A method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis and a method for diagnosing insulation defects.

Abstract

This invention relates to the field of equipment insulation defect detection technology, and in particular to a method for constructing a rotationally invariant partial discharge (PDD) map for insulation defect diagnosis, as well as an insulation defect diagnosis method. The method for constructing the PDD map includes: acquiring PDD signals, determining the origin of the polar coordinate system, and constructing a polar coordinate system; determining the optimal number of display points for map plotting based on clustering quality evaluation; and performing a final resampling of the original PDD signals based on the optimal number of display points, mapping the sampling results to the polar coordinate system to generate a rotationally invariant PDD map for insulation defect diagnosis. This method adaptively determines the optimal number of display points, avoiding both insufficient points leading to blurred feature information and excessive points introducing information redundancy. This improves the comparability of the maps and the consistency of feature extraction, thereby significantly enhancing the accuracy and robustness of subsequent deep learning models in identifying insulation defects.

Description

Technical Field

[0001] This invention relates to the field of equipment insulation defect detection technology, and in particular to a method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, as well as an insulation defect diagnosis method. Background Technology

[0002] High-Temperature Gas-cooled Reactors (HTGRs), as advanced representatives of fourth-generation nuclear reactors, prioritize the safety and reliability of their operation. In HTGRs, the main helium blower, as the core equipment for transporting coolant in the loop, operates under extremely harsh environments with high temperatures (up to 750°C), high pressures (up to 7 MPa helium gas), and strong radiation. The insulation system of the main helium blower motor is crucial for its safe and stable operation, and its insulation performance directly affects the safety of the entire reactor. However, under the long-term effects of multiple physical stresses (thermal, electrical, radiation, and mechanical), the polymer materials (such as epoxy resin) in the motor insulation system undergo irreversible thermo-oxidative aging and radiation damage, leading to deterioration of the material's physicochemical properties, such as molecular chain breakage, oxidation, and cracking, thus forming weak insulation regions within the material. When the local electric field strength within the insulation structure exceeds the material's breakdown threshold, partial discharge (PD) is induced. Partial discharge is an early sign of insulation failure before complete breakdown. The charged particles, ultraviolet radiation, and reactive gases it generates further erode and damage the insulation material, accelerating the deterioration of insulation performance and creating a vicious cycle that can ultimately lead to catastrophic through-breakdown failures. Partial discharge is particularly problematic in high-temperature gas-cooled reactors, where the high-pressure helium gas used as a coolant has relatively low insulation strength. This characteristic further increases the probability and severity of partial discharge. Therefore, real-time and accurate monitoring and analysis of partial discharge signals are crucial for assessing the insulation status of the main helium blower motor, predicting potential faults, and ensuring the long-term safe and stable operation of the reactor.

[0003] Currently, phase-resolved partial discharge (PRPD) mapping is one of the most widely used and effective methods for identifying and diagnosing different types of insulation defects. PRPD mapping involves statistically analyzing the amplitude of partial discharge signals over one or more power frequency cycles. q Phase (φ) and number ( nThis process generates two-dimensional or three-dimensional images with specific "fingerprint" characteristics. With the rapid development of artificial intelligence technology, especially deep learning, the use of convolutional neural networks (CNNs) for automatic feature extraction and pattern recognition of PRPD maps has become the mainstream trend for achieving intelligent diagnosis of insulation defects.

[0004] However, in engineering practice, directly using PRPD maps as input to deep learning models still faces significant challenges: the instability of map features due to the randomness of partial discharge signals. Partial discharge phenomena themselves exhibit a degree of randomness and fluctuation; even for the same defect, the number and amplitude of partial discharge pulses collected at different time periods may vary considerably. Furthermore, because PD events are unstable across different periods, relying solely on time window division can lead to significant differences in map density and morphological structure. This inconsistency weakens the "fingerprint" recognition of PRPD maps, severely impacting the discriminative performance and diagnostic reliability of subsequent deep learning models.

[0005] In summary, to meet the high reliability and real-time requirements of online monitoring of insulation status for critical equipment such as the main helium blower of high-temperature gas-cooled reactors, there is an urgent need for a spectrum construction method that can effectively suppress random disturbances of partial discharge and improve the consistency of PRPD spectrum. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a method for constructing rotationally invariant partial discharge maps and a method for diagnosing insulation defects. When constructing the partial discharge map, the optimal number of display points is adaptively determined. This avoids both the blurring of feature information due to too few points and the introduction of information redundancy due to too many points, thereby improving the comparability of the maps and the consistency of feature extraction. This significantly enhances the accuracy and robustness of subsequent deep learning models in identifying insulation defects.

