Direct-current distribution network high-resistance fault identification method based on VMD and convolutional neural network

Abstract

The application relates to a direct-current distribution network high-resistance fault identification method based on VMD and a convolutional neural network, input signals are decomposed into multiple intrinsic mode components (IMFs) through variational mode decomposition (VMD), each IMF contains specific frequency range and amplitude information, the convolutional neural network can better combine the time-frequency characteristics provided by VMD and the convolution operation of the CNN, more abundant and meaningful features are extracted, and the accuracy and robustness of fault identification are improved, the inception module in the convolutional network is used to solve the problems of too many neural network parameters, large calculation amount and overfitting, the generalization ability of the model is improved, and good performance can be maintained when facing new data.

Description

Technical Field

[0001] This invention relates to the field of power system fault detection, specifically to a method for identifying high-resistivity faults in DC distribution networks based on VMD and convolutional neural networks. Background Technology

[0002] With the surge in power grid data volume and the significant improvement in computing power, artificial neural network intelligent algorithms have demonstrated great superiority. As the network depth increases, the data dimensionality reduction and processing capabilities are further enhanced, enabling the accurate and effective automatic extraction of information useful for fault identification from the complex external and internal environments.

[0003] For example, CN111598166A, "A Method and System for Classifying Single-Phase Ground Faults Based on Principal Component Analysis and Softmax Function," discloses a method and system for classifying single-phase ground faults based on principal component analysis and Softmax function. This method first obtains the fault components of the three-phase voltage, three-phase current, zero-sequence voltage, and zero-sequence current of the busbar one to two weeks after the fault occurs. Then, it performs singular value decomposition on the data matrix composed of the fault components, calculates the covariance matrix, performs principal component decomposition, extracts fault feature values ​​and normalized feature vectors, reduces the dimension of the fault feature vector matrix, and obtains the output matrix. The output matrix is ​​input into a softmax classifier to train the fault feature quantity training samples. The probability value is estimated to achieve fault type identification. Based on the method proposed in this invention, this invention also proposes a classification system. This invention is based on actual distribution network fault recording data and realizes the classification of single-phase ground faults by classifying faulty equipment, establishing a more accurate and faster data classification model. However, the classifier model has a large number of parameters, high computational cost, and is prone to overfitting as the network depth and width increase.

[0004] Therefore, improving the accuracy of fault identification while addressing the problem of overfitting in network models has become a popular research direction for fault identification in distribution networks. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for identifying high-resistivity faults in DC distribution networks based on VMD and convolutional neural networks, the specific steps of which include:

[0006] The positive transient voltage time-domain waveform signal at the fault point of the DC distribution network system is acquired, and the positive transient voltage time-domain waveform signal is preprocessed to obtain the preprocessed signal;

[0007] The preprocessed signal is decomposed using VMD to obtain the intrinsic mode components (IMFs).

[0008] A convolutional neural network classifier is constructed, and the classifier is trained using the IMF to obtain a trained convolutional neural network classifier. The trained convolutional neural network classifier is then used to identify and classify faults in the data to be identified.

[0009] Preferably, preprocessing the positive transient voltage time-domain waveform signal to obtain the preprocessed signal specifically involves filtering and denoising the positive transient voltage time-domain waveform signal to obtain the preprocessed signal, wherein the filtering is expressed by the formula:

[0010] V filtered (t)=H filter (V(t));

[0011] In the formula, V(t) is the time-domain waveform signal of the positive transient voltage, and H filter () represents the transfer function of the filter, V filtered (t) represents the filtered waveform;

[0012] Denoising is performed using a wavelet denoising algorithm, expressed by the following formula:

[0013] W = wavelet transform (V filtered (t));

[0014] In the formula, V filtered (t) represents the filtered waveform, wavelet transform () represents the wavelet transform function, and W represents the wavelet coefficients;

[0015] T = threshold estimate (W);

[0016] In the formula, threshold estimate () is a function that estimates the threshold based on the statistical properties of wavelet coefficients, where T represents the threshold.

[0017] W denoised =threshold process (W,T);

[0018] In the formula, threshold process () is a function that processes wavelet coefficients based on a threshold, W denoised These are the processed wavelet coefficients;

[0019] V denoised (t) = inverse_wavelet transform (W_denoised);

[0020] In the formula, inverse_wavelet transform() is the inverse wavelet transform function, V denoised (t) represents the denoised waveform signal, i.e., the preprocessed signal.

