A transformer leakage magnetic field signal measurement method based on multi-window STFT time-frequency redistribution and UKF fusion

Abstract

The present application belongs to the technical field of power system equipment state monitoring and signal processing, and particularly relates to a transformer leakage magnetic field signal measurement method based on multi-window STFT time-frequency redistribution and UKF fusion. The method comprises the following steps: step S1: leakage magnetic signal acquisition and preprocessing; step S2: multi-window STFT calculation; step S3: time-frequency redistribution, time-frequency redistribution is performed on the multi-window STFT spectrum; step S4: frequency ridge line extraction and complex observation construction; step S5: nonlinear state space model construction; step S6: UKF state estimation; step S7: measurement quality evaluation; and step S8: leakage magnetic time domain signal reconstruction. The beneficial effects are as follows: the present application uses multi-window STFT and time-frequency redistribution to obtain time-frequency focused power frequency and low-order harmonic energy ridges, and constructs complex observation; then, the UKF is used to perform nonlinear state estimation on the amplitude and phase of each frequency component, so as to realize smooth tracking and high signal-to-noise ratio reconstruction of the key components of the leakage magnetic signal.

Description

Technical Field

[0001] This invention belongs to the field of power system equipment condition monitoring and signal processing technology, specifically relating to a method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion. Background Technology

[0002] Power transformers are core equipment in power transmission and distribution systems, and their operating status directly affects the safety and reliability of the power grid. When transformer windings are subjected to short-circuit current surges, prolonged overload operation, and repeated electromagnetic forces, structural and electrical hazards such as axial compression, radial bulging, inter-turn short circuits, and insulation aging can easily occur. Once these hazards develop into actual faults, they can lead to transformer damage or even widespread power outages. Therefore, online monitoring and early warning of winding conditions are of significant engineering importance.

[0003] The leakage magnetic field near the winding comprehensively reflects information from multiple aspects, including the core magnetic circuit, winding structure, and current distribution. Compared to relying solely on electrical quantities such as current and voltage, the leakage magnetic field is more sensitive to changes in winding geometry and inter-turn anomalies. By placing magnetic sensors outside the transformer body to measure and analyze the leakage magnetic field signal, indirect monitoring of winding deformation, local overheating, and inter-turn faults can be achieved, which has become an important direction in research and engineering practice in recent years.

[0004] In existing technologies, leakage flux timing signals are typically acquired by placing fixed magnetic sensors on the outer surface of the transformer windings. Then, Discrete Fourier Transform (DFT) or simple filtering methods are used to extract characteristic quantities such as the power frequency and low-order harmonic amplitudes. These methods implicitly assume that the signal is approximately stationary within the analysis period. However, under actual operating conditions, transformer load levels, power grid operation modes, and environmental electromagnetic interference are dynamically changing. The leakage flux signal often exhibits significant non-stationarity, low signal-to-noise ratio, and multiple harmonic superposition characteristics. Using only static frequency domain analysis and linear filtering is insufficient to accurately characterize the changes in power frequency and harmonics over time; characteristic quantities fluctuate significantly, and the measurement results lack stability.

[0005] To improve the characterization of non-stationary signals, existing technologies have attempted to introduce time-frequency analysis tools such as short-time Fourier transform, wavelet transform, and empirical mode decomposition to describe the time-frequency characteristics of leakage flux or current and voltage signals, thereby enhancing the ability to identify transient disturbances and harmonic components. However, in the actual substation environment, circuit breaker operation, switching of adjacent equipment, grounding grid current, and communication equipment generate complex background electromagnetic interference, resulting in a low signal-to-noise ratio for leakage flux signals. Energy diffusion and cross-term problems are prominent in the time-spectrum diagram, and the energy concentration of power frequency and low-order harmonics is insufficient, leading to unclear and unstable frequency trajectories and affecting the reliability of subsequent diagnostic models.

[0006] On the other hand, the truly useful information in transformer leakage flux signals mainly lies in the amplitude and phase of the power frequency and several low-order harmonics. These quantities typically change slowly and continuously with load variations, operational mode adjustments, and early fault evolution, exhibiting significant time correlation. If only time-frequency analysis is used without combining it with state estimation methods to smoothly track these characteristics, it is easily affected by instantaneous noise and local interference, leading to short-term drastic fluctuations in characteristic quantities, making it difficult to distinguish between "real changes" and "noise disturbances." Furthermore, existing methods primarily focus on feature extraction and fault identification, lacking explicit quantification and evaluation of "measurement quality" itself, and failing to provide maintenance personnel with clear decision-making criteria such as "whether the current data is reliable" and "which time periods' data should be downweighted or discarded."

