CN113673471A - Transformer winding vibration signal feature extraction method - Google Patents

Transformer winding vibration signal feature extraction method Download PDF

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CN113673471A
CN113673471A CN202111010400.7A CN202111010400A CN113673471A CN 113673471 A CN113673471 A CN 113673471A CN 202111010400 A CN202111010400 A CN 202111010400A CN 113673471 A CN113673471 A CN 113673471A
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CN113673471B (en
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吕学宾
毛惠卿
陈翼
李蓬
王晖
高涛
牛健飞
朱洪防
郭增民
杨超
吴晓东
王官涛
鲍国华
刘博�
夏瑞瑞
闫志伟
胡凯
刘延清
杨锟
杨洪波
苏同斐
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State Grid Shandong Electric Power Co Ltd
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Abstract

A transformer winding vibration signal feature extraction method realizes the optimal selection of decomposition modal number and penalty factor, and provides a method for using the energy distribution of each modal quantity as the feature value of a vibration signal. It comprises the following steps: firstly, performing VMD pre-decomposition on the obtained transformer winding vibration signal under an initial decomposition mode number K and a penalty factor alpha; secondly, the optimization selection of the variational modal decomposition parameters (K, alpha) is realized by improving the artificial bee colony algorithm; and thirdly, calculating the signal energy distribution to obtain a characteristic value representing the mechanical state of the winding. The invention can realize the optimal selection of the decomposition mode number and the penalty factor.

Description

Transformer winding vibration signal feature extraction method
Technical Field
The invention relates to the technical field of transformer fault diagnosis, in particular to a transformer winding vibration signal feature extraction method.
Background
The safe and stable operation of a power system is endangered by the fault of the transformer, and the mechanical fault of the winding accounts for a great proportion of the fault of the transformer, so that the state of the winding of the transformer needs to be effectively sensed and diagnosed. The method aims to quickly and accurately identify the state information of the transformer winding and realize fault diagnosis, and the method is provided with effective characteristic extraction on the state signal of the transformer winding.
During the use of the transformer, the load current flowing through the winding is acted by the electrodynamic force under the leakage magnetic field, so that the winding generates mechanical vibration, and the vibration of the winding is transmitted to the surface of the transformer through the connecting part. At present, analyzing the mechanical state of the winding based on the vibration signal is an important means for diagnosing the winding fault. The existing signal analysis methods include wavelet singular decomposition, wavelet packet decomposition, and Variational Modal Decomposition (VMD). Variational modal decomposition can decompose a nonlinear, non-stationary signal into a sum of a number of simple stationary signals, each having a center frequency, but the method itself has disadvantages that can produce over-or under-decomposition of the signal that can interfere with the analysis of the original signal components.
Disclosure of Invention
The invention aims to provide a transformer winding vibration signal characteristic extraction method, which realizes the optimal selection of decomposition modal number and penalty factor and provides a method for using the energy distribution of each modal quantity as the characteristic value of a vibration signal.
