A method for identifying cloud-to-ground lightning characteristic signals based on distributed tangent space mapping

Abstract

The present invention provides a method for identifying characteristic signals of cloud-to-ground lightning based on distributed tangent space mapping, and belongs to the technical field of lightning electric field signal analysis. It solves the problem that low-frequency electric field signals of lightning are easily interfered by environmental noise, resulting in the inability of the collected data to reflect the real characteristic information. The technical scheme is as follows: it includes the following steps: step one, frame processing of lightning electric field signals; step two, extraction of lightning electric field signal permutation entropy features based on distributed local mean decomposition; step three, ELM lightning electric field signal processing method of local tangent space permutation reconstruction; step four, fitting the lightning electric field signal through the above-mentioned model, thereby obtaining the identification result of the cloud-to-ground lightning type using a distributed signal acquisition device. The beneficial effects of the present invention are as follows: the present invention can effectively improve the filtering capability of lightning electric field signals and extract lightning characteristic information.

Description

Technical Field

[0001] The present invention relates to the technical field of lightning electric field signal analysis, and in particular to a method for identifying cloud-to-ground lightning characteristic signals using distributed tangent space mapping. Background Art

[0002] Lightning is one of the major serious natural disasters, which can cause forest and oil depot fires, power supply and communication information system failures or damage, and pose a major threat to aerospace, mining and some important and sensitive high-tech equipment. After the 1980s, the hazards caused by lightning increased significantly, especially in areas closely related to high-tech, such as aerospace, national defense, communications, electricity, computers, and the electronics industry. The widespread use of large-scale and ultra-large-scale integrated circuits that are extremely sensitive to lightning electromagnetic interference has greatly increased the probability of being struck by lightning.

[0003] Compared with cloud-to-ground lightning, ground-to-ground lightning is more destructive to the safety of people and property on the ground. Distinguishing between cloud-to-ground lightning and ground-to-ground lightning is crucial for the study of lightning physics, thunderstorm prediction, and the improvement of lightning protection technology. The scientific research team has been committed to studying the characteristics of lightning discharge. Different lightning starting positions, charge structures, and lightning transmission forms will affect the subsequent discharge type of lightning. Whether lightning will eventually develop into ground-to-ground lightning or cloud-to-ground lightning is subject to many conditions and is difficult to predict.

[0004] Ground-to-ground lightning and cloud-to-ground lightning have different discharge characteristics during their development. For example, ground-to-ground lightning, when the leader develops from the cloud to the ground, it goes through pre-breakdown, leader step development, and return stroke, and these processes all have unique discharge characteristics. Usually, the electric field waveform characteristics of the discharge in these processes can be analyzed to distinguish cloud-to-ground lightning. For example, the document "Analysis of Time Domain Characteristics of Lightning Electric Field Changing Waveforms and Identification of Discharge Types" ("Meteorology") identifies cloud-to-ground lightning by the characteristics of the electric field waveform (pulse waveform rise time, width, etc.). However, identification based solely on individual pulse waveform characteristics is not very efficient. First, the current understanding of cloud-to-ground lightning is not comprehensive enough, and the pulses of cloud-to-ground lightning are very likely to have a high degree of similarity. Secondly, the types of ground lightning are also different, and the pulses generated by ground lightning under different thunderstorms may vary greatly.

[0005] The paper "Study on Identification of Lightning Electric Field Signals Based on EMD and Fractal Theory" (Journal of Northwest Normal University (2019)) studied the fractal characteristics of lightning electric field signals and used support vector machines to extract and identify lightning electric field signals. This provides a new idea for identifying cloud-to-ground lightning signals, but there are still problems: if only single-station data is used for signal analysis, it is very dependent on the accuracy of the signal, and the low-frequency electric field signal of lightning is very susceptible to interference from environmental noise. This environmental noise may be white noise or noise with a wide frequency band and unidentified source, resulting in the collected data being unable to reflect the true feature information.

