CN112101144A - Self-adaptive method for improving transformer vibration signal processing precision - Google Patents

Self-adaptive method for improving transformer vibration signal processing precision Download PDF

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CN112101144A
CN112101144A CN202010879772.2A CN202010879772A CN112101144A CN 112101144 A CN112101144 A CN 112101144A CN 202010879772 A CN202010879772 A CN 202010879772A CN 112101144 A CN112101144 A CN 112101144A
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姜毅
严娜
田耕
贾誉
苗洪岩
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Zhaotong Power Supply Bureau of Yunnan Power Grid Co Ltd
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Abstract

The invention relates to an adaptive method and an adaptive system for improving the processing precision of a vibration signal of a transformer, and belongs to the technical field of vibration measurement of power equipment. The method comprises the steps of vibration signal acquisition, filtering processing, Hilbert transformation, spectrum movement to a fundamental frequency band, construction of a constraint variational model and the like. The method combines the characteristics of the vibration signals of 110kv-750kv, makes targeted improvement, can effectively separate the vibration signals of 5hz-3000hz, obtains the signals of a specific section for analysis, greatly simplifies the operation amount, improves the analysis precision, simultaneously, thoroughly avoids mode aliasing, accurately identifies the mixed signals, and lays a solid foundation for further processing.

Description

Self-adaptive method for improving transformer vibration signal processing precision
Technical Field
The invention belongs to the technical field of power equipment vibration measurement, and particularly relates to an adaptive method for improving the processing precision of a transformer vibration signal.
Background
At the present stage, the detection of the deformation of the transformer winding is mainly a test detection method after the operation is stopped. Mainly comprises a low-voltage pulse method, a frequency response method, a short-circuit reactance test method, a capacitance test method and the like. The off-line detection methods have poor economy and reliability, and most importantly, the deformation of the transformer winding cannot be timely and effectively found, and the transformer needs to be quit from running, so that a large amount of manpower and material resources are consumed.
The iron core, the winding and the accessories in the transformer can generate vibration with various frequencies under the action of electromagnetic force. These vibrations are transmitted to the tank wall through the connector, the cooling oil, and the like. The sensor is arranged on the wall of the oil tank, vibration signals are collected, various analysis and processing are carried out, and the running states of an iron core, a winding and the like in the transformer are analyzed by combining with a necessary model, which is a common mode of the current vibration method. However, the method is not suitable for large-scale automatic monitoring and brings huge manual operation. In addition, with the improvement of the computing capability and the new algorithm of the hardware, the possibility of further improving the computing precision is brought, and the computing method is required to be improved to adapt to the new trend.
Although the existing transformer vibration signal device can collect vibration signals, a highly synthesized signal of the collected signals has a very wide frequency range from a few hertz to a few kilohertz, and each sensor collects the signals in a limited area, so that extremely high requirements are provided for a post-stage processing algorithm. On the premise of ensuring that the system acquisition value is effective, how to quickly and effectively extract effective signals is a problem which is continuously solved in the technical field.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides an adaptive method for improving the processing precision of a transformer vibration signal, the method combines the characteristics of the vibration signal of 110kv-750kv, makes targeted improvement, can effectively separate the vibration signal of 5hz-3000hz, obtains the signal of a specific section for analysis, greatly simplifies the operation amount and improves the analysis precision.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an adaptive method for improving the processing precision of a vibration signal of a transformer comprises the following steps:
step (1), acquiring a vibration signal acquired by a transformer vibration sensor;
Figure BDA0002653756580000011
uk(t) is a vibration signal collected by the transformer vibration sensor, which is an instantaneous superposition mixed signal,
Figure BDA0002653756580000021
being the phase of the signal, Ak(t) is the instantaneous amplitude, t is time;
step (2), carrying out high-frequency passband filtering processing on the vibration signal obtained in the step (1) to obtain a filtered signal Xii;
obtaining analysis signals of each modal function by Hilbert transform on the filtered signal Xii, and aiming at obtaining a single-side frequency spectrum of the signal Xii;
presetting the center frequency of the analytic signal of each mode function, and modulating the frequency spectrum of each mode to a corresponding fundamental frequency band;
step (4), calculating the square L of the above demodulation signal gradient2And (3) squaring the norm, and constructing a constraint variational model as follows:
Figure BDA0002653756580000022
wherein, { uk}＝{u1,u2,…,uKRepresents K modal components obtained by decomposition, { omega }k}＝{ω1,ω2,…,ωKDenotes the center frequency of each component,
Figure BDA0002653756580000023
representing the derivation of the function, (t) is the Dirac function, j represents the imaginary unit, t is time, uk(t) is the instantaneous superimposed mixed signal, f (t) is the original signal;
and (5) introducing a secondary penalty factor alpha and a Lagrange multiplication operator lambda (t) to solve the constraint variation problem in the step (4) and changing the constraint variation problem into an unconstrained variation problem, wherein the secondary penalty factor can ensure the reconstruction accuracy of the signal under the condition of Gaussian noise. Lagrange operators keep the constraint conditions strict, and the extended Lagrange expression is as follows:
Figure BDA0002653756580000024
alpha is a penalty factor, and lambda (t) is a Lagrange multiplier; k represents the maximum number of decompositions;
step (6), a multiplicative operator alternative direction method is adopted in the VMD to solve the variation problem in the step (4), and the alternative updating is carried out
Figure BDA0002653756580000031
And
Figure BDA0002653756580000032
and searching saddle points of the augmented Lagrange expression so as to complete the solution of the constraint variation problem in the constraint variation model.
