Transformer state evaluation method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering

Abstract

The invention discloses a transformer state evaluation method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering, and the method comprises the steps: enabling historical monitoring data of a transformer to generate a multi-dimensional reference vector according to a to-be-evaluated transformer state evaluation monitoring index; mapping the multi-dimensional reference vector to a high-dimensional space for dimension reduction through kernel principal component analysis and a kernel function; the data dimension is reduced, feature extraction is completed, and transformer state evaluation monitoring principal component indexes are determined; preprocessing the transformer state evaluation monitoring principal component index data; comprising extraction of labeled sample data and normalization processing of the data; carrying out improved semi-supervised fuzzy C-means clustering on the preprocessed sample data; and carrying out validity and accuracy analysis on the state evaluation result. According to the method, the problem that data information mining of a current transformer state evaluation model is not deep enough is solved, transformer state evaluation can be carried out objectively, accurately and efficiently, and a decision basis is provided for state maintenance of the transformer.

Description

Technical Field

[0001] The invention belongs to the technical field of transformer state assessment, and relates to a transformer state assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering. Background Art

[0002] As the installed capacity and voltage level of the power system continue to increase, higher requirements are placed on the safe, economical and reliable operation of power transmission and transformation equipment. As an important distribution and transmission equipment in the power system, once a power transformer fails, it will seriously affect the normal operation of the power system, causing serious accidents such as large-scale load loss, and bring huge economic losses. At present, the maintenance method of transformers is mainly a combination of regular maintenance and post-maintenance, without considering the real-time health status of the transformer, which is very likely to cause problems of "over-maintenance" and "under-maintenance". With the development and progress of monitoring technologies such as sensors, condition monitoring-based maintenance technology has gradually emerged. This method can greatly reduce the waste of manpower and material resources and the risk of failure caused by improper maintenance. As a necessary support for the formulation of condition maintenance strategies, transformer condition assessment is an important means to judge the operating status and discover safety hazards.

[0003] The transformer mechanism is complex and has many state quantities. There are many state assessment indicators used to characterize the transformer state. The correlation between the indicators leads to information duplication and redundancy, which affects the accuracy of the state assessment. Therefore, it is necessary to extract useful feature information from a large amount of monitoring data and select the most relevant features for state assessment. On the other hand, a small number of state assessment result reports will be generated during the production, delivery, testing, maintenance, and operation of the transformer. At present, the data-driven transformer state assessment method fails to apply this type of prior information to the state assessment model. As a result, the current assessment method has poor accuracy and low reliability, resulting in unreasonable transformer state assessment and poor engineering application. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a transformer state assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering, so as to provide accurate transformer state assessment results for power transmission and transformation equipment operation and maintenance personnel.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a transformer state assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering, including the following process: Step 1: Generate a multi-dimensional reference vector from the historical monitoring data of the transformer according to the transformer condition evaluation monitoring index to be evaluated; Step 2: Use kernel principal component analysis to map the multidimensional reference vector to a high-dimensional space through a kernel function, and apply principal component analysis to reduce the dimension; reduce the data dimension, complete feature extraction, retain the vectors with a cumulative contribution rate of more than 90% as the main component, and determine the main component indicators for transformer condition evaluation monitoring; Step 3: Preprocess the main component index data of transformer condition evaluation monitoring, including sample data extraction with labels and data normalization. Step 4: Perform improved semi-supervised fuzzy C-means clustering on the preprocessed sample data to obtain the membership set and cluster center of the set number of clusters, and determine the state classification of each cluster based on the label information; Step five: Analyze the effectiveness and accuracy of the status assessment results.

[0006] In step 1, the multidimensional reference vectors are: oil breakdown voltage, water content, acid value, oil color, oil quality, interfacial tension, TDCG, CO 2 / CO indicator data.

[0007] In step 2, The multidimensional reference vector is mapped to a high-dimensional space through a kernel function, and the principal component analysis method is used for dimensionality reduction; if the original index sample is x={x ij} m*n , where m represents the dimension, x i Represents the i-th sample, the original sample x i In the feature space F, there is f(x k ) features; let the mapping data f(x i ) has a mean of zero. In the feature space F, the sample covariance matrix is:

[0008] The kernel variance matrix K of m·m dimension is expressed as:

[0009] Then we have:

[0010] In formula (3), mλ is the eigenvalue of K, α=[α 1 ,α 2 ,...,α m ] T is the corresponding eigenvector; To ensure that the input data f(x i ) has a mean of zero, and K needs to be corrected as follows:

[0011] I mrepresents a matrix of order m with a value of 1. The eigenvalue λ of K′ is calculated by equation (2): i and the eigenvector p i Then, calculate the eigenvalue λ i The cumulative contribution of k ; Set the threshold ε, if T k ≥ε, then k sequences are selected as the main elements, and the cumulative contribution rate T k for:

[0012] The main component indicators of transformer condition evaluation and monitoring are obtained after dimensionality reduction.