[0006] How to solve the above technical problems is the subject faced by the present invention. Summary of the invention

[0007] The purpose of the present invention is to provide a method for identifying lightning characteristic signals of distributed tangent space mapping; the tangent space lightning electric field signal processing method based on distributed local mean decomposition entropy of the present invention can obtain more realistic lightning electric field characteristic information, thereby providing accurate cloud-to-ground lightning type identification results.

[0008] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically as follows:

[0009] A method for identifying lightning characteristic signals using distributed tangent space mapping, the method comprising the following steps:

[0010] Step 1: Frame processing of lightning electric field signals;

[0011] Step 2: Extracting lightning electric field signal permutation entropy features based on distributed local mean decomposition;

[0012] Step 3: ELM lightning electric field signal processing method based on local tangent space arrangement reconstruction;

[0013] Step 4: Fit the lightning electric field signal through the above model, and then use the distributed signal acquisition device to obtain the identification result of the cloud-to-ground lightning type.

[0014] In step 1, N sampling points of each collection station are selected as the standard length of time-frequency processing. The data segment composed of N sampling points is called a frame. In order to avoid the lightning electric field signal appearing between two frames and affecting the signal analysis and feature extraction, each frame contains M sampling points of the previous frame; among them, N and M are both constants, and the value of N must be greater than the number of sampling points contained in the lightning process cycle.

[0015] In step 2,

[0016] The amount of information obtained through the traditional single-station method is limited. In the increasingly complex space environment, signal detection data is easily interfered by environmental noise. Distributed observations can obtain more spatial diversity and more information that is beneficial to lightning electric fields. Combined with information theory methods, the local mean decomposition-permutation entropy feature can effectively separate the signal space and the noise space, and obtain the entropy value feature that can characterize the cloud-to-ground lightning signal.

[0017] The lightning electric field signal of a single collection station is x p (t), where p is the number of the acquisition station and t is the time; calculate the local mean function m ji (t) and the envelope estimation function a ji (t):

[0018]

[0019] Among them, m ji (t) is the local mean function of the i-th PF component (Product Function component, referred to as PF component, is a product function with physical meaning of multiple instantaneous frequencies decomposed from the lightning electric field signal) of the j-th collection station; ji (t) is the envelope estimation function of the i-th PF component of the j-th acquisition station; n i For x p (t) at t i The extreme point of the moment;

[0020] Connect all extreme points and perform smoothing; use the local mean function m ji (t) From the original signal x p (t) and divided by the envelope estimation function, we get:

[0021]

[0022] Where x(t) is the original lightning signal collected by the first collection station. 11 (t) is the PF component.

[0023] If 11 (t) satisfies the range [-1,1], and a 11 (t)=1, then s 11 (t) is the first PF component, and let x(t) = x(t)-s 11 (t), continue to calculate the second PF component according to formula (1)(2)(3); if the conditions are not met, repeat formula (1)(2)(3) until the signal is iterated:

[0024]

[0025] Multiply all the iterated envelope estimation functions to obtain the envelope signal of the first round of iteration:

[0026]

[0027] The signal s 1n (t) is multiplied by the envelope signal a1(t) to obtain the first PF component:

[0028] PF1(t)=a1(t)s 1n (t) (6)

[0029] Separating PF1(t) from the original signal x(t), the remainder is:

[0030] u1(t)=x(t)-PF1(t) (7)

[0031] Take u1(t) as the original signal and repeat the above steps to obtain the subsequent PF components. During the iteration process, the following equation holds true:

[0032]

[0033] Then, for each PF component (PF i (t), i = 1, 2, ..., k) to reconstruct the phase space, with an embedding dimension of m and a time delay of t; then k subsequences are obtained:

[0034] k=n-(m-1)t (9)

[0035] Arrange the above sequence according to size relationship and calculate the probability P of each size relationship arrangement:

[0036] P=Z / k (10)

[0037] Among them, Z is the number of times the arrangement occurs; then the information entropy of each PF component is:

[0038]

[0039] Where m is the number of possible permutations of the permutation relation;

[0040] Then, the jth PF component characteristic of the i-th base station signal is The total characteristic PF is:

[0041]

[0042] Step 3

[0043] Although the information obtained by distributed observation stations contains more information, the high-dimensional features make it difficult to fit the lightning position function. The local tangent space arrangement method can effectively map and reconstruct high-dimensional features and reduce the impact of high-dimensional feature redundancy on function fitting.

