基于
  <strong>ICA</strong>的引潮力互相关谱分析

doi:10.11867/j.issn.1001-8166.2019.01.0103

地球科学进展 ›› 2019, Vol. 34 ›› Issue (1): 103 -112. doi: 10.11867/j.issn.1001-8166.2019.01.0103

基于 ICA的引潮力互相关谱分析

邢德钊(

),全海燕 ^*(

)

1. 昆明理工大学，信息工程与自动化学院,云南昆明 650500

收稿日期:2018-09-13 修回日期:2018-12-08 出版日期:2019-01-10
通讯作者: 全海燕 E-mail:1329459095@qq.com;quanhaiyan@163.com
基金资助:
国家自然科学基金项目“提取重力固体潮信号中地球物理信息和地震前兆信息的关键信号处理算法研究”(编号：41364002)

Independent Component Extraction and Cross-correlation Spectrum Analysis of Gravity Tide Signal

Dezhao Xing( ),Haiyan Quan ^*( )

1. Kunming University of Science and Technology, Faculty of Information Engineering and Automation, Kunming 650500, China

Received:2018-09-13 Revised:2018-12-08 Online:2019-01-10 Published:2019-03-05
Contact: Haiyan Quan E-mail:1329459095@qq.com;quanhaiyan@163.com
About author:Xing Dezhao (1992-), male, Shenze County, Hebei Province, Master student. Research areas include digital signal processing and geophysical information. E-mail: 1329459095@qq.com |Quan Haiyan (1970-), male, Shiping County, Yunnan Province, Associate professor. Research areas include signal and information processing, intelligent optimization decision-making, geophysical information. E-mail: quanhaiyan@163.com
Supported by:
Project supported by the National Natural Science Foundation of China "Research on key signal processing algorithms for extracting geophysical information and earthquake precursor information from gravity tide signals"(No. 41364002)

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重力固体潮信号包括日波、半日波和年波、月波谐波分量，但是日波和半日波分量能量相对强，年波和月波分量能量相对较弱。为了有效提取出这些有较大能量差异的谐波分量，并揭示它们间的调制关系，根据重力固体潮的产生机理，采用一种重力固体潮信号分解模型，将强度不同的潮汐谐波分量以独立成分的形式，分解到不同的正交方向上。同时，利用一种新型的优化算法，改进独立成分分析算法，并将不同正交方向的独立分量进行分离。在对独立成分分量的谱相关分析中，自相关运算会使强的分量更强，而弱的分量更弱，针对这一问题，采用独立成分间的互相关谱，来揭示重力固体潮信号中谐波分量间的调制关系。实验结果表明，提出的算法，不但从加性分解的角度有效分离了重力固体潮信号中强度差异比较大的独立成分，而且基于互相关谱，揭示了相应潮汐谐波间的乘性调制关系。

关键词: 重力固体潮, 智能优化算法, 独立成分分析, 乘性解调, 互相关谱

The gravity solid tide signal includes daily wave, half-day wave and annual wave and moon wave harmonic component, but the energy of day wave and half-day wave component is relatively strong, and the energy of annual wave and moon wave component is relatively weak. In order to effectively extract these harmonic components with large energy differences and reveal the modulation relationship between them, according to the cause of gravity tide, a gravity solid tide signal decomposition model is used to compare the tidal harmonic components with different strengths. The form of the independent component is decomposed into different orthogonal directions. At the same time, a new optimization algorithm is used to improve the independent component analysis algorithm and separate the independent components of different orthogonal directions. In the spectral correlation analysis of the components of independent components, the autocorrelation operation will make the strong component stronger and the weak component weaker. For this problem, the cross-correlation spectrum between independent components is used to reveal the gravity tide signal., the modulation relationship between harmonic components. The experimental results show that the proposed algorithm not only effectively separates the independent components with large intensity difference in the gravity tide signal from the perspective of additive decomposition, but also reveals the multiplicative modulation relationship between the corresponding tidal harmonics based on the cross-correlation spectrum.

Key words: Gravity solid tide, Intelligent optimization algorithm, Independent Component Analysis, Multiplicative demodulation, Cross-correlation spectrum.

