Partial discharge positioning method and system based on beam forming
Through the local discharge positioning method based on beam formation, the sensor array and fitting model are used to solve the problems of high positioning accuracy and cost in the prior art, and efficient and low-cost local discharge power positioning in complex environments is achieved.
Patent Information
- Application Number
- CN202510418259.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-03
- Publication Date
- 2025-07-08
AI Technical Summary
The existing local discharge positioning method is affected by electromagnetic interference and medium at the substation site, resulting in reduced positioning accuracy and sensitivity and higher cost.
The local discharge positioning method based on beam formation is adopted, and the discharge signals are collected through the sensor array, and the model is constructed by decomposition and fitting. Combined with weighted filtering and interpolation processing, the position of the local discharge power supply is accurately determined.
It improves the accuracy of local discharge positioning and reduces costs, and can effectively extract useful signals in complex environments to achieve accurate positioning of local discharge power.
Smart Images
Figure CN120278029A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of partial discharge detection and location of electrical equipment, and specifically to a partial discharge location method and system based on beamforming. Background Art
[0002] Partial discharge is a precursor to the insulation aging and failure of electrical equipment. By detecting and locating partial discharge early, potential insulation defects can be discovered in time, equipment failures and accidents can be avoided, and the safe operation of the power system can be ensured.
[0003] Currently, the commonly used partial discharge location methods include electrical location method, ultrasonic location method, ultra-high frequency location method, etc. The electrical location method determines the location of partial discharge by analyzing the pulse current generated during partial discharge. However, due to the strong electromagnetic interference at the substation site, the measured pulse current is severely affected, thereby reducing the accuracy of location. The ultrasonic method uses ultrasonic sensors to detect the ultrasonic signals generated by partial discharge, and calculates the time difference between the arrival of each ultrasonic signal at different sensors to inversely deduce the location of partial discharge. However, in the actual process, due to the strong influence of the medium on ultrasonic signals in the air, the ultrasonic signals attenuate too quickly, so it is only suitable for locating partial discharge within a short distance, greatly reducing the sensitivity of location. The principle of the ultra-high frequency method is similar to that of the ultrasonic method. Although ultra-high frequency signals have strong propagation ability, due to the high frequency band of the signals detected by the ultra-high frequency method, even reaching the GHz level, there are very high requirements for the signal acquisition device, increasing the cost of partial discharge location.
[0004] Therefore, there is an urgent need for a partial discharge location method with accurate location and low cost. Summary of the Invention
[0005] The present invention provides a partial discharge location method and system based on beamforming.
[0006] The technical solution of the present invention is as follows: A partial discharge location method based on beamforming includes the following steps: S1. Collect the discharge signals of the partial discharge source at a set sampling frequency based on the sensor array as discrete discharge signals; set a reference sensor, and respectively obtain the propagation time delays of the discharge signals received by other sensors relative to the reference sensor; S2. Perform a first decomposition process on the discrete discharge signals, decompose the discrete discharge signals into component signals at different frequencies to obtain the first decomposition signals; perform a second decomposition process on the first decomposition signals to obtain several decomposition coefficients, and based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the several decomposition coefficients in sequence to obtain several denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain the denoised discrete location signals; S3. Construct a fitting model based on the denoised discrete positioning signals. Calculate the residual function by computing the residuals between the predicted values and the actual values of the denoised discrete positioning signals based on the fitting model. Take the sum of squares of several residual functions and minimize it to obtain the objective function. Estimate the parameters of the fitting model based on the objective function to obtain the fitting discharge curve. Perform interpolation processing on the fitting discharge curve to expand the sampling points and obtain the interpolated discharge signals of different sensors. S4. Adjust the phases of the interpolated discharge signals of all sensors with reference to the discharge signal received by the reference sensor, and further perform weighted filtering on them based on the set weighting function to obtain the array output signals and corresponding array output powers in different directions. S5. Based on the array output powers in different directions, perform normalization processing and high-order power transformation processing on them in sequence. Take the direction of the maximum array output power as the positioning direction of the partial discharge source to obtain the positioning result of the partial discharge source.