[0044] First, principal component analysis (PCA) is used to map the high-dimensional features (data with a dimension greater than 3) PE of lightning electric field signals to obtain the main subspace; let the transformation matrix be A pca , and obtain low-dimensional features (data with dimensions less than or equal to 3 and greater than 0) C = [c1, c2, ..., c N ];

[0045] Secondly, the K nearest neighbor algorithm is used to construct the Euclidean distance between each data point; and C is calculated i H kThe singular eigenvectors corresponding to the q largest right singular values ​​of , find the local low-dimensional space matrix V, and calculate W i =H k (IV i V i T ), where H is the centralized matrix, i.e. H = I-ee T / N, I is the unit matrix, e is the N-dimensional column vector with 1 as the element, and N is the number of features. q is the set dimension value, which is usually estimated by the maximum likelihood value estimation to obtain the latitude value. i is the category of the sample, and k is the sample centering matrix corresponding to category i

[0046] Then, let the initial permutation matrix B = 0, and calculate B(I i ,I i )=B(I i ,I i )+W i W i T ; Compute the eigenvalues ​​and eigenvectors of the generalized eigenproblem:

[0047] XH N BH N C T α=λXH N C T α (13)

[0048] Eigenvalue λ1<λ2…<λ q The corresponding eigenvectors are α1, α2…α q , then A lltsa =(α1,α2…α q ); so the transformation matrix A=A pca A lltsa , the low-dimensional feature coordinates of lightning are Y = A T CH N ;

[0049] The number of neurons in the hidden layer is set to L, the activation function is g(·), and the mathematical description of the extreme learning machine (ELM) is expressed as:

[0050]

[0051] Where j = 1, 2, ..., N, ω i is the connection weight between the input node and the i-th hidden layer neuron, β i is the connection weight between the ith hidden neuron and the output node, b i is the bias of the i-th hidden layer neuron.

[0052] Approximate N samples (X) with zero error i ,t i ), and satisfies Among them, O j is the actual output value of the ELM algorithm for the jth sample, t j is the actual value of the jth sample. Then β i ,ω i , b i satisfy:

[0053]

[0054] The above formula can be simplified as:

[0055]

[0056] in is the output matrix of the hidden layer, β is the output weight matrix, and T is the expected output matrix; then the output weight β = H + T;

[0057] H + is the Moore-Penrose generalized inverse of the hidden layer output matrix H.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] 1. Compared with the traditional single-station sensor signal processing method, more information that can characterize the characteristics of cloud-to-ground flash types can be obtained through distributed information collection.

[0060] 2. The local mean decomposition-permutation entropy feature can effectively separate the signal space and noise space information, and combine with the information theory method to obtain characteristic information that can effectively characterize the type of cloud-to-ground flash.

[0061] 3. The local tangent space reconstruction ELM lightning electric field signal processing method reduces the influence of multi-base high-dimensional information on the lightning electric field signal function fitting, avoids the restriction of invalid features on ELM classification performance, and ensures the recognition accuracy of cloud-to-ground lightning types by the distributed system.

[0062] 4. In summary, compared with traditional methods, this invention has new improvements and innovations in noise separation, feature extraction and positioning methods, which can effectively improve the lightning electric field signal filtering ability and extract lightning feature information. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0064] Figure 1It is a schematic diagram of the process of the present invention.

