CN103198175A - Transformer fault diagnosis method based on fuzzy cluster - Google Patents

Abstract

The transformer fault diagnosis method based on fuzzy clustering disclosed by the present invention is implemented according to the following steps: 1) establish the original data matrix according to the online monitoring data; 2) standardize the data in the original data matrix to obtain the fuzzy matrix; 3) establish the fuzzy matrix Similarity matrix; 4) Use the square method to calculate the transitive closure matrix R' of the fuzzy similarity matrix R, that is, the fuzzy equivalent matrix t(R)=R'; 5) According to the lower triangle of t(R), the t(R ) are arranged from large to small; 6) The classification threshold λ is taken out from large to small, and when the data in the fuzzy equivalent matrix t(R) is greater than the selected λ, the corresponding fuzzy equivalent matrix t(R) ) is replaced with 1, otherwise replaced with 0, and the columns with the same data elements in each column of the fuzzy equivalent matrix t(R) are classified into one category; 7) According to λ, the dynamic clustering diagram is obtained, and it is determined by combining DGA technology Transformer fault type. The transformer fault testing method of the invention establishes a transformer fault diagnosis model based on fuzzy clustering, which can improve the accuracy of power transformer fault diagnosis.

Description

Transformer Fault Diagnosis Method Based on Fuzzy Clustering

technical field

The invention belongs to the technical field of transformer fault online monitoring, and in particular relates to a transformer fault diagnosis method based on fuzzy clustering.

Background technique

At the present stage of our country, with the rapid development of the national economy, the demand for electricity also shows a trend of rapid growth. Due to the continuous expansion of power installed capacity and grid scale, my country's power industry has entered a period of development of large power grids, large units, high voltage and high automation. In 2009, the State Grid Corporation proposed to build a smart grid with UHV as the backbone grid and coordinated development of grids at all levels, and the six links of the smart grid development strategy framework further highlighted the importance of power transmission and transformation. Ensuring the safe and reliable operation of intelligent substations is one of the main conditions for realizing the stable operation of the entire smart grid, and intelligent power transformers are an important part of intelligent substations, so timely and reliable diagnosis of potential faults of intelligent power transformers , which has far-reaching significance for ensuring the operation of the smart grid.

Dissolved gas analysis technology is the main means of transformer internal fault diagnosis, which provides a basis for indirect understanding of the general hidden dangers in the transformer; however, dissolved gas in oil is the result of many factors, so the type of power transformer insulation fault and dissolved gas in oil There is a certain degree of fuzziness and uncertainty in the relationship between the component contents. Introducing the analysis method of fuzzy clustering into transformer fault diagnosis is a relatively new research direction at this stage.

Contents of the invention

The object of the present invention is to provide a transformer fault diagnosis method based on fuzzy clustering, establish a transformer fault diagnosis model based on fuzzy clustering, and further improve the accuracy of power transformer fault diagnosis.

The technical scheme adopted in the present invention is, based on the transformer fault diagnosis method of fuzzy clustering, specifically implement according to the following steps:

Step 1. According to the online monitoring data, input the number n of objects to be classified and the number m of characteristic variables, and establish the original data matrix Y=(y _ij ) _n×m :

According to the online monitoring data, the domain of discourse U={y ₁ ,y ₂ ,y ₃ ...,y _n } is used as the object to be classified, and each object has m indicators to represent its performance, that is, Y _i ={y _i1 ,y _i2 ..., y _im }, (i=1,2,...n), establish the original data matrix, the original data matrix is Y=(y _ij ) _n×m ;

Step 2. Standardize the data in the original data matrix to [0, 1] to obtain the fuzzy matrix:

To standardize the i-th variable in the original data matrix Y=(y _ij ) _n×m established in step 1 is to convert y _ij into y′ _ij through an algorithm, specifically according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

in, $\stackrel{\&OverBar;}{{\mathrm{the\; y}}_i}=\frac{1}{m}{\mathrm{the\; y}}_{\mathrm{ij}},$ $T_i=\sqrt{\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{the\; y}}_{\mathrm{ij}}-\stackrel{\&OverBar;}{{\mathrm{the\; y}}_i})}^2}{m-1}};$

