CN112766127A - Thundercloud point charge positioning method based on complementary set modal decomposition and SG filtering - Google Patents
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Abstract
The invention discloses a thunderstorm cloud point charge positioning method based on complementary set empirical mode decomposition CEEMDAN and Savitzky-Golay filtering, which comprises the following specific steps: decomposing the atmospheric electric field signal into a series of Intrinsic Mode Functions (IMF) components by adopting CEEMDAN; carrying out SG filtering denoising and signal reconstruction on IMF with dominant noise; realizing point charge positioning by using data processed by CEEMDAN-SG; the number of signal samples is changed, and the decomposition order, the signal-to-noise ratio and the point charge localization performance of CEEMDAN-SG are analyzed. Simulation results show that compared with the signal before denoising, the signal to noise ratio of the denoised signal is improved by about 2%, which shows that the method can better display the electric field signal characteristics and has better positioning effect.
Description
Technical Field
The invention relates to a point charge positioning method, in particular to a thunderstorm cloud point charge positioning method based on complementary set modal decomposition and SG filtering.
Background
Atmospheric electric field strength is a fundamental parameter of atmospheric physics and atmospheric electricity. Thunderstorm activities tend to cause changes in the ground electric field, which has a vertically downward atmospheric electric field in sunny days, while the ground atmospheric electric field is significantly enhanced in thunderstorm days. The formation, development and dissipation processes of the thunderstorm cloud can be inverted through the change of the ground atmospheric electric field. The research and analysis of the atmospheric electric field signal are effective ways for improving the lightning early warning accuracy rate, and have important practical significance for analyzing lightning activities and realizing lightning directional monitoring.
In the prior art, a thunder and lightning early warning model based on a plurality of physical parameters such as an atmospheric electric field, temperature, air pressure and the like is constructed by using a BP neural network, but the method has extremely short early warning time and insufficient utilization rate of atmospheric electric field signals. These studies neglect the non-linear non-stationary characteristics of the atmospheric electric field signal while facilitating thunderstorm cloud detection based on three-dimensional atmospheric electric field measurements.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a high-precision and low-noise thundercloud point charge positioning method based on complementary set modal decomposition and SG filtering.
The technical scheme is as follows: the thundercloud point charge positioning method based on complementary set modal decomposition and SG filtering is characterized by comprising the following steps of:
decomposing an atmospheric electric field signal into a series of Intrinsic Mode Functions (IMF) components by complementary set empirical mode decomposition;
removing noise and reconstructing signals of the intrinsic mode function IMF through Savitzky-Golay filtering;
and thirdly, carrying out thunderstorm cloud point charge positioning on the data subjected to denoising and signal reconstruction, changing the number of signal samples, and carrying out comparative analysis on the decomposition order, the signal-to-noise ratio and the point charge positioning performance of the data.
Further, in the first step, the atmospheric electric field signal decomposition includes the following steps:
the method comprises the following steps of (I) setting an original atmospheric electric field signal as x (n), and respectively adding and subtracting white noise omega (n) to the signal to obtain an ith signal as:
wherein i is the number of times of adding Gaussian white noise, and i is 1, 2.
(II) pair of signals
Decomposing to obtain M
Likewise, decompose
To obtain K
wherein ,
respectively representing j-th IMF obtained by decomposing after adding and subtracting white noise at the ith time, wherein j is 1, 2.
(III) after ensemble averaging, the jth IMF component IMFj(n) is:
(IV) calculating each IMF separatelyj(n) value of the autocorrelation function IMFj'(n)。
Further, the signal
Decomposition is using the same algorithm steps as classical EMD.
