High-voltage insulator string zero-value insulator fault detection method based on unmanned aerial vehicle and space electric field model compensation

Abstract

This invention discloses a method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation, comprising: Step 1, establishing a model of the relationship between the electric field and the latent potential function, assigning a Gaussian process prior distribution to the latent potential function, and performing a low-rank approximation to obtain the eigenvalues ​​and basis functions in the bounded region, representing the latent potential function as a finite linear group; Step 2, solving the finite linear combination to obtain the posterior mean vector, thereby constructing an electrostatic physics learning model; Step 3, determining whether the actual measurement point deviates from the ideal measurement point when the UAV flies along the ideal measurement path. If there is a deviation, based on the posterior mean vector and the electrostatic physics learning model, correcting the deviated actual scalar electric field intensity value to the pure scalar electric field intensity value of the ideal measurement point, obtaining a pure scalar electric field intensity sequence; Step 4, determining whether a zero-value insulator fault exists based on the scalar electric field intensity distribution curve of the pure scalar electric field intensity sequence.

Description

Technical Field

[0001] This invention relates to the field of insulator string fault detection methods, specifically a method for detecting zero-value insulator faults in high-voltage insulator strings based on compensation by unmanned aerial vehicles and a space electric field model. Background Technology

[0002] To detect faults in high-voltage insulator strings, existing technology involves using a drone equipped with a Pockels electric field sensor to fly around the high-voltage insulator string. The Pockels electric field sensor measures scalar electric field intensity data at various sampling points around the high-voltage insulator string, and then uses the scalar electric field intensity data at each sampling point to determine whether there is a fault in the high-voltage insulator string.

[0003] However, existing technologies for inspecting the electric field of high-voltage insulator strings using drones rely on the drone maintaining an absolutely perfect straight flight trajectory (i.e., an ideal measurement path). Once affected by sudden gusts of wind from high-altitude wind fields, turbulent airflow from the drone's onboard rotor, or tracking errors in the flight control system, the drone will deviate from the preset ideal measurement path, resulting in a non-ideal three-dimensional spatial offset. Because the electrostatic field around the high-voltage insulator string has extremely high spatial gradient sensitivity, this geometric positional offset introduces significant abrupt changes in field strength noise into the raw electric field strength data measured by the Pockels electric field sensor, leading to misjudgments or missed detections when subsequently using the raw electric field strength data for fault diagnosis. Summary of the Invention This invention provides a method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation. This method addresses the problems in existing high-voltage insulator string electric field fault judgment, where UAVs are interfered with and measure the electric field strength along non-ideal measurement paths, leading to noise in the measurement data and misjudgments or omissions when judging faults based on the measurement data.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A fault detection method for zero-value insulators in high-voltage insulator strings based on UAV and spatial electric field model compensation is as follows:

[0006] Step 1: Establish a mathematical model of the relationship between the scalar electric field strength output by the UAV-borne Pockels electric field sensor and the latent space electrostatic potential function when the sensing axis of the Pockels electric field sensor coincides with the spatial geometric axis of the high-voltage insulator string; assign a zero-mean Gaussian process prior distribution to the latent space electrostatic potential function; then, perform a low-rank approximation on the Gaussian process prior distribution to obtain multiple eigenvalues ​​and characteristic basis functions in the bounded region; based on each eigenvalue and characteristic basis function, approximate the latent space electrostatic potential function in continuous space as a finite linear set.

[0007] Step 2: Command the UAV to fly over the clearance area around the high-voltage insulator string and measure the scalar electric field intensity observations at multiple sampling points in the clearance area using the airborne Pockels electric field sensor; then concatenate the scalar electric field intensity observations at each sampling point into an observation vector.

[0008] Then, based on the three-dimensional absolute coordinates of the sampling location point corresponding to each sample, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in step 1, the electric field observation matrix corresponding to the sampling location point is constructed. Then, combined with the observation vector, the low-rank linear Gaussian closed-form solution of the finite linear combination of the latent space electrostatic potential function obtained in step 1 is solved to obtain the posterior mean vector of the prior distribution of the feature basis function weights in the confined region around the high-voltage insulator string. Thus, the electrostatic physics learning model of the confined region around the high-voltage insulator string is constructed.

