﻿ 一种水声弱信号奇异熵特征提取方法
 舰船科学技术  2022, Vol. 44 Issue (18): 155-158    DOI: 10.3404/j.issn.1672-7649.2022.18.032 PDF

Research on extraction method of underwater acoustic singular entropy features
YE Bo-yuan, LIANG Zhe, LIU Wen-shuai, LU Meng-ting, SONG Jian-qiang
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: This paper proposes a method for screening and recombination of intrinsic mode functions based on singular value entropy. The intrinsic mode functions obtained from empirical mode decomposition are filtered through information entropy calculations to remove high-energy environmental noise in low signal-to-noise ratio signals, and improve The signal-to-noise ratio of the ship's radiation noise characteristics can improve the long-distance recognition of ship targets to a certain extent. The experimental results show that the inherent modal function reconstructed signal after information entropy screening clearly highlights the original characteristics of the ship's radiated noise signal, which can effectively improve the recognition rate of long-distance targets.
Key words: ship target recognition     empirical mode decomposition     hilbert-huang transform     singular value entropy     BP neural network
0 引　言

HHT(Hilbert-Huang Transform)以傅里叶变换为基础，能自适应性地对线性稳态信号和非线性非稳态信号进行分析[6]

1 希尔伯特黄变换（HHT） 1.1 经验模态分解

 ${m}_{1}\left(t\right)=\left[{x}_{{\rm{max}}}\left(t\right)+{x}_{{\rm{min}}}\left(t\right)\right]/2\text{。}$ (1)

 ${h}_{1}\left(t\right)=x\left(t\right)-{m}_{1}\left(t\right)\text{。}$ (2)

 ${h}_{1k}\left(t\right)={h}_{1\left(k-1\right)}\left(t\right)-{m}_{1k}\left(t\right)\text{。}$ (3)

 ${c}_{1}\left(t\right)={h}_{1k}\left(t\right)\text{。}$ (4)

 ${r}_{1}\left(t\right)=x\left(t\right)-{c}_{1}\left(t\right)\text{。}$ (5)

 $x\left(t\right)=\sum _{m=1}^{M}{c}_{m}\left(t\right)+r\left(t\right)\text{。}$ (6)

 $SD=\frac{\displaystyle \sum _{t=0}^{r}{\left|{h}_{1\left(k-1\right)}\left(t\right)-{h}_{1k}\left(t\right)\right|}^{2}}{\displaystyle\sum _{t=0}^{r}{{h}_{1\left(k-1\right)}}^{2}\left(t\right)}\text{。}$ (7)

$0.2\leqslant SD\leqslant 0.3$ 时，停止筛选IMF分量。

1.2 解调谱分析

DEMON（detection of envelope modulation on noise）分析算法被广泛地应用于水声声呐信号分析过程中，其对接收的宽带信号采用平方解调、希尔伯特变换等方法以计算低频解调谱，包络信号为其解调后的低频时域信号，DEMON谱为其功率谱。

 $x\left(t\right)=A\cdot\left(1+m\mathrm{\cdot}\mathrm{sin}\varOmega t\right)\cdot\mathrm{cos}\omega t \text{。}$ (8)

 图 1 解调谱分析流程 Fig. 1 Spectrum of demodulation on frequency analysis process
2 基于信息熵筛选IMF分量

2.1 奇异谱熵

 ${\boldsymbol{A}}=\left[\begin{array}{*{20}{c}} x_1 & x_2 & \cdots &x_M\\ x_2 & x_3 & \cdots & x_{M+1}\\ \vdots & \vdots & \cdots &\vdots\\ x_{N-M}&x_{N-M+1}&\cdots & x_N\end{array}\right] \text{。}$ (9)

 ${p}_{i}=\frac{{\delta }_{i}}{\displaystyle\sum _{i=1}^{M}{\delta }_{i}}\text{。}$ (10)

 $H=-\sum _{i=1}^{M}{p}_{i}\mathrm{log}{p}_{i}\text{。}$ (11)
2.2 基于奇异谱熵值筛选IMF分量的重构信号

 Fig. 2 Original signal

 图 3 各阶IMF分量 Fig. 3 IMF components of each order

 图 4 4~6阶IMF重构信号 Fig. 4 4~6 order IMF reconstruction signal

 图 5 1~3阶IMF重构信号 Fig. 5 1~3 order IMF reconstruction signal

 图 6 近距离测量目标的辐射噪声特征 Fig. 6 The measuring characteristics of radiated noise of targets at close range
3 舰船目标识别试验

4 结　语

 [1] 张岩. 多元统计分析在舰船辐射噪声分类识别中的应用 [D]. 北京: 中国科学院声学研究所, 2007. [2] 吴国清, 李靖, 陈耀明, 等. 舰船噪声识别(I)-总体框架、线谱分析和提取[J]. 声学学报, 1998, 23(5): 394-400. [3] 章新华, 王骥程, 林良骥. 基于小波变换的舰船辐射噪声特征提取[J]. 声学学报, 1997, 22(2): 139-144. DOI:10.15949/j.cnki.0371-0025.1997.02.007 [4] 李亚安, 徐德民, 张效民. 舰船噪声信号的混沌特性研究[J]. 西北工业大学学报, 2001, 19(2): 266-269. DOI:10.3969/j.issn.1000-2758.2001.02.026 [5] 杨 宏, 李亚安, 李国辉. 基于集合经验模态分解的舰船辐射噪声能量分析[J]. 振动与冲击, 2015, 34(16): 55-59. DOI:10.13465/j.cnki.jvs.2015.16.010 [6] HUANG N E, SHEN Z, LONG S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995. DOI:10.1098/rspa.1998.0193 [7] 王森, 单矢量水听器潜标目标航迹提取及频谱分析技术研究[D]. 青岛: 海军潜艇学院, 2018. [8] 畅志明, 基于EEMD分解和多信息熵的气门间隙故障信号研究[D]. 太原: 中北大学, 2018. [9] 王玉梅, 董洋洋, 刘兴艳. 高阶小波包奇异谱熵在故障选线中的应用研究[J]. 电力系统保护与控制, 2011, 39(8). [10] 潘玉娜, 陈进, 李兴林. 奇异谱熵在滚动轴承性能退化评估中的应用研究[C]//全国振动工程及应用学术会议, 2012. [11] 高清清, 贾民平. 基于 EEMD 的奇异谱熵在旋转机械故障诊断中的应用[J]. 东南大学学报(自然科学版), 2011, 41(5): 998-1001. DOI:10.3969/j.issn.1001-0505.2011.05.020