Data enhancement model-based transformer fault diagnosis method and related equipment

By using the CTGAN-CRS data enhancement model and full-type gas ratio and random forest algorithm for feature processing in transformer fault diagnosis, the problems of poor data generation quality and low diagnostic accuracy in the prior art are solved, and higher quality data generation and more accurate fault diagnosis are achieved.

CN119598201APending Publication Date: 2025-03-11XIAN HIGH VOLTAGE APP RES INST CO LTD

Patent Information

Application Number
CN202411737986.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-29
Publication Date
2025-03-11

AI Technical Summary

Technical Problem

In the prior art, the quality of the transformer fault diagnosis data generation is poor, resulting in low diagnostic accuracy.

Method used

The data augmentation model based on CTGAN-CRS is used to enhance and balance the original DGA data, combine the full-type gas ratio and the random forest algorithm for feature amplification, screening and dimensional transformation, and finally use the CNN model for fault diagnosis.

Benefits of technology

By optimizing the data generation process, the quality of DGA data is improved, the feature expression power is enhanced, and the accuracy of transformer fault diagnosis is significantly improved.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a transformer fault diagnosis method based on a data enhancement model and related equipment, and the method achieves the training process optimization of a CTGAN through introducing a CRS module under the condition of considering different data types of a data column, achieves the high-quality generation of DGA table data, and improves the efficiency. Evaluating the quality of the generated data by using a KS index and a CNN model; dGA data features are amplified and screened based on full-type gas ratios and a random forest algorithm, and large-scale abundant and effective screening of gas ratio features is achieved under the original background that only part of empirical features are selected. The effectiveness of the data dimension amplification method is verified by using a CNN model subsequently, and the feature expressive power is improved while feature dimension amplification is realized; through the data processing operation, the problems of poor data generation quality and low transformer fault diagnosis precision in the prior art are solved.
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Description

Background Art

[0002] As an important part of the power system, power transformers are responsible for converting high and low voltages of the power system and distributing electric energy to various end users. They play a vital role in the stable operation of power generation, transformation, transmission, distribution, power consumption, and power storage systems. Due to the combined influence of multiple factors such as the operating environment, electrical and thermal conditions, power transformers that have been running for a long time may have many different types of faults.

[0003] Dissolved Gas Analysis (DGA) is the most widely used and effective fault diagnosis method. However, due to the common problem of imbalanced fault types in DGA data, how to efficiently enhance and balance data and how to effectively select a suitable diagnostic model to further improve the accuracy of fault diagnosis have become research hotspots in transformer fault diagnosis.

[0004] Gao Shuguo et al. disclosed in their patent document with application number 201910717685.4 a "transformer fault diagnosis method based on k-neighboring SMOTE and deep learning". The implementation steps are as follows: the first step is to preprocess the initial unbalanced samples, which includes four steps: calculating the characteristic ratio of the oil chromatogram dissolved gas sample set, dividing the data set, synthesizing new samples based on k-neighboring SMOTE, and testing the test set; the second step is DNN neural network training, which includes three steps: training the DNN neural network with balanced training samples, error back propagation and gradient descent iterations, and testing the DNN performance with a test set; however, this method has the following shortcomings: first, the data generated by k-neighboring SMOTE oversampling is too close to the original data, and the data boundaries are unclear, resulting in poor data generation quality; second, the DNN neural network cannot achieve high-dimensional extraction of features, resulting in poor performance of the diagnostic model.

[0005] Wang Lizhong and others disclosed in their patent document with application number 202310630341.6 "An online diagnosis method for transformer faults based on NNTR-SMOTE oversampling to process unbalanced small samples". The implementation steps are: the first step is to standardize the fault samples and use NNTR-SMOTE technology to oversample to obtain balanced data; the second step is to construct features based on uncoded ratios; the third step is to perform feature fusion based on multidimensional scaling analysis to achieve feature dimensionality reduction; the fourth step is to use genetic algorithms to optimize and verify the fault diagnosis model built based on XGBoost; however, this method has the following shortcomings: First, NNTR-SMOTE is an oversampling technology, and the data depends on the original data, which can easily lead to model overfitting; second, the XGBoost algorithm has problems such as low diagnostic accuracy. Summary of the invention

[0006] The purpose of the present invention is to provide a transformer fault diagnosis method and related equipment based on a data enhancement model to solve the technical problems of poor data generation quality and low diagnostic accuracy in the prior art.