[0013] In step 3, the main component index data of transformer condition evaluation monitoring is preprocessed; in order to eliminate the influence of different dimensions, each index data is normalized according to formula (6):

[0014] The normalized data range is [0,1], where min(x i )、max(x i ) respectively find the minimum and maximum values ​​of the sample data; Classify the sample data with state evaluation information and without state evaluation information, u ij (L) indicates a label, u ij (U) indicates no label.

[0015] In step 4, the preprocessed sample data is subjected to improved semi-supervised fuzzy C-means clustering. The specific process is as follows: Step SA1, input stage; a transformer index data object set X to be clustered and a transformer index data constraint set S with label information; Step SA2, initialization phase; set the number of clusters c, adjust the balance index α of the ratio of unlabeled information to labeled information, calculate the binary vector b=[bj] and the initial membership matrix F=[fij] of labeled information based on the labeled information; Step SA3, optimization iteration phase; calculate the distance between all labeled and unlabeled sample points and the cluster center; Step SA4, calculate the new membership matrix U by formula (7);

[0016] Step SA5, calculate the new cluster center V by formula (8);

[0017] Step SA6: When the following judgment condition J(t+1)-J(t)<ε is met or the number of iterations t exceeds the maximum number of iterations M, the algorithm stops; otherwise, return to step SA2; the objective function J is expressed by formula (9);

[0018] Step SA7, output stage; when the algorithm terminates, the iteratively optimized membership partition matrix U' and the class center V' are output.

[0019] In step five, the effectiveness and accuracy of the status assessment results are analyzed, and K-means, FCM, SFCM and the proposed method are used for testing and comparison.

[0020] The main beneficial effects of the present invention are: According to the dimension of the multidimensional vector of transformer condition evaluation indicators, kernel principal component analysis is introduced to obtain the main reference vector, which simplifies the input of parameters and avoids the redundancy and repetition of evaluation indicators.

[0021] By introducing a transformer index data set with state label information into the improved semi-supervised fuzzy C-means clustering model and adjusting the proportion of supervised information, the prior information is fully and effectively utilized, and the accuracy of the clustering model is improved. The present invention overcomes the problem of less prior information on transformer status and lack of application, making the transformer status assessment result more accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] Figure 1 It is a flow chart of the present invention.

[0024] Figure 2 The flowchart of semi-supervised fuzzy C-means clustering is improved for the present invention.

[0025] Figure 3 This is a diagram of the kernel principal component analysis results of the present invention.

[0026] Figure 4 This is the clustering result diagram of the transformer condition assessment model of the present invention. DETAILED DESCRIPTION

[0027] like Figure 1~Figure 4 In this paper, a transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering is proposed. Embodiment 1, as Figure 1~Figure 2 ; Step 1: Generate a multi-dimensional reference vector from the historical monitoring data of the transformer according to the transformer condition evaluation monitoring index to be evaluated; Step 2: Use kernel principal component analysis to map the multidimensional reference vector to a high-dimensional space through a kernel function, and apply principal component analysis to reduce the dimension; reduce the data dimension, complete feature extraction, retain the vectors with a cumulative contribution rate of more than 90% as the main component, and determine the main component indicators for transformer condition evaluation monitoring; Step 3: Preprocess the main component index data of transformer condition evaluation monitoring, including sample data extraction with labels and data normalization. Step 4: Perform improved semi-supervised fuzzy C-means clustering on the preprocessed sample data to obtain the membership set and cluster center of the set number of clusters, and determine the state classification of each cluster based on the label information; Step five: Analyze the effectiveness and accuracy of the status assessment results.

[0028] In the preferred solution, in step 1, the multidimensional reference vectors are: oil breakdown voltage, trace water content, acid value, oil color, oil quality, interfacial tension, TDCG, CO 2 / CO indicator data.

