A DC arc fault detection method and system based on time-frequency composite recurrence graph

Abstract

The invention discloses a DC arc fault detection method and system based on a time-frequency composite recursive graph. The method comprises: using a current sensor to collect a current signal of a DC arc; using a variational modal decomposition algorithm to decompose the current signal into K modal components; based on a time-frequency composite recursive graph, converting the modal components into multiple two-dimensional matrices; based on a singular value decomposition algorithm, extracting singular values ​​in the two-dimensional matrix to construct a high-dimensional feature vector; based on a limit tree, processing the high-dimensional feature vector to obtain a detection result; the time-frequency composite recursive graph proposed by the invention can simultaneously analyze the composite similarity of phase space states in the time domain and the frequency domain, thereby effectively overcoming the disadvantages that the similarity analysis index of the traditional recursive graph is too single and the frequency domain fault information cannot be analyzed.

Description

Technical Field

[0001] The present invention relates to a direct current arc fault detection method and system, and in particular to a direct current arc fault detection method and system based on a time-frequency composite recursive graph, belonging to the technical field of arc fault detection. Background Art

[0002] Excessive consumption of traditional fossil fuels has aggravated environmental pollution and the global greenhouse effect. Therefore, it is crucial to vigorously develop new alternative energy sources. Photovoltaic energy has the advantages of abundant reserves, clean and pollution-free, and no geographical restrictions. In theory, photovoltaic energy can meet the energy needs of all countries. By 2023, the global installed capacity of photovoltaic systems will reach 444 GW, and photovoltaic energy is playing an increasingly critical role in the world. However, the safety of photovoltaic systems is extremely vulnerable to DC arc faults in long-term operation. The National Electrical Code of the United States stipulates that photovoltaic systems with voltage levels higher than 80V must have arc fault detection capabilities. Compared with DC parallel arc faults, DC series arc faults pose a greater hazard to photovoltaic systems. Therefore, how to accurately and quickly detect series arc faults in photovoltaic systems is a challenge that needs to be solved urgently.

[0003] Scholars have proposed series arc fault detection methods based on physical phenomena (such as sound, light, and electromagnetic radiation). However, these methods are only applicable to scenarios with limited space. The series arc fault detection method based on current signals is not limited by the size of the application scenario and is currently the main means of detecting series arc faults. Some researchers have extracted a single feature from the arc current signal and implemented series arc fault detection based on a set threshold, but the detection method based on a single threshold is difficult to effectively adapt to the complex operating state of the system. Other researchers have used machine learning algorithms to fuse different types of fault information in one-dimensional current signals to enhance the adaptability of the detection method.

[0004] However, compared with the original one-dimensional signal, the converted two-dimensional matrix can contain more obvious structural information and spatial correlation information between data points, which is more conducive to extracting subtle internal features. Nowadays, fault diagnosis methods based on converting one-dimensional signals into two-dimensional matrices are receiving more and more attention.

[0005] Some researchers use wavelet transform to decompose arc current into multiple one-dimensional components, and then use these components to construct a two-dimensional matrix, and realize series arc fault detection by mining the texture information in the matrix. Some researchers use fractional Fourier transform to process the current signal to obtain a two-dimensional time-frequency matrix, and then fuse the singular values ​​extracted from the two-dimensional time-frequency matrix based on support vector machine. The two-dimensional matrix obtained from the recursive graph contains the key chaotic information of the arc current, and the deterministic characteristics of the two-dimensional matrix can distinguish the normal state from the series arc fault state. In order to overcome the shortcomings of the traditional recursive graph that easily loses high-frequency fault information, some researchers proposed an improved recursive graph and extracted features and singular values ​​based on recursive quantization analysis from the two-dimensional matrix to realize series arc fault detection. Some researchers use the reconstruction of attractor trajectories to convert different empirical wavelet components into two-dimensional matrices, and input the singular values ​​extracted from different matrices into the support vector machine, which can obtain satisfactory detection results. Some researchers use Gramian angular field and convert arc current into a two-dimensional matrix to enhance the characteristic information of arc current.