[0007] Specifically, the specific process formula for obtaining the array output signals and corresponding array output powers in different directions in S4 is as follows: , where is the array output power in different directions, is the array output signal in different directions, is the incident angle of the discharge signal, is the direction vector, is the minimum eigenvalue obtained by eigenvalue decomposition, is the sample covariance matrix, is the identity matrix, is the conjugate transpose.
[0008] Specifically, in S2, based on the set threshold function, perform dynamic threshold processing on several decomposition coefficients in sequence. The set threshold function is expressed by the formula: , where is the adjustment factor, is the j th decomposition coefficient at the k th scale obtained by the second decomposition process, is the threshold, , is the variance of the noise, and L is the number of sampling points.
[0009] Specifically, the residual function is calculated based on the predicted value of the denoised discrete positioning signal by the fitting model and the actual value of the denoised discrete positioning signal, and the sum of squares of the residual function is taken to obtain the minimum value, resulting in the objective function, which is expressed by the formula: , wherein, is the objective function, is the serial number of the sampling point, is the residual function, and L is the number of sampling points; is the actual value of the denoised discrete positioning signal at the sampling point , is the predicted value of the fitting model at the time point , is the parameter vector of the fitting model, .
[0010] Specifically, in the S1, a reference sensor is set, and the propagation delays of the discharge signals received by other sensors relative to the reference sensor are obtained respectively, specifically: Set the first sensor that receives the discharge signal as the reference sensor, and obtain the propagation delays of the discharge signals received by other sensors relative to the reference sensor , which is expressed by the formula: , where M is the Mth sensor that receives the discharge signal, is the distance between two adjacent sensors in the sensor array, is the incident angle of the discharge signal, is the speed of the discharge signal propagating in the air.
[0011] Furthermore, in the S1, the sensor array is arranged on an omnidirectional mobile robot, and the number of sensors in the sensor array ≥ 4.
[0012] Furthermore, in the S2, the discrete discharge signal is subjected to a first decomposition process to decompose the discrete discharge signal into component signals at different frequencies, obtaining the first decomposition signal, which is expressed by the formula: , wherein, is the discrete discharge signal, is the i th component signal obtained by the first decomposition process, is the residual signal, is the total number of component signals at different frequencies, is the serial number of the sampling point.
[0013] Specifically, S3 estimates the parameters of the fitting model based on the objective function, and also includes iteratively updating the parameters of the fitting model. Specifically, it is to obtain the partial derivative of the residual function with respect to the parameters of the fitting model, construct the Jacobian matrix, and update the parameters of the fitting model in the previous iteration based on the Jacobian matrix, damping factor, and residual function to obtain the parameters of the fitting model in this iteration. The formula is expressed as: , where, is the parameter of the fitting model in this iteration, is the parameter of the fitting model in the previous iteration, is the Jacobian matrix, is the damping factor, is the identity matrix, is the matrix transpose operation, is the residual function.