中图分类号:

P312.4

图1 重力固体潮正交分解模型

Fig. 1 The orthogonal decomposition model of Gravity Earth Tide signal

图2 ICA解混原理图

Fig.2 Procedure of ICA

图3 ICA与互相关谱分析流程图

Fig. 3 Flow chart of ICA and cross-correlation spectral analysis

图4 昆明地区重力固体潮信号

Fig. 4 Gravity solid tidal signal of Kunming

图5 ICA独立分量波形图

Fig. 5 Waveform of independent component of ICA

图6 y ₁ ( t ) , y ₂ ( t )和 y ₃ ( t )的自相关谱

Fig.6 Autocorrelation spectrum of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

表1 y ₁ ( t ) , y ₂ ( t )和 y ₃ ( t )的自相关谱分析

Table 1 Autocorrelation spectrum analysis of y ₁ ( t ) , y ₂ ( t ) and y ₃ ( t )

乘性调制频率/Hz	解调对应的潮汐谐波频率/Hz	潮汐谐波频率理论计算值/Hz
$f 11 = 2.411 × 10 - 7$ $a 11 = 1.777 × 10 - 7$	$F 1 = f 11 + a 11 = 4.188 × 10 - 7$	$4.2004 × 10 - 7$
$f 11 = 2.411 × 10 - 7$ $a 11 = 1.777 × 10 - 7$	$F 2 = f 11 - a 11 = 6.34 × 10 - 8$	$6.3377 × 10 - 8$
$f 12 = 4.569 × 10 - 7$ $a 12 = 3.934 × 10 - 7$	$F 3 = f 12 + a 12 = 8.503 × 10 - 7$	$8.4725 × 10 - 7$
$f 12 = 4.569 × 10 - 7$ $a 12 = 3.934 × 10 - 7$	$F 4 = f 12 - a 12 = 6.35 × 10 - 8$	$6.3377 × 10 - 8$
$f 13 = 6.345 × 10 - 7$ $a 13 = 2.157 × 10 - 7$	$F 5 = f 13 + a 13 = 8.502 × 10 - 7$	$8.4725 × 10 - 7$
$f 13 = 6.345 × 10 - 7$ $a 13 = 2.157 × 10 - 7$	$F 6 = f 13 + a 13 = 4.188 × 10 - 7$	$4.2004 × 10 - 7$
$f 21 = 2.275 × 10 - 5$ $a 21 = 3.934 × 10 - 7$	$F 7 = f 21 + a 21 = 2.3143 × 10 - 5$	$2.3148 × 10 - 5$
$f 21 = 2.275 × 10 - 5$ $a 21 = 3.934 × 10 - 7$	$F 8 = f 21 - a 21 = 2.2357 × 10 - 5$	$2.2364 × 10 - 5$
$f 31 = 1.157 × 10 - 5$ $a 31 = 3.807 × 10 - 8$	$F 9 = f 31 + a 31 = 1.1608 × 10 - 5$	$1.1606 × 10 - 5$
$f 31 = 1.157 × 10 - 5$ $a 31 = 3.807 × 10 - 8$	$F 10 = f 31 - a 31 = 1.1532 × 10 - 5$	$1.1542 × 10 - 5$
$f 32 = 1.118 × 10 - 5$ $a 32 = 4.188 × 10 - 7$	$F 11 = f 32 + a 32 = 1.1599 × 10 - 5$	$1.1606 × 10 - 5$
$f 32 = 1.118 × 10 - 5$ $a 32 = 4.188 × 10 - 7$	$F 12 = f 32 - a 32 = 1.0761 × 10 - 5$	$1.0759 × 10 - 5$
$f 33 = 1.115 × 10 - 5$ $a 33 = 3.934 × 10 - 7$	$F 13 = f 33 + a 33 = 1.1543 × 10 - 5$	$1.1542 × 10 - 5$
$f 33 = 1.115 × 10 - 5$ $a 33 = 3.934 × 10 - 7$	$F 14 = f 33 - a 33 = 1.0757 × 10 - 5$	$1.0759 × 10 - 5$

表1 y ₁ ( t ) , y ₂ ( t )和 y ₃ ( t )的自相关谱分析

Table 1 Autocorrelation spectrum analysis of y ₁ ( t ) , y ₂ ( t ) and y ₃ ( t )

