Time-frequency Analysis of BGabor-NSPWVD Algorithm With Strong Robustness and High Sharpening Concentration
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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.
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关键词:
- 时频分析 /
- 交叉项抑制 /
- 鲁棒性 /
- BGabor-NWVD /
- BGabor-NSPWVD
Abstract: For the time-frequency resolution fuzziness and cross-term interference caused by short-time Fourier transform (STFT), Gabor transform and Wigner-Ville distribution (WVD), this paper proposes the binarized Gabor-normalized WVD (BGabor-NWVD) and binarized Gabor-normalized smoothed pseudo WVD (BGabor-NSPWVD) algorithms, which combine partial binaryzation and normalization. Experiment results show that the BGabor-NWVD and BGabor-NSPWVD algorithms can effectively reduce the cross-term interference and have high sharpening resolution of high TF concentration degree. The algorithms can suppress the cross-term, and the anti-noise performance and robustness of the two algorithms are also ideal. Based on the methods, a TF analysis of the suspected rupture signal generated during the work of the carbide torch is carried out to suppress the noise and the cross-term. At the same time, the frequency discrimination window of the sensor can be found accurately, which can be used as threshold reference for the data acquisition board of the metal rupture monitoring equipment.-
Key words:
- Time-frequency analysis /
- cross term inhibition /
- robustness /
- BGabor-NWVD /
- BGabor-NSPWVD
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 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
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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