陈竹安,熊鑫,李亦佳

• 1:东华理工大学测绘工程学院
• 2:江西省数字国土重点实验室

摘要(Abstract)：

为了滤除变形数据中含有的白噪声,该文提出一种基于粒子群优化算法的双重变分模态分解-小波阈值去噪模型。首先利用VMD对变形数据进行初次分解,初次分解层数K_1由频谱图波峰个数确定,根据相关性分析将分量分为噪声分量和信号分量;然后针对信号分量出现模态混叠的现象,首次分解的信号分量再次进行粒子群优化的VMD分解,得到二次信号分量和二次噪声分量;对二次VMD分解得到的噪声分量进行小波阈值降噪;最后重构实现噪声的有效剔除。模拟实验结果显示,利用本文方法去噪得到的均方根误差降低至0.418 0 mm、信噪比提升至10.174 0 dB,对比小波阈值、总体经验模态分解(EEMD)、VMD等方法,降噪效果有明显的提升。在实际变形数据去噪中,相比于其他去噪方法,本文方法能够很好地抑制模态混叠的现象,且均方根误差降低至0.151 0 mm、信噪比提升至23.821 0 dB,验证了本文方法在实际应用中的有效性。

关键词(KeyWords)： 粒子群优化算法;双重变分模态分解;总体经验模态分解;小波阈值去噪;变形监测;去噪

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(51708098);; 江西省自然科学基金项目(20171BAA218018)

作者(Author): 陈竹安,熊鑫,李亦佳

DOI: 10.16251/j.cnki.1009-2307.2020.08.007

参考文献(References)：

• [1] 罗甘,梁月吉,黄仪邦.基于双树复小波的变形监测数据去噪分析[J].大地测量与地球动力学,2018,38(9):958-963.(LUO Gan,LIANG Yueji,HUANG Yibang.Deformation analysis based on a dual-tree complex wavelet transform method[J].Journal of Geodesy and Geodynamics,2018,38(9):958-963.)
• [2] 吴金斌,周世健.经验模式分解联合独立分量分析降噪研究[J].测绘科学,2016,41(7):197-201.(WU Jinbin,ZHOU Shijian.The de-noising study based on empirical mode decomposition and independent component analysis[J].Science of Surveying and Mapping,2016,41(7):197-201.)
• [3] HUANG N E,SHEN Z,LONG S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings:Mathematical,Physical and Engineering Sciences,1998,454(1971):903-995.
• [4] WU Z H,HUANG N E.Ensemble empirical mode decomposition:a noise-assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
• [5] 史恒,李桂林,王伟,等.基于总体经验模式分解的地震信号随机噪声消除[J].地球物理学进展,2011,26(1):71-78.(SHI Heng,LI Guilin,WANG Wei,et al.Random noise attenuation based on ensemble empirical mode decomposition[J].Progress in Geophysics,2011,26(1):71-78.)
• [6] 肖小兵,刘宏立,马子骥.基于奇异谱分析的经验模态分解去噪方法[J].计算机工程与科学,2017,39(5):919-924.(XIAO Xiaobing,LIU Hongli,MA Ziji.An empirical mode decomposition de-noising method based on singular spectrum analysis[J].Computer Engineering & Science,2017,39(5):919-924.)
• [7] TORRES M E,COLOMINAS M A,SCHLOTTHAUER G,et al.A complete ensemble empirical mode decomposition with adaptive noise[C]//IEEE International Conference on Acoustics,Speech and Signal Processing.[S.l.]:IEEE,2011:4144-4147.
• [8] 龙丹,牛聪,周怀来,等.基于VMD算法在地震数据时频分析中的应用[J/OL].地球物理学进展.[2019-03-14].http://kns.cnki.net/kcms/detail/11.2982.p.20190304.1020.162.html.(LONG Dan,NIU Cong,ZHOU Huailai,et al.The application of VMD algorithm in time-frequency analysis of seismic data[J/OL].Progress in Geophysics.[2019-03-14].http://kns.cnki.net/kcms/detail/11.2982.p.20190304.1020.162.html.)
• [9] 鲍克勤,卢丹,吴文峰,等.基于VMD算法的光栅莫尔条纹去噪方法[J].光通信技术,2019,43(1):28-31.(BAO Keqin,LU Dan,WU Wenfeng,et al.Grating moire fringe denoising method based on VMD algorithm[J].Optical Communication Technology,2019,43(1):28-31.)
• [10] 张杏莉,卢新明,贾瑞生,等.基于变分模态分解及能量熵的微震信号降噪方法[J].煤炭学报,2018,43(2):356-363.(ZHANG Xingli,LU Xinming,JIA Ruisheng,et al.Micro-seismic signal denoising method based on variational modedecomposition and energy entropy[J].Journal of China Coal Society,2018,43(2):356-363.)
• [11] 许军才,任青文,黄临平.基于变分模态分解的探地雷达信号分析方法[J].河海大学学报(自然科学版),2018,46(6):545-550.(XU Juncai,REN Qingwen,HUANG Linping.GPR signal analysis method based on variational mode decomposition[J].Journal of Hohai University(Natural Sciences),2018,46(6):545-550.)
• [12] 陆振宇,卢亚敏,夏志巍,等.基于变分模态分解和小波分析的语音信号去噪方法[J].现代电子技术,2018,41(13):47-51.(LU Zhenyu,LU Yamin,XIA Zhiwei,et al.Speech signal denoising method based on VMD and wavelet analysis[J].Modern Electronics Technique,2018,41(13):47-51.)
• [13] 王晶.基于VMD分解和小波阈值的语音信号去噪[J].软件导刊,2017,16(10):12-14,18.(WANG Jing.Speech signal denoising based on VMD decomposition and wavelet threshold[J].Software Guide,2017,16(10):12-14,18.)
• [14] 徐帆,常建华,刘秉刚,等.基于VMD的激光雷达回波信号去噪方法研究[J].激光与红外,2018,48(11):1443-1448.(XU Fan,CHANG Jianhua,LIU Binggang,et al.De-noising method research for lidar echo signal basedon variational mode decomposition[J].Laser & Infrared,2018,48(11):1443-1448.)
• [15] 江春冬,王景玉,杜太行,等.基于变分模态分解算法的单通道无线电混合信号分离[J].上海交通大学学报,2018,52(12):1618-1626.(JIANG Chundong,WANG Jingyu,DU Taihang,et al.Separation of single channel radio mixed signal based on variational mode decomposition[J].Journal of Shanghai Jiaotong University,2018,52(12):1618-1626.)
• [16] DRAGOMIRETSKIY K,ZOSSO D.Variational mode decomposition[J].IEEE Transactions on Signal Processing,2014,62(3):531-544.
• [17] 王丽馨,蔡国伟,杨德友,等.基于自适应变分模态分解的电力系统机电振荡特征提取[J/OL].电网技术.[2019-03-29].https://doi.org/10.13335/j.1000-3673.pst.2018.1060.(WANG Lixin,CAI Guowei,YANG Deyou,et al.Extracting modes from electromechanical oscillation signals for power system based on adaptive variational mode decomposition[J/OL].Power System Technology.[2019-03-29].https://doi.org/10.13335/j.1000-3673.pst.2018.1060.)
• [18] KENNDY J,EBERHART R C.A new optimizer using particle swarm theory[C]//Proceedings the Sixth International Symposiumm on Micromachine and Human Science.[S.l.]:[s.n.],1995:39-43.