DC arc detection method and system based on time-frequency Markov permutation transfer matrix

Abstract

The invention discloses a DC arc detection method and system based on a time-frequency Markov permutation transfer matrix. The method comprises: using a current sensor to collect a current signal of a DC arc; using a variational mode decomposition algorithm to decompose the current signal into a plurality of mode components; based on a time-frequency Markov permutation transfer matrix, converting the mode components into a plurality of 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 kernel extreme learning mechanism, processing the high-dimensional feature vector to obtain a detection result; the time-frequency Markov permutation transfer matrix of the invention can simultaneously analyze the state transfer characteristics of the permutation mode in the time domain and the frequency domain, thereby effectively overcoming the shortcomings of the traditional Markov transfer matrix that cannot analyze frequency domain fault information and lacks information for describing data correlation in continuous time.

Description

Technical Field

[0001] The present invention relates to a direct current arc detection method and system, and in particular to a direct current arc detection method and system based on a time-frequency Markov permutation transfer matrix, and belongs 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. DC arc faults are highly concealed, and how to accurately and quickly detect arc faults in photovoltaic systems is a challenge that needs to be solved urgently.

[0003] Scholars have proposed 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 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 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 between the normal state and the 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 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 arc fault detection method based on two-dimensional matrix construction has brought positive effects to obtain high-performance detection results. However, the fluctuation pattern of arc current in photovoltaic system is complex, and the arc-like component caused by transient operation of the system brings great challenges to the detection of series arc fault. Therefore, in order to further improve the performance of arc fault detection, it is still necessary to study the method of converting one-dimensional arc current into two-dimensional matrix from different angles. Markov transfer matrix can mine the state transition information of one-dimensional signal. Compared with the above matrix transformation method, Markov transfer matrix provides a unique perspective for analyzing the intrinsic characteristics of the signal. However, Markov transfer matrix lacks the ability to comprehensively analyze the state transition characteristics of high-dimensional space and time-frequency domain. In order to accurately detect DC arc faults, it is necessary to further improve the Markov transfer matrix. Summary of the invention

[0007] Purpose of the invention: The purpose of the present invention is to provide a DC arc detection method and system based on a time-frequency Markov permutation transfer matrix that helps to improve the accuracy of arc fault detection.

[0008] Technical solution: The DC arc detection method based on the time-frequency Markov permutation transfer matrix of the present invention comprises the following steps:

[0009] (1) Using a current sensor to collect the current signal of the DC arc;

[0010] (2) Decompose the current signal into K modal components {u k , k = 1, 2, ..., K};

[0011] (3) converting the modal components into a plurality of two-dimensional matrices based on a time-frequency Markov permutation transfer matrix;

[0012] (4) extracting singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0013] (5) Processing the high-dimensional feature vector based on a kernel extreme learning machine to obtain a detection result.

[0014] Furthermore, the step (2) is specifically to decompose the current signal into K modal components {u 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:

[0015]

[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 symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, and u k (y) 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 Markov permutation transfer matrices and one frequency-domain Markov permutation transfer matrix.

[0019] Furthermore, the calculation method of the time domain Markov permutation transfer matrix is ​​as follows:

[0020] The modal components {u k , k = 1, 2, ..., K} is converted into a high-dimensional space as shown in the following formula:

[0021] UT k，i = {u k，i ,u k，i+1 ,…,u k，i+(m-1)}

[0022] Among them, 1≤i≤n-(m-1), m is the embedding dimension, UT k，i is the i-th vector in the high-dimensional space; u k，i+1 is the modal component uk The corresponding i+1th data point;

[0023] About UT k，i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0024]

[0025] Among them, v1, v2, …, v m Indicates UT k，i The corresponding flag bit of the data point in the

[0026] Vector UT k contains m data points and has m! permuted mode states; each Corresponding to a unique arrangement mode state πt g ,g={1,2,…,m!};get mode u k The corresponding time domain Markov permutation transfer matrix TMPTM k ,k∈{1,2,…,K}; as shown in the following formula:

[0027]

[0028] in, Num 1，2 Indicates UT k，i At the same time, it has the arrangement mode state πt1 and The number of cases with the arrangement mode state πt2 at the same time; Num represents the matrix The number of row vectors in .

