基于小波变换模改进Perona-Malik模型的强噪声信号滤波算法
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摘要
鉴于偏微分方程在图像去噪中的原理和应用,针对传统机械振动信号去噪方法的局限性,提出了一种基于小波变换模改进Perona-Malik模型的强噪声信号滤波算法并用于机械振动信号去噪。首先研究了小波阈值去噪和Perona-Malik非线性各向异性扩散滤波模型之间的相关性,其次用小波变换模替代梯度模构建改进的扩散系数,并推导出了基于小波变换模的改进Perona-Malik模型。实验结果表明,与传统去噪方法和基本Perona-Malik模型相比,改进Perona-Malik模型不仅较好地实现了强噪声背景信号有效去噪,而且同时保留了信号细节特征,改进算法抗噪声干扰能力强,去噪之后信号畸变小,改进算法使信噪比平均提高了约3 dB。
Aiming at traditional mechanical vibration signals de-noising method 's limitation,considering partial differential equations ' principle and application in image de-noising,a strong noise signal filtering algorithm based on wavelet transform module and modified Perona-Malik model was proposed. Firstly,the correlation between the wavelet threshold de-noising and Perona-Malik nonlinear anisotropic diffusion filtering model was studied. Secondly,wavelet transform module was used to substitute gradient module and construct an improved diffusion coefficient. The modified Perona-Malik model was derived based on wavelet transform module. The test results showed that compared with the traditional de-noising method and the basic Perona-Malik model,the modified Perona-Malik model can not only realize mechanical vibration signals' effective de-noising under strong noise background,but also keep signals' detail features with little signal distortion; it has a strong anti-noise capacity,the new algorithm makes the average SNR increase by about 3 dB.
Aiming at traditional mechanical vibration signals de-noising method 's limitation,considering partial differential equations ' principle and application in image de-noising,a strong noise signal filtering algorithm based on wavelet transform module and modified Perona-Malik model was proposed. Firstly,the correlation between the wavelet threshold de-noising and Perona-Malik nonlinear anisotropic diffusion filtering model was studied. Secondly,wavelet transform module was used to substitute gradient module and construct an improved diffusion coefficient. The modified Perona-Malik model was derived based on wavelet transform module. The test results showed that compared with the traditional de-noising method and the basic Perona-Malik model,the modified Perona-Malik model can not only realize mechanical vibration signals' effective de-noising under strong noise background,but also keep signals' detail features with little signal distortion; it has a strong anti-noise capacity,the new algorithm makes the average SNR increase by about 3 dB.
引文
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[18]尹爱军,孙丽萍,王见.偏微分方程在轴心轨迹提纯中的应用[J].重庆大学学报,2011,34(12):72-77.YIN Aijun,SUN Liping,WANG Jian.Purification of the shaft centerline orbit with partial differential equation[J].Journal of Chongqing Unoversity,2011,34(12):72-77.
[19]徐叶雷,黄青华,方勇.一种基于偏微分方程的车辆加速度信号自适应降噪方法[J].传感器技术学报,2009,22(11):1606-1611.XU Yelei,HUANG Qinghua,FANG Yong.An adaptive denoising method for vehicle's acceleration signal based on PDE[J].Chinese Journal of Sensors and Actuators,2009,22(11):1606-1611.
[20]CANNY J.A computational approach to edge detection[J].IEEE Transactions an Pattern Analysis and Machine Intelligence,1986,8(6):679-698.
[2]包广清,常勇,杨国金.基于EMD阈值方法的轴承故障振动信号去噪[J].计算机工程与应用,2015,51(10):205-210.BAO Guangqing,CHANG Yong,YANG Guojin.De-noising of rolling bearing fault vibration signal based on empirical mode decomposition threshold[J].Computer Engineering and Applications,2015,51(10):205-210.
[3]魏振春,王婿,徐娟.基于改进阈值自适应冗余小波的振动信号去噪[J].计算机仿真,2014,31(11):192-197.WEI Zhenchun,WANG Xu,XU Juan.Denoising method of vibration signal based on improved threshold and adaptive redundant second generation wavelet[J].Computer Simulation,2014,31(11):192-197.
[4]苏祖强,萧红,张毅,等.基于小波包分解与主流形识别的非线性降噪[J].仪器仪表学报,2016,37(9):1954-1961.SU Zuqiang,XIAO Hong,ZHANG Yi,et al.Nonlinear noise reduction method based on wavelet packet decomposition and principle manifold learning[J].Chinese Journal of Scientific Instrucment,2016,37(9):1954-1961.