Further, it is preferable that, in the step (2), the passband of the high-frequency passband filtering process is in a range of 10hz to 2000 hz.
Further, it is preferable that in the step (3), the center frequency ω of each modal analysis signal is presetkThe specific method of (2) is to take the median of the frequency band where the mode is located as the preset center frequency.
Further, it is preferable that, in the step (6), in the process of searching for the saddle point, the corresponding variable update expression is as follows:
Figure BDA0002653756580000033
Figure BDA0002653756580000034
Figure BDA0002653756580000035
in the formula: Λ represents fourier transform; n is the number of iterations; tau, in the process of iteratively solving the variational model, each BIMF is a fidelity coefficient; ω represents a variable; λ is lagrange multiplier;
Figure BDA0002653756580000036
n-phase representing the kth center frequency;
Figure BDA0002653756580000037
a Fourier transform representing the phases of i modal components n + 1; k represents the kth BIMF;
Figure BDA0002653756580000038
a Fourier transform representing the nth stage of the Lagrangian multiplier;
Figure BDA0002653756580000039
a fourier transform representing the original signal;
the frequency center and bandwidth of the component are continuously updated until an iteration stop condition is satisfied.
Further, it is preferable that when the iteration stop condition is satisfied:
Figure BDA00026537565800000310
finishing the whole cycle, finally completing the self-adaptive division of the signal frequency band according to the frequency domain characteristics of the actual signal, and carrying out Fourier inversion transformation on the obtained signal frequency band
Figure BDA00026537565800000311
The BIMF component converted into the time domain,each BIMF is the final decomposition of finally required equipment operation information, and can directly reflect the operation state or effective information of the equipment; where it is the convergence constant.
Further, it is preferably 0.01.
Further, it is preferable to calculate the number of the optimal component BIMF by using the PSO algorithm, the number range is defined between 1 and 6, and the excess is partially discarded.
Further, preferably, the K value range for VMD is obtained by the optimal BIMF number obtained by the PSO algorithm, which is of great significance for VMD decomposition;
in the PSO algorithm:
Vt+1＝w·Vt+c1r1·(pBest-Xt)+c2r2·(gBest-Xt) (1-9)
Xt+1＝Xt+Vt+1 (1-10)
in the formula: v is the speed, t is the algebra, X is the position, w is the inertia weight, c is the learning factor, r is the random number, Pbest is the optimal solution found by the particle itself, Gbest is the optimal solution found by the whole population at present, i.e. the global extremum.
The invention also provides a system for improving the processing precision of the vibration signal of the transformer, which comprises the following components:
the signal acquisition module is used for acquiring vibration signals acquired by the transformer vibration sensor;
the filtering processing and converting module is used for carrying out high-frequency passband filtering processing on the obtained signals and then carrying out Hilbert conversion on the obtained filtered signals to obtain analytic signals of each modal function;
the first processing module is used for presetting the center frequency of each modal analysis signal and modulating the frequency spectrum of each modal to a corresponding fundamental frequency band;
a constraint variation model building module for calculating the L of the square of the demodulation signal gradient2Squaring the norm to construct a constraint variational model;
a solving and outputting module for introducing a penalty factor alpha and a Lagrange multiplicationSub lambda changes the constraint variation problem into the non-constraint variation problem and uses the alternative direction multiplier algorithm to update the iteration
Figure BDA0002653756580000042
And
Figure BDA0002653756580000041
and searching saddle points of the augmented Lagrange expression, completing solution, outputting the BIMF components converted into time domains, wherein each output BIMF is the final needed decomposition containing the equipment operation information.
