优化递归变分模态分解及其在非线性信号处理中的应用

许子非; 岳敏楠; 李春

doi:10.7498/aps.68.20191005

摘要

经验模态分解一类的递归算法所产生的模态混淆和端点效应将导致所获物理信息失真, 变分模态分解可改善这些问题. 但因其需预设参数, 对信号分解精度影响显著, 为此, 提出采用目标信号功率谱峰值所对应的频率以初始化变分模态分解所需中心频率, 借鉴经验模态分解递归模型, 基于能量截止法将变分模态分解改进为递归模式算法, 并采用粒子群优化算法对具有带宽约束能力的惩罚因子进行最优取值, 构成优化递归变分模态分解. 通过对比分析经验模态分解, 集成经验模态分解及优化递归变分模态分解在分解信号时的计算精度; 研究传统变分模态分解与优化递归变分模态分解在处理实际振动信号时计算速率. 结果表明: 优化递归变分模态分解在处理目标信号时精度最高, 与原分量相关性达99.9%; 与集成经验模态分解对比, 可由低至高将信号分解至不同频段, 物理意义更加清晰且不产生虚假模态; 处理实际非线性信号时, 优化递归变分模态分解无需预设分解模态个数, 相比于传统变分模态分解, 计算速率高12.5%—18.5%.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
上海理工大学能源与动力工程学院, 上海　200093

2.
上海市动力工程多相流动与传热重点实验室, 上海　200093

通信作者: 李春, lichunusst@163.com

基金项目: 国家自然科学基金(批准号: 51976131, 51676131)、国家自然科学地区合作与交流项目(批准号: 51811530315)和上海市“科技创新心动计划”地方院校能力建设项目(批准号: 19060502200)资助的课题

Authors and contacts

1.
University of Shanghai for Science and Technology, Energy and Power Engineering Institute, Shanghai 200093, China

2.
Shanghai Key Laboratory of Multiphase Flow and Heat Transfer for Power Engineering, Shanghai 200093, China

Corresponding author: Li Chun, lichunusst@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51976131, 51676131), the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No. 51811530315), and the Shanghai Committee of Science and Technology, China (Grant No. 19060502200)

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参考文献

[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
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[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 物理学报 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)
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[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
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[31]	Shao X D, Chen F 2019 Signal Process. 160 237 Google Scholar

施引文献

图 1 递归VMD流程

Fig. 1. The recursive VMD diagram.

下载: 全尺寸图片幻灯片

图 2 基于PSO优化改进递归VMD参数流程

Fig. 2. The process of using PSO to optimize recursive VMD parameter.

下载: 全尺寸图片幻灯片

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

Fig. 3. Analog signal and its component waveform:　(a) s₁; (b) s₂; (c) s₃; (d) f.

下载: 全尺寸图片幻灯片

图 4 EMD分解结果　(a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) res

Fig. 4. The results of EMD: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) res.

下载: 全尺寸图片幻灯片

图 5 EEMD分解结果　(a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) res

Fig. 5. The results of EEMD: (a) IMF1; (b) IMF2; (c) IMF3; (d) IMF4; (e) IMF5; (f) IMF6; (g) IMF7; (h) res.

下载: 全尺寸图片幻灯片

图 6 ORVMD分解结果　(a) IMF1; (b) IMF2; (c) IMF3

Fig. 6. The results of ORVMD: (a) IMF1; (b) IMF2; (c) IMF3.

下载: 全尺寸图片幻灯片

图 7 早期轴承内圈故障信号　(a) 时域; (b) 频谱

Fig. 7. Early inner race fault diagnosis signal.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

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

Fig. 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.

下载: 全尺寸图片幻灯片

图 10 VMD与ORVMD计算耗时

Fig. 10. The duration of calculation for VMD and ORVMD.

下载: 全尺寸图片幻灯片

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	—	—

下载: 导出CSV

[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 物理学报 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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