A method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm

Abstract

The invention discloses a transformer winding loose fault feature extraction method based on chaos theory and an ephemeral optimization K-means algorithm. The method comprises the following steps: step 1: setting measuring points on a transformer box, obtaining vibration signals of each measuring point, and selecting a measuring point D with the largest vibration amplitude as the optimal measuring point; step 2: calculating the maximum Lyapunov exponent of the vibration signal collected by the measuring point D, and judging its chaotic characteristics; step 3: calculating the correlation dimension and Kolmogorov entropy of the vibration signal with chaotic characteristics as the chaotic characteristics of the transformer winding loose fault; step 4: reconstructing the vibration signal in phase space to obtain a phase space trajectory; step 5: optimizing the initial cluster centers of the K-means algorithm by using the ephemeral optimization algorithm, clustering the phase space trajectory, and finally calculating the sum of the cluster center moments and the radial vector offset of the obtained K cluster centers as the geometric characteristics of the transformer winding loose fault; and step 6: comparing the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding with reference values ​​to achieve accurate identification.

Description

Technical Field

[0001] The present invention belongs to the field of power equipment vibration signal analysis, and in particular relates to a transformer winding looseness fault feature extraction method based on chaos theory and an ephemeral optimized K-means algorithm. Background Art

[0002] As a key piece of power transmission and transformation equipment in power systems, the reliable operation of power transformers is crucial for the safe, economical, and stable operation of these systems. However, loosening and deformation of transformer windings due to external short circuits are common faults during transformer operation, posing a serious threat to the safe operation of the system. Therefore, it is necessary to study the fault characteristics associated with loose transformer windings to accurately identify them, which is crucial for reducing transformer accidents. In field testing, vibration signal analysis is widely used in transformer fault diagnosis because it does not require electrical connection to the transformer and is a non-destructive measurement and detection method. Currently, vibration signal feature analysis methods primarily use time-frequency analysis methods such as empirical mode decomposition (EMD), variational mode decomposition (VMD), and improved ensemble EMD and complementary lumped EMD methods to decompose the original nonlinear, non-stationary vibration signal into multiple stationary signals for analysis. However, these feature analysis methods often suffer from modal aliasing and endpoint effects during the time-frequency conversion process, resulting in partial loss of information in the original signal. Unlike time-frequency analysis, time series analysis based on chaos theory analyzes the chaotic properties of time-domain signals. This method, also known as chaotic time series analysis, exploits the chaotic properties of the original signal and has been increasingly applied to power equipment fault feature analysis in recent years. Summary of the Invention

[0003] Purpose of the Invention: Based on the chaotic properties and geometric morphology of the phase space trajectory of transformer vibration signals, this invention proposes a method for extracting transformer winding looseness fault features based on chaos theory and the Mayfly Optimization K-means algorithm. Based on the chaotic characteristics of the transformer vibration signal, chaotic features are calculated and extracted from the vibration signal with chaotic characteristics. Simultaneously, the Mayfly Optimization Algorithm (MOA) is used to optimize the initial cluster centers of the K-means algorithm, and geometric features are extracted from the K cluster centers of the resulting phase space trajectory. The extracted chaotic and geometric features described in this invention can not only separately identify the degree of transformer winding looseness faults, but can also be combined into a set of feature vectors to accurately represent the characteristics of the transformer winding looseness state.

[0004] Technical solution: To achieve the purpose of the present invention, the technical solution adopted by the present invention is: a transformer winding loose fault feature extraction method based on chaos theory and ephemeral optimized K-means algorithm, comprising the following steps:

[0005] Step 1: Set P measuring points on the transformer box in normal state, obtain the transformer vibration signal, and select the measuring point D with the largest vibration amplitude as the optimal measuring point;

[0006] Step 2: Calculate the maximum Lyapunov exponent of the vibration signal collected at measuring point D to determine its chaotic characteristics;

[0007] Step 3: Calculate the correlation dimension and Kolmogorov entropy of the vibration signal with chaotic characteristics as the chaotic characteristic reference value of the transformer winding loose fault;

[0008] Step 4: Reconstruct the phase space of the vibration signal to obtain the phase space trajectory;

[0009] Step 5: Use the Mayfly Optimization Algorithm to optimize the initial cluster centers of the K-means algorithm, then cluster the phase space trajectory, and finally calculate the sum of the cluster center moments and the radial offset of the obtained K cluster centers as the geometric feature reference values ​​of the transformer winding loosening fault;

[0010] Step 6: Compare the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding with the reference values ​​to accurately identify the fault.