[0007] This invention is achieved by adopting the following technical solution: A method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis includes the following steps: Step S1. Acquire partial discharge signals, determine the reference origin of polar coordinates, and construct a polar coordinate system; Step S2. Based on cluster quality evaluation, determine the optimal number of display points for map plotting; specifically including the following steps: Step S 21 The acquired partial discharge signals are subjected to hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points; Step S 22Dimensionality reduction and clustering operations are performed on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics; Step S 23 Based on the clustering results, determine the optimal number of display points; Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled for the last time, and the sampling result is mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis.

[0008] The step S 23 Specifically, it includes: Construct a multi-index objective function: , In the formula, The number of clusters is n Multi-index objective function at time, The number of clusters is n Clustering performance evaluation metrics at different times; For the dimensionality reduction process KL divergence, n The number of clusters in the clustering. N The total number of samples, , and These are the weight coefficients for the corresponding items; draw The curve determines whether the marginal gain is below a given threshold. The smallest : , , , in, To achieve the optimal number of display points, The increment step size for the number of clusters, For marginal gain, This is the absolute threshold of the marginal gain.

[0009] Step S1 specifically includes: arbitrarily selecting an initial phase reference point, using the power frequency period... T The signal segment is divided into sub-segments to create intervals; a polar coordinate system is established with the selected initial phase reference point as the origin of the polar coordinate system.

[0010] Step S3 specifically includes: Define the polar angle and polar radius of each partial discharge event in polar coordinates as follows: , in, tPD The moment when the partial discharge event occurs. q PD This represents the discharge amount during a partial discharge event. T For power frequency cycle, Polar angle, Polar radius; The occurrence time of each partial discharge event is determined using modulo operations. t PD Map the signal to the standard power frequency cycle; combine the optimal number of display points determined in step S2, perform final resampling on the original partial discharge signal, and select partial discharge events that match the optimal number of display points from the resampled dataset; map the selected partial discharge events to the polar coordinate system according to the polar angle and polar radius defined above to form a closed polar coordinate spectrum.

[0011] The step S 21 Specifically, this refers to: constructing kernel density functions for partial discharge events in the phase angle direction and polar radius direction based on Gaussian kernel density estimation, and constructing sampling probability functions in combination with preset weighting coefficients; performing hierarchical probability resampling on the original partial discharge events according to the sampling probability functions to generate multiple sets of polar coordinate map subsets with different numbers of candidate points.

[0012] The sampling probability function is: , In the formula, For the first i The sampling probability of a partial discharge event. The preset weighting coefficients, Let be the kernel density function in the phase angle direction. Let be the kernel density function along the polar radius. For the first i The phase angle of a partial discharge event. For the first i The polar radius of a partial discharge event. N This represents the total number of original partial discharge events in the current sampling window.

[0013] The kernel density function in the phase angle direction is: , The kernel density function in the radial direction is: , In the formula, N This represents the total number of original partial discharge events in the current sampling window. For Gaussian kernel function, , These are the nuclear bandwidth in the phase angle direction and the nuclear bandwidth in the polar radius direction, respectively. For the firsti The phase angle of a partial discharge event. For the first i The radius of a partial discharge event.

[0014] The kernel bandwidths in the phase angle direction and polar radius direction are adaptively determined by combining the Silverman rule with sample features.

[0015] An insulation defect diagnosis method includes the following steps: Step A. For the rotationally invariant partial discharge pattern constructed above, a fixed-center polar coordinate transformation network is used for feature extraction to generate a polar coordinate transformed feature map X. polar ; Step B. Transfer feature map X polar The input is fed into a pre-trained insulation defect diagnosis model, which outputs insulation defect diagnosis results; wherein, the insulation defect diagnosis model uses a fixed regularization penalty factor. Coupled with the overall mean of the Fisher Information Matrix (FIM), its loss function is defined as: , In the formula, For loss function, These are the initial regularization hyperparameters. For the first t Phase 1 l The mean of the layer Fisher Information Matrix (FIM). Let the cross-entropy loss function be the current stage. For the first l The first in the layer i The current values ​​of the parameters, For the first t Phase 1 l The first in the layer i The target value of each parameter For the first t Phase 1 l The first in the layer i The Fisher information matrix elements corresponding to each parameter This represents the total number of training phases. L This represents the total number of layers in the network.

[0016] Step A specifically includes: Step A1. Input the rotation-invariant partial discharge pattern constructed above, and define the geometric center of the pattern as the polar coordinate transformation center; Step A2. Define the polar coordinate network size as H×W, and perform uniform discretization sampling along the radial and angular directions to generate a standard polar coordinate grid: , In the formula, The maximum radius of the polar coordinate network. For the first i The polar radius of each sampling point For the first i The polar angle of each sampling point; Step A3. Map the grid coordinates using the inverse transformation from polar coordinates to Cartesian coordinates to obtain the corresponding sampling point positions in the Cartesian coordinate system: , Step A4. The sampling grid G ​​is formed by all polar coordinate sampling points: , Step A5. Utilize the bilinear interpolation sampling function F of the deep learning framework. grid_sample Sampling is performed on the original input map X to generate a feature map X after polar coordinate transformation. polar .