[0007] Kalman filtering and its improved form, unscented Kalman filtering, are mature tools in the field of nonlinear state estimation. They can recursively estimate slowly changing states even in the presence of measurement noise and model uncertainty, balancing estimation accuracy and real-time performance. Although there are related applications in other scenarios of power system signal processing, research on a comprehensive measurement method that closely integrates multi-window short-time Fourier time-frequency analysis with unscented Kalman filtering, specifically targeting transformer leakage magnetic field signals, and constructing an integrated measurement method of "time-frequency focusing - state smoothing estimation - measurement quality evaluation," is still relatively limited. Related technical solutions need further improvement.

[0008] In summary, existing transformer leakage magnetic field signal measurement technologies still suffer from problems such as insufficient anti-interference capability, inadequate characterization of non-stationary characteristics, lack of smooth tracking of power frequency and harmonic amplitude and phase, and insufficient quantification of measurement quality under complex electromagnetic environments. It is necessary to propose a new leakage magnetic field signal measurement method that is engineering-feasible and possesses strong professionalism and innovation. Summary of the Invention

[0009] The purpose of this invention is to provide a transformer leakage magnetic field signal measurement method based on multi-window STFT time-frequency redistribution and UKF fusion, which can overcome the problems of non-stationarity, low signal-to-noise ratio, multiple harmonic superposition and lack of measurement quality quantification in existing transformer leakage magnetic field signal measurement methods.

[0010] The technical solution of the present invention is as follows: A method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion, comprising the following steps: Step S1: Leakage magnetic field signal acquisition and preprocessing; Multiple leakage flux measurement points are arranged along the axial direction outside the transformer winding, with a sampling frequency. Collect discrete leakage magnetic field signals at each measuring point , Number the measurement points and simultaneously acquire the transformer winding current signal; Step S2: Multi-window STFT calculation; Step S3: Time-frequency redistribution, for multi-window STFT spectrum Perform time-frequency reallocation; Step S4: Frequency ridge extraction and complex observation construction; Step S5: Constructing the nonlinear state-space model; Step S6: UKF state estimation; Step S7: Measurement quality evaluation; Step S8: Reconstruction of leakage magnetic field time domain signal.

[0011] The preprocessing of the leakage magnetic signal in step S1 includes: DC removal: Subtract the average value from the signal at each measurement point; Detrending: Use linear fitting or high-pass filtering to remove slow drift; Band-limited filtering: preserves the frequency band covering power frequency and some low-order harmonics; The preprocessed signal is denoted as .

[0012] Step S2 includes preprocessing the signal for each measurement point. Construct a sliding time window on the timeline and select... Seeding window function The window length is Step size is ; For the first A window function, whose short-time Fourier transform is abbreviated as: Equation (1) in, For frequency index, Index for time windows; The short-time spectra obtained from different window functions are weighted and summed according to frequency correlation weights to obtain the multi-window fused spectrum. .

[0013] In step S3, the local instantaneous frequency of each time-frequency unit is estimated based on the change of the spectral phase over time. Then, the energy of that unit is "transferred" from the original frequency grid point to the estimated instantaneous frequency. The original STFT is at the grid point. The energy on is denoted as After redistribution, the energy is re-accumulated to the corresponding instantaneous frequency index. The redistribution spectrum is obtained above. .

[0014] Step S4 includes the redistribution spectrum In the middle, around the power frequency And several low-order harmonic frequency bands are searched, in each time window The system identifies locations with localized maximum energy that do not significantly change frequency from the previous time window, forming frequency ridges that vary continuously over time, including power frequency ridges. Second harmonic ridge Third harmonic ridge At the ridge line location, from the multi-window fused spectrum The complex value is read and used as the complex observation of that frequency component.