Compared with the prior art, the invention has the beneficial effects that:
the method disclosed by the invention combines the characteristics of the vibration signals of 110kv-750kv, makes targeted improvement, can effectively separate the vibration signals of 5hz-3000hz, obtains the signals of a specific section for analysis, greatly simplifies the operation amount and improves the analysis precision.
By the method, the optimal decomposition BIMF number K is automatically calculated, the optimal solution of signal processing is obtained, and the method is applied to actual field signal processing and has universality on signal processing.
As shown in fig. 3 and 4, by comparing the results of the pre-processing and the post-processing of the same signal, it can be clearly seen that the improved algorithm completely avoids mode aliasing, accurately identifies the mixed signals, and lays a solid foundation for the subsequent further processing.
Drawings
FIG. 1 is a flow chart of the VMD algorithm in the method of the present invention;
FIG. 2 is a schematic diagram of the calculation of speed and position updates according to the present invention;
FIG. 3 is a waveform diagram of a vibration signal with modal aliasing after EMD processing; the abscissa is frequency;
FIG. 4 is a waveform diagram of a vibration signal processed by VMD without modal aliasing;
fig. 5 is a schematic structural diagram of a system for improving the processing accuracy of the transformer vibration signal according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples.
It will be appreciated by those skilled in the art that the following examples are illustrative of the invention only and should not be taken as limiting the scope of the invention. The examples do not specify particular techniques or conditions, and are performed according to the techniques or conditions described in the literature in the art or according to the product specifications. The materials or equipment used are not indicated by manufacturers, and all are conventional products which can be obtained by purchase.
An adaptive method for improving the processing precision of a vibration signal of a transformer comprises the following steps:
step (1), acquiring a vibration signal acquired by a transformer vibration sensor;
Figure BDA0002653756580000051
uk(t) is a vibration signal collected by the transformer vibration sensor, which is an instantaneous superposition mixed signal,
Figure BDA0002653756580000052
being the phase of the signal, Ak(t) is the instantaneous amplitude, t is time;
step (2), carrying out high-frequency passband filtering processing on the vibration signal obtained in the step (1) to obtain a filtered signal Xii;
obtaining analysis signals of each modal function by Hilbert transform on the filtered signal Xii, and aiming at obtaining a single-side frequency spectrum of the signal Xii;
presetting the center frequency of the analytic signal of each mode function, and modulating the frequency spectrum of each mode to a corresponding fundamental frequency band;
step (4), calculating the square L of the above demodulation signal gradient2And (3) squaring the norm, and constructing a constraint variational model as follows:
Figure BDA0002653756580000061
wherein, { uk}＝{u1,u2,…,uKRepresents K modal components obtained by decomposition, { omega }k}＝{ω1,ω2,…,ωKDenotes the center frequency of each component,
Figure BDA0002653756580000062
representing the derivation of the function, (t) is the Dirac function, j represents the imaginary unit, t is time, uk(t) is the instantaneous superimposed mixed signal, f (t) is the original signal;
and (5) introducing a secondary penalty factor alpha and a Lagrange multiplication operator lambda (t) to solve the constraint variation problem in the step (4) and changing the constraint variation problem into an unconstrained variation problem, wherein the secondary penalty factor can ensure the reconstruction accuracy of the signal under the condition of Gaussian noise. Lagrange operators keep the constraint conditions strict, and the extended Lagrange expression is as follows:
Figure BDA0002653756580000063
alpha is a penalty factor, and lambda (t) is a Lagrange multiplier; k represents the maximum number of decompositions;
step (6), a multiplicative operator alternative direction method is adopted in the VMD to solve the variation problem in the step (4), and the alternative updating is carried out
Figure BDA0002653756580000064
And
Figure BDA0002653756580000065
and searching saddle points of the augmented Lagrange expression so as to complete the solution of the constraint variation problem in the constraint variation model.
In the step (2), the passband range of the high-frequency passband filtering processing is 10hz to 2000 hz.
In the step (3), the center frequency ω of each modal analysis signal is presetkThe specific method is to take the median of the frequency band where the mode is located as the preset center frequency.