[0029] In a preferred embodiment, in step 2, The multidimensional reference vector is mapped to a high-dimensional space through a kernel function, and the principal component analysis method is used for dimensionality reduction; if the original index sample is x={x ij} m*n , where m represents the dimension, x i Represents the i-th sample, the original sample x i In the feature space F, there is f(x k ) features; let the mapping data f(x i ) has a mean of zero. In the feature space F, the sample covariance matrix is:

[0030] The kernel variance matrix K of m·m dimension is expressed as:

[0031] Then we have:

[0032] In formula (3), mλ is the eigenvalue of K, α=[α 1 ,α 2 ,...,α m ] T is the corresponding eigenvector; To ensure that the input data f(x i ) has a mean of zero, and K needs to be corrected as follows:

[0033] I mrepresents a matrix of order m with a value of 1. The eigenvalue λ of K′ is calculated by equation (2): i and the eigenvector p i Then, calculate the eigenvalue λ i The cumulative contribution of k ; Set the threshold ε, if T k ≥ε, then k sequences are selected as the main elements, and the cumulative contribution rate T k for:

[0034] The main component indicators of transformer condition evaluation and monitoring are obtained after dimensionality reduction.

[0035] In the preferred solution, in step 3, the transformer status evaluation monitoring main component index data is preprocessed; in order to eliminate the influence of different dimensions, each index data is normalized according to formula (6):

[0036] The normalized data range is [0,1], where min(x i )、max(x i ) respectively find the minimum and maximum values ​​of the sample data; Classify the sample data with state evaluation information and without state evaluation information, u ij (L) indicates a label, u ij (U) indicates no label.

[0037] In the preferred solution, in step 4, the preprocessed sample data is subjected to improved semi-supervised fuzzy C-means clustering, and the specific process is as follows: Step SA1, input stage; a transformer index data object set X to be clustered and a transformer index data constraint set S with label information; Step SA2, initialization phase; set the number of clusters c, adjust the balance index α of the ratio of unlabeled information to labeled information, calculate the binary vector b=[bj] and the initial membership matrix F=[fij] of labeled information based on the labeled information; Step SA3, optimization iteration phase; calculate the distance between all labeled and unlabeled sample points and the cluster center; Step SA4, calculate the new membership matrix U by formula (7);

[0038] Step SA5, calculate the new cluster center V by formula (8);

[0039] Step SA6: When the following judgment condition J(t+1)-J(t)<ε is met or the number of iterations t exceeds the maximum number of iterations M, the algorithm stops; otherwise, return to step SA2; the objective function J is expressed by formula (9);

[0040] Step SA7, output stage; when the algorithm terminates, the iteratively optimized membership partition matrix U' and the class center V' are output.

[0041] In the preferred solution, in step five, the effectiveness and accuracy of the state assessment results are analyzed, and K-means, FCM, SFCM and the method of this paper are used for testing and comparison.

[0042] Embodiment 2, In order to verify the accuracy of the state assessment model, the Rand index (RI) is used as the evaluation index. The larger the RI, the more consistent the clustering results are with the true results. Its expression is:

[0043] In the formula, a represents the number of sample pairs that belong to the same cluster in both the predicted results and the true labels, and b represents the number of sample pairs that do not belong to the same cluster in both the predicted results and the true labels. 500 groups of monitoring data generated by 32 500kV oil-immersed transformers in a power station were collected for the combination number, of which 30 groups of data had corresponding actual status classification information. The typical 8 types of status evaluation index data were sorted out as shown in the following table.

[0044]

[0045] Performing kernel principal component analysis on the data in the above table, we can obtain the cumulative contribution rate of each indicator eigenvalue as follows: Figure 3 The cumulative contribution rate of the first five indicator eigenvalues ​​in the transformer data set has reached 91%, so five types of state indicator vectors are taken: TDCG, oil breakdown voltage, micro-water, interfacial tension, CO 2 / CO is used as the main component indicator.

[0046] After the principal component data is normalized, the data sets of 500 groups of state indicators and 30 groups of state indicator data sets with label information are input into the improved semi-supervised fuzzy C-means clustering model. The number of clusters is set to 4, the maximum number of iterations M = 100, and the balance factor α is improved during the model training process. The clustering results are shown in Figure 2. Figure 4 shown. The state assessment results of this method are compared with those of K-means, FCM, and SFCM methods. The results are shown in the following table:

[0047] As can be seen from the table, the evaluation results of the improved semi-supervised fuzzy C-means clustering state evaluation model proposed in this paper are optimal in accuracy, number of iterations, and running time compared with the evaluation results of the K-means, FCM, and SFCM methods, which proves the effectiveness of the method proposed in this invention.