After the data in the original data matrix Y=(y _ij ) _n×m is transformed by standard deviation standardization, if there are individual Then the data should continue to be subjected to range normalization processing, and the range normalization processing is implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; ;</span>$

After the range normalization process, all y″ _ij ∈[0,1] are obtained, and there is no influence of the dimension matrix, that is, the fuzzy matrix Y=(y″ _ij ) _n×m is obtained;

Step 3, using one of the similarity coefficient method, the distance method or the closeness method to determine the similarity coefficient, and establish a fuzzy similarity matrix;

Step 4, calculate the transitive closure matrix R' that obtains fuzzy similarity matrix R through step 3 with square method, namely fuzzy equivalence matrix t(R)=R';

Step 5. Observe the lower triangle of the fuzzy equivalence matrix t(R) obtained in step 4, and then arrange the data in the fuzzy equivalence matrix t(R) from large to small. These data from large to small are the classification thresholds The value point of λ;

Step 6. Take the classification threshold λ in step 5 from large to small one by one. When the data in the fuzzy equivalent matrix t(R) is greater than the selected classification threshold λ, the corresponding fuzzy equivalent matrix t(R) The data in is replaced with 1, otherwise, replaced with 0, the final fuzzy equivalent matrix t(R) contains only two elements of 0 and 1; observe each column of the fuzzy equivalent matrix t(R), the columns with the same data elements Classify them into one category, and then classify them;

Step 7. According to the different classification thresholds λ in step 5, use MATLAB software programming simulation, and finally obtain the dynamic clustering diagram of the transformer fault diagnosis model based on fuzzy clustering, and then combine DGA technology to determine the type of transformer fault.

The present invention is also characterized in that,

The method of standardizing the original data matrix in step 2 can also use range standardization or maximum value standardization.

The processing method of extreme difference standardization in step 2 is specifically implemented according to the following algorithm:

The method of performing range standardization processing on the original data matrix obtained in step 1 is specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; .</span>$

The processing method of the maximum value standardization in step 2 is specifically implemented according to the following algorithm: the maximum value standardization process is performed on the original data matrix obtained in step 1, specifically according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$

Wherein, M _j =max(y _1j ,y _2j . . . y _nj ).

The similarity coefficient method in step 3 includes the following two algorithms:

The first one, the angle cosine method, is specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The second method, the correlation coefficient method, is specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; |</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The distance method in step 3 includes the following three algorithms:

The first distance method, Hamming distance:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$

The second distance method, Euclid distance:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

The third distance method, Chebyshev distance:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; .</span>$

The maximum value standardization processing method is specifically implemented according to the following algorithm: the maximum value standardization process is performed on the original data matrix obtained in step 1, specifically according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$

Wherein, M _j =max(y _1j ,y _2j . . . y _nj ).

The proximity method in step 3 includes the following three algorithms:

The first closeness method, the large minimum method:

The second closeness method, the geometric mean minimum method:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; ^</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\sqrt{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The third closeness method, arithmetic mean minimum method:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; ^</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The beneficial effects of the present invention are:

(1) The transformer fault diagnosis method based on fuzzy clustering of the present invention is a new type of transformer fault diagnosis and analysis method proposed on the basis of the previously studied DGA analysis method. This method can perform fault diagnosis based on a large number of transformer monitoring data. Classification, which helps to quickly diagnose the fault type of the transformer.

(2) The data of the transformer fault diagnosis method based on fuzzy clustering of the present invention comes from the on-site gas data monitored in real time by the transformer online monitoring system, which can not only monitor the hydrogen, methane, ethane, ethylene, acetylene, The information of carbon monoxide and carbon dioxide can also predict the failure of transformers according to the sudden change of certain gases.