The technical scheme adopted by the invention for solving the technical problems is as follows: a transformer winding vibration signal feature extraction method is characterized by comprising the following steps:
firstly, performing VMD pre-decomposition on the obtained transformer winding vibration signal under an initial decomposition mode number K and a penalty factor alpha;
given an input signal y, decompose y into K eigenmode functions uk(t)，k＝1,2,…,K：
uk(t)＝Ak(t)cos(φk(t)) (1)
In the formula: a. thek(t) is uk(t) instantaneous amplitude, d φk(t)/dt＝ωk(t)，ωk(t) is uk(t) instantaneous frequency; there are two constraints: 1. the sum of the modes is equal to the input signal; 2. the sum of the estimated bandwidths of the eigenmode functions is minimal;
the variable problem with constraint conditions is as follows:
Figure BDA0003238311520000021
introducing a secondary penalty factor alpha and a Lagrangian lambda (t) to convert the problem into a variation problem without constraint conditions, as shown in a formula (3),
Figure BDA0003238311520000022
solving the variation problem by a multiplicative operator alternating direction method, and updating
Figure BDA0003238311520000023
And λn+1Finding a saddle point of formula (3) wherein
Figure BDA0003238311520000024
The expression of (a) is:
Figure BDA0003238311520000025
converting the formula (4) into a frequency domain by utilizing Fourier equidistant transformation, expanding the value problem of the central frequency to the frequency, obtaining an updating method of the central frequency, and finishing the updating of the lambda; the expression is as follows:
Figure BDA0003238311520000026
Figure BDA0003238311520000031
Figure BDA0003238311520000032
and (3) continuously alternating the center frequency and the bandwidth of the intrinsic mode function component in the variational model with the constraint condition through the calculation and iterative solution until the iteration stop condition formula (8) is met:
Figure BDA0003238311520000033
for the given discrimination accuracy e >0, ending the whole cycle, finally obtaining K narrow-band IMF components according to the frequency domain characteristics of the actual signals, and completing the self-adaptive segmentation of the signal frequency band;
secondly, the optimization selection of the variational modal decomposition parameters (K, alpha) is realized by improving the artificial bee colony algorithm; (1) initializing parameters and generating an initial solution;
the control parameters of ABC algorithm mainly comprise the number of swarms CSN and the number of food sources SNNamely the number of bees to be picked, the maximum number of cycles limit of food sources, and the number of termination cycles Nmc。
(2) Setting a fitness function;
after VMD decomposition, the measured vibration signals of the transformer winding form K Intrinsic Mode Functions (IMF), and each IMF component corresponds to a central frequency; aiming at the characteristics of the vibration signal of the transformer winding, the concept of signal energy entropy is introduced:
calculate the energy of each IMF component:
Figure BDA0003238311520000034
in the formula ui(t) is the i-th order IMF component;
solving for the normalized energy of each IMF component:
Figure BDA0003238311520000035
wherein K is the total order of IMF components;
calculating the signal energy entropy of the component decomposition signals:
Figure BDA0003238311520000041
the magnitude of the signal energy entropy reflects the sparseness of the signal;
the concept of introducing energy errors: according to the calculation formula of each IMF component, the energy calculation formula of the original signal can be obtained as
Figure BDA0003238311520000042
Wherein f (t) is the original signal, K is the number of decomposition modes;
the total energy of each IMF component is
Figure BDA0003238311520000043
The energy error between the original signal and the decomposed signal is obtained as
Ee＝Ea-E (14)
The ratio of the energy entropy to the energy error is used as an algorithm fitness function;
Figure BDA0003238311520000044
(3) initializing the search range of the model, and starting to circularly search by adopting bees, observing bees and detecting bees, wherein the search process comprises the following steps:
firstly, the honey bee produces a new candidate position according to the local information in the memory and calculates the nectar amount of the new position, if the nectar amount is better than the original position, the honey bee remembers the new position and forgets the original position; the expression for generating the new position, i.e. the search equation, is:
vij＝xij+φij(xij-xkj) (16)
where k is a honey source other than i, j is a randomly selected subscript, φijIs [ -1,1 [ ]]A random number in between, which controls xijGenerating a honey source position in the neighborhood;
