CN112766127B - Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering - Google Patents
Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering Download PDFInfo
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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 IMF components by CEEMDAN; performing SG filtering denoising and signal reconstruction on IMF with dominant noise effect; realizing point charge positioning by using CEEMDAN-SG processed data; the number of signal samples is changed, and the decomposition order, the signal-to-noise ratio and the point charge positioning performance of CEEMDAN-SG are analyzed. Simulation results show that compared with the signal to noise ratio before denoising, the signal to noise ratio after denoising is improved by about 2%, and the method can display electric field signal characteristics and has a good 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 is vertically downward on the ground in sunny days, and which is significantly enhanced in thunderstorm weather. The ground atmosphere electric field changes can reverse the formation, development and dissipation process of thunderstorm cloud. The research and analysis of the atmospheric electric field signals are effective ways for improving the lightning early warning accuracy, analyze the lightning activity, realize the lightning directional monitoring, and have important practical significance.
In the prior art, a 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 utilizing a BP neural network, but the early warning time of the method is extremely short, and the utilization rate of the atmospheric electric field signal is insufficient. These studies have ignored the nonlinear 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 invention aims to: the invention aims to provide a Lei Yundian charge positioning method with high accuracy and low noise based on complementary set modal decomposition and SG filtering.
The technical scheme is as follows: the Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering is characterized by comprising the following steps of:
step one, decomposing an atmospheric electric field signal into a series of intrinsic mode function IMF components by utilizing complementary set empirical mode decomposition;
removing noise and reconstructing signals from an intrinsic mode function IMF through Savitzky-Golay filtering;
and thirdly, carrying out thunderstorm cloud point charge positioning on the data after 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:
setting the 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 follows:
where i is the number of times white gaussian noise is added, i=1, 2, …, N;
(II) pair of signalsDecomposing to obtain M->Likewise, break up->Obtaining K-> wherein ,/>Respectively representing the j-th IMF obtained by decomposing the i-th added and subtracted white noise, j=1, 2, … and M;
(III) after ensemble averaging, the jth IMF component IMF j (n) is:
(IV) calculating each IMF separately j (n) autocorrelation function value IMF j '(n)。
Further, the signalThe decomposition is the same algorithmic step with classical EMD.
Further, in the second step, the noise removal and signal reconstruction includes the following steps:
based on the autocorrelation characteristics of noise and signal, judging the mode component with dominant noise as IMF 1 (n)～IMF k (n)；
(II) using Savitzky-Golay filtering on modal components with dominant noise to obtain IMF (inertial measurement Filter) of each denoised component 1 ”(n)～IMF k ”(n)；
And thirdly, obtaining a reconstructed atmospheric electric field signal x '(n) by using the filtered modal component and the residual component, wherein the reconstructed atmospheric electric field signal x' (n) is:
further, in the third step, the thunderstorm cloud point charge positioning includes the following steps:
firstly, taking N points as origin points of coordinates to build three-dimensionalRectangular coordinate system, wherein: s (x, y, z) is the position of the thunderstorm cloud point charge; n (0, 0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the altitude 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 elevation angle of the thunderstorm cloud point charge are alpha and beta respectively; r is the distance from the point charge S to the electric field instrument N; at the position of the atmospheric electric field instrument N, the atmospheric electric field signal of S is measured as x (N), and according to the orthogonality of the electric field components, the electric field components in the x, y and z directions are obtained as E respectively x 、E y 、E z ；
And (II) obtaining the relation between the thunderstorm cloud point charge spherical coordinates (r, alpha, beta) and rectangular coordinates (x, y, z) by using a mirror image method:
wherein ,
(III) considering the corresponding relation between the electric field component and the thunderstorm cloud point charge azimuth, defining the north direction E x Greater than 0, forward direction E y Greater than 0, the point charge azimuth is corrected. The corrected point charge spherical coordinates (r ', α', β ') and rectangular coordinates (x', y ', z') are respectively:
the beneficial effects are that: compared with the prior art, the invention has the following remarkable advantages:
(1) According to the invention, the complementary set empirical mode decomposition and Savitzky-Golay filtering are applied to lightning detection, a three-dimensional atmospheric electric field measurement model is established, and thunderstorm cloud point charges are accurately positioned, so that the lightning detection capability is further improved.