[0006] The series arc fault detection method based on two-dimensional matrix construction has played a positive role in obtaining high-performance detection results. However, the fluctuation pattern of arc current in photovoltaic systems is complex, and the arc-like components caused by system transient operations pose a huge challenge to series arc fault detection. Therefore, in order to further improve the performance of series arc fault detection, it is still necessary to study the method of converting one-dimensional arc current into a two-dimensional matrix from different perspectives.

[0007] Recursion graph is a high-performance matrix conversion method. The matrix obtained based on recursion graph contains many arc current features that are difficult to extract by other tools. However, recursion graph and its improved form have the following shortcomings: using Euclidean distance as a single similarity evaluation index, lacking the ability to fully reveal the similarity between different states in phase space; only analyzing the dynamic characteristics of time series from the time domain, and not making full use of the key fault information hidden in the frequency domain. Recursion graph provides a new concept for arc fault detection. In order to accurately detect DC arc faults, it is necessary to further improve the recursion graph algorithm. Summary of the invention

[0008] Purpose of the invention: The purpose of the present invention is to provide a DC arc fault detection method and system based on a time-frequency composite recursive graph that helps to improve the accuracy of arc fault detection.

[0009] Technical solution: The DC arc fault detection method based on the time-frequency composite recursive graph of the present invention comprises the following steps:

[0010] (1) Using a current sensor to collect the current signal of the DC arc;

[0011] (2) Decompose the current signal into K modal components {v k , k = 1, 2, ..., K};

[0012] (3) converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recursive graph;

[0013] (4) extracting singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0014] (5) Process the high-dimensional feature vector based on the extreme tree to obtain a detection result.

[0015] Furthermore, the step (2) is specifically to decompose the current signal into K modal components {v k , k = 1, 2, ..., K}, so that different frequency components in the current signal are separated to avoid mutual interference of different frequency components in the subsequent feature extraction process. The variational mode decomposition algorithm is as follows:

[0016]

[0017] Where K is the number of modes obtained by decomposition, F(t)={x t |t=1,2,…,n} is the arc current to be decomposed, x t is the data point in F(t), n is the number of data points, δ(t) represents the Dirac function, j is the complex number symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, and v k (t) represents the modal set, {ω k} represents the center frequency, represents the partial derivative operation with time t.

[0018] Furthermore, the two-dimensional matrix in step (3) includes K time-domain composite recursive graphs and one frequency-domain composite recursive graph.

[0019] Furthermore, the method for obtaining the time domain composite recursive graph is as follows:

[0020] The modal components are converted into the form of phase space as shown below:

[0021]

[0022] Among them, the number of phase space states is N = n-(m-1)τ, m is the embedding dimension, τ is the delay time; the modal components are VT k is the modal component v k The corresponding phase space matrix, vt k，N VT kThe Nth phase space vector of is the nth data point in the kth mode; n is the modal component v k (t) The number of data points;

[0023] The modal component v is obtained using the following formula: k (t) time domain composite recurrence graph TCRP k :

[0024]

[0025]

[0026] In the formula, ||vt k，i -vt k，j || is vt k，i With vt k，j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vt k，i , vt k，j ) means vt k，i With vt k，j The cosine distance between them, Cosd∈(0,2); the smaller the Cosd value, the higher the directional similarity of the two vectors; <vt k，i , vt k，j > is vt k，i With vt k，j The inner product between ||vt k，i || and ||vt k，j || respectively vt k，i With vt k，j The modulus value of Indicates TCRP k The data corresponding to the i-th row and j-th column in .

