多金属离子极谱信号的改进经验模态分解降噪
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摘要
针对多金属离子极谱2阶导数信号易受外部环境和内部电路噪声干扰的问题,结合极谱2阶导数信号的峰形特点,提出一种基于改进经验模态分解(EMD)的极谱信号降噪方法。首先对信号进行EMD分解得到固有模态函数(IMF)分量,统计IMF分量中的局部极大值点数目,判断EMD分解是否停止;再根据IMF分量与原信号之间的关联度,将IMF分量分为3类,对不同类分量分别进行降噪处理;最后进行重构。仿真实验结果表明:该方法与标准EMD法相比能有效减少分解步骤,缩短分解时间;与小波阈值法相比,对信噪比的提升更大,最小均方误差更小。对铜钴镍3种离子的2阶导数极谱信号的降噪结果表明,该方法有效去除了离子极谱信号的噪声,并较好地保留了信号的细节特征,对极谱法测量多金属离子浓度有重要意义。
Aiming at the problem that the second-order derivative polarographic signal of multi-metal ions suffers from the noise interference of external environment and internal circuit, combining the peak shape characteristic of the second-order derivative polarographic signal, a polarographic signal denoising method based on improved empirical mode decomposition(EMD) is proposed. Firstly, the signal is decomposed to obtain the intrinsic mode function(IMF) components through EMD. Then, the number of local maximum points in the IMF components is counted to determine the termination condition of EMD decomposition. Next, the IMF components are divided into three categories according to the degree of correlation between the IMF components and the original signal. Subsequently, the noise reduction processing is carried out to different categories of IMF components, respectively. Finally, the denoised components are reconstructed. Simulation and experiment results show that compared with the standard EMD method the proposed method can effectively reduce the EMD decomposition steps and shorten the decomposition time. Compared with traditional wavelet threshold method, the proposed method has the advantage that the improvement of signal to noise ratio is significant and the minimum mean square error is smaller. The denoising results of the second derivative polarographic signals of copper, cobalt and nickel ions indicate that the proposed method can effectively decrease the noise of ion polarographic signal, retains the detailed features of the signal, and has great significance for the measurement of multi-metal ion concentration with polarographic method.
Aiming at the problem that the second-order derivative polarographic signal of multi-metal ions suffers from the noise interference of external environment and internal circuit, combining the peak shape characteristic of the second-order derivative polarographic signal, a polarographic signal denoising method based on improved empirical mode decomposition(EMD) is proposed. Firstly, the signal is decomposed to obtain the intrinsic mode function(IMF) components through EMD. Then, the number of local maximum points in the IMF components is counted to determine the termination condition of EMD decomposition. Next, the IMF components are divided into three categories according to the degree of correlation between the IMF components and the original signal. Subsequently, the noise reduction processing is carried out to different categories of IMF components, respectively. Finally, the denoised components are reconstructed. Simulation and experiment results show that compared with the standard EMD method the proposed method can effectively reduce the EMD decomposition steps and shorten the decomposition time. Compared with traditional wavelet threshold method, the proposed method has the advantage that the improvement of signal to noise ratio is significant and the minimum mean square error is smaller. The denoising results of the second derivative polarographic signals of copper, cobalt and nickel ions indicate that the proposed method can effectively decrease the noise of ion polarographic signal, retains the detailed features of the signal, and has great significance for the measurement of multi-metal ion concentration with polarographic method.
引文
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[14] HUANG N E, WU M L C, LONG S R, et al. A confidence limit for the empirical mode decomposition and hilbert spectral analysis[J]. Proceedings Mathematical Physical & Engineering Sciences, 2003, 459(2037):2317- 2345.
[15] 赵志宏, 杨绍普, 申永军. 基于独立分量分析与相关系数的机械故障特征提取[J]. 振动与冲击, 2013, 32(6):67-72.ZHAO ZH H, YANG SH P, SHEN Y J. Machinery fault feature extraction based on independent component analysis and correlation coefficient [J]. Journal of Vibration and Shock, 2013, 32(6):67-72.
[16] 孙灵芳, 王彤彤, 徐曼菲,等. 基于改进CEEMD的薄层污垢超声检测信号去噪[J]. 仪器仪表学报, 2017,38(12):2879- 2887.SUN L F, WANG T T, XU M F, et al. Thin fouling ultrasonic detection signal denoising based on improved CEEMD[J]. Chinese Journal of Scientific Instrument, 2017,38(12):2879- 2887.
[17] ZHAO R M, CUI H M. Improved threshold denoising method based on wavelet transform[C]. International Conference on Modelling, Identification and Control, 2016:1354-1359.
[2] 朱红求, 王国伟, 阳春华,等. 基于类Gaussian分布的线性扫描极谱重叠峰分离方法[J]. 中国有色金属学报(英文版), 2013(7):2181- 2186.ZHU H Q, WANG G W, YANG CH H, et al. Overlapped peaks resolution for linear sweep polarography using Gaussian-like distribution [J]. Transactions of Nonferrous Metals Society of China, 2013(7):2181- 2186.