(3) The transformer fault diagnosis method based on fuzzy clustering of the present invention is based on the fuzzy clustering analysis method of the transitive closure method after transforming the data, and then using the square method to obtain the transitive closure matrix of the fuzzy similarity matrix, namely Fuzzy equivalent matrix, combined with DGA technology and cluster analysis, on this basis, a transformer fault diagnosis model based on fuzzy clustering is established. This model can further improve the accuracy of power transformer fault diagnosis, and has important theoretical research and practical application value.

Description of drawings

Fig. 1 is the flowchart of the transformer fault diagnosis method based on fuzzy clustering of the present invention;

Fig. 2 is a dynamic cluster diagram drawn by using the transformer fault diagnosis method based on fuzzy clustering of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Transformer fault testing method based on fuzzy clustering of the present invention, its technological process as shown in Figure 1, concrete algorithm is implemented according to the following steps:

Step 1. According to the online monitoring data, input the number n of objects to be classified and the number m of characteristic variables, and establish the original data matrix Y=(y _ij ) _n×m :

According to the online monitoring data, the domain of discourse U={y ₁ ,y ₂ ,y ₃ ...,y _n } is used as the object to be classified, and each object has m indicators to represent its performance, that is, Y _i ={y _i1 ,y _i2 ..., y _im }, (i=1,2,...n), establish the original data matrix, the original data matrix is Y=(y _ij ) _n×m ;

Step 2. Standardize the data in the original data matrix to [0, 1] to obtain the fuzzy matrix:

In practical problems, the dimensions of different data are generally not uniform. In order to compare data of different dimensions, it is usually necessary to standardize the data, that is, to make the data in the original data matrix meet the requirements of According to the requirements of fuzzy clustering, standardize the data in the original data matrix Y=(y _ij ) _n×m established in step 1 according to the following algorithms:

The method of first kind of standardization processing is standard deviation standardization processing, promptly carries out standard deviation standardization processing to the data in the original data matrix Y=(y _ij ) _n×m that step 1 establishes, obtains fuzzy matrix, concrete method is as follows:

To standardize the i-th variable in the original data matrix Y=(y _ij ) _n×m established in step 1 is to convert y _ij into y′ _ij through an algorithm, specifically according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

in, $\stackrel{\&OverBar;}{{\mathrm{the\; y}}_i}=\frac{1}{m}{\mathrm{the\; y}}_{\mathrm{ij}},$ $T_i=\sqrt{\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{the\; y}}_{\mathrm{ij}}-\stackrel{\&OverBar;}{{\mathrm{the\; y}}_i})}^2}{m-1}};$

则要对这些数据继续进行极差正规化处理，极差正规化处理按照以下算法实施：After the data in the original data matrix Y=(y _ij ) _n×m is transformed by standard deviation standardization, if there are individual

Then the data should continue to be subjected to range normalization processing, and the range normalization processing is implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; ;</span>$

After the range normalization process, all y″ _ij ∈[0,1] are obtained, and there is no influence of the dimension matrix, that is, the fuzzy matrix Y=(y″ _ij ) _n×m is obtained;

The second normalization method is the range standardization process, that is, the range standardization process is performed on the data in the original data matrix Y=(y _ij ) _n×m obtained in step 1 to obtain the fuzzy matrix Y=(y′ _ij ) _n×m , specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; ;</span>$

The third standardization method is the maximum value standardization process, that is, the data in the original data matrix Y=(y _ij ) _n×m obtained in step 1 is subjected to the maximum value standardization process to obtain the fuzzy matrix Y=(y′ _ij ) _n×m , specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>$

Among them, M _j =max(y _1j ,y _2j ... y _nj );

Step 3, determine the similarity coefficient and establish the fuzzy similarity matrix:

According to the original data matrix Y=(y _ij ) _n×m established in step 1, the degree of similarity between y _i and y _j is r _ij =R(y _i , y _j ), which is called the similarity coefficient, and the blur is established according to the similarity coefficient Similarity matrix, the methods used to determine the similarity coefficient are: similarity coefficient method, distance method or closeness method;

The similarity coefficient method is used to determine the similarity coefficient and establish a fuzzy similarity matrix. The similarity coefficient method mainly includes the following two algorithms:

The first method, the included angle cosine method, is specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The second method, the correlation coefficient method, is specifically implemented according to the following algorithm:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; |</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The distance method is used to determine the similarity coefficient and establish the fuzzy similarity matrix. The distance method mainly includes the following three algorithms:

Generally, take r _ij =1-α(d(y _i ,y _j )) ^β , where α, β are properly selected parameters, so that 0≤r _ij ≤1, and there are three commonly used distance methods:

The first distance method, Hamming distance, is implemented according to the following algorithm:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$

The second distance method, Euclid distance, is implemented according to the following algorithm:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

The third distance method, Chebyshev distance, is implemented according to the following algorithm:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$

The closeness method is used to determine the similarity coefficient and establish the fuzzy similarity matrix, mainly including the following three algorithms:

The first closeness method, the large minimum method:

The second closeness method, the geometric mean minimum method:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; ^</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\sqrt{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The third closeness method, arithmetic mean minimum method:

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; ^</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; jl</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Among the three algorithms, the closeness method is preferred to establish the fuzzy similarity matrix of the fuzzy matrix;

Step 4, calculate the transitive closure matrix R' that obtains fuzzy similarity matrix R through step 3 with square method, namely fuzzy equivalence matrix t(R)=R';

Step 5. Observe the lower triangle of the fuzzy equivalence matrix t(R) obtained in step 4, and then arrange the data in the fuzzy equivalence matrix t(R) from large to small. These data from large to small are the classification thresholds The value point of λ;

Step 6. Take the classification threshold λ in step 5 from large to small one by one. When the data in the fuzzy equivalent matrix t(R) is greater than the selected classification threshold λ, the corresponding fuzzy equivalent matrix t(R) The data in is replaced with 1, otherwise replaced with 0, the final fuzzy equivalence matrix t(R) only contains two elements of 0 and 1; observe each column of the fuzzy equivalence matrix t(R), the columns with the same data elements Classify them into one category, and then classify them;

Step 7. According to the different classification thresholds λ in step 5, use MATLAB software programming simulation to finally obtain the dynamic cluster diagram of the transformer fault diagnosis model based on fuzzy clustering, and then determine the type of transformer fault by combining DGA technology.

Example

The original data matrix is shown in Table 1 below:

Table 1 Raw data

The seven groups of data in Table 1 were standardized using the range normalization method, and the data after the unified dimensions are shown in Table 2:

Table 2 Data after normalization

1 2 3 4 5 6 7 H ₂ 0 0.0442 0.0284 0.3754 1 0.0315 0.5016 CH ₄ 0.0569 0.0569 0.0772 1 0.1992 0.0072 0 C ₂ H ₆ 0.1563 0.2031 0.0781 1 0 0.0781 0.0625 C ₂ H ₄ 0.0163 0.2061 0 1 0.1286 0 0.0143 C ₂ H ₂ 0 0.1077 0 0.0462 1 0 0.8308

When calculating the fuzzy relationship matrix r _ij , the closeness method is used, as shown in Table 3:

Table 3 fuzzy relationship matrix r _ij

The transitive closure matrix t(R) obtained by the square method is shown in Table 4.