[0021] Preferably, the preprocessed signal is decomposed using VMD to obtain the IMF, expressed by the formula:

[0022] V denoised (t)=∑[u k [(t)+r(t)];

[0023] In the formula, u k r(t) represents the k-th IMF, and r(t) represents the remaining terms.

[0024] The VMD decomposition constraints are expressed by the following formula:

[0025]

[0026] In the formula, {u k} represents the k IMF sets obtained from the decomposition, {ω k Let} be the set of frequency centers corresponding to each IMF, j be the imaginary part of the complex number, and δ(t) be the Dirac distribution. The partial derivative of variable t;

[0027] By introducing a quadratic penalty term α and the Lagrange multiplier λ(t), the constrained problem is transformed into an unconstrained problem. The k IMFs are obtained by calculating the unconstrained problem using the alternating direction multiplier method. The unconstrained problem is expressed by the formula:

[0028]

[0029] Preferably, the step of performing VMD decomposition on the preprocessed signal to obtain IMF further includes optimizing the parameters k and α in the VMD decomposition process using the fruit fly optimization algorithm.

[0030] Preferably, the constructed convolutional neural network classifier includes convolutional layers, pooling layers, an Inception module, a Dropout layer, and a fully connected layer. Using IMF as input data, convolutional kernels are used to perform local perception on the IMF data to extract time-series features. Pooling operations are then used to downsample and compress these time-series features. The Inception module captures combined features of the IMF, and convolutional and pooling layers connected to the Inception module extract higher-level time-series features from these combined features. The Dropout layer reduces the risk of overfitting, converting the feature maps from the Dropout layer into one-dimensional vectors, and a fully connected layer is used for fault identification.

[0031] Preferably, the Inception module includes three parallel 1x1 convolutional kernels, two of which are connected to a 3x3 convolutional kernel and a 5x5 convolutional kernel, respectively, for extracting features at different scales. The Inception module also includes a 3x3 max pooling layer, the output of which is fed to a new 1x1 convolutional kernel for downsampling, filtering, and combining the extracted features at different scales to obtain output features.

[0032] Preferably, the convolutional neural network classifier introduces non-linear property functions, i.e., activation functions, in the convolutional and fully connected layers, as expressed by the formula:

[0033] f(x) = max(0,x);

[0034] The pooling layer employs max pooling, and its mathematical model expression is as follows:

[0035]

[0036] In the formula, down() is the pooling sampling function; β is the network multiplicative bias;

[0037] The mathematical model of the convolutional neural network is expressed by the following formula:

[0038]

[0039] In the formula, It is the output of the j-th neuron in the l-th layer; It is the input of the i-th neuron in the (l-1)-th layer; M j is the input feature map; l is the l-th layer of the network; ω is the weight matrix; It is the bias of the j-th neuron network in the l-th layer;

[0040] The loss function of the convolutional neural network classifier is the cross-entropy function, expressed by the formula:

[0041]

[0042] In the formula, n is the total number of input data samples, t is the predicted value, and y is the actual value.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] 1. This invention provides a method for identifying high-impedance faults in DC distribution networks based on VMD and convolutional neural networks. By using VMD decomposition technology, the fault signal can be decomposed into multiple modal components, each of which contains specific frequency range and amplitude information. This allows the convolutional neural network to better combine the time-frequency characteristics provided by VMD and the convolution operation of CNN to extract richer and more meaningful features, thereby improving the accuracy and robustness of fault identification.

[0045] 2. This invention provides a method for identifying high-resistivity faults in DC distribution networks based on VMD and convolutional neural networks. By using the Inception module, the number of parameters and computational complexity of the neural network are reduced. The Inception module can effectively reduce the number of parameters in the network and improve computational efficiency through the combination of multiple convolutional kernels and feature splicing. It can also capture features at multiple scales and levels at the same time, reducing computational complexity while maintaining high performance.

