基于稀疏指标的优化变分模态分解方法

PDF(7723 KB)

振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 234-250.

论文

基于稀疏指标的优化变分模态分解方法

张露1,2，理华1，崔杰1，王晓东1，肖灵1

作者信息 +

An optimal variational mode decomposition method based on sparse index

ZHANG Lu1,2,LI Hua1,CUI Jie1,WANG Xiaodong1,XIAO Ling1

Author information +

文章历史 +

摘要

针对复合信号源信号数目未知，无法正确预设分解模态数K值而不能对信号进行有效VMD分解的问题，本文提出了一种基于稀疏指标的优化变分模态分解方法。该方法基于VMD分解所构建变分模型中各个分量的稀疏先验知识，实现了VMD自适应寻优K值，其将最佳K值确定为稀疏指标由上升至下降的转折点。计算VMD分解各个分量的稀疏度时，考虑到不同分量间的能量差异加入了能量权值因子，最后将稀疏指标确定为分解后各分量边际谱稀疏度的平均值。仿真信号与实际信号分解实验验证表明，相较于其它两种VMD分解K值确定方法，本文方法确定的K值结果更为准确，实现的优化VMD分解自适应性更强，较其它信号分解方法如EMD分解有更好的分解效果，为源信号数目未知的复合信号VMD分解提供了新思路。此外，噪声的鲁棒性实验证明所提基于稀疏指标的优化变分模态分解方法具有一定的抗噪能力，较为稳健，可开发应用于实际工程。

Abstract

This paper presents a sparse index-based variational mode decomposition method to deal with the challenge of determining the decomposition mode number K when the number of composite signal sources is unknown. Based on the sparse prior theory of each component in the VMD decomposition, the adaptive optimal K value of VMD is discovered as the turning point of the sparse index from rising to falling. Considering the energy difference between different components, the energy weight factor is added in the computation of sparsity index. Finally, the sparsity index is determined as the average value of the marginal spectral sparsity of each component after decomposition. The results of simulations and real-world signal decomposition experiments prove the superiority of this method. Compared with the other two modified VMD methods, proposed method determines a more accurate K value and is more adaptive. Moreover, The results of experiment show that the method has a better decomposition effect than other signal decomposition methods like EMD. Proposed method introduces a novel concept for adaptive and efficient VMD decomposition of composite signals with unknown source numbers. To the next level, the robust noise experiment demonstrates that the suggested sparse index approach has a certain anti-noise ability. It shows that this method is relatively robust and it can be developed and applied to practical engineering.

导出引用

张露1,2，理华1，崔杰1，王晓东1，肖灵1. 基于稀疏指标的优化变分模态分解方法[J]. 振动与冲击, 2023, 42(8): 234-250

ZHANG Lu1,2,LI Hua1,CUI Jie1,WANG Xiaodong1,XIAO Ling1. An optimal variational mode decomposition method based on sparse index[J]. Journal of Vibration and Shock, 2023, 42(8): 234-250