[0009] Step 3: The UAV is instructed to fly along the preset ideal measurement path around the high-voltage insulator string, and the actual scalar electric field strength value at each actual measurement location point during the flight is obtained by the airborne Pockels electric field sensor.

[0010] Determine whether each actual measurement location point deviates from the corresponding ideal measurement location point. If there is a deviation, based on the posterior mean vector and electrostatic physics learning model obtained in step 2, correct the actual scalar electric field intensity value of each actual measurement location point with deviation to the pure scalar electric field intensity value of the corresponding ideal measurement location point. The actual scalar electric field intensity value of the actual measurement location point without deviation is regarded as the pure scalar electric field intensity value of the corresponding ideal measurement location point, and the pure scalar electric field intensity values ​​of each ideal measurement location point form a pure scalar electric field intensity sequence.

[0011] Step 4: Perform wavelet analysis on the pure scalar electric field intensity sequence to obtain the scalar electric field intensity distribution curve, and then determine whether there is a zero-value insulator fault in the high-voltage insulator string based on the scalar electric field intensity distribution curve.

[0012] Furthermore, in step 1, the kernel function in the prior distribution of the Gaussian process is the squared exponential covariance function.

[0013] Furthermore, in step 1, during the low-rank approximation, an air domain is extended outward by a predetermined distance from the approximate center point of the high-voltage insulator string, thereby defining a cubic bounded region around the high-voltage insulator string; then, multiple eigenvalues ​​and eigenbasis functions are solved within the bounded region.

[0014] Furthermore, in step 2, the three-dimensional absolute coordinates of each sampling location point are obtained by the trilateration method.

[0015] Furthermore, in step 2, based on the three-dimensional absolute coordinates of each sampling location point, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in step 1, an electric field observation matrix corresponding to the sampling location point is constructed; the electric field observation matrices of all sampling location points are vertically spliced ​​together to form a global single-axis electric field observation matrix.

[0016] Based on the global uniaxial electric field observation matrix, the low-rank linear Gaussian closed-form solution of the finite linear combination of latent space electrostatic potential functions obtained in step 1 is solved to obtain the posterior covariance matrix of the prior distribution of characteristic basis function weights in the confined region around the high-voltage insulator string; then, based on the posterior covariance matrix and the observation vector, the posterior mean vector of the prior distribution of characteristic basis function weights in the confined region around the high-voltage insulator string is solved.

[0017] Furthermore, in step 3, based on the three-dimensional spatial position difference between the three-dimensional spatial coordinates of each actual measurement location point and the three-dimensional spatial coordinates of the corresponding ideal measurement location point, it is determined whether each actual measurement location point deviates from the corresponding ideal measurement location point.

[0018] Furthermore, in step 3, if there is a deviation, based on the posterior mean vector obtained in step 2, the environmental field strength distortion difference between the predicted scalar electric field strength of the electrostatic physics learning model obtained in step 2 and the corresponding ideal measurement location point at each actual measurement location point with deviation is calculated; based on the environmental field strength distortion difference of each actual measurement location point with deviation, the actual scalar electric field strength value of each actual measurement location point with deviation is corrected to the pure scalar electric field strength value of the corresponding ideal measurement location point.

[0019] Furthermore, in step 4, the pure scalar electric field intensity sequence is preprocessed before wavelet analysis is performed. The preprocessing includes outlier removal and interpolation repair.

[0020] Furthermore, in step 4, during wavelet analysis, the pure scalar electric field intensity values ​​in the pure scalar electric field intensity sequence are first decomposed into a multi-scale orthogonal system. During the multi-scale decomposition, the pure scalar electric field intensity sequence is decomposed into low-frequency approximation coefficients and high-frequency detail coefficients. Then, the high-frequency detail coefficients obtained from each decomposition layer are nonlinearly shrunk using a soft thresholding function based on a globally unified threshold. Finally, the low-frequency approximation coefficients representing the background trend of the field strength are fully preserved, and the high-frequency detail coefficients of each layer after thresholding and shrinking are substituted into the system. The signal is then reconstructed using inverse wavelet transform to obtain the scalar electric field intensity distribution curve.