[0046] 3. This invention provides a high-resistivity fault identification method for DC distribution networks based on VMD and convolutional neural networks. By using VMD decomposition and the Inception module in the overall architecture, it provides richer and more diverse feature representations, reduces the model's sensitivity to some noise or redundant features, thereby effectively reducing overfitting, improving the generalization ability of the overall model of the convolutional neural network classifier, and maintaining good performance when facing new data. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0048] Figure 2 This is a structural diagram of a 10kV flexible DC distribution network in an embodiment of the present invention;

[0049] Figure 3 This is a model structure diagram of the convolutional neural network classifier in an embodiment of the present invention;

[0050] Figure 4 This is a model diagram of the Inception module in this embodiment of the invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] Example 1

[0053] Embodiment 1 of this invention discloses a high-impedance fault identification method for DC distribution networks based on VMD and convolutional neural networks. In this embodiment, a PSCAD / EMTDC simulation platform is used to build such a method. Figure 4 The ±10kV DC distribution network structure shown has an AC side voltage of 10kV. The AC side transformer adopts a Δ / Yn type grounding method with a large resistance. The system frequency is 50Hz, the bridge arm reactance is 10mH, the submodule capacitor is 4500uF, and the number of submodules is 50. The cable is connected to the AC grid through a multilevel converter (MMC). This system is a low-current grounding system. When a single-pole ground fault occurs in the DC line, the fault current has no return path to ground. The DC line current remains at its rated value, the system zero potential shifts, the voltage of the grounded electrode line drops to 0, the voltage of the ungrounded electrode line rises to twice its original value, and the inter-electrode voltage remains unchanged. The system can still operate for two hours after a single-pole ground fault occurs.

[0054] Compared to single-pole grounding faults, inter-pole short-circuit faults in DC distribution networks are more severe. These faults cause a sharp rise in current, a rapid drop in the voltage between the grounding electrode and its positive and negative poles to zero, and a drop in the inter-pole voltage to zero. If the fault cannot be cleared in time after the converter is locked out, the system will remain in this state, compromising the safety of the distribution network equipment. In AC-side asymmetrical faults, the zero-sequence voltage component causes power frequency common-mode fluctuations in the DC-side positive and negative pole voltages, with transient characteristics similar to those of DC high-resistance grounding faults. Therefore, timely fault identification and maintenance of DC distribution networks are essential. This application provides a method for identifying high-resistance faults in DC distribution networks based on VMD and convolutional neural networks, with specific steps including:

[0055] S1. Acquire the positive transient voltage time-domain waveform signal of the fault point in the DC distribution network system, and preprocess the positive transient voltage time-domain waveform signal to obtain the preprocessed signal;

[0056] The time-domain waveform signal of the positive transient voltage at the fault point was collected during fault testing of the constructed 10kV flexible DC distribution network structure. The positive transient voltage time-domain waveform signal was then preprocessed to obtain the preprocessed signal, where:

[0057] S11, Signal Preprocessing

[0058] The preprocessing of the positive electrode transient voltage time-domain waveform signal to obtain the preprocessed signal specifically involves filtering and denoising the positive electrode transient voltage time-domain waveform signal. The filtering is expressed by the following formula:

[0059] V filtered (t)=H filter (V(t));

[0060] In the formula, V(t) is the time-domain waveform signal of the positive transient voltage, and Hfilter () represents the transfer function of the filter, V filtered (t) represents the filtered waveform;

[0061] Denoising is performed using a wavelet denoising algorithm, expressed by the following formula:

[0062] W = wavelet transform (V filtered (t));

[0063] In the formula, V filtered (t) represents the filtered waveform, wavelet transform () represents the wavelet transform function, and W represents the wavelet coefficients;

[0064] T = threshold estimate (W);

[0065] In the formula, threshold estimate () is a function that estimates the threshold based on the statistical properties of wavelet coefficients, where T represents the threshold.

[0066] W denoised =threshold process (W,T);

[0067] In the formula, threshold process () is a function that processes wavelet coefficients based on a threshold, W denoised These are the processed wavelet coefficients;

[0068] V denoised (t) = inverse_wavelet transform (W_denoised);

[0069] In the formula, inverse_wavelet transform () is the inverse wavelet transform function, V denoised (t) represents the denoised waveform signal, i.e., the preprocessed signal;

[0070] It is worth noting that this embodiment uses denoising and filtering for signal preprocessing, but this does not limit the signal preprocessing of this invention to denoising and filtering. Detrending, resampling, and normalization are also signal preprocessing methods. Specifically, the following signal preprocessing can be performed according to specific needs:

[0071] Detrending: By using methods such as linear fitting and polynomial fitting, the trend component of the positive transient voltage time-domain waveform signal is removed to eliminate the influence of long-term changes, and the trend function of the positive transient voltage time-domain waveform signal is obtained, which is then subtracted from the original data;

[0072] Resampling: The time-domain waveform signal of the positive transient voltage is resampled according to actual needs to adjust the sampling rate or time resolution. Common resampling methods include linear interpolation, nearest neighbor interpolation, spline interpolation, etc.