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention determines the optimal number of display points based on clustering quality evaluation, and then proposes a polar coordinate partial discharge map construction strategy with a fixed number of partial discharges. This strategy avoids the blurring of feature information due to too few points, and effectively prevents information redundancy introduced by too many points, thereby improving the comparability of the map and the consistency of feature extraction. This significantly improves the accuracy and robustness of subsequent deep learning models in identifying insulation defects.

[0018] 2. This invention scientifically determines the optimal number of display points by introducing a multi-index objective function and further combining it with marginal gain analysis. Specifically, the objective function comprehensively considers multiple clustering quality indicators such as silhouette coefficient, KL divergence, and cluster granularity, and introduces corresponding weight coefficients to fully reflect the structural separability of the PRPD map under different point numbers. Based on this, by analyzing the marginal gain trend of the objective function as the number of points increases, the inflection point where it tends to saturate is identified, thereby reducing redundancy and improving the training efficiency of subsequent deep learning models while preserving the main cluster structure and ensuring sufficient feature expression.

[0019] 3. The present invention does not rely on the selection of a specific initial phase when drawing polar coordinate graphs. The polar coordinate graph maps the partial discharge mode from a linear phase distribution to an angular ring expression, so that different initial phases only show the rotation of the graph without changing its structural morphology, which can effectively eliminate the interference of the initial phase.

[0020] 4. This invention is the first to apply dual-dimensional kernel density estimation, weighted sampling probability, and hierarchical resampling to the construction of partial discharge maps. This not only accurately captures the dual distribution characteristics of phase and intensity of partial discharge, but also forms a synergistic optimization with subsequent dimensionality reduction and clustering operations. With a limited number of display points, it maximizes the retention of the most valuable information for diagnosis, making it more suitable for the complex partial discharge conditions that this invention addresses.

[0021] 5. This defect diagnosis method employs a fixed-center polar coordinate transformation network, avoiding the need for a subnet to learn the transformation center in traditional polar coordinate transformation neural networks. This simplifies the model structure and improves training stability. Specifically, based on this fixed-center design, network parameters are reduced by approximately 15%, and training time is reduced by more than 30%, making it suitable for edge computing and online detection systems.

[0022] 6. This insulation defect diagnosis model will use a fixed regularization penalty factor. Coupling with the overall mean of the Fisher Information Matrix (FIM) allows the regularization strength to be dynamically scaled according to the overall distribution of parameter importance, ensuring a more stable regularization strength during the continuous learning process across stages.

[0023] Compared to fixed Compared with the traditional Elastic Weight Consolidation (EWC) method, this invention uses the FIM mean as a normalization factor to dynamically adjust the actual constraint strength of the current stage, so that the regularization coefficient can be automatically scaled between different stages and different layers, avoiding the instability caused by the difference in FIM numerical scale.

[0024] 7. This invention utilizes the bilinear interpolation sampling function F of the deep learning framework. grid_sample Sampling is performed on the original input map X to generate a feature map X after polar coordinate transformation. polar This operation is differentiable during the network's forward propagation, thus facilitating end-to-end training with subsequent convolutional networks. Attached Figure Description

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments, wherein: Figure 1 This is a flowchart illustrating the partial discharge pattern construction method in this invention. Figure 2 This is a flowchart illustrating the insulation defect diagnosis method of the present invention; Figure 3 This is a polar coordinate graph of the random perturbation of different phases in this invention; Figure 4 A visualization of the original data after introducing phase perturbation in the first stage; Figure 5 This is a visualization of the data output by the convolutional layer after phase perturbation is introduced in the first stage of this invention. Detailed Implementation

[0026] Example 1 As a basic embodiment of the present invention, the present invention includes a method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, comprising the following steps: Step S1. Acquire partial discharge signals, determine the reference origin of polar coordinates, and construct a polar coordinate system.

[0027] Step S2. Based on clustering quality evaluation, determine the optimal number of display points for map plotting. This includes the following steps: Step S 21 The acquired partial discharge signal is subjected to hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points.

[0028] Step S 22 Dimensionality reduction and clustering operations are performed on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics.

[0029] Step S 23 Based on the clustering results, determine the optimal number of display points.

[0030] Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled for the last time, and the sampling result is mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis.

[0031] Example 2 As a preferred embodiment of the present invention, the present invention includes a method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, comprising the following steps: Step S1. Acquire partial discharge signals, determine the origin of the polar coordinate system, and construct a polar coordinate system. Specifically, arbitrarily select an initial phase reference point, using the power frequency period... T The signal segment is divided into sub-segments to create intervals. A polar coordinate system is established with the selected initial phase reference point as the origin of the polar coordinate system.