参考文献

[1] 周晨赓. 几种信号分析方法对非线性、非平稳信号分析效果的比较[J]. 山东电子, 2003, 000(004):43-45.
        ZHOU Chen-geng. Comparison of several signal analysis methods for nonlinear and nonstationary signals [J] . Journal of Shandong electronics, 2003, 000(004) : 43-45.
[2] Dragomiretskiy K, Zosso D. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62(3):531-544.
[3] 张爽，王晓东，李祥，等. 基于FVMD的滚动轴承故障特征提取方法[J]. 振动与冲击, 2022, 41(6): 236-244.
ZHANG Shuang, WANG Xiao-dong, LI Xiang,et al. Extraction method of rolling bearing fault characteristics based on FVMD[J]. Journal of vibration and shock, 2022, 41(6): 236-244.
[4] 李双江，辛景舟，付雷，等. 基于VMD-KLD的桥梁挠度监测数据温度效应分离方法[J]. 振动与冲击，2022, 41(5): 105-113.
LI Shuang-jiang, XIN Jing-zhou, FU Lei,et al. Temperature effect separation method of bridge deflection monitoring data based on VMD-KLD[J]. Journal of vibration and shock, 2022, 41(5): 105-113.
[5] 吕明珠，刘世勋，苏晓明，等. 基于自适应变分模态分解和包络谐噪比的滚动轴承早期退化检测[J]. 振动与冲击，2021, 40(13): 271-280.
LU Ming-zhu, LIU Shi-xun, SU Xiao-ming,et al. Early degradation detection of rolling bearings based on adaptive variational mode decomposition and envelope harmonic noise ratio[J]. Journal of vibration and shock, 2021, 40(13) : 271-280.
[6] 郝家琦，徐金海，鲍超超，等. 基于VMD与SVM的电梯鼓式制动器故障诊断研究[J]. 机电工程, 2022, 39(1):8.
HAO Jia-qi, XU Jin-hai, BAO Chao-chao,et al. Fault diagnosis of elevator drum brake based on VMD and SVM [J]. Journal of Mechanical & Electrical Engineering, 2022, 39(1) : 8.
[7] 张玉良，马宏忠，蒋梦瑶. 基于VMD-MSVM的同步调相机载荷分配故障诊断方法[J]. 电力工程技术，2022, 41(1):7.
ZHANG Yu-liang, MA Hong-zhong, JIANG Meng-yao. Load distribution fault diagnosis method of synchronous condenser based on VMD-MSVM [J]. Electric Power Engineering Technology, 2022, 41(1) : 7.
[8] 胡威，张新燕，李振恩，等. 基于优化的VMD-mRMR-LSTM模型的短期负荷预测[J]. 电力系统保护与控制，2022, 50(1):10.
HU Wei, ZHANG Xin-yan, LI Zhen-en,et al. Short term load forecasting based on optimized vmd-mr-lstm model [J]. Journal of Power System Protection and control, 2022, 50(1) : 10.
[9] 唐贵基，王晓龙. IVMD融合奇异值差分谱的滚动轴承早期故障诊断[J]. 振动．测试与诊断, 2016, 36(4):8.
        TANG gui-ji, WANG Xiao-long. An incipient fault diagnosis method for rolling bearing based on improved variational mode decomposition and singular value difference spectrum [J]. Journal of Vibration.,Measurement &Diagnosis, 2016, 36(4) : 8.
[10] 吴文轩，王志坚，张纪平，等. 基于峭度的VMD分解中k值的确定方法研究[J]. 机械传动, 2018, 42(8):5.
        WU Wen-xuan, WANG Zhi-jian, ZHANG Ji-ping,et al. Research of the Method of Determining k Value in VMD based on Kurtosis[J]. Journal of Mechanical Transmission, 2018, 42(8) : 5.
[11] 赵知劲，黄艳波，强芳芳，等. 基于反馈变分模式分解的单通道盲源分离算法[J]. 振动与冲击, 2019, 38(13):6.
ZHAO Zhi-jin, HUANG Yan-bo, QIANG Fang-fang,et al. Single channel blind source separation algorithm based on feedback variational mode decomposition[J]. Journal of vibration and shock, 2019, 38(13): 261-267.
[12] 宋玉琴，邓思成，路彦刚. K值优化的VMD在轴承故障诊断中的应用[J]. 测控技术, 2019, 038(004):117-121.
        SONG Yu-qin, DENG Si-cheng, LU Yan-gang. Application of K value optimized VMD in bearing fault diagnosis [J]. Journal of Measurement and control technology, 2019, 038(004):117-121.
[13] 何勇，王红，谷穗. 一种基于遗传算法的VMD参数优化轴承故障诊断新方法[J]. 振动与冲击，2021, 40(6):6.
HE Yong, WANG Hong, GU Sui. New fault diagnosis approach for bearings based on parameter optimized VMD and genetic algorithm[J]. Journal of vibration and shock, 2021, 40(6): 184-189.
[14] 唐贵基，王晓龙. 参数优化变分模态分解方法在滚动轴承早期故障诊断中的应用[J]. 西安交通大学学报, 2015, 49(05):73-81.
TANG Gui-ji,WANG Xiao-long. Parameter Optimized Variational Mode Decomposition Method with Application to Incipient Fault Diagnosis of Rolling Bearing[J]. Journal of Xi'an Jiaotong University, 2015, 49(05):73-81.
[15] 李翠省，刘永强，廖英英. 基于EEMD和参数自适应VMD的高速列车轮对轴承故障诊断[J]. 振动与冲击，2022, 41(1): 68-77.
LI Cui-xing, LIU Yong-qiang, LIAO Ying-ying. Fault diagnosis of wheelset bearing of high-speed train based on EEMD and parameter adaptive VMD[J]. Journal of vibration and shock, 2022, 41(1): 68-77
[16] 刘建昌，权贺，于霞，等. 基于参数优化 VMD 和样本熵的滚动轴承故障诊断[J]. 自动化学报，2022, 48(3):808-819.
         LIU Jian-chang, QUAN He, Yu Xia,et al. Rolling bearing fault diagnosis based on parameter optimization VMD and sample entropy[J]. Journal of ACTA AUTOMATICA SINICA, 2022, 48(3) : 808-819.
[17] Lu N , Zhou T X , Wei J F,et al. Application of a whale optimized variational mode decomposition method based on envelope sample entropy in the fault diagnosis of rotating machinery[J]. Measurement Science and Technology, 2022, 33(1):015014 (16pp).
[18] 杨宇，于德介，程军圣. 基于Hilbert边际谱的滚动轴承故障诊断方法[J]. 振动与冲击，2005，24(1):70-72.
YANG Yu, YU De-jie, CHENG jun-sheng. Roller bearing fault diagnosis based on Hilbert marginal spectrum [J] . Journal of vibration and shock, 2005, 24(1) : 70-72.
[19] 何昭水，谢胜利，傅予力. 信号的稀疏性分析[J]. 自然科学进展，2006, 16(9):7.
        HE Zhao-shui, XIE Sheng, FU Yu-li. Signal sparsity analysis [ J ] . Journal of Progress in Natural Science, 2006, 16(9) : 7.
[20] Randall R B, Antoni J, Chobsaard S. THE RELATIONSHIP BETWEEN SPECTRAL CORRELATION AND ENVELOPE ANALYSIS IN THE DIAGNOSTICS OF BEARING FAULTS AND OTHER CYCLOSTATIONARY MACHINE SIGNALS[J]. Mechanical Systems & Signal Processing, 2001, 15(5):945-962.
[21] Case Western Reserve University（CWRU）bearing data center[EB/OL].[2019-08-19].https：//csegroups.case.edu/ bearingdatacenter/.
[22] Lessmeier C , Kimotho J K , D Zimmer, et al. Condition Monitoring of Bearing Damage in Electromechanical Drive Systems by Using Motor Current Signals of Electric Motors: A Benchmark Data Set for Data-Driven Classification[C]// European Conference of the Prognostics and Health Management Society. 2016.