[0027] Furthermore, the method for obtaining the frequency domain composite recursive graph is as follows:

[0028] Based on the modal components {v k , k=1, 2, ..., K} construct the time-frequency matrix of the current signal, as shown in the following formula:

[0029]

[0030] in, is a column vector, VF consists of n column vectors;

[0031] The modal component v is obtained using the following formula: k Frequency domain composite recurrence graph FCRP of (t):

[0032] FCRP i，j =β||vfi -vf j ||+(1-β)Cosd(vf i , vf j )

[0033]

[0034] In the formula, ||vf i -vf j || is vf i With vf j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vf i , vf j ) represents vf i With vf j The cosine distance between them, Cosd∈[0,2], when the Cosd value is smaller, the direction similarity of the two vectors is higher; <vf i , vf j > is vf i With vf j The inner product between ||vf i || and ||vf j || respectively vf i With vf j The modulus value of .

[0035] Furthermore, the step (5) is specifically as follows: training each decision tree in the extreme tree, splitting each node in the decision tree, completing the training of the decision tree, and then completing the training of the extreme tree, using the trained extreme tree to process the high-dimensional feature vector to obtain the detection result;

[0036] The splitting step comprises:

[0037] (51) Randomly select m features {sv1, sv2, ..., sv m};

[0038] (52) Calculate the feature sv in the data set i The maximum value of and minimum value

[0039] (53) Randomly select feature sv i The split point

[0040] (54) Calculate feature sv i The split point Gini index

[0041] (55) Select the split point with the largest Gini index as feature sv i The final split point is used to split the current node.

[0042] Based on the same inventive concept, the present invention also provides a DC arc fault detection system based on a time-frequency composite recursive graph, comprising:

[0043] A collection module, used for collecting the current signal of the DC arc by using a current sensor;

[0044] A decomposition module is used to decompose the current signal into K modal components {v k , k = 1, 2, ..., K};

[0045] A conversion module, used for converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recurrence graph;

[0046] A fault feature extraction module extracts singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0047] The detection module processes the high-dimensional feature vector based on the extreme tree to obtain a detection result.

[0048] Furthermore, the two-dimensional matrix of the conversion module includes K time-domain composite recursive graphs and one frequency-domain composite recursive graph.

[0049] Furthermore, the method for obtaining the time domain composite recursive graph is as follows:

[0050] The modal components are converted into the form of phase space as shown below:

[0051]

[0052] Among them, the number of phase space states is N = n-(m-1)τ, m is the embedding dimension, τ is the delay time; the modal components are VT k is the modal component v k The corresponding phase space matrix, vt k，N VT k The Nth phase space vector of is the nth data point in the kth mode; n is the modal component v k (t) The number of data points;

[0053] The modal component v is obtained using the following formula: k (t) time domain composite recurrence graph TCRP k :

[0054]

[0055]

[0056] In the formula, ||vt k，i -vt k，j || is vt k，i With vt k，j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vt k，i , vt k，j ) means vt k，i With vt k，j The cosine distance between them, Cosd∈(0,2); the smaller the Cosd value, the higher the directional similarity of the two vectors; <vt k，i , vt k，j > is vt k，i With vt k，j The inner product between ||vt k，i || and ||vt k，j || respectively vt k，i With vt k，j The modulus value of Indicates TCRP k The data corresponding to the i-th row and j-th column in .

[0057] Furthermore, the method for obtaining the frequency domain composite recursive graph is as follows:

[0058] Based on the modal components {v k , k=1, 2, ..., K} construct the time-frequency matrix of the current signal, as shown in the following formula:

[0059]

[0060] in, is a column vector, VF consists of n column vectors;

[0061] The modal component v is obtained using the following formula: k Frequency domain composite recurrence graph FCRP of (t):

[0062] FCRP i，j =β||vf i -vf j ||+(1-β)Cosd(vf i , vf j )

[0063]

[0064] In the formula, ||vf i -vf j || is vf i With vfj The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vf i , vf j ) represents vf i With vf j The cosine distance between them, Cosd∈[0,2], when the Cosd value is smaller, the direction similarity of the two vectors is higher; <vf i , vf j > is vf i With vf j The inner product between ||vf i || and ||vf j || respectively vf i With vf j The modulus value of .

