﻿ 基于循环调制谱熵的螺旋桨噪声分频段调制特征提取方法
 舰船科学技术  2023, Vol. 45 Issue (10): 41-45    DOI: 10.3404/j.issn.1672-7649.2023.10.009 PDF

1. 海军驻上海地区第七军事代表处，上海 201108;
2. 上海船舶电子设备研究所，上海 201108

The extract method for subband modulation characteristics of propeller noise based on cyclic modulation spectrum entropy
SONG Jun-cai1, WANG Yi-ming2
1. The Seventh Military Representation Office of the Navy in Shanghai, Shanghai 201108, China;
2. Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
Abstract: According to the modulation characteristics of marine propeller radiated noise signal in different frequency bands, the method of weighted fusion modulation spectrum extraction of marine propeller radiated noise in different frequency bands is studied. Modulation spectrum entropy is proposed based on cyclic spectrum of ship radiated noise of propeller points weighted fusion modulation spectrum extraction method, first of all, the cyclic spectrum method for ship radiation noise of propeller cycle modulation spectrum, and then based on cycle modulation spectrum entropy estimation points frequency modulation fusion of the weighted coefficient, finally, the DEMON was obtained by using the modulation spectrum frequency weighted coefficient fusion processing. The effectiveness of this method is verified by simulation and measured data.
Key words: cyclic spectrum     cyclic modulation spectrum     propeller noise     sub-band fusion     modulation spectrum
0 引　言

1 循环谱理论 1.1 循环功率谱与循环调制谱

 $\left\{ \begin{gathered} {g_s}(t) = E[s(t)] = {g_s}(t + T)，\\ {R_{ss}}(t,\tau ) = E[s(t){s^ * }(\tau )] = {R_{ss}}(t + T,\tau + T) ，\\ \end{gathered} \right.$ (1)

 ${R_{ss}}(t,\tau ) = E[s(t + \tau /2){s^ * }(t - \tau /2)] 。$ (2)

 ${R_{ss}}(t + \tau /2,t - \tau /2) = \sum\limits_\alpha {R_{ss}^\alpha (\tau ){e^{i2{\text{π}} \alpha t}}}。$ (3)

 $R_{ss}^\alpha (\tau ) = \frac{1}{T}{\int\limits}_{ - T/2}^{T/2} {{R_{ss}}(t + \tau /2,t - \tau /2){e^{ - i2{\text{π}} \alpha t}}} {\rm{d}}t。$ (4)

 $R_{ff}^\alpha (\tau ) = R_{ss}^\alpha (\tau ){e^{i2{\text{π}} \alpha {t_0}}}。$ (5)

 $R_{ss}^\alpha (f) = {\int\limits}_{ - \infty }^\infty {R_{ss}^\alpha (\tau ){e^{ - i2{\text{π}} f{\text{ }}t}}} {\rm{d}}\tau。$ (6)

 ${Spec} (n,f) = {\left| {{\rm{STFT}}(n,f)} \right|^2} = {\left| {\sum\limits_{m = 0}^{N - 1} {\omega (m)x(n + m){e^{ - i2{\text{π}} fm/N}}} } \right|^2} 。$ (7)

 \begin{aligned} CMS(\alpha ,f,{X_{0,L}}) = & {\rm{DFT}}(Spec(n,f)) =\\ & \sum\limits_0^{K - 1} {Spec(n,f){e^{ - i2{\text{π}} n\alpha /K}}} 。\end{aligned} (8)

1.2 船舶螺旋桨辐射噪声循环平稳性分析

 $p(t)=[1+h(t)]\cdot s(t)+n(t) 。$ (9)

 ${g_p}(t) = E[p(t)] = {g_s}(t)[1 + h(t)] + {g_n}(t)，$ (10)
 \begin{aligned} {R_p}(t,\tau ) = & E[p(t)p(t + t)] = \\&p(t)p(t + t){R_p}(t) + p(t)({R_s}(t) + {g_s}(t){g_n}(t)) +\\ & p(t + t)({R_s}(t) + {g_s}(t){g_n}(t)) + 2{g_s}(t){g_n}(t) + {R_n}(t) 。\end{aligned} (11)

1.3 基于循环调制谱熵的分频段调制谱融合算法

 ${g_\alpha }[f] = \frac{{R_s^\alpha [f]}}{{\sum\limits_{\alpha = 1}^W {R_s^\alpha [f]} }} 。$ (12)

 $F[f] = - \sum\limits_{\alpha = 1}^W {{g_\alpha }[f]} \cdot \log ({g_\alpha }[f]) 。$ (13)

1）循环调制谱熵 $F[f]$ 平滑处理；

2）对循环调制谱熵值取倒数，得到循环调制谱质量系数 $\rho [f] = 1/F[f]$

3）计算得到高斯噪声循环调制谱熵值 $\beta$ ，得到分频段调制谱加权系数 $\chi [f] = \rho [f] - 1/\beta$

4）对步骤3得到的分频段调制谱加权系数归一化处理，得到分频段调制谱归一化加权系数：

 $\overline \chi [f] = \frac{{\chi [f] - \min (\chi [f])}}{{\max (\chi [f]) - \min (\chi [f])}} 。$ (14)
2 仿真分析

 图 1 仿真信号循环谱处理结果 Fig. 1 Simulation signal cycle spectrum processing results
3 试验验证 3.1 空泡水筒试验数据验证

 图 2 空泡水筒螺旋桨辐射噪声循环谱处理结果 Fig. 2 Results of cyclic spectrum of cavitation tunnel propeller radiated noise

3.2 实测舰船辐射噪声

 图 3 实测船舶辐射噪声循环谱处理结果 Fig. 3 Experimental results of cyclic spectrum processing of ship radiated noise

4 结　语

1）船舶螺旋桨辐射噪声具有循环平稳特性，调制线谱对不同频段内的噪声信号具有不同的调制能力，不同频段内调制谱融合处理有利于调制谱提取。

2）基于循环调制谱熵建立分频段调制谱融合加权系数，避免人工设置加权系数带来的影响，提升调制谱提取质量。

3）通过仿真试验、空泡水筒试验及海试试验数据，对所提出的基于调制谱熵分频段加权融合调制谱提取方法进行了验证。结果表明，船舶螺旋桨不同频段内的调制线谱均被有效提取，分频段加权融合处理的结果优于全频段调制处理结果。

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