(2) Aiming at the non-stable nonlinear characteristic of the atmospheric electric field signal, the method can not only denoise the electric field signal to reduce the electric field measurement error, but also effectively improve the point charge positioning precision.
Drawings
FIG. 1 is a diagram of a three-dimensional atmospheric electric field measurement model of the present invention;
FIG. 2 is a flow chart of a thunderstorm cloud point charge positioning method of the present invention;
FIG. 3 is a graph showing the vertical component decomposition results of the CEEMDAN-based atmospheric electric field signal according to the present invention;
FIG. 4 is a graph of normalized autocorrelation function of modal components of the present invention;
FIG. 5 is a graph of signals of an atmospheric electric field before and after denoising by SG filtering according to the present invention;
FIG. 6 is a graph of distance, electric field component measurement error versus range error for the present invention;
FIG. 7 is a graph of elevation angle, electric field component measurement error versus horizontal deflection angle measurement error in accordance with the present invention.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying 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:
1. CEEMDAN and SG filtering treatment is carried out on the atmospheric electric field signal, and the method specifically comprises the following steps:
the atmospheric electric field signal has the characteristics of nonlinearity and non-stability, and CEEMDAN is a powerful method for researching nonlinear and non-stability signals. The method is adopted to decompose the atmospheric electric field signals to obtain signal components and trend items 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) Let the original atmospheric electric field signal be x (n), add, subtract white noise ω (n) to this signal separately, get the ith signal as:
where i is the number of times white gaussian noise is added, i=1, 2,..n.
(2) Using the same steps as classical EMD algorithm [1,2 ]]For signalsDecomposing to obtain M->Likewise, break up->Obtaining K-> wherein ,/>The j-th IMF, j=1, 2, M, decomposed after adding and subtracting white noise for the i-th time, respectively.
(3) After the integration average, the jth IMF component IMF j (n) is:
(4) Separately calculating each IMF j (n) autocorrelation function value IMF j '(n)。
(5) According to the autocorrelation characteristics of noise and signals, judging that the modal component with dominant noise is IMF 1 (n)～IMF k (n)。
(6) SG filtering is used for modal components with dominant noise, and each denoised component is IMF 1 ”(n)～IMF k ”(n)。
(7) And obtaining a reconstructed atmosphere electric field signal x '(n) by using the filtered modal component and the residual component, wherein the reconstructed atmosphere electric field signal x' (n) is as follows:
2. the invention provides a thunderstorm cloud point charge positioning method based on complementary set empirical mode decomposition and Savitzky-Golay filtering, which specifically comprises the following steps:
based on the electrostatic field theory, the thunderstorm cloud point charge positioning is performed by using the three-dimensional atmospheric electric field measurement model shown in fig. 1. In fig. 1, a three-dimensional rectangular coordinate system is established with N points as origin points, wherein: s (x, y, z) is the position of the thunderstorm cloud point charge; n (0, 0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the altitude of the atmospheric electric field meter itself and the altitude at which it is located. The horizontal deflection angle and elevation angle of the thunderstorm cloud point charge are alpha and beta respectively; r is the distance from the point charge S to the electric field instrument N; at the position of the atmospheric electric field instrument N, the atmospheric electric field signal of S is measured as x (N), and according to the orthogonality of the electric field components, the electric field components in the x, y and z directions are obtained as E respectively x 、E y 、E z 。
Further, the relationship between the spherical coordinates (r, alpha, beta) and the rectangular coordinates (x, y, z) of the thunderstorm cloud point charge is obtained by using a mirror image method and is respectively as follows:
wherein ,
the corresponding relation between the electric field component and the thunderstorm cloud point charge azimuth is considered to define the north direction E x Greater than 0, the east is rightDirection E y Greater than 0, the point charge azimuth is corrected. The corrected point charge spherical coordinates (r ', α', β ') and rectangular coordinates (x', y ', z') are respectively:
a flow of a thunderstorm cloud point charge positioning method based on complementary set empirical mode decomposition and Savitzky-Golay filtering is shown in figure 2.
According to the embodiment method described above, the following performance analysis is performed on the thunderstorm cloud point charge localization method based on the complementary set empirical mode decomposition and Savitzky-Golay filtering.