[0048] The above-mentioned embodiments are only preferred technical solutions of the present invention and should not be regarded as limitations of the present invention. The embodiments and features in the embodiments of the present application can be arbitrarily combined with each other without conflict. The protection scope of the present invention shall be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering, characterized in that: The process includes: Step 1: Generate a multi-dimensional reference vector from the historical monitoring data of the transformer according to the transformer condition evaluation monitoring index to be evaluated; Step 2: Use kernel principal component analysis to map the multidimensional reference vector to a high-dimensional space through a kernel function, and apply principal component analysis to reduce the dimension; reduce the data dimension, complete feature extraction, retain the vectors with a cumulative contribution rate of more than 90% as the main component, and determine the main component indicators for transformer condition evaluation monitoring; Step 3: preprocessing the transformer status evaluation monitoring main component index data; Including labeled sample data extraction and data normalization; Step 4: Perform improved semi-supervised fuzzy C-means clustering on the preprocessed sample data to obtain the membership set and cluster center of the set number of clusters, and determine the state classification of each cluster based on the label information; Step five: Analyze the effectiveness and accuracy of the status assessment results.

2. The transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering according to claim 1 is characterized in that: In step 1, the multidimensional reference vector is: indicator data of oil breakdown voltage, trace water content, acid value, oil color, oil quality, interfacial tension, TDCG, and CO2 / CO.

3. The transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering according to claim 1 is characterized in that: In step 2, The multidimensional reference vector is mapped to a high-dimensional space through a kernel function, and the principal component analysis method is used for dimensionality reduction; if the original index sample is x={x ij } m*n , where m represents the dimension, x i Represents the i-th sample, the original sample x i In the feature space F, there is f(x k ) features; let the mapping data f(x i ) has a mean of zero. In the feature space F, the sample covariance matrix is: The kernel variance matrix K of m·m dimension is expressed as: Then we have: In formula (3), mλ is the eigenvalue of K, α=[α1,α2,...,α m ] T is the corresponding eigenvector; To ensure that the input data f(x i ) has a mean of zero, and K needs to be corrected as follows: I m represents a matrix of order m with a value of 1. The eigenvalue λ of K′ is calculated by equation (2): i and the eigenvector p i Then, calculate the eigenvalue λ i The cumulative contribution of k ; Set the threshold ε, if T k ≥ε, then k sequences are selected as the main elements, and the cumulative contribution rate T k for: The main component indicators of transformer condition evaluation and monitoring are obtained after dimensionality reduction.

4. The transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering according to claim 1 is characterized in that: exist In step 3, the main component index data of transformer condition evaluation monitoring is preprocessed; in order to eliminate the influence of different dimensions, each index data is normalized according to formula (6): The normalized data range is [0,1], where min(x i )、max(x i ) respectively find the minimum and maximum values ​​of the sample data; Classify the sample data with state evaluation information and without state evaluation information, u ij (L) indicates a label, u ij (U) indicates no label.

5. The transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering according to claim 1 is characterized in that: exist In step 4, the preprocessed sample data is subjected to improved semi-supervised fuzzy C-means clustering. The specific process is as follows: Step SA1, input stage; a transformer index data object set X to be clustered and a transformer index data constraint set S with label information; Step SA2, initialization phase; Set the number of clusters c, adjust the balance index α of the ratio of unlabeled information to labeled information, and calculate the binary vector b=[bj] and the initial membership matrix F=[fij] of labeled information based on the labeled information; Step SA3, optimization iteration phase; calculate the distance between all labeled and unlabeled sample points and the cluster center; Step SA4, calculate the new membership matrix U by formula (7); Step SA5, calculate the new cluster center V by formula (8); Step SA6: When the following judgment condition J(t+1)-J(t)<ε is met or the number of iterations t exceeds the maximum number of iterations M, the algorithm stops; otherwise, return to step SA2; The objective function J is expressed by formula (9); Step SA7, output stage; when the algorithm terminates, the iteratively optimized membership partition matrix U' and the class center V' are output.

6. The transformer condition assessment method based on kernel principal component analysis and improved semi-supervised fuzzy C-means clustering according to claim 1 is characterized by: exist In step five, the effectiveness and accuracy of the status assessment results are analyzed, and K-means, FCM, SFCM and the method proposed in this paper are used for testing and comparison.

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