In the step (6), in the process of searching for the saddle point, the corresponding variable update expression is as follows:
Figure BDA0002653756580000066
Figure BDA0002653756580000071
Figure BDA0002653756580000072
in the formula: Λ represents fourier transform; n is the number of iterations; tau, in the process of iteratively solving the variational model, each BIMF is a fidelity coefficient; ω represents a variable; λ is lagrange multiplier;
Figure BDA0002653756580000073
n-phase representing the kth center frequency;
Figure BDA0002653756580000074
a Fourier transform representing the phases of i modal components n + 1; k represents the kth BIMF;
Figure BDA0002653756580000075
a Fourier transform representing the nth stage of the Lagrangian multiplier;
Figure BDA0002653756580000076
a fourier transform representing the original signal;
the frequency center and bandwidth of the component are continuously updated until an iteration stop condition is satisfied.
When the iteration stop condition is satisfied:
Figure BDA0002653756580000077
finishing the whole cycle, finally completing the self-adaptive division of the signal frequency band according to the frequency domain characteristics of the actual signal, and carrying out inverse Fourier transform on the obtained signal frequency bandIs/are as follows
Figure BDA0002653756580000078
Converting the BIMF into a time domain BIMF component, wherein each BIMF is the final decomposition of the finally required equipment operation information, and can directly reflect the operation state or effective information of the equipment; where, the convergence constant is 0.01.
And calculating the number of the optimal BIMF components by using a PSO algorithm, wherein the number is limited within the range of 1-6, and the excess part is discarded. The optimal BIMF number obtained by the PSO algorithm is used for the value range of the K value used for VMD, and has important significance for VMD decomposition;
in the PSO algorithm:
Vt+1＝w·Vt+c1r1·(pBest-Xt)+c2r2·(gBest-Xt) (1-9)
Xt+1＝Xt+Vt+1 (1-10)
in the formula: v is the speed, t is the algebra, X is the position, w is the inertia weight, c is the learning factor, r is the random number, Pbest is the optimal solution found by the particle itself, Gbest is the optimal solution found by the whole population at present, i.e. the global extremum.
The vibration signal is, fundamentally, also generated by mechanical movement. Currently, mainstream vibration signal processing methods include EMD, EEMD, etc., and in these algorithm processes, various filters are used, including common high-pass and low-pass filtering, chebyshev filtering, etc., and these filters are used in different situations. Compared with the results of modal mixing and end effects commonly existing in the traditional signal processing methods, the invention provides an adaptive method for improving the processing precision of the vibration signal of the transformer, the method is an improved VMD (spatial mode decomposition) decomposition method combining the advantages of PSO (Particle Swarm Optimization), the analysis quality of the vibration signal can be greatly improved, the operation amount is reduced, and the result is very ideal through the practical application of nearly 30 main transformers on site.
Fundamental principle of variational modal decomposition
In the VMD method, the 'mode' is redefined as an am-fm signal, which is expressed as:
Figure BDA0002653756580000081
in the formula: u. ofk(t) is a vibration signal collected by the transformer vibration sensor, which is an instantaneous superposition mixed signal,
Figure BDA0002653756580000082
being the phase of the signal, Ak(t) is the instantaneous amplitude, t is time;
the VMD method may decompose a real signal into a predetermined number of quasi-orthogonal sub-modal' components, each having a frequency center and a finite bandwidth. To distinguish from the Intrinsic Mode Function (IMF) in the EMD method, the 'modal' component in the VMD method is called Band-Limited Intrinsic Mode Function (BIMF).
When the VMD method obtains the signal component, the processing mode of circular recursive screening adopted by the EMD method is completely abandoned, the EMD method is transferred to a variation frame in a unique way, and the decomposition process of the signal is completed by constructing and solving a constraint variation model, so that the method has a solid theoretical foundation.