Example 2:
1. CEEMDAN and SG filter performance analysis
Selecting the vertical component data E of the atmospheric electric field signals from 0:00 to 0:10 in 2017, 4 and 14 days z As samples, the number of samples was 600, and the effects of CEEMDAN and SG filtering were analyzed. The results after decomposition by CEEMDAN are shown in fig. 3.
As can be seen from fig. 3, the vertical component signal is mainly composed of the modal component IMF 1 (n)～IMF 9 (n) composition. Respectively solving normalized autocorrelation functions of all components to obtain IMF 1 '(n)～IMF 9 ' (n) as shown in FIG. 4.
In FIG. 4, the autocorrelation characteristics of the first 4 th order modal component are similar to noise, and therefore, for IMF 1 (n)～IMF 4 (n) performing SG filtering treatment, and then performing IMF on the filtered modal components 1 ”(n)～IMF 4 "(n) and residual component IMF 5 (n)～IMF 9 And (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 atmospheric electric field signal vertical component data E was measured from 0:00 to 0:30 at 14.4.4.5 z 600,8 are respectively selected00 The number of samples of 1000, with the addition of noise with a signal to noise ratio of 10dB, was compared with CEEMD, EEMD, EMD and the results are shown in table 1.
TABLE 1 CEEMDAN-SG validity verification results
In table 1, the signal-to-noise ratio based on CEEMDAD algorithm is higher compared to EMD and EEMD. After SG filtering, the signal to noise ratio of the signal is larger, which indicates that CEEMDAN-SG has better denoising effect. Meanwhile, as the number of samples increases, the signal-to-noise ratio of the signal gradually decreases. In addition, the CEEMDAN algorithm has a relatively large decomposition order because it continuously balances the signal-to-noise ratio during the decomposition process. In general, the three algorithms do not differ significantly in the resolution order.
2. Point charge positioning method performance analysis
According to the electric field distribution of the aerial charge and the principle of thunderstorm cloud charge structure, taking the dielectric constant epsilon of the air 1 1, the dielectric constant epsilon of the ground where the atmospheric electric field instrument N is located 2 The charge amount q was 5C, and the point charge positioning performance was further studied. Let the standard deviation of the three-dimensional atmospheric electric field component measurement be sigma Ei 。
Obtaining the measurement error sigma from the electric field component by using (6) Ei The measurement error sigma of the distance r, the horizontal deflection angle alpha and the elevation angle beta is caused r ，σ α ，σ β Is [3]]：
As can be seen from (8), the atmospheric electric field measurement error sigma Ei Is a main factor affecting the accuracy of point charge positioning ranging and direction finding. Error sigma Ei The smaller the distance r, the smaller the ranging direction finding error. Error sigma corresponding to the number of samples 600, 800 and 1000 measured by CEEMDAN-SG r Reduced by 0.0223kV/m, 0.0190kV/m and 0.0189kV/m respectively, assuming the error sigma before denoising Ei Is 0.05kV/mFurther analysis of error sigma Ei Relationship to the point charge localization performance.
Using (8), the distance r and the electric field component measurement error sigma are studied Ei And distance measurement error sigma r The results are shown in FIG. 6. In fig. 6, the distance measurement error σ before and after filtering is performed by SG r Both increase with increasing distance r. In particular the pre-filter error sigma r The most obvious variation of (a) was up to 0.3340km. Increasing the distance r, and performing SG filtering on the error sigma of 600 samples r The slowest increase with this is only 0.1850km at maximum. Error sigma after SG filtering is carried out on 800 and 1000 samples r The variation is close, and the maximum error reaches 0.2071km and 0.2077km respectively. In general, the CEEMDAN-SG is utilized to effectively reduce the thunderstorm cloud point charge positioning range error, and a better effect is obtained.