[0032] Step S2. Based on clustering quality evaluation, determine the optimal number of display points for map plotting. This includes the following steps: Step S 21 The acquired partial discharge signal is subjected to hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points.

[0033] Step S 22Dimensionality reduction and clustering operations are performed on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics.

[0034] Step S 23 Based on clustering results, the optimal number of display points is determined. Specifically, this includes: Construct a multi-index objective function: , In the formula, The number of clusters is n Multi-index objective function at time, The number of clusters is n Clustering performance evaluation metrics at different times; For the dimensionality reduction process KL divergence, n The number of clusters in the clustering. N The total number of samples, , and These are the weight coefficients for the corresponding items.

[0035] draw The curve determines whether the marginal gain is below a given threshold. The smallest : , , , in, To achieve the optimal number of display points, The increment step size for the number of clusters, For marginal gain, This is the absolute threshold of the marginal gain.

[0036] Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled for the last time, and the sampling result is mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis.

[0037] Example 3 In another preferred embodiment of the present invention, the present invention includes a method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, comprising the following steps: Step S1. Acquire partial discharge signals, determine the reference origin of polar coordinates, and construct a polar coordinate system.

[0038] Step S2. Based on clustering quality evaluation, determine the optimal number of display points for map plotting. This includes the following steps: Step S 21The acquired partial discharge signals undergo hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points. Specifically, kernel density functions for partial discharge events in the phase angle and radial direction are constructed based on Gaussian kernel density estimation, and sampling probability functions are constructed by combining them with preset weighting coefficients. The original partial discharge events are then subjected to hierarchical probability resampling according to the sampling probability functions to generate multiple polar coordinate map subsets with different numbers of candidate points.

[0039] Step S 22 Dimensionality reduction and clustering operations are performed on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics.

[0040] Step S 23 Based on the clustering results, determine the optimal number of display points.

[0041] Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled, and the sampling results are mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis. Specifically, this includes: Define the polar angle and polar radius of each partial discharge event in polar coordinates as follows: , in, t PD The moment when the partial discharge event occurs. q PD This represents the discharge amount during a partial discharge event. T For power frequency cycle, Polar angle, It is the polar radius.

[0042] The occurrence time of each partial discharge event is determined using modulo operations. t PD The partial discharge signal is mapped to a standard power frequency cycle. Based on the optimal number of display points determined in step S2, the original partial discharge signal is resampled. Partial discharge events matching the optimal number of display points are selected from the resampled dataset. The selected partial discharge events are then mapped to a polar coordinate system according to the defined polar angles and radii, forming a closed polar coordinate map.

[0043] Example 4 As another preferred embodiment of the present invention, the present invention includes a method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, as described in the appendix to the specification. Figure 1 This includes the following steps: Step S1. Acquire partial discharge signals, determine the reference origin of polar coordinates, and construct a polar coordinate system.

[0044] When acquiring partial discharge signals on-site, the initial phase reference point of the power frequency voltage cycle is usually arbitrarily selected. Different initial phase choices, while not altering the physical nature of the partial discharge, cause a cyclic translation of the generated PRPD map along the phase axis. For a standard PRPD map, this cyclic translation visually appears as a rotation of the map. Traditional convolutional neural networks, due to their inherent structure, are highly sensitive to geometric transformations such as target rotation. Map rotation severely interferes with the network's effective extraction of deep features, potentially causing the identification model to misclassify the same type of defect as different categories, thus significantly reducing the accuracy and robustness of the diagnosis.

[0045] Therefore, for a continuous partial discharge signal acquired on-site, this invention first arbitrarily selects an initial phase reference point, using the power frequency period... T The signal segment is divided into sub-segments to create intervals. Then, a polar coordinate system is established with the selected initial phase reference point as the origin of the polar coordinate system.

[0046] Step S2. Based on the clustering quality assessment, determine the optimal number of display points for map drawing.

[0047] To ensure the consistency of input data across different samples, it is necessary to uniformly control the number of PD events. Since PD events exhibit instability across different periods, simply relying on time window division may lead to significant differences in spectral density, thus affecting the discrimination performance of subsequent models. Therefore, this invention proposes an optimal point number selection method based on clustering feature evaluation, aiming to avoid feature information ambiguity due to too few points, while preventing information redundancy introduced by too many points. Specifically, this invention randomly re-extracts the collected PD signals according to a fixed number, constructing a series of polar coordinate spectral subsets with different point numbers, and then uses the t-SNE algorithm for clustering. To quantify the clustering effect of the spectral data under different point numbers, this invention selects the Silhouette Score (SC) as an evaluation index, which comprehensively measures the intra-class compactness and inter-class separation of samples. The specific steps include: Step S 21 The acquired partial discharge signals are subjected to hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points. Specifically, this includes: Based on Gaussian kernel density estimation, kernel density functions for partial discharge events are constructed in the phase angle direction and the polarity direction, respectively: The kernel density function in the phase angle direction is: , The kernel density function in the radial direction is: , In the formula, NThis represents the total number of original partial discharge events in the current sampling window. For the first i The phase angle of a partial discharge event. For the first i The radius of a partial discharge event. For Gaussian kernel function, . , These represent the kernel bandwidth in the phase angle direction and the kernel bandwidth in the polar radius direction, respectively, controlling the smoothness of the kernel function. Larger values ​​result in a smoother estimated curve, determined using the Silverman rule. ; .