[0015] Step S5 includes converting the actual amplitude values ​​of the power frequency and each low-order harmonic. and phase Treating it as a state variable, the state vector in the case of a single frequency and a single measurement point can be written as: (3), For multiple frequencies and multiple measurement points, the amplitude and phase of each frequency and each measurement point are sequentially concatenated into a large-dimensional state vector; The state equation, in the form of a random walk or first-order autoregressive equation, represents the slow change of amplitude and phase over time: (4), in, An identity mapping or a slightly smooth mapping may be used. This is process noise; An observation equation is established to describe the nonlinear relationship from state to complex observation, for a certain frequency component: (5), in To observe the noise, the overall observation equation is denoted as: (6), function That is, generate the corresponding complex exponential form according to the amplitude and phase of each frequency component, and then superimpose it with noise.

[0016] Step S6 includes recursive estimation using UKF, the process of which is as follows: Based on the state estimation mean and covariance from the previous step, construct several sigma points; Substitute each sigma point into the state equation to obtain the predicted state; Substituting the predicted state into the observation equation, we obtain the predicted observation; The Kalman gain is calculated based on the difference between the actual and predicted observations, and the state estimate and covariance are updated.

[0017] Step S7 includes defining the amount of innovation for each time window in the UKF recursive process as follows: (7), in, For UKF's predicted values ​​of observations, "normalized innovation" is calculated based on innovation covariance, and then the average energy or mean square value is calculated, which is used as the basis for measuring quality indicators.

[0018] Step S8 includes synthesizing the estimated amplitude and phase of each frequency component at the center of each time window to reconstruct the leakage magnetic flux time-domain signal, as follows: (8), in, Indicates power frequency, Represents each order of harmonics; By interpolating or resampling the time window, a continuous high signal-to-noise ratio leakage magnetic waveform is obtained, and it corresponds sequentially with the quality score in step S7, thereby realizing the joint output of waveform and quality label.

[0019] The beneficial effects of this invention are as follows: This invention utilizes multi-window STFT and time-frequency redistribution to obtain the power frequency and low-order harmonic energy ridges for time-frequency focusing, constructing complex observables; then, through UKF, it performs nonlinear state estimation of the amplitude and phase of each frequency component, achieving smooth tracking and high signal-to-noise ratio reconstruction of key components of the leakage magnetic field signal; and utilizes innovative statistics to provide measurement quality indicators, thereby obtaining leakage magnetic field measurement results with a "quality label." This invention also has the following advantages: (1) Improve time-frequency focusing capability By using multi-window STFT and time-frequency redistribution, this invention significantly improves the energy concentration of leakage magnetic signals near the power frequency and low-order harmonics, reduces energy diffusion and cross-term effects, makes the frequency ridge line clearer, and facilitates stable extraction.

[0020] (2) Achieve nonlinear smooth estimation of amplitude and phase. This invention models the true amplitude and phase of power frequency and harmonics as state variables and uses UKF to perform nonlinear recursive estimation, making full use of time correlation. Even under strong noise conditions, it can still obtain smooth, stable and accurate estimation results.

[0021] (3) Give explicit measurement quality indicators By constructing a measurement quality score using UKF's innovative statistics, the reliability of leakage flux measurement results at different time periods is quantitatively evaluated, providing data quality labels for subsequent winding fault diagnosis and improving the reliability of diagnostic decisions.

[0022] (4) The method has a clear structure and is easy to implement in engineering. This invention is based solely on publicly available signal processing and estimation methods such as STFT, time-frequency redistribution, and UKF. The parameters have intuitive meanings and the calculation process is clear, making it easy to integrate into existing online transformer monitoring systems as a software algorithm. It has good engineering promotion value. Attached Figure Description

[0023] Figure 1 The overall flowchart of a transformer leakage magnetic field signal measurement method based on multi-window STFT time-frequency redistribution and UKF fusion provided by the present invention is shown below. Figure 2 This is a schematic diagram of the transformer and leakage flux measurement point arrangement in this invention. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] The present invention provides a method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion, comprising the following steps: Step S1: Leakage Magnetic Signal Acquisition and Preprocessing Multiple leakage flux measurement points are arranged along the axial direction outside the transformer winding, with a sampling frequency. Collect discrete leakage magnetic field signals at each measuring point ,in The measurement points are numbered, and the transformer winding current signal is collected simultaneously.

[0026] Flux leakage signal preprocessing includes: DC removal: Subtract the average value from the signal at each measurement point; Detrending: Use linear fitting or high-pass filtering to remove slow drift; Band-limited filtering: preserves the frequency band covering the power frequency and some low-order harmonics.

