海洋环境噪声中的α稳定分布模型
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摘要
针对海洋环境噪声的非高斯特性,将α稳定分布模型应用到噪声统计建模中。基于模型特征指数与样本峰度物理意义的相似性,建立了二者的对应关系,并推导得出相互独立的两个随机变量之和的峰度。通过数值仿真,表明了α稳定分布对尖峰态噪声建模的可行性和适应性。以安静环境、气枪干扰、航船干扰3种典型环境下的海上实测数据为样本,借助分位数图判断了样本的非高斯特性,并利用分位数法和特征函数法联合估计了模型的参数,得出了特征指数的统计规律:安静环境下特征指数接近2.0,趋近于正态分布;气枪干扰下特征指数介于1.2～1.7之间,具有尖峰厚尾特性;航船干扰下与航速、干扰源到接收位置距离有关,航船影响越显著,特征指数越小,该现象恰好与干扰噪声的峰度变化在物理意义上一致。模型验证结果表明,α稳定分布对3类样本均表现出良好的建模效果,尤其对具有尖峰特性的气枪干扰噪声,效果远远优于正态分布。
In view of the non-Gaussian of ocean ambient noise, the a stable distribution is applied to the statistical modeling. Firstly, the correspondence between the model characteristic exponent and the sample kurtosis is established based on the similarity in physical meaning of the two. And the kurtosis of the sum of two independent random variables is deduced, and this can be used to explain the kurtosis characteristic of interfered background noise. Secondly,some numerical simulations are made to model samples with higher and lower kurtosis than three, the results show good adaptability in leptokurtic distribution. Finally, three typical samples are taken under quiet environment, air gun interference and ship interference environment. Their Gaussianities are judged by the Quantile Quantile plot. And then the four parameters of the model are estimated by the quantile based method and characteristic function based method jointly of the three categories. The statistical law of the characteristic exponent is emphatically analyzed: in the quiet environment, the characteristic exponent is close to 2.0, which is the value of Gaussian model; but for the air gun data,it is between 1.2 and 1.7, which means leptokurtic; and under the interference of the sailing ship, the value of a is related to the ship speed and the distance from the ship source to the receiving location, the more significant the ship impact is, the smaller the characteristic exponent is, which is consistent with the variation of kurtosis of disturbing noise in physical meaning. The results of the model verification show that the a stable distribution behaves well under the above three kinds of trial conditions, especially for the air gun environment which is far superior to the normal distribution.
In view of the non-Gaussian of ocean ambient noise, the a stable distribution is applied to the statistical modeling. Firstly, the correspondence between the model characteristic exponent and the sample kurtosis is established based on the similarity in physical meaning of the two. And the kurtosis of the sum of two independent random variables is deduced, and this can be used to explain the kurtosis characteristic of interfered background noise. Secondly,some numerical simulations are made to model samples with higher and lower kurtosis than three, the results show good adaptability in leptokurtic distribution. Finally, three typical samples are taken under quiet environment, air gun interference and ship interference environment. Their Gaussianities are judged by the Quantile Quantile plot. And then the four parameters of the model are estimated by the quantile based method and characteristic function based method jointly of the three categories. The statistical law of the characteristic exponent is emphatically analyzed: in the quiet environment, the characteristic exponent is close to 2.0, which is the value of Gaussian model; but for the air gun data,it is between 1.2 and 1.7, which means leptokurtic; and under the interference of the sailing ship, the value of a is related to the ship speed and the distance from the ship source to the receiving location, the more significant the ship impact is, the smaller the characteristic exponent is, which is consistent with the variation of kurtosis of disturbing noise in physical meaning. The results of the model verification show that the a stable distribution behaves well under the above three kinds of trial conditions, especially for the air gun environment which is far superior to the normal distribution.