Table 4 transitive closure matrix t(R)

Arrange the data in t(R) from small to large as follows:

0.7465<0.8828<0.9474<0.9557<0.9999

When λ=0.7465, we get

$\mathrm{<span\; class="notranslate">\; t</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{ccccccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)$

Y is divided into 2 classes: {1, 3, 6}, {2, 4, 5, 7}

By analogy, when λ=0.8828, Y is divided into 3 categories: {1, 3, 6}, {2}, {4, 5, 7};

When λ=0.9474, Y is divided into 4 categories: {1, 3, 6}, {2}, {4}, {5, 7};

When λ=0.9557, Y is divided into 4 categories: {1, 3, 6}, {2}, {4}, {5, 7};

When λ=0.9999, Y is divided into 5 categories: {1}, {2}, {3, 6}, {4}, {5}, {7};

The dynamic clustering diagram is shown in Figure 2;

Combined with DGA technology to determine the transformer fault type as shown in Table 5 below:

Claims (7)

1. The transformer fault diagnosis method based on fuzzy clustering is characterized by being implemented according to the following steps:

step 1, inputting the number n and the number m of characteristic variables of objects to be classified according to online monitoring data, and establishing an original data matrix Y (Y ═ Y)_ij)_n×m：

Discourse domain U is { y ═ y according to online monitoring data₁,y₂,y₃…,y_nAs objects to be classified, where each object has its performance represented by m indices, i.e. Y_i＝{y_i1,y_i2…,y_imAnd (i ═ 1,2, … n), establishing an original data matrix, wherein the original data matrix is Y ═ Y_ij)_n×m；

Step 2, standardizing the data in the original data matrix to be between [0, 1] to obtain a fuzzy matrix:

for the original data matrix Y established in step 1 ═ Y_ij)_n×mIs normalized by normalizing y_ijConversion to y 'by algorithm'_ijSpecifically, the conversion is performed according to the following algorithm:

$y_{\mathrm{ij}}^{\&prime;}=\frac{y_{\mathrm{ij}}-\stackrel{\&OverBar;}{y_i}}{T_i},(1\&le;i\&le;n,1\&le;j\&le;m);$

wherein, $\stackrel{\&OverBar;}{y_i}=\frac{1}{m}{y}_{\mathrm{ij}},$ $T_i=\sqrt{\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{ij}}-\stackrel{\&OverBar;}{y_i})}^2}{m-1}};$

the original data matrix Y is equal to (Y)_ij)_n×mAfter standard deviation normalization transformation of the data in (1), if any, the data in (1)

Then the data is subjected to a range normalization process, which is implemented according to the following algorithm:

$y_{\mathrm{ij}}^{\&prime;\&prime;}=\frac{y_{\mathrm{ij}}-\min \left\{y_{\mathrm{ij}}^{\&prime;}\right\}}{\max \left\{y_{\mathrm{ij}}^{\&prime;}\right\}-\min \left\{y_{\mathrm{ij}}^{\&prime;}\right\}};$

all y' obtained after range normalization_ij∈[0,1]And the fuzzy matrix Y ═ (Y ″) can be obtained without the influence of the dimensional matrix_ij)_n×m；

Step 3, determining a similarity coefficient by adopting one of a similarity coefficient method, a distance method or a proximity method, and establishing a fuzzy similarity matrix;

step 4, calculating a transfer closure matrix R 'of the fuzzy similar matrix R obtained in the step 3 by using a flat method, namely the fuzzy equivalent matrix t (R) is R';

step 5, observing the lower triangle of the fuzzy equivalent matrix t (R) obtained in the step 4, and then arranging the data in the fuzzy equivalent matrix t (R) from large to small, wherein the data from large to small are the value-taking points of the classification threshold lambda;

step 6, taking out the classification threshold value lambda in the step 5 from large to small one by one, and when the data in the fuzzy equivalent matrix t (R) is larger than the taken classification threshold value lambda, replacing the data in the corresponding fuzzy equivalent matrix t (R) with 1, otherwise, replacing the data with 0, and finally, only containing two elements of 0 and 1 in the fuzzy equivalent matrix t (R); observing each column of the fuzzy equivalent matrix t (R), classifying the columns with the same data elements into one class, and further classifying the columns;

and 7, according to the different classification threshold values lambda in the step 5, programming and simulating by using MATLAB software to finally obtain a dynamic cluster map of the transformer fault diagnosis model based on fuzzy clustering, and determining the fault type of the transformer by combining a DGA technology.