[0073] Normalization: Normalize the time-domain waveform signal of the positive transient voltage so that its value falls within a specific range, which facilitates subsequent processing. Common normalization methods include maximum and minimum value normalization and Z-score normalization.

[0074] S2. Perform VMD decomposition on the preprocessed signal to obtain the intrinsic mode components (IMFs);

[0075] VMD is a time-frequency analysis algorithm that redefines a signal with adjustable amplitude and frequency, decomposes the original signal into a series of Intrinsic Mode Functions (IMFs), constructs and solves a variational problem, extracts useful components in the frequency domain, overcomes mode aliasing and endpoint effects, has a certain anti-interference capability, can fully decompose fault signals, obtain hidden feature information in the signal, and obtain the optimal solution to the variational problem.

[0076] The VMD algorithm has two constraints: (1) The sum of all modes is equal to the input signal f; under this constraint, the optimal solution of the model is searched iteratively to obtain the center frequency and bandwidth of each decomposed component. (2) By constructing and solving the variational problem, the sum of the estimated bandwidths of the center frequencies of each eigenmode function uk(t) is minimized.

[0077] In this embodiment, the preprocessed signal is decomposed using VMD to obtain the IMF, expressed by the formula:

[0078] V denoised (t)=∑[u k [(t)+r(t)];

[0079] In the formula, u k r(t) represents the k-th IMF, and r(t) represents the remaining terms.

[0080] For each IMF, calculate [u] using the Hilbert transform. k The analytic signal of (t) is expressed by the formula:

[0081]

[0082] By estimating the center frequency ω of each analytical signal k Multiplying the one-sided spectrum obtained from the above formula by an exponential term signal transforms the spectrum of each analytic signal into the fundamental frequency band, as expressed by the formula:

[0083]

[0084] Gaussian smoothing is used to demodulate the analytical signal to prevent overfitting, and the bandwidth of each IMF is estimated to finally obtain the VMD decomposition constraints. The VMD decomposition constraints are expressed by the following formula:

[0085]

[0086] In the formula, {u k} represents the k IMF sets obtained from the decomposition, {ω k Let} be the set of frequency centers corresponding to each IMF, j be the imaginary part of the complex number, δ(t) be the Dirac distribution, and θ be the frequency center. t The partial derivative of variable t;

[0087] By introducing a quadratic penalty term α and the Lagrange multiplier λ(t), the constrained problem is transformed into an unconstrained problem. The k IMFs are obtained by calculating the unconstrained problem using the alternating direction multiplier method. The unconstrained problem is expressed by the formula:

[0088]

[0089] The unconstrained problem is solved using the alternating direction multiplier method, thereby decomposing it into k IMFs. The u obtained during the decomposition process... k ω k The update expression for λ is as follows:

[0090]

[0091]

[0092]

[0093] The above formula is used to solve the problem iteratively, and the u of each IMF is continuously updated during the iteration process. k ω k The three parameters, λ, are used until the discrimination accuracy is met, and k IMFs are output.

[0094] Preferably, the step of obtaining IMF by VMD decomposition of the preprocessed signal further includes optimizing the parameters k and α in the VMD decomposition process using the fruit fly optimization algorithm. Specifically, the approximate entropy value of each IMF is calculated and used as the objective function. The iterative optimization capability of the fruit fly optimization algorithm is used to optimize the parameters k and α to find the optimal solution.

[0095] S3. Construct a convolutional neural network classifier, train the convolutional neural network classifier using the IMF, obtain the trained convolutional neural network classifier, and use the trained convolutional neural network classifier to identify and classify faults in the data to be identified.

[0096] CNN is a supervised machine learning method that is now widely used in image recognition, object detection, and fault identification. Its main learning process consists of forward propagation (FP) and back propagation (BP). Forward propagation primarily includes convolutional layers, pooling layers, and dense layers. The basic model structure is as follows: Figure 1 As shown, this process can extract and pre-classify the preprocessed signal, while the reverse parameter update can compare the pre-classification result with the expectation, automatically adjust the learnable parameters of the model, and achieve accurate classification of fault categories.