[0011] Furthermore, in step 1, P measuring points are set on the transformer box in a normal state to obtain the transformer vibration signal, and the measuring point D with the largest vibration amplitude is selected as the optimal measuring point. The steps are as follows:

[0012] Step 1.1: Fix P piezoelectric accelerometers to the top of the transformer box through magnetic bases to obtain transformer surface vibration data;

[0013] Step 1.2: Measure the vibration signal of the transformer measurement point. According to the time domain signal diagram, select the measurement point D with the largest vibration amplitude as the optimal measurement point of the transformer.

[0014] Furthermore, in step 2, the maximum Lyapunov exponent of the vibration signal collected at measuring point D is calculated to determine its chaotic characteristics. The steps are as follows:

[0015] Step 2.1: For the vibration signal time series x1, x2, ..., x k ,…, embedding dimension m, time delay τ, then the reconstructed phase space

[0016] Y(t i )=(x(t i ), x(ti +τ),…,x(t i +(m-1)τ)),i=1,2,…,N (1)

[0017] The embedding dimension m and the delay time τ are determined as follows:

[0018] The correlation integral introduced into the time series is defined as

[0019]

[0020] Where: M = N-(m-1)τ; d ij =max||x i -x j ||; θ(x) is the switching function; r is the search radius.

[0021]

[0022] For a known time series {x i}, i = 1, 2, ..., N, divide it into τ non-overlapping subsets

[0023]

[0024] Define S(m, N, r, τ) for each subset as

[0025]

[0026] Defining the delta

[0027] ΔS(m, τ)=max{S(m, r j ,τ)}-min{S(m,r j ,τ)} (6)

[0028] Equation (6) describes the maximum deviation about the search radius r. The delay time τ can be obtained at the zero point of S(m, r, τ) and the first minimum value of ΔS(m, τ).

[0029] The statistical conclusions drawn by Brock et al. show that when 2≤m≤5, (s is the mean square error of the time series), when N ≥ 500, the asymptotic distribution (the limiting distribution when the sample size is sufficiently large) can be well approximated.

[0030] Based on this, take m = 2, 3, 4, 5, calculate

[0031]

[0032]

[0033]

[0034] From formula (7), we can calculate The first zero point of or calculated by formula (8) The smaller value of the delay time corresponding to the first minimum of is taken as the result of τ. S can be calculated by formula (9) cor The minimum value of τ corresponds to w As a time window, according to τ ω =(m-1)τ, the result of m can be calculated as

[0035] Step 2.2: Take the initial point Y(t0), and set the distance between it and the nearest neighbor point Y0(t0) as L0. Track the time evolution of these two points until the time t1, when the distance between them exceeds a certain value ε>0, L′0=|Y(t1)-Y0(t1)|>ε, and keep Y(t1) adjacent to another point Y1(t1), so that L′1=|Y(t1)-Y1(t1)|<ε, and the angle between them is as small as possible. Continue the above process until Y(t) reaches the end point N of the time series. At this time, the total number of iterations of the tracking evolution process is M, and the maximum Lyapunov exponent is

[0036]

[0037] Determine whether the maximum Lyapunov exponent of the vibration signal is greater than 0. If it is greater than 0, it proves that it has chaotic characteristics.

[0038] Furthermore, in step 3, the correlation dimension and Kolmogorov entropy of the vibration signal with chaotic characteristics are calculated as chaotic characteristic reference values ​​of the transformer winding loosening fault, and the method is as follows:

[0039] Step 3.1: Select the correlation dimension as the chaotic characteristic quantity to be calculated.

[0040] The correlation dimension calculation method is:

[0041] The point in the reconstructed phase space is

[0042] y j =(y j ,y j+τ ,…,y j+(m-1)τ ), 1≤j≤M (11)

[0043] The maximum component difference r between two points ij for

[0044]

[0045] Where: y ik 、yjk Respectively represent the kth component of two points in space.

[0046] Similar to formula (2), given a sufficiently small positive number r, define the correlation integral here

[0047]

[0048] Then the correlation dimension is

[0049]

[0050] Step 3.2: Select Kolmogorov entropy as the chaotic characteristic quantity to be calculated.

[0051] The Kolmogorov entropy calculation expression is:

[0052]

[0053] Furthermore, in step 4, the vibration signal is reconstructed in phase space to obtain the phase space trajectory. The steps are as follows:

[0054] Step 4.1: Generate phase space points according to the embedding dimension m and delay time τ calculated in step 2.1:

[0055]

[0056] Where: M = N-(m-1)τ.

