﻿ 基于贝叶斯的舰船辐射噪声特征识别方法
 舰船科学技术  2023, Vol. 45 Issue (7): 70-73    DOI: 10.3404/j.issn.1672-7649.2023.07.015 PDF

Characteristic recognition method of ship radiated noise based on Bayesian
YUE Li
College of Computer Science and Technology, Changchun University, Changchun 130022, China
Abstract: Aiming at the problem that the characteristics of ship radiated noise have nonlinear and non-stationary time-varying characteristics, which leads to high difficulty in feature recognition, this paper proposes a method of ship radiated noise feature recognition based on Bayesian. The Doppler transform method is used to transform the ship radiated sound field signal by selecting Gaussian function as the basis function. The VMD algorithm is used to obtain the optimal solution of the search constrained variational model. The transformed ship radiation signal is decomposed into multiple IMF components to extract the characteristics of ship radiation noise. The feature sample set is constructed by using the extracted ship radiated noise features, and the state probability of each sample in the sample set is calculated by Bayesian network to identify the ship radiated noise features. The results show that this method can effectively identify the radiated noise of different types of ships, such as surface ships and underwater low-speed moving ships, and is suitable for ship target recognition applications.
Key words: Bayessian     ship radiation noise     feature recognition method     gaussian function     VMD algorithm     state probability
0 引　言

1 舰船辐射噪声特征识别方法 1.1 Dopplerlet变换的舰船辐射信号变换

Dopplerlet变换方法是一种信号时频分解方法，利用Dopplerlet变换方法分解舰船辐射信号时，为了令信号表征更加高效与简洁，选取与舰船辐射信号形态类似的基函数。舰船辐射信号的频率成分，伴随时间呈现非线性变化时，该方法可以改善信号分解时的混合畸变与截断情况。信号伴随时间变化呈现非线性变化时，仍然可以精准地划分频率，实现舰船辐射信号的时频分解。

 $f = \dfrac{{a{f_0}}}{{a - \dfrac{{{v^2}\left( {t - {t_0}} \right)}}{{\sqrt {{l^2} + {v^2}\left( {t - {t_0}} \right)} }}}},$ (1)

 $b\left( t \right) = \exp \left[ {2\text{π} f\left( {t - {t_0}} \right)} \right],$ (2)

 $g\left( t \right) = \exp b\left( t \right)\left[ { - \frac{1}{2}{{\left( {\frac{t}{{{\Delta _t}}}} \right)}^2}} \right]。$ (3)

 $g\left( t \right)' = \frac{{b\left( t \right)}}{{\sqrt {\text{π}} {\Delta _t}}}\exp \left[ { - \frac{v}{2}{{\left( {\frac{{t - {t_0}}}{{{\Delta _t}}}} \right)}^2}} \right] \text{,}$ (4)

 $G\left( {t,f} \right) = \left\langle {s\left( t \right),g\left( t \right)'} \right\rangle 。$ (5)

1.2 基于VMD算法的舰船辐射噪声特征提取

 $d\left( t \right) = \frac{{A\left( t \right)\cos \left( {\phi \left( t \right)} \right)}}{{G\left( {t,f} \right)}},$ (6)

 $x = \min \left\{ {\sum\limits_{k = 1}^K {\left\| {\partial t\left( {\phi \left( t \right){w_k} + \frac{{{d_k}\left( t \right)}}{{\text{π} t}}} \right){e^{ - kt}}} \right\|_2^2} } \right\}。$ (7)

 $\begin{split} L\left( {{d_k},{w_k},\theta } \right) = &\alpha \sum\limits_{k = 1}^K {\left\| {\partial t\left[ {\phi \left( t \right) + \frac{{x{d_k}\left( t \right)}}{{\text{π} t}}} \right]{e^{ - kt}}} \right\|} _2^2 + \\ & \left\| {f\left( t \right) - \sum\limits_{k = 1}^K {{d_k}\left( t \right)} } \right\|_2^2 + \left\langle {\theta \left( t \right) - \sum\limits_{k = 1}^K {{d_k}\left( t \right)} } \right\rangle 。\end{split}$ (8)

 $\sum\limits_k {\left\| {\hat d_k^{n + 1} - \hat d_k^n} \right\|_2^2} /L\left( {{d_k},{w_k},\theta } \right) < \zeta 。$ (9)

1.3 贝叶斯网络的舰船辐射噪声特征识别

 $P\left( {X\left| e \right.} \right) = P\left( {{e^c}\left| X \right.} \right) * P\left( {X\left| {{e^f}} \right.} \right)。$ (10)

 $P\left( {{e^c}\left| X \right.} \right) = \zeta \prod\limits_{i = 1}^m {P\left( {{e_{ci}}\left| {{c_{ij}}} \right.} \right)P\left( {{c_{ij}}\left| X \right.} \right)},$ (11)

 $P\left( {X\left| {{e^f}} \right.} \right) = \sum\limits_p^{} {P\left( {x\left| {{P_{ij}}} \right.} \right)} \prod\limits_{w = 1}^{\left| P \right|} {P\left( {{e^c}\left| X \right.} \right)}。$ (12)

2 实例分析

 图 1 舰船辐射噪声特征提取结果 Fig. 1 Feature extraction results of ship radiated noise

 图 2 舰船辐射噪声波形图 Fig. 2 Waveform of ship radiated noise

3 结　语

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