The corresponding constraint variational model can be described as seeking K BIMF components u with specific sparsityk(t) minimizing the sum of the estimated bandwidths of the components, and defining a constraint condition that the sum of the components is equal to the original signal f (t), wherein the specific construction steps of the model are as follows:
(1) obtaining each BIMF component u through Hilbert conversionk(t) the analytic signal, in order to obtain its single-sided spectrum:
Figure BDA0002653756580000083
in the formula: (t) is a Dirac function, j represents an imaginary unit, t is time, uk(t)Mixing signals for instantaneous superposition;
(2) for each resolved signal of the BIMF component, the corresponding center frequency omega is estimatedkIt is then compared with the index signal
Figure BDA0002653756580000091
Multiplication, moving the spectrum to the base band:
Figure BDA0002653756580000092
in the formula: (t) is a Dirac function, j represents an imaginary unit, t is time, uk(t) is the instantaneous superimposed mixed signal;
(3) calculating L of the above modulation signal gradient2And (3) estimating the bandwidth of each BIMF component by the square of the norm, and finally constructing a constraint variation model in the following form:
Figure BDA0002653756580000093
in the formula: { uk}＝{u1,u2,…,uKDenotes the K BIMF components resulting from the decomposition, { ωk}＝{ω1,ω2,…,ωKDenotes the center frequency of each component,
Figure BDA0002653756580000094
representing the derivation of the function, (t) is the Dirac function, j represents the imaginary unit, t is time, uk(t) is the instantaneous superimposed hybrid signal, s.t. subject to, limited by (being a mathematical operation), f (t) is the original signal.
Solving the variation problem, introducing a penalty factor alpha and a Lagrange multiplier lambda, changing the constraint variation problem into an unconstrained variation problem, and obtaining an augmented Lagrange expression in the following form:
Figure RE-GDA0002725674440000095
wherein, alpha is a penalty factor, and lambda is a Lagrange multiplier.
Iterative update using an alternating Direction multiplier algorithm (Alternate Direction Method of Multipliers (ADMM)
Figure BDA0002653756580000096
And
Figure BDA0002653756580000097
to search the 'saddle point' of the formula (1-5), and complete the solution of the constraint variation problem in the formula (1-4). In the process of searching for 'saddle point', the corresponding variable update expression is as follows:
Figure BDA0002653756580000098
Figure BDA0002653756580000101
Figure BDA0002653756580000102
in the formula: the lambda represents Fourier transformation, n is iteration times, and in the process of solving a variational model through iteration, each BIMF is a fidelity coefficient; ω denotes the center frequency and λ is the lagrange multiplier.
The frequency center and bandwidth of the component are continuously updated until an iteration stop condition is satisfied.
When in use
Figure BDA0002653756580000103
Finishing the whole cycle, finally finishing the self-adaptive division of the signal frequency band according to the frequency domain characteristics of the actual signal, and carrying out Fourier inversion transformation on the obtained signal
Figure BDA0002653756580000104
Converted to a BIMF component in the time domain.
The invention solves the relationship between the optimal solutions of the BIMF component number value by a PSO calculation method, achieves the optimal matching, obtains the optimal solution, and provides theoretical support for equipment signal processing. Usually, the number of the BIMF can be up to 14. The invention utilizes PSO algorithm to calculate the optimal number of the BIMF components, the number range is defined between 1 and 6, and the excess part is abandoned.
The PSO is initialized to a population of random particles (random solution). The optimal solution is then found by iteration. In each iteration, the particle updates itself by tracking two "extrema". The first is the best solution found by the particle itself, pbest. The other extreme is the best solution currently found for the entire population, i.e. the global extreme gbest. The particles update their velocity and position by the following formula.
Just as the flight path of a bird can be doubly influenced by the optimal food that the bird has found and the optimal food that the bird group has found, in the algorithm, each iteration, the particle updates its own velocity through two "extrema" (global history optimal solution gBest and individual history optimal solution pBest), which is the key to updating the particle's position, which indicates the distance from the optimal solution, and is the only criterion to evaluate the particle (solution).
The core of the algorithm is how to update the speed and the position of the particles according to pBest and gBest, and the standard particle group gives the following update formula:
Vt+1＝w·Vt+c1r1·(pBest-Xt)+c2r2·(gBest-Xt) (1-9)
Xt+1＝Xt+Vt+1 (1-10)
in the formula: v is speed, t is algebra, X is position, w is inertia weight, c is a learning factor, r is random number, Pbest is the optimal solution found by the particle itself, Gbest is the optimal solution found by the whole population at present, namely a global extreme value;
the implementation flow of the VMD algorithm is shown in FIG. 1, and the relationship between the speed and the position is shown in FIG. 2.
The whole solving operation flow of each component of the VMD is as follows: and (3) eliminating each data through initialization, then updating by using a formula (1-6), if the condition is met, entering the next step, updating according to a formula (1-8) to obtain a result, if the condition is met, outputting each component, and if the condition is not met, returning to continue.