Similarly, the elevation angle β and the electric field component measurement error σ are studied by using equation (8) Ei Error sigma measured from horizontal deflection angle α The results are shown in FIG. 7. In FIG. 7, when the elevation angle β is smaller than 80 degrees, the horizontal offset angle error σ α Hardly varies with the variation of the elevation angle beta. And when the elevation angle beta is greater than 80 degrees, the error sigma α This trend is more pronounced when SG filtering is not performed, as the elevation angle β increases. After SG filtering, as the elevation angle beta increases, the error sigma is measured based on 800 and 1000 samples α And the variation of 600 samples is nearly uniform, while the resulting variation is relatively small. In summary, the introduction of CEEMDAN-SG can reduce the horizontal deflection angle error sigma α . In addition, elevation measurement error sigma β And error sigma α Is similar to the analysis of (c), and will not be described in detail. From the above analysis, the following conclusion was reached: by utilizing CEEMDAN self-adaptive decomposition algorithm to preprocess the three-dimensional atmospheric electric field signal, the measurement error of the atmospheric electric field component can be effectively reduced, and the electric field changes at different times can be more accurately grasped. And (3) establishing a three-dimensional atmospheric electric field measurement model, and introducing a thunderstorm cloud point charge positioning method by utilizing the reconstructed signal after SG filtering, so that the moving path of the point charge can be tracked in real time, and the lightning activity can be visualized.
Claims (4)
1. A Lei Yundian charge localization method based on complementary set modal decomposition and SG filtering, comprising the steps of:
step one, decomposing an atmospheric electric field signal into a series of intrinsic mode function IMF components by utilizing complementary set empirical mode decomposition;
removing noise and reconstructing signals from an intrinsic mode function IMF through Savitzky-Golay filtering;
step three, carrying out thunderstorm cloud point charge positioning on the data after 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, wherein the thunderstorm cloud point charge positioning comprises the following steps:
firstly, taking N points as origin points of coordinates, and establishing a three-dimensional rectangular coordinate system, wherein: s (x, y, z) is the position of the thunderstorm cloud point charge q; n (0, 0) is the position of the test point of the three-dimensional atmospheric electric field instrument; h represents the sum of the altitude 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 elevation angle of the thunderstorm cloud point charge are alpha and beta respectively; r is the distance from the point charge S to the electric field instrument N; at the position of the atmospheric electric field instrument N, the atmospheric electric field signal of S is measured as x (N), and according to the orthogonality of the electric field components, the electric field components in the x, y and z directions are obtained as E respectively x 、E y 、E z ；
And (II) obtaining the relation between the spherical coordinates (r, alpha, beta) and the rectangular coordinates (x, y, z) of the thunderstorm cloud point charge q by using a mirror image method:
wherein ,q represents point electricityThe charge amount of the charge; epsilon 1 、ε 2 The dielectric constants of the air and the ground where the atmospheric electric field instrument N is positioned are respectively;
(III) considering the corresponding relation between the electric field component and the thunderstorm cloud point charge azimuth, defining the north direction E x Greater than 0, forward direction E y More than 0, correcting the point charge azimuth, wherein the corrected point charge spherical coordinates (r ', alpha', beta ') and rectangular coordinates (x', y ', z') are respectively as follows:
2. the Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering of claim 1, wherein in step one, the atmospheric electric field signal decomposition comprises the steps of:
setting the 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 follows:
where i is the number of times white gaussian noise is added, i=1, 2, N;
(II) pair of signalsDecomposing to obtain M->Likewise, break up->Obtaining K-> wherein ,the j-th IMF, j=1, 2, M, decomposed after adding and subtracting white noise for the i-th time, respectively;
(III) after ensemble averaging, the jth IMF component IMF j (n) is:
(IV) calculating each IMF separately j (n) autocorrelation function value IMF j '(n)。
3. The Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering of claim 2, wherein in step (two), the signalThe decomposition is the same algorithmic step with classical EMD.
4. The Lei Yundian charge positioning method based on complementary set modal decomposition and SG filtering of claim 1, wherein in step two, the noise removal and signal reconstruction comprises the steps of:
based on the autocorrelation characteristics of noise and signal, judging the mode component with dominant noise as IMF 1 (n)～IMF k (n)；
(II) using Savitzky-Golay filtering on modal components with dominant noise to obtain IMF (inertial measurement Filter) of each denoised component 1 ”(n)～IMF k ”(n)；
And thirdly, obtaining a reconstructed atmospheric electric field signal x '(n) by using the filtered modal component and the residual component, wherein the reconstructed atmospheric electric field signal x' (n) is:
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