[0029] Furthermore, the calculation method of the frequency domain Markov permutation transfer matrix is ​​as follows:

[0030] Based on the modal components {u k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula:

[0031]

[0032] Among them, uf i =[u 1，i ;u 2，i ;u 3，i ;…;u K，i ] is a column vector containing components of different frequency bands, u K，n is the nth data point corresponding to the Kth modal component;

[0033] For uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0034]

[0035] Among them, h1,h2,…,h K represents uf i The corresponding flag bit of the data point in the

[0036] Vector uf i contains K data points and has K! permuted mode states; each uf i Corresponding to a unique permutation mode state πf g ,g={1,2,…,K!};The calculation method of the frequency domain Markov permutation transfer matrix FMPTM corresponding to the current signal is shown in the following formula:

[0037]

[0038] in, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the arrangement pattern state πf2 at the same time; Num represents the number of row vectors in the matrix UF.

[0039] Furthermore, the step (5) is specifically as follows: training the kernel extreme learning machine, assuming that the training data set containing Q feature vectors is {FV 1 , FV 2 , …, FV Q}, the sample to be tested is FV * ; The output of the kernel extreme learning machine with kernel function K(·) is as follows:

[0040]

[0041]

[0042] Where τ is the regularization parameter, which is significantly related to the stability of the kernel extreme learning machine output; β * =(HH T +τI) -1 T is the output matrix; radial basis function is used as the kernel function, The parameter δ is used to control the sensing range of K(·). The grid search method is used to search for the optimal values ​​of the parameters τ and δ. The search range and search step are set. By calculating β * =(HH T +τI) -1 T, get the output matrix β * , complete the training of the kernel extreme learning machine, use the trained kernel extreme learning machine to process the high-dimensional feature vector, and obtain the detection result.

[0043] Based on the same inventive concept, the present invention also provides a DC arc fault detection system based on a time-frequency Markov permutation transfer matrix, comprising:

[0044] A collection module, used for collecting the current signal of the DC arc by using a current sensor;

[0045] A decomposition module is used to decompose the current signal into K modal components {u k , k = 1, 2, ..., K};

[0046] A conversion module, used for converting the modal components into a plurality of two-dimensional matrices based on a time-frequency Markov permutation transfer matrix;

[0047] 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;

[0048] The detection module processes the high-dimensional feature vector based on a kernel extreme learning machine to obtain a detection result.

[0049] Furthermore, the two-dimensional matrix of the conversion module includes K time-domain Markov permutation transfer matrices and one frequency-domain Markov permutation transfer matrix.

[0050] Furthermore, the calculation method of the time domain Markov permutation transfer matrix is ​​as follows:

[0051] The modal components {u k , k = 1, 2, ..., K} is converted into a high-dimensional space as shown in the following formula:

[0052] UT k，i = {u k，i ,u k，i+1 ,…,u k，i+(m-1 )}

[0053] Among them, 1≤i≤n-(m-1), m is the embedding dimension, UT k，i is the i-th vector in the high-dimensional space; u k，i+1 is the modal component u k The corresponding i+1th data point;

[0054] About UT k，i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0055]

[0056] Among them, v1, v2, …, v m Indicates UT k，i The corresponding flag bit of the data point in the

[0057] Vector UT k contains m data points and has m! permuted mode states; each Corresponding to a unique arrangement mode state πt g ,g={1,2,…,m!};get mode u k The corresponding time domain Markov permutation transfer matrix TMPTM k ,k∈{1,2,…,K}; as shown in the following formula:

[0058]

[0059] in, Num 1，2 Indicates UT k，i It also has the arrangement mode states πt1 and UT k，i-1 The number of cases with the arrangement mode state πt2 at the same time; Num represents the matrix The number of row vectors in .

[0060] Furthermore, the method for obtaining the frequency domain Markov permutation transfer matrix is ​​as follows:

[0061] Based on the modal components {u k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula:

[0062]

[0063] Among them, u fi =[u 1，i ;u 2，i ;u 3，i ;...;u K，i ] is a column vector containing components of different frequency bands, u K，n is the nth data point corresponding to the Kth modal component;

[0064] For uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0065]

[0066] Among them, h1,h2,…,h K represents uf i The corresponding flag bit of the data point in the

[0067] Vector uf i contains K data points and has K! permuted mode states; each uf i Corresponding to a unique arrangement mode state uf g,g={1,2,…,K!};The calculation method of the frequency domain Markov permutation transfer matrix FMPTM corresponding to the current signal is shown in the following formula:

[0068]

[0069] in, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the arrangement pattern state πf2 at the same time; Num represents the number of row vectors in the matrix UF.