Assuming that this is a problem to be solved for finding the optimal solution in a 2-dimensional plane, a certain particle Xt at a certain time is at the origin. The updated velocity of the particle is shown in figure 2.
The update formula can be divided into three parts:
part.1: the "inertial" or "momentum" portion, reflecting the tendency of the particle to maintain its previous velocity;
part.2: the cognitive department reflects the trend that the particles approach to the historical optimal positions of the particles;
part.3: the 'social' department reflects the trend that the particles approach to the optimal positions of the group history;
and solving the number of optimal solutions by utilizing a particle swarm algorithm, and bringing the optimal solutions into a VMD (virtual matrix decomposition) algorithm to obtain an extremely accurate vibration signal decomposition result. Through the test of 30 actual transformers, the decomposition precision is improved by more than 2 times, and modal aliasing and end point effects are basically avoided.
A system for improving the accuracy of processing a vibration signal of a transformer as shown in fig. 5 comprises:
the signal acquisition module 101 is used for acquiring vibration signals acquired by the transformer vibration sensor;
the filtering processing and converting module 102 is configured to perform high-frequency passband filtering processing on the obtained signal, and then perform Hilbert conversion on the obtained filtered signal to obtain an analytic signal of each modal function;
the first processing module 103 is configured to preset a center frequency of each modal analysis signal, and modulate a frequency spectrum of each modal to a corresponding baseband;
constraint variational model structureA block 104 for calculating L of the square of the gradient of the demodulated signal2The norm is squared, and a constraint variational model is constructed;
a solving and outputting module 105, which is used for introducing a penalty factor alpha and a Lagrange multiplier lambda, changing the constraint variation problem into an unconstrained variation problem, and utilizing an alternate direction multiplier algorithm to update in an iterative manner
Figure BDA0002653756580000111
And
Figure BDA0002653756580000112
and searching saddle points of the augmented Lagrange expression, solving and outputting the BIMF components converted into time domains, wherein each output BIMF is the final needed decomposition containing the equipment operation information.
The method is compared with the EMD through the discontinuous synthesis signal and the near frequency synthesis signal, as shown in fig. 3 and fig. 4, the result shows that the method can separate the modes with different central frequencies to a greater extent (obtain 3 BIMF), not only effectively inhibits the mode aliasing caused by signal discontinuity, but also successfully solves the mode aliasing caused by the signal frequency being too close, and is obviously superior to the EMD method in the aspect of avoiding the two types of mode aliasing. The equivalent filtering characteristics of the method and the EMD are compared through fractional Gaussian noise numerical simulation, and the result shows that the frequency domain subdivision characteristics of the method are completely different from those of the EMD, the method has similar band-pass filtering properties but different from wavelet packet transformation, and the method can be used for carrying out fine analysis on a signal high-frequency region.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (9)

1. An adaptive method for improving the processing precision of a vibration signal of a transformer is characterized by comprising the following steps:
step (1), acquiring a vibration signal acquired by a transformer vibration sensor;
Figure FDA0002653756570000011
uk(t) is a vibration signal collected by the transformer vibration sensor,
Figure FDA0002653756570000012
being the phase of the signal, Ak(t) is the instantaneous amplitude, t is time;
step (2), carrying out high-frequency passband filtering processing on the vibration signal obtained in the step (1) to obtain a filtered signal Xii;
obtaining analysis signals of each modal function by Hilbert transformation on the filtered signals Xii;
presetting the center frequency of the analytic signal of each mode function, and modulating the frequency spectrum of each mode to a corresponding fundamental frequency band;
step (4), calculating the square L of the above demodulation signal gradient2And (3) squaring the norm, and constructing a constraint variational model as follows:
Figure FDA0002653756570000013
wherein, { uk}＝{u1,u2,…,uKRepresents K modal components obtained by decomposition, { omega }k}＝{ω1,ω2,…,ωKDenotes the center frequency of each component,
Figure FDA0002653756570000014
representing the derivation of the function, (t) is the Dirac function, j represents the imaginary unit, t is time, uk(t) is instantaneousSuperposing the mixed signal, f (t) is an original signal;
step (5), in order to solve the constraint variation problem in step (4), a secondary penalty factor alpha and a Lagrangian multiplier lambda (t) are introduced, the constraint variation problem is changed into an unconstrained variation problem, and an expanded Lagrangian expression is as follows:
Figure FDA0002653756570000015
alpha is a penalty factor, and lambda (t) is a Lagrange multiplier; k represents the maximum number of decompositions;
step (6), a multiplicative operator alternative direction method is adopted in the VMD to solve the variation problem in the step (4), and the alternative updating is carried out
Figure FDA0002653756570000021
And searching saddle points of the augmented Lagrange expression so as to complete the solution of the constraint variation problem in the constraint variation model.
