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Variational mode decomposition can improve traditional recursive algorithms, such as empirical mode decomposition, resulting modal aliasing and endpoint effects, but it has a significant influence on signal decomposition accuracy due to its pre-set parameters. The frequency corresponding to the peak value of the target signal power spectrum is proposed to initialize the center frequency required for the variational mode decomposition. The empirical mode decomposition and recursive model is used to improve the variational mode decomposition into the recursive mode algorithm based on the energy cutoff method. The group optimization algorithm optimally takes the penalty factor with bandwidth constraint ability to form an optimized recursive variational mode decomposition. By comparing with and analyzing empirical mode decomposition, integrating empirical mode decomposition and optimizing the computational accuracy of recursive variational mode decomposition in decomposing signals; studying traditional variational mode decomposition and optimizing recursive variational mode decomposition in dealing with actual vibration signals calculating rate, the results are obtained, showing that the optimized recursive variational mode decomposition has the highest accuracy when dealing with the target signal, and the correlation with the original component is 99.9%. Comparing with the integrated empirical mode decomposition, the signal can be decomposed into different frequency bands from low to high, and the physical meaning is clearer. No false modality is generated. When the actual nonlinear signal is processed, the optimized recursive variational mode decomposition does not need to preset the number of decomposition modes, and the calculation rate is 12.5%–18.5% higher than thay of the traditional variational mode decomposition.
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Keywords:
- variational mode decomposition /
- nonlinear /
- signal process
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Zheng X X, Chen G N, Ren H H, Li D D 2019 J. Vib. Shock 38 153
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Lv Z L 2016 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese)
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Google Scholar
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图 1 递归VMD流程
Figure 1. The recursive VMD diagram.
图 2 基于PSO优化改进递归VMD参数流程
Figure 2. The process of using PSO to optimize recursive VMD parameter.
图 3 合成信号及其分量 (a) 分量s1; (b) 分量s2; (c) 分量s3; (d) 合成信号f
Figure 3. Analog signal and its component waveform: (a) s1; (b) s2; (c) s3; (d) f.
图 4 EMD分解结果 (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) res
Figure 4. The results of EMD: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) res.
图 5 EEMD分解结果 (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) res
Figure 5. The results of EEMD: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) res.
图 6 ORVMD分解结果 (a) IMF1; (b) IMF2; (c) IMF3
Figure 6. The results of ORVMD: (a) IMF1; (b) IMF2; (c) IMF3.
图 7 早期轴承内圈故障信号 (a) 时域; (b) 频谱
Figure 7. Early inner race fault diagnosis signal.
图 8 故障信号EEMD分解结果 (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) IMF8; (i) IMF9; (j) IMF10; (k) IMF11; (l) IMF12
Figure 8. The results of EEMD for fault signal: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) IMF8; (i) IMF9; (j) IMF10; (k) IMF11; (l) IMF12.
图 9 故障信号ORVMD分解结果 (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) IMF8; (i) IMF9
Figure 9. The results of ORVMD for fault diagnosis: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) IMF8; (i) IMF9.
图 10 VMD与ORVMD计算耗时
Figure 10. The duration of calculation for VMD and ORVMD.
表 1 ORVMD参数组合
Table 1. Parameter set of ORVMD.