[0057] Step 4.2: Construct the phase space trajectory in the coordinate system.

[0058] Furthermore, in step 5, the ephemeral optimization algorithm is used to optimize the initial cluster centers of the K-means algorithm, and then the phase space trajectory is clustered. Finally, the sum of the cluster center moments and the radial offset of the obtained K cluster centers are calculated as the geometric feature reference values ​​of the transformer winding loosening fault. The method is as follows:

[0059] Step 5.1: Treat each point in the phase space as a population of mayflies. Randomly divide the population into two groups: males and females. The position x of the male individual in n-dimensional space is i =(x1, x2, ..., x n ), flight speed v mi =(v m1 , v m2 ,…,v mn ); the position y of the female individual i =(y1, y2, ..., y n ), flight speed v fi =(v f1 , v f2 ,…,v fn).

[0060] Male individuals gather into groups and adjust the speed and arrival position of the next flight through equations (17) and (18).

[0061]

[0062] x′ mi =x mi +v′ mi (18)

[0063] In formula (17): p ibest =(p i1 , p i2 ,…,p in ) is the optimal position that male individual i passes through; g best =(g1, g2, ..., g n ) is the best position among all male individuals; a1 and a2 are positive attraction constants, which are used to measure the contribution of cognitive and social components, and are generally taken as 1 and 1.5 respectively; b is the visibility coefficient, which is used to limit the visibility of the individual to other individuals, and is generally taken as 2; r p =||p ibest -x mi ||、r g =||g best -x mi ||.

[0064] Specifically, the male individual j in the current best position updates its flight speed according to formula (4).

[0065] v′ mj =v mj +d*r (19)

[0066] Where: d is the dance coefficient, usually 5; r∈[-1, 1] is a random number.

[0067] Female individuals do not group together. They are sorted by fitness function value. The best female is paired with the best male, and the second best female is paired with the second best male. Each female moves towards the male mate with a better fitness function value than herself. If the male mate's fitness function value is weaker than hers, she will not be attracted, but will search and move on her own. The speed and position update formula is:

[0068]

[0069] Where: r mf =||x mi -x fi ||; f(·) is the fitness function; fl is the random walk coefficient, which is generally 1.

[0070] After pairing, mating produces two offspring

[0071]

[0072] Where: L is a random number in a specific range, usually (0, 1).

[0073] Then, the offspring are randomly divided into males and females. In order to keep the overall population size constant, if the offspring's fitness function value is better than that of the previous generation of the same sex, it will be replaced.

[0074] At this point, update p ibest and g best , and proceed to the next iteration until the maximum number of iterations is reached.

[0075] The overall clustering square error is

[0076]

[0077] Where: It is cluster C i The mean vector of ; ||·||2 is the Euclidean distance.

[0078] The fitness function is constructed as

[0079]

[0080] Based on the phase space trajectory of the transformer vibration signal, the MOA is used to search for the initial cluster center of the K-means algorithm in the spatial range near the phase space trajectory. The main steps are as follows:

[0081] (1) Initialize the number of mayflies N and the individual position x i , flight speed v i , the number of cluster centers K and p ibest and g best .

[0082] (2) Randomly divide the sexes of mayflies and determine the number of males and females to be N / 2.

[0083] (3) Calculate the fitness value using formula (23) and take the optimal value as the target position.

[0084] (4) The male updates his position before the female does.

[0085] (5) After pairing one by one according to the principle of optimization, each pair produces two offspring and replaces the inferior same-sex individuals of the previous generation.

[0086] (6) Repeat steps (2), (3), (4), and (5) until the maximum number of iterations is reached.

[0087] (7) The obtained optimal location solution is used as the initial cluster center of the K-means algorithm.

[0088] (8) Calculate the overall clustering square error E using formula (22).

[0089] Following the above steps, the number of cluster centers K is calculated from 1 to 20, and the curve of E changing with K is obtained. The K value when the degree of E decreases steadily is selected as the number of cluster centers of the phase space trajectory of the transformer vibration signal in this paper.

[0090] Step 5.2: Select the sum of cluster center moments as the geometric feature quantity to be calculated.

[0091] The central moment, that is, the distance from the vector point to the origin in the coordinate system, is called the central moment, and the calculation formula is:

[0092]

[0093] Where: M is the number of feature points.

[0094] Step 5.3: Select radial vector offset as the geometric characteristic quantity for calculation.

