Abstract：Extreme-point symmetric mode decomposition (ESMD) has an end-effect problem in power harmonic detection. Based on the analysis and summary of current suppression methods, an extended-point-symmetry-mode-decomposition algorithm based on improved extreme-wave extension and symmetry is proposed. Midpoint interpolation combined with the ESMD endpoint effect suppression method. Firstly, the signal is extended at both ends by using the modified extremum wave continuation method, and then the symmetry mid-point interpolation is used to perform the ESMD decomposition, and the continuation parts at both ends are truncated to limit the end effect from contaminating the internal signal. At the same time, an end-effect evaluation index that adaptively determines the effective data length is proposed, which can effectively avoid the problem caused by artificially determining the data length, and more objectively quantify the degree of "drift" of the endpoints of the intrinsic mode function (IMF). Through the simulation and experimental results analysis, and compared with the extreme wave extension, this method is proved to be effective in suppressing the end effect of the ESMD power harmonics.
[1] 王丽梅, 孙璐, 初升. 基于经验模态分解算法的永磁直线同步电机迭代学习控制[J]. 电工技术学报, 2017, 32(6): 164-171. Wang Limei, Sun Lu, Chu Sheng.Iterative learning control of permanent magnet linear synchronous motor based on empirical mode decomposition algorithm[J]. Transactions of China Electrotechnical Society, 2017, 32(6): 164-171. [2] 孙曙光, 于晗, 杜太行, 等. 基于振动信号样本熵和相关向量机的万能式断路器分合闸故障诊断[J]. 电工技术学报, 2017, 32(7): 20-30. Sun Shuguang, Yu Han, Du Taihang, et al.Fault diagnosis of universal circuit breaker closing and closing based on sample entropy of vibration signal and correlation vector machine[J]. Transactions of China Electrotechnical Society, 2017, 32(7): 20-30. [3] 李东东, 周文磊, 郑小霞, 等. 基于自适应EEMD和分层分形维数的风电机组行星齿轮箱故障检测[J]. 电工技术学报, 2017, 32(22): 233-241. Li Dongdong, Zhou Wenlei, Zheng Xiaoxia, et al.Fault detection of planetary gearbox for wind turbine based on adaptive EEMD and hierarchical fractal dimensions[J]. Transactions of China Electro- technical Society, 2017, 32(22): 233-241. [4] 丁晓慧, 刘俊杰, 邢强. 基于自适应局部均值的EMD方法及其在谐波检测中的应用[J]. 电力系统保护与控制, 2017, 45(14): 17-25. Ding Xiaohui, Liu Junjie, Xing Qiang.Adaptive local mean based EMD method and its application in harmonic detection[J]. Power System Protection and Control, 2017, 45(14): 17-25. [5] 吕敬祥, 刘国强. 磁声电无损检测及改进的EMD消噪方法[J]. 电工技术学报, 2018, 33(17): 3935-3942. Lü Jingxiang, Liu Guoqiang.Non-magnetic nonde- structive testing and improved EMD denoising method[J]. Transactions of China Electrotechnical Society, 2018, 33(17): 3935-3942. [6] 朱永利, 王刘旺. 并行EEMD算法及其在局部放电信号特征提取中的应用[J]. 电工技术学报, 2018, 33(11): 2508-2519. Zhu Yongli, Wang Liuwang.Parallel EEMD algo- rithm and its application in feature extraction of partial discharge signals[J]. Transactions of China Electrotechnical Society, 2018, 33(11): 2508-2519. [7] Wang Jinliang, Li Zongjun.Extreme-point symmetric mode decomposition method for nonlinear and non- stationary signal processing[J]. Advances in Adaptive Data Analysis, 2013, 5(3): 1350014. [8] 王金良, 李宗军. 