[0048] Construct a sampling probability function by combining preset weighting coefficients: , In the formula, For the first i The sampling probability of a partial discharge event. The preset weighting coefficients, Let be the kernel density function in the phase angle direction. Let be the kernel density function along the polar radius. For the first i The phase angle of a partial discharge event. For the first i The polar radius of a partial discharge event. N This represents the total number of original partial discharge events in the current sampling window.

[0049] Based on the sampling probability function, the original partial discharge event is resampled in a stratified probability manner to generate multiple polar coordinate map subsets with different numbers of candidate points.

[0050] Step S 22 t-SNE is used to perform dimensionality reduction and clustering operations on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics. Specifically, this includes: Constructing conditional probabilities in high-dimensional space: , in, xi Indicates the first i The vector of a partial discharge event in the high-dimensional input feature space (t-SNE input).

[0051] Objective function: , in, yi express iThe embedding coordinates of each sample in the low-dimensional space (the output data of t-SNE).

[0052] Calculate the silhouette coefficient after clustering: , , in, a i Indicates sample x i The average distance to other samples within its cluster. b i express x i The average distance to the nearest other samples within the cluster. The overall silhouette coefficient is the average of the silhouette values ​​of all samples. .

[0053] Step S 23 Based on clustering results, determine the optimal number of display points. Specifically, this includes: Construct a multi-index objective function: , In the formula, The number of clusters is n Multi-index objective function. The number of clusters is n The clustering performance evaluation index is the overall profile coefficient in this embodiment. For the dimensionality reduction process KL divergence, n The number of clusters in the clustering. 、 and These are the weight coefficients for the corresponding items.

[0054] draw The curve determines whether the marginal gain is below a given threshold. The smallest : , , , in, To achieve the optimal number of display points, The increment step size for the number of clusters, For marginal gain, This is the absolute threshold of the marginal gain.

[0055] This step ensures that redundancy is reduced and model training efficiency is improved while preserving the main cluster structure.

[0056] Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled, and the sampling results are mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis. Specifically, this includes: Define the polar angle and polar radius of each partial discharge event in polar coordinates as follows: , in, t PD The moment when the partial discharge event occurs. q PD This represents the discharge amount during a partial discharge event. T For power frequency cycle, Polar angle, It is the polar radius.

[0057] The occurrence time of each partial discharge event is determined using modulo operations. t PD Mapped to a standard power frequency cycle. Based on the optimal number of display points determined in step S2, the original partial discharge signal is resampled, and partial discharge events matching the optimal number of display points are selected from the resampled dataset. The selected partial discharge events are then mapped to a polar coordinate system according to the polar angle and polar radius defined above. Based on this mapping, the partial discharge signal within each power frequency cycle will be transformed into a closed polar coordinate spectrum.

[0058] This method does not depend on the choice of a specific initial phase when plotting polar coordinate maps. In fact, different initial phase choices are merely equivalent to performing a rotational transformation on the map: , in, The initial phase offset is used to obtain the initial polar coordinate spectrum. .

[0059] Since the rotation operation does not change the morphological characteristics of the spectrum itself, this method fundamentally guarantees the robustness of the spectrum to the initial phase selection.

[0060] Example 5 In another preferred embodiment of the present invention, the present invention includes an insulation defect diagnosis method, comprising the following steps: Step A. For the rotationally invariant partial discharge spectrum constructed in any of the embodiments 1 to 4 above, a fixed-center polar coordinate transformation network is used to extract features, generating a polar coordinate transformed feature map X. polar .

[0061] Step B. Transfer feature map X polarThe input is fed into a pre-trained insulation defect diagnosis model, which outputs insulation defect diagnosis results. The insulation defect diagnosis model uses a fixed regularization penalty factor. Coupled with the overall mean of the Fisher Information Matrix (FIM), its loss function is defined as: , In the formula, For loss function, These are the initial regularization hyperparameters. For the first t Phase 1 l The mean of the layer Fisher Information Matrix (FIM). Let the cross-entropy loss function be the current stage. For the first l The first in the layer i The current values ​​of the parameters, For the first t Phase 1 l The first in the layer i The target value of each parameter For the first t Phase 1 l The first in the layer i The Fisher information matrix elements corresponding to each parameter This represents the total number of training phases. L This represents the total number of layers in the network.