[0065] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) The present invention proposes a DC arc fault detection method based on a time-frequency composite recursive graph, which can mine the phase space state similarity information of the current signal in the time-frequency domain, and is helpful to improve the detection accuracy of the series arc fault; (2) In the time-frequency composite recursive graph, the present invention proposes a composite similarity analysis method to address the limitations of the single similarity analysis method based on the Euclidean distance in the traditional recursive graph; the proposed composite similarity analysis method not only measures the Euclidean distance between different states in the phase space, but also analyzes the directional similarity between different states based on the cosine distance; the time-frequency composite recursive graph realizes the fusion of the Euclidean distance and the cosine distance based on the weighting factor; (3) The time-frequency composite recursive graph of the present invention can analyze the similarity information of the dynamic frequency domain energy state, which overcomes the limitation of the traditional recursive graph that lacks the ability to analyze frequency domain fault information; the arc current is decomposed into different modes, and the time-frequency energy state matrix is ​​constructed. The time-frequency composite recursive graph calculates the composite similarity of the frequency domain energy state at different times; the time-frequency composite recursive graph innovatively realizes the extraction of frequency domain fault information based on the recursive graph theory. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0067] Figure 2 Schematic diagram of the implementation process of the method of the embodiment of the present invention;

[0068] Figure 3 Schematic diagram of arc state of the time-frequency composite recursive graph according to an embodiment of the present invention;

[0069] Figure 4 It is a t-SNE visualization diagram of the singular values ​​of an embodiment of the present invention;

[0070] Figure 5Schematic diagram of the structure of the limit tree according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in combination with the accompanying drawings and embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] As attached Figure 1 As shown, the DC arc fault detection method based on the time-frequency composite recursive graph of this embodiment includes the following steps:

[0073] Step 1): using a current sensor to collect a current signal of a DC arc;

[0074] Step 2): Decompose the current signal into K modal components {v k , k = 1, 2, ..., K};

[0075] Step 3): converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recursive graph;

[0076] Step 4): extracting singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0077] Step 5): Process the high-dimensional feature vector based on the extreme tree to obtain a detection result.

[0078] Specifically, Figure 2 As shown, step 1): arc current signal is collected at a frequency of 100 kHz based on a current sensor.

[0079] Step 2): Decompose the current into four modal components {v k , k = 1, 2, 3, 4}. The principle of variational mode decomposition is shown in the following formula.

[0080]

[0081] Where K is the number of modes obtained by decomposition. Since it is decomposed into 4 modal components, K = 4. t |t=1,2,…,n} is the arc current to be decomposed, x t is the data point in F(t), n is the number of data points; δ(t) represents the Dirac function, j is the complex number symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, v k (t) represents the modal set, {ω k} represents the center frequency, represents the partial derivative operation with time t.

[0082] Step 3): Based on the time-frequency composite recurrence diagram, the modal components {v k , k=1,2,…,4} are converted into multiple two-dimensional matrices. The obtained two-dimensional matrix includes 4 time domain composite recursion graphs and 1 frequency domain composite recursion graph. The images of the time domain composite recursion graph (TCRP) and the frequency domain composite recursion graph (FCRP) in normal state and arc fault state are as follows: Figure 3 shown.

[0083] Step 3-1): Obtaining the Time Domain Composite Recurrence Plot (TCRP). First, the modal components Converted into phase space, as shown in formula (1):

[0084]

[0085] The number of phase space states is N = n-(m-1)τ, where m is the embedding dimension and τ is the delay time. m = 4, τ = 2. The modal components are VT k is the modal component v k The corresponding phase space matrix, vt k，N VT k The Nth phase space vector of . n is the modal component v k The number of data points in (t), n = 512.

[0086] The modal component v can be obtained using formula (2): k (t) Time domain composite recurrence plot (TCRP).