[0070] 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 Markov permutation transfer matrix, which can mine the permutation mode state transition information of the current signal in the time-frequency domain, and is helpful to improve the accuracy of DC arc fault detection; (2) The present invention proposes a mechanism for analyzing the state transition characteristics in the time-frequency domain in the time-frequency Markov permutation transfer matrix. The time-frequency Markov permutation transfer matrix can overcome the shortcomings of the Markov transfer matrix that only analyzes the state transition characteristics from the time domain and ignores the key dynamic fault information hidden in the frequency domain; (3) The present invention proposes a method for permutation mode state transfer information in the time-frequency Markov permutation transfer matrix, which can simultaneously analyze the permutation mode state transition characteristics in the time domain and the frequency domain. When using the time-frequency Markov permutation transfer matrix to calculate the transition probability of the permutation mode state, the correlation between multiple continuous data points can be fully considered, thereby overcoming the limitation that the Markov transfer matrix only considers the state transition characteristics of a single data point. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0072] Figure 2 Schematic diagram of the implementation process of the method of the embodiment of the present invention;

[0073] Figure 3 A schematic diagram of arc states of a time-frequency Markov permutation transfer matrix according to an embodiment of the present invention;

[0074] Figure 4 It is a t-SNE visualization diagram of the singular values ​​of an embodiment of the present invention;

[0075] Figure 5 Schematic diagram of the structure of the kernel extreme learning machine according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] 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.

[0077] As attached Figure 1 As shown, the DC arc detection method based on the time-frequency Markov permutation transfer matrix of this embodiment includes the following steps:

[0078] Step 1): using a current sensor to collect a current signal of a DC arc;

[0079] Step 2): Decompose the current signal into K modal components {u k , k = 1, 2, ..., K};

[0080] Step 3): converting the modal components into a plurality of two-dimensional matrices based on a time-frequency Markov permutation transfer matrix;

[0081] Step 4): extracting singular values ​​in the two-dimensional matrix based on a singular value decomposition algorithm to construct a high-dimensional feature vector;

[0082] Step 5): Process the high-dimensional feature vector based on the kernel extreme learning machine to obtain a detection result.

[0083] Specifically, Figure 2 As shown, step 1): arc current signal is collected at a frequency of 100 kHz based on a current sensor.

[0084] Step 2): Decompose the current into four modal components {u k , k = 1, 2, 3, 4}. The principle of variational mode decomposition is shown in the following formula.

[0085]

[0086]

[0087] 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 x to be decomposed 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 symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, u k (t) represents the modal set, {ω k} represents the center frequency, represents the partial derivative operation with time t.

[0088] Step 3): Based on the time-frequency Markov permutation transfer matrix, the modal components {u k , k=1,2,...,4} are converted into multiple two-dimensional matrices. The obtained two-dimensional matrices include 4 time-domain Markov permutation transfer matrices and 1 frequency-domain Markov permutation transfer matrix. The images of the time-domain Markov permutation transfer matrix (TMPTM) and the frequency-domain Markov permutation transfer matrix (FMPTM) in normal state and arc fault state are shown as follows: Figure 3 shown.

[0089] Step 3-1): To obtain the time-domain Markov permutation transfer matrix, we first need to transform the modal components {u k , k = 1, 2, ..., 4} is converted into a high-dimensional space as shown in the following formula:

[0090] UT k，i = {u k，i ,ku k，i+1 ,…,u k，i+(m-1)}

[0091] Where 1≤i≤n-(m-1), m is the embedding dimension, and m=4; UT k，i is the i-th vector in the high-dimensional space; u k，i+1 is the modal component u k The corresponding i+1th data point;

[0092] Then for UT k，i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0093]

[0094] Among them, v1, v2, …, v m Indicates UT k， The corresponding flag bit of the data point in i. For example, v1=2 means U k，i The second data point (u k，i+1 ) has the smallest value.

[0095] A vector UT containing 4 data points k There are 4! = 24 permutation mode states. Each Corresponding to a unique arrangement mode state πt g ,g={1,2,…,m!}。 The modal u can be obtained k The corresponding time-domain Markov permutation transfer matrix (TMPTM k ),k∈{1, 2,...,K}. TMPTM kThe calculation method is as follows:

[0096]

[0097] For example, Num 1，2 Indicates UT k， i has both the permutation mode states πt1 and UT k，i-1 The number of cases with the arrangement mode state πt2 at the same time. Nun represents the matrix The number of row vectors in .