[0014] The present invention also provides a partial discharge localization system based on beamforming, including: Data acquisition module: used to collect the discharge signals of the partial discharge source based on the sensor array at a set sampling frequency as discrete discharge signals; set a reference sensor and obtain the propagation delays of the discharge signals received by other sensors relative to the reference sensor respectively; Data processing module: used to perform the first decomposition process on the discrete discharge signals, decompose the discrete discharge signals into component signals at different frequencies to obtain the first decomposition signals; perform the second decomposition process on the first decomposition signals to obtain several decomposition coefficients, and based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the several decomposition coefficients in sequence to obtain several denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain the denoised discrete localization signals; Data fitting module: used to construct a fitting model based on the denoised discrete localization signals, calculate the residual between the predicted value and the actual value of the denoised discrete localization signals based on the fitting model to obtain the residual function, take the sum of squares of several residual functions and then take the minimum value to obtain the objective function, estimate the parameters of the fitting model based on the objective function to obtain the fitting discharge curve, and perform interpolation processing on the fitting discharge curve to expand the sampling points to obtain the interpolated discharge signals of different sensors; Weighted filtering module: used to adjust the phases of the interpolated discharge signals of all sensors based on the discharge signal received by the reference sensor, and further perform weighted filtering processing on them based on the set weighted function to obtain the array output signals and corresponding array output powers in different directions; Discharge positioning module: It is used to perform normalization processing and high-order power transformation processing on the array output power in different directions in sequence, and take the direction of the maximum value of the array output power as the positioning direction of the partial discharge source to obtain the positioning result of the partial discharge source.
[0015] The beneficial effects of the present invention are as follows: 1. By performing the first decomposition process and the second decomposition process on the acquired discrete discharge signals, the present invention can extract the local features of the discrete discharge signals more meticulously. And through dynamic threshold processing based on the set threshold function, the threshold can be adaptively adjusted according to the characteristics of the signals and the noise level, providing a more accurate denoising effect. By constructing a fitting model, obtaining a fitting positioning curve, and performing interpolation processing on it, a high-sampling-rate signal can be generated based on the initially set low sampling frequency, reducing the dependence on high-frequency sampling equipment, lowering the cost of signal acquisition, and more accurately describing the signal characteristics, and making a more precise judgment on the position of the partial discharge source.
[0016] 2. The present invention adjusts the phase of the interpolated discharge signals of all sensors with the discharge signal received by the reference sensor as the reference, and further performs weighted filtering processing on it based on the set weighting function, which can further reduce the influence of background noise and reverberation on the discharge signals, enhance the signals in a specific direction, help extract useful signals in a complex environment, take the direction of the maximum output power as the positioning direction of the partial discharge source, and finally obtain the positioning result of the partial discharge source. Description of the Drawings
[0017] In the drawings: Figure 1 It is a schematic flow chart of the partial discharge positioning method based on beamforming in the embodiment; Figure 2 It is a three-dimensional diagram of the partial discharge source positioning effect in the embodiment; Figure 3 It is a plan view of the partial discharge source positioning effect in the embodiment. Detailed Embodiments
[0018] The following will describe the exemplary embodiments of the present disclosure in more detail with reference to the drawings.
[0019] Embodiment This embodiment provides a partial discharge positioning method based on beamforming. Refer to Figure 1 , including the following steps: S1. Collect the discharge signals of the partial discharge source based on the sensor array at a set sampling frequency as discrete discharge signals; set a reference sensor and obtain the propagation delays of the discharge signals received by other sensors relative to the reference sensor respectively.
[0020] In this embodiment, the sensor array can collect, for example, the partial discharge localization signals generated by insulation defects of high-voltage equipment. The shape of the sensor array can be linear, circular, or rhombic. Based on the sensor array, the discharge signals of the partial discharge source are collected at a set sampling frequency. The sampling frequency is set to 2 GSa / s. The initially set sampling frequency is relatively low, and a high sampling rate signal is generated based on this in subsequent steps, which can reduce the dependence on high-frequency sampling equipment and lower the cost of signal acquisition.
[0021] To obtain discharge signals at different angles and improve the spatial resolution, the number of sensors in the sensor array is set to ≥4. In this embodiment, the number of sensors is set to 9.
[0022] Set a reference sensor and obtain the propagation time delays of the discharge signals received by other sensors relative to the reference sensor respectively. Specifically: Set the first sensor that receives the discharge signal as the reference sensor, and obtain the propagation time delays of the discharge signals received by other sensors relative to the reference sensor , which is expressed by the formula: , where M is the Mth sensor that receives the discharge signal, is the spacing between two adjacent sensors in the sensor array, is the incident angle of the discharge signal, is the speed of the discharge signal propagating in the air, and the value is .