[0065] Figure 2 It is the three-dimensional entropy value feature map before the local tangent space arrangement mapping of the present invention.

[0066] Figure 3 It is a three-dimensional entropy value feature map after local cut space arrangement mapping of the present invention. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0068] Embodiment 1:

[0069] Figure 1 The implementation and calculation process of the proposed method are demonstrated; 8 lightning observation stations with an average distance of 15 kilometers are used to synchronously collect lightning electric field signals of a thunderstorm. Each observation station is equipped with a fast antenna, which mainly includes an induction plate, an amplifier and an RC charging and discharging circuit. When lightning in the atmosphere breaks down and discharges, the environmental electric field around the fast antenna induction plate will cause an induced current. By adjusting the parameters of the RC circuit, different time constants (τ) can be obtained. The effective frequency band of the fast antenna ranges from 1.5kHz to 2MHz, and the time constant is 100μs. The collected lightning electric field signal is subjected to local mean decomposition, and the corresponding permutation entropy is extracted to form a high-dimensional entropy value feature. Thus, a high-dimensional entropy value feature is formed. Then, the high-dimensional features are reconstructed by local tangent space arrangement to remove feature redundancy. Finally, the reconstructed feature set is used to establish the ELM cloud-to-ground lightning recognition model to identify the cloud-to-ground lightning type.

[0070] Figure 2 The spatial distribution diagram of the first three-dimensional features of the high-dimensional entropy value features is shown. From the figure, it can be seen that in the high-dimensional features, the distribution of the two types is close, and it is difficult to distinguish cloud-to-ground flashes by the distribution distance between different types.

[0071] Figure 3 The spatial distribution diagram of the first three-dimensional features of the low-dimensional entropy value features (features processed by local tangent space arrangement) is shown. As can be seen from the figure, the spatial distribution of the two types of cloud-to-ground flashes is significantly different through the features processed by local tangent space arrangement, which is conducive to improving the performance and accuracy of the cloud-to-ground flash type recognition model.

[0072] See also Figure 1 and Figure 2 The present invention provides a technical solution as follows: a method for identifying lightning characteristic signals using distributed tangent space mapping, the method comprising the following steps:

[0073] Step 1: Frame processing of lightning electric field signals;

[0074] Step 2: Extracting lightning electric field signal permutation entropy features based on distributed local mean decomposition;

[0075] Step 3: ELM lightning electric field signal processing method based on local tangent space arrangement reconstruction;

[0076] Step 4: Fit the lightning electric field signal through the above model, and then use the distributed signal acquisition device to obtain the identification result of the cloud-to-ground lightning type.

[0077] In step 1, N sampling points of each acquisition station are selected as the standard length of time-frequency processing. The data segment composed of N sampling points is called a frame. In order to avoid the lightning electric field signal appearing between two frames and affecting the analysis and feature extraction of the signal, each frame contains M sampling points of the previous frame; where N and M are both constants, and the value of N needs to be greater than the number of sampling points contained in the lightning process cycle. In this embodiment, N is set to 2 23 , M takes half of the value of N.

[0078] In step 2,

[0079] The amount of information obtained through the traditional single-station method is limited. In the increasingly complex space environment, signal detection data is easily interfered by environmental noise. Distributed observations can obtain more spatial diversity and more information that is beneficial to lightning electric fields. Combined with information theory methods, the local mean decomposition-permutation entropy feature can effectively separate the signal space and the noise space, and obtain the entropy value feature that can characterize the cloud-to-ground lightning signal.

[0080] The lightning electric field signal of a single collection station is x p (t), where p is the number of the acquisition station and t is the time; calculate the local mean function m ji (t) and the envelope estimation function a ji (t):

[0081]

[0082] Among them, m ji (t) is the local mean function of the i-th PF component (Product Function component, referred to as PF component, is a product function with physical meaning of multiple instantaneous frequencies decomposed from the lightning electric field signal) of the j-th collection station; ji (t) is the envelope estimation function of the i-th PF component of the j-th acquisition station; n i For x p (t) at t i The extreme point of the moment;

[0083] Connect all extreme points and perform smoothing; use the local mean function m ji (t) From the original signal x p (t) and divided by the envelope estimation function, we get:

[0084]

[0085] Where x(t) is the original lightning signal collected by the first collection station. 11 (t) is the PF component.