[0095] The radial offset is the distance of the point relative to the main diagonal, which describes the degree of closure of the phase space trajectory. The calculation formula is

[0096]

[0097] Where: M is the number of feature points; θ is the unit vector in the main diagonal direction.

[0098] Furthermore, in step 6, the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding are compared with the reference values ​​to achieve accurate fault identification, as follows:

[0099] Step 6.1: Compare the chaotic features of the vibration signals of the transformer windings in different loose states with the chaotic feature reference values ​​extracted above.

[0100] Step 6.2: Compare the geometric features of the vibration signals of the transformer windings in different loose states with the geometric feature reference values ​​extracted above.

[0101] Step 6.3: Combine the chaotic features with the geometric features to construct a new feature vector, which can accurately identify the loose transformer winding fault.

[0102] Beneficial Effects: Compared with existing technologies, the technical solution of this invention has the following beneficial effects: Based on the analysis of the chaotic characteristics of transformer vibration signals using chaos theory and the extraction of chaotic features, this invention further analyzes the cluster centers of phase space trajectories by integrating the MOA algorithm with the K-means algorithm, extracting their geometric features that reflect the shape characteristics of the phase space trajectories. The research results provide a theoretical basis for troubleshooting transformer winding loosening faults from the perspective of chaotic time series. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 is a flow chart of the present invention;

[0104] Figure 2 It is the location of transformer measurement points;

[0105] Figure 3 It is a diagram of the solution process of embedding dimension m and delay time τ.

[0106] Figure 4 is the phase space trajectory of the transformer vibration signal;

[0107] Figure 5 It is the curve of the overall clustering square error E changing with the number of cluster centers K;

[0108] Figure 6 This is a comparison chart of the K-means algorithm optimized by MOA and the traditional K-means algorithm clustering;

[0109] Figure 7 This is a comparison diagram of the chaotic characteristics of transformer vibration signals;

[0110] Figure 8 It is a comparison chart of geometric characteristics of transformer vibration signals. DETAILED DESCRIPTION

[0111] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0112] The present invention describes a method for extracting transformer winding loose fault features based on chaos theory and ephemeral optimization K-means algorithm. The specific process is shown in Figure 1 , the method comprises the following steps:

[0113] Step 1: Set three measuring points on the transformer box in normal state, obtain the transformer vibration signal, and select the measuring point with the largest vibration amplitude as the optimal measuring point. The steps are as follows:

[0114] Step 1.1: Fix three piezoelectric accelerometers to the top of the transformer box using magnetic bases to obtain transformer surface vibration data.

[0115] Step 1.2: Measure the vibration signal of the transformer measurement point. According to the time domain signal diagram, select the measurement point 1 with the largest vibration amplitude as the best measurement point of the transformer. Figure 2 shown.

[0116] Step 2: Calculate the maximum Lyapunov exponent of the vibration signal collected at measurement point 1 to determine its chaotic characteristics. The implementation steps are as follows:

[0117] Step 2.1: Define the correlation integral introduced into the time series as

[0118]

[0119] Where: M = N-(m-1)τ; d ij =max||x i -x j ||; θ(x) is the switching function; r is the search radius.

[0120]

[0121] For a known time series {x i}, i = 1, 2, ..., N, divide it into τ non-overlapping subsets

[0122]

[0123] Define S(m, N, r, τ) for each subset as

[0124]

[0125] Defining the delta

[0126] ΔS(m, τ)=max{S(m, r j ,τ)}-min{S(m,r j ,τ)} (5)

[0127] Equation (6) describes the maximum deviation about the search radius r. The delay time τ can be obtained at the zero point of S(m, r, τ) and the first minimum value of ΔS(m, τ).

[0128] The statistical conclusions drawn by Brock et al. show that when 2≤m≤5, (s is the mean square error of the time series), when N ≥ 500, the asymptotic distribution (the limiting distribution when the sample size is sufficiently large) can be well approximated.

[0129] Based on this, take m = 2, 3, 4, 5, calculate

[0130]

[0131]

[0132]

[0133] Figure 3 is the calculation result of the above three formulas for the vibration signal of measuring point 1. Figure 3 (a) It can be seen that All are greater than 0, and there is no zero point. Figure 3 (b) Get The first minimum point of corresponds to τ=14, which is the required delay time. Figure 3 (c) It can be seen that S cor τ corresponding to the minimum point w =25, so Rounding up yields m = 3. Therefore, in this embodiment, m = 3 and τ = 14.