[0097] In this embodiment, the constructed convolutional neural network classifier includes convolutional layers, pooling layers, an Inception module, a Dropout layer, and a fully connected layer. Using IMF as input data, convolutional kernels are used to perform local perception on the IMF data, extracting time-series features. Pooling operations are then used to downsample and compress the time-series features. The Inception module is used to capture combined features of the IMF, and the convolutional and pooling layers connected to the Inception module extract higher-level time-series features from these combined features. The Dropout layer is used to reduce the risk of overfitting, converting the feature maps after the Dropout layer into one-dimensional vectors, and a fully connected layer is used for fault identification.

[0098] S31, Inception module;

[0099] Increasing the depth or width of a network introduces two problems to convolutional networks: 1) The number of parameters required for training increases with the number of network layers, inevitably leading to overfitting; 2) As the required training parameters increase, the model training speed decreases, making the convolutional model difficult to apply in practical engineering. Therefore, this embodiment introduces the Inception module into the convolutional neural network. The core idea of ​​this module is to combine different convolutional layers in parallel.

[0100] Preferably, the Inception module includes three parallel 1x1 convolutional kernels, where two 1x1 convolutional kernels are connected to a 3x3 convolutional kernel and a 5x5 convolutional kernel, respectively, for extracting features at different scales. The Inception module also includes a 3x3 max pooling layer, the output of which is fed to a new 1x1 convolutional kernel for downsampling, filtering, and combining the extracted features at different scales to obtain the output features. The Inception module increases the network depth and width while reducing the data dimensionality, transforming the fully connected structure into a sparse connection, effectively reducing the number of parameters, and significantly improving the model accuracy.

[0101] S32, activation function and pooling layer;

[0102] Preferably, the convolutional neural network classifier introduces non-linear property functions, i.e., activation functions, in the convolutional and fully connected layers, as expressed by the formula:

[0103] f(x) = max(0,x);

[0104] If the input is greater than 0, the input value is returned directly; if the output is less than or equal to 0, 0 is returned. Compared with the commonly used Tanh and Sigmoid functions, ReLU can speed up the training of the model, reduce the computational difficulty, and has strong robustness. The gradient vanishing problem is also partially solved.

[0105] Pooling sampling layers extract local features and can detect the same features at different locations, exhibiting good spatial and structural invariance. Common sampling methods include max pooling and average pooling. This embodiment uses max pooling, and the mathematical model expression is as follows:

[0106]

[0107] In the formula, down() is the pooling sampling function; β is the network multiplicative bias; after pooling, the number of features possessed by the sampling layer and the convolutional layer remains unchanged, but the size is reduced by a factor of n;

[0108] After multiple convolutional pooling operations, a fully connected layer is used to connect the neuron weights, and the activation function places the probability of each output in [0,1], thereby classifying data for different features.

[0109] S33. The mathematical model of the convolutional neural network is expressed by the following formula:

[0110]

[0111] In the formula, It is the output of the j-th neuron in the l-th layer; It is the input of the i-th neuron in the (l-1)-th layer; M j is the input feature map; l is the l-th layer of the network; ω is the weight matrix; It is the bias of the j-th neuron network in the l-th layer;

[0112] S34, Loss Function

[0113] For classification problems, minimizing the model's loss function is crucial to maximizing its accuracy; therefore, the choice of loss function is extremely important. Common loss functions include root mean square error (RMSE), mean absolute error (MAE), and cross-entropy cost function. This embodiment selects the cross-entropy function as the loss function, expressed by the formula:

[0114]

[0115] In the formula, n is the total number of input data samples, t is the predicted value, and y is the actual value. During backpropagation, the gradient descent method is commonly used to continuously update the iterative process. The first derivative of the above formula is obtained to adjust the learnable parameters of the network, as follows:

[0116]

[0117]

[0118] Where ω' is the updated weight; b' is the updated bias; ω is the unupdated weight; b is the unupdated bias; and η is the learning rate parameter, used to control the step size of weight updates.