[0087]

[0088]

[0089] In the formula, ||vt k，i -vt k，j || is vt k，i With vt k，j The Euclidean distance between them, β is the weight factor, β = 0.7. Cosd(vt k，i , vt k，j ) represents vt k，i With vt k，j The cosine distance between the two vectors, Cosd∈(0,2). The smaller the Cosd value, the higher the directional similarity of the two vectors. <vt k，i , vt k，j > is vt k，i With vt k，j The inner product between ||vtk，i || and ||vt k，j || respectively vt k，i With vt k，j β can control the proportion of Euclidean distance and cosine distance, thus realizing the fusion of the two similarity indicators of Euclidean distance and cosine distance in the time-domain composite recursive graph (TCRP).

[0090] Step 3-2): To obtain the frequency domain composite recurrence diagram, we first need to calculate the modal component {v k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in formula (4):

[0091]

[0092] Where VF consists of n column vectors, n = 512, K = 4. For example, the column vector

[0093] The modal component v can be obtained using formula (5): k Frequency domain composite recurrence plot (FCRP) of (t).

[0094] FCRP i，j =β||vf i -vf j ||+(1-β)Cosd(vf i , vf j ) (5)

[0095]

[0096] In the formula, ||vf i -vf j || is vf i With vf j The Euclidean distance between them, β is the weight factor, β = 0.7. Cosd(vf i , vf j ) represents vf i With vf j The cosine distance between the two vectors, Cosd∈[0,2]. The smaller the Cosd value, the higher the directional similarity of the two vectors. <vf i , vf j > is vf i With vf j The inner product between ||vf i || and ||vf j || respectively vf i With vf iβ can control the proportion of Euclidean distance and cosine distance, thus realizing the fusion of the two similarity indicators of Euclidean distance and cosine distance in the frequency domain composite recursive graph (FCRP).

[0097] Step 4): Extract the singular values ​​in the two-dimensional matrix in step 3) based on the singular value decomposition algorithm to construct a high-dimensional feature vector. The t-SNE visualization of the singular values ​​in the arc fault state and the normal state is shown in the figure below: Figure 4 As shown;

[0098] Step 5): Based on the extreme tree processing of the high-dimensional feature vector constructed in step 4), the detection result can be obtained. The structural diagram of the extreme tree is shown in Figure 5 ET is an ensemble learning algorithm that includes multiple decision trees. The training process of each decision tree in the extreme tree is mainly to split the random feature value at each node. The splitting steps are as follows: a) Randomly select m features {sv1, sv2, ..., sv m}; b) Calculate the feature sv in the dataset i The maximum value of and minimum value c) Randomly select feature sv i The split point d) Calculate the feature sv i The split point Gini index e) Select the split point with the largest Gini index as feature sv i The final split point is used to split the current node.

[0099] Each node in the tree is split according to the above process, so that all decision trees in the extreme tree can be trained. For classification problems, the output of the extreme tree is obtained based on the majority voting principle.

[0100] The above embodiments can realize accurate detection of DC series arc faults. The present invention verifies the performance of the proposed series arc fault detection method based on the collected experimental data. 31,500 samples were collected on the established experimental platform, of which 18,900 samples were used to construct a training set and 12,600 samples were used as a test set. Each sample contains 512 data points. The experimental conditions corresponding to the data set are shown in Table 1. Note that the normal sample contains transient conditions.