[0021] Furthermore, in step 4, the first and second derivatives of the scalar electric field intensity distribution curve are calculated; the extreme points where the first derivative is zero and the inflection points where the second derivative is zero are taken as the characteristic points of the scalar electric field intensity distribution curve, and the rate of change of electric field intensity between two adjacent characteristic points is calculated.

[0022] If a negative abrupt change in the rate of change of electric field intensity between adjacent feature points is detected within a certain continuous sub-interval, and the absolute value of the rate of change of electric field intensity is higher than the average attenuation level of the same spatial location interval of a normal high-voltage insulator string, and the physical width of the spatial interval of the abrupt change in the rate of change of electric field intensity falls within the typical physical height / thickness range of a single insulator in a high-voltage insulator string, the insulator corresponding to the spatial interval of the abrupt change in the rate of change of electric field intensity is diagnosed as a zero-value insulator fault with conduction breakdown.

[0023] This invention utilizes a low-rank Gaussian process to bind the electromagnetic mechanism of the entire space with measured data, establishing a dedicated spatial electrostatic physical digital model for high-voltage insulator strings. Based on this, the three-dimensional spatial position difference between the actual measurement position point of the UAV and the ideal measurement position point on the ideal measurement path is calculated in real time. The spatial electrostatic physical digital model automatically calculates the environmental field strength distortion increment caused by the irregular geometric deviation, and then accurately compensates and projects the scalar electric field strength data from the non-ideal actual measurement position point coordinates to the preset ideal measurement position point coordinates.

[0024] Traditional Gaussian processes (GPs) suffer from computational complexity that increases exponentially with the amount of data when processing large-scale UAV high-frequency inspection sampling data. cubic level The explosive growth makes it impossible to run on ordinary ground stations or airborne edge chips.

[0025] This invention innovatively introduces a low-rank approximation framework for Hilbert space based on Laplace characteristic basis functions. This framework successfully transforms the infinite-dimensional continuous space problem of Gaussian processes into a linear combination of multiple fixed low-rank basis functions. This ensures that the dimension of the inverse matrix is ​​fixed when solving for the weighted posterior distribution, significantly reducing the computational complexity to a linear relationship with the number of sampled data points. This allows the entire space physics model to be constructed in a closed-form solution within seconds on a standard ground station system, greatly accelerating data processing and online evaluation, and facilitating large-scale industrial application. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method according to an embodiment of the present invention.

[0027] Figure 2 The diagram shows the predicted electric field distribution on a plane with a fixed height (z=0.5), where (a) is a thermal diagram and (b) is a vector diagram.

[0028] Figure 3 It is a spatial distribution map of the compensation electric field amplitude at the detection point.

[0029] Figure 4 This is a graph showing the characteristic points and rate of change of the spatial electric field intensity of a normal high-voltage insulator string.

[0030] Figure 5 This is a graph showing the characteristic points and rate of change of the spatial electric field intensity of a high-voltage insulator string containing a zero-value fault. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0032] like Figure 1 As shown in the figure, this embodiment discloses a method for detecting zero-value insulator faults in high-voltage insulator strings based on compensation by a UAV and a space electric field model. The process is as follows:

[0033] Step 1: Establish a mathematical model of the relationship between the scalar electric field strength output by the UAV-borne Pockels electric field sensor and the latent space electrostatic potential function when the sensing axis of the Pockels electric field sensor coincides with the spatial geometric axis of the high-voltage insulator string. Furthermore, assume that the latent space electrostatic potential function follows a Gaussian process distribution, and assign a zero-mean Gaussian process prior distribution to the latent space electrostatic potential function. Then, perform a low-rank approximation on the Gaussian process prior distribution to obtain multiple eigenvalues ​​and characteristic basis functions in the bounded region. Based on each eigenvalue and characteristic basis function, the latent space electrostatic potential function in continuous space is approximately represented as a finite linear combination.

[0034] In this embodiment, according to the principles of electrostatics, the steady-state electric field intensity vector E in the air surrounding the high-voltage insulator string satisfies the irrotation condition as shown in the following equation:

[0035]

[0036] In the formula: This represents the curl operator.