[0027] If reference measurement points are set far from the transformer body, linear regression compensation can be performed on the signal at each measurement point using the reference signal to reduce background electromagnetic interference. The preprocessed signal is denoted as... .

[0028] Step S2: Multi-window STFT calculation Preprocessed signal for each measuring point Construct a sliding time window on the time axis. Let's assume we choose... Seeding window function (Such as Hanning windows, flat-top windows, etc.), window length is Step size is .

[0029] For the first The window function, and its short-time Fourier transform, can be simplified as follows: (1) in, For frequency index, Index for time windows.

[0030] The short-time spectra obtained from different window functions are weighted and summed according to frequency correlation weights to obtain the multi-window fused spectrum. Intuitively, different window functions complement each other in terms of low-frequency resolution, temporal resolution, and sidelobe suppression, resulting in a more concentrated energy in the power frequency and low-order harmonics area of ​​the fused spectrum.

[0031] Step S3: Time-Frequency Reassignment To further improve frequency focusing, the multi-window STFT spectrum was analyzed. Perform time-frequency redistribution.

[0032] The local instantaneous frequency of each time-frequency cell is estimated based on the change of the spectral phase over time. Then, the energy of that cell is "transferred" from the original frequency grid point to the estimated instantaneous frequency. The original STFT at the grid point... The energy on can be denoted as After redistribution, this energy is re-accumulated to the corresponding instantaneous frequency index. The redistribution spectrum is obtained above. After redistribution, the power frequency and low-order harmonics appear as clear "energy ridges" in the time-frequency plane, while background noise and cross terms are significantly suppressed.

[0033] Step S4: Frequency Ridge Extraction and Complex Observation Construction In the redistribution spectrum In the middle, around the power frequency and several low-order harmonic frequency bands (such as , Search within each time window The system identifies locations with localized maximum energy that do not significantly change frequency from the previous time window, forming frequency ridges that vary continuously over time, including power frequency ridges. Second harmonic ridge Third harmonic ridge Etc. At the ridge location, from the multi-window fused spectrum The complex value is read and used as the complex observable for that frequency component. For example, the complex observable for the power frequency component is: (2) Similarly, complex observations of each harmonic can be obtained. The observations from multiple measurement points and frequencies are pieced together in a certain order to form an observation vector. .

[0034] Step S5: Construction of Nonlinear State-Space Model The true amplitude of power frequency and various low-order harmonics and phase Consider them as state variables. Taking a single frequency and single measurement point as an example, the state vector can be written as: (3) For multiple frequencies and multiple measurement points, the amplitude and phase of each frequency and each measurement point can be sequentially concatenated into a large-dimensional state vector. Here, A1 represents the true amplitude of the l-th frequency component, and ϕl represents the true phase of the l-th frequency component.

[0035] The state equation, in the form of a simple random walk or first-order autoregressive equation, represents the slow changes in magnitude and phase over time: (4) in An identity mapping or a slightly smooth mapping may be used. This is process noise.

[0036] An observation equation is established to describe the nonlinear relationship between the state and complex observations. For example, for a certain frequency component: (5) in For observation noise. The overall observation equation can be written as: (6) function That is, a complex exponential form is generated according to the amplitude and phase of each frequency component, and then superimposed with noise. Since this mapping is nonlinear, UKF is used for state estimation.

[0037] Step S6: UKF State Estimation For the aforementioned nonlinear state-space model, UKF is used for recursive estimation. The basic process is as follows: Based on the state estimation mean and covariance from the previous step, construct several sigma points; Substitute each sigma point into the state equation to obtain the predicted state; Substituting the predicted state into the observation equation, we obtain the predicted observation; The Kalman gain is calculated based on the difference between the actual and predicted observations (the innovation amount), and the state estimate and covariance are updated.

[0038] In this invention, UKF outputs amplitude estimates for each frequency component within each time window. and phase estimation The process noise covariance and observation noise covariance can be adaptively adjusted according to the degree of load change and the local signal-to-noise ratio of the redistribution spectrum, so that the filter can both track the real changes and suppress noise interference.