[0134] Step 2.2: Take the initial point Y(t0), and set the distance between it and the nearest neighbor point Y0(t0) as L0. Track the time evolution of these two points until the time t1, when the distance between them exceeds a certain value ε>0, L′0=|Y(t1)-Y0(t1)|>ε, and keep Y(t1) adjacent to another point Y1(t1), so that L′1=|Y(t1)-Y1(t1)|<ε, and the angle between them is as small as possible. Continue the above process until Y(t) reaches the end point N of the time series. At this time, the total number of iterations of the tracking evolution process is M, and the maximum Lyapunov exponent is

[0135]

[0136] The maximum Lyapunov exponent corresponding to the vibration signal of measuring point 1 is calculated to be 0.0026>0, so it has chaotic characteristics.

[0137] Step 3: Calculate the correlation dimension and Kolmogorov entropy of the chaotic vibration signal as chaotic characteristic reference values ​​for transformer winding loosening fault. The specific steps are as follows:

[0138] Step 3.1: Select the correlation dimension as the chaotic characteristic quantity to be calculated.

[0139] The correlation dimension calculation method is:

[0140] The point in the reconstructed phase space is

[0141] y j =(y j ,y j+τ ,…,y j+(m-1)τ ), 1≤j≤M (10)

[0142] The maximum component difference r between two points ij for

[0143]

[0144] Where: y ik 、y jk Respectively represent the kth component of two points in space.

[0145] Similar to formula (2), given a sufficiently small positive number r, define the correlation integral here

[0146]

[0147] Then the correlation dimension is

[0148]

[0149] Step 3.2: Select Kolmogorov entropy as the chaotic characteristic quantity to be calculated.

[0150] The Kolmogorov entropy calculation expression is:

[0151]

[0152] In order to fully represent the chaotic characteristics of the transformer vibration signal, the vibration signals of the three measuring points are calculated, and the results are shown in Tables 1 and 2.

[0153] Table 1 Calculation results of correlation dimension of vibration signals at each measuring point

[0154]

[0155] Table 2 K entropy calculation results of vibration signals at each measuring point

[0156]

[0157] Step 4: Reconstruct the vibration signal in phase space to obtain the phase space trajectory. The specific steps are as follows:

[0158] Step 4.1: Generate phase space points based on the embedding dimension 3 and delay time 14 calculated in step 2.1:

[0159]

[0160] Where: M = N-(m-1)τ.

[0161] Step 4.2: Construct the phase space trajectory in the coordinate system. The result is as follows Figure 4 shown.

[0162] Step 5: Use the Mayfly Optimization Algorithm to optimize the initial cluster centers of the K-means algorithm, then cluster the phase space trajectory, and finally calculate the sum of the cluster center moments and the radial offset of the obtained K cluster centers as the geometric feature reference values ​​of the transformer winding loosening fault. The specific steps are as follows:

[0163] Step 5.1: Treat each point in the phase space as a population of mayflies. Randomly divide the population into two groups: males and females. The position x of the male individual in n-dimensional space is i =(x1, x2, ..., x n ), flight speed v mi =(v m1 , v m2 ,…,v mn ); the position y of the female individual i =(y1, y2, ..., y n ), flight speed v fi =(v f1 , v f2 ,…,v fn ).

[0164] Male individuals gather into groups and adjust the speed and arrival position of the next flight through equations (17) and (18).

[0165]

[0166] x′ mi =x mi +v′ mi (17)

[0167] In formula (16): p ibest =(p i1 , p i2 ,…,p in ) is the optimal position that male individual i passes through; g best =(g1, g2, ..., g n ) is the best position among all male individuals; a1 and a2 are positive attraction constants, which are used to measure the contribution of cognitive and social components, and are generally taken as 1 and 1.5 respectively; b is the visibility coefficient, which is used to limit the visibility of the individual to other individuals, and is generally taken as 2; r p =||p ibest -x mi ||、r g =||g best -x mi ||.

[0168] Specifically, the male individual j in the current best position updates its flight speed according to formula (4).

[0169] v′ mj =vmj +d*r (18)

[0170] Where: d is the dance coefficient, usually 5; r∈[-1, 1] is a random number.

[0171] Female individuals do not group together. They are sorted by fitness function value. The best female is paired with the best male, and the second best female is paired with the second best male. Each female moves towards the male mate with a better fitness function value than herself. If the male mate's fitness function value is weaker than hers, she will not be attracted, but will search and move on her own. The speed and position update formula is:

[0172]

[0173] Where: r mf =||x mi -x fi ||; f(·) is the fitness function; fl is the random walk coefficient, which is generally 1.

