基于VMD的瓦斯信号自适应压缩感知算法
|
摘要
将压缩感知算法和变分模态分解相结合,应用于煤矿瓦斯数据的处理。考虑到现有的压缩感知算法在对瓦斯处理的过程中存在着重构精度低,重构过程复杂和需要较多的样本观测值等问题,因此提出一种基于VMD和自适应观测矩阵的压缩感知算法,有效解决了以较少的样本观测值数据实现信号高精度重构的问题,同时自适应地选择观测矩阵,避免了对稀疏信号的同类化投影选择。首先将瓦斯信号经过VMD进行分离,得到一系列瓦斯信号的本征模态函数分量,通过设定阈值保留有效信息,使得信号更加稀疏化;其次通过自适应地观测矩阵对稀疏信号进行投影变换,从而降低观测矩阵和稀疏字典的不相关性。实验以煤矿瓦斯数据为研究对象,将瓦斯数据经过VMD分解进行稀疏化处理和使用构造的自适应观测矩阵进行投影选择,MATLAB仿真实验证明,文中的算法有更高的信噪比和更好的重构质量。
In this paper,the compressed sensing algorithm was combined with the variational mode decomposition to deal with the gas data in the process of coal mining. Considering that the existing compressed sensing algorithm had low reconstruction accuracy,complex reconstruction process and more sample observations in the process of gas processing,a compressed sensing algorithm based on VMD and adaptive observation matrix was proposed,which could effectively solve the problem of high reconstruction accuracy of signal with less sample observations data,and adaptively select the observation matrix to avoid the similar projection selection of sparse signals. Firstly,the gas signal was decomposed through VMD to gain a series of the Intrinsic Mode Function of the gas signal,and by setting the threshold,effective information was retained to make the signal more sparse; Secondly,the sparse signal was projected and transformed by the adaptive observation matrix,which reduced the correlation between the observation matrix and sparse dictionary. Taken the coal mine gas data as the research object in the experiment,the gas data was decomposed by VMD and the adaptive observation matrix was used for projection selection. MATLAB simulation shows that the algorithm has higher signal-to-noise ratio and better reconstruction quality.
In this paper,the compressed sensing algorithm was combined with the variational mode decomposition to deal with the gas data in the process of coal mining. Considering that the existing compressed sensing algorithm had low reconstruction accuracy,complex reconstruction process and more sample observations in the process of gas processing,a compressed sensing algorithm based on VMD and adaptive observation matrix was proposed,which could effectively solve the problem of high reconstruction accuracy of signal with less sample observations data,and adaptively select the observation matrix to avoid the similar projection selection of sparse signals. Firstly,the gas signal was decomposed through VMD to gain a series of the Intrinsic Mode Function of the gas signal,and by setting the threshold,effective information was retained to make the signal more sparse; Secondly,the sparse signal was projected and transformed by the adaptive observation matrix,which reduced the correlation between the observation matrix and sparse dictionary. Taken the coal mine gas data as the research object in the experiment,the gas data was decomposed by VMD and the adaptive observation matrix was used for projection selection. MATLAB simulation shows that the algorithm has higher signal-to-noise ratio and better reconstruction quality.
引文
[1] Candès E J,Romberg J,Tao T. Robust uncertainty principles:exact signal frequency information[J]. IEEE Transactions on Information Theory,2006,52(2):489-509.
[2] Candès E J,Romberg J K,Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics,2010,59(8):1207-1223.
[3]姚顽强,蔺小虎,马飞,等.基于改进坐标增量的点云数据压缩算法[J].西安科技大学学报,2016,36(6):849-856.YAO Wan-qiang,LIN Xiao-hu,MA Fei,et al. Point cloud data compression algorithm based on improved coordinate increment[J]. Journal of Xi’an University of Science and Technology,2016,36(6):849-856.
[4]李树涛,魏丹.压缩传感综述[J].自动化报,2009,35(11):1369-1377.LI Shu-tao,WEI Dan. A survey of compressive sensing[J]. Automation News,2009,35(11):1369-1377.
