AM-FM算子分解方法在滚动轴承故障诊断中的应用

黄武; 郑近德; 童靳于; 潘海洋; 刘庆运

doi:10.13433/j.cnki.1003-8728.20230019

AM-FM算子分解方法在滚动轴承故障诊断中的应用

doi: 10.13433/j.cnki.1003-8728.20230019

安徽工业大学机械工程学院，安徽马鞍山 243032

基金项目:

国家自然科学基金项目 51975004

安徽省自然科学基金项目 2008085QE215

详细信息

作者简介:
黄武，硕士研究生，wuhwang1999@163.com

通讯作者:
郑近德，教授，硕士生导师，博士，jdzheng@ahut.edu.cn

中图分类号: TN911.7; TH165.3
计量
- 文章访问数: 13
- HTML全文浏览量: 3
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2022-04-08
- 刊出日期: 2024-07-25

AM-FM Operator Decomposition Method and Its Application in Rolling Bearing Fault Diagnosis

School of Mechanical Engineering, Anhui University of Technology, Ma′anshan 243032, Anhui, China

摘要

摘要: 基于算子的零空间追踪算法能够实现复杂信号的自适应分解，其关键在于信号模型的构造与求解。通过定义一种新的可完全消除调幅调频信号的调幅调频算子(AFO)，进一步建立了一种基于AFO的信号分解新模型。为了提高参数对信号分解的鲁棒性，将非参数正则化(NPR)方法用于解决上述模型的约束优化问题，提出了一种基于NPR的自适应信号分解方法——NPR-AFO。论文将NPR-AFO方法引入到机械故障诊断中，并通过仿真和滚动轴承局部故障实测数据分析，与现有的其他分解方法进行了对比。结果表明: 所提方法不仅可以有效的提取故障特征，而且状态故障特征更加明显。
- 经验模态分解 /
- 零空间算子 /
- 调幅调频信号 /
- 故障诊断 /
- 非参数正则化
Abstract: The operator-based null-space tracking algorithm can realize the adaptive decomposition of complex signals, and it is a key step to construct and solve the signal model. A new signal decomposition model based on AFO is further established by defining a new AM-FM operator (AFO) which can completely annihilate AM-FM signals. In order to improve the robustness of parameters to signal decomposition, a nonparametric regularization (NPR) method is used to solve the constrained optimization problem of the above models, and an NPR-based adaptive signal decomposition method, called NPR-AFO, is proposed. This paper introduces the NPR-AFO method into mechanical fault diagnosis, and compares it with other existing decomposition methods through simulation and analysis of the measured data of local faults of rolling bearings. The results show that the proposed method can not only effectively extract fault features, but also the state failure characteristics are more obvious.
- empirical mode decomposition /
- null space operator /
- amplitude-modulated and frequency-modulated (AM-FM) signal /
- fault diagnosis /
- nonparametric regularization

HTML全文

图 1 NPR-AFO流程图

Figure 1. The flowchart of NPR-AFO

下载: 全尺寸图片幻灯片

图 2 S₁(t)及其分量

Figure 2. S₁(t) and its components

下载: 全尺寸图片幻灯片

图 3 5种信号分解方法分解的结果

Figure 3. The components of five signal decomposition methods

下载: 全尺寸图片幻灯片

图 4 寿命预测模拟实验台

Figure 4. Life prediction simulation test bench

下载: 全尺寸图片幻灯片

图 5 外圈故障的滚动轴承

Figure 5. Rolling bearing with outer ring failure

下载: 全尺寸图片幻灯片

图 6 外圈故障的滚动轴承信号的时域波形

Figure 6. Time domain waveform of rolling bearing signal with outer ring faults

下载: 全尺寸图片幻灯片

图 7 5种方法分解的分量

Figure 7. The components decomposed with the five methods

下载: 全尺寸图片幻灯片

图 8 分量的平方包络谱

Figure 8. The squared envelope spectrum of components

下载: 全尺寸图片幻灯片

表 1 5种方法分解的分量的正交性和信噪比指标的对比

Table 1. Comparison of component orthoganality and SNR indexes using the five methods

方法	IO	SNR₁	SNR₂
NPR-AFO	0.006 4	16.793 9	17.045 3
NS-SO	0.039 8	5.156 4	5.407 8
VMD	0.075 8	-1.022 2	5.214 3
EWT	0.234 2	5.671 7	5.386 8
EEMD	0.137 8	1.071 4	1.678 3

下载: 导出CSV

表 2 4个分量的故障特征能量占比指标对比

Table 2. Comparison of fault characterization energy share metrics for the four components

方法	ER₁	ER₂	ER₃	ER₄
NPR-AFO	0.957 5	0.947 4	0.888 0	0.029 2
NS-SO	0.158 5	0.090 1	0.010 9	0.561 9
VMD	0.943 9	0.612 2	0.012 3	0.013 0
EWT	0.353 2	0.112 3	0.026 2	3.6×10^-4
EEMD	0.553 0	0.341 9	0.096 8	0.049 5

下载: 导出CSV

参考文献(24)

