基于终止准则改进K-SVD字典学习的稀疏表示特征增强方法
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摘要
针对传统K奇异值分解(K-Singular value decomposition, K-SVD)算法在稀疏表示过程中,由于目标信号稀疏度难以确定以及字典原子受噪声干扰大导致稀疏表示效果较差的问题,结合变分模态分解(Variational mode decomposition, VMD)算法,提出了基于VMD与终止准则改进K-SVD字典学习的稀疏表示方法。借助VMD算法剔除信号中的干扰分量,依据相关分析与峭度准则选择最优模态分量;采用终止准则改进的K-SVD字典学习算法对最优分量的特征信息进行学习,优化目标函数与约束条件,在无需设置稀疏度的前提下,构造出准确匹配故障冲击成分的字典;此外,构建一种残差阈值改进的正交匹配追踪算法(OMPerr)实现稀疏重构及微弱故障特征增强。通过仿真及试验信号进行验证,结果表明:基于VMD与改进K-SVD字典学习的稀疏表示方法在字典原子构建、稀疏重构精度以及故障特征增强等方面均优于传统K-SVD稀疏表示方法,可以有效实现微弱故障的诊断。
A sparse representation method based on VMD and termination criteria improved K-SVD dictionary learning algorithm is proposed to solve the issues about the choice of signal sparsity and the interference of noise. With the aid of VMD algorithm, the interference components can be removed. According to correlation analysis and kurtosis criterion, the optimal modal component can be selected successfully. Then the characteristic information of the optimal component is learned by termination criteria improved K-SVD algorithm, optimizing the objective function and constraints, and the sparse representation dictionary matched the fault impact components can be constructed without setting the sparsity. In addition, an improved orthogonal matching pursuit algorithm with residual error threshold is constructed to achieve sparse reconstruction and weak fault feature enhancement. Verification by simulated and experimental signals show that the sparse representation method based on VMD and modified K-SVD could effectively diagnose the weak fault, which outperformed the traditional K-SVD algorithm in terms of the construction of dictionary atom, sparse reconstruction accuracy and fault feature enchantment.
A sparse representation method based on VMD and termination criteria improved K-SVD dictionary learning algorithm is proposed to solve the issues about the choice of signal sparsity and the interference of noise. With the aid of VMD algorithm, the interference components can be removed. According to correlation analysis and kurtosis criterion, the optimal modal component can be selected successfully. Then the characteristic information of the optimal component is learned by termination criteria improved K-SVD algorithm, optimizing the objective function and constraints, and the sparse representation dictionary matched the fault impact components can be constructed without setting the sparsity. In addition, an improved orthogonal matching pursuit algorithm with residual error threshold is constructed to achieve sparse reconstruction and weak fault feature enhancement. Verification by simulated and experimental signals show that the sparse representation method based on VMD and modified K-SVD could effectively diagnose the weak fault, which outperformed the traditional K-SVD algorithm in terms of the construction of dictionary atom, sparse reconstruction accuracy and fault feature enchantment.
引文
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[17]郭俊锋.基于K-SVD字典学习算法的稀疏表示振动信号压缩测量重构方法[J].机械工程学报,2017,54(7):97-106.GUO Junfeng.A method of reconstruction of compressed measuring for mechanical vibration signals based on K-SVD dictionary-training algorithm[J].Journal of Mechanical Engineering,2017,54(7):97-106.
[18]马增强,李亚超,刘政,等.基于变分模态分解和Teager能量算子的滚动轴承故障特征提取[J].振动与冲击,2016,35(13):134-139.MA Zengqiang,LI Yachao,LIU Zheng,et al.Rolling bearings’fault feature extraction based on variational mode decomposition and teager energy operator[J].Journal of Vibration and Shock,2016,35(13):134-139.
[19]AHARON M,ELAD M,BRUCKSTEIN A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[20]YANG B,LIU R,CHEN X.Fault diagnosis for a wind turbine generator bearing via sparse representation and shift-invariant K-SVD[J].IEEE Transactions on Industrial Informatics,2017,13(3):1321-1331.
[21]YANG H,LIN H,DING K.Sliding window denoising K-singular value decomposition and its application on rolling bearing impact fault diagnosis[J].Journal of Sound&Vibration,2018,421:205-219.
[22]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 Xiuqing,et al.Application of adaptive-morphology in bearing fault diagnosis based on VMD[J].Journal of Vibration and Shock,2017,36(3):227-233.
[2]SONG L,WANG H,CHEN P.Vibration-based intelligent fault diagnosis for roller bearings in low-speed rotating machinery[J].IEEE Transactions on Instrumentation&Measurement,2018,8(67):1887-1899.
[3]HAO Y,SONG L,CUI L,et al.A three-dimensional geometric features-based SCA algorithm for compound faults diagnosis[J].Measurement,2019(134):480-491.
[4]雷亚国,贾峰,孔德同,等.大数据下机械智能故障诊断的机遇与挑战[J].机械工程学报,2018,54(5):94-104.LEI Yaguo,JIA Feng,KONG Detong,et al.Opportunities and challenges of machinery intelligent fault diagnosis in big data era[J].Journal of Mechanical Engineering,2018,54(5):94-104.