乘性调制频率/Hz	解调对应的潮汐谐波频率/Hz	潮汐谐波频率理论计算值/Hz
$f 11 = 2.411 × 10 - 7$ $a 11 = 1.777 × 10 - 7$	$F 1 = f 11 + a 11 = 4.188 × 10 - 7$	$4.2004 × 10 - 7$
$f 11 = 2.411 × 10 - 7$ $a 11 = 1.777 × 10 - 7$	$F 2 = f 11 - a 11 = 6.34 × 10 - 8$	$6.3377 × 10 - 8$
$f 12 = 4.569 × 10 - 7$ $a 12 = 3.934 × 10 - 7$	$F 3 = f 12 + a 12 = 8.503 × 10 - 7$	$8.4725 × 10 - 7$
$f 12 = 4.569 × 10 - 7$ $a 12 = 3.934 × 10 - 7$	$F 4 = f 12 - a 12 = 6.35 × 10 - 8$	$6.3377 × 10 - 8$
$f 13 = 6.345 × 10 - 7$ $a 13 = 2.157 × 10 - 7$	$F 5 = f 13 + a 13 = 8.502 × 10 - 7$	$8.4725 × 10 - 7$
$f 13 = 6.345 × 10 - 7$ $a 13 = 2.157 × 10 - 7$	$F 6 = f 13 + a 13 = 4.188 × 10 - 7$	$4.2004 × 10 - 7$
$f 21 = 2.275 × 10 - 5$ $a 21 = 3.934 × 10 - 7$	$F 7 = f 21 + a 21 = 2.3143 × 10 - 5$	$2.3148 × 10 - 5$
$f 21 = 2.275 × 10 - 5$ $a 21 = 3.934 × 10 - 7$	$F 8 = f 21 - a 21 = 2.2357 × 10 - 5$	$2.2364 × 10 - 5$
$f 31 = 1.157 × 10 - 5$ $a 31 = 3.807 × 10 - 8$	$F 9 = f 31 + a 31 = 1.1608 × 10 - 5$	$1.1606 × 10 - 5$
$f 31 = 1.157 × 10 - 5$ $a 31 = 3.807 × 10 - 8$	$F 10 = f 31 - a 31 = 1.1532 × 10 - 5$	$1.1542 × 10 - 5$
$f 32 = 1.118 × 10 - 5$ $a 32 = 4.188 × 10 - 7$	$F 11 = f 32 + a 32 = 1.1599 × 10 - 5$	$1.1606 × 10 - 5$
$f 32 = 1.118 × 10 - 5$ $a 32 = 4.188 × 10 - 7$	$F 12 = f 32 - a 32 = 1.0761 × 10 - 5$	$1.0759 × 10 - 5$
$f 33 = 1.115 × 10 - 5$ $a 33 = 3.934 × 10 - 7$	$F 13 = f 33 + a 33 = 1.1543 × 10 - 5$	$1.1542 × 10 - 5$
$f 33 = 1.115 × 10 - 5$ $a 33 = 3.934 × 10 - 7$	$F 14 = f 33 - a 33 = 1.0757 × 10 - 5$	$1.0759 × 10 - 5$

图7 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的互相关谱

Fig.7 Cross-correlation spectrum of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

表2 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的互相关谱峰点

Table 2 Cross-correlation peaks of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

互相关谱峰点
1 $(5.863 × 10 - 6, 5.799 × 10 - 6)$	2 $(5.774 × 10 - 6, 5.711 × 10 - 6)$	3 $(6.015 × 10 - 6, 5.596 × 10 - 6)$
4 $(6.193 × 10 - 6, 5.343 × 10 - 6)$	5 $(5.406 × 10 - 6, 5.343 × 10 - 6)$	6 $(1.164 × 10 - 5, 1.157 × 10 - 5)$
7 $(1.16 × 10 - 5, 1.154 × 10 - 5)$	8 $(1.181 × 10 - 5, 1.14 × 10 - 5)$	9 $(1.203 × 10 - 5, 1.118 × 10 - 5)$
10 $(1.142 × 10 - 5, 1.136 × 10 - 5)$	11 $(1.131 × 10 - 5, 1.124 × 10 - 5)$	12 $(1.11 × 10 - 5, 1.104 × 10 - 5)$
13 $(1.1 × 10 - 5, 1.094 × 10 - 5)$	14 $(1.161 × 10 - 5, 1.076 × 10 - 5)$	15 $(1.695 × 10 - 5, 6.193 × 10 - 6)$
16 $(1.737 × 10 - 5, 5.774 × 10 - 6)$	17 $(1.695 × 10 - 5, 5.406 × 10 - 6)$