[0062] Example 6 To address the image rotation problem, existing technologies typically employ two strategies. The first is data augmentation, which involves randomly rotating samples from multiple angles before training to allow the model to learn rotation-invariant features. However, this method significantly increases training time and computational cost, and it struggles to cover all possible rotation angles, limiting the model's generalization ability. The second approach uses special network structures with rotation invariance, such as Spatial Transformer Networks (STNs) or Polar Transformer Networks (PTNs) developed from them. The core idea of ​​this approach is to add a localization subnetwork to learn a suitable transformation center point from the input image, and then perform coordinate transformations (such as converting Cartesian coordinates to polar coordinates) based on this center point, transforming the rotation problem into a translation problem in polar coordinates, thus achieving rotation invariance. However, this method, which relies on an additional subnetwork to regress the transformation center point, makes the model structure more complex, the training process unstable and difficult to converge, and increases the number of model parameters and computational burden. It is unsuitable for online monitoring systems and edge computing devices with high real-time requirements or limited computational resources.

[0063] As another preferred embodiment of the present invention, the present invention includes an insulation defect diagnosis method, as described in the appendix to the specification. Figure 2 This includes the following steps: Step A. For the rotationally invariant partial discharge spectrum constructed in any of the embodiments 1 to 4 above, a fixed-center polar coordinate transformation network is used to extract features, generating a polar coordinate transformed feature map X. polar This model utilizes the geometric properties of polar coordinate transformation to effectively resist rotational and translational disturbances in the input data, thereby enhancing the model's generalization ability. Specifically, it includes: Step A1. Input the rotation-invariant partial discharge pattern constructed in any of the embodiments 1 to 4 above, and define the geometric center of the pattern as the polar coordinate transformation center. In deep learning frameworks, image coordinates are usually normalized and mapped to... The interval is defined, therefore the new coordinates in the image are naturally fixed at the origin [0,0]. In the polar coordinate domain, the coordinates of any point on the image can be represented as: .

[0064] Step A2. To complete the sampling operation in polar coordinate space, define the polar coordinate network size as H×W, and perform uniform discretization sampling along the radial and angular directions to generate a standard polar coordinate grid: , In the formula, The maximum radius of the polar coordinate network. For the first i The polar radius of each sampling point For the first i The polar angle of each sampling point.

[0065] Step A3. Map the grid coordinates using the inverse transformation from polar coordinates to Cartesian coordinates to obtain the corresponding sampling point positions in the Cartesian coordinate system: , Step A4. The sampling grid G ​​is formed by all polar coordinate sampling points: .

[0066] Step A5. Utilize the bilinear interpolation sampling function F of the deep learning framework. grid_sample Sampling is performed on the original input map X to generate a feature map X after polar coordinate transformation. polar This operation is differentiable during the network's forward propagation, thus facilitating end-to-end training with subsequent convolutional networks.

[0067] Step B. Transfer feature map X polarInput the data into the already trained insulation defect diagnosis model and output the insulation defect diagnosis results.

[0068] Existing technologies generally employ Elastic Weight Consolidation (EWC) for insulation defect diagnosis models. Its core idea is to introduce a regularization term to penalize and constrain important network parameters, thereby preserving as much key information learned in the previous stage as possible. The original loss function of EWC can be described as: , in, This represents the cross-entropy loss function for the current stage. These are the parameters to be optimized for the current task. This represents the optimal parameter values ​​learned in the previous stage. For the Fisher information matrix i The diagonal elements at each parameter measure the importance of that parameter; λ is the regularization strength coefficient that balances the absorption of new knowledge with the retention of old knowledge.

[0069] Traditional EWC methods have two limitations when dealing with long-term, slowly evolving features such as partial discharge signals: First, the penalty coefficient λ is a fixed value throughout the training process and cannot be dynamically adjusted according to the feature similarity or complexity between tasks during the defect degradation process, thus limiting the network's flexibility and adaptability. Second, EWC treats all network parameters equally and does not distinguish the differences in sensitivity of different layers to task transfer. In particular, the adaptability requirements of the feature extraction layer and the classification layer to new and old tasks are not consistent, and excessive constraints may reduce the generalization performance under new tasks.

[0070] Therefore, the insulation defect diagnosis model of the present invention will have a fixed regularization penalty factor. The loss function is coupled with the overall mean of the Fisher Information Matrix (FIM) to dynamically scale according to the overall distribution of parameter importance, ensuring more stable regularization strength during cross-stage continuous learning. The improved loss function is defined as follows: , In the formula, For loss function, These are the initial regularization hyperparameters. For the first t Phase 1 l The mean of the layer Fisher Information Matrix (FIM). Let the cross-entropy loss function be the current stage. For the first l The first in the layer i The current values ​​of the parameters, For the first t Phase 1l The first in the layer i The target value of each parameter For the first t Phase 1 l The first in the layer i The Fisher information matrix elements corresponding to each parameter This represents the total number of training phases. L This represents the total number of layers in the network.