[5]刘盛纲.大数据时代信息的高效获取与分析-评《稀疏感知导论》[J].电子与信息学报,2018(3):83.LIU Shenggang.Efficient acquisition and analysis of information in the era of big data-review of“Introduction to sparse perception”[J].Journal of Electronics and Information,2018(3):83.
[6]SONG L,WANG H,CHEN P.Step-by-step fuzzy diagnosis method for equipment based on symptom extraction and trivalent logic fuzzy diagnosis theory[J].IEEE Transactions on Fuzzy Systems,2018(99):1-13.
[7]HAN T,JIANG D,SUN Y,et al.Intelligent fault diagnosis method for rotating machinery via dictionary learning and sparse representation-based classification[J].Measurement,2018,118:181-193.
[8]石娟娟,王林,罗春艳,等.基于优化最小算法的齿轮箱复合故障特征稀疏表示[J].振动工程学报,2017(6):1045-1055.SHI Juanjuan,WANG Lin,LUO Chunyan,et al.Sparse representation for gearbox compound fault feature extraction based on majorization-minimization algorithm[J].Journal of Vibration Engineering,2017(6):1045-1055.
[9]CUI L,LI B,MA J,et al.Quantitative trend fault diagnosis of a rolling bearing based on Sparsogram and Lempel-Ziv[J].Measurement,2018(128):410-418.
[10]REN B,HAO Y,WANG H,et al.A sparsity-promoted method based on majorization-minimization for weak fault feature enhancement[J].Sensors,2018,18(4):1003-1022.
[11]樊薇,李双,蔡改改,等.瞬态成分Laplace小波稀疏表示及其轴承故障特征提取应用[J].机械工程学报,2015,51(15):110-118.FAN Wei,LI Shuang,CAI Gaigai,et al.Sparse representation for transients in Laplace wavelet basis and its application in feature extraction of bearing fault[J].Journal of Mechanical Engineering,2015,51(15):110-118.
[12]WANG L,CAI G,YOU W,et al.Transients extraction based on averaged random orthogonal matching pursuit algorithm for machinery fault diagnosis[J].IEEETransactions on Instrumentation&Measurement,2017,66(12):3237-3248.
[13]WANG H,KE Y,SONG L,et al.A sparsity-promoted decomposition for compressed fault diagnosis of roller bearings[J].Sensors,2016,16(9):1524-1544.
[14]张峻宁,张培林,张云强,等.融合字典学习的滑动轴承摩擦故障趋势自记忆预测[J].振动工程学报,2017,30(3):519-526.ZHANG Junning,ZHANG Peilin,ZHANG Yunqiang,et al.Self-memorization model for predicting the wearing trend of sliding bearing with fusion dictionary learning[J].Journal of Vibration Engineering,2017,30(3):519-526.
[15]刘畅,伍星,毛剑琳,等.基于改进MOD学习的滚动轴承振动信号稀疏表示[J].计算机工程与应用,2016,52(17):257-260.LIU Chang,WU Xing,MAO Jianlin,et al.Sparse representation of rolling bearing vibration signal based on improved MOD dictionary learning[J].Computer Engineering and Applications,2016,52(17):257-260.
[16]余发军,周凤星,严保康.基于字典学习的轴承早期故障稀疏特征提取[J].振动与冲击,2016,35(6):181-186.YU Fajun,ZHOU Fengxing,YAN Baokang.Bearing initial fault feature extraction via sparse representation based on dictionary learning[J].Journal of Vibration and Shock,2016,35(6):181-186.
[17]郭俊锋.基于K-SVD字典学习算法的稀疏表示振动信号压缩测量重构方法[J].机械工程学报,2017,54(7):97-106.GUO Junfeng.A method of reconstruction of compressed measuring for mechanical vibration signals based on K-SVD dictionary-training algorithm[J].Journal of Mechanical Engineering,2017,54(7):97-106.
[18]马增强,李亚超,刘政,等.基于变分模态分解和Teager能量算子的滚动轴承故障特征提取[J].振动与冲击,2016,35(13):134-139.MA Zengqiang,LI Yachao,LIU Zheng,et al.Rolling bearings’fault feature extraction based on variational mode decomposition and teager energy operator[J].Journal of Vibration and Shock,2016,35(13):134-139.
[19]AHARON M,ELAD M,BRUCKSTEIN A.K-SVD:An algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[20]YANG B,LIU R,CHEN X.Fault diagnosis for a wind turbine generator bearing via sparse representation and shift-invariant K-SVD[J].IEEE Transactions on Industrial Informatics,2017,13(3):1321-1331.
[21]YANG H,LIN H,DING K.Sliding window denoising K-singular value decomposition and its application on rolling bearing impact fault diagnosis[J].Journal of Sound&Vibration,2018,421:205-219.
[22]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 Xiuqing,et al.Application of adaptive-morphology in bearing fault diagnosis based on VMD[J].Journal of Vibration and Shock,2017,36(3):227-233.
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