Further, in step two, the noise removal and signal reconstruction includes the following steps:
judging that the modal component dominated by the noise is IMF according to the autocorrelation characteristics of the noise and the signal1(n)～IMFk(n)；
(II) noise occupationThe dominant mode component uses Savitzky-Golay filtering to obtain IMF (intrinsic mode function) as each denoised component1”(n)～IMFk”(n)；
And (III) obtaining a reconstructed atmosphere electric field signal x '(n) by using the filtered modal component and residual component, wherein the reconstructed atmosphere electric field signal x' (n) is as follows:
further, in step three, the thunderstorm cloud point charge localization includes the following steps:
establishing a three-dimensional rectangular coordinate system by taking N points as coordinate origin, wherein: s (x, y, z) is the position of the charge of the thunderstorm cloud point; n (0,0,0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the height of the atmospheric electric field instrument and the altitude of the position where the atmospheric electric field instrument is located; the horizontal deflection angle and the elevation angle of the charge of the thunderstorm cloud point are respectively alpha and beta; r is the distance from the point charge S to the electric field instrument N; measuring an atmospheric electric field signal of S as x (N) at an atmospheric electric field instrument N, and obtaining electric field components E in x, y and z directions according to the orthogonality of every two electric field componentsx、Ey、Ez；
And (II) obtaining the relation between the charge spherical coordinates (r, alpha, beta) and the rectangular coordinates (x, y, z) of the thunderstorm cloud point by using a mirror image method:
wherein ,
(III) considering the corresponding relation between the electric field component and the charge azimuth of the thunderstorm cloud point, defining the north direction ExGreater than 0, east-ward direction EyGreater than 0, correcting the point charge orientationIs positive. The corrected point charge spherical coordinates (r ', α', β '), and rectangular coordinates (x', y ', z') are:
has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
(1) according to the method, complementary set empirical mode decomposition and Savitzky-Golay filtering are applied to lightning detection, a three-dimensional atmospheric electric field measurement model is established, the cloud point charges of the thunderstorm are accurately positioned, and the lightning detection capability is further improved.
(2) Aiming at the non-stable and non-linear characteristics of the atmospheric electric field signal, the method not only can denoise the electric field signal to reduce the electric field measurement error, but also can effectively improve the point charge positioning precision.
Drawings
FIG. 1 is a diagram of a three-dimensional atmospheric electric field measurement model according to the present invention;
FIG. 2 is a flow chart of a method for locating charge in a cloud point of a thunderstorm according to the present invention;
FIG. 3 is a diagram showing the decomposition result of the vertical component of the atmospheric electric field signal based on CEEMDAN in the present invention;
FIG. 4 is a graph of normalized autocorrelation functions for each modal component of the present invention;
FIG. 5 is an atmospheric electric field signal diagram before and after denoising by SG filtering according to the present invention;
FIG. 6 is a graph showing the relationship between the distance and the measurement error of the electric field component and the distance measurement error according to the present invention;
FIG. 7 is a graph showing the relationship between the measurement error of elevation angle and electric field component and the measurement error of horizontal deflection angle.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
Example 1:
the invention provides a thunderstorm cloud point charge positioning method based on complementary set empirical mode decomposition CEEMDAN and Savitzky-Golay (SG) filtering, which comprises the following steps:
firstly, CEEMDAN and SG filtering processing is carried out on an atmospheric electric field signal, and the method specifically comprises the following steps:
the atmospheric electric field signal has the characteristics of nonlinearity and non-stationarity, and CEEMDAN is a powerful method for researching the nonlinearity and non-stationarity signal. By adopting the method, the atmospheric electric field signal is decomposed to obtain signal components and trend terms with different oscillation scales, so that SG filtering can be conveniently carried out according to the autocorrelation characteristics of each component. The method comprises the following specific steps:
(1) setting the original atmospheric electric field signal as x (n), and adding and subtracting white noise omega (n) to the signal respectively to obtain the ith signal as:
wherein i is the number of times of adding gaussian white noise, and i is 1, 2.
(2) Using the same steps [1,2 ] as in the classical EMD algorithm]To the signal
Decomposing to obtain M
Likewise, decompose
To obtain K
wherein ,
the i-th IMF obtained by decomposition after adding and subtracting white noise is represented by j, which is 1, 2.