引文
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2 Arveson P T, Vendittis D J. Radiated noise characteristics of a modern cargo ship. J. Acoust. Soc. Am., 2000;107(1):118-129
3 Wales S C, Heitmeyer R M. An ensemble source spectra model for merchant ship-radiated noise. J. Acoust. Soc.Am., 2002; 111(3):1211-1231
4郑作虎,王首勇,杜鹏飞.非高斯相关杂波背景下雷达目标检测方法研究.信号处理,2013; 29(8):925-932
5李风华,刘珊琪,王璟琰.台风激发水下噪声场的建模及其在台风风速反演中的应用.声学学报,2016; 41(5):750-757
6江鹏飞,林建恒,孙军平.考虑噪声源深度分布的海洋环境噪声模型及地声参数反演.物理学报,2017; 66(1):014306-1-014306-12
7孙军平,杨军,林建恒.船舶水下辐射噪声信号理论模型及仿真.物理学报,2016; 65(12):124301-1-124301-10
8朱广平,殷敬伟,陈文剑,胡思为,周焕玲,郭龙祥.北极典型冰下声信道建模及特性.声学学报,2017; 42(2):152-158
9 Asolkar P, Das A, Gajre S, Joshi Y. Tropical littoral ambient noise probability density function model based on sea surface temperature. J. Acoust. Soc. Am.,2016; 140(5):452-456
10 Bouvet M, Schwartz S C. Underwater noises:Statistical modeling, detection, and normalization. J. Acoust. Soc.Am., 1988; 83(3):1023-1033
11 Webster R J. Ambient noise statistics. IEEE Trans. Signal Pro., 1993; 41(6):2249-2253
12周越,韩鹏,杨杰.基于小波域多尺度统计建模的水下噪声的检测与识别.声学学报,2003; 28(6):518-525
13郭新毅,李凡,铁广鹏等.海洋环境噪声研究发展概述及应用前景.物理,2014; 43(11):723-731
14铁广鹏,郭新毅.两种非高斯海洋环境噪声统计模型分析.声学技术,2014; 33(3):209-212
15郑作虎,王首勇.基于alpha稳定分布杂波模型的雷达目标检测方法.电子与信息学报,2014; 36(12):2963-2968
16张安清,邱天爽,章新华.α稳定分布的水声信号处理新方法.电子与信息学报,2005; 27(8):1201-1204
17 Georgiou P G, Tsakalides P, Kyriakakis C. Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise. IEEE, 1999; 1(3):291-301
18 Pelekanakis K, Liu H, Chitre M. An algorithm for sparse underwater acoustic channel identification under symmetric a stable noise. Oceans-Spain, 2011:6003413
19刘晔,黄芝平,刘纯武.Alpha稳定分布混响建模及信号检测.国防科技大学学报,2012; 34(4):148-153
20 Samorodnitsky G, Taqqu M S. Stable non-Gaussian ran-dom Processes:Stochastic models with infinite variance.J. Am. Stat. Assoc., 1995; 90(430):805-806
21 Snyder M A. Long-term ambient noise statistics in the Gulf of Mexico. PhD. Thesis, University of New Orleans, 2007
22 McCulloch J H. Simple consistent estimators of stable distribution parameters. Commun. Statist.-Simula., 1986;15(4):1109-1136
23 Koutrouvelis I A. Regression-type estimation of the parameters of stable laws. J. Am. Stat. Assoc., 1980; 75(372):918-928
2 Arveson P T, Vendittis D J. Radiated noise characteristics of a modern cargo ship. J. Acoust. Soc. Am., 2000;107(1):118-129
3 Wales S C, Heitmeyer R M. An ensemble source spectra model for merchant ship-radiated noise. J. Acoust. Soc.Am., 2002; 111(3):1211-1231
4郑作虎,王首勇,杜鹏飞.非高斯相关杂波背景下雷达目标检测方法研究.信号处理,2013; 29(8):925-932
5李风华,刘珊琪,王璟琰.台风激发水下噪声场的建模及其在台风风速反演中的应用.声学学报,2016; 41(5):750-757
6江鹏飞,林建恒,孙军平.考虑噪声源深度分布的海洋环境噪声模型及地声参数反演.物理学报,2017; 66(1):014306-1-014306-12
7孙军平,杨军,林建恒.船舶水下辐射噪声信号理论模型及仿真.物理学报,2016; 65(12):124301-1-124301-10
8朱广平,殷敬伟,陈文剑,胡思为,周焕玲,郭龙祥.北极典型冰下声信道建模及特性.声学学报,2017; 42(2):152-158
9 Asolkar P, Das A, Gajre S, Joshi Y. Tropical littoral ambient noise probability density function model based on sea surface temperature. J. Acoust. Soc. Am.,2016; 140(5):452-456
10 Bouvet M, Schwartz S C. Underwater noises:Statistical modeling, detection, and normalization. J. Acoust. Soc.Am., 1988; 83(3):1023-1033
11 Webster R J. Ambient noise statistics. IEEE Trans. Signal Pro., 1993; 41(6):2249-2253
12周越,韩鹏,杨杰.基于小波域多尺度统计建模的水下噪声的检测与识别.声学学报,2003; 28(6):518-525
13郭新毅,李凡,铁广鹏等.海洋环境噪声研究发展概述及应用前景.物理,2014; 43(11):723-731
14铁广鹏,郭新毅.两种非高斯海洋环境噪声统计模型分析.声学技术,2014; 33(3):209-212
15郑作虎,王首勇.基于alpha稳定分布杂波模型的雷达目标检测方法.电子与信息学报,2014; 36(12):2963-2968
16张安清,邱天爽,章新华.α稳定分布的水声信号处理新方法.电子与信息学报,2005; 27(8):1201-1204
17 Georgiou P G, Tsakalides P, Kyriakakis C. Alpha-stable modeling of noise and robust time-delay estimation in the presence of impulsive noise. IEEE, 1999; 1(3):291-301
18 Pelekanakis K, Liu H, Chitre M. An algorithm for sparse underwater acoustic channel identification under symmetric a stable noise. Oceans-Spain, 2011:6003413
19刘晔,黄芝平,刘纯武.Alpha稳定分布混响建模及信号检测.国防科技大学学报,2012; 34(4):148-153
20 Samorodnitsky G, Taqqu M S. Stable non-Gaussian ran-dom Processes:Stochastic models with infinite variance.J. Am. Stat. Assoc., 1995; 90(430):805-806
21 Snyder M A. Long-term ambient noise statistics in the Gulf of Mexico. PhD. Thesis, University of New Orleans, 2007
22 McCulloch J H. Simple consistent estimators of stable distribution parameters. Commun. Statist.-Simula., 1986;15(4):1109-1136
23 Koutrouvelis I A. Regression-type estimation of the parameters of stable laws. J. Am. Stat. Assoc., 1980; 75(372):918-928