[1]	YING W M, ZHENG J D, PAN H Y, et al. Permutation entropy-based improved uniform phase empirical mode decomposition for mechanical fault diagnosis[J]. Digital Signal Processing, 2021, 117: 103167. doi: 10.1016/j.dsp.2021.103167
[2]	YING W M, TONG J Y, DONG Z L, et al. Composite multivariate multi-scale permutation entropy and Laplacian score based fault diagnosis of rolling bearing[J]. Entropy, 2022, 24(2): 160. doi: 10.3390/e24020160
[3]	HUANG N E, WU Z H. A review on Hilbert-Huang transform: method and its applications to geophysical studies[J]. Reviews of Geophysics, 2008, 46(2): RG2006.
[4]	PENG S L, HWANG W L. Adaptive signal decomposition based on local narrow band signals[J]. IEEE Transactions on Signal Processing, 2008, 56(7): 2669-2676. doi: 10.1109/TSP.2008.917360
[5]	DAUBECHIES I, LU J F, WU H T. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool[J]. Applied and Computational Harmonic Analysis, 2011, 30(2): 243-261. doi: 10.1016/j.acha.2010.08.002
[6]	LIU Z L, XU K L, LI D, et al. Automatic mode extraction of ultrasonic guided waves using synchrosqueezed wavelet transform[J]. Ultrasonics, 2019, 99: 105948. doi: 10.1016/j.ultras.2019.105948
[7]	HU Y, TU X T, LI F C. High-order synchrosqueezing wavelet transform and application to planetary gearbox fault diagnosis[J]. Mechanical Systems and Signal Processing, 2019, 131: 126-151. doi: 10.1016/j.ymssp.2019.05.050
[8]	程军圣, 郑近德, 杨宇. 一种新的非平稳信号分析方法——局部特征尺度分解法[J]. 振动工程学报, 2012, 25(2): 215-220. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201202018.htm CHENG J S, ZHENG J D, YANG Y. A nonstationary signal analysis approach-the local characteristic-scale decomposition method[J]. Journal of Vibration Engineering, 2012, 25(2): 215-220. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201202018.htm
[9]	DRAGOMIRETSKIY K, ZOSSO D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62(3): 531-544. doi: 10.1109/TSP.2013.2288675
[10]	HUANG Y, LIN J H, LIU Z C, et al. A modified scale-space guiding variational mode decomposition for high-speed railway bearing fault diagnosis[J]. Journal of Sound and Vibration, 2019, 444: 216-234. doi: 10.1016/j.jsv.2018.12.033
[11]	GILLES J. Empirical wavelet transform[J]. IEEE Transac-tions on Signal Processing, 2013, 61(16): 3999-4010. doi: 10.1109/TSP.2013.2265222
[12]	郑近德, 潘海洋, 程军圣, 等. 基于自适应经验傅里叶分解的机械故障诊断方法[J]. 机械工程学报, 2020, 56(9): 125-136. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB202009015.htm ZHENG J D, PAN H Y, CHENG J S, et al. Adaptive empirical Fourier decomposition based mechanical fault diagnosis method[J]. Journal of Mechanical Engineering, 2020, 56(9): 125-136. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB202009015.htm
[13]	PENG S L, HWANG W L. Null space pursuit: an operator-based approach to adaptive signal separation[J]. IEEE Transactions on Signal Processing, 2010, 58(5): 2475-2483. doi: 10.1109/TSP.2010.2041606
[14]	HU X Y, PENG S L, GUO B K, et al. Accurate AM-FM signal demodulation and separation using nonparametric regularization method[J]. Signal Processing, 2021, 186: 108131. doi: 10.1016/j.sigpro.2021.108131
[15]	HU X Y, PENG S L, HWANG W L. Operator based multicomponent AM-FM signal separation approach[C]//2011 IEEE International Workshop on Machine Learning for Signal Processing. Beijing: IEEE, 2011: 1-6.
[16]	HU X Y, PENG S L, HWANG W L. Multicomponent AM-FM signal separation and demodulation with null space pursuit[J]. Signal, Image and Video Processing, 2013, 7(6): 1093-1102. doi: 10.1007/s11760-012-0354-9
[17]	BIRGIN E G, MARTÍNEZ J M. Complexity and performance of an augmented Lagrangian algorithm[J]. Optimization Methods and Software, 2020, 35(5): 885-920. doi: 10.1080/10556788.2020.1746962
[18]	BIRGIN E G, MARTÍNEZ J M. Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization[J]. Computational Optimization and Applications, 2012, 51(3): 941-965. doi: 10.1007/s10589-011-9396-0
[19]	ANDREANI R, HAESER G, MITO L M, et al. On the best achievable quality of limit points of augmented Lagrangian schemes[J]. Numerical Algorithms, 2022, 90(2): 851-877. doi: 10.1007/s11075-021-01212-8
[20]	HUANG B H, MA C F. An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations[J]. Applied Mathematics and Computation, 2018, 328: 58-74. doi: 10.1016/j.amc.2018.01.020
[21]	AMIRI ROSHAN S, RAHMANI M. Consensus-based robust least-squares filter for multi-sensor systems[J]. International Journal of Adaptive Control and Signal Processing, 2022, 36(5): 1098-1115. doi: 10.1002/acs.3385
[22]	BOT R I, CSETNEK E R, NGUYEN D K. A proximal minimization algorithm for structured nonconvex and nonsmooth problems[J]. SIAM Journal on Optimization, 2019, 29(2): 1300-1328. doi: 10.1137/18M1190689
[23]	JIA Z H, HUANG J R, CAI X J. Proximal-like incremental aggregated gradient method with Bregman distance in weakly convex optimization problems[J]. Journal of Global Optimization, 2021, 80(4): 841-864. doi: 10.1007/s10898-021-01044-9
[24]	CARVALHO M L, IL'YASOV Y, SANTOS C A. Separating solutions of nonlinear problems using nonlinear generalized Rayleigh quotients[J]. Topological Methods in Nonlinear Analysis, 2021, 58(2): 453-480.