(3) After ensemble averaging, the jth IMF component IMFj(n) is：
(4) Calculate each IMF separatelyj(n) value of the autocorrelation function IMFj'(n)。
(5) According to the autocorrelation characteristics of the noise and the signal, judging that the modal component dominated by the noise is IMF1(n)～IMFk(n)。
(6) SG filtering is used for modal components with dominant noise, and each denoised component is IMF1”(n)～IMFk”(n)。
(7) And obtaining a reconstructed atmospheric electric field signal x' (n) by using the filtered modal component and the residual component as follows:
secondly, a thunderstorm cloud point charge positioning method based on complementary set empirical mode decomposition and Savitzky-Golay filtering is provided, and the method specifically comprises the following steps:
based on the electrostatic field theory, the charge positioning of the thunderstorm cloud point is carried out by utilizing the three-dimensional atmospheric electric field measurement model shown in the figure 1. In fig. 1, a three-dimensional rectangular coordinate system is established with N points as the origin of coordinates, wherein: s (x, y, z) is the position of the charge of the thunderstorm cloud point; n (0,0,0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the height of the atmospheric electric field instrument and the altitude of the position where the atmospheric electric field instrument is located. The horizontal deflection angle and the elevation angle of the charge of the thunderstorm cloud point are respectively alpha and beta; r is the distance from the point charge S to the electric field instrument N; measuring an atmospheric electric field signal of S as x (N) at an atmospheric electric field instrument N, and obtaining electric field components E in x, y and z directions according to the orthogonality of every two electric field componentsx、Ey、Ez。
Further, the relationship between the charge spherical coordinates (r, α, β) and the rectangular coordinates (x, y, z) of the thunderstorm cloud point is obtained by a mirror image method as [3 ]:
wherein ,
considering the corresponding relation between the electric field component and the charge azimuth of the thunderstorm cloud point, defining the positive north direction ExGreater than 0, east-ward direction EyAbove 0, the point charge orientation is corrected. The corrected point charge spherical coordinates (r ', α', β '), and rectangular coordinates (x', y ', z') are:
a flow of a method for positioning a charge of a cloud point of a thunderstorm based on complementary ensemble empirical mode decomposition and Savitzky-Golay filtering is shown in fig. 2.
According to the above embodiment method, the performance analysis of the thunderstorm cloud point charge localization method based on complementary set empirical mode decomposition and Savitzky-Golay filtering is performed as follows.
Example 2:
1. CEEMDAN and SG Filter Performance analysis
Selecting atmospheric electric field signal vertical component data E of 0:00 to 0:10 in 14 days of 4 months and 4 months in 2017zAs samples, the number of samples was 600, and the effect of CEEMDAN and SG filtering was analyzed. The results after decomposition by CEEMDAN are shown in FIG. 3.
As seen in FIG. 3, the vertical component signal is primarily composed of the modal component IMF1(n)～IMF9(n) is prepared. Respectively solving normalized autocorrelation of each componentFunction to obtain IMF1'(n)～IMF9' (n) as shown in FIG. 4.
In FIG. 4, the autocorrelation characteristics of the first 4-order modal components are similar to noise, and thus, for IMF1(n)～IMF4(n) SG filtering treatment is carried out, and then the filtered modal component IMF is carried out1”(n)～IMF4"(n) and a residual component IMF5(n)～IMF9And (n) reconstructing to obtain the denoised atmospheric electric field vertical component data, as shown in fig. 5.
To verify the effectiveness of CEEMDAN-SG, the data E of the vertical component of the atmospheric electric field signal was measured at 0:00 to 0:30 on 14 days 4 months 4 and 2017zThe sample numbers of 600, 800 and 1000 are respectively selected, noise with the signal-to-noise ratio of 10dB is added, and the noise is compared with CEEMD, EEMD and EMD for analysis, and the result is shown in table 1.
