Short-circuit impedance identification method and system based on VMD noise reduction and probability density optimization

Abstract

The invention relates to the technical field of power equipment monitoring, and discloses a short-circuit impedance identification method and system based on VMD noise reduction and probability density optimization, and the method comprises the steps: decomposing an electrical signal through a VMD method, removing random noise, and effectively filtering external interference; meanwhile, the short-circuit impedance is calculated through probability density distribution based on fast neighbor search, so that errors caused by random fluctuation are reduced. According to the method, the reliability of electrical signal acquisition and the accuracy of short-circuit impedance identification can be remarkably improved, the method is suitable for online monitoring of power equipment such as a transformer, and important technical support is provided for equipment fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of power equipment monitoring, and in particular to a short-circuit impedance identification method and system based on VMD noise reduction and probability density optimization. Background Art

[0002] With the rapid development of power systems and the expansion of their application scale, the stability and reliability of power equipment have become key factors in ensuring the safe operation of power systems. Power equipment such as transformers and generators will be affected by external factors during long-term operation, such as mechanical stress, electromagnetic environment, thermal effects, etc., which will cause deformation or aging of the winding structure inside the equipment, thereby affecting its electrical performance. As one of the important parameters of power equipment, short-circuit impedance can effectively reflect the physical state and health of the equipment windings, and is an important basis for evaluating potential equipment failures and predicting life.

[0003] In the traditional short-circuit impedance measurement method, the measurement data is easily affected by external electromagnetic interference and signal noise, especially in the field environment, the complex electromagnetic environment may cause a large amount of random noise and high-frequency interference in the short-circuit impedance signal. These noises and interferences not only affect the stability of the signal, but also greatly reduce the accuracy of short-circuit impedance identification. In order to cope with these problems, fixed frequency sampling or simple filtering methods are usually used in the prior art to perform noise reduction. However, these methods often fail to achieve the desired effect when the noise is large or the signal frequency components are complex. Fixed frequency sampling cannot dynamically adjust the sampling rate according to signal changes, resulting in low data quality, while simple filtering methods cannot effectively remove high-frequency random noise, thereby affecting the accurate identification of short-circuit impedance. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is that the existing short-circuit impedance identification method has poor stability and accuracy and is easily affected by external interference.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: a short-circuit impedance identification method based on VMD noise reduction and probability density optimization, comprising: Collect the operating data of the transformer under actual normal operating conditions, establish a 1:1 simulation model based on the actual structure and operating conditions of the transformer, simulate the deformation of the winding, simulate the winding deformation condition in the simulation model, and obtain the operating data under deformation; After data acquisition, signal preprocessing is performed; The preprocessed electrical signal is decomposed using VMD technology to obtain modal components of different frequencies; The obtained fundamental modal component is divided into N time windows, and the short-circuit impedance in each time window is calculated using the least squares algorithm; The calculated short-circuit impedance is subjected to kernel density estimation by fast nearest neighbor search, and the short-circuit impedance value corresponding to the maximum density value in the probability density distribution is found as the optimal estimate of the short-circuit impedance.

[0007] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, wherein: the operating data is data representing the conventional operating characteristics of the transformer, including but not limited to voltage and current; The simulation of the winding deformation includes simulating four deformation modes of compression, expansion, elongation and shortening of the winding geometric model in finite element simulation analysis; By adjusting the winding geometry model, the modified geometry model is applied to electromagnetic field simulation to simulate the electromagnetic behavior and operating characteristics of the transformer under normal load conditions.

[0008] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, the preprocessing includes smoothing the signal through a sliding window using a moving average filtering method to reduce the impact of transient anomalies; Set the sliding window size N to 5 sampling points and the sampling frequency to 2.5kHz. Calculate the mean of the data in each sliding window and replace the data point in the center of the current window with the mean value in the window. , in, is the data point in the window, is the mean of the current data point, and t represents the current moment.

