基于量子高斯混合模型的振动信号降噪方法
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摘要
由于机械设备振动信号受到背景噪声的干扰,造成机械设备故障状态特征不明显,因此提出了一种基于量子高斯混合模型的振动信号降噪方法。首先,对振动信号进行双树复小波包变换,对双树复小波包系数建立高斯混合模型,根据贝叶斯最大后验估计准则,得到双树复小波包系数收缩函数;然后,利用双树复小波包系数父代和子代的空间相关性,结合量子叠加态理论计算噪声信号和有用信号小波系数出现的概率值;最后,根据量子叠加态得到的概率参数值调节高斯混合模型中的小波包系数收缩函数,使小波包系数自适应非线性收缩,提高高斯混合模型的局部自适应性,实现机械振动信号的降噪处理。仿真信号和实测行星齿轮箱振动信号实验结果表明,该方法能够有效地去除振动信号中的噪声,凸显机械设备的故障状态特征。
Vibration signals of machinery equipment are often disturbed by background noise to cause machinery equipment's fault features being not obvious. Here, a de-noising algorithm of vibration signals based on quantum Gaussian mixture model was proposed. Firstly, the dual-tree complex wavelet packet transform was performed on vibration signals, and Gaussian mixture model was established for dual-tree complex wavelet packet coefficients. According to Bayesian maximum posteriori estimation criterion, shrinkage function of dual-tree complex wavelet packet coefficients was acquired. Then the spatial correlation between dual-tree complex wavelet packet coefficients' father generation and child one was used to combine the quantum superposition state theory, and calculate appearing probabilities of noise signal and useful one' wavelet coefficients, respectively. Lastly, the shrinkage function of dual-tree complex wavelet packet coefficients was adjusted with probability parameters achieved with the quantum superposition state theory to make wavelet packet coefficients shrink adaptively and nonlinearly, and the local adaptability of Gaussian mixture model was improved to realize machinery vibration signals' de-noising processing. The test results of simulated signals and measured planetary gearbox vibration signals indicated that this proposed method can be used to effectively get rid of noise in vibration signals and highlight fault state features of machinery equipment.
Vibration signals of machinery equipment are often disturbed by background noise to cause machinery equipment's fault features being not obvious. Here, a de-noising algorithm of vibration signals based on quantum Gaussian mixture model was proposed. Firstly, the dual-tree complex wavelet packet transform was performed on vibration signals, and Gaussian mixture model was established for dual-tree complex wavelet packet coefficients. According to Bayesian maximum posteriori estimation criterion, shrinkage function of dual-tree complex wavelet packet coefficients was acquired. Then the spatial correlation between dual-tree complex wavelet packet coefficients' father generation and child one was used to combine the quantum superposition state theory, and calculate appearing probabilities of noise signal and useful one' wavelet coefficients, respectively. Lastly, the shrinkage function of dual-tree complex wavelet packet coefficients was adjusted with probability parameters achieved with the quantum superposition state theory to make wavelet packet coefficients shrink adaptively and nonlinearly, and the local adaptability of Gaussian mixture model was improved to realize machinery vibration signals' de-noising processing. The test results of simulated signals and measured planetary gearbox vibration signals indicated that this proposed method can be used to effectively get rid of noise in vibration signals and highlight fault state features of machinery equipment.
引文
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[19] RABBANI H,VAFADUST M.Image/video denoising based on a mixture of Laplace distributions with local parameters in multidimensional complex wavelet domain[J].Signal Processing,2008,88:158-173.
[20] 周扬,吕进,刘铁兵,等.小波域高斯混合模型方差估计近红外降噪方法[J].光电工程,2011,38(8):96-100.ZHOU Yang,Lü Jin,LIU Tiebing,et al.NIR spectroscopy noise reduction method using noise variance estimation by gaussian mixture model in wavelet domain[J].Opto-Electronic Engineering,2011,38(8):96-100.
[21] DONOHO D L,JOHNSTONE I M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
[2] 冯志鹏,褚福磊,左明健.行星齿轮箱振动故障诊断方法[M].北京:科学出版社,2015.
[3] 程卫东,赵德尊.用于滚动轴承转频估计的EMD软阈值降噪算法[J].浙江大学学报(工学版),2016,50(3):428-435.CHENG Weidong,ZHAO Dezun.EMD soft-thresholding denosing algorithm for rolling element bearing rotational frequency estimation[J].Journal of Zhejiang University (Engineering Science),2016,50(3):428-435.
