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摘要: 针对高聚集度Wigner-Ville distribution (WVD)时频分析方法存在严重的交叉项干扰问题, 利用广义Warblet变换(Generalized Warblet transform, GWT)不产生虚假频率分量的特点, 提出了WVD与GWT相结合的归一化广义Warblet-WVD (Normalized generalized Warblet-WVD, NGWT-WVD)算法. 该算法将GWT与WVD进行矩阵运算, 实现滤波效应, 抑制WVD产生的新交叉项以及混入自项的交叉项, 提高WVD的时频分析质量. 实验结果表明, NGWT-WVD方法有效地去除了多分量信号的交叉项干扰, 提高信号分析结果的时频聚集度, 还原多分量信号的真实时频分布. 采用NGWT-WVD方法处理金属疑似破裂样本信号, 获取破裂发生区间的时间和频率标志段, 为监测传感器设置有效门限值提供判据, 取得了良好效果.
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关键词:
- 时频分析 /
- 交叉项干扰 /
- Wigner-Ville分布 /
- 广义Warblet变换 /
- 疑似金属破裂信号
Abstract: To solve the cross-terms interference of the high-aggregation Wigner-Ville distribution (WVD) time-frequency analysis method, a normalized generalized Warblet-WVD (NGWT-WVD) algorithm combining WVD and generalized Warblet transform (GWT) is proposed by using the characteristics of GWT without false frequency components. The algorithm can achieve the filtering effect by matrix operations on the GWT and WVD, and suppress new cross terms generated by WVD and cross terms mixed with its self terms. At the same time, it also improves the time-frequency analysis quality of WVD. The experimental results show that the NGWT-WVD method effectively removes the crossterm interference of multi-component signals and improves the time-frequency aggregation of the analysis results, the truly time-frequency distribution of the multi-component signal is restored. The NGWT-WVD method is used to process the sample signal suspected rupture of the metal, and the time and frequency flag segments of the rupture interval are obtained, which provides the basis for determining the effective threshold value of the monitoring sensor and achieves satisfactory results. -
图 5 三分量信号三维时频图比较
Fig. 5 Three-dimensional time-frequency diagrams comparison of three-component signals
图 9 两分量调频信号时频图
Fig. 9 Time-frequency diagram of two-component frequency modulated signal
图 10 各算法的时变功率谱误差柱形图
Fig. 10 Time-varying power spectrum error column chart of each algorithm
图 11 各算法的时变功率谱误差折线图
Fig. 11 Time-varying power spectrum error line chart of each algorithm
图 13 各算法的CM值折线图
$(\times{10^{ - 3}})$ Fig. 13 CM value line chart of each algorithm
$(\times{10^{ - 3}})$ 表 1 各算法的时变功率谱误差比较
Table 1 Time-varying power spectrum error comparison of each algorithm
算法类型 ${ {z_1}( t )}$ ${{z_2}( t )}$ ${{z_3}( t )}$ ${{z_4}( t )}$ WVD 0.6061 0.3153 0.5139 0.5603 Gabor-WVD 0.3095 0.0854 0.0599 0.0736 GWT-WVD 0.2072 0.1084 0.1287 0.1394 VMD-WVD 0.0720 0.0274 0.0105 0.2375 NGWT-WVD 0.0210 0.0587 0.0099 0.0136 
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表 2 各算法的CM值比较
$(\times{10^{ - 3}})$ Table 2 CM value comparison of each algorithm
$(\times{10^{ - 3}})$ 算法类型 ${{z_1}( t )}$ ${{z_2}( t)}$ ${{z_3}( t )}$ ${{z_4}( t )}$ GWT 0.0079 0.0282 0.0167 0.0194 Gabor-WVD 0.0303 0.0852 0.0576 0.0554 GWT-WVD 0.0386 0.0921 0.0596 0.1164 WVD 0.0687 0.1821 0.0776 0.1008 VMD-WVD 0.0649 0.2143 0.1204 0.1526 NGWT-WVD 0.0722 0.2254 0.1336 0.1625
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表 3 六种算法的CM值比较
$(\times{10^{ - 5}})$ Table 3 CM value comparison of six algorithms
$(\times{10^{ - 5}})$ 算法类型 CM 值 GWT 4.3669 Gabor-WVD 5.6375 GWT-WVD 7.5044 WVD 7.5046 VMD-WVD 17.6381 NGWT-WVD 20.8527
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