[0009] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, wherein: the decomposition of the pre-processed electrical signal using VMD technology includes removing noise and extracting signal features through modal decomposition, converting the input signal Decompose into K modes , so that the bandwidth of each mode is concentrated at the center frequency Nearby, thus achieving the goal of minimizing the bandwidth of each mode; When decomposing the electrical signal, the constraints are: , Introducing Lagrange multipliers , to constrain the difference between the original signal and the modal component, so that VMD can ensure the original signal in the decomposition process is equal to the sum of the modal components while minimizing the bandwidth of each mode: , Where k represents the index of the mode; is the kth modal component; is the Lagrange multiplier that controls the difference between each modal component and the original signal; is the center frequency; is the bandwidth measure of the mode; VMD updates the modal components by alternating iterations , Lagrange multipliers and center frequency , gradually approaching the optimal solution, the specific iterative steps are as follows: In each iteration, for each modal component , update the modal components by minimizing the bandwidth and the constraints: , Update the Lagrange multipliers according to the constraints: , in, is the update step size, which is used to control the adjustment rate of the Lagrange multiplier; The center frequency of each mode Update by minimizing the spectral difference of the modes: , in, is modulated to the center frequency by Hilbert transform modal signal.

[0010] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, the calculation of the short-circuit impedance in each time window includes: , Where k is the transformer ratio, , are the high and low voltage side winding voltages respectively; , are the leakage inductance of the transformer high and low voltage sides respectively; , They are high and low voltage side winding currents respectively; , They are high and low voltage side resistors respectively.

[0011] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, wherein: the kernel density estimation includes decomposing the signal parameters through VMD to obtain multiple signal parameters about the time series; The calculated short-circuit impedance is also a sequence value with the same dimension as the time series; The kernel density method is used to calculate the probability density distribution of short-circuit impedance, assigning a Gaussian kernel function to each data point in the sequence. : , Calculate the contribution of each point to the kernel function and add the kernel functions of all points to get the overall density estimate: , in, is the probability density estimate at x, N is the total number of data, h is the bandwidth of the kernel function, and K is the Gaussian kernel function.

[0012] As a preferred solution of the short-circuit impedance identification method based on VMD noise reduction and probability density optimization described in the present invention, wherein: the fast neighbor search includes using a ball tree structure to perform a fast neighbor search, only calculating the kernel function value for the data points close to the target point x, and ignoring the points far away from x; According to the bandwidth h of kernel density estimation, a search radius r = 2h is set; Use the ball tree structure to find the set of neighboring data points within radius r, neighbors(x); .

[0013] A short-circuit impedance identification system based on VMD noise reduction and probability density optimization using the method of the present invention is characterized by: The simulation unit collects the operating data of the transformer under the actual normal operating state, establishes a 1:1 simulation model according to the actual structure and operating conditions of the transformer, simulates the deformation of the winding, simulates the deformation condition of the winding in the simulation model, and obtains the operating data under the deformation condition; The processing unit performs signal preprocessing after data acquisition; A decomposition unit decomposes the preprocessed electrical signal using VMD technology to obtain modal components of different frequencies; The calculation unit divides the obtained fundamental modal component into N time windows, and calculates the short-circuit impedance in each time window using a least squares algorithm; The analysis unit performs a kernel density estimation of a fast nearest neighbor search on the calculated short-circuit impedance, and finds the short-circuit impedance value corresponding to the maximum density value in the probability density distribution as the optimal estimate of the short-circuit impedance.

[0014] A computer device comprises: a memory and a processor; the memory stores a computer program, wherein: the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0015] A computer-readable storage medium stores a computer program, wherein: when the computer program is executed by a processor, the steps of any one of the methods of the present invention are implemented.

