基于无参考信号的传声器阵列序列测量理论与方法研究

Inverse acoustic reconstruction consists in measuring the acoustic quantity in the field by a sensor array (forward problem) and reconstructing the image of noise sources by back-propagation algorithms (inverse problem), which has a wide range of applications in machine fault diagnosis, identification of vibration excitations. A fundamental limitation of the inverse acoustic problem is determined by the size of the array and the microphone density. A solution proposed in this project to achieve large array and/or high microphone density is to scan the object of interest by moving sequentially a small prototype array, which is referred to as sequential measurements. The main issues of sequential measurements is that the phase information is missed due to the asynchronous measurements and scattering errors of microphones measurement at high frequency. In this project, these problems are tried to be solved based on the Empirical Bayes theory. First, the physical sources are modeled as low dimensional source of statistical representation; second, the statistical representation of acoustical source, propagation function and the sequential measurements are modeled as the forward problem; last, the acoustical sources are reconstructed by Empirical Bayes theory. The three contribution of this project is as follows: (1) the uncertainties of sequential measurements are modeled under the Empirical Bayes framework; (2) the missing phases during the asynchronous measurements are reconstructed by the rebuilt statistical forward model of sequential measurements; (3) scattering errors of microphones measurement at high frequency is modeled into the statistical forward model of sequential measurements, which make the proposed methodology with the potential to be applied at high frequency. The proposed methodology will be validated both in simulation and laboratory experiment.

声源成像理论在噪声源可视化、定位（或者量化噪声）以及故障诊断等领域有广泛的应用。在传统声源成像理论中，声源成像分辨率受到传声器阵列空间采样分辨率限制，即声源成像分辨率受阵列的孔径大小与传声器个数限制。本项目针对声源成像分辨率限制这个基本问题，研究针对声源高分辨率成像的传声器阵列无参考序列测量理论与方法。通过多次序列的移动单个基本传声器阵列，组成一个传声器阵列孔径尺寸足够大，传声器分布密度足够高的合成传声器阵列，从而提高单个传声器阵列的空间采样率和声源的成像分辨率。围绕传声器阵列序列测量中导致的空间相位信息丢失（异步测量在无参考信号下无法同步空间信号相位）与在高频测量时产生的高频散射两大关键科学问题，基于经验贝叶斯理论，分别对声源、声场的传播模型以及序列测量进行统计建模，将相位信息丢失与高频散射误差建模到提出的前向模型并求解反问题，建立基于无参考信号的传声器阵列序列测量理论与方法。

声源成像理论在噪声源可视化、定位（或者量化噪声）以及故障诊断等领域有广泛的应用。在传统声源成像理论中，声源成像分辨率受到传声器阵列空间采样分辨率限制，即声源成像分辨率受阵列的孔径大小与传声器个数限制。本项目针对声源成像分辨率限制这个基本问题，研究针对声源高分辨率成像的传声器阵列非同步测量理论与方法。本课题的主要研究内容及相应的结论如下：.（1）基于经验贝叶斯框架，建立了声源的统计模型，提出了确定性空间基展开与空间系数的低维模型分解（数据基与随机系数的组合），发展了基于测量数据的随机变量概率分布函数的超参数的估计方法。仿真与实验结果表明了该理论模型的正确性。.（2）基于声源的统计表达模型与瑞利积分公式，在非同步测量的非均匀噪声随机场假设下提出了随机过程模型，建立了声源统计模型到非同步测量模型的前向模型，解决了非同步测量中空间相位信息丢失的问题。提出的CP、FISTA、ALM以及ADMM矩阵补全迭代算法成功应用于非同步测量，FISTA无需声源数量的先验条件，ALM和ADMM在此基础上优化了迭代速度。仿真与实验验证了算法和该理论模型的正确性。.（3）基于非同步测量方法，研究了基于经验贝叶斯的反问题求解，建立了似然函数、先验分布和模型证据的全贝叶斯表达，提出了基于变分推断的求解算法。仿真和实验结果表明，基于非同步测量的贝叶斯推理方法（Bi-NAM）能在低频和低信噪比下，得到高分辨率声成像，其改进的变分贝叶斯推理方法 (VB-NAM ) 加快了迭代速度，计算时间减半。.（4）提出了将非同步测量用于3D波束形成，发展了从2D到3D的常规波束成形。通过在空间中移动传声器阵列，非同步测量可以显著提高平面阵列在法线方向上的空间定位分辨率。