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强鲁棒性和高锐化聚集度的BGabor-NSPWVD时频分析算法

郝国成 谈帆 程卓 王巍 冯思权 张伟民

郝国成, 谈帆, 程卓, 王巍, 冯思权, 张伟民. 强鲁棒性和高锐化聚集度的BGabor-NSPWVD时频分析算法. 自动化学报, 2019, 45(3): 566-576. doi: 10.16383/j.aas.c170530
引用本文: 郝国成, 谈帆, 程卓, 王巍, 冯思权, 张伟民. 强鲁棒性和高锐化聚集度的BGabor-NSPWVD时频分析算法. 自动化学报, 2019, 45(3): 566-576. doi: 10.16383/j.aas.c170530
HAO Guo-Cheng, TAN Fan, CHENG Zhuo, WANG Wei, FENG Si-Quan, ZHANG Wei-Min. Time-frequency Analysis of BGabor-NSPWVD Algorithm With Strong Robustness and High Sharpening Concentration. ACTA AUTOMATICA SINICA, 2019, 45(3): 566-576. doi: 10.16383/j.aas.c170530
Citation: HAO Guo-Cheng, TAN Fan, CHENG Zhuo, WANG Wei, FENG Si-Quan, ZHANG Wei-Min. Time-frequency Analysis of BGabor-NSPWVD Algorithm With Strong Robustness and High Sharpening Concentration. ACTA AUTOMATICA SINICA, 2019, 45(3): 566-576. doi: 10.16383/j.aas.c170530

强鲁棒性和高锐化聚集度的BGabor-NSPWVD时频分析算法

doi: 10.16383/j.aas.c170530
基金项目: 

武汉市科技局攻关计划项目 2016060101010073

111项目 B17040

复杂系统先进控制与智能自动化湖北省重点实验室基金 ACIA2017002

智能地学信息处理湖北省重点实验室开放课题 KLIGIP2017A01

大地测量与地球动力学国家重点实验室开放基金 SKLGED2018- 5-4-E

国家自然科学基金 61333002

教育部博士后基金 2015M582293

详细信息
    作者简介:

    谈帆  中国地质大学(武汉)机械与电子信息学院硕士研究生.主要研究方向为信号处理, 时频分析算法.E-mail:akafan@cug.edu.cn

    程卓  中国地质大学(武汉)机械与电子信息学院讲师.主要研究方向为认知无线电, 差分跳频, 混沌通信.E-mail:chengzhuo@cug.edu.cn

    王巍  中国地质大学(武汉)机械与电子信息学院讲师.主要研究方向为FPGA开发, 信号检测.E-mail:geo_wangwei@cug.edu.cn

    冯思权  中国地质大学(武汉)机械与电子信息学院硕士研究生.主要研究方向为图像处理, 时频分析算法.E-mail:fengsq@cug.edu.cn

    张伟民  中国地质大学(武汉)副教授.主要研究方向为机电一体化技术及应用, 检测技术.E-mail:wmzhang@cug.edu.cn

    通讯作者:

    郝国成  中国地质大学(武汉)副教授.主要研究方向为信号处理, 时频分析, ENPEMF方法和设备.本文通信作者.E-mail:haogch@cug.edu.cn

Time-frequency Analysis of BGabor-NSPWVD Algorithm With Strong Robustness and High Sharpening Concentration

Funds: 

Research Projects Foundation of Wuhan Science and Technology Bureau 2016060101010073

111 Project B17040

Foundation of the Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems ACIA2017002

Open Research Project of the Hubei Key Laboratory of Intelligent Geo-Information Processing KLIGIP2017A01

Open Research Foundation of the State Key Laboratory of Geodesy and Earth0s Dynamics SKLGED2018- 5-4-E

Supported by National Natural Science Foundation of China 61333002

China Postdoctoral Science Foundation 2015M582293

More Information
    Author Bio:

     Master student at Faculty of Mechanical & Electronic Information, China University of Geosciences (Wuhan). His research interest covers signal processing and time-frequency analysis algorithm