[0016] Beneficial effects of the present invention: The short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided by the present invention can decompose the signal into multiple modal components, separate the characteristic signal and remove the interference noise; at the same time, the probability density calculation is used to identify the optimal short-circuit impedance value, thereby reducing the randomness in the measurement process, reducing the error caused by random fluctuations, and ensuring the stability and accuracy of impedance identification. It can significantly improve the reliability of electrical signal acquisition and the accuracy of short-circuit impedance identification, and is suitable for online monitoring of power equipment such as transformers, providing important technical support for equipment fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0018] Figure 1 An overall flow chart of a short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided by the first embodiment of the present invention; Figure 2 A current waveform diagram containing noise in the short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided in the second embodiment of the present invention; Figure 3 A schematic diagram of mode 1 after VMD decomposition in the short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided by the second embodiment of the present invention; Figure 4 A schematic diagram of mode 2 after VMD decomposition in the short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided by the second embodiment of the present invention; Figure 5 A schematic diagram of mode 3 after VMD decomposition in the short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided by the second embodiment of the present invention; Figure 6A short-circuit impedance identification sequence diagram in a short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided in a second embodiment of the present invention; Figure 7 A probability density curve diagram of short-circuit impedance in a short-circuit impedance identification method based on VMD noise reduction and probability density optimization provided in the second embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0020] Example 1, reference Figure 1 , which is an embodiment of the present invention, provides a short-circuit impedance identification method based on VMD noise reduction and probability density optimization, including: S1: Collect key operating data of the transformer under actual normal operating conditions, including parameters such as voltage and current. Establish a 1:1 simulation model based on the actual structure and operating conditions of the transformer to simulate the winding deformation. Simulate the winding deformation condition in the simulation model and obtain the operating data under deformation.

[0021] It should be noted that in the finite element simulation analysis, the deformation behavior of the transformer winding can be accurately reproduced by simulating four deformation modes such as compression, expansion, elongation and shortening of the winding geometric model. These deformation modes correspond to the geometric deformations that may occur in the winding during operation, such as shape changes caused by mechanical stress, temperature changes or electromagnetic forces. By adjusting the winding geometric model, the modified geometric model is further applied to electromagnetic field simulation, which can simulate the electromagnetic behavior and operating characteristics of the transformer under normal load conditions. In this way, the operating data of the transformer under deformation is obtained.

[0022] S2: After data acquisition, signal preprocessing is performed to reduce the impact of DC offset and sudden spikes on the signal.

[0023] Furthermore, the moving average filter method is used to smooth the signal through the sliding window to reduce the impact of transient anomalies. The sliding window size N is set to 5 sampling points, the sampling frequency is 2.5kHz, the mean or weighted mean is calculated for the data in each sliding window, and the data point in the center of the current window is replaced with the mean in the window.

[0024] , in, is the data point in the window, is the mean of the current data point, and t represents the current moment.

[0025] S3: The preprocessed electrical signal is decomposed using VMD technology to obtain a series of modal components with different frequencies.

[0026] Using modal decomposition to perform noise reduction and extract voltage and current signal features can effectively filter out high-frequency noise or other unnecessary signal components and achieve high-precision signal noise reduction. This modal-based noise reduction method is more flexible and targeted than traditional filtering methods, and can retain the main features of the signal while reducing information loss.

[0027] Furthermore, the goal of VMD is to convert the signal Decomposed into several modal components , so that the bandwidth of each mode is concentrated at its center frequency To this end, the goal of VMD is to minimize the bandwidth of each mode and make the sum of the modal components as close to the original signal as possible. In order to constrain the correctness of signal decomposition, the constraints are: , In order to perform optimization, Lagrange multipliers are introduced to constrain the difference between the original signal and the modal components. The optimization problem can be expressed as: , in: is the kth modal component; is the Lagrange multiplier that controls the difference between each modal component and the original signal; is the center frequency; is a measure of the bandwidth of the mode.

[0028] By introducing the Lagrange multiplier , VMD can ensure the original signal during the decomposition process is equal to the sum of the modal components while minimizing the bandwidth of each mode.

[0029] VMD updates the modal components by alternating iterations , Lagrange multipliers and center frequency , to gradually approach the optimal solution. The specific iterative steps are as follows: In each iteration, for each modal component , update the modal components by minimizing the bandwidth and the constraints: , Update the Lagrange multipliers according to the constraints: , in: is the update step size, which is used to control the adjustment rate of the Lagrange multiplier.

[0030] The center frequency of each mode It can be updated by minimizing the difference in the modes’ spectra: , in, is modulated to the center frequency by Hilbert transform modal signal.

[0031] S4: Divide the obtained fundamental modal component into N time windows, and calculate the short-circuit impedance in each time window using the least squares algorithm.