[0101] Table 1 Experimental conditions corresponding to experimental data

[0102]

[0103] Table 2 Detection results of the series arc fault detection method proposed in the present invention under different experimental conditions

[0104]

[0105] The detection results of the arc fault detection method proposed in the present invention under different experimental conditions are shown in Table 2. Table 2 shows the detection results of the method proposed in the present invention under different conditions. The overall detection accuracy of the method is 98.75%. Among the 12,600 samples in the test set, only 158 samples were misdetected. The detection accuracy under normal conditions is 99.18% (6427 / 6480), and the detection accuracy of the corresponding resistive load (99.53%) is higher than that of DC-DC (98.80%) and inverter (99.19%). This is because DC-DC and inverter are both nonlinear loads, and the arc-like noise introduced by their internal high-frequency switching actions increases the difficulty of detection. The detection accuracy under SAF conditions is 98.28% (6015 / 6120), which is significantly lower than the detection accuracy under normal conditions. SAF is an unstable plasma state. Compared with normal conditions, the random fluctuations of the arc current will have a stronger interference on the detection algorithm, resulting in the detection accuracy under SAF conditions being significantly lower than normal conditions. The experimental results show that the proposed method can handle false alarms under normal conditions and detect arc faults in various operating states of the system with an accuracy rate of more than 98.5%, indicating the effectiveness of the method.

[0106] This example also compares the detection accuracy of the proposed method with three comparison methods under the same experimental conditions.

[0107] Comparison method 1: Comparison method 1 is based on lifting recursive graph and singular value decomposition. Comparison method 3 extracts features based on recursive quantitative analysis (recurrence rate, certainty, entropy, average diagonal length) and constructs feature vectors with 5 largest singular values. In comparison method 1, the embedding dimension is 4 and the time delay is 2. The classifier used is a back propagation neural network with a network structure of [920 2].

[0108] Comparison method 2: Comparison method 2 is a method based on support vector machine. The arc current is decomposed into 8 modes using variational mode decomposition, and then the sample entropy and energy entropy of the first 3 modes are extracted to construct the feature vector. The feature vector is processed using support vector machine to realize arc fault detection. In the support vector machine, the penalty parameter c and the kernel parameter g are optimized using particle swarm algorithm. The relative tolerance r is set to 0.1 and the embedding dimension is set to 2.

[0109] Comparison method 3: Comparison method 3 is a method based on gradient boosting decision tree. First, the variance, normalized energy ratio and energy entropy of the current signal are extracted based on db2 wavelet, and then the energy entropy of the current signal is extracted based on empirical mode decomposition. The gradient boosting decision tree is used to fuse the extracted multiple features to obtain the detection results. The number of wavelet layers is 5, and the number of trees in the gradient boosting decision tree is 30.

[0110] Table 3 Detection results of different detection methods

[0111]

[0112] Table 3 shows the detection results of different methods. The detection accuracy of the method proposed in the present invention, comparative method 1, comparative method 2 and comparative method 3 are 98.75%, 96.42%, 94.37% and 89.69% respectively. The detection accuracy of the method proposed in the present invention is significantly higher than that of the three comparative methods, which further proves the advancement and effectiveness of the method proposed in the present invention.

[0113] Based on the same inventive concept, this embodiment also provides a DC arc fault detection system based on a time-frequency composite recursive graph, comprising:

[0114] A collection module, used for collecting the current signal of the DC arc by using a current sensor;

[0115] A decomposition module is used to decompose the current signal into K modal components {v k , k = 1, 2, ..., K};

[0116] A conversion module, used for converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recurrence graph;

[0117] A fault feature extraction module extracts singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0118] The detection module processes the high-dimensional feature vector based on the extreme tree to obtain a detection result.

[0119] Furthermore, the two-dimensional matrix of the conversion module includes K time-domain composite recursive graphs and one frequency-domain composite recursive graph.

[0120] Furthermore, the method for obtaining the time domain composite recursive graph is as follows:

[0121] The modal components are converted into the form of phase space as shown below:

[0122]

[0123] Among them, the number of phase space states is N = n-(m-1)τ, m is the embedding dimension, τ is the delay time; the modal components are VT k is the modal component v k The corresponding phase space matrix, vt k，N VT k The Nth phase space vector of is the nth data point in the kth mode; n is the modal component v k (t) The number of data points;

[0124] The modal component v is obtained using the following formula: k (t) of the time domain composite recurrence graph (TCRP k ):

[0125]

[0126]

[0127] In the formula, ||vt k，i -vt k，j || is vt k，i With vt k，j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vt k，i , vt k，j ) means vt k，i With vt k，j The cosine distance between them, Cosd∈(0,2); the smaller the Cosd value, the higher the directional similarity of the two vectors; <vt k，i , vt k，j > is vt k，i With vt k，j The inner product between ||vt k，i || and ||vt k，j || respectively vt k，i With vt k，j The modulus value of .