     Lecturer at Faculty of Mechanical & Electronic Information, China University of Geosciences (Wuhan). His research interest covers cognitive radio and differential frequency hopping and chaotic communication

     Lecturer at Faculty of Mechanical & Electronic Information, China University of Geosciences (Wuhan). His research interest covers FPGA development and signal detection

     Master student at Faculty of Mechanical & Electronic Information, China University of Geosciences (Wuhan). His research interest covers image processing and time-frequency analysis algorithm

     Associate professor at China University of Geosciences (Wuhan). His research interest covers mechatronics technology and applications and detection technology

    Corresponding author: HAO Guo-Cheng   Associate professor at China University of Geosciences (Wuhan). His research interest covers signal processing and timefrequency analysis, method and device of ENPEMF. Corresponding author of this paper
  • 摘要: 针对短时傅里叶变换(Short-time Fourier transform,STFT)、Gabor变换和魏格纳-维尔分布(Wigner-Ville distribution,WVD)出现的时频分辨率模糊和交叉项干扰,以及目前一些主流改进算法如STFT-WVD和Gabor-WVD存在的频率分量三维幅度失真,且抗噪性能及鲁棒性能不理想等问题,提出基于局部二值化、归一化处理再结合的二值化Gabor-归一化WVD(Binarized Gabor-normalized WVD,BGabor-NWVD)和二值化Gabor-归一化伪平滑WVD(Binarized Gabor-normalized smoothed pseudo WVD,BGabor-NSPWVD)算法.数值仿真实验结果表明,BGabor-NWVD和BGabor-NSPWVD算法较好地抑制了交叉项干扰,具有较高的时频锐化聚集度,且两种算法的抗噪性能和鲁棒性也较为理想.基于本文方法对硬质合金顶锤工作时产生的疑似破裂信号进行时频分析,在抑制噪声和交叉项的同时能够较为准确地寻找传感器的频率判别窗口,为金属破裂监测设备数据采集卡提供有效的阈值参考.
    1)  本文责任编委 张俊
  • 图  1  信号$f_1$的理想时频、Gabor和WVD对比图

    Fig.  1  Ideal time-frequency spectrum, Gabor, WVD of $f_1$

    图  2  BGabor-NWVD算法流程图

    Fig.  2  BGabor-NWVD algorithm flow chart

    图  3  四分量$f_2$和三分量$f_3$的二维时频图

    Fig.  3  Two-dimensional time-frequency diagram of four components signal $f_2$ and three components signal $f_3$

    图  4  四分量$f_2$的三维时频图

    Fig.  4  Three-dimensional time-frequency diagram of four components signal $f_2$

    图  5  基于Gabor和WVD的四分量$f_2$(上)和三分量$f_3$ (下)的三维时频比较图

    Fig.  5  Three-dimensional time-frequency diagram of four-components $f_2$ (upper) and three-components $f_3$ (bottom) based on Gabor and WVD

    图  6  基于Gabor和SPWVD的四分量$f_2$(上)和三分量$f_3$ (下)的三维时频比较图

    Fig.  6  Three-dimensional time-frequency diagram of four-components $f_2$ (upper) and three-components $f_3$ (bottom) based on Gabor and SPWVD

    图  7  含噪信号$f_4$的二维时频分布比较(SNR = 2dB)

    Fig.  7  The two-dimensional time-frequency distribution of the noisy signal $f_4$ (SNR = 2dB)

    图  8  时频聚集度参数$E_{JP}$评价比较

    Fig.  8  Comparison of time-frequency aggregation degree evaluation on $E_{JP}$

    图  9  硬质合金顶锤的现场实物图与三维模拟图

    Fig.  9  Carbide anvil physical site map and 3D simulation figure

    图  10  疑似金属破裂样本的时频分析

    Fig.  10  Time-frequency analysis of suspected metal rupture samples

    表  1  仿真函数$f_4$在不同噪声条件下各方法的聚集度$E_{JP}$数值比较

    Table  1  The $E_{JP}$ numerical comparison of experimental function $f_4$ in different noise conditions