[0098] Step 3-2): To obtain the frequency domain Markov permutation transfer matrix, we first need to calculate the modal components {u k , k = 1, 2, ..., 4} construct the time-frequency matrix of the current signal, as shown in the following formula:

[0099]

[0100] Among them, uf i =[u 1，i ;u 2，i ;u 3，i ;…;u K，i ] is a column vector containing components of different frequency bands, i∈{1, 2, …, n}. n is the number of current signal data points, n=1024.

[0101] Then for uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0102]

[0103] Among them, h1, h2, ..., h4 represent uf i The corresponding flag bit of the data point in the i The second data point (u 2，i ) has the smallest value.

[0104] A vector uf containing K data points i There are 4! = 24 permutation mode states. Each uf i Corresponding to a unique permutation mode state πf g ,g={1,2,…,4!}。 The calculation method of the frequency domain Markov permutation transfer matrix (FMPTM) corresponding to the current signal is shown in the following formula:

[0105]

[0106] For example, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the permutation pattern state πf2 at the same time. Num represents the number of row vectors in the matrix UF.

[0107] 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 FV. 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;

[0108] Step 5): Based on the kernel extreme learning machine, the high-dimensional feature vector FV constructed in step 4) is processed to obtain a detection result.

[0109] The structural diagram of the kernel extreme learning machine is as follows Figure 5 As shown. Assume that the training data set containing Q feature vectors is {FV 1 ,FV 2 ,…,FV Q}, the sample to be tested is FV * The output of KELM with kernel function K(·) is as follows:

[0110]

[0111] Where τ is the regularization parameter, which is significantly related to the stability of KELM output. * =(HH T +τI) -1 T is the output matrix. This paper uses radial basis function as the kernel function. The parameter δ can control the sensing range of K(·). The grid search method is used to search for the optimal values ​​of parameters τ and δ. The search ranges of parameters τ and δ are [0, 50] and [0, 20000] respectively, and the search step is one percent of the search space.

[0112] The above embodiments can realize accurate detection of DC arc faults. The present invention verifies the performance of the proposed DC 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 1,024 data points. The experimental conditions corresponding to the data set are shown in Table 1. Note that the normal sample contains transient conditions.

[0113] Table 1 Experimental conditions corresponding to experimental data

[0114]

[0115] The detection results of the arc fault detection method proposed in the present invention under different experimental conditions are shown in Table 2. The overall detection accuracy is 98.97% (12471 / 12600). The detection accuracy under normal and arc fault conditions is 99.24% (6431 / 6480) and 98.69% (6040 / 6120), respectively. This method can not only accurately realize DC arc fault detection, but also effectively suppress false alarms under normal conditions. Since series arc faults can cause complex random fluctuations in the current signal, the detection accuracy under normal conditions is higher than the detection accuracy under DC arc fault conditions, thereby increasing the difficulty of detection. Under normal circumstances, the detection accuracy corresponding to the resistive load (99.93%) is higher than the detection accuracy corresponding to the inverter (99.11%) and the detection accuracy corresponding to the DC-DC (98.86%). This is because the resistor is a linear load, and the inverter and DC-DC are nonlinear loads. The high-frequency switching operation of the nonlinear load will introduce complex noise into the current signal.

[0116] Table 2 Detection results of the DC arc fault detection method proposed in the present invention under different experimental conditions

[0117]

[0118] The present invention also compares the detection accuracy of the proposed method with three comparison methods under the same experimental conditions.

[0119] Comparison method 1: Comparison method 1 uses the traditional Markov transfer matrix and singular value decomposition to extract features, and uses the kernel extreme learning machine as a classifier. First, the Markov transfer matrix of the current signal is constructed, and then the singular values ​​of the Markov transfer matrix are extracted to construct the feature vector. Comparison method 1 can be used to verify whether the performance of the proposed time-frequency Markov permutation transfer matrix is ​​better than that of the traditional Markov transfer matrix.

[0120] Comparison method 2: Comparison method 2 is a method based on recurrence graph. First, a recurrence graph of arc current is constructed. Then, feature extraction is performed on the recurrence graph to obtain the recurrence rate, certainty, entropy and average diagonal length to construct the feature vector. In the recurrence graph, the embedding dimension is 4, the time delay is 2, and the criterion threshold is 0.6021.

[0121] Comparative Method 3: Comparative Method 3 is based on lifting recursive graph and singular value decomposition. Comparative 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 Comparative Method 3, the embedding dimension is 4 and the time delay is 2.