[0007] In order to achieve the above object, the present invention adopts the following technical scheme: A transformer fault diagnosis method based on a data enhancement model comprises the following steps: Collect transformer DGA data to form the original data set; The original data set is input into the trained data enhancement model to obtain a generated data set, and the generated data set is used to perform data enhancement and balance on the original data set to obtain a balanced data set; Based on all-type gas ratios and random forest algorithm, the balanced data set is expanded, screened and dimensionally transformed; The balanced training data set after feature amplification, screening and dimension transformation is input into the fault diagnosis model for training to obtain a trained fault diagnosis model, and the test set after feature amplification, screening and dimension transformation is input into the trained fault diagnosis model to output the fault diagnosis result; The trained data enhancement model is obtained by training the data enhancement model using the original data set, and the data enhancement model is constructed based on CTGAN-CRS.

[0008] Furthermore, the specific steps of constructing the data enhancement model are: The CRS module is introduced into the generator G of CTGAN to obtain CTGAN-CRS; The original data set is input into CTGAN-CRS for training to obtain a data augmentation model.

[0009] Furthermore, the CRS module is obtained by cascading integration of three basis rejection sampler models, and the three basis rejection sampler models are constructed using non-negative judgment method, IEC three-ratio method and Rogers four-ratio method respectively.

[0010] Furthermore, before the balanced dataset is amplified, screened, and dimensionally transformed, the KS Complement value is used to evaluate the similarity between the generated dataset and the original dataset; The calculation formula of the KS Complement value is:

[0011]

[0012] Where D is the KS statistic, is the cumulative distribution of the original data set, To generate the cumulative distribution of the dataset.

[0013] Furthermore, the step of amplifying the balanced data set is: Construct all types of combined features for the n features of the balanced data set and obtain Combined features; right Combined features are used to construct pairwise ratio features, and the Ratio feature; The number of features of the augmented dataset is + .

[0014] Furthermore, the object of the screening is the data set after the balanced data set is expanded, and the random forest algorithm is selected to evaluate the feature importance, and the features are sorted according to the importance, and the features with the highest importance and non-zero value are selected. Features form the optimal feature dataset .

[0015] Furthermore, the trained fault diagnosis model is obtained by training a fault diagnosis model based on CNN.

[0016] In a second aspect, a transformer fault diagnosis system based on a data enhancement model includes an acquisition module, a generation module, a data set processing module, and a fault diagnosis module, wherein: Acquisition module: used to collect transformer DGA data to form the original data set; Generation module: used to input the original data set into the trained data enhancement model to obtain the generated data set, and use the generated data set to perform data enhancement and balance on the original data set to obtain a balanced data set; Data processing module: amplify, filter and transform the dimension of the balanced data set based on all types of gas ratios and random forest algorithm; Fault diagnosis module: input the balanced training data set after feature amplification, screening and dimension transformation into the fault diagnosis model for training, obtain the trained fault diagnosis model, input the test set after feature amplification, screening and dimension transformation into the trained fault diagnosis model, and output the fault diagnosis result; The trained data enhancement model is obtained by training the data enhancement model using the original data set, and the data enhancement model is constructed based on CTGAN-CRS.

[0017] In a third aspect, a terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0018] In a fourth aspect, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0019] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention provides a transformer fault diagnosis method based on a data enhancement model. By introducing a CRS module under the condition of considering different data types of data columns through rejection sampling of generated data, the training process of CTGAN is optimized, thereby achieving high-quality generation of DGA table data; the DGA data features are amplified and screened based on the all-type gas ratio and random forest algorithm, so that the feature dimension is amplified and the feature expression is improved; through the above data processing operations, the problems of poor data generation quality and low transformer fault diagnosis accuracy in the prior art are solved.

[0020] Preferably, the KS Complement value is used to evaluate the similarity between the generated data set and the original data set, thereby achieving quality assessment of the DGA generated data.

[0021] Preferably, all-type combination feature construction and pairwise ratio feature construction are used to achieve feature dimension expansion of the balanced data set.