编号 K, α 编号 K, α 1 12, 12100 14 12, 12400 2 12, 12900 15 12, 12000 3 12, 11800 16 12, 12000 4 12, 11900 17 13, 11900 5 12, 11800 18 12, 11900 6 12, 12700 19 12, 11400 7 12, 12100 20 12, 11900 8 12, 13100 21 13, 11900 9 12, 12100 22 12, 11900 10 12, 12000 23 12, 12000 11 11, 12000 24 12, 12000 12 11, 12000 25 11, 12100 13 12, 13200 — — 
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[1] Ingerman E A, London R A, Heintzmann R, Gustafsson M G L 2019 J. Microsc. 273 11
[2] Banjade T P, Yu S, Ma J 2019 J. Seismol. 5 1
[3] Yang F, Shen X, Wang Z 2018 Entropy 20 8
[4] Lian J J, Zhuo L, Wang H J, Dong X F 2018 Mech. Syst. Sig. Process. 107 53
Google Scholar
[5] Klionskiy D M, Kaplun D I, Geppener V V 2018 Pattern Recognit Image Anal. 28 122
Google Scholar
[6] Chervyakov N, Lyakhov P, Kaplun D, Butusov D, Nagornov N 2018 Electronics 8 135
[7] Qiu X, Ren Y, Suganthan P N, Amaratunga G A J 2017 Appl. Soft Comput. 54 246
Google Scholar
[8] Sweeney K T, Mcloone S F, Ward T E 2013 IEEE Trans. Biomed. Eng. 60 97
Google Scholar
[9] Guo Y, Naik G R, Nguyen H 2017 IEEE Eng. Med. Biol. Soc. 2013 6812
[10] Wang Y, Liu F, Jiang Z S, He S L, Mo Q Y 2017 Mech. Syst. Sig. Process. 86 75
Google Scholar
[11] Xiong T, Bao Y, Zhongyi H U 2014 Neurocomputing 123 174
Google Scholar
[12] Dragomiretskiy K, Zosso D 2014 IEEE Trans. Sig. Process. 62 531
[13] Wang Y X, Markert R, Xiang J W, Zheng W G 2015 Mech. Syst. Sig. Process. 60 243
[14] Yang F R, Bi X, Li C C, Liu C F, Tian T 2019 Measurement 140 1
Google Scholar
[15] 郑小霞, 陈广宁, 任浩翰, 李东东 2019 振动与冲击 38 153
Zheng X X, Chen G N, Ren H H, Li D D 2019 J. Vib. Shock 38 153
[16] 唐贵基, 王晓龙 2015 西安交通大学学报 49 73
Google Scholar
Tang G J, Wang X L 2015 J. Xi'an Jiaotong Univ. 49 73
Google Scholar
[17] 刘备, 胡伟鹏, 邹孝, 丁亚军, 钱盛友 2019 68 028702
Google Scholar
Liu B, Hu E P, Zou X, Ding Y J, Qian S Y 2019 Acta Phys. Sin. 68 028702
Google Scholar
[18] Baldini G, Steri G, Dimc F, Giuliani R 2016 Sensors 16 818
Google Scholar
[19] Chen X J, Yang Y M, Cui Z X, Shen J 2019 Energy 174 1110
Google Scholar
[20] Cui J, Yu R Z, Zhao D B, Yang J Y, Ge W C, Zhou X M 2019 Appl. Energy 247 480
Google Scholar
[21] Huang N E, Shen Z, Long S R 1998 Proc. Roy. Soc. A 454 903
Google Scholar
[22] Damerval C, Meignen S, Valerie P 2005 IEEE Signal Process Lett. 12 701
Google Scholar
[23] Cheng J S, Yu D J, Yang Y 2006 Mech. Syst. Sig. Process. 20 817
Google Scholar
[24] Kennedy J, Eberhart R 1995 IEEE Int. Conf. Neural Networks 4 1942
[25] 吕中亮 2016 博士学位论文(重庆: 重庆大学)
Lv Z L 2016 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese)
[26] Mcfadden P D, Smith J D 1984 J. Sound Vib. 96 69
Google Scholar
[27] Smith W A, Randall R B 2015 Mech. Syst. Sig. Process. 64–65 100
Google Scholar
[28] Chen F, Shi T, Duan S K, Wang L D, Wu J G 2017 Signal Process. 142 423
[29] Chen F, Li X Y, Duan S K, Wang L D, Wu J G 2018 Digit. Signal Prog. 81 16
Google Scholar
[30] Chen F, Shao X D 2017 Signal Process. 133 213
Google Scholar
[31] Shao X D, Chen F 2019 Signal Process. 160 237
Google Scholar
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