after all the honey bees finish the self searching process, sharing the memorized honey source information with the observation bees through the dance area; observing bees are based on the information obtained from the honey bees and according to the probability p related to the amount of nectariSelecting a honey source position, probability value piThe calculation formula of (2) is as follows:
Figure BDA0003238311520000051
wherein fitiTo solve XiThe fitness value of (1), 2, …, SN, SN is the number of solutions in the population; finally, selecting a honey source position according to a roulette method, changing the position in memory to a certain extent, checking the nectar amount of the new position, and replacing if the nectar amount is better than the original position; in the search equation of the honey bee, a new solution is generated by pulling an old solution closer to or away from a random individual, so that the generated solution has high randomness and is easy to jump out of local optimality, but the individual with higher fitness in the population has a certain mining space, so that the search equation of the observation bee is optimized, and the search equation of the observation bee after optimization is as follows:
vij＝xb,j+φij[ε1(xk1,j-xk2,j)+ε2(xij-xb,j)] (18)
in the formula, xb,jOptimal solution, x, for the current miningk1,jAnd xk2,jIs different from xijTwo random solutions of phiijIs [ -1,1 [ ]]Random number of between, epsilon1、ε2Are differential operators, all are [0,1 ]]A random number in between, and epsilon1+ε2＝1；
Position X of honey sourceiCannot be improved after limit times of cyclic search of honey bees and observation beesThe position is abandoned, the honey bee adopted at the moment is converted into a detection bee, and a honey source is randomly searched to replace the original honey source; limit is an important control parameter in the ABC algorithm and controls the selection of the scout bees; the formula for searching new honey source by the scout bees is as follows:
Figure BDA0003238311520000052
thirdly, calculating signal energy distribution to obtain characteristic values representing mechanical states of the winding
Selecting a decomposition parameter corresponding to the energy entropy which enables the energy entropy to be the maximum under an allowable condition, wherein the energy values of IMF components are different at the moment and represent different energy distribution characteristics of different frequency components, and the energy distribution of the frequency components of a transformer winding is different under different working conditions, so that a vibration characteristic vector is extracted; calculating the energy value of each component after the vibration signal is decomposed according to the following formula:
Figure BDA0003238311520000053
the total energy of the signal is:
Figure BDA0003238311520000061
the IMF energy ratio is:
Figure BDA0003238311520000062
and (4) arranging the IMF energy occupation ratios into eigenvectors in sequence to represent the operation condition of the transformer winding.
The invention has the beneficial effects that: the invention provides a transformer winding vibration signal feature extraction method, which aims at the problem of processing the mechanical vibration signal feature extraction of a winding by a current variational modal decomposition method (VMD). the current VMD algorithm is influenced by two parameters, namely a modal decomposition number K and a punishment parameter alpha, in the signal decomposition process, an artificial bee colony optimization Algorithm (ABC) in a cluster intelligent optimization algorithm is introduced, in order to avoid the problem that the original algorithm is trapped in a local extreme value and has low convergence speed, a search function is improved, concepts of signal energy entropy and energy error are introduced at the same time, and the ratio of the two is used as a punishment function of the artificial bee colony algorithm, so that the optimal selection of the decomposition modal number and the punishment factor is realized.
Drawings
FIG. 1 is a time-frequency diagram of an obtained original vibration signal of a transformer;
FIG. 2 is a time-frequency diagram of IMF components formed after VMD decomposition of a measured vibration signal of a transformer winding;
FIG. 3 is a flow chart of the algorithm of the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 3, a transformer winding vibration signal feature extraction method includes the following steps:
firstly, performing VMD pre-decomposition on the obtained transformer winding vibration signal under an initial decomposition mode number K and a penalty factor alpha;
the mechanical vibration data of 60 groups of transformer windings are collected through experiments and simulation, and as shown in fig. 1, 20 groups of normal working condition data, 20 groups of insulation falling working conditions and 20 groups of winding deformation working conditions are collected.