[0122] 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 98.97%, 92.85%, 94.51% and 97.93% 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.

[0123] Table 3 Detection results of different detection methods

[0124]

[0125] Based on the same inventive concept, this embodiment also provides a DC arc fault detection system based on a time-frequency Markov permutation transfer matrix, including:

[0126] A collection module, used for collecting the current signal of the DC arc by using a current sensor;

[0127] A decomposition module is used to decompose the current signal into K modal components {u k , k = 1, 2, ..., K};

[0128] A conversion module, used for converting the modal components into a plurality of two-dimensional matrices based on a time-frequency Markov permutation transfer matrix;

[0129] 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;

[0130] The detection module processes the high-dimensional feature vector based on the kernel limit learning mechanism to obtain a detection result.

[0131] Furthermore, the two-dimensional matrix of the conversion module includes K time-domain Markov permutation transfer matrices and one frequency-domain Markov permutation transfer matrix.

[0132] Furthermore, the calculation method of the time domain Markov permutation transfer matrix is ​​as follows:

[0133] The modal components {u k ,k=1,2,…,K} is converted into a high-dimensional space as shown in the following formula:

[0134] UT k,i = {u k,i ,u k,i+1 ,…,u k,i+(m-1)}

[0135] Where 1≤i≤n-(m-1), m is the embedding dimension; UT k,i is the i-th vector in the high-dimensional space; u k,i+1 is the modal component uk The corresponding i+1th data point;

[0136] About UT k,i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0137]

[0138] Among them, v1, v2, …, v m Indicates UT k，i The corresponding flag bit of the data point in the k，i The second data point (u k，i+1 ) has the smallest value.

[0139] Vector UT k contains m data points and has m! permuted mode states; each Corresponding to a unique arrangement mode state πt g ,g={1,2,...,m!};get mode u k The corresponding time domain Markov permutation transfer matrix TMPTM k ,k∈{1,2,…,K}; as shown in the following formula:

[0140]

[0141] in, Num 1，2 Indicates UT k，i It also has the arrangement mode states πt1 and UT k，i-1 The number of cases with the arrangement mode state πt2 at the same time; Num represents the matrix The number of row vectors in .

[0142] Furthermore, the method for obtaining the frequency domain Markov permutation transfer matrix is ​​as follows:

[0143] Based on the modal components {u k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula:

[0144]

[0145] Among them, uf i =[u 1，i ;u 2，i ;u 3，i ;…;u K，i ] is a column vector containing components of different frequency bands;

[0146] For uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula:

[0147]

[0148] Among them, h1,h2,…,h K represents uf i The corresponding flag bit of the data point in the

[0149] Vector uf i contains K data points and has K! permuted mode states; each uf i Corresponding to a unique permutation mode state πf g ,g={1,2,…,K!};The calculation method of the frequency domain Markov permutation transfer matrix FMPTM corresponding to the current signal is shown in the following formula:

[0150]

[0151] in, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the arrangement pattern state πf2 at the same time; Num represents the number of row vectors in the matrix UF.

[0152] 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 detection method based on a time-frequency Markov permutation transfer matrix, 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 {u k , k = 1, 2, ..., K}; (3) converting the modal components into a plurality of two-dimensional matrices based on a time-frequency Markov permutation transfer matrix; the two-dimensional matrix includes K time-domain Markov permutation transfer matrices and one frequency-domain Markov permutation transfer matrix; The calculation method of the time domain Markov permutation transfer matrix is ​​as follows: The modal components {u k , k = 1, 2, ..., K} is converted into a high-dimensional space as shown in the following formula: UT k，i ={u k，i ,u k，i+1 ,…,u k，i+(m-1) } Among them, 1≤i≤n-(m-1), m is the embedding dimension, UT k，i is the i-th vector in the high-dimensional space; u k，i+1 is the modal component u k The corresponding i+1th data point; About UT k，i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula: Among them, v1, v2, …, v m Indicates UT k，i The corresponding flag bit of the data point in the Vector UT k，i contains m data points and has m! permuted mode states; each Corresponding to a unique arrangement mode state πt g , g = {1, 2, ..., m! ); get the mode u k The corresponding time domain Markov permutation transfer matrix TMPTM k , k∈{1, 2, …, K}; as shown in the following formula: in, Num 1，2 Indicates UT k，i It also has the arrangement mode states πt1 and UT k，i-1 The number of cases with the arrangement mode state πt2 at the same time; Num represents the matrix The number of row vectors in The calculation method of the frequency domain Markov permutation transfer matrix is ​​as follows: Based on the modal components {u k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula: Among them, uf i =[u 1，i ;u 2，i ;u 3，i ;…;u K，i ] is a column vector containing components of different frequency bands, u K，n is the nth data point corresponding to the Kth modal component; For uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula: Among them, h1, h2, …, h K represents uf i The corresponding flag bit of the data point in the Vector uf i contains K data points and has K! permuted mode states; each uf i Corresponding to a unique permutation mode state πf g , g = {1, 2, ..., K!}; The calculation method of the frequency domain Markov permutation transfer matrix FMPTM corresponding to the current signal is shown in the following formula: in, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the permutation pattern state πf2 at the same time; Num represents the number of row vectors in the matrix UF; (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 a kernel extreme learning machine to obtain a detection result.