[0023] S2. Perform the first decomposition process on the discrete discharge signal, decompose the discrete discharge signal into component signals at different frequencies to obtain the first decomposition signal; perform the second decomposition process on the first decomposition signal to obtain several decomposition coefficients, and based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the several decomposition coefficients in sequence to obtain several denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain the denoised discrete localization signal.
[0024] In this step, the obtained discrete discharge signal is decomposed twice in sequence. Perform the first decomposition process on the discrete discharge signal, decompose the discrete discharge signal into component signals at different frequencies to obtain the first decomposition signal, which is expressed by the formula: , where is the discrete discharge signal, is the i th component signal obtained by the first decomposition process, is the residual signal, is the total number of component signals at different frequencies, is the serial number of the sampling point.
[0025] Then, the first decomposed signal is subjected to a second decomposition process to obtain a number of decomposition coefficients. When performing the second decomposition process, the db8 wavelet basis in the wavelet basis function is used, and the decomposition level is selected as three layers.
[0026] Furthermore, a number of decomposition coefficients are successively subjected to dynamic threshold processing based on the set threshold function. The set threshold function is expressed by the formula: , where is the adjustment factor, is the j th decomposition coefficient on the k th scale obtained by the second decomposition process, is the threshold, , is the variance of the noise, and L is the number of sampling points.
[0027] Finally, all the denoised discrete components are superimposed and reconstructed to obtain the denoised discrete positioning signal.
[0028] S3. Construct a fitting model based on the denoised discrete positioning signal. Calculate the residual function by calculating the difference between the predicted value and the actual value of the denoised discrete positioning signal based on the fitting model. Take the sum of squares of a number of residual functions and then take the minimum value to obtain the objective function. Estimate the parameters of the fitting model based on the objective function to obtain the fitting discharge curve. Perform interpolation processing on the fitting discharge curve to expand the sampling points and obtain the interpolated discharge signals of different sensors.
[0029] In this step, a fitting model is constructed based on the denoised discrete positioning signal. The expression of the fitting model is specifically as follows: , where is the expression of the constructed fitting model, which is in the form of oscillatory decay; is the time variable, and are respectively the amplitudes of the two exponential terms, , are the two decay constants, which determine the decay rate of the oscillation; , are the two angular frequencies of the oscillation, , are the two phase angles, which affect the initial position of the oscillation; is the constant term, representing the steady-state value or the offset; Further, based on the fitting model, the residual function is calculated by taking the difference between the predicted value of the denoised discrete positioning signal and the actual value of the denoised discrete positioning signal. After taking the sum of squares of the residual function, the minimum value is obtained to get the objective function, which is expressed by the formula: , where, is the residual function, is the predicted value of the fitting model at the time point ; is the parameter vector of the fitting model, ; is the actual value of the denoised discrete positioning signal at the sampling point ; , where, is the objective function, is the serial number of the sampling point, is the residual function, and L is the number of sampling points.
[0030] In this embodiment, parameter estimation of the fitting model based on the objective function further includes iterative updating of the parameters of the fitting model. Specifically, the partial derivative of the residual function with respect to the parameters of the fitting model is obtained, the Jacobian matrix is constructed, and based on the Jacobian matrix, the damping factor, and the residual function, the parameters of the fitting model in the previous iteration are updated to obtain the parameters of the fitting model in this iteration, which is expressed by the formula: , where, is the parameter of the fitting model in this iteration, is the parameter of the fitting model in the previous iteration, is the Jacobian matrix, which can represent the sensitivity to the parameters of the fitting model; is the damping factor, is the identity matrix, is the matrix transpose operation, is the residual function.