[0128] Furthermore, the method for obtaining the frequency domain composite recursive graph is as follows:

[0129] Based on the modal components {v k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula:

[0130]

[0131] in, is a column vector, VF consists of n column vectors;

[0132] The modal component v is obtained using the following formula: k Frequency domain composite recurrence plot (FCRP) of (t):

[0133] FCRP i，j =β||vf i -vf j ||+(1-β)Cosd(vf i , vf j)

[0134]

[0135] In the formula, ||vf i -vf j || is vf i With vf j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vf i , vf j ) represents vf i With vf j The cosine distance between them, Cosd∈[0,2], when the Cosd value is smaller, the direction similarity of the two vectors is higher; <vf i , vf j > is vf i With vf j The inner product between ||vf i || and ||vf j || respectively vf i With vf j The modulus value of .

[0136] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A DC arc fault detection method based on a time-frequency composite recursive graph, characterized in that: The following steps are involved: (1) Using a current sensor to collect the current signal of the DC arc; (2) Decompose the current signal into K modal components {v k ,k=1,2,…,K}; (3) converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recursive graph; the two-dimensional matrix includes K time-domain composite recursive graphs and one frequency-domain composite recursive graph; The method for obtaining the time domain composite recurrence graph is as follows: The modal components are converted into the form of phase space as shown below: Among them, the number of phase space states is N = n-(m-1)τ, m is the embedding dimension, τ is the delay time; the modal components are VT k is the modal component v k The corresponding phase space matrix, vt k,N VT k The Nth phase space vector of is the nth data point in the kth mode; n is the modal component v k (t) The number of data points; The modal component v is obtained using the following formula: k (t) time domain composite recurrence graph TCRP k : In the formula, ‖vt k,i -vt k,j ‖ is vt k,i With vt k,j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vt k,i ,vt k,j ) means vt k,i With vt k,j The cosine distance between them, Cosd∈(0,2); the smaller the Cosd value, the higher the directional similarity of the two vectors; <vt k,i ,vt k,j > is vt k,i With vt k,j The inner product between ‖vt k,i ‖ and ‖vt k,j ‖ are vt k,i With vt k,j The modulus value of Indicates TCRP k The data corresponding to the i-th row and j-th column in; The method for obtaining the frequency domain composite recursive graph is as follows: Based on the modal components {v k ,k=1,2,…,K} construct the time-frequency matrix of the current signal, as shown in the following formula: in, is a column vector, VF consists of n column vectors; The modal component v is obtained using the following formula: k Frequency domain composite recurrence graph FCRP of (t): FCRP i,j =β‖vf i -vf j ‖+(1-β)Cosd(vf i ,vf j ) In the formula, ‖vf i -vf j ‖ is vf i With vf j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vf i ,vf j ) indicates vf i With vf j The cosine distance between them, Cosd∈[0,2], when the Cosd value is smaller, the direction similarity of the two vectors is higher; <vf i ,vf j > is vf i With vf j The inner product between them, ‖vf i ‖ and ‖vf j ‖ are vf i With vf j The modulus value of (4) extracting singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector; (5) Processing the high-dimensional feature vector based on the extreme tree to obtain a detection result, specifically: training each decision tree in the extreme tree, splitting each node in the decision tree, completing the training of the decision tree, and then completing the training of the extreme tree, using the trained extreme tree to process the high-dimensional feature vector to obtain a detection result.