[0174] After pairing, mating produces two offspring

[0175]

[0176] Where: L is a random number in a specific range, usually (0, 1).

[0177] Then, the offspring are randomly divided into males and females. In order to keep the overall population size constant, if the offspring's fitness function value is better than that of the previous generation of the same sex, it will be replaced.

[0178] At this point, update p ibest and g best , and proceed to the next iteration until the maximum number of iterations is reached.

[0179] The overall clustering square error is

[0180]

[0181] Where: It is cluster C i The mean vector of ; ||·||2 is the Euclidean distance.

[0182] The fitness function is constructed as

[0183]

[0184] Based on the phase space trajectory of the transformer vibration signal, the MOA is used to search for the initial cluster center of the K-means algorithm in the spatial range near the phase space trajectory. The main steps are as follows:

[0185] (1) Initialize the number of mayflies N and the individual position xi , flight speed v i , the number of cluster centers K and p ibest and g best .

[0186] (2) Randomly divide the sexes of mayflies and determine the number of males and females to be N / 2.

[0187] (3) Calculate the fitness value using formula (22) and take the optimal value as the target position.

[0188] (4) The male updates his position before the female does.

[0189] (5) After pairing one by one according to the principle of optimization, each pair produces two offspring and replaces the inferior same-sex individuals of the previous generation.

[0190] (6) Repeat steps (2), (3), (4), and (5) until the maximum number of iterations is reached.

[0191] (7) The obtained optimal location solution is used as the initial cluster center of the K-means algorithm.

[0192] (8) Calculate the overall clustering square error E through formula (21).

[0193] According to the above steps, the number of cluster centers K is calculated from 1 to 20, and the curve of E changing with K is obtained. The K value when the degree of E decreases steadily is selected as the number of cluster centers of the phase space trajectory of the transformer vibration signal in this paper, as shown in Figure 5 As shown in the figure, in this embodiment, when K changes from 14 to 15, the decrease rate of E in the four states is less than 10%, and the subsequent decrease rate is stable below 10%, so K = 15 is selected. The comparison of the K-means algorithm optimized by MOA and the traditional K-means algorithm clustering is shown in the figure. Figure 6 shown.

[0194] Step 5.2: Select the sum of cluster center moments as the geometric feature quantity to be calculated.

[0195] The central moment, that is, the distance from the vector point to the origin in the coordinate system, is called the central moment, and the calculation formula is:

[0196]

[0197] Where: M is the number of feature points.

[0198] Step 5.3: Select radial vector offset as the geometric characteristic quantity for calculation.

[0199] The radial offset is the distance of the point relative to the main diagonal, which describes the degree of closure of the phase space trajectory. The calculation formula is

[0200]

[0201] Where: M is the number of feature points; θ is the unit vector in the main diagonal direction.

[0202] The calculation results of this embodiment are shown in Table 3 and Table 4.

[0203] Table 4 Calculation results of the sum of central moments of vibration signal clusters at each measuring point

[0204]

[0205] Table 5 Calculation results of radial vector offset of vibration signals at each measuring point

[0206]

[0207] Step 6: Compare the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding with the reference values ​​to accurately identify the fault. The specific steps are as follows:

[0208] Step 6.1: Compare the chaotic characteristics of the vibration signal of the transformer winding in different loose states with the chaotic characteristic reference value extracted above. Figure 7 shown.

[0209] Step 6.2: Compare the geometric features of the vibration signals of the transformer windings in different loose states with the geometric feature reference values ​​extracted above. Figure 8 shown.

[0210] Step 6.3: Combine the chaotic features with the geometric features to construct a new feature vector, which can accurately identify transformer winding looseness faults. In this embodiment, the feature vector describing the normal state of the winding is [1.4324, 0.1314, 4.1087, 0.0082].