[0031] The damping factor can be adjusted according to the change of the residual function to balance the convergence speed and stability. In each round of iteration, when the parameter estimation causes the objective function to decrease, then is reduced, and it can be multiplied by a factor less than 1. For example, it is multiplied by 0.1; when the parameter estimation causes the objective function to increase, then is increased, and it can be multiplied by a factor greater than 1. For example, it is multiplied by 10.
[0032] When the number of iterations of the fitting model reaches the set number threshold, the convergence condition is satisfied, and the fitting curve is obtained.
[0033] Further interpolate the fitted discharge curve to expand the sampling points and obtain the interpolated discharge signals of different sensors. Specifically, within the duration range of the discharge signal, generate multiple uniformly distributed abscissa points, such as 2L points, where L is the number of sampling points. According to the expression of the fitted curve, calculate the ordinate value corresponding to each abscissa point, combine the generated abscissa points and the calculated ordinate values to form new sampling points, and obtain the interpolated discharge signals of different sensors.
[0034] S4. Adjust the phase of the interpolated discharge signals of all sensors based on the discharge signal received by the reference sensor, and further perform weighted filtering processing on them based on the set weighting function to obtain the array output signals in different directions and the corresponding array output powers.
[0035] After interpolating the fitted discharge curve, the discharge signal on the Mth sensor that receives the discharge signal is expressed as: , where, is the discharge signal received by the reference sensor, is the phase shift of the discharge signal propagation.
[0036] , where, is the angular frequency, is the propagation delay, is the center frequency of the discharge signal, is the spacing between two adjacent sensors in the sensor array, is the incident angle of the discharge signal, is the speed of the discharge signal propagating in the air.
[0037] Adjust the phase of the interpolated discharge signals of all sensors based on the discharge signal received by the reference sensor, and further perform weighted filtering processing on them based on the set weighting function to obtain the array output signals in different directions and the corresponding array output powers. The specific process formula is expressed as: , where, is the interpolated discharge signal of all sensors after phase adjustment based on the discharge signal received by the reference sensor, M is the Mth sensor that receives the discharge signal, is the phase shift of the discharge signal propagation, , where is the angular frequency, is the propagation delay, is the transpose operation; is the direction vector, is the discharge signal received by the reference sensor; , , wherein, is the array output signal in different directions, is the set weighting function, is the conjugate transpose, is the incident angle of the discharge signal; is the sample covariance matrix, , is the minimum eigenvalue obtained by eigenvalue decomposition, is the identity matrix, is the direction vector; , wherein, is the array output power in different directions.
[0038] S5. Based on the array output power in different directions, perform normalization processing and high-order power transformation processing on it in sequence, and use the direction with the maximum array output power as the positioning direction of the partial discharge source to obtain the positioning result of the partial discharge source.
[0039] The normalization processing formula is expressed as: , wherein, is the normalized power value, is the maximum value among all output powers, is the array output power in different directions. After normalization processing, the array output power in different directions can be scaled to the range of (0, 1].
[0040] Perform high-order power transformation processing on the normalized array output power, and the formula is expressed as: , wherein, is the value after high-order power transformation processing, is the power, , and or can be selected.
[0041] Through high-order power transformation processing, the array output power less than 1 can be further reduced, while the array output power at the maximum value of 1 remains unchanged, which is conducive to visual distinction. The specific experimental simulation results are as shown in Figure 2 and Figure 3 , where x and y respectively represent the abscissa and ordinate positions of the partial discharge source in the coordinate system.
[0042] Retrieving and identifying the direction of the maximum output power of the array can determine the direction where the power source is located and obtain the positioning result of the partial discharge source.
