地震研究

介绍了希尔伯特-黄变换方法的基本原理和实现方法,分析了该方法在仿真信号处理中的适用性和稳定性。针对模拟信号中的阶跃、突跳、随机噪声对HHT分析结果的影响进行了分类研究,结果表明该方法具有很好的时频分辨率,对前兆资料中典型的阶跃、突跳反应明显,稳定性较好,能将高于噪声2倍标准差的信号进行有效分离。最后,通过前兆资料的2个实例验证了该方法在前兆数据分析中的适用性,发现HHT方法可以有效的识别出实际观测资料中的固体潮信息,对干扰排除和异常提取具有一定的参考意义。

We introduce basic principles and implementation of Hilbert-Huang Transform method and analyze applicability and stability of this method in signal simulation processing.Studying the impact of step,jump and random noise on HHT analysis of analog signal,the results show that the method has high time-frequency resolution,reflect to the typical abnormal in the precursor data such as steps or jumps significantly,and has good stability,and is able to separate the signal which is higher than the 2 times standard deviation of the noise effectively.Finally,we verify the applicability of the method in the analysis of precursor data by using two cases and find that the HHT method can identify the tidal from the real observational data effectively,and have some reference meaning for disturbing rejection and extracting exception.

引言
1 HHT方法基本原理
2 HHT方法仿真实验及特性分析
3 形变资料分析实例
4 讨论与结论

图1 基础信号经HHT方法分析结果<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.1 Analysis result of the original signal by the HHT method(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图1 基础信号经HHT方法分析结果
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.1 Analysis result of the original signal by the HHT method(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图2 t=700 s时刻加入幅度为20的阶跃<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.2 Original signal with the step of amplitude of 20 when time is 700s(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图2 t=700 s时刻加入幅度为20的阶跃
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.2 Original signal with the step of amplitude of 20 when time is 700s(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图3 t=428、1010、1605 s时刻加入3个幅度为20的单点突跳<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.3 Original signal with three sudden jumps with amplitude of 20 when time are 428,1010 and 1605s(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图3 t=428、1010、1605 s时刻加入3个幅度为20的单点突跳
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.3 Original signal with three sudden jumps with amplitude of 20 when time are 428,1010 and 1605s(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图4 附加误差函数后HHT结果(噪声标准差为0.2)<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.4 HHT results of the original signal with error function(noise standard deviation is 0.2)(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图4 附加误差函数后HHT结果(噪声标准差为0.2)
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.4 HHT results of the original signal with error function(noise standard deviation is 0.2)(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图5 附加不同标准差误差响应<br/>(a)标准差为0.5;(b)标准差为1;(c)标准差为1.2的经验模态分解;(d)标准差为1.2的HHT谱<br/>Fig.5 Error response of the original signal with different standard deviation(a)Standard deviation is 0.5;(b)Standard deviation is 1;(c)EMD with a standard deviation of 1.2;(d)HHT spectrum with a standard deviation of 1.2

图5 附加不同标准差误差响应
(a)标准差为0.5;(b)标准差为1;(c)标准差为1.2的经验模态分解;(d)标准差为1.2的HHT谱
Fig.5 Error response of the original signal with different standard deviation(a)Standard deviation is 0.5;(b)Standard deviation is 1;(c)EMD with a standard deviation of 1.2;(d)HHT spectrum with a standard deviation of 1.2

图6 复合信号希尔伯特-黄变换分析<br/>(a)原始信号和误差;(b)经验模态分解;(c)HHT谱;(d)瞬时能量谱<br/>Fig.6 Analysis result of composite signal by HHT(a)Original signal and error;(b)EMD;(c)HHT spectrum;(d)Instantaneous energy spectrum

图6 复合信号希尔伯特-黄变换分析
(a)原始信号和误差;(b)经验模态分解;(c)HHT谱;(d)瞬时能量谱
Fig.6 Analysis result of composite signal by HHT(a)Original signal and error;(b)EMD;(c)HHT spectrum;(d)Instantaneous energy spectrum

图7 2009年5月宝鸡水管倾斜仪北东分量整点值数据分析<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.7 Analysis results of the NE component of integral point value recorded by water tube tiltmeter at Baoji Station in May,2009(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图7 2009年5月宝鸡水管倾斜仪北东分量整点值数据分析
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.7 Analysis results of the NE component of integral point value recorded by water tube tiltmeter at Baoji Station in May,2009(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图8 2010年6月临汾垂直摆倾斜仪北南分量整点值数据分析<br/>(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱<br/>Fig.8 Analysis results of the NS component of integral point value recorded by vertical pendulum tiltmeter at Linfen Station in June,2010(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

图8 2010年6月临汾垂直摆倾斜仪北南分量整点值数据分析
(a)经验模态分解;(b)HHT谱;(c)瞬时能量谱
Fig.8 Analysis results of the NS component of integral point value recorded by vertical pendulum tiltmeter at Linfen Station in June,2010(a)EMD;(b)HHT spectrum;(c)Instantaneous energy spectrum

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备注

引言

1 HHT方法基本原理

2 HHT方法仿真实验及特性分析

3 形变资料分析实例

4 讨论与结论

期刊信息