Given an input signal y, decompose y into K eigenmode functions uk(t)，k＝1,2,…,K：
uk(t)＝Ak(t)cos(φk(t)) (1)
In the formula: a. thek(t) is uk(t) instantaneous amplitude, d φk(t)/dt＝ωk(t)，ωk(t) is uk(t) instantaneous frequency. There are two constraints: 1. the sum of the modes is equal to the input signal; 2. the sum of the estimated bandwidths of the eigenmode functions is minimal. The variable problem with constraint conditions is as follows:
Figure BDA0003238311520000071
introducing a secondary penalty factor alpha and a Lagrangian lambda (t) to convert the problem into a variation problem without constraint conditions, as shown in a formula (3),
Figure BDA0003238311520000072
solving the variation problem by a multiplicative operator alternating direction method, and updating
Figure BDA0003238311520000073
And λn+1Finding a saddle point of formula (3) wherein
Figure BDA0003238311520000074
The expression of (a) is:
Figure BDA0003238311520000075
and (3) converting the formula (4) into a frequency domain by utilizing Fourier equidistant transformation, expanding the value problem of the central frequency to the frequency, obtaining an updating method of the central frequency, and finishing the updating of the lambda. The expression is as follows:
Figure BDA0003238311520000076
Figure BDA0003238311520000077
Figure BDA0003238311520000078
and (3) continuously alternating the center frequency and the bandwidth of the intrinsic mode function component in the variational model with the constraint condition through the calculation and iterative solution until the iteration stop condition formula (8) is met:
Figure BDA0003238311520000081
and for the given discrimination accuracy e >0, ending the whole cycle, and finally obtaining K narrow-band IMF components according to the frequency domain characteristics of the actual signal to finish the self-adaptive segmentation of the signal frequency band.
And secondly, realizing the optimized selection of the variational modal decomposition parameters (K, alpha) by improving an artificial bee colony algorithm. The artificial bee colony Algorithm (ABC) simulates the honey collection process of bees in nature, and divides the bees into 3 different working species, namely honey collection peak, observation bee and reconnaissance bee. The number of the food sources is equal to that of the bee collecting bees. The location of each food source represents one possible solution to the optimization problem, and the amount of nectar for each food source corresponds to the fitness of each solution. The process of bee performing search activities is summarized as follows:
(1) the honeybees are adopted to determine honey sources, the honeybees are adopted to memorize related information, and the honey sources are shared with the observation bees;
(2) observing bees to reselect honey sources in adjacent honey sources according to a certain selection strategy;
(3) the honey bees at the abandoned honey source are changed into the scout bees, and then new honey sources are mined.
The process of improving the ABC algorithm comprises the following steps:
(1) initializing parameters and generating an initial solution;
the control parameters of ABC algorithm mainly comprise the number of swarms CSN and the number of food sources SNNamely the number of bees to be picked, the maximum number of cycles limit of food sources, and the number of termination cycles Nmc。
(2) Setting a fitness function;
as shown in fig. 2, the VMD decomposition of the measured vibration signal of the transformer winding results in K eigenmode functions (IMFs), each IMF component corresponding to a center frequency. The number of IMF components is determined by the preset K value, and when the number of modal decomposition is small, some important information in the original signal is filtered and lost. When the number of signal decompositions is large, the frequency centers of adjacent modal components are close to each other, and frequency aliasing is generated. The penalty function a determines the width of the IMF component bandwidth. The smaller the penalty function alpha is, the larger the bandwidth of each IMF component is; conversely, the smaller the bandwidth of the IMF component. Aiming at the characteristics of the vibration signal of the transformer winding, the concept of signal energy entropy is introduced:
calculate the energy of each IMF component:
Figure BDA0003238311520000091
in the formula uiAnd (t) is an i-th order IMF component.
Solving for the normalized energy of each IMF component:
Figure BDA0003238311520000092
where K is the total order of the IMF components.
Calculating the signal energy entropy of the component decomposition signals:
Figure BDA0003238311520000093
the size of the signal energy entropy reflects the sparse characteristic of the signal, the most uncertain energy distribution has the maximum energy entropy, when the signal decomposition is insufficient, the obvious sparse characteristic appears when the energy of a certain frequency is increased, the energy entropy is reduced, and the larger the signal energy entropy is, the more sufficient the decomposition is.
The concept of introducing energy errors: according to the calculation formula of each IMF component, the original signal energy can be obtained
Is calculated by the formula
Figure BDA0003238311520000094
Wherein f (t) is the original signal, and K is the number of decomposition modes.
