基于增广Huber正则化稀疏低秩矩阵的旋转机械微弱故障诊断
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摘要
在多重故障相互耦合和强烈背景噪声下,提取大型旋转机械中的复合微弱故障特征是一个难点,针对这一问题,提出一种新的基于增广Huber正则化稀疏低秩矩阵(augmented Huber regularized sparse low-rank-matrix,AHR-SLM)的旋转机械故障特征提取方法,以大型减速机齿轮箱复合微弱诊断为例。该方法借助于非凸罚正则化稀疏低秩矩阵的思想,通过引入增广Huber罚函数代替传统最小化L1-norm融合套索算法,建立正则化目标成本函数,推导所建立模型的严格凸性,同时讨论模型严格凸性前提下的模型参数最优取值问题,并利用前向–后向算法对所建立模型进行求解。仿真算例与大型减速机齿轮箱微弱故障诊断实例表明:该方法不仅能提取隐藏在强烈外界噪声中的复合微弱故障特征,而且改善传统最小化L1-norm融合套索算法在提取微弱故障冲击时产生的稀疏系数低估与故障频率丢失问题,以及变分模态分解与快速谱峭度图特征提取算法产生的能量衰减与故障频率丢失问题。
It is a challenging difficulty to accurately extract the weak fault characteristics of large rotating machinery under the environment of multiple faults coupling and strong background noise. In this paper, a novel weak multi-fault feature extraction methodology based on augmented Huber regularized sparse low-rank-matrix(AHR-SLM) was proposed,taking a large reducer gearbox as an example. Illuminated by the idea of nonconvex penalty regularization of sparse low rank matrix, in this paper, the augmented Huber regularized penalty function was introduced to substitute the L1-norm fused lasso optimization(LFLO), and the convexity of the proposed objective cost function(OCF) was proved via the non-diagonal characteristic of the matrix, meanwhile, the model parameters were discussed to guarantee the strictly convex property of objective cost function, besides, the solution of the proposed OCF was solved by the forward-backward algorithm(FBA).The diagnosis results of simulation case and large reducer gearbox with weak faults indicate that the proposed method not only extract multiple weak fault characteristics under heavy background noise, but also the underestimate of sparse coefficients and frequencies missed issues of LFLO method, as well as the energy attenuation and frequencies missed issues of variational modal decomposition and fast spectral kurtosis diagram(VMD-FSKD) are improved, respectively.
It is a challenging difficulty to accurately extract the weak fault characteristics of large rotating machinery under the environment of multiple faults coupling and strong background noise. In this paper, a novel weak multi-fault feature extraction methodology based on augmented Huber regularized sparse low-rank-matrix(AHR-SLM) was proposed,taking a large reducer gearbox as an example. Illuminated by the idea of nonconvex penalty regularization of sparse low rank matrix, in this paper, the augmented Huber regularized penalty function was introduced to substitute the L1-norm fused lasso optimization(LFLO), and the convexity of the proposed objective cost function(OCF) was proved via the non-diagonal characteristic of the matrix, meanwhile, the model parameters were discussed to guarantee the strictly convex property of objective cost function, besides, the solution of the proposed OCF was solved by the forward-backward algorithm(FBA).The diagnosis results of simulation case and large reducer gearbox with weak faults indicate that the proposed method not only extract multiple weak fault characteristics under heavy background noise, but also the underestimate of sparse coefficients and frequencies missed issues of LFLO method, as well as the energy attenuation and frequencies missed issues of variational modal decomposition and fast spectral kurtosis diagram(VMD-FSKD) are improved, respectively.
引文
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[2]Zhong Zhixian,Jiang Zhansi,Long Yuhong,et al.Analysis on the noise for the different gearboxes of the heavy truck[J].Shock and Vibration,2015,2015:476460.
[3]Kia S H,Henao H,Capolino G A.Torsional vibration effects on induction machine current and torque signatures in gearbox-based electromechanical system[J].IEEETransactions on Industrial Electronics,2009,56(11):4689-4699.
[4]Li Qing,Liang S Y.Incipient fault diagnosis of rolling bearings based on impulse-step impact dictionary and re-weighted minimizing nonconvex penalty Lq regular technique[J].Entropy,2017,19(8):421.
[5]Feng Zhipeng,Liang Ming.Complex signal analysis for planetary gearbox fault diagnosis via shift invariant dictionary learning[J].Measurement,2016,90:382-395.
[6]Candès E J,Wakin M B,Boyd S P.Enhancing sparsity by reweighted minimization[J].Journal of Fourier Analysis and Applications,2008,14(5-6):877-905.
[7]Parekh A,Selesnick I W.Improved sparse low-rank matrix estimation[J].Signal Processing,2017,139:62-69.
[8]Rakotomamonjy A,Flamary R,Gasso S,et al.?p-?q penalty for sparse linear and sparse multiple kernel multitask learning[J].IEEE Transactions on Neural Networks,2011,22(8):1307-1320.
[9]Wipf D,Nagarajan S.Iterative reweighted?1 and?2methods for finding sparse solutions[J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):317-329.
[10]Ding Yin,He Wangpeng,Chen Binqiang,et al.Detection of faults in rotating machinery using periodic time-frequency sparsity[J].Journal of Sound and Vibration,2016,382:357-378.
[11]He Wangpeng,Ding Yin,Zi Yanyang,et al.Repetitive transients extraction algorithm for detecting bearing faults[J].Mechanical Systems and Signal Processing,2017,84:227-244.
[12]He Wangpeng,Ding Yin,Zi Yanyang,et al.Sparsity-based algorithm for detecting faults in rotating machines[J].Mechanical Systems and Signal Processing,2016,72-73:46-64.
[13]Li Qing,Liang S Y.Multiple faults detection for rotating machinery based on Bicomponent sparse low-rank matrix separation approach[J].IEEE Access,2018,6:20242-20254.
[14]Du Zhaohui,Chen Xuefeng,Zhang Han,et al.Weighted low-rank sparse model via nuclear norm minimization for bearing fault detection[J].Journal of Sound and Vibration,2017,400:270-287.
[15]Donoho D L.De-noising by soft-thresholding[J].IEEETransactions on Information Theory,1995,41(3):613-627.
[16]Selesnick I W.Total variation denoising via the Moreau envelope[J].IEEE Signal Processing Letters,2017,24(2):216-220.
[17]Condat L.A direct algorithm for 1-D total variation denoising[J].IEEE Signal Processing Letters,2013,20(11):1054-1057.
[18]Huber P J.Robust regression:asymptotics,conjectures and Monte Carlo[J].The Annals of Statistics,1973,1(5):799-821.
[19]Parikh N,Boyd S.Proximal algorithms[J].Foundations and Trends in Optimization,2013,1(3):123-231.
[20]Donoho D L,Johnstone L M.Ideal spatial adaptation by wavelet shrinkage[J].Biometrika,1994,81(3):425-455.
[21]Bauschke H H,Combettes P L.Convex analysis and monotone operator theory in Hilbert spaces[M].New York,NY:Springer,2011.
[22]Li Qing,Ji Xia,Liang S Y.Incipient fault feature extraction for rotating machinery based on improved AR-minimum entropy deconvolution combined with variational mode decomposition approach[J].Entropy,2017,19(7):317.
[23]Zhang Ming,Jiang Zhinong,Feng Kun.Research on variational mode decomposition in rolling bearings fault diagnosis of the multistage centrifugal pump[J].Mechanical Systems and Signal Processing,2017,93:460-493.