TABLE 1 CEEMDAN-SG effectiveness verification results
In table 1, the signal to noise ratio based on the CEEMDAD algorithm is higher compared to EMD and EEMD. After SG filtering, the signal-to-noise ratio of the signal is larger, which shows that CEEMDAN-SG has better denoising effect. Meanwhile, the signal-to-noise ratio gradually decreases as the number of samples increases. In addition, the CEEMDAN algorithm balances the signal-to-noise ratio during the decomposition process, so that the decomposition order is relatively large. Overall, the three algorithms do not differ significantly in the decomposition order.
2. Point charge localization method performance analysis
According to the distribution of charge electric field in the air and the charge structure principle of thunderstorm cloud, the dielectric constant epsilon of air is taken11, the ground dielectric constant ε of the atmospheric electric field instrument N2At 5, the charge amount q was 5C, and the point charge localization performance was investigated. Let the standard deviation of the three-dimensional atmospheric electric field component measurement be sigmaEi。
By the equation (6), the measurement error σ from the electric field component is obtainedEiMeasurement errors sigma causing distance r, horizontal declination angle alpha and elevation angle betar，σα，σβIs [3]]：
As can be seen from equation (8), the measurement error σ of the atmospheric electric fieldEiIs the main factor influencing the point charge positioning distance measurement and direction finding precision. Error sigmaEiThe smaller the distance r, the smaller the range and direction finding error. The CEEMDAN-SG is used for measuring the errors sigma corresponding to the sample numbers of 600, 800 and 1000rRespectively reduces 0.0223kV/m, 0.0190kV/m and 0.0189kV/m, and supposes that the error sigma before denoising isEi0.05kV/m, and further analyzed for error σEiRelationship to point charge localization performance.
Using equation (8), the distance r, the electric field component measurement error σ, is studiedEiAnd the distance measurement error sigmarThe results are shown in FIG. 6. In fig. 6, the range error σ before and after filtering with SGrBoth increase with increasing distance r. In particular the filter front error sigmarThe most obvious change is 0.3340km at the maximum. Increasing the distance r, SG-filtered error sigma of 600 samplesrThe slowest of the increase follows, with a maximum of only 0.1850 km. Error sigma after SG filtering 800 and 1000 samplesrThe variation phases are close, and the maximum errors respectively reach 0.2071km and 0.2077 km. In general, the CEEMDAN-SG is utilized to effectively reduce the charge positioning and ranging error of the thunderstorm cloud point, and a better effect is obtained.
Similarly, using equation (8), the elevation angle β and the electric field component measurement error σ are investigatedEiError of measurement of deviation angle from horizontal sigmaαThe results are shown in FIG. 7. In fig. 7, when the elevation angle β is less than 80 degrees, the horizontal deflection angle error σαHardly changes with the change of the elevation angle beta. And when the elevation angle beta is greater than 80 degrees, the error sigmaαThis trend, which is more pronounced without SG filtering, rises sharply with increasing elevation angle β. After filtering with SG, the error σ is measured on the basis of 800, 1000 samples as the elevation angle β increasesαThe variation of (c) is almost uniform, while the variation of the results for 600 samples is relatively small. In summary,the introduction of CEEMDAN-SG can reduce the horizontal deflection angle error sigmaα. In addition, the elevation measurement error σβAnd error sigmaαThe analysis is similar and will not be described in detail. From the above analysis, the following conclusions were drawn: by utilizing a CEEMDAN self-adaptive decomposition algorithm, the three-dimensional atmospheric electric field signal is preprocessed, so that the measurement error of atmospheric electric field components can be effectively reduced, and the electric field change at different times can be more accurately mastered. A three-dimensional atmospheric electric field measurement model is established, a thunderstorm cloud point charge positioning method is introduced by using a reconstructed signal after SG filtering, and the moving path of point charges can be tracked in real time, so that lightning activities can be visualized as possible.
Claims (5)
1. A thundercloud point charge positioning method based on complementary set modal decomposition and SG filtering is characterized by comprising the following steps:
decomposing an atmospheric electric field signal into a series of Intrinsic Mode Functions (IMF) components by complementary set empirical mode decomposition;
removing noise and reconstructing signals of the intrinsic mode function IMF through Savitzky-Golay filtering;
and thirdly, carrying out thunderstorm cloud point charge positioning on the data subjected to denoising and signal reconstruction, changing the number of signal samples, and carrying out comparative analysis on the decomposition order, the signal-to-noise ratio and the point charge positioning performance of the data.