The total energy of each IMF component is
Figure BDA0003238311520000095
The energy error between the original signal and the decomposed signal is obtained as
Ee＝Ea-E (14)
If the signal over-decomposition has frequency aliasing, the orthogonality among the components is deteriorated, which shows that the independence among the components is weak, the energy sum among the components is greatly different from the energy of the source signal, which shows that EeThe smaller the better.
In order to ensure that the signal decomposition is sufficient and the over-decomposition phenomenon does not exist, two parameters are considered at the same time, and the ratio of the signal energy entropy to the energy error is used as an algorithm fitness function.
Figure BDA0003238311520000101
(3) Initializing the search range of the model, and starting to circularly search by adopting bees, observing bees and detecting bees, wherein the search process comprises the following steps:
the honey bee collecting device comprises a honey bee collecting device, a memory device and a control device, wherein the honey bee collecting device is used for storing local information of the honey bee collecting device, the memory device is used for memorizing a new position, and the honey bee collecting device is used for calculating the nectar amount of the new position according to the local information in the memory. The expression for generating the new position, i.e. the search equation, is:
vij＝xij+φij(xij-xkj) (16)
where k is a honey source other than i, j is a randomly selected subscript, φijIs [ -1,1 [ ]]A random number in between, which controls xijGeneration of a source location within a neighborhood.
Secondly, after all the honey bees finish the searching process, the honey source information in the memory is shared with the observation bees through the dance area. Observing bees are based on the information obtained from the honey bees and according to the probability p related to the amount of nectariSelecting a honey source positionProbability value piThe calculation formula of (2) is as follows:
Figure BDA0003238311520000102
wherein fitiTo solve XiThe fitness value of (1), (2), (…), and SN, which is the number of solutions in the population. Finally, a honey source position is selected according to a roulette method, meanwhile, the position in the memory is changed to a certain extent, the amount of nectar in the new position is checked, and if the nectar amount is better than the original position, the nectar amount is replaced. In the search equation of the honey bee, a new solution is generated by pulling an old solution closer to or away from a random individual, so that the generated solution has high randomness and is easy to jump out of local optimality, but the individual with higher fitness in the population has a certain mining space, so that the search equation of the observation bee is optimized, and the search equation of the observation bee after optimization is as follows:
vij＝xb,j+φij[ε1(xk1,j-xk2,j)+ε2(xij-xb,j)] (18)
in the formula, xb,jOptimal solution, x, for the current miningk1,jAnd xk2,jIs different from xijTwo random solutions of phiijIs [ -1,1 [ ]]Random number of between, epsilon1、ε2Are differential operators, all are [0,1 ]]A random number in between, and epsilon1+ε2＝1。
Position X of honey sourceiAfter limit times of cyclic search of the honey miners and the observers, the positions cannot be improved, and the positions are abandoned, the honey miners are changed into detection bees, and a honey source is randomly searched to replace the original honey source. The limit is an important control parameter in the ABC algorithm and controls the selection of the scout bees. The formula for searching new honey source by the scout bees is as follows:
Figure BDA0003238311520000111
thirdly, calculating signal energy distribution to obtain characteristic values representing mechanical states of the winding
In the energy entropy value calculation, a decomposition parameter corresponding to the energy entropy which enables the energy entropy to be the maximum under an allowable condition is selected, energy values of IMF components at the moment are different and represent different energy distribution characteristics of different frequency components, and energy distribution of the frequency components of a transformer winding is different under different working conditions, so that a vibration characteristic vector is extracted. Calculating the energy value of each component after the vibration signal is decomposed according to the following formula:
Figure BDA0003238311520000112
the total energy of the signal is:
Figure BDA0003238311520000113
the IMF energy ratio is:
Figure BDA0003238311520000114
and (3) arranging the IMF energy ratios into eigenvectors in sequence to represent the operation conditions of the transformer winding, wherein part of data is shown in a table 1.