[0039] Step S7: Measurement Quality Evaluation In the UKF recursive process, the amount of innovation for each time window is defined as: (7) in This represents the UKF's predicted values ​​for the observations. Based on the innovation covariance, "normalized innovation" can be calculated, followed by the average energy or mean square value, which serves as the basis for measuring quality indicators. When the innovation amount remains consistently low and stable within a certain time window, the current measurement is considered to match the model well, indicating high measurement quality. Conversely, when the innovation amount increases significantly or fluctuates drastically, the current measurement is considered to be significantly affected by noise or modeling errors, indicating low quality. Quality indicators can be normalized to the 0-1 interval, for example, using an exponential function or piecewise linear function, and used as the quality score for each time window. This can guide the adaptive adjustment of the UKF noise covariance, allowing for the deweighting or removal of low-quality data in subsequent diagnostics.

[0040] Step S8: Reconstruction of Leakage Magnetic Time Domain Signal At the center of each time window, the estimated amplitude and phase of each frequency component are synthesized to reconstruct the leakage magnetic flux time-domain signal, which can be expressed as: (8) in Indicates power frequency, Represents each order of harmonics.

[0041] In the formula, H represents the upper limit of the harmonic order. The estimated amplitude of the leakage magnetic flux measurement point at time t and the h-th order frequency component (h=0 is the power frequency, h≥1 is the harmonic) is calculated. The estimated phase of the h-th frequency component at time t of the m-th leakage magnetic field measurement point, together with the amplitude, is used to synthesize a time-domain signal.

[0042] By interpolating or resampling the time window, a continuous high signal-to-noise ratio leakage magnetic waveform can be obtained, which corresponds sequentially with the quality score in step S7, thus realizing the joint output of waveform and quality label.

[0043] The following detailed description of a specific embodiment of the present invention, in conjunction with the accompanying drawings, is provided. Those skilled in the art should understand that this embodiment is merely illustrative of the technical solution of the present invention and is not intended to limit the scope of protection of the present invention.

[0044] Example: Method for Measuring Leakage Magnetic Field Signal of Laboratory Dry-Type Transformer This embodiment uses a laboratory three-phase dry-type power transformer as an example to measure and process its leakage magnetic field signal in a laboratory environment, illustrating the specific implementation steps of the method of the present invention. The overall process can be found in [link to documentation]. Figure 1 The layout of the measuring points is shown in the diagram. Figure 2 .

[0045] Experimental subjects and measurement point layout The experimental subject was a three-phase dry-type transformer with a capacity of 50kVA and a rated frequency of 50Hz. The operating mode was a laboratory controllable load, with the load gradually increasing from a light load to the rated load and then decreasing to a light load.

[0046] Five leakage magnetic flux measurement points, designated P1, P2, P3, P4, and P5, are arranged axially around the outside of the high-voltage winding, evenly spaced along the winding height. Each measurement point is equipped with a leakage magnetic flux sensor to measure the radial leakage magnetic field near the winding (the specific sensor type is not limited). This embodiment does not include a distant reference measurement point, resulting in weak background interference. If necessary, a "reference measurement point" can be added in the same manner to compensate for environmental electromagnetic interference. The sampling frequency is set to... Each data collection session lasts approximately 20 seconds, corresponding to the number of sample points. The primary current signal of the transformer is collected synchronously for subsequent operating condition verification and comparison.

[0047] Data preprocessing raw signal for each measurement point ( Preprocess according to the following steps: (1) Remove DC component Calculate the average value of the signal at each measuring point. And subtract: Equation (9) To eliminate sensor bias and DC drift in the measurement system.

[0048] (2) Detrending First-order polynomial fitting or high-pass filters are used to remove slowly changing trend terms, causing the signal to oscillate around the zero mean, thus avoiding low-frequency drift from affecting subsequent time-frequency analysis.

[0049] (3) Band-limited filtering Based on the system power frequency of 50 Hz, the analysis frequency band is selected. For example, designing bandpass filters (filter types are not limited to Butterworth, Chebyshev, etc.) for... Filtering is performed to obtain the band-limited signal. The lower pass threshold is slightly lower than the power frequency to preserve the basic power frequency components; the upper pass threshold can cover the 3rd to 5th harmonics and some broadband interference, facilitating unified processing.

[0050] In this embodiment, since there are few interference sources and the noise level is low in the laboratory, reference measurement point compensation is not used; in field applications, a "reference signal linear compensation" step can be added on this basis.

[0051] Multi-window STFT calculation To simultaneously achieve both frequency and time resolution, the preprocessed signal Multi-window STFT analysis was used.