[5]王宏志,高源龙,周明月.基于EMD的语音信号压缩感知算法[J].南京邮电大学学报(自然科学版),2016,36(4):22-27.WANG Hong-zhi,GAO Yuan-long,ZHOU Ming-yue.Compressed sensing algorithm of speech signal based on EMD[J]. Journal of Nanjing University of Posts and Telecommunications(Natural Science Edition),2016,36(4):22-27.
[6] Konstantin Dragomiretskiy,Dominique Zosso. Variational mode decomposition[J]. IEEE Transactions on Signal Processing,2014,62(3):531-544.
[7]胡爱军,孙敬敬,向玲.经验模态分解中的模态混叠问题[J].振动、测试与诊断,2011,31(4):429-434.HU Ai-jun,SUN Jing-jing,XIANG Ling. The problem of modal aliasing in empirical mode decomposition[J].Journal of Vibration,Measurement and Diagnosis,2011,31(4):429-434.
[8]钱林,康敏,傅秀清,等.基于VMD的自适应形态学在轴承故障诊断中的应用[J].振动与冲击,2017,36(3):227-233.QIAN Lin,KANG Min,FU Xiu-qing,et al. Application of adaptive morphology based on VMD in bearing fault diagnosis[J]. Journal of Vibration and Shock,2017,36(3):227-233.
[9]费佩燕,郭宝龙.单小波去噪方法在多小波去噪中的应用研究[J].信号处理,2004,20(6):658-661.FEI Pei-yan,GUO Bao-long. Application of single wavelet denoising in multi-wavelet denoising[J]. Signal Processing,2004,20(6):658-661.
[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 Xing-li,LU Xin-ming,JIA Rui-sheng,et al. Micro-seismic signal denoising method based on variational mode decomposition and energy entropy[J]. Journal of China Coal Society,2018,43(2):356-363.
[11]谢平,杨芳梅,李欣欣,等.基于变分模态分解-传递熵的脑肌电信号耦合分析[J].物理学报,2016,65(11):277-285.XIE Ping,YANG Fang-mei,LI Xin-xin,et al. Coupled analysis of brain EMG signals based on variational mode decomposition transfer entropy[J]. Acta Physica Sinica,2016,65(11):277-285.
[12]杨海蓉,张成,丁大为,等.压缩传感理论与重构算法[J].电子学报,2011,39(1):142-148.YANG Hai-rong,ZHANG Cheng,DING Da-wei,et al.Compressed sensing theory and reconstruction algorithm[J]. Chinese Journal of Electronics,2011,39(1):142-148.
[13]方红,杨海蓉.贪婪算法与压缩感知理论[J].自动化学报,2011,37(12):1413-1421.FANG Hong,YANG Hai-rong. Greedy algorithm and compressed sensing theory[J]. Acta Automatica Sinica,2011,37(12):1413-1421.
[14]焦李成,杨淑媛,刘芳,等.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.JIAO Li-cheng,YANG Shu-yuan,LIU Fang,et al. Retrospect and prospect of compressive sensing[J]. Chinese Journal of Electronics,2011,39(7):1651-1662.
[15] Candès,Emmanuel J. The restricted isometry property and its implications for compressedsensing[J]. Comptes Rendus Mathematique,2008,346(9):589-592.
[16]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(s1):225-232.LI Shen,MA Cai-wen,LI Yan,et al. Review of compressed sensing reconstruction algorithms[J]. Infrared and Laser Engineering,2013,42(s1):225-232.
[17]付争,芮国胜,田文飚.准稀疏信号的压缩感知重构[J].电子测量技术,2011,34(6):33-36.FU Zheng,RUI Guo-sheng,TIAN Wen-yu. Compressive sensing reconstruction of quasi-sparse signals[J]. Electronic Measurement Technology,2011,34(6):33-36.
[2] Candès E J,Romberg J K,Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics,2010,59(8):1207-1223.
[3]姚顽强,蔺小虎,马飞,等.基于改进坐标增量的点云数据压缩算法[J].西安科技大学学报,2016,36(6):849-856.YAO Wan-qiang,LIN Xiao-hu,MA Fei,et al. Point cloud data compression algorithm based on improved coordinate increment[J]. Journal of Xi’an University of Science and Technology,2016,36(6):849-856.