[0037] Therefore, there must exist a latent space electrostatic potential (potential) function that cannot be directly measured in space. Satisfying the negative gradient relationship .in, In three-dimensional space coordinates, , These are the coordinate values ​​of the X-axis, Y-axis, and Z-axis in three-dimensional space, respectively. Let be the three-dimensional steady-state electric field function in the air surrounding the high-voltage insulator string.

[0038] The UAV-borne Pockels electric field sensor, based on the Pockels effect, performs uniaxial scalar electric field measurements around a high-voltage insulator string. It is assumed that the sensing axis of the UAV-borne Pockels electric field sensor coincides with the spatial geometric axis of the high-voltage insulator string, and that the unit direction vectors of both the sensing axis and the spatial geometric axis of the high-voltage insulator string are... ,in These are the direction vectors of the X-axis, Y-axis, and Z-axis in three-dimensional spatial coordinates, respectively.

[0039] When the sensitive axis of the UAV-borne Pockels electric field sensor coincides with the spatial geometric axis of the high-voltage insulator string, the scalar electric field strength measured and output by the UAV-borne Pockels electric field sensor will be... It is the projection (directional derivative) of the three-dimensional electric field onto the sensor's sensing axis, combined with the latent space electrostatic potential function. Satisfying the negative gradient relationship, we can establish the scalar electric field intensity output by the Pockels electric field sensor and the latent space electrostatic potential function. The mathematical relationship model is shown in the following formula:

[0040]

[0041] In this embodiment, the latent space electrostatic potential function is set. It follows a Gaussian process distribution and is the latent space electrostatic potential function. Assign a prior distribution of a Gaussian process with zero mean, as shown in the following equation:

[0042]

[0043] In the formula: Represent the prior distribution of a Gaussian process; Represents the kernel function; These represent the positions of different points in the prior distribution space of the Gaussian process.

[0044] Among them, kernel function The squared exponential (SE) covariance function is used to describe the correlation between different points in the prior distribution of a Gaussian process. The signal variance of the squared exponential (SE) covariance function... With spatial length These are known hyperparameters.

[0045] In this embodiment, to address the issue of excessive computational cost of Gaussian process prior distribution in large spaces, a low-rank approximation is performed on the zero-mean Gaussian process prior distribution. The process is as follows:

[0046] (A1) Boundary Delineation

[0047] Retrieve the three-dimensional coordinates of the high-voltage insulator string hanging points in the target tower from the power GIS system or transmission line ledger. and the standard length of high-voltage insulator strings Three-dimensional coordinates of high voltage insulator string hanging points and the standard length of high-voltage insulator strings The approximate center point of the high-voltage insulator string is calculated. .

[0048] With the approximate center point of the high-voltage insulator string An air domain of 0.5 to 1 meter is redundantly extended outward from the center, thereby automatically defining a cubic boundary region around the high-voltage insulator string. As shown in the following formula:

[0049]

[0050] In the formula: These are the approximate center points of the high-voltage insulator string. The distance extended from the center in different directions along the X-axis; These are the approximate center points of the high-voltage insulator string. The distance extended from the center in different directions along the Y-axis; These are the approximate center points of the high-voltage insulator string. The distance extended from the center in different directions along the Z-axis; , , The values ​​range from 0.5 to 1 meter.

[0051] (A2) Basis function expansion

[0052] In the boundary area Above, pre-analyzed and calculated (in this embodiment) =1024) Eigenvalues ​​of the Laplace operator and characteristic basis functions As shown in the following formula:

[0053]

[0054]

[0055] In the formula: Represents any j-th eigenvalue; This represents the spatial mode order of the j-th characteristic basis function in the X-axis direction; Let denote the spatial mode order of the j-th characteristic basis function in the Y-axis direction; Let denote the spatial mode order of the j-th characteristic basis function in the Z-axis direction; Let j represent any j-th characteristic basis function.

[0056] Use to obtain the total The characteristic basis functions will define the latent space electrostatic potential function in continuous space. It can be approximated as a finite linear combination, as shown in the following equation:

[0057]

[0058] In the formula: Let be the weight of any j-th characteristic basis function; The prior distribution of the feature basis function weights. It follows a normal Gaussian distribution, that is , Indicates a normal Gaussian distribution. Let be the prior covariance diagonal matrix, and let be the prior covariance diagonal matrix. The elements are ,in The signal variance is the squared exponential (SE) covariance function. Let be the spatial length of the squared exponential (SE) covariance function.