[3] 吴维昌. 二阶导数单扫描示波极谱法[J]. 分析化学, 1987(8):754-755.WU W CH. Second-order derivative single-sweeping oscillopolarography[J]. Analytical Chemistry, 1987(8): 754-755.
[4] 娄本浊. DLS粒度测量实验中噪声的影响与克服[J]. 中国测试, 2008, 20(5):126-129.LOU B ZH. The influence and corresponding solution of noise in DLS particle sizing experiment [J]. China Measurement & Testing Technology, 2008, 20(5):126-129.
[5] MALIK H, SHARMA R. EMD and ANN based intelligent fault diagnosis model for transmission line[J]. Journal of Intelligent & Fuzzy Systems, 2017, 32(4):3043-3050.
[6] KOPSINIS Y, MCLAUGHLIN S. Development of EMD-based denoising methods inspired by wavelet thresholding[J]. IEEE Transactions on Signal Processing, 2009, 57(4):1351-1362.
[7] 蒋婷, 滕召胜, 顾红艳,等. 基于EMD与分批估计的动态称量快速融合方法[J]. 仪器仪表学报, 2015, 36(6):1406-1414.JIANG T, TENG ZH SH, GU H Y, et al. Fast fusion method of dynamic based on EMD and batch estimation[J]. Chinese Journal of Scientific Instrument, 2015, 36(6):1406-1414.
[8] 贺利芳,曹莉,张天骐. Levy噪声中EMD降噪的随机共振研究[J].电子测量与仪器学报,2017,31(1):21- 28.HE L F, CAO L, ZHANG T Q. Stochastic resonance research with EMD de-noising under Levy noise[J]. Journal of Electronic Measurement and Instrumentation, 2017,31(1): 21- 28
[9] 吴江伟,王雪,孙欣尧,等.采用优化经验模态分解的电力谐波辨识方法[J].电子测量与仪器学报,2012, 26(10):858- 863.WU J W, WANG X, SUN X Y, et al. The method for harmonic identification based on optimal empirical mode decomposition[J]. Journal of Electronic Measurement and Instrumentation, 2012,26(10):858- 863.
[10] 赵利强, 王建林, 于涛. 基于改进EMD的输油管道泄漏信号特征提取方法研究[J]. 仪器仪表学报, 2013, 34(12): 2696- 2702.ZHAO L Q, WANG J L, YU T. Study on the extraction method for oil pipeline leakage signal feature based on improved empirical mode decomposition[J]. Chinese Journal of Scientific Instrument, 2013, 34(12):2696- 2702.
[11] 王闺臣, 李科, 吴佳晔. 基于EMD技术的弹性波信号降噪技术[J]. 四川理工学院学报(自然科学版), 2015, 28(1):50- 53.WANG Y CH, LI K, WU J Y. Elastic wave signal denoising technology based on EMD technology[J]. Journal of Sichuan University of Science & Engineering (Natural Science Edition), 2015, 28(1):50- 53.
[12] 黎恒, 李智, 莫玮,等. 噪声干扰环境下抑制EMD模态混叠方法[J]. 信号处理, 2015(8):956-961.LI H, LI ZH, MO W, et al. Resolving the mode-mixing problem of EMD in the presence of noise [J]. Journal of Signal Processing, 2015(8): 956-961.
[13] 汤宝平, 董绍江, 马靖华. 基于独立分量分析的EMD模态混叠消除方法研究[J]. 仪器仪表学报, 2012, 33(7) : 1477-1482.TANG B P, DONG SH J, MA J H. Study on the method for eliminating mode mixing of empirical mode decomposition based on independent component analysis [J]. Chinese Journal of Scientific Instrument, 2012, 33(7): 1477-1482.
[14] HUANG N E, WU M L C, LONG S R, et al. A confidence limit for the empirical mode decomposition and hilbert spectral analysis[J]. Proceedings Mathematical Physical & Engineering Sciences, 2003, 459(2037):2317- 2345.
[15] 赵志宏, 杨绍普, 申永军. 基于独立分量分析与相关系数的机械故障特征提取[J]. 振动与冲击, 2013, 32(6):67-72.ZHAO ZH H, YANG SH P, SHEN Y J. Machinery fault feature extraction based on independent component analysis and correlation coefficient [J]. Journal of Vibration and Shock, 2013, 32(6):67-72.
[16] 孙灵芳, 王彤彤, 徐曼菲,等. 基于改进CEEMD的薄层污垢超声检测信号去噪[J]. 仪器仪表学报, 2017,38(12):2879- 2887.SUN L F, WANG T T, XU M F, et al. Thin fouling ultrasonic detection signal denoising based on improved CEEMD[J]. Chinese Journal of Scientific Instrument, 2017,38(12):2879- 2887.
[17] ZHAO R M, CUI H M. Improved threshold denoising method based on wavelet transform[C]. International Conference on Modelling, Identification and Control, 2016:1354-1359.