﻿ 基于小波解调-1(1/2)维谱的舰船辐射噪声调制特征提取
 舰船科学技术  2019, Vol. 41 Issue (8): 122-126 PDF

Modulation feature extraction of ship-radiated noise based on wavelet demodulation-1(1/2) D spectrum
ZHAO Mian, SONG Yu-long, ZHENG Wei
School of Electrical and Information Engineering, Jiangsu University of Science and Technogly, Zhenjiang 212003, China
Abstract: The modulation spectrum of ship-radiated noise contains a large number of inherent characteristics of the ship, which can be used to estimate the speed of ship and target classification and identification. This paper proposes a joint analysis method based on wavelet demodulation and 1(1/2)-dimensional spectrum. Firstly, the signal is demodulated by using the band-pass filtering capability of the Morlet wavelet and the signal demodulation function provided by the orthogonality of real and imaginary parts. The scale envelope spectrum is selected and the scale components containing the modulation information are selected, and 1(1/2) spectrum analysis is performed to obtain the basic frequency and harmonic information of the ship shaft frequency. The actual data results show that this method can effectively extract the modulation characteristic information in ship noise and has a good application prospect.
Key words: ship-radiated noise     wavelet demodulation     1(1/2) D spectrum     modulation feature extraction
0 引　言

1 方法原理 1.1 Morlet小波解调

Morlet小波是高斯包络下的复指数小波，其定义式为：

 ${{h}}\left( t \right) = \frac{1}{{\sqrt {{\text{π}} {f_b}} }}{e^{\left( {j2{\text{π}} {f_c}t - {t^2}/{f_b}} \right)}} {\text{，}}$ (1)

 ${{H}}\left( {{f}} \right) = {e^{ - {{\text{π}} ^2}{f_b}{{\left( {f - {f_c}} \right)}^2}}}{\text{。}}$ (2)

 ${H_i}\left( f \right) = - j{\rm{sgn}} \left( f \right){H_r}\left( f \right){\text{。}}$ (3)

 $cwt\left( {s,t} \right) = \frac{1}{s}\int_{ - \infty }^{ + \infty } {x\left( f \right)} h\left( {\frac{{t - f}}{s}} \right){\rm d}f{\text{。}}$ (4)

 $cwt\left( {s,t} \right) = x\left( t \right) * {h_s}\left( t \right){\text{，}}$ (5)

 $\begin{gathered} cwt\left( {s,t} \right) = x\left( t \right) * h_s^r\left( t \right) + x\left( t \right) * jh_s^i\left( t \right) =\\ {\rm{Re}} \left( {cwt\left( {s,t} \right)} \right) + {\rm{Im}} \left( {cwt\left( {s,t} \right)} \right){\text{。}} \end{gathered}$ (6)

 $\mu \left( {s,t} \right) = \sqrt {{\rm{Re}} {{\left( {cwt\left( {s,t} \right)} \right)}^2} + {\rm{Im}} {{\left( {cwt\left( {s,t} \right)} \right)}^2}}{\text{。}}$ (7)

1.2 1（1/2）维谱特性分析

 $R\left( {{\tau _1},{\tau _2}} \right) = E\left\{ {d\left( t \right)d\left( {t + {\tau _1}} \right)d\left( {t + {\tau _2}} \right)} \right\}{\text{，}}$ (8)

3阶累积量 $R\left( {{\tau _1},{\tau _2}} \right)$ 的对角线切片为：

 $c\left( \tau \right) = c\left( {\tau ,\tau } \right) = E\left\{ {d\left( t \right)d\left( {t + \tau } \right)d\left( {t + \tau } \right)} \right\}{\text{，}}$ (9)

$c\left( \tau \right)$ 作一维 $\rm {\text{，}}Fourier$ 变换，即可得到小波系数 $d\left( t \right)$ 的1（1/2）维谱

 $C\left( \omega \right) = \sum\limits_{\tau = - \infty }^\infty {c\left( \tau \right)} {e^{ - j\omega \tau }}{\rm d}\tau{\text{。}}$ (10)

1）去除各数据段中的直流分量；

2）参照式（9），计算各个数据的3阶累积量，并得到其对角线切片 ${c_i}\left( \tau \right)$

3）取所有数据段的 ${c_i}\left( \tau \right)$ 的均值，可到 $\mathop c\limits^ \wedge \left( \tau \right) =$ $\dfrac{1}{K}\sum\limits_{i = 1}^k {{c^{\left( i \right)}}} \left( \tau \right)$

4）对均值 $\mathop c\limits^ \wedge \left( \tau \right)$ 作一维Fourier变换，即可得到待处理信号的1（1/2）维谱。

2 舰船辐射噪声调制特征提取 2.1 调制特征提取流程

 图 1 工作流程图 Fig. 1 Work flow chart
2.2 特征提取方法具体实现

 ${F_a} = \frac{1}{S} * {f_c} * {f_s}{\text{，}}$ (11)

 ${S_j} = {c / {\left( {m - j} \right)}}\;\;\;j = 0,1, \cdots ,m - 1{\text{。}}$ (12)

3 实验数据处理分析

 图 2 舰船噪声原始信号及功率谱 Fig. 2 Ship noise original signal and power spectrum

 图 3 Morlet小波分解图 Fig. 3 Morlet wavelet decomposition chart

 图 4 小波分量功率谱 Fig. 4 Wavelet component power spectrum

 图 5 信号包络及其功率谱 Fig. 5 Signal envelope and its power spectrum

 图 6 1（1/2）维谱分析图 Fig. 6 1（1/2）Dspectrum analysis

 图 7 不同航速下的（1/2）维谱图 Fig. 7 1（1/2）dimension spectrum at different speeds
4 结　语

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