2. The DC arc fault detection method based on time-frequency composite recursive graph according to claim 1 is characterized in that: The step (2) is specifically to decompose the current signal into K modal components {v k , k=1,2,…,K}, so that different frequency components in the current signal are separated to avoid mutual interference of different frequency components in the subsequent feature extraction process. The variational mode decomposition algorithm is as follows: Where K is the number of modes obtained by decomposition, F(t)={x t |t=1,2,…,n} is the arc current to be decomposed, x t is the data point in F(t), n is the number of data points, δ(t) represents the Dirac function, j is the complex number symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, and v k (t) represents the modal set, {ω k } represents the center frequency, represents the partial derivative operation with time t.

3. The DC arc fault detection method based on time-frequency composite recursive graph according to claim 1, characterized in that: The splitting step in step (5) comprises: (51) Randomly select m features {sv1, sv2, …, sv m }; (52) Calculate the feature sv in the data set i The maximum value of and minimum value (53) Randomly select feature sv i The split point (54) Calculate feature sv i The split point Gini index (55) Select the split point with the largest Gini index as feature sv i The final split point is used to split the current node.

4. A DC arc fault detection system based on a time-frequency composite recursive graph, characterized in that: include: A collection module, used for collecting the current signal of the DC arc by using a current sensor; A decomposition module is used to decompose the current signal into K modal components {v k ,k=1,2,…,K}; A conversion module, used for converting the modal components into a plurality of two-dimensional matrices based on a time-frequency composite recursive graph; the two-dimensional matrix includes K time-domain composite recursive graphs and one frequency-domain composite recursive graph; The method for obtaining the time domain composite recurrence graph is as follows: The modal components are converted into the form of phase space as shown below: Among them, the number of phase space states is N = n-(m-1)τ, m is the embedding dimension, τ is the delay time; the modal components are VT k is the modal component v k The corresponding phase space matrix, vt k,N VT k The Nth phase space vector of is the nth data point in the kth mode; n is the modal component v k (t) The number of data points; The modal component v is obtained using the following formula: k (t) time domain composite recurrence graph TCRP k : In the formula, ‖vt k,i -vt k,j ‖ is vt k,i With vt k,j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vt k,i ,vt k,j ) means vt k,i With vt k,j The cosine distance between them, Cosd∈(0,2); the smaller the Cosd value, the higher the directional similarity of the two vectors; <vt k,i ,vt k,j > is vt k,i With vt k,j The inner product between ‖vt k,i ‖ and ‖vt k,j ‖ are vt k,i With vt k,j The modulus value of Indicates TCRP k The data corresponding to the i-th row and j-th column in; The method for obtaining the frequency domain composite recursive graph is as follows: Based on the modal components {v k ,k=1,2,…,K} construct the time-frequency matrix of the current signal, as shown in the following formula: in, is a column vector, VF consists of n column vectors; The modal component v is obtained using the following formula: k Frequency domain composite recurrence graph FCRP of (t): FCRP i,j =β‖vf i -vf j ‖+(1-β)Cosd(vf i ,vf j ) In the formula, ‖vf i -vf j ‖ is vf i With vf j The Euclidean distance between them, β is the weight factor, which is used to control the proportion of Euclidean distance and cosine distance; Cosd(vf i ,vf j ) indicates vf i With vf j The cosine distance between them, Cosd∈[0,2], when the Cosd value is smaller, the direction similarity of the two vectors is higher; <vf i ,vf j > is vf i With vf j The inner product between them, ‖vf i ‖ and ‖vf j ‖ are vf i With vf j The modulus value of A fault feature extraction module extracts singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector; The detection module processes the high-dimensional feature vector based on the extreme tree to obtain the detection result, specifically: training each decision tree in the extreme tree, splitting each node in the decision tree, completing the training of the decision tree, and then completing the training of the extreme tree, using the trained extreme tree to process the high-dimensional feature vector to obtain the detection result.

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