[0059] Therefore, in this embodiment, by applying a low-rank approximation to the prior distribution of the zero-mean Gaussian process, multiple eigenvalues ​​in the bounded space are obtained. Multiple characteristic basis functions and the latent space electrostatic potential function It can be approximated as a finite linear combination.

[0060] Step 2: The UAV flies over the confined area around the high-voltage insulator string. Using an onboard Pockels electric field sensor, it measures the scalar electric field intensity at multiple sampling points within the confined area. The three-dimensional absolute coordinates and the Pockels electric field sensor's sensitive axis direction are obtained for each sampling point. The scalar electric field intensity observations at each sampling point are concatenated into an observation vector. A sample is constructed using the scalar electric field intensity observation, the three-dimensional absolute coordinates, and the Pockels electric field sensor's sensitive axis direction for each sampling point. The original dataset is then constructed based on the three-dimensional absolute coordinates of the sampling point corresponding to each sample in the original dataset, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in Step 1. An electric field observation matrix corresponding to the corresponding sampling point is constructed. Combined with the observation vector, the low-rank linear Gaussian closed-form solution of the finite linear combination of the latent space electrostatic potential functions obtained in Step 1 is solved. This yields the posterior mean vector of the prior distribution of the feature basis function weights in the confined area around the high-voltage insulator string, thus constructing an electrostatic physics learning model for the confined area around the high-voltage insulator string.

[0061] In this embodiment, an airborne ultra-wideband (UWB) tag is installed on the drone and placed in the confined area. At least three spatially fixed ultra-wideband (UWB) base stations are deployed. When the UAV, equipped with an airborne Pockels electric field sensor and an airborne UWB tag, flies in the survey area, the location of the UAV within the boundary zone is determined using trilateration. The high-precision three-dimensional absolute coordinates x of each sampling location point.

[0062] In the trilateration method, the ranging results between three UWB base stations A, B, and C and the airborne UWB tag are used. Based on the known locations of the three UWB base stations, a trilateration geometry calculation is performed. Let the three-dimensional coordinates of UWB base station A be... Let the three-dimensional location coordinates of UWB base station B be... Let the three-dimensional location coordinates of UWB base station C be... Let the three-dimensional absolute coordinates of the sampling location point to be determined by the UAV be... Based on the distance formula between two points in space, a nonlinear multivariate equation system is constructed as follows:

[0063]

[0064] By linearizing the nonlinear multivariate equations (e.g., by subtracting quadratic terms from each pair of equations), the three-dimensional absolute coordinates of the N sampling points of the UAV can be calculated in real time with high precision. .

[0065] Then, using a timestamp alignment algorithm, the UAV in the restricted area calculated by the trilateration method is located. The precise coordinates (including timestamps) of each sampling location point. 3D absolute coordinates The body attitude (including timestamps) output by the UAV inertial navigation system at each sampling location point. Sensor sensing axis direction Each sampling location is measured by readings from an airborne Pukers electric field sensor (timestamp). scalar electric field strength observations The samples are merged to obtain the scalar electric field intensity, coordinates, and sensitive axis direction of the Pockels electric field sensor for each sampling location. The original dataset is constructed from the samples of a total of N sampling locations. ,in, For the i-th sample, This represents the three-dimensional absolute coordinates of the i-th sampling position point corresponding to the i-th sample. This indicates the direction of the sensor's sensitive axis at the i-th sampling position. This represents the observed scalar electric field intensity at the i-th sampling location. And the total... The scalar electric field intensity observations of each sample are spliced ​​together. observation vector .

[0066] In this embodiment, based on the three-dimensional absolute coordinates of the sampling location point corresponding to each sample in the original dataset, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in step 1, a model of size corresponding to the sampling location point is constructed. The electric field observation matrix is ​​given below. The electric field observation matrix for each sampling point is shown in the following formula:

[0067]

[0068] In the formula: This represents the electric field observation matrix at any i-th sampling location; Let represent the projection components of the 1st to mth basis functions at the i-th sampling position point on the current sampling point and along the sensor's sensitive axis, respectively. The projection components of any j-th basis function at the i-th sampling position point on the current sampling point and along the sensor's sensitive axis are denoted as . As shown in the following formula:

[0069]

[0070] In the formula: The characteristic basis function represents the i-th sampling location point; , , These are the components of the sensor's sensitive axis direction in the X, Y, and Z directions corresponding to the i-th sampling position point.