[4] 胥永刚,赵国亮,侯少飞,等.DT-CWT相关滤波在齿轮箱故障诊断中的应用[J].振动、测试与诊断,2016,36(1):138-144.XU Yonggang,ZHAO Guoliang,HOU Shaofei,et al.DT-CWT domain correlation filter and its application in incipient gearbox fault diagnosis[J].Journal of Vibration,Measurement & Diagnosis,2016,36(1):138-144.
[5] CHEN Y,ZHANG P,WANG Z,et al.Denoising algorithm for mechanical vibration signal using quantum Hadamard transformation[J].Measurement,2015,66:168-175.
[6] SADOOGHI M S,KHADEM S E.A new performance evaluation scheme for jet engine vibration signal denoising[J].Mechanical Systems and Signal Processing,2016,76/77(1):201-212.
[7] DONG B,JIANG Q,LIU C,et al.Multiscale representation of surfaces by tight wavelet frames with applications to denoising[J].Applied and Computational Harmonic Analysis,2016,41:561-589.
[8] 张立国,胡永涛,张淑清,等.基于改进双树复小波的光谱去噪算法研究[J].仪器仪表学报,2016,37(9):2061-2067.ZHANG Liguo,HU Yongtao,ZHANG Shuqing,et al.Research on spectrum denoising based on improved dual-tree complex wavelet transform[J].Chinese Journal of Scientific Instrument,2016,37(9):2061-2067.
[9] 曲巍崴,高峰.基于噪声方差估计的小波阈值降噪研究[J].机械工程学报,2010,46(2):28-33.QU Weiwei,GAO Feng.Study on wavelet threshold denoising algorithm based on estimation of noise variance[J].Journal of mechanical engineering,2010,46(2):28-33.
[10] 张宝华,刘鹤.采用子带分量阈值估计的红外图像去噪方法[J].中国激光,2014,41(8):1-8.ZHANG Baohua,LIU He.Infrared image denoising algorithm based on sub-band component threshold estimation[J].Chinese Journal of Lasers,2014,41(8):1-8.
[11] ELDAR Y C,OPPENHEIM A V.Quantum signal processing[J].IEEE Singal Process Mag,2002,19(6):12-32.
[12] 张毅,卢凯,高颖慧.量子算法与量子衍生算法[J].计算机学报,2013,36(9):1835-1842.ZHANG Yi,LU Kai,GAO Yinghui.Quantum algorithms and quantum-inspired algorithms[J].Chinese Journal of computers,2013,36(9):1835-1842.
[13] YANG Y G,TIAN J,LEI H,et al.Novel quantum image encryption using one-dimensional quantum cellular automata[J].Information Sciences,2016,345(1):257-270.
[14] 王波,刘树林,张宏利.基于QGA优化广义S变换的滚动轴承故障特征提取[J].振动与冲击,2017,36(5):108-113.WANG Bo,LIU Shulin,ZHANG Hongli.Fault feature extraction for rolling bearings based on generalized S transformation optimized with quantum genetic algorithm[J].Journal of Vibration and Shock,2017,36(5):108-113.
[15] YANG Y G,TIAN J,SUN S J,et al.Quantum-assisted encryption for digital audio signals[J].Optik-International Journal for Light and Electron Optics,2015,126(21):3221-3226.
[16] 李盼池,曹梓崎.一种彩色图像的量子描述方法及应用[J].控制与决策,2017,32(3):443-450.LI Panchi,CAO Ziqi.Quantum description method of color image and its application[J].Control and Decision,2017,32(3):443-450.
[17] SELESNICK I W,BARANIUK R G,KINGSBURY N G.The dual-tree complex wavelet transform[J].IEEE Digital Signal Processing Magazine,2005,22(6):123-151.
[18] 陶新民,徐晶,杜宝祥,等.基于小波域广义高斯分布的轴承故障诊断方法[J].机械工程学报,2009,45(10):61-67.TAO Xinmin,XU Jing,DU Baoxiang,et al.Bearing fault diagnosis based on wavelet-domain generalized Gaussian distribution[J].Journal of Mechanical Engineering,2009,45(10):61-67.
[19] RABBANI H,VAFADUST M.Image/video denoising based on a mixture of Laplace distributions with local parameters in multidimensional complex wavelet domain[J].Signal Processing,2008,88:158-173.
[20] 周扬,吕进,刘铁兵,等.小波域高斯混合模型方差估计近红外降噪方法[J].光电工程,2011,38(8):96-100.ZHOU Yang,Lü Jin,LIU Tiebing,et al.NIR spectroscopy noise reduction method using noise variance estimation by gaussian mixture model in wavelet domain[J].Opto-Electronic Engineering,2011,38(8):96-100.
[21] DONOHO D L,JOHNSTONE I M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81(3):425-455.