表2 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的互相关谱峰点

Table 2 Cross-correlation peaks of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

互相关谱峰点
1 $(5.863 × 10 - 6, 5.799 × 10 - 6)$	2 $(5.774 × 10 - 6, 5.711 × 10 - 6)$	3 $(6.015 × 10 - 6, 5.596 × 10 - 6)$
4 $(6.193 × 10 - 6, 5.343 × 10 - 6)$	5 $(5.406 × 10 - 6, 5.343 × 10 - 6)$	6 $(1.164 × 10 - 5, 1.157 × 10 - 5)$
7 $(1.16 × 10 - 5, 1.154 × 10 - 5)$	8 $(1.181 × 10 - 5, 1.14 × 10 - 5)$	9 $(1.203 × 10 - 5, 1.118 × 10 - 5)$
10 $(1.142 × 10 - 5, 1.136 × 10 - 5)$	11 $(1.131 × 10 - 5, 1.124 × 10 - 5)$	12 $(1.11 × 10 - 5, 1.104 × 10 - 5)$
13 $(1.1 × 10 - 5, 1.094 × 10 - 5)$	14 $(1.161 × 10 - 5, 1.076 × 10 - 5)$	15 $(1.695 × 10 - 5, 6.193 × 10 - 6)$
16 $(1.737 × 10 - 5, 5.774 × 10 - 6)$	17 $(1.695 × 10 - 5, 5.406 × 10 - 6)$

表3 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的互相关谱分析

Table 3 Table 3 Cross correlation spectrum analysis of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

潮汐谐波理论计算值/Hz		对应于乘性调制谱相关点	对应于线性差频谱相关点	对应于线性和频谱相关点
长周期波	$3.1687 × 10 - 8$
	$6.3377 × 10 - 8$		1，2，5，6，7，10，11，12，13
	$4.2004 × 10 - 7$		3，8
	$8.4725 × 10 - 7$		4，9，14
日波	$1.0338 × 10 - 5$
	$1.0759 × 10 - 5$	14	15	5
	$1.1186 × 10 - 5$	9
	$1.1511 × 10 - 5$	8		2
	$1.1542 × 10 - 5$	7	17	4
	$1.1574 × 10 - 5$	6
	$1.1606 × 10 - 5$	7，14	16	3
	$1.1637 × 10 - 5$	6
	$1.1669 × 10 - 5$	8		1
	$1.2026 × 10 - 5$	9
	$1.2453 × 10 - 5$
半日波	$2.1524 × 10 - 5$
	$2.1580 × 10 - 5$
	$2.1944 × 10 - 5$			13
	$2.2000 × 10 - 5$			12
	$2.2364 × 10 - 5$			14，17
	$2.2728 × 10 - 5$			11
	$2.2784 × 10 - 5$			10
	$2.3116 × 10 - 5$
	$2.3148 × 10 - 5$			7，15，16
	$2.318 × 10 - 5$
	$2.3212 × 10 - 5$			6，8，9

表3 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的互相关谱分析

Table 3 Table 3 Cross correlation spectrum analysis of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