2. The transformer fault diagnosis method based on fuzzy clustering according to claim 1, wherein the method of normalizing the raw data matrix in step 2 further adopts range normalization or maximum normalization.

3. The transformer fault diagnosis method based on fuzzy clustering according to claim 2, wherein the range standardization processing method is specifically implemented according to the following algorithm:

the method for performing range standardization processing on the original data matrix obtained in the step 1 is implemented according to the following algorithm:

$y_{\mathrm{ij}}^{\&prime;}=\frac{y_{\mathrm{ij}}-\stackrel{\&OverBar;}{y_i}}{\max \left\{y_{\mathrm{ij}}\right\}-\min \left\{y_{\mathrm{ij}}\right\}}.$

4. the transformer fault diagnosis method based on fuzzy clustering according to claim 2, characterized in that the maximum value normalization processing method is specifically implemented according to the following algorithm: carrying out maximum value standardization processing on the original data matrix obtained in the step 1, and specifically implementing the maximum value standardization processing according to the following algorithm:

$y_{\mathrm{ij}}^{\&prime;}=\frac{y_{\mathrm{ij}}}{M_j},$

wherein M is_j＝max(y_1j,y_2j…y_nj)。

5. The transformer fault diagnosis method based on fuzzy clustering according to claim 1, wherein the similarity coefficient method in step 3 comprises the following two algorithms:

the first method, the cosine method of the included angle, is implemented according to the following algorithm:

$r_{\mathrm{ij}}=\frac{|\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_{\mathrm{il}}*y_{\mathrm{jl}}|}{\sqrt{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_{\mathrm{il}}^2*\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_{\mathrm{jl}}^2}},(i,j=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;n);$

the second kind, the correlation coefficient method is implemented according to the following algorithm:

$r_{\mathrm{ij}}=\frac{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}|y_{\mathrm{il}}-\stackrel{\&OverBar;}{y_i}|\&CenterDot;|y_{\mathrm{jl}}-\stackrel{\&OverBar;}{y_j}|}{\sqrt{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{il}}-\stackrel{\&OverBar;}{y_i})}^2}\&CenterDot;\sqrt{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{jl}}-\stackrel{\&OverBar;}{y_j})}^2}},(i,j=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,n).$

6. the transformer fault diagnosis method based on fuzzy clustering according to claim 1, wherein the distance method in step 3 comprises the following three algorithms:

first distance method, Hamming distance:

$d(y_i,y_j)=\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}|y_{\mathrm{il}}-y_{\mathrm{jl}}|;$

second distance method, euclidd distance:

$d(y_i,y_j)=\sqrt{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{il}}-y_{\mathrm{jl}})}^2};$

third distance method, Chebyshev distance:

$d(y_i,y_j)=\underset{1\&le;l\&le;n}{\max }|y_{\mathrm{il}}-y_{\mathrm{jl}}|.$

7. the transformer fault diagnosis method based on fuzzy clustering according to claim 1, wherein the closeness method in step 3 comprises the following three algorithms:

the first closeness method, the maximum-minimum method:

second closeness method, geometric mean minimization method:

$r_{\mathrm{ij}}=\frac{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}(y_{\mathrm{il}}^y_{\mathrm{jl}})}{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}\sqrt{y_{\mathrm{il}}\&CenterDot;y_{\mathrm{jl}}}},(i,j=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,n);$

the third closeness method, the number average minimum method:

$r_{\mathrm{ij}}=\frac{\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}(y_{\mathrm{il}}^y_{\mathrm{jl}})}{\frac{1}{2}\underset{l=1}{\overset{m}{\mathrm{\&Sigma;}}}(y_{\mathrm{il}}+y_{\mathrm{jl}})},(i,j=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,n).$

Images