[0032] , Where k is the transformer ratio, , is the high and low voltage side winding voltage; , are the leakage inductance of the transformer high and low voltage sides respectively; , is the high and low voltage side winding current; , It is the high and low voltage side resistor.

[0033] S5: Perform probability density estimation on the calculated short-circuit impedance and construct a probability density distribution curve of the short-circuit impedance value.

[0034] It should be noted that when performing kernel density estimation (KDE), the complexity of calculating the kernel function value of each data point to the target point and summing them is high, especially when the amount of data is large. The traditional kernel density estimation method has a time complexity of O(N2), which means that each target point needs to calculate the distance to all data points, which is very time-consuming for large data sets. Therefore, fast neighbor search is introduced to speed up the calculation to reduce unnecessary calculations. Choosing an appropriate data structure can significantly improve the computational efficiency, and the ball tree is a structure suitable for processing high-dimensional data and can be effectively used in fast neighbor search.

[0035] The kernel density method is used to calculate the probability density distribution of short-circuit impedance. The signal parameters after VMD decomposition are several time series. The short-circuit impedance obtained by calculation is also a sequence value with the same dimension as the time series. A Gaussian kernel function is assigned to each data point in the sequence. : , Calculate the contribution of each point to the kernel function and add the kernel functions of all points to get the overall density estimate: , in, is the probability density estimate at x, N is the total number of data, h is the bandwidth of the kernel function, and K is the Gaussian kernel function.

[0036] In order to reduce the amount of calculation, the ball tree structure is used to perform fast neighbor search. The kernel function value is only calculated for the data points close to the target point x, while the points far away from x are ignored. This can greatly reduce the computational complexity. According to the bandwidth h of the kernel density estimate, a search radius r = 2h is set. The ball tree structure is used to find the set of data points neighbors(x) that are close to the target point within the radius r.

[0037] The fast neighbor search includes using a ball tree structure to perform a fast neighbor search, only calculating the kernel function value for data points close to the target point x, and ignoring points far away from x.

[0038] According to the bandwidth h of the kernel density estimation, a search radius r = 2h is set.

[0039] The set of neighboring data points neighbors(x) within radius r is obtained using the ball tree structure.

[0040] , The ball tree is a space partitioning data structure. By establishing this tree structure, the set of neighboring data points near the target point can be efficiently found without traversing all data points. The ball tree divides the data space into nested spheres, so that points in a certain area can be quickly located. By limiting the kernel density calculation to neighboring points within the search radius, r = 2h, the influence of distant data points on the estimation can be ignored, reducing the computational complexity while ensuring the accuracy of the density estimation.

[0041] S6: Finally, the short-circuit impedance value corresponding to the maximum density value is found in the probability density distribution, which is the optimal estimate of the short-circuit impedance.

[0042] On the other hand, this embodiment also provides a short-circuit impedance identification system based on VMD noise reduction and probability density optimization, which includes: The simulation unit collects the operating data of the transformer under actual normal operating conditions, establishes a 1:1 simulation model according to the actual structure and operating conditions of the transformer, simulates the deformation of the winding, simulates the winding deformation condition in the simulation model, and obtains the operating data under the deformation condition.

[0043] The processing unit performs signal preprocessing after data acquisition.

[0044] The decomposition unit decomposes the preprocessed electrical signal using VMD technology to obtain modal components of different frequencies.

[0045] The calculation unit divides the obtained fundamental modal component into N time windows, and calculates the short-circuit impedance in each time window using a least squares algorithm.

[0046] The analysis unit performs a kernel density estimation of a fast nearest neighbor search on the calculated short-circuit impedance, and finds the short-circuit impedance value corresponding to the maximum density value in the probability density distribution as the optimal estimate of the short-circuit impedance.

[0047] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0048] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0049] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0050] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0051] Example 2, reference Figure 2-7 , which is an embodiment of the present invention, provides a short-circuit impedance identification method based on VMD noise reduction and probability density optimization. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0052] Attached Figure 2 Current waveform with noise: shows a current waveform with high-frequency noise. Although the waveform presents a relatively regular sine shape, there are irregular small jitters at the peaks and troughs, which is a typical high-frequency noise phenomenon superimposed on the original signal. This noise may come from external high-frequency interference or electromagnetic interference within the system. The signal in the figure has not been processed for noise reduction, so the noise is clearly visible, which has a certain impact on the accuracy of the signal, but the basic fluctuation trend of the current can still be observed.