Claims

1. A method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm, characterized by: The method comprises the following steps: Step 1: Set P measuring points on the transformer box in normal state, obtain the transformer vibration signal, and select the measuring point D with the largest vibration amplitude as the optimal measuring point; Step 2: Calculate the maximum Lyapunov exponent of the vibration signal collected at measuring point D to determine its chaotic characteristics; Step 3: Calculate the correlation dimension and Kolmogorov entropy of the vibration signal with chaotic characteristics as the chaotic characteristic reference value of the transformer winding loose fault; Step 4: Reconstruct the phase space of the vibration signal to obtain the phase space trajectory; Step 5: Use the Mayfly Optimization Algorithm to optimize the initial cluster centers of the K-means algorithm, then cluster the phase space trajectory, and finally calculate the sum of the cluster center moments and the radial offset of the obtained K cluster centers as the geometric feature reference values ​​of the transformer winding loosening fault. The steps are as follows: Step 5.1: Treat each point in the phase space as a population of mayflies; randomly divide the population into two groups: males and females. The position x of the male individual in n-dimensional space is i =(x1, x2, L, x n ), flight speed v mi =(v m1 , v m2 ,L,v mn ); the position y of the female individual i =(y1, y2, L, y n ), flight speed v fi =(v f1 , v f2 ,L,v fn ); Male individuals gather into groups and adjust the speed and arrival position of the next flight through equations (1) and (2); x′ mi =x mi +v′ mi (2) In formula (1): p ibest =(p i1 , p i2 ,L,p in ) is the optimal position that male individual i passes through; g best =(g1, g2, L, g n ) is the best position among all male individuals; a1 and a2 are positive attraction constants, which are used to measure the contribution of cognitive and social components, and are generally taken as 1 and 1.5 respectively; b is the visibility coefficient, which is used to limit the visibility of the individual to other individuals, and is generally taken as 2; r p =||p ibest -x mi ||、r g =||g best -x mi ||; Specifically, the male individual j in the current best position updates its flight speed according to formula (3); v′ mj =v mj +d*r (3) Where: d is the dance coefficient, usually 5; r∈[-1,1] is a random number; Female individuals do not group together. They are sorted by fitness function value. The best female is paired with the best male, and the second best female is paired with the second best male. Each female moves towards the male mate with a better fitness function value than herself. If the male mate's fitness function value is weaker than her own, she will not be attracted, but will search and move on her own. The speed and position update formula is: Where: r mf =||x mi -x fi ||; f(·) is the fitness function; fl is the random walk coefficient, which is generally 1; After pairing, mating produces two offspring Where: L is a random number in a specific range, usually (0, 1); Then, the offspring are randomly divided into males and females; in order to keep the overall population size unchanged, if the offspring's fitness function value is better than that of the same-sex parent, it will be replaced; At this point, update p ibest and g best , proceed to the next iteration until the maximum number of iterations is reached; The overall clustering squared error is Where: It is cluster C i The mean vector of ;||·||2 is the Euclidean distance; The fitness function is constructed as Based on the phase space trajectory of the transformer vibration signal, the MOA algorithm is used to search for the initial cluster center of the K-means algorithm in the spatial range near the phase space trajectory. The main steps are as follows: (1) Initialize the number of mayflies N and the individual position x i , flight speed v i , the number of cluster centers K and p ibest and g best ; (2) Randomly divide the sexes of mayflies and determine the number of males and females to be N / 2; (3) Calculate the fitness value using formula (7) and take the optimal value as the target position; (4) the male updates the position followed by the female; (5) After pairing one by one according to the principle of optimal selection, each pair produces two offspring and replaces the inferior same-sex individuals of the previous generation; (6) Repeat steps (2), (3), (4), and (5) until the maximum number of iterations is reached; (7) The obtained optimal location solution is used as the initial cluster center of the K-means algorithm; (8) Calculate the overall clustering square error E by formula (6); According to the above steps, the number of cluster centers K is calculated from 1 to 20, and the curve of E changing with K is obtained; the K value when the degree of E decreases steadily is selected as the number of cluster centers of the phase space trajectory of the transformer vibration signal in this paper; Step 5.2: Select the sum of cluster center moments as the geometric feature quantity for calculation; The central moment, that is, the distance from the vector point to the origin in the coordinate system, is called the central moment, and the calculation formula is: Where: M is the number of feature points; Step 5.3: Select radial vector offset as the geometric characteristic quantity for calculation; The radial offset is the distance of the point relative to the main diagonal, which describes the degree of closure of the phase space trajectory; The calculation formula is Where: M is the number of feature points; θ is the unit vector in the main diagonal direction; Step 6: Compare the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding with the reference values ​​to accurately identify the fault.

2. The method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm according to claim 1, characterized in that: In step 1, set P measuring points on the transformer box in normal state, obtain the transformer vibration signal, and select the measuring point D with the largest vibration amplitude as the optimal measuring point. The steps are as follows: Step 1.1: Fix P piezoelectric accelerometers to the top of the transformer box through magnetic bases to obtain transformer surface vibration data; Step 1.2: Measure the vibration signal of the transformer measurement point. According to the time domain signal diagram, select the measurement point D with the largest vibration amplitude as the optimal measurement point of the transformer.