2. The thundercloud point charge localization method based on complementary ensemble modal decomposition and SG filtering according to claim 1, wherein in step one, the atmospheric electric field signal decomposition comprises the following steps:
the method comprises the following steps of (I) setting an original atmospheric electric field signal as x (n), and respectively adding and subtracting white noise omega (n) to the signal to obtain an ith signal as:
wherein i is the number of times of adding Gaussian white noise, and i is 1, 2.
(II) pair of signals
Decomposing to obtain M
Likewise, decompose
To obtain K
wherein ,
respectively representing j-th IMF obtained by decomposing after adding and subtracting white noise at the ith time, wherein j is 1, 2.
(III) after ensemble averaging, the jth IMF component IMFj(n) is:
(IV) calculating each IMF separatelyj(n) value of the autocorrelation function IMFj'(n)。
3. The method according to claim 2, wherein in step (two), the signals are used for positioning the charges of the thundercloud points based on the complementary ensemble modal decomposition and SG filtering
Decomposition is using the same algorithm steps as classical EMD.
4. The thundercloud point charge localization method based on complementary ensemble modal decomposition and SG filtering according to claim 1, wherein in step two, the removing noise and signal reconstruction comprises the following steps:
judging that the modal component dominated by the noise is IMF according to the autocorrelation characteristics of the noise and the signal1(n)～IMFk(n)；
(II) carrying out Savitzky-Golay filtering on the modal components with the noise dominant action to obtain IMF (intrinsic mode function) serving as each denoised component1″(n)～IMFk″(n)；
And (III) obtaining a reconstructed atmosphere electric field signal x '(n) by using the filtered modal component and residual component, wherein the reconstructed atmosphere electric field signal x' (n) is as follows:
5. the method of claim 1, wherein in step three, the method for thundercloud point charge localization based on complementary ensemble modal decomposition and SG filtering comprises the following steps:
establishing a three-dimensional rectangular coordinate system by taking N points as coordinate origin, wherein: s (x, y, z) is the position of the charge of the thunderstorm cloud point; n (0,0,0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the height of the atmospheric electric field instrument and the altitude of the position where the atmospheric electric field instrument is located; the horizontal deflection angle and the elevation angle of the charge of the thunderstorm cloud point are respectively alpha and beta; r is the distance from the point charge S to the electric field instrument N; measuring an atmospheric electric field signal of S as x (N) at an atmospheric electric field instrument N, and obtaining electric field components E in x, y and z directions according to the orthogonality of every two electric field componentsx、Ey、Ez；
And (II) obtaining the relation between the charge spherical coordinates (r, alpha, beta) and the rectangular coordinates (x, y, z) of the thunderstorm cloud point by using a mirror image method:
wherein ,
(III) considering the corresponding relation between the electric field component and the charge azimuth of the thunderstorm cloud point, defining the north direction ExGreater than 0, east-ward direction EyAbove 0, the point charge orientation is corrected. The corrected point charge spherical coordinates (r ', α', β '), and rectangular coordinates (x', y ', z') are:
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| CN117648557A (en) * | 2024-01-30 | 2024-03-05 | 山东科技大学 | SOH prediction method and device based on SOH combined noise reduction |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113255510A (en) * | 2021-05-21 | 2021-08-13 | 南京信息工程大学 | Rainbow cloud point charge moving path imaging method based on multi-time scale DBSCAN and sample entropy |
| CN113255510B (en) * | 2021-05-21 | 2023-07-25 | 南京信息工程大学 | Thunderstorm cloud point charge moving path imaging method based on multi-time scale DBSCAN and sample entropy |
| CN117648557A (en) * | 2024-01-30 | 2024-03-05 | 山东科技大学 | SOH prediction method and device based on SOH combined noise reduction |
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