[0119] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for identifying high-resistivity faults in DC distribution networks based on VMD and convolutional neural networks, characterized in that, The specific steps include: The positive transient voltage time-domain waveform signal at the fault point of the DC distribution network system is acquired, and the positive transient voltage time-domain waveform signal is preprocessed to obtain the preprocessed signal. The preprocessing includes filtering and denoising the positive transient voltage time-domain waveform signal. The preprocessed signal is decomposed using VMD to obtain the intrinsic mode components (IMFs). During the VMD decomposition process, the fruit fly optimization algorithm is used to optimize the parameters k and . ; A convolutional neural network (CNN) classifier is constructed, comprising an Inception module. The Inception module includes three parallel 1x1 convolutional kernels, two of which are connected to a 3x3 convolutional kernel and a 5x5 convolutional kernel, respectively. The Inception module also includes a 3x3 max-pooling layer, the output of which is fed to a new 1x1 convolutional kernel. The CNN classifier is trained using the Inception Matrix Factorization (IMF) to obtain a trained CNN classifier. This trained CNN classifier is then used to identify and classify faults in the data to be identified.

2. The DC distribution network high-resistivity fault identification method based on VMD and convolutional neural network according to claim 1, characterized in that, The filtering is expressed by the following formula: V filtered (t) = H filter (V(t)); In the formula, V(t) is the time-domain waveform signal of the positive transient voltage, and H filter ( ) represents the transfer function of the filter, V filtered (t) represents the filtered waveform; Denoising is performed using a wavelet denoising algorithm, expressed by the following formula: W = wavelet transform ( V filtered (t)); In the formula, V filtered (t) represents the filtered waveform, wavelet transform ( ) represents the wavelet transform function, and W represents the wavelet coefficients; T = threshold estimate (W); In the formula, threshold estimate ( ) is a function that estimates the threshold based on the statistical properties of wavelet coefficients, where T represents the threshold; W denoised = threshold process (W, T); In the formula, threshold process ( ) is a function that processes wavelet coefficients based on a threshold, W denoised These are the processed wavelet coefficients; V denoised (t) = inverse_wavelet transform (W_denoised); In the formula, inverse_wavelet transform ( ) represents the inverse wavelet transform function, V denoised (t) represents the denoised waveform signal, i.e., the preprocessed signal.

3. The DC distribution network high-resistivity fault identification method based on VMD and convolutional neural network according to claim 2, characterized in that, The preprocessed signal is decomposed using VMD to obtain the IMF, expressed by the formula: V denoised (t)= ∑[u k (t) + r(t)]; In the formula, u k r(t) represents the k-th IMF, and r(t) represents the remaining terms. The VMD decomposition constraints are expressed by the following formula: ； In the formula, To obtain the k IMF sets through decomposition, Let j be the set of frequency centers corresponding to each IMF, j be the imaginary part of the complex number, and δ(t) be the Dirac distribution. The partial derivative of variable t; Introducing a secondary penalty term and Lagrange multipliers The constrained problem is transformed into an unconstrained problem, and the k IMFs are obtained by calculating the unconstrained problem using the alternating direction multiplier method. The unconstrained problem is expressed by the following formula:

4. The DC distribution network high-resistivity fault identification method based on VMD and convolutional neural network according to claim 1, characterized in that, The constructed convolutional neural network classifier also includes convolutional layers, pooling layers, dropout layers, and fully connected layers. Using IMF as input data, convolutional kernels are used to perform local perception on the IMF data to extract time-series features. Pooling operations are then used to downsample and compress these time-series features. The Inception module captures combined features from the IMF, and convolutional and pooling layers connected to the Inception module extract higher-level time-series features from these combined features. The Dropout layer reduces the risk of overfitting, converting the feature maps from the Dropout layer into one-dimensional vectors, and a fully connected layer is used for fault identification.

5. The DC distribution network high-resistivity fault identification method based on VMD and convolutional neural network according to claim 4, characterized in that, The convolutional neural network classifier introduces non-linear properties, i.e., activation functions, into the convolutional and fully connected layers, expressed by the formula: ； The pooling layer employs max pooling, and its mathematical model expression is as follows: ； In the formula, It is the pool sampling function; It is a network multiplicative bias; The mathematical model of the convolutional neural network is expressed by the following formula: ； In the formula, It is the first The output of the j-th neuron in the layer; It is the first Layer The input of each neuron; It is the input feature map; It is the first Layered networks; It is a weight matrix; It is the first The bias of the j-th neuron network in the layer; The loss function of the convolutional neural network classifier is the cross-entropy function, expressed by the formula: ； In the formula, n is the total number of input data samples, t is the predicted value, and y is the actual value.

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