极点对称模态分解方法: 数据分析与科学探索的新途径[M]. 北京: 高等教育出版社, 2015. [9] 张淑清, 徐剑涛, 姜安琦, 等. 基于极点对称模态分解和概率神经网络的轴承故障诊断[J]. 中国机械工程, 2017, 28(4): 425-431. Zhang Shuqing, Xu Jiantao, Jiang Anqi, et al.Bearing fault diagnosis based on polar symmetric modal decomposition and probabilistic neural net- work[J]. China Mechanical Engineering, 2017, 28(4): 425-431. [10] 晏飞, 杨涛, 庞毅飞, 等. 基于波形平均的经验模态分解端点效应抑制方法[J]. 机械设计与制造, 2017, 38(5): 212-215. Yan Fei, Yang Tao, Pang Yifei, et al.End effect suppression method based on waveform averaging of empirical mode decomposition[J]. Mechanical Design & Manufacture, 2017, 38(5): 212-215. [11] 顾小兴, 金涛, 郭艳威. 改进EMD端点效应电力系统HHT谐波检测研究[J]. 中国测试, 2015, 41(3): 99-102. Gu Xiaoxing, Jin Tao, Guo Yanwei.Research on HHT harmonic detection of power system based on improved EMD endpoint effect[J]. China Test, 2015, 41(3): 99-102. [12] 郭艳威, 金涛. 一种基于改进EMD端点效应的电能质量分析新方法[J]. 电气技术, 2013, 14(12): 13-15. Guo Yanwei, Jin Tao.A new method of power quality analysis based on improved EMD endpoint effect[J]. Electrical Technology, 2013, 14(12): 13-15. [13] 刘德利, 曲延滨. 改进的希尔伯特-黄变换在电力谐波中的应用研究[J]. 电力系统保护与控制, 2012, 40(6): 69-73. Liu Deli, Qu Yanbin.Application of improved Hilbert Huang transform in power harmonics[J]. Power System Protection and Control, 2012, 40(6): 69-73. [14] 王学敏, 黄方林. EMD端点效应抑制的一种实用方法[J]. 振动、测试与诊断, 2012, 32(3): 493-497. Wang Xuemin, Huang Fanglin.A practical method for EMD endpoint effect suppression[J]. Vibration, Testing and Diagnosis, 2012, 32(3): 493-497. [15] 王录雁, 王强, 鲁冬林, 等. EMD自适应三角波匹配延拓算法[J]. 振动与冲击, 2014, 33(4): 94-99. Wang Luyan, Wang Qiang, Lu Donglin, et al.EMD adaptive triangle wave matching continuation algo- rithm[J]. Vibration and Shock, 2014, 33(4): 94-99. [16] 魏永合, 牛保国, 刘雪丽, 等. 波形曲率延拓在局域均值分解中的应用[J]. 中国机械工程, 2016, 27(3): 343-348. Wei Yonghe, Niu Baoguo, Liu Xueli, et al.Appli- cation of wave curvature continuation in local mean decomposition[J]. China Mechanical Engineering, 2016, 27(3): 343-348. [17] 杨小强, 李沛, 黄杰, 等. 基于极值波延拓的端点效应处理方法[J]. 系统工程与电子技术, 2016, 38(9): 1987-1992. Yang Xiaoqiang, Li Pei, Huang Jie, et al.Terminal point effect processing method based on extreme wave continuation[J]. System Engineering and Elec- tronic Technology, 2016, 38(9): 1987-1992. [18] 李伟红, 田真真, 龚卫国, 等. 改进的ESMD用于公共场所异常声音特征提取[J]. 仪器仪表学报, 2016, 37(11): 2429-2437. Li Weihong, Tian Zhenzhen, Gong Weiguo, et al.Improved ESMD for the extraction of anomalous sound features in public places[J]. Journal of Instrument and Meter, 2016, 37(11): 2429-2437. [19] 任达千, 吴昭同, 严拱标. EMD端点效应的评价指标及抑制端点效应的窗函数法[J]. 制造业自动化, 2007, 29(1): 21-24. Ren Daqian, Wu Zhaotong, Yan Gongbiao.EMD endpoint effect evaluation index and window function method for restraining endpoint effect[J]. Manufacturing Automation, 2007, 29(1): 21-24. [20] 宁宁, 张骏, 高向阳. 有效数据在局域波端点效应评价指标中的应用[J]. 计算机工程与应用, 2009, 45(22): 215-217. Ning Ning, Zhang Jun, Gao Xiangyang.Application of effective data to local wave end effect evaluation index[J]. Computer Engineering and Applications, 2009, 45(22): 215-217.
2020, Vol. 35 