[0022] Preferably, a random forest algorithm is used to evaluate feature importance, thereby implementing feature screening and obtaining a feature-optimized data set. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of a transformer fault diagnosis method based on a data enhancement model in an embodiment of the present invention; Figure 2 The flowchart of transformer fault diagnosis based on CTGAN-CRS data enhancement. DETAILED DESCRIPTION

[0024] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are 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.

[0025] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0026] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0027] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0028] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0029] Glossary:

[0030] The present invention is further described in detail below in conjunction with the accompanying drawings: like Figure 1 As shown, a transformer fault diagnosis method based on a data enhancement model includes the following steps: Step 1: Collect transformer DGA data to form the original data set: Specifically, the original data set Data is:

[0031] In the above formula, x is the feature data, n is the number of features, m is the sample size of the DGA dataset, y is the fault label, and k is the fault label category.

[0032] Step 2: Input the original data set into the trained data enhancement model to obtain a generated data set, and use the generated data set to perform data enhancement and balance on the original data set to obtain a balanced data set; Specifically, this step includes building a data enhancement model based on CTGAN-CRS and DGA data enhancement and balancing. The trained data enhancement model is obtained by training the data enhancement model using the original data set. The data enhancement model is built based on CTGAN-CRS. The CRS module is introduced into the generator G of CTGAN to obtain CTGAN-CRS. Generate data using the CTGAN-CRS module ,use For the original data set Perform data enhancement and balancing to obtain a balanced data set .

[0033] Step 3: amplify, filter and transform the dimension of the balanced data set; Specifically, the balanced data set is expanded based on the full-type ratio construction, and the specific steps are as follows: Construct all types of combined features for the n features of the balanced data set and obtain Combined features; right Combined features are used to construct pairwise ratio features, and the Ratio feature; The number of features of the augmented dataset is + .

[0034] The amplified data set is screened based on the features of random forest to obtain the feature data set .

[0035] Finally, the obtained feature data set Perform dimension transformation, that is, One-dimensional features are processed as Two-dimensional features, get the data set .

[0036] Step 4: Input the balanced training data set after feature amplification, screening and dimension transformation into the fault diagnosis model for training to obtain a trained fault diagnosis model; input the test set after feature amplification, screening and dimension transformation into the trained fault diagnosis model to output the fault diagnosis result; The trained fault diagnosis model is obtained by training the fault diagnosis model based on CNN. The set is divided into training set and test set in proportion, a CNN-based fault diagnosis model is built and trained, and the trained CNN model is used for online diagnosis.

[0037] In one embodiment of the present invention, a transformer fault diagnosis method based on a data enhancement model is provided. Figure 2 As shown, including: (1) Data enhancement model and balance based on CTGAN-CRS; This section proposes a data augmentation method based on the Conditional Tabular GAN (CTGAN) combined with Cascade Reject Sampling (CRS), hereinafter referred to as the CTGAN-CRS method. The steps of this method are as follows: (1a) Collect transformer DGA data to form a data set Data:

[0038] In the above formula, x is the feature data, n is the number of features, m is the sample size of the DGA dataset, y is the fault label, and k is the fault label category; (1b) Based on CTGAN-CRS data enhancement model construction: CTGAN is a model based on conditional generative adversarial networks (Conditional GAN, CGAN). CGAN introduces the conditional vector c in the construction of the generator G and the discriminator D, and guides data generation by adding prior knowledge (such as data category labels). On this basis, CTGAN introduces tabular data metadata to distinguish between continuous and discrete features. The objective function of this model is:

[0039] In the above formula, 𝑧 is random noise that follows a Gaussian distribution; c is a table condition vector; 𝐺 represents the generator; 𝐷 represents the discriminator; 𝑃d(𝑥) represents the probability distribution of real data; 𝑃𝑧(z) represents the probability distribution of random noise 𝑧; 𝐷(𝑥,c) and 𝐺(𝑧,c) represent the vectors output by the discriminator D and the generator G after receiving the input in the brackets. is the generator objective function that is expected to be minimized; is the discriminator objective function of expectation maximization; in, The vector generated by the generator The vector obtained after the CRS module operation, the following introduces the rejection sampling (CRS) model based on the cascade integration strategy: Assume that the CTGAN-CRS module generates m×j vectors in batches during training. , convert the vector into a synthetic sample It is expressed as follows:

[0040] In the above formula, n is the number of features of generated data, and m is the number of generated data batches; Three basis rejection sampler models are constructed using the non-negative judgment method (NoNe), the IEC three-ratio method (IEC), and the Rogers four-ratio method (Rogers); the three basis rejection sampler models are cascaded to obtain the CRS module; Perform CRS operation and use the result as the marker vector flag to concatenate with the original data to obtain data According to the actual situation, there are 5 types of flag vectors, named , , , , ;

[0041] In the above formula, Represents the concatenation of two vectors by row; Count the number of occurrences of 5 different flags and convert the data Divided into five categories ; The data middle Proportion Sample usage The sample is processed without replacement as follows:

[0042] In the above formula, is the sample matrix with flag e ( etc. with similar meaning); is the replacement ratio, which is a random number in the range of (1,0); is the sample matrix number of rows; After the replacement is completed, Get the data ,Will Convert to Vector , and put it back into the CTGAN-CRS module to continue training, and obtain the CTGAN-CRS module; (1c) DGA data enhancement and balancing: Generate dataset using CTGAN-CRS module ,use For the original data set Perform data enhancement and balancing to obtain a balanced data set ; (1d) Quality assessment of DGA generated data: The KS Complement value is used to evaluate the similarity between the generated data and the original data, which is calculated based on the KS statistic D. If the KS Complement value is close to 1, it means that the distribution of the generated data is very close to that of the original data, that is, the quality of the generated data is higher.

[0043]

[0044]

[0045] In the above formula, is the KS statistic; is the cumulative distribution of the original data set; To generate the cumulative distribution of the data set; (2) DGA data feature amplification and screening based on GRRF; This step combines gas ratios and random forests (GRRF) to construct features, where the gas ratio method enriches data features and the random forests screens important features.

[0046] (2a) Feature amplification based on all-type gas ratios: Get the dataset n features of , construct all types of combined features, and obtain Combination features; The features are constructed by pairwise ratio feature, and the ratio features; a total of features indivual;

[0047]

[0048]

[0049] In the above formula, C(n,k) represents the number of combinations of k features selected from n different features.

[0050] (2b) Feature screening based on random forest: Considering the increase in the number of features, the random forest algorithm is selected to evaluate the feature importance, sort the features according to their importance, and select the features with the highest importance and non-zero value. Features form the optimal feature dataset ;

[0051] In the above formula, k is a The largest integer whose importance is not 0; (2c) Feature dimension transformation: Use a balanced dataset , and the dimension is The dataset is reconstructed to obtain a dimension of The dataset is the sample One-dimensional features are processed as Two-dimensional features, the data set ; (3) Fault diagnosis based on CNN model; (3a) Dataset division: Using the Dataset ; Divide the data set proportionally to obtain an internal balanced training set , test set ; (3b) Construction and training of fault diagnosis model based on CNN: CNN model input balanced training set , the input data dimension is (n, n); the CNN model contains 3 convolutional layers, 3 maximum pooling layers, and 3 fully connected layers, and the output vector dimension is (1, k), and the value of this vector represents the probability of k types of faults. During the training process, the model updates the weights of neurons in different layers through error back propagation and gradient descent according to the given batch size and learning rate, using cross entropy as the loss function, until the stopping condition is met and the model completes the training.

[0052] (3c) Online diagnosis using the trained CNN model: The test set Input the trained CNN model, and the model outputs the fault diagnosis results of the test set ;use Evaluate model performance, mainly including accuracy (Acc), recall (Recall), and F1 score.

[0053] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as systems, methods or program products. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: complete hardware implementation, complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which may be collectively referred to herein as "circuits", "modules" or "platforms".