2. The DC arc fault detection method based on time-frequency Markov permutation transfer matrix according to claim 1 is characterized in that: The step (2) is specifically to decompose the current signal into K modal components {u 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 symbol, β is the penalty factor, λ(t) is the Lagrange multiplier, * represents the convolution operation, and u 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 Markov permutation transfer matrix according to claim 1 is characterized in that: The step (5) is specifically as follows: training the kernel extreme learning machine, assuming that the training data set containing Q feature vectors is {FV 1 , FV 2 , …, FV Q }, the sample to be tested is FV * ; The output of the kernel extreme learning machine with kernel function K(·) is as follows: Where τ is the regularization parameter, which is significantly related to the stability of the kernel extreme learning machine output; β * =(HH T +τI) -1 T is the output matrix; radial basis function is used as the kernel function, The parameter δ is used to control the sensing range of K(·). The grid search method is used to search for the optimal values ​​of the parameters τ and δ. The search range and search step are set. By calculating β * =(HH T +τI) -1 T, get the output matrix β * , complete the training of the kernel extreme learning machine, use the trained kernel extreme learning machine to process the high-dimensional feature vector, and obtain the detection result.

4. A DC arc fault detection system based on time-frequency Markov permutation transfer matrix, 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 {u 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 Markov permutation transfer matrix; the two-dimensional matrix includes K time-domain Markov permutation transfer matrices and one frequency-domain Markov permutation transfer matrix; The calculation method of the time domain Markov permutation transfer matrix is ​​as follows: The modal components {u k , k = 1, 2, ..., K} is converted into a high-dimensional space as shown in the following formula: UT k，i ={u k，i ,u k，i+1 ,…,u k，i+(m-1) } Among them, 1≤i≤n-(m-1), m is the embedding dimension, UT k，i is the i-th vector in the high-dimensional space; u k，i+1 is the modal component u k The corresponding i+1th data point; About UT k，i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula: Among them, v1, v2, …, v m Indicates UT k，i The corresponding flag bit of the data point in the Vector UT k，i contains m data points and has m! permuted mode states; each Corresponding to a unique arrangement mode state πt g , g = {1, 2, ..., m! ); get the mode u k The corresponding time domain Markov permutation transfer matrix TMPTM k , k∈{1, 2, …, K}; as shown in the following formula: in, Num 1，2 Indicates UT k，i It also has the arrangement mode states πt1 and UT k，i-1 The number of cases with the arrangement mode state πt2 at the same time; Num represents the matrix The number of row vectors in The method for obtaining the frequency domain Markov permutation transfer matrix is ​​as follows: Based on the modal components {u k , k = 1, 2, ..., K} to construct the time-frequency matrix of the current signal, as shown in the following formula: Among them, uf i =[u 1，i ;u 2，i ;u 3，i ;...;u K，i ] is a column vector containing components of different frequency bands, u K，n is the nth data point corresponding to the Kth modal component; For uf i The data points are sorted in ascending order to obtain the corresponding sorting vector, as shown in the following formula: Among them, h1, h2, …, h K represents uf i The corresponding flag bit of the data point in the Vector uf i contains K data points and has K! permuted mode states; each uf i Corresponding to a unique permutation mode state πf g , g = {1, 2, ..., N!}; The calculation method of the frequency domain Markov permutation transfer matrix FMPTM corresponding to the current signal is shown as follows: in, Num 1，2 express At the same time, it has the permutation mode state πf1 and The number of cases with the permutation pattern state πf2 at the same time; Num represents the number of row vectors in the matrix UF; 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 a kernel extreme learning machine to obtain a detection result.

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