[0043] The present invention also provides a partial discharge positioning system based on beamforming, including: Data acquisition module: used to collect the discharge signals of the partial discharge source based on the sensor array at a set sampling frequency as discrete discharge signals; set a reference sensor and obtain the propagation delays of the discharge signals received by other sensors relative to the reference sensor respectively; Data processing module: used to perform a first decomposition process on the discrete discharge signals, decompose the discrete discharge signals into component signals at different frequencies to obtain the first decomposition signals; perform a second decomposition process on the first decomposition signals to obtain a number of decomposition coefficients, and based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the number of decomposition coefficients in sequence to obtain a number of denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain the denoised discrete positioning signals; Data fitting module: used to construct a fitting model based on the denoised discrete positioning signals, calculate the residual function between the predicted value and the actual value of the denoised discrete positioning signals based on the fitting model to obtain the residual function, take the sum of squares of the number of residual functions and then take the minimum value to obtain the objective function, estimate the parameters of the fitting model based on the objective function to obtain the fitting discharge curve, and perform interpolation processing on the fitting discharge curve to expand the sampling points to obtain the interpolation discharge signals of different sensors; Weighted filtering module: used to adjust the phases of the interpolation discharge signals of all sensors based on the discharge signal received by the reference sensor, and further perform weighted filtering processing on them based on the set weighted function to obtain the array output signals and the corresponding array output powers in different directions; Discharge positioning module: used to perform normalization processing and high-order power transformation processing on the array output powers in different directions in sequence, take the direction of the maximum array output power as the positioning direction of the partial discharge source, and obtain the positioning result of the partial discharge source.
Claims
1. A partial discharge location method based on beamforming, characterized in that, Including the following steps: S1. Collect the discharge signals of the partial discharge source at a set sampling frequency based on the sensor array as discrete discharge signals; set a reference sensor and obtain the propagation delays of the discharge signals received by other sensors relative to the reference sensor respectively; S2. Perform a first decomposition process on the discrete discharge signals to decompose the discrete discharge signals into component signals at different frequencies to obtain a first decomposition signal; Perform a second decomposition process on the first decomposition signal to obtain a number of decomposition coefficients. Based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the number of decomposition coefficients in sequence to obtain a number of denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain a denoised discrete positioning signal; S3. Construct a fitting model based on the denoised discrete positioning signal, calculate the residual function based on the predicted value and the actual value of the denoised discrete positioning signal of the fitting model, take the sum of squares of a number of residual functions and then take the minimum value to obtain an objective function, and perform parameter estimation on the fitting model based on the objective function to obtain a fitting discharge curve; Perform interpolation processing on the fitting discharge curve to expand the sampling points to obtain the interpolation discharge signals of different sensors; S4. Adjust the phases of the interpolation discharge signals of all sensors based on the discharge signal received by the reference sensor, and further perform weighted filtering processing on them based on the set weighting function to obtain array output signals and corresponding array output powers in different directions; S5. Based on the array output powers in different directions, perform normalization processing and high-order power transformation processing on them in sequence, take the direction of the maximum array output power as the positioning direction of the partial discharge source, and obtain the positioning result of the partial discharge source.
2. The method for local discharge positioning based on beamforming according to claim 1, wherein The specific process formula for obtaining the array output signals and corresponding array output powers in different directions in S4 is as follows: ， Among them, is the array output power in different directions, is the array output signal in different directions, is the incident angle of the discharge signal, is the direction vector, is the minimum eigenvalue obtained by eigen decomposition, is the sample covariance matrix, is the identity matrix, is the conjugate transpose.
3. The method for local discharge positioning based on beamforming according to claim 1, wherein In S2, based on the set threshold function, dynamic threshold processing is performed on a number of decomposition coefficients in sequence, and the set threshold function is expressed by the formula: ， Among them, is a regulation factor, is the j th decomposition coefficient on the k th scale obtained by the second decomposition process, is a threshold, , is the variance of the noise, and L is the number of sampling points.
4. The method for local discharge positioning based on beamforming according to claim 1, wherein In S3, calculate the residual function based on the predicted value and the actual value of the denoised discrete positioning signal of the fitting model, take the sum of squares of the residual function and then take the minimum value to obtain an objective function, and the formula is as follows: ， Among them, is the objective function, is the serial number of the sampling point, is the residual function, and L is the number of sampling points; is the actual value of the denoised discrete positioning signal at the sampling point ; is the predicted value of the fitting model at the time point ; is the parameter vector of the fitting model, .
