复杂信号的组合去噪方法

摘要/Abstract

摘要： 复杂环境中信号的降噪处理对信号的准确提取和分析至关重要. 现有研究多聚焦于单一或组合方法在特定场景中的应用, 难以有效应对复杂信号的非线性和非平稳性问题. 该文基于非平稳性度量, 提出了一种 CEEMDAN 两阶段降噪策略, 通过 NS 指标量化模态分量的非平稳性, 实现高频噪声与低频信号的精准分离; 采用新型对数型阈值函数去除高频噪声, 并结合 SG 滤波法平滑低频信号, 显著提高了降噪效果和信号重构精度. 结果表明, 新方法在不同信噪比和噪声类型下均展现出卓越的模态区分与降噪性能.

关键词: 复杂信号去噪, CEEMDAN, 非平稳性度量 (NS), S-G 滤波, 小波阈值去噪

Abstract:

Noise reduction in complex environments is of paramount importance for the accurate extraction and analysis of signals. Prevailing research predominantly centers on the application of single or combined methods in specific scenarios, but encounters challenges in effectively addressing the nonlinearity and non-stationarity of complex signals. Based on the measurement of non-stationarity, this study proposes a two-stage noise reduction strategy using CEEMDAN. The NS index is used to quantify the non-stationarity of modal components, achieving precise separation of high-frequency noise from low-frequency signals. A novel logarithmic threshold function is adopted to remove high-frequency noise, and the SG filtering method is combined to smooth low-frequency signals, significantly improving the noise reduction effect and signal reconstruction accuracy. The results indicate that the new method demonstrates outstanding modal discrimination and noise reduction performance under different signal-to-noise ratios and noise types.

Key words: complex signal denoising, CEEMDAN, non-stationarity measure (NS), S-G filtering, wavelet threshold denoising

中图分类号:

TN911.7

王佳兴, 杨双全, 董怡超. 复杂信号的组合去噪方法[J]. 数学物理学报, 2025, 45(4): 1229-1244.

Wang Jiaxing, Yang Shuangquan, Dong Yichao. Combined Denoising Methods for Complex Signals[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1229-1244.