2. The adaptive method for improving the processing accuracy of the transformer vibration signal according to claim 1, wherein in the step (2), the passband of the high-frequency passband filtering process is in a range of 10hz to 2000 hz.
3. The adaptive method for improving the accuracy of processing the vibration signal of the transformer according to claim 1, wherein in the step (3), each modal analysis signal is preset to have a center frequency ωkThe specific method is to take the median of the frequency band where the mode is located as the preset central frequency.
4. The adaptive method for improving the accuracy of processing the vibration signal of the transformer according to claim 1, wherein in the step (6), in the process of searching for the saddle point, the corresponding variable update expression is as follows:
Figure FDA0002653756570000022
Figure FDA0002653756570000023
Figure FDA0002653756570000024
in the formula: Λ represents fourier transform; n is the number of iterations; tau, in the process of iteratively solving the variational model, each BIMF is a fidelity coefficient; ω represents a variable; λ is lagrange multiplier;
Figure FDA0002653756570000025
n-phase representing the kth center frequency;
Figure FDA0002653756570000026
a Fourier transform representing the phases of i modal components n + 1; k represents the kth BIMF;
Figure FDA0002653756570000027
a Fourier transform representing the nth stage of the Lagrangian multiplier;
Figure FDA0002653756570000028
a fourier transform representing the original signal;
the frequency center and bandwidth of the component are continuously updated until an iteration stop condition is satisfied.
5. The adaptive method for improving the processing accuracy of the transformer vibration signal according to claim 1, wherein when the iteration stop condition is satisfied:
Figure FDA0002653756570000029
finishing the whole cycle, finally completing the self-adaptive division of the signal frequency band according to the frequency domain characteristics of the actual signal, and converting the frequency band by inverse Fourier transformObtained (a)
Figure FDA0002653756570000031
Converting into time domain BIMF components, wherein each BIMF is the final decomposition of the finally required equipment operation information; where it is the convergence constant.
6. The adaptive method for improving the accuracy of processing the vibration signal of the transformer according to claim 5, wherein the value is 0.01.
7. The adaptive method for improving the processing accuracy of the vibration signals of the transformer as claimed in claim 5, wherein the optimal BIMF number of the components is calculated by using a PSO algorithm, the number is defined in a range of 1-6, and more than part of the components are discarded.
8. The adaptive method for improving the processing precision of the vibration signals of the transformer according to claim 7, wherein the optimal BIMF number is obtained through a PSO algorithm; in the PSO algorithm:
Vt+1＝w·Vt+c1r1·(pBest-Xt)+c2r2·(gBest-Xt) (1-9)
Xt+1＝Xt+Vt+1 (1-10)
in the formula: v is the speed, t is the algebra, X is the position, w is the inertia weight, c is the learning factor, r is the random number, Pbest is the optimal solution found by the particle itself, Gbest is the optimal solution found by the whole population at present, i.e. the global extremum.
9. Improve system of transformer vibration signal processing accuracy, its characterized in that includes:
the signal acquisition module is used for acquiring vibration signals acquired by the transformer vibration sensor;
the filtering processing and converting module is used for carrying out high-frequency passband filtering processing on the obtained signals and then carrying out Hilbert conversion on the obtained filtered signals to obtain analytic signals of each modal function;
the first processing module is used for presetting the center frequency of each modal analysis signal and modulating the frequency spectrum of each mode to a corresponding baseband;
a constraint variation model building module for calculating the L of the square of the demodulation signal gradient2Squaring the norm to construct a constraint variational model;
a solving and outputting module for introducing a penalty factor alpha and a Lagrange multiplier lambda, changing the constraint variation problem into an unconstrained variation problem and utilizing an alternate direction multiplier algorithm to update in an iterative manner
Figure FDA0002653756570000032
And searching saddle points of the augmented Lagrange expression, completing solution, outputting the BIMF components converted into time domains, wherein each output BIMF is the final needed decomposition containing the equipment operation information.
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