5. The method for local discharge location based on beamforming according to claim 1, characterized in that In S1, setting the reference sensor and obtaining the propagation delays of the discharge signals received by other sensors relative to the reference sensor respectively are specifically as follows: Set the first sensor that receives the discharge signal as the reference sensor, and obtain the propagation delays of the other sensors relative to the reference sensor when receiving the discharge signal respectively , which is expressed by the formula as follows: ， Among them, M is the M-th sensor that receives the discharge signal, is the distance between two adjacent sensors in the sensor array, is the incident angle of the discharge signal, is the speed at which the discharge signal propagates in the air.
6. The method for local discharge positioning based on beamforming according to claim 1, characterized in that In S1, the sensor array is arranged on an omnidirectional mobile robot, and the number of sensors in the sensor array ≥ 4.
7. The method for local discharge positioning based on beamforming according to claim 1, characterized in that In S2, performing a first decomposition process on the discrete discharge signals to decompose the discrete discharge signals into component signals at different frequencies to obtain a first decomposition signal, and the formula is as follows: ， Among them, is a discrete discharge signal, is the i th component signal obtained by the first decomposition process, is a residual signal, is the total number of component signals at different frequencies, is the serial number of the sampling point.
8. The method for local discharge positioning based on beamforming according to claim 4, characterized in that Based on the objective function, performing parameter estimation on the fitting model in S3 further includes iteratively updating the parameters of the fitting model. Specifically, obtain the partial derivative of the residual function with respect to the parameters of the fitting model, construct a Jacobian matrix, and update the parameters of the fitting model in the previous iteration based on the Jacobian matrix, damping factor, and residual function to obtain the parameters of the fitting model in this iteration, and the formula is as follows: ， Among them, is the parameter of the fitting model for the current iteration, is the parameter of the fitting model for the previous iteration, is the Jacobian matrix, is the damping factor, is the identity matrix, is the matrix transpose operation, is the residual function.
9. A partial discharge localization system based on beamforming, characterized in that, Including: Data acquisition module: used to collect the discharge signals of the partial discharge source at a set sampling frequency based on the sensor array as discrete discharge signals; Set a reference sensor and respectively obtain the propagation delays of other sensors receiving discharge signals relative to the reference sensor; Data processing module: used to perform a first decomposition process on the discrete discharge signal, decompose the discrete discharge signal into component signals at different frequencies, and obtain the first decomposition signal; Perform a second decomposition process on the first decomposition signal to obtain a number of decomposition coefficients. Based on the set threshold function, perform dynamic threshold processing and inverse transformation processing on the number of decomposition coefficients in sequence to obtain a number of denoised discrete components, and superimpose and reconstruct all the denoised discrete components to obtain a denoised discrete positioning signal; Data fitting module: used to construct a fitting model based on the denoised discrete positioning signal, calculate the residual function between the predicted value and the actual value of the denoised discrete positioning signal based on the fitting model to obtain a residual function, take the sum of squares of a number of residual functions and then take the minimum value to obtain an objective function, estimate the parameters of the fitting model based on the objective function to obtain a fitted discharge curve, and perform interpolation processing on the fitted discharge curve to expand the sampling points to obtain the interpolated discharge signals of different sensors; Weighted filtering module: used to perform phase adjustment on the interpolated discharge signals of all sensors with the discharge signal received by the reference sensor as a reference, and further perform weighted filtering processing on them based on the set weighted function to obtain array output signals in different directions and the corresponding array output powers; Discharge positioning module: used to perform normalization processing and high-order power transformation processing on the array output powers in different directions in sequence, take the direction of the maximum value of the array output power as the positioning direction of the partial discharge source, and obtain the positioning result of the partial discharge source.