Both example experiments and engineering application experiments will be utilized to examine the correctness, validity, practicability and superiority of the built theory and algorithm. The research achievements will be of great significance to the perfection of the acoustic source identification function of spherical arrays, help to identify noise sources in complicated three-dimensional environments, like in a car or an airplane, more accurately and effectively, and ultimately make positive contributions to the development of the noise test, analysis and control discipline.

运用球面阵波束形成技术识别声源时，传统算法的结果因受低空间分辨率及高旁瓣污染的影响而承受严重不确定性，已有的清晰化改进算法存在无法准确识别相干声源、无法稳健识别非稳态声源的固有缺陷，最终致使该技术的应用受限。关于一维线阵及二维平面阵波束形成技术的已有研究启示：基于压缩感知理论的压缩波束形成有望解决上述问题。鉴于此，本项目推导构建球面阵声源识别的感知矩阵，建立球面阵压缩波束形成声源识别数学模型，探索准确快速稳健的数学模型求解方法，揭示典型几何因素及测试因素对声源识别性能的影响规律，探明影响机理，最终建立完整的球面阵压缩波束形成声源识别理论、形成数值算法，并基于算例验证试验及工程应用试验检验其正确性、有效性、实用性及优越性。项目研究成果对完善球面阵声源识别功能具有重要意义，有助于更准确有效地识别诸如飞机客舱、汽车驾驶室等复杂三维声学环境内的噪声源，为噪声测试、分析及控制学科的发展做出积极贡献。

基于传声器阵列测量的波束形成技术被广泛应用于军事、工业、环境等领域的噪声源识别。在已有的众多传声器阵列形式中，球面传声器阵列(球面阵)凭借旋转对称性好、声场记录全面、可全景识别声源等优势备受关注。申请项目围绕球面阵压缩波束形成声源识别理论及算法，综合运用理论推导、数学建模、数值模拟、试验验证等方法开展研究，先后建立了球面阵定网格在网和无网格压缩波束形成声源识别方法。首先，在离散压缩感知框架下，推导构建了球面阵定网格在网压缩波束形成声源识别的数学模型，建立并发展了正交匹配追踪、自适应同伦、迭代重加权L1范数最小化、稀疏贝叶斯学习等多种数学模型求解方法，揭示了典型几何因素及测试因素对各种算法下声源识别性能的影响规律并探明了影响机理。在此基础上，为解决球面阵定网格在网压缩波束形成方法存在的基不匹配缺陷，申请项目基于球谐函数的特殊结构，建立可转化为半正定规划进行求解的基于原子范数最小化(ANM)的传声器测量声压信号去噪声数学模型，发展基于交替方向乘子方法(ADMM)的半正定规划求解器，引入球面旋转不变参数估计(ESPRIT)后处理求解结果来提取声源波达方向(DOA)进而量化声源强度，最终建立了球面阵无网格连续压缩波束形成声源识别方法。项目研究成果对完善球面阵声源识别功能具有重要意义，有助于更准确有效地识别诸如飞机客舱、汽车驾驶室等复杂三维声学环境内的噪声源，为噪声测试、分析及控制学科的发展做出了积极贡献。