[0053] Attached Figure 3 Mode 1 after VMD decomposition: The first mode diagram shows the lower frequency components of the signal, with high amplitude and periodic changes over time. The amplitude of the signal reaches the maximum in the middle part, then gradually decreases, and the waveform is relatively smooth overall. Mode 1 reflects the trend part of the original signal and represents the low-frequency characteristics of the signal.

[0054] Attached Figure 4Mode 2 after VMD decomposition: The second mode diagram shows a signal component with a slightly higher frequency than the first mode. Its amplitude variation is more complex, showing fluctuations of different amplitudes. This mode contains more frequency components and is relatively complex, reflecting the intermediate frequency part of the signal. Mode 2 represents the secondary components or intermediate frequency characteristics in the signal.

[0055] Attached Figure 5 Mode 3 after VMD decomposition: The third mode diagram shows the main frequency component of the signal, which has the highest frequency and a relatively constant amplitude, showing a stable oscillation. This mode successfully extracts the main frequency components of the signal and effectively filters out the noise, making the waveform purer and more stable. Mode 3 reflects the core frequency characteristics of the signal, which helps to further analyze the main frequency response of the signal.

[0056] Attached Figure 6 Short circuit impedance identification sequence diagram: Figure 5 The original impedance sequence calculated from the mode 3 voltage and current time series after VMD decomposition is shown. It can be seen that the impedance value fluctuates significantly between sampling points, with a fluctuation range of about 8 to 24, and fluctuates around the average value. Since the fluctuation of short-circuit impedance is relatively frequent and lacks stability, it is difficult to observe the overall trend directly from this sequence.

[0057] Attached Figure 7 Probability density curve of short-circuit impedance: This figure shows the impedance probability density curve obtained by the kernel density estimation method of fast neighbor search. The horizontal axis is the impedance value and the vertical axis is the probability density. The curve shows a bell-shaped distribution with a peak value concentrated near 15.9, representing the stable trend of impedance. Kernel density estimation smoothes the original fluctuation sequence, eliminates the impact of short-term random fluctuations, and makes the main range of impedance changes clearer. This stable trend provides a reliable reference benchmark that can be used for long-term monitoring of equipment. If the impedance value deviates from this stable area in subsequent monitoring, it may indicate that the system is abnormal or has potential faults.

[0058] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A short-circuit impedance identification method based on VMD noise reduction and probability density optimization, characterized in that: include: Collect the operating data of the transformer under actual normal operating conditions, establish a 1:1 simulation model based on the actual structure and operating conditions of the transformer, simulate the deformation of the winding, simulate the winding deformation condition in the simulation model, and obtain the operating data under deformation; After data acquisition, signal preprocessing is performed; The preprocessed electrical signal is decomposed using VMD technology to obtain modal components of different frequencies; The obtained fundamental modal component is divided into N time windows, and the short-circuit impedance in each time window is calculated using the least squares algorithm; For the calculated short-circuit impedance, a kernel density estimation of fast nearest neighbor search is performed to find the short-circuit impedance value corresponding to the maximum density value in the probability density distribution as the optimal estimate of the short-circuit impedance; The operating data is data representing the normal operating characteristics of the transformer, including but not limited to voltage and current; The simulation of the winding deformation includes simulating four deformation modes of compression, expansion, elongation and shortening of the winding geometric model in finite element simulation analysis; By adjusting the winding geometry model, the modified geometry model is applied to electromagnetic field simulation to simulate the electromagnetic behavior and operating characteristics of the transformer under normal load conditions.

2. The short-circuit impedance identification method based on VMD noise reduction and probability density optimization as claimed in claim 1, characterized in that: The preprocessing includes using a moving average filter method to smooth the signal through a sliding window to reduce the impact of transient anomalies; Set the sliding window size N to 5 sampling points and the sampling frequency to 2.5kHz. Calculate the mean of the data in each sliding window and replace the data point in the center of the current window with the mean value in the window. ， in, is the data point in the window, is the mean of the current data point, and t represents the current moment.