[0071] Compared to fixed Compared to traditional EWC methods, this invention uses the FIM mean as a normalization factor to dynamically adjust the actual constraint strength at the current stage. In this way, the regularization coefficient can be automatically scaled across different stages and layers, avoiding instability caused by differences in FIM numerical scales.

[0072] To evaluate the effectiveness of the method of the present invention in cable defect identification, four typical defect samples were prepared. To simulate the deterioration process caused by the evolution of defects over time in actual working conditions, accelerated aging experiments were carried out on the samples, and partial discharge signal data were collected at different aging stages to simulate a multi-stage dataset covering the entire life cycle of the defect.

[0073] To verify the applicability of the proposed method in scenarios where voltage phase information is missing, this invention performs artificial phase perturbation processing on the raw partial discharge signals collected in the laboratory. Specifically, a random phase shift angle is applied to each segment of collected data, and a polar coordinate partial discharge map is constructed based on the processed data. Taking a knife mark defect as an example, refer to the appendix of the specification. Figure 3 The diagram shows polar coordinate spectra under different phase random perturbations. It can be seen that when faced with phase shifts, the polar coordinate spectra only exhibit overall graphic rotation, and the spatial distribution structure of the point clusters remains stable, without any changes in quantity or shape.

[0074] The neural network structure of the insulation defect diagnosis model built in this invention is shown in Table 1 below. The insulation defect diagnosis model was trained on an HP Zhan66 desktop workstation equipped with an NVIDIA GeForce RTX 4060 graphics card and 16GB of memory. The software environment was based on Python 3.11, and the deep learning framework was built using PyTorch. Each type of defect had 500 data points at each aging stage, and the training set and test set were divided in a 7:3 ratio. The training process incorporated the DEWC strategy proposed by III-C, the model learning rate was set to 0.0001, and the initial hyperparameters for regularization were set to... The maximum number of training rounds is set to 20.

[0075] Table 1 Neural Network Parameter Configuration

[0076] Table 2 summarizes the model's performance, demonstrating the stability and reliability of the proposed method. As shown in Table 2, the diagnostic method based on polar coordinate maps combined with this model achieves accuracies of 92.15%, 88.24%, and 85.43% in the three stages, respectively, while the forgetting rates are controlled within 5.37%, 4.89%, and 3.76%. This result indicates that despite facing complex multi-stage data, the method of this invention maintains high and stable classification performance, effectively mitigating the forgetting problem during continuous learning.

[0077] Table 2 Training results of the insulation defect diagnosis model

[0078] Refer to the instruction manual appendix Figure 4 Included with instruction manual Figure 5 This invention further presents the visualization effect of data after introducing phase perturbation. By comparing the original data with the data output from the model's convolutional layer, it was found that there are large overlapping regions among the four types of defect clusters in the original data, and the boundaries between classes are blurred. However, after feature extraction by the model, the clustering degree of data points within each defect class is significantly improved, and the distinction between classes is clearer. Although there are still a few misclassified data points, the overall visualization effect is significantly improved, demonstrating the superiority of the proposed feature extraction strategy and further verifying the effectiveness of the method of this invention in processing real-world perturbation data.

[0079] In summary, any other corresponding modifications made by those skilled in the art after reading this invention document, without requiring creative mental effort, based on the technical solutions and concepts of this invention, are all within the scope of protection of this invention.

Claims

1. A method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis, characterized in that: Includes the following steps: Step S1. Acquire partial discharge signals, determine the reference origin of polar coordinates, and construct a polar coordinate system; Step S2. Based on cluster quality evaluation, determine the optimal number of display points for map plotting; specifically including the following steps: Step S 21 The acquired partial discharge signals are subjected to hierarchical probability resampling to generate multiple polar coordinate map subsets with different numbers of candidate points; Step S 22 Dimensionality reduction and clustering operations are performed on each subset of the graph, and the clustering effect of each subset is quantified based on evaluation metrics; Step S 23 Based on the clustering results, determine the optimal number of display points; Step S3. Based on the optimal number of display points, the original partial discharge signal is resampled for the last time, and the sampling result is mapped to the polar coordinate system to generate a rotationally invariant partial discharge map for insulation defect diagnosis.

2. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 1, characterized in that: The step S 23 Specifically, it includes: Construct a multi-index objective function: ， In the formula, The number of clusters is n Multi-index objective function at time, The number of clusters is n Clustering performance evaluation metrics at different times; For the dimensionality reduction process KL divergence, n The number of clusters in the clustering. N The total number of samples, , and These are the weight coefficients for the corresponding items; draw The curve determines whether the marginal gain is below a given threshold. The smallest : ， ， ， in, To achieve the optimal number of display points, The increment step size for the number of clusters, For marginal gain, This is the absolute threshold of the marginal gain.

3. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 1, characterized in that: Step S1 specifically includes: arbitrarily selecting an initial phase reference point, using the power frequency period... T The signal segment is divided into sub-segments to create intervals; a polar coordinate system is established with the selected initial phase reference point as the origin of the polar coordinate system.

4. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 1, characterized in that: Step S3 specifically includes: Define the polar angle and polar radius of each partial discharge event in polar coordinates as follows: ， in, t PD The moment when the partial discharge event occurs. q PD This represents the discharge amount during a partial discharge event. T For power frequency cycle, Polar angle, Polar radius; The occurrence time of each partial discharge event is determined using modulo operations. t PD Map the signal to the standard power frequency cycle; combine the optimal number of display points determined in step S2, perform final resampling on the original partial discharge signal, and select partial discharge events that match the optimal number of display points from the resampled dataset; map the selected partial discharge events to the polar coordinate system according to the polar angle and polar radius defined above to form a closed polar coordinate spectrum.

5. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 1, characterized in that: The step S 21 Specifically, this refers to: constructing kernel density functions for partial discharge events in the phase angle direction and polar radius direction based on Gaussian kernel density estimation, and constructing sampling probability functions in combination with preset weighting coefficients; performing hierarchical probability resampling on the original partial discharge events according to the sampling probability functions to generate multiple sets of polar coordinate map subsets with different numbers of candidate points.

6. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 5, characterized in that: The sampling probability function is: ， In the formula, For the first i The sampling probability of a partial discharge event. The preset weighting coefficients, Let be the kernel density function in the phase angle direction. Let be the kernel density function along the polar radius. For the first i The phase angle of a partial discharge event. For the first i The polar radius of a partial discharge event. N This represents the total number of original partial discharge events in the current sampling window.

7. The method for constructing a rotationally invariant partial discharge pattern for insulation defect diagnosis according to claim 6, characterized in that: The kernel density function in the phase angle direction is: ， The kernel density function in the radial direction is: ， In the formula, N This represents the total number of original partial discharge events in the current sampling window. For Gaussian kernel function, , These are the nuclear bandwidth in the phase angle direction and the nuclear bandwidth in the polar radius direction, respectively. For the first i The phase angle of a partial discharge event. For the first i The radius of a partial discharge event.

8. The method for constructing rotationally invariant partial discharge patterns for insulation defect diagnosis according to claim 7, characterized in that: The kernel bandwidths in the phase angle direction and polar radius direction are adaptively determined by combining the Silverman rule with sample features.

9. A method for diagnosing insulation defects, characterized in that: Includes the following steps: Step A. For the rotationally invariant partial discharge spectrum constructed according to any one of claims 1 to 8, feature extraction is performed using a fixed-center polar coordinate transformation network to generate a feature map X after polar coordinate transformation. polar ; Step B. Transfer feature map X polar The input is fed into a pre-trained insulation defect diagnosis model, which outputs insulation defect diagnosis results; wherein, the insulation defect diagnosis model uses a fixed regularization penalty factor. Coupled with the overall mean of the Fisher Information Matrix (FIM), its loss function is defined as: ， In the formula, For loss function, These are the initial regularization hyperparameters. For the first t Phase 1 l The mean of the layer Fisher Information Matrix (FIM). Let the cross-entropy loss function be the current stage. For the first l The first in the layer i The current values ​​of the parameters, For the first t Phase 1 l The first in the layer i The target value of each parameter For the first t Phase 1 l The first in the layer i The Fisher information matrix elements corresponding to each parameter This represents the total number of training phases. L This represents the total number of layers in the network.

10. The insulation defect diagnosis method according to claim 9, characterized in that: Step A specifically includes: Step A1. Input the rotation-invariant partial discharge pattern constructed above, and define the geometric center of the pattern as the polar coordinate transformation center; Step A2. Define the polar coordinate network size as H×W, and perform uniform discretization sampling along the radial and angular directions to generate a standard polar coordinate grid: ， In the formula, The maximum radius of the polar coordinate network. For the first i The polar radius of each sampling point For the first i The polar angle of each sampling point; Step A3. Map the grid coordinates using the inverse transformation from polar coordinates to Cartesian coordinates to obtain the corresponding sampling point positions in the Cartesian coordinate system: ， Step A4. The sampling grid G ​​is formed by all polar coordinate sampling points: ， Step A5. Utilize the bilinear interpolation sampling function F of the deep learning framework. grid_sample Sampling is performed on the original input map X to generate a feature map X after polar coordinate transformation. polar .

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