[0052] (1) Window function selection This embodiment selects two window functions ( Window 1: Hanning window, window length Window 2: Flat-top window, window length , in Each sampling point represents one power frequency cycle, corresponding to 20 ms. Therefore, the length of window 1 is... Points (4 power frequency cycles), emphasizing frequency resolution and sidelobe suppression, window 2 length is (2 power frequency cycles), emphasizing time resolution.

[0053] (2) Setting sliding parameters Time step The point refers to sliding once every half power frequency cycle. There is overlap between adjacent time windows, which helps to smooth out the time variation characteristics.

[0054] (3) STFT calculation For each measuring point STFT calculations are performed using window 1 and window 2 respectively, and can be represented in the form of equation (1), where Indicates the window type. For frequency index, Index for time windows.

[0055] (4) Multi-window spectral fusion To combine the advantages of the two window functions, the two sets of STFT spectra are weighted and summed according to frequency correlation weights to form a fused spectrum: Equation (10) Among them, low frequency band Slightly larger (with greater emphasis on the long-window Hanning spectrum), high-frequency band Slightly larger (while also considering time resolution). The specific values ​​of the weights can be determined based on experience or offline simulation.

[0056] Time-frequency redistribution and energy ridge extraction (1) Time-frequency redistribution Multi-window STFT fusion spectrum Some energy diffusion still exists. To improve frequency focusing, this embodiment employs time-frequency redistribution technology. Based on the change of spectral phase over time, the instantaneous frequency is estimated, and the energy of each time-frequency unit is "moved" to the vicinity of the corresponding instantaneous frequency position, thus obtaining the redistributed spectrum. .

[0057] (2) Frequency Ridge Extraction In the redistribution spectrum, each time window is searched around the power frequency and the second and third harmonic frequency bands. The frequency point with the highest internal energy is identified, and frequency continuity constraints are imposed (e.g., the frequency change between adjacent windows must not exceed a set threshold), thereby obtaining a frequency ridge that changes smoothly over time, i.e., the power frequency ridge. Second harmonic ridge Third harmonic ridge .

[0058] (3) Complex observation construction For each ridge, at the corresponding time-frequency position, from the fused spectrum The complex spectrum values ​​are read and used as observations for the UKF: Equation (11) in These represent the power frequency, second harmonic, and third harmonic, respectively.

[0059] For 5 measurement points and 3 frequency components, all can be... Arranged into observation vectors in a certain order .

[0060] UKF State Modeling and Estimation (1) State vector setting This embodiment takes a single measurement point with multiple frequencies as an example. For a given measurement point, the amplitudes and phases of the power frequency, second harmonic, and third harmonic are used to construct a state vector: Equation (12) The five measurement points can also be extended to a higher-dimensional state.

[0061] (2) Equations of state Since the load changes relatively slowly in the laboratory, the actual amplitude and phase of the power frequency and harmonics do not change much between adjacent time windows, so the state equation takes the form of a random walk: Equation (13) in This is process noise.

[0062] (3) Observation equation For a certain frequency component, the observation The relationship between the state and the map satisfies equation (5), which is nonlinear; therefore, UKF is used for estimation. Global observation function This is the process of converting the amplitude and phase of each frequency component into a complex spectrum.

[0063] Observation equations The main steps of UKF are: 1) Generate a set of sigma points based on the state estimate and covariance of the previous time step; 2) Substitute the sigma points into the state equation to obtain the predicted state; 3) Map the predicted state to the observation space through the observation equation to obtain the predicted observation; 4) Based on the actual observations... 5) Calculate the Kalman gain based on the difference between the observed and predicted values ​​(innovation amount); 6) Update the state estimate and covariance to obtain the amplitude and phase estimates at this moment.

[0064] Leakage signal reconstruction and quality evaluation (1) Temporal reconstruction At the center of each time window The leakage magnetic signal is synthesized using the amplitude and phase estimation of the UKF output: Equation (14) By interpolating or resampling all time windows, a continuous reconstructed magnetic leakage time-domain waveform can be obtained.

[0065] (2) Construction and visualization of quality indicators In the UKF recursive process, normalized innovation is calculated based on the innovation quantity and its covariance, yielding a statistic reflecting the difference between predictions and actual observations. This statistic is then averaged over a sliding time window and converted into a quality score between 0 and 1 using a simple function mapping (such as an exponential decay function). .