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参考文献 25

[1]	柯水霞. 信号降噪与解调技术研究. 南昌: 南昌大学, 2016
	Ke S X. Signal Denoising and Demodulation Techniques Research. Nanchang: Nanchang University, 2016
[2]	黄显高, 徐健学, 何岱海, 等. 利用小波多尺度分解算法实现混沌系统的噪声减缩. 物理学报, 1999 (10): 1810-1817
	Huang X G, Xu J X, He D H, et al. Noise reduction in chaotic systems via wavelet multiscale decomposition algorithm. Acta Physica Sinica, 1999 (10): 1810-1817
[3]	雷达, 钟诗胜. 基于奇异值分解和经验模态分解的航空发动机健康信号降噪. 吉林大学学报 (工学版), 2013, 43(3): 764-770
	Lei D, Zhong S S. Aircraft engine health signal denoising based on singular value decomposition and empirical mode decomposition. Journal of Jilin University (Engineering Edition), 2013, 43(3): 764-770
[4]	Lee D, Shin S R, Chung W, et al. Denoising sparker seismic data with Deep BiLSTM in fractional Fourier transform. Computers & Geosciences, 2024, 1.4: 105519
[5]	贾瑞生, 赵同彬, 孙红梅, 等. 基于经验模态分解及独立成分分析的微震信号降噪方法. 地球物理学报, 2015, 58(3): 1013-1023 doi: 10.6038/cjg20150326
	Jia R S, Zhao T L, Sun H M, et al. Microseismic signal denoising method based on empirical mode decomposition and independent component analysis. Journal of Geophysics, 2015, 58(3): 1013-1023 doi: 10.6038/cjg20150326
[6]	Ma Y, Cheng J, Wang P, et al. A novel Lanczos quaternion singular spectrum analysis method and its application to bevel gear fault diagnosis with multi-channel signals. Mechanical Systems and Signal Processing, 2021, 1.8: 108679
[7]	Ma Y, Cheng J, Hu N, et al. Symplectic quaternion singular mode decomposition with application in gear fault diagnosis. Mechanical Systems and Signal Processing, 2021, 1.0: 104266
[8]	Zhou J, Cheng J, Wu X, et al. Adaptive quaternion multivariate local characteristic-scale decomposition and its application to gear fault diagnosis. Digital Signal Processing, 2022, 1.9: 103655
[9]	Zhong J, Bi X, Shu Q, et al. Partial discharge signal denoising based on singular value decomposition and empirical wavelet transform. IEEE Trans Instrum Meas, 2020, 69(11): 8866-8873
[10]	Bandt C, Pompe B. Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 2002, 88(17): 174102
[11]	Azami H, Escudero J. Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation. Comput Methods Programs Biomed, 2016, 1.8: 40-51
[12]	Huang J D, Ling L, Xiao Q X. Research on weak signal detection method for power system fault based on improved wavelet threshold. Energy Reports, 2022, 8(12): 290-296
[13]	陈克, 张晓冬, 李宁. 基于 CEEMD 与自适小波阈值组合降噪在 OPAX 方法的应用. 振动与冲击, 2021, 40(16): 192-198
	Chen K, Zhang X D, Li N. Application of CEEMD and adaptive wavelet thresholding combination denoising in the OPAX method. Vibration and Impact, 2021, 40(16): 192-198
[14]	Yang Y, Li S S, Li C, et al. Research on ultrasonic signal processing algorithm based on CEEMDAN joint wavelet packet thresholding. Measurement, 2022, 2.1: 111751
[15]	马星河, 孔卫东, 李自强, 等. 一种基于 S_VMD 与 Sdr_SampEn 的局部放电信号去噪方法. 电力系统保护与控制, 2022, 50(18): 29-38
	Ma X H, Kong W D, Li Z Q, et al. A denoising method for partial discharge signals based on S_VMD and Sdr_SampEn. Power System Protection and Control, 2022, 50(18): 29-38
[16]	周怡娜, 路敬祎, 张勇, 等. VMD-SG-WT 去噪法及其在混沌去噪中的应用. 东北石油大学学报, 2020, 44(4): 113-120; 132; IX
	Zhou Y N, Lu J Y, Zhang Y, et al. Denoising method based on VMD-SG-WT and its application in chaotic denoising. Journal of Northeast Petroleum University, 2020, 44(4): 113-120; 132; IX
[17]	谭秋衡. 时间序列的非平稳性度量及其应用. 武汉: 中国科学院研究生院(武汉物理与数学研究所), 2013
	Tan Q H. Measurement of Nonstationarity in Time Series and Its Applications. Wuhan: Graduate School of the Chinese Academy of Sciences (Wuhan Institute of Physics and Mathematics), 2013
[18]	张聪, 丁义明. 基于重对数律的非平稳性度量. 数学物理学报, 2023, 43A(6): 1855-1868
	Zhang C, Ding Y M. Non-stationarity measure based on logarithmic law. Acta Math Sci, 2023, 43A(6): 1855-1868
[19]	谭秋衡, 吴量, 李波. 基于 EMD 及非平稳性度量的趋势噪声分解方法. 数学物理学报, 2016, 36A(4): 783-794
	Tan Q H, Wu L, Li B. Trend noise decomposition method based on EMD and non-stationarity measurement. Acta Math Sci, 2016, 36A(4): 783-794
[20]	Li S, Qin N, Huang D, et al. Damage localization of Stacker's track based on EEMD-EMD and DBSCAN cluster algorithms. IEEE Trans Instrum Meas, 2020, 69: 1981-1992
[21]	Torres M, Colominas M A, Schlotthauer G, et al. A complete ensemble empirical mode decomposition with adaptive noise//Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Prague, Czech Republic: IEEE, 2011: 4144-4147
[22]	Savitzky A, Golay M J E. Soothing and differentiation of data by simplifying least squares procedures. Anal Chem, 1964, 36: 1627-39
[23]	Schafer R W. What is a Savitzky-Golay filter?. IEEE Signal Process Mag, 2011, 28(4): 111-117
[24]	Li H, Li S S, Sun J, et al. Ultrasound signal processing based on joint GWO-VMD wavelet threshold functions. Measurement, 2024, 2.6: 114143
[25]	Donoho D L, Johnstone I M. Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc, 1995, 90: 1200-1224