[5]周祥鑫,王小敏,杨扬,等.基于小波阈值的高速道岔振动信号降噪[J].振动与冲击,2014,33(23):200-206.ZHOU Xiangxin,WANG Xiaomin,YANG Yang,et al.Denoising of high-speed turnout vibration signals based on wavelet threshold[J].Journal of Vibration and Shock,2014,33(23):200-206.
[6]李红延,周云龙,田峰,等.一种新的小波自适应阈值函数振动信号去噪算法[J].仪器仪表学报,2015,36(10):2200-2206.LI Hongyan,ZHOU Yunlong,TIAN Feng,et al.Waveletbased vibration signal de-noising algorithm with a new adaptive threshpld function[J].Chinese Journal of Scientific Instrucment,2015,36(10):2200-2206.
[7]付海燕,吉小军,李兴旺.基于TSA的直升机传动系统振动信号处理[J].计算机测量与控制,2014,22(3):930-931.FU Haiyan,JI Xiaojun,LI Xingwang.TSA-based helicopter transmission system vibration signal processing[J].Computer Measurement&Control,2014,22(3):930-931.
[8]周晓峰,杨世锡,甘春标.一种旋转机械振动信号的盲源分离消噪方法[J].振动、测试与诊断,2012,32(5):714-717.ZHOU Xiaofeng,YANG Shixi,GAN Chunbiao.De-noising vibration signal of rotating machinery with blind sources separation[J].Journal of Vibration,Measurement&Diagnosis,2012,32(5):714-717.
[9]隋文涛,张丹.总变差降噪方法在轴承故障诊断中的应用[J].振动、测试与诊断,2014,34(6):1033-1037.SUI Wentao,ZHANG Dan.Total variation denoising method and its application in fault diagnosis of bearings[J].Journal of Vibration,Measurement&Diagnosis,2014,34(6):1033-1037.
[10]PERONA P,MALIK J.Scale-space and edge detection using anisotropic diffusion[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[11]CATTE F,LIONS P L,MOREL J,et al.Image selective smoothing and edge detection by nonlinear diffusion[J].SIAM Journal on Numerical Analysis,1992,29(3):182-193.
[12]REN Z,HE C,ZHANG Q.Fractional order total variation regularization for image super-resolution[J].Signal Processing,2013,93(9):2408-2421.
[13]LIU Feng.Diffusion filtering in image processing based on wavelet transform[J].Science in China Series F:Information Science,2006,49(4):494-503.
[14]姜东焕,冯象初,宋国乡.基于非线性小波阈值的各向异性扩散方程[J].电子学报,2006,34(1):170-172.JIANG Donghuan,FENG Xiangchu,SONG Guoxiang.An anisotropic diffusion equation based on nonlinear wavelet shrinkage[J].Acta Electronica Sinica,2006,34(1):170-172.
[15]刘晨华,冯象初.基于连续状态小波阈值的各向异性扩散去噪方法[J].系统工程与电子技术,2009,31(4):750-753.LIU Chenhua,FENG Xiangchu.Denoising method of anisotropic diffusion based on continuous state wavelet threshold[J].Systems Engineering and Electronics,2009,31(4):750-753.
[16]陈利霞,丁宣浩,宋国乡,等.基于总变分与小波变换的图像去噪算法[J].西安电子科技大学学报(自然科学版),2008,35(6):1075-1079.CHEN Lixia,DING Xuanhao,SONG Guoxiang,et al.Image de-noising algorithm based on total variation and wavelet transform[J].Journal of Xidian University,2008,35(6):1075-1079.
[17]吴宏钢,尹爱军,秦树人.基于PDE的振动信号去噪[J].机械工程学报,2009,45(5):91-94.WU Honggang,YIN Aijun,QIN Shuren.Vibration signal denoising based on partial differential equation[J].Journal of Mechanical Engineering,2009,45(5):91-94.
[18]尹爱军,孙丽萍,王见.偏微分方程在轴心轨迹提纯中的应用[J].重庆大学学报,2011,34(12):72-77.YIN Aijun,SUN Liping,WANG Jian.Purification of the shaft centerline orbit with partial differential equation[J].Journal of Chongqing Unoversity,2011,34(12):72-77.
[19]徐叶雷,黄青华,方勇.一种基于偏微分方程的车辆加速度信号自适应降噪方法[J].传感器技术学报,2009,22(11):1606-1611.XU Yelei,HUANG Qinghua,FANG Yong.An adaptive denoising method for vehicle's acceleration signal based on PDE[J].Chinese Journal of Sensors and Actuators,2009,22(11):1606-1611.
[20]CANNY J.A computational approach to edge detection[J].IEEE Transactions an Pattern Analysis and Machine Intelligence,1986,8(6):679-698.