Claims

1. A method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion, characterized in that, Includes the following steps: Step S1: Leakage magnetic field signal acquisition and preprocessing; Multiple leakage flux measurement points are arranged along the axial direction outside the transformer winding, with a sampling frequency. Collect discrete leakage magnetic field signals at each measuring point , Number the measurement points and simultaneously acquire the transformer winding current signal; Step S2: Multi-window STFT calculation; Step S3: Time-frequency redistribution, for multi-window STFT spectrum Perform time-frequency reallocation; Step S4: Frequency ridge extraction and complex observation construction; Step S5: Constructing the nonlinear state-space model; Step S6: UKF state estimation; Step S7: Measurement quality evaluation; Step S8: Reconstruction of leakage magnetic field time domain signal.

2. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that, The preprocessing of the leakage magnetic signal in step S1 includes: DC removal: Subtract the average value from the signal at each measurement point; Detrending: Use linear fitting or high-pass filtering to remove slow drift; Band-limited filtering: preserves the frequency band covering power frequency and some low-order harmonics; The preprocessed signal is denoted as .

3. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: Step S2 includes preprocessing the signal for each measurement point. Construct a sliding time window on the timeline and select... Seeding window function The window length is Step size is ; For the A window function, whose short-time Fourier transform is abbreviated as: Equation (1) in, For frequency index, Index for time windows; The short-time spectra obtained from different window functions are weighted and summed according to frequency correlation weights to obtain the multi-window fused spectrum. .

4. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: In step S3, the local instantaneous frequency of each time-frequency unit is estimated based on the change of the spectral phase over time. Then, the energy of that unit is "transferred" from the original frequency grid point to the estimated instantaneous frequency. The original STFT is at the grid point. The energy on is denoted as After redistribution, the energy is re-accumulated to the corresponding instantaneous frequency index. The redistribution spectrum is obtained above. .

5. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: Step S4 includes the redistribution spectrum In the middle, around the power frequency And several low-order harmonic frequency bands are searched, in each time window The system identifies locations with localized maximum energy that do not significantly change frequency from the previous time window, forming frequency ridges that vary continuously over time, including power frequency ridges. Second harmonic ridge Third harmonic ridge At the ridge line location, from the multi-window fused spectrum The complex value is read and used as the complex observation of that frequency component.

6. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: Step S5 includes converting the actual amplitude values ​​of the power frequency and each low-order harmonic. and phase Treating it as a state variable, the state vector in the case of a single frequency and a single measurement point can be written as: （3）， For multiple frequencies and multiple measurement points, the amplitude and phase of each frequency and each measurement point are sequentially concatenated into a large-dimensional state vector; The state equation, in the form of a random walk or first-order autoregressive equation, represents the slow change of amplitude and phase over time: （4）， in, An identity mapping or a slightly smooth mapping may be used. This is process noise; An observation equation is established to describe the nonlinear relationship from state to complex observation, for a certain frequency component: （5）， in To observe the noise, the overall observation equation is denoted as: （6）， function That is, generate the corresponding complex exponential form according to the amplitude and phase of each frequency component, and then superimpose it with noise.

7. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that, Step S6 includes recursive estimation using UKF, the process of which is as follows: Based on the state estimation mean and covariance from the previous step, construct several sigma points; Substitute each sigma point into the state equation to obtain the predicted state; Substituting the predicted state into the observation equation, we obtain the predicted observation; The Kalman gain is calculated based on the difference between the actual and predicted observations, and the state estimate and covariance are updated.

8. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: Step S7 includes defining the amount of innovation for each time window in the UKF recursive process as follows: （7）， in, For UKF's predicted values ​​of observations, "normalized innovation" is calculated based on innovation covariance, and then the average energy or mean square value is calculated, which is used as the basis for measuring quality indicators.

9. The method for measuring transformer leakage magnetic field signals based on multi-window STFT time-frequency redistribution and UKF fusion as described in claim 1, characterized in that: Step S8 includes synthesizing the estimated amplitude and phase of each frequency component at the center of each time window to reconstruct the leakage magnetic flux time-domain signal, as follows: （8）， in, Indicates power frequency, Represents each order of harmonics; By interpolating or resampling the time window, a continuous high signal-to-noise ratio leakage magnetic waveform is obtained, and it corresponds sequentially with the quality score in step S7, thereby realizing the joint output of waveform and quality label.

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