3. The short-circuit impedance identification method based on VMD noise reduction and probability density optimization as claimed in claim 2, characterized in that: The method of decomposing the pre-processed electrical signal by using VMD technology includes removing noise and extracting signal features by modal decomposition. Decompose into K modes , so that the bandwidth of each mode is concentrated at the center frequency Nearby, thus achieving the goal of minimizing the bandwidth of each mode; When decomposing the electrical signal, the constraints are: ， Introducing Lagrange multipliers , to constrain the difference between the original signal and the modal component, so that VMD can ensure the original signal in the decomposition process is equal to the sum of the modal components while minimizing the bandwidth of each mode: ， Where k represents the index of the mode; is the kth modal component; is the Lagrange multiplier that controls the difference between each modal component and the original signal; is the center frequency; is the bandwidth measure of the mode; VMD updates the modal components by alternating iterations , Lagrange multipliers and center frequency , gradually approaching the optimal solution, the specific iterative steps are as follows: In each iteration, for each modal component , update the modal components by minimizing the bandwidth and the constraints: ， Update the Lagrange multipliers according to the constraints: ， in, is the update step size, which is used to control the adjustment rate of the Lagrange multiplier; The center frequency of each mode Update by minimizing the spectral difference of the modes: ， in, is modulated to the center frequency by Hilbert transform modal signal.

4. The short-circuit impedance identification method based on VMD noise reduction and probability density optimization as claimed in claim 3, characterized in that: The calculation of the short-circuit impedance in each time window includes: ， Where k is the transformer ratio, , are the high and low voltage side winding voltages respectively; , are the leakage inductance of the transformer high and low voltage sides respectively; , are the high and low voltage side winding currents respectively; , They are high and low voltage side resistors respectively.

5. The short-circuit impedance identification method based on VMD noise reduction and probability density optimization as claimed in claim 4, characterized in that: The kernel density estimation includes decomposing the signal parameters through VMD to obtain multiple signal parameters about the time series; The calculated short-circuit impedance is also a sequence value with the same dimension as the time series; The kernel density method is used to calculate the probability density distribution of short-circuit impedance, assigning a Gaussian kernel function to each data point in the sequence. : ， Calculate the contribution of each point to the kernel function and add the kernel functions of all points to get the overall density estimate: ， in, is the probability density estimate at x, N is the total number of data, h is the bandwidth of the kernel function, and K is the Gaussian kernel function.

6. The short-circuit impedance identification method based on VMD noise reduction and probability density optimization as claimed in claim 5, characterized in that: The fast neighbor search includes performing a fast neighbor search using a ball tree structure, calculating kernel function values ​​only for data points close to the target point x, and ignoring points far from x; According to the bandwidth h of kernel density estimation, a search radius r = 2h is set; Use the ball tree structure to find the set of neighboring data points within radius r, neighbors(x); 。 7. A short-circuit impedance identification system based on VMD noise reduction and probability density optimization using the method according to any one of claims 1 to 6, characterized in that: The simulation unit collects the operating data of the transformer under the actual normal operating state, establishes a 1:1 simulation model according to the actual structure and operating conditions of the transformer, simulates the deformation of the winding, simulates the deformation condition of the winding in the simulation model, and obtains the operating data under the deformation condition; The processing unit performs signal preprocessing after data acquisition; A decomposition unit decomposes the preprocessed electrical signal using VMD technology to obtain modal components of different frequencies; The calculation unit divides the obtained fundamental modal component into N time windows, and calculates the short-circuit impedance in each time window using a least squares algorithm; The analysis unit performs a kernel density estimation of a fast nearest neighbor search on the calculated short-circuit impedance, and finds the short-circuit impedance value corresponding to the maximum density value in the probability density distribution as the optimal estimate of the short-circuit impedance.

8. A computer device comprising: Memory and processor; The memory stores a computer program, wherein the processor implements the steps of any one of the methods of claims 1-6 when executing the computer program.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

Images