TABLE 1 Transformer winding eigenvectors
Figure BDA0003238311520000115
Figure BDA0003238311520000121
From the results in table 1, it can be seen that the winding operates normally and the eigenvectors differ under fault conditions. The calculated data is analyzed, and for a normal working condition, 100Hz is the main component of the sensor, a small amount of 50Hz signals are contained, and a small amount of 200Hz and 300Hz signals are contained. The fault signal contains more high frequency signals than the normal signal.
In order to verify that the improved ABC algorithm has the capability of jumping out of a local optimal solution and has better optimization performance and convergence, the improved ABC optimization VMD algorithm is compared with the standard particle swarm optimization VMD and the standard ABC optimization VMD, VMD decomposition is carried out on the same vibration signal under the condition that given parameters are not changed, the running times of different algorithms are compared respectively, and the result is shown in Table 2.
TABLE 2 run time comparison of algorithms
Algorithm Run time(s)
PSO-VMD 97.7
ABC-AMD 95.4
IABC-VMD 92.3
The results show that the transformer winding state signal extraction algorithm based on the improved artificial bee colony algorithm optimized variation modal decomposition can effectively decompose the original vibration signals and extract characteristic values with discrimination, which can reflect different mechanical states of the winding, and compared with other algorithms, the transformer winding state signal extraction algorithm has excellent and stable performance, good convergence, is simple and easy to implement, can provide a powerful basis for fault diagnosis of the transformer winding, and provides reference for operation and maintenance personnel.

Claims (1)

1. A transformer winding vibration signal feature extraction method is characterized by comprising the following steps:
firstly, performing VMD pre-decomposition on the obtained transformer winding vibration signal under an initial decomposition mode number K and a penalty factor alpha;
given an input signal y, decompose y into K eigenmode functions uk(t)，k＝1,2,…,K：
uk(t)＝Ak(t)cos(φk(t)) (1)
In the formula: a. thek(t) is uk(t) instantaneous amplitude, d φk(t)/dt＝ωk(t)，ωk(t) is uk(t) instantaneous frequency; there are two constraints: 1. the sum of the modes is equal to the input signal; 2. the sum of the estimated bandwidths of the eigenmode functions is minimal;
the variable problem with constraint conditions is as follows:
Figure FDA0003238311510000011
introducing a secondary penalty factor alpha and a Lagrangian lambda (t) to convert the problem into a variation problem without constraint conditions, as shown in a formula (3),
Figure FDA0003238311510000012
solving the variation problem by a multiplicative operator alternating direction method, and updating
Figure FDA0003238311510000013
And λn+1Finding a saddle point of formula (3) wherein
Figure FDA0003238311510000014
The expression of (a) is:
Figure FDA0003238311510000015
converting the formula (4) into a frequency domain by utilizing Fourier equidistant transformation, expanding the value problem of the central frequency to the frequency, obtaining an updating method of the central frequency, and finishing the updating of the lambda; the expression is as follows:
Figure FDA0003238311510000021
Figure FDA0003238311510000022
Figure FDA0003238311510000023
and (3) continuously alternating the center frequency and the bandwidth of the intrinsic mode function component in the variational model with the constraint condition through the calculation and iterative solution until the iteration stop condition formula (8) is met:
Figure FDA0003238311510000024
for the given discrimination accuracy e >0, ending the whole cycle, finally obtaining K narrow-band IMF components according to the frequency domain characteristics of the actual signals, and completing the self-adaptive segmentation of the signal frequency band;
secondly, the optimization selection of the variational modal decomposition parameters (K, alpha) is realized by improving the artificial bee colony algorithm;
(1) initializing parameters and generating an initial solution;
the control parameters of ABC algorithm mainly comprise the number of swarms CSN and the number of food sources SNNamely the number of bees to be picked, the maximum number of cycles limit of food sources, and the number of termination cycles Nmc。
(2) Setting a fitness function;
after VMD decomposition, the measured vibration signals of the transformer winding form K Intrinsic Mode Functions (IMF), and each IMF component corresponds to a central frequency; aiming at the characteristics of the vibration signal of the transformer winding, the concept of signal energy entropy is introduced:
calculate the energy of each IMF component:
Figure FDA0003238311510000025
in the formula ui(t) is the i-th order IMF component;
solving for the normalized energy of each IMF component:
Figure FDA0003238311510000031
wherein K is the total order of IMF components;
calculating the signal energy entropy of the component decomposition signals:
Figure FDA0003238311510000032
the magnitude of the signal energy entropy reflects the sparseness of the signal;
the concept of introducing energy errors: according to the calculation formula of each IMF component, the original signal energy can be obtained
Is calculated by the formula
Figure FDA0003238311510000033
Wherein f (t) is the original signal, K is the number of decomposition modes;
the total energy of each IMF component is
Figure FDA0003238311510000034
The energy error between the original signal and the decomposed signal is obtained as
Ee＝Ea-E (14)
The ratio of the energy entropy to the energy error is used as an algorithm fitness function;
Figure FDA0003238311510000035
(3) initializing the search range of the model, and starting to circularly search by adopting bees, observing bees and detecting bees, wherein the search process comprises the following steps:
firstly, the honey bee produces a new candidate position according to the local information in the memory and calculates the nectar amount of the new position, if the nectar amount is better than the original position, the honey bee remembers the new position and forgets the original position; the expression for generating the new position, i.e. the search equation, is:
vij＝xij+φij(xij-xkj) (16)
where k is a honey source other than i, j is a randomly selected subscript, φijIs [ -1,1 [ ]]A random number in between, which controls xijGenerating a honey source position in the neighborhood;
after all the honey bees finish the self searching process, sharing the memorized honey source information with the observation bees through the dance area; observing bees are based on the information obtained from the honey bees and according to the probability p related to the amount of nectariSelecting a honey source position, probability value piThe calculation formula of (2) is as follows:
Figure FDA0003238311510000041
wherein fitiTo solve XiThe fitness value of (1), 2, …, SN, SN is the number of solutions in the population; finally, selecting a honey source position according to a roulette method, changing the position in memory to a certain extent, checking the nectar amount of the new position, and replacing if the nectar amount is better than the original position; in the search equation for the honey bee, the new solution is generated by pulling the old solution closer to or further from a random individualThe generated solution randomness is large and easy to jump out of local optima, but individuals with higher fitness in the population have certain mining space, so that the search equation of the observation bees is optimized, and the search equation of the observation bees after optimization is as follows:
vij＝xb,j+φij[ε1(xk1,j-xk2,j)+ε2(xij-xb,j)] (18)
in the formula, xb,jOptimal solution, x, for the current miningk1,jAnd xk2,jIs different from xijTwo random solutions of phiijIs [ -1,1 [ ]]Random number of between, epsilon1、ε2Are differential operators, all are [0,1 ]]A random number in between, and epsilon1+ε2＝1；
Position X of honey sourceiAfter limit times of cyclic search of the honey bees and the observation bees, the position cannot be improved, the honey bees are abandoned, the honey bees are converted into detection bees, and a honey source is randomly searched to replace the original honey source; limit is an important control parameter in the ABC algorithm and controls the selection of the scout bees; the formula for searching new honey source by the scout bees is as follows:
Figure FDA0003238311510000051
thirdly, calculating signal energy distribution to obtain characteristic values representing mechanical states of the winding
Selecting a decomposition parameter corresponding to the energy entropy which enables the energy entropy to be the maximum under an allowable condition, wherein the energy values of IMF components are different at the moment and represent different energy distribution characteristics of different frequency components, and the energy distribution of the frequency components of a transformer winding is different under different working conditions, so that a vibration characteristic vector is extracted; calculating the energy value of each component after the vibration signal is decomposed according to the following formula:
Figure FDA0003238311510000052
the total energy of the signal is:
Figure FDA0003238311510000053
the IMF energy ratio is:
Figure FDA0003238311510000054
and (4) arranging the IMF energy occupation ratios into eigenvectors in sequence to represent the operation condition of the transformer winding.
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