[0086] If 11 (t) satisfies the range [-1,1], and a 11 (t)=1, then s 11 (t) is the first PF component, and let x(t) = x(t)-s 11 (t), continue to calculate the second PF component according to formula (1)(2)(3); if the conditions are not met, repeat formula (1)(2)(3) until the signal is iterated:

[0087]

[0088] Multiply all the iterated envelope estimation functions to obtain the envelope signal of the first round of iteration:

[0089]

[0090] The signal s 1n (t) is multiplied by the envelope signal a1(t) to obtain the first PF component:

[0091] PF1(t)=a1(t)s 1n (t) (6)

[0092] Separating PF1(t) from the original signal x(t), the remainder is:

[0093] u1(t)=x(t)-PF1(t) (7)

[0094] Take u1(t) as the original signal and repeat the above steps to obtain the subsequent PF components. During the iteration process, the following equation holds true:

[0095]

[0096] Then, for each PF component (PF i (t), i = 1, 2, ..., k) to reconstruct the phase space, with an embedding dimension of m and a time delay of t; then k subsequences are obtained:

[0097] k=n-(m-1)t (9)

[0098] Arrange the above sequence according to size relationship and calculate the probability P of each size relationship arrangement:

[0099] P=Z / k (10)

[0100] Among them, Z is the number of times the arrangement occurs; then the information entropy of each PF component is:

[0101]

[0102] Where m is the number of possible permutations of the permutation relation;

[0103] Then, the jth PF component characteristic of the i-th base station signal is The total characteristic PF is:

[0104]

[0105] Step 3

[0106] Although the information obtained by distributed observation stations contains more information, the high-dimensional features make it difficult to fit the lightning position function. The local tangent space arrangement method can effectively map and reconstruct high-dimensional features and reduce the impact of high-dimensional feature redundancy on function fitting.

[0107] First, principal component analysis (PCA) is used to map the high-dimensional features (data with a dimension greater than 3) PE of lightning electric field signals to obtain the main subspace; let the transformation matrix be A pca , and obtain low-dimensional features (data with dimensions less than or equal to 3 and greater than 0) C = [c1, c2, ..., c N ];

[0108] Secondly, the K nearest neighbor algorithm is used to construct the Euclidean distance between each data point; and C is calculated i H k The singular eigenvectors corresponding to the q largest right singular values ​​of , find the local low-dimensional space matrix V, and calculate W i =H k (IV i V i T ), where H is the centralized matrix, i.e. H = I-ee T / N, I is the unit matrix, e is the N-dimensional column vector with 1 as the element, and N is the number of features. q is the set dimension value, which is usually estimated by the maximum likelihood value estimation to obtain the latitude value. i is the category of the sample, and k is the sample centering matrix corresponding to category i

[0109] Then, let the initial permutation matrix B = 0, and calculate B(Ii ,I i )=B(I i ,I i )+W i W i T ; Compute the eigenvalues ​​and eigenvectors of the generalized eigenproblem:

[0110] XH N BH N C T α=λXH N C T α (13)

[0111] Eigenvalue λ1<λ2…<λ q The corresponding eigenvectors are α1, α2…α q , then A lltsa =(α1,α2…α q ); so the transformation matrix A=A pca A lltsa , the low-dimensional feature coordinates of lightning are Y = A T CH N ;

[0112] The number of neurons in the hidden layer is set to L, the activation function is g(·), and the mathematical description of the extreme learning machine (ELM) is expressed as:

[0113]

[0114] Where j = 1, 2, ..., N, ω i is the connection weight between the input node and the i-th hidden layer neuron, β i is the connection weight between the ith hidden neuron and the output node, b i is the bias of the i-th hidden layer neuron.