    不同方法 SNR = -10 SNR = -5 SNR = 0 SNR = 5 SNR = 10 SNR = 15 SNR = 20
    Gabor $9.35\, \times\, 10^{-7}$ $2.03\, \times\, 10^{-6}$ $5.71\, \times\, 10^{-6}$ $1.22\, \times\, 10^{-5}$ $1.65\, \times\, 10^{-5}$ $1.87\, \times\, 10^{-5}$ $1.96\, \times\, 10^{-5}$
    WVD $3.10\, \times\, 10^{-6}$ $3.50\, \times\, 10^{-6}$ $8.21\, \times\, 10^{-6}$ $2.62\, \times\, 10^{-5}$ $4.74\, \times\, 10^{-5}$ $5.95\, \times\, 10^{-5}$ $6.59\, \times\, 10^{-5}$
    SPWVD $8.35\, \times\, 10^{-7}$ $5.26\, \times\, 10^{-6}$ $7.55\, \times\, 10^{-6}$ $1.18\, \times\, 10^{-5}$ $1.21\, \times\, 10^{-5}$ $1.27\, \times\, 10^{-5}$ $1.27\, \times\, 10^{-5}$
    Gabor-WVD (二值化) $4.61\, \times\, 10^{-6}$ $1.21\, \times\, 10^{-5}$ $1.00\, \times\, 10^{-4}$ $1.22\, \times\, 10^{-4}$ $1.19\, \times\, 10^{-4}$ $1.19\, \times\, 10^{-4}$ $1.24\, \times\, 10^{-4}$
    Gabor-WVD (幂系数调节) $1.83\, \times\, 10^{-6}$ $2.85\, \times\, 10^{-6}$ $1.12\, \times\, 10^{-5}$ $3.06\, \times\, 10^{-5}$ $5.43\, \times\, 10^{-5}$ $6.33\, \times\, 10^{-5}$ $6.68\, \times\, 10^{-5}$
    Gabor-WVD (最小值) $2.76\, \times\, 10^{-6}$ $3.35\, \times\, 10^{-6}$ $7.43\, \times\, 10^{-6}$ $2.43\, \times\, 10^{-5}$ $5.92\, \times\, 10^{-5}$ $7.92\, \times\, 10^{-5}$ $8.85\, \times\, 10^{-5}$
    Gabor-SPWVD (二值化) $2.24\, \times\, 10^{-6}$ $1.23\, \times\, 10^{-5}$ $3.43\, \times\, 10^{-5}$ $4.78\, \times\, 10^{-5}$ $4.77\, \times\, 10^{-5}$ $4.85\, \times\, 10^{-5}$ $4.86\, \times\, 10^{-5}$
    Gabor-SPWVD (幂系数调节) $1.76\, \times\, 10^{-6}$ $3.75\, \times\, 10^{-6}$ $1.14\, \times\, 10^{-5}$ $2.04\, \times\, 10^{-5}$ $2.70\, \times\, 10^{-5}$ $3.07\, \times\, 10^{-5}$ $3.22\, \times\, 10^{-5}$
    Gabor-SPWVD (最小值) $2.02\, \times\, 10^{-6}$ $4.04\, \times\, 10^{-6}$ $1.49\, \times\, 10^{-5}$ $3.13\, \times\, 10^{-5}$ $3.81\, \times\, 10^{-5}$ $3.94\, \times\, 10^{-5}$ $3.99\, \times\, 10^{-5}$
    BGabor-NWVD $6.73\, \times\, 10^{-6}$ $4.37\, \times\, 10^{-5}$ $1.47\, \times\, 10^{-4}$ $1.53\, \times\, 10^{-4}$ $1.42\, \times\, 10^{-4}$ $1.39\, \times\, 10^{-4}$ $1.44\, \times\, 10^{-4}$
    BGabor-NSPWVD $3.48\, \times\, 10^{-6}$ $3.26\, \times\, 10^{-5}$ $4.66\, \times\, 10^{-5}$ $6.16\, \times\, 10^{-5}$ $6.11\, \times\, 10^{-5}$ $6.08\, \times\, 10^{-5}$ $6.03\, \times\, 10^{-5}$
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