潮汐谐波理论计算值/Hz		对应于乘性调制谱相关点	对应于线性差频谱相关点	对应于线性和频谱相关点
长周期波	$3.1687 × 10 - 8$
	$6.3377 × 10 - 8$		1，2，5，6，7，10，11，12，13
	$4.2004 × 10 - 7$		3，8
	$8.4725 × 10 - 7$		4，9，14
日波	$1.0338 × 10 - 5$
	$1.0759 × 10 - 5$	14	15	5
	$1.1186 × 10 - 5$	9
	$1.1511 × 10 - 5$	8		2
	$1.1542 × 10 - 5$	7	17	4
	$1.1574 × 10 - 5$	6
	$1.1606 × 10 - 5$	7，14	16	3
	$1.1637 × 10 - 5$	6
	$1.1669 × 10 - 5$	8		1
	$1.2026 × 10 - 5$	9
	$1.2453 × 10 - 5$
半日波	$2.1524 × 10 - 5$
	$2.1580 × 10 - 5$
	$2.1944 × 10 - 5$			13
	$2.2000 × 10 - 5$			12
	$2.2364 × 10 - 5$			14，17
	$2.2728 × 10 - 5$			11
	$2.2784 × 10 - 5$			10
	$2.3116 × 10 - 5$
	$2.3148 × 10 - 5$			7，15，16
	$2.318 × 10 - 5$
	$2.3212 × 10 - 5$			6，8，9

图8 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的部分互相关谱

Fig. 8 Partial cross-correlation spectrum of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

表4 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的部分互相关谱分析

Table 4 Partial cross-correlation spectral analysis of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

潮汐谐波理论计算值/Hz		对应于乘性调制谱相关点	对应于线性差频谱相关点	对应于线性和频谱相关点
长周期波	$3.1687 × 10 - 8$		5
	$6.3377 × 10 - 8$		1,2,3,21,22
	$4.2004 × 10 - 7$		23,24
	$8.4725 × 10 - 7$		9,
日波	$1.0338 × 10 - 5$		13
	$1.0759 × 10 - 5$	4,11,12	14
	$1.1186 × 10 - 5$	4,10	15
	$1.1511 × 10 - 5$	8	18
	$1.1542 × 10 - 5$	7	17
	$1.1574 × 10 - 5$	6,8	19
	$1.1606 × 10 - 5$	7	16,20
	$1.1637 × 10 - 5$	6		21
	$1.1669 × 10 - 5$	11		24
	$1.2026 × 10 - 5$	10		23
	$1.2453 × 10 - 5$	12		22
半日波	$2.1524 × 10 - 5$			2
	$2.1580 × 10 - 5$			1
	$2.1944 × 10 - 5$			17
	$2.2000 × 10 - 5$			3
	$2.2364 × 10 - 5$			13,15
	$2.2728 × 10 - 5$			16
	$2.2784 × 10 - 5$			9
	$2.3116 × 10 - 5$			20
	$2.3148 × 10 - 5$			5,19
	$2.318 × 10 - 5$			14
	$2.3212 × 10 - 5$			18

表4 y ₁ ( t ), y ₂ ( t )和 y ₃ ( t )的部分互相关谱分析

Table 4 Partial cross-correlation spectral analysis of y ₁ ( t ), y ₂ ( t ) and y ₃ ( t )

潮汐谐波理论计算值/Hz		对应于乘性调制谱相关点	对应于线性差频谱相关点	对应于线性和频谱相关点
长周期波	$3.1687 × 10 - 8$		5
	$6.3377 × 10 - 8$		1,2,3,21,22
	$4.2004 × 10 - 7$		23,24
	$8.4725 × 10 - 7$		9,
日波	$1.0338 × 10 - 5$		13
	$1.0759 × 10 - 5$	4,11,12	14
	$1.1186 × 10 - 5$	4,10	15
	$1.1511 × 10 - 5$	8	18
	$1.1542 × 10 - 5$	7	17
	$1.1574 × 10 - 5$	6,8	19
	$1.1606 × 10 - 5$	7	16,20
	$1.1637 × 10 - 5$	6		21
	$1.1669 × 10 - 5$	11		24
	$1.2026 × 10 - 5$	10		23
	$1.2453 × 10 - 5$	12		22
半日波	$2.1524 × 10 - 5$			2
	$2.1580 × 10 - 5$			1
	$2.1944 × 10 - 5$			17
	$2.2000 × 10 - 5$			3
	$2.2364 × 10 - 5$			13,15
	$2.2728 × 10 - 5$			16
	$2.2784 × 10 - 5$			9
	$2.3116 × 10 - 5$			20
	$2.3148 × 10 - 5$			5,19
	$2.318 × 10 - 5$			14
	$2.3212 × 10 - 5$			18

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