[4]李树涛,魏丹.压缩传感综述[J].自动化报,2009,35(11):1369-1377.LI Shu-tao,WEI Dan. A survey of compressive sensing[J]. Automation News,2009,35(11):1369-1377.
[5]王宏志,高源龙,周明月.基于EMD的语音信号压缩感知算法[J].南京邮电大学学报(自然科学版),2016,36(4):22-27.WANG Hong-zhi,GAO Yuan-long,ZHOU Ming-yue.Compressed sensing algorithm of speech signal based on EMD[J]. Journal of Nanjing University of Posts and Telecommunications(Natural Science Edition),2016,36(4):22-27.
[6] Konstantin Dragomiretskiy,Dominique Zosso. Variational mode decomposition[J]. IEEE Transactions on Signal Processing,2014,62(3):531-544.
[7]胡爱军,孙敬敬,向玲.经验模态分解中的模态混叠问题[J].振动、测试与诊断,2011,31(4):429-434.HU Ai-jun,SUN Jing-jing,XIANG Ling. The problem of modal aliasing in empirical mode decomposition[J].Journal of Vibration,Measurement and Diagnosis,2011,31(4):429-434.
[8]钱林,康敏,傅秀清,等.基于VMD的自适应形态学在轴承故障诊断中的应用[J].振动与冲击,2017,36(3):227-233.QIAN Lin,KANG Min,FU Xiu-qing,et al. Application of adaptive morphology based on VMD in bearing fault diagnosis[J]. Journal of Vibration and Shock,2017,36(3):227-233.
[9]费佩燕,郭宝龙.单小波去噪方法在多小波去噪中的应用研究[J].信号处理,2004,20(6):658-661.FEI Pei-yan,GUO Bao-long. Application of single wavelet denoising in multi-wavelet denoising[J]. Signal Processing,2004,20(6):658-661.
[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 Xing-li,LU Xin-ming,JIA Rui-sheng,et al. Micro-seismic signal denoising method based on variational mode decomposition and energy entropy[J]. Journal of China Coal Society,2018,43(2):356-363.
[11]谢平,杨芳梅,李欣欣,等.基于变分模态分解-传递熵的脑肌电信号耦合分析[J].物理学报,2016,65(11):277-285.XIE Ping,YANG Fang-mei,LI Xin-xin,et al. Coupled analysis of brain EMG signals based on variational mode decomposition transfer entropy[J]. Acta Physica Sinica,2016,65(11):277-285.
[12]杨海蓉,张成,丁大为,等.压缩传感理论与重构算法[J].电子学报,2011,39(1):142-148.YANG Hai-rong,ZHANG Cheng,DING Da-wei,et al.Compressed sensing theory and reconstruction algorithm[J]. Chinese Journal of Electronics,2011,39(1):142-148.
[13]方红,杨海蓉.贪婪算法与压缩感知理论[J].自动化学报,2011,37(12):1413-1421.FANG Hong,YANG Hai-rong. Greedy algorithm and compressed sensing theory[J]. Acta Automatica Sinica,2011,37(12):1413-1421.
[14]焦李成,杨淑媛,刘芳,等.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.JIAO Li-cheng,YANG Shu-yuan,LIU Fang,et al. Retrospect and prospect of compressive sensing[J]. Chinese Journal of Electronics,2011,39(7):1651-1662.
[15] Candès,Emmanuel J. The restricted isometry property and its implications for compressedsensing[J]. Comptes Rendus Mathematique,2008,346(9):589-592.
[16]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(s1):225-232.LI Shen,MA Cai-wen,LI Yan,et al. Review of compressed sensing reconstruction algorithms[J]. Infrared and Laser Engineering,2013,42(s1):225-232.
[17]付争,芮国胜,田文飚.准稀疏信号的压缩感知重构[J].电子测量技术,2011,34(6):33-36.FU Zheng,RUI Guo-sheng,TIAN Wen-yu. Compressive sensing reconstruction of quasi-sparse signals[J]. Electronic Measurement Technology,2011,34(6):33-36.