3. The method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm according to claim 1 or 2, characterized in that: In step 2, the maximum Lyapunov exponent of the vibration signal collected at measuring point D is calculated to determine its chaotic characteristics. The steps are as follows: Step 2.1: For the vibration signal time series x1, x2,…, x k ,…, embedding dimension m, time delay τ, then reconstruct the phase space Y(t i )=(x(t i ),x(t i +τ),L,x(t i +(m-1)τ)),i=1,2,L,N (10) The embedding dimension m and the delay time τ are determined as follows: The correlation integral introduced into the time series is defined as Where: M = N-(m-1)τ; d ij =max||x i -x j ||; θ(x) is the switching function; r is the search radius; For a known time series {x i }, i = 1, 2, L, N, divide it into τ non-overlapping subsets Define S(m, N, r, τ) for each subset as Defining the delta ΔS(m,τ)=max{S(m,r j ,τ)}-min{S(m,r j ,t)} (15) Equation (15) describes the maximum deviation about the search radius r. The delay time τ can be obtained at the zero point of S(m, r, τ) and the first minimum value of ΔS(m, r); The statistical conclusions drawn by Brock et al. show that when 2≤m≤5, (s is the mean square error of the time series), when N ≥ 500, the asymptotic distribution (the limiting distribution with a sufficiently large sample size) can be well approximated; Based on this, take m=2,3,4,5, calculate From formula (16), we can calculate The first zero point of or calculated by formula (17) The smaller value of the delay time corresponding to the first minimum value of is taken as the result of τ; S can be calculated by formula (18) cor The minimum value of τ corresponds to w As a time window, according to τ ω =(m-1)τ, the result of m can be calculated as Step 2.2: Take the initial point Y(t0), set the distance between it and the nearest neighbor point Y0(t0) as L0, and track the time evolution of these two points until the time t1, the distance between them exceeds a certain value ε>0, L′0=|Y(t1)-Y0(t1)|>ε, keep Y(t1) close to another point Y1(t1), so that L′1=|Y(t1)-Y1(t1)|<ε, and the angle between them is as small as possible. Continue the above process until Y(t) reaches the end point N of the time series. At this time, the total number of iterations of the tracking evolution process is M, and the maximum Lyapunov exponent is Determine whether the maximum Lyapunov exponent of the vibration signal is greater than 0. If it is greater than 0, it proves that it has chaotic characteristics.

4. The method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm according to claim 1, characterized in that: In step 3, the correlation dimension and Kolmogorov entropy of the vibration signal with chaotic characteristics are calculated as chaotic characteristic reference values ​​of transformer winding loosening fault. The steps are as follows: Step 3.1: Select the correlation dimension as the chaotic characteristic quantity to be calculated; The correlation dimension calculation method is: The point in the reconstructed phase space is and j =(and j ,and j+r ,L,y j+(m-1)τ ),1≤j≤M (20) The maximum component difference r between two points ij for Where: y ik 、y jk Respectively represent the kth component of two points in space; Similar to formula (11), given a sufficiently small positive number r, define the correlation integral here Then the correlation dimension is Step 3.2: Select Kolmogorov entropy as the chaotic characteristic quantity to be calculated; The Kolmogorov entropy calculation expression is:

5. The method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm according to claim 1 or 4, characterized in that: In step 4, the vibration signal is reconstructed in phase space to obtain the phase space trajectory. The steps are as follows: Step 4.1: Generate phase space points according to the embedding dimension m and delay time τ calculated in step 2.1: Where: M = N-(m-1)τ; Step 4.2: Construct the phase space trajectory in the coordinate system.

6. The method for extracting transformer winding looseness fault features based on chaos theory and ephemeral optimized K-means algorithm according to claim 1, characterized in that: In step 6, the chaotic characteristics and geometric characteristics of the abnormal state of the transformer winding are compared with the reference values ​​to achieve accurate fault identification. The steps are as follows: Step 6.1: Compare the chaotic features of the vibration signals of the transformer windings in different loose states with the chaotic feature reference values ​​extracted above; Step 6.2: Compare the geometric features of the vibration signals of the transformer windings in different loose states with the geometric feature reference values ​​extracted above; Step 6.3: Combine the chaotic features with the geometric features to construct a new feature vector, which can accurately identify the loose transformer winding fault.

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