[0071] Total The electric field observation matrices of each sampling location point are vertically spliced ​​together to form a matrix of size [size missing]. Global single-axis electric field observation matrix As shown in the following formula:

[0072]

[0073] Then, based on the global uniaxial electric field observation matrix Solving for the low-rank linear Gaussian closed-form solution of the finite linear combination of the latent space electrostatic potential functions obtained in step 1 yields the boundary region around the high-voltage insulator string. The posterior covariance matrix of the prior distribution of the weights of the characteristic basis functions (size is) Based on the posterior covariance matrix... and observation vector The boundary region around the high-voltage insulator string is obtained by solving the problem. The posterior mean vector of the prior distribution of the feature basis function weights (size is) ), posterior covariance matrix and posterior mean vector As shown in the following formula:

[0074]

[0075]

[0076] In the formula: This represents the noise variance of the airborne Pockels electric field sensor.

[0077] This completes the construction of an electrostatic physics learning model for the boundary region surrounding the high-voltage insulator string.

[0078] Step 3: Instruct the UAV to fly at a constant speed along a preset ideal measurement path around the high-voltage insulator string. This ideal measurement path includes the three-dimensional spatial coordinates of multiple ideal measurement positions around the high-voltage insulator string. During the flight, acquire the three-dimensional spatial coordinates of each actual measurement position around the high-voltage insulator string, as well as the actual scalar electric field strength value obtained by the airborne Pockels electric field sensor at each actual measurement position. Then, calculate the three-dimensional spatial position difference between each ideal measurement position and the corresponding actual measurement position, and determine whether each actual measurement position deviates from the corresponding ideal measurement position based on the three-dimensional spatial position difference.

[0079] If a deviation exists, based on the posterior mean vector obtained in step 2, the predicted scalar electric field intensity of the electrostatic physics learning model obtained in step 2 along the sensor sensitive axis direction is calculated for each actual measurement location point with deviation and the corresponding ideal measurement location point. Based on the predicted scalar electric field intensity along the sensor sensitive axis direction for each actual measurement location point with deviation and the corresponding ideal measurement location point, the environmental field strength distortion difference value for each actual measurement location point with deviation is calculated. Finally, based on the environmental field strength distortion difference value for each actual measurement location point with deviation, the actual scalar electric field intensity value for each actual measurement location point with deviation is corrected to the pure scalar electric field intensity value for the corresponding ideal measurement location point. The actual scalar electric field intensity value for the actual measurement location point without deviation is regarded as the pure scalar electric field intensity value for the corresponding ideal measurement location point, and the pure scalar electric field intensity values ​​of each ideal measurement location point form a pure scalar electric field intensity sequence.

[0080] In this embodiment, an ideal measurement path is preset around the high-voltage insulator string. This ideal measurement path includes multiple ideal measurement position points arranged in a perfect straight line around the high-voltage insulator string, and the three-dimensional spatial coordinates of each ideal measurement position point are known. When the UAV is controlled to fly at a constant speed along the preset ideal measurement path, due to various disturbances, the UAV may deviate from the ideal flight path, causing the actual measurement position point of the UAV to deviate from the corresponding ideal measurement position point. That is, assuming that the ideal measurement path includes 10 ideal measurement position points, when the UAV flies at a constant speed along the ideal measurement path, it should be measuring at all 10 ideal measurement position points. However, due to interference, one or more of the actual measurement position points may deviate from the ideal measurement position points. Therefore, due to interference, when the UAV performs actual measurements at the 10 position points, at least one of the actual measurement position points may deviate from the corresponding ideal measurement position point. Consequently, the actual scalar electric field strength value measured by the UAV may not be the result of measurements at all 10 ideal measurement position points.

[0081] Therefore, in this embodiment, the three-dimensional spatial coordinates of the actual measurement position point corresponding to each ideal measurement position point are obtained by the trilateration method in step 2. Furthermore, the