[0115] Approximate N samples (X) with zero error i ,t i ), and satisfies Among them, O j is the actual output value of the ELM algorithm for the jth sample, t j is the actual value of the jth sample. Then β i ,ω i , b i satisfy:

[0116]

[0117] The above formula can be simplified as:

[0118]

[0119] in is the output matrix of the hidden layer, β is the output weight matrix, and T is the expected output matrix; then the output weight β = H + T;

[0120] H + is the Moore-Penrose generalized inverse of the hidden layer output matrix H.

[0121] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying cloud-to-ground lightning characteristic signals using distributed tangent space mapping, characterized in that: The following steps are involved: Step 1: Frame processing of lightning electric field signals; Step 2: Extracting lightning electric field signal permutation entropy features based on distributed local mean decomposition; Step 3: ELM lightning electric field signal processing method based on local tangent space arrangement reconstruction; Step 4: Fit the lightning electric field signal through the above model, so as to obtain the identification result of the cloud-to-ground lightning type by using the distributed signal acquisition device; In step 1, select the sampling points as the standard length for time-frequency processing, The data segment consisting of sampling points is called a frame, and each frame contains ì sampling points of the previous frame; and ì are both constants, The value must be greater than the number of sampling points included in the lightning process cycle; In step 2, the lightning electric field signal of a single collection station is x p (t), where p is the acquisition station number and t is time; the PF components corresponding to each signal are obtained by local mean decomposition; For each PF component PF calculated i (t), the phase space is reconstructed, the embedding dimension is m, and the time delay is t; then we get k * Subsequences: k * =n-(m-1)t (1) Arrange the above sequence according to size relationship and calculate the probability P of each size relationship arrangement: P=Z / k * (2) Among them, Z is the number of times the arrangement occurs; then the information entropy of each PF component is: Among them, m is the number of possible permutations of the permutation relationship; Then, the jth PF component characteristic of the σth base station signal is The characteristic PE is: In step 3, the high-dimensional feature PE of the lightning electric field signal is mapped using principal component analysis to obtain the main subspace; let the transformation matrix of principal component analysis be A pca , and obtain the low-dimensional feature C = [c1, c2, ... c N ]; Use the K nearest neighbor algorithm to construct the Euclidean distance between each data point; and calculate C i H k The singular eigenvectors corresponding to the q largest right singular values ​​of are obtained to obtain the local low-dimensional space matrix V and calculate W i =H k (IV i V i T ); Let the initial permutation matrix B = 0, and calculate B(I i ,I i )=B(I i ,I i )+W i W i T ; Calculate the eigenvalue λ and eigenvector α of the generalized eigenproblem: XH N BH N C T a=λXH N C T a (5) Eigenvalue λ1<λ2…<λ q The corresponding eigenvectors are α1, α2…α q , then the intermediate transformation matrix A lltsa =(α1,α2…α q ); therefore, the overall transformation matrix A = A pca A lltsa , the low-dimensional feature coordinates of lightning are Y = A T CH N ; The number of neurons in the hidden layer is set to L, the activation function is g(·), and the mathematical description of the extreme learning machine is expressed as: Among them, ω f is the connection weight between the input node and the fth hidden layer neuron, β f is the connection weight between the fth hidden neuron and the output node, b f is the bias of the fth hidden layer neuron; Approximation with zero error samples, and satisfy Among them, O e is the actual output value of the ELM algorithm for the e-th sample, t e is the actual value of the e-th sample; Then β f ,ω f , b f satisfy: The above formula can be simplified as in is the output matrix of the hidden layer, β is the output weight matrix, and T is the expected output matrix; then the output weight β = H + T; H + is the Moore-Penrose generalized inverse of the hidden layer output matrix.

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