基于张量分解的简正波模态参数估计  

Tensor decomposition based normal mode parameter estimation

作　　者：路达 段睿[1,3] 杨坤德 LU Da;DUAN Rui;YANG Kunde(School of Marine Science and Technology,Northwestern Polytechnical University,Xi’an 710072;Ocean Institute,Northwestern Polytechnical University,Taicang 215400;Key Laboratory of Ocean Acoustic and Sensing(Northwestern Polytechnical University),Ministry of Industry and Information Technology,Xi’an 710072)

机构地区：[1]西北工业大学航海学院,西安710072 [2]西北工业大学海洋研究院,太仓215400 [3]海洋声学信息感知工业和信息化部重点实验室(西北工业大学),西安710072

出　　处：《声学学报》2023年第4期743-760,共18页Acta Acustica

基　　金：国家自然科学基金项目(12074315,52231013,61901383)资助。

摘　　要：提出了一种基于张量分解的模态深度函数和模态水平波数(统称模态参数)估计方法,解决了传统子空间方法对模态正交性的依赖。利用经距离补偿后声场的平移不变性,将模态参数估计问题转化为三阶张量的规范多元分解(CPD)问题,分解得到的因子矩阵可用于同时估计模态深度函数和模态水平波数。推导了模态参数估计问题下张量分解的唯一性条件,结果表明该方法可在模态深度函数采样向量线性无关的条件下,使用较少的深度维采样和距离维采样实现模态参数估计。仿真结果还表明该方法在距离采样孔径较小时依然具有较好的估计性能。将该方法应用于SwellEx-96实验数据,得到了与实验海域环境较吻合的模态参数估计结果。仿真和实验数据均验证了该方法的有效性。A tensor-decomposition-based method is proposed for modal depth function and modal horizontal wavenumber(i.e.,modal parameter) estimation,which avoids the dependence of the traditional subspace-based methods on modal orthogonality.The method exploits the shift-invariance of the range-compensated pressure field to transform the mode parameter estimation problem into the canonical polyadic decomposition(CPD) problem of a third-order tensor.Decomposed factor matrices are used to simultaneously yield the modal depth function and the modal horizontal wavenumber estimates.The uniqueness condition of tensor decomposition for the modal parameter estimation problem is also given,which shows that modal parameter estimation can be achieved by using a small number of depth-dimension samplings and range-dimension samplings under the condition that the sampling vectors of modal depth function are linearly independent.Simulation results also demonstrate the method has a good performance when the range aperture is short.The method is applied to SwellEx-96 experiment data and the obtained modal parameter estimates are consistent with the environment at the experiment sea.Both simulation and experimental data verify the effectiveness of the method.

关 键 词：简正波 张量分解 垂直阵 模态参数估计 

分 类 号：O427[理学—声学] O212.1[理学—物理]