[0054] In yet another embodiment of the present invention, a transformer fault diagnosis system based on a data enhancement model is provided, comprising an acquisition module, a generation module, a data set processing module, and a fault diagnosis module, wherein: Acquisition module: used to collect transformer DGA data to form the original data set; Generation module: used to input the original data set into the trained data enhancement model to obtain the generated data set, and use the generated data set to perform data enhancement and balance on the original data set to obtain a balanced data set; Data processing module: used to amplify, filter and transform the dimension of the balanced data set; Fault diagnosis module: used to input the balanced data set after amplification, screening and dimension transformation into the trained fault diagnosis model and output the fault diagnosis results; The trained data enhancement model is obtained by training the data enhancement model using the original data set, and the data enhancement model is constructed based on CTGAN-CRS.

[0055] A terminal device provided in one embodiment of the present invention comprises: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of the modules / units in the above-mentioned device embodiments are implemented.

[0056] The computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to accomplish the present invention.

[0057] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0058] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0059] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0060] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by the processor, the steps of the above-mentioned various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0061] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A transformer fault diagnosis method based on a data enhancement model, characterized in that: The following steps are involved: Collect transformer DGA data to form the original data set; The original data set is input into the trained data enhancement model to obtain a generated data set, and the generated data set is used to perform data enhancement and balance on the original data set to obtain a balanced data set; Based on all-type gas ratios and random forest algorithm, the balanced data set is feature expanded, screened, and dimensionally transformed; The balanced training data set after feature amplification, screening and dimension transformation is input into the fault diagnosis model for training to obtain the trained fault diagnosis model. The test set after feature amplification, screening and dimension transformation is input into the trained fault diagnosis model to output the fault diagnosis results: The trained data enhancement model is obtained by training the data enhancement model using the original data set, and the data enhancement model is constructed based on CTGAN-CRS.

2. A transformer fault diagnosis method based on a data enhancement model according to claim 1, characterized in that: The specific steps of constructing the data enhancement model are: The CRS module is introduced into the generator G of CTGAN to obtain CTGAN-CRS; The original data set is input into CTGAN-CRS for training to obtain a data augmentation model.

3. A transformer fault diagnosis method based on a data enhancement model according to claim 2, characterized in that: The CRS module is obtained by cascading integration of three basis rejection sampler models, and the three basis rejection sampler models are constructed using non-negative judgment method, IEC three-ratio method and Rogers four-ratio method respectively.

4. A transformer fault diagnosis method based on a data enhancement model according to claim 1, characterized in that: Before the balanced dataset is amplified, screened, and dimensionally transformed, the KS Complement value is used to evaluate the similarity between the generated dataset and the original dataset; The calculation formula of the KS Complement value is: Where D is the KS statistic, is the cumulative distribution of the original data set, To generate the cumulative distribution of the dataset.

5. The transformer fault diagnosis method based on data enhancement model according to claim 1 is characterized in that: The steps of amplifying the balanced data set are: Construct all types of combined features for the n features of the balanced data set and obtain Combined features; right Combined features are used to construct pairwise ratio features, and the Ratio feature; The number of features of the augmented dataset is + .

6. A transformer fault diagnosis method based on a data enhancement model according to claim 1, characterized in that: The object of the screening is the data set after the balanced data set is expanded, and the random forest algorithm is selected to evaluate the feature importance, and the features are sorted according to the importance, and the features with the highest importance and non-zero value are selected. Features form the optimal feature dataset .

7. The transformer fault diagnosis method based on data enhancement model according to claim 1 is characterized in that: The trained fault diagnosis model is obtained by training a fault diagnosis model based on CNN.

8. A transformer fault diagnosis system based on a data enhancement model, characterized in that: It includes acquisition module, generation module, data set processing module and fault diagnosis module, among which: Acquisition module: used to collect transformer DGA data to form the original data set; Generation module: used to input the original data set into the trained data enhancement model to obtain the generated data set, and use the generated data set to perform data enhancement and balance on the original data set to obtain a balanced data set; Data processing module: amplify, filter and transform the dimension of the balanced data set based on all types of gas ratios and random forest algorithm; Fault diagnosis module: used to input the balanced training data set after feature amplification, screening and dimension transformation into the fault diagnosis model for training, to obtain the trained fault diagnosis model, input the test set after feature amplification, screening and dimension transformation into the trained fault diagnosis model, and output the fault diagnosis result; The trained data enhancement model is obtained by training the data enhancement model using the original data set, and the data enhancement model is constructed based on CTGAN-CRS.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Citation Information

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