基于小波包变换的自适应混沌信号降噪算法

刘云侠; 贝广霞; 蒋忠贇; 孟强; 时慧喆

doi:10.11999/JEIT221137

基于小波包变换的自适应混沌信号降噪算法

doi: 10.11999/JEIT221137

山东科技大学工程实训中心青岛 266590

基金项目: 全国金工与工训青年教师教学方法创新研究项目(2022JJGX-WKJY-40)，山东科技大学2022年度在线课程建设项目(ZXK202242)，山东科技大学2022年教育教学研究“群星计划”项目(QX2022M91)

详细信息

作者简介:
刘云侠：女，工程师，研究方向为智能控制和非线性信号处理

贝广霞：女，工程师，研究方向为智能控制

蒋忠贇：男，工程师，研究方向为信号处理

孟强：男，工程师，研究方向为系统工程

时慧喆：男，工程师，研究方向为电气工程

通讯作者:
蒋忠贇　skd994602@sdust.edu.cn

中图分类号: TN911.2
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-30
- 修回日期: 2022-11-27
- 网络出版日期: 2022-11-30
- 刊出日期: 2023-10-31

Adaptive Noise Reduction Algorithm for Chaotic Signals Based on Wavelet Packet Transform

Engineering Training Center, Shandong University of Science and Technology, Qingdao 266590, China

Funds: The National Metalworking and Engineering Training Young Teachers' Teaching Method Innovation Research Project (2022JJGX-WKJY-40), The 2022 Online Course Construction Project of Shandong University of Science and Technology (ZXK202242),The 2022 Education and Teaching Research “Stars Program” Project of Shandong University of Science and Technology (QX2022M91)

摘要

摘要: 为了更好地体现混沌系统的内在特征，该文提出一种基于小波包变换的自适应混沌信号降噪算法。首先，该算法根据不同分解尺度小波包系数的相关性不同，确定了最佳分解层数；以对数能量熵为代价函数，得到了最优小波包基。然后，在局部邻域内对近似系数进行投影分析，利用神经网络梯度下降法对细节系数进行自适应选择。通过最小化损失函数，最大限度降低噪声对混沌信号的影响。最后，通过对来自Rossler混沌模型的状态变量进行仿真分析，证实了该算法对混沌信号降噪的优越性。
- 小波包 /
- 局部投影 /
- 神经网络 /
- 混沌 /
- 降噪
Abstract: To reflect better the inherent characteristics of chaotic systems, an adaptive noise reduction algorithm for chaotic signals based on wavelet packet transform is proposed. Firstly, the best decomposition level is determined according to the different correlation of wavelet packet coefficients in different decomposition scales, while the optimal wavelet packet basis is obtained with the logarithmic energy entropy as the cost function. Then, the approximate coefficients are projected in the local neighborhood and the detail coefficients are adaptively selected with the gradient descent algorithm in neural network. By minimizing the loss function, the influence of noises on chaotic signals is reduced to the greatest extent. Finally, simulations on the state variables originating from Rossler chaotic model verify the denoising superiority of the proposed algorithm for the chaotic signals.
- Wavelet packet /
- Local projection /
- Neural network /
- Chaos /
- Noise reduction

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图 1 基于小波包变换的自适应混沌降噪算法流程图

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图 2 自相关函数曲线

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图 3 误差平均值变化曲线

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图 4 相空间图

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图 5 自相关系数图

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图 6 信号功率谱

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表 1 不同噪声水平下的最优小波包基

噪声水平(%)	坐标轴	近似系数	细节系数
5	x, y	$ s_3^1 $	$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
10	x, y	$ s_3^1 $	$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
20	x, y	$ s_3^1 $	$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
35	x, y	$ s_3^1 $	$ s_2^4,\;s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6 $
60	x, y	$ s_3^1 $	$ s_2^3,\;s_2^4,\;s_3^2,\;s_3^3,\;s_3^4 $
90	x	$ s_3^1 $	$ s_1^2,\;s_3^2,\;s_3^3,\;s_3^4 $
90	y	$ s_3^1 $	$ s_2^3,\;s_2^4,\;s_3^2,\;s_3^3,\;s_3^4 $
5～90	z	$ s_2^1 $	$ s_2^2,\;s_2^3,\;s_2^4 $

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表 2 SNR和RMSE对比表(x轴)

降噪指标	噪声水平(%)	降噪前	小波阈值降噪	小波包阈值降噪	本文算法降噪
SNR	5	26.115 8	34.414 2	34.223 6	34.681 2
	10	20.095 2	28.880 6	28.507 3	29.632 4
	20	14.074 6	23.581 5	22.568 6	24.660 0
	35	9.213 9	18.781 0	17.677 5	20.736 2
	60	4.532 2	14.898 4	11.920 3	17.144 2
	90	1.010 4	11.359 3	6.676 8	14.668 1
RMSE	5	0.174 2	0.067 0	0.068 5	0.065 0
	10	0.348 3	0.126 7	0.132 2	0.116 2
	20	0.696 6	0.233 2	0.262 0	0.205 9
	35	1.219 1	0.405 2	0.460 1	0.323 5
	60	2.089 8	0.633 6	0.892 7	0.489 2
	90	3.134 8	0.952 3	1.632 6	0.650 6

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表 3 SNR和RMSE对比表(y轴和z轴)

坐标轴	降噪指标	降噪前	小波阈值降噪	小波包阈值降噪	本文算法降噪
y	SNR	14.074 6	22.589 2	22.589 2	25.895 2
y	RMSE	0.639 3	0.239 9	0.239 9	0.208 4
z	SNR	14.074 6	20.336 5	19.751 8	21.650 9
z	RMSE	0.310 0	0.150 7	0.161 2	0.129 6

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表 4 信号的自相关函数值

延迟时间(s)	噪声水平(%)	加噪信号	小波阈值降噪	小波包阈值降噪	本文算法降噪
1	5	0.995 0	0.997 3	0.997 3	0.997 4
	10	0.988 1	0.997 3	0.997 3	0.997 4
	20	0.961 5	0.997 3	0.997 2	0.997 4
	35	0.896 1	0.997 3	0.996 7	0.997 4
	60	0.752 7	0.996 7	0.981 4	0.997 5
	90	0.583 4	0.996 6	0.904 0	0.997 7
2	5	0.989 1	0.991 5	0.991 5	0.991 6
	10	0.981 9	0.991 5	0.991 4	0.991 7
	20	0.954 2	0.991 4	0.991 0	0.991 7
	35	0.886 1	0.991 2	0.989 7	0.991 8
	60	0.736 8	0.989 3	0.970 6	0.992 1
	90	0.560 7	0.988 5	0.885 0	0.992 5
5	5	0.953 2	0.955 6	0.955 5	0.955 9
	10	0.946 1	0.955 4	0.955 1	0.956 1
	20	0.918 9	0.954 9	0.953 3	0.956 6
	35	0.852 2	0.953 8	0.948 0	0.956 9
	60	0.705 8	0.943 9	0.919 6	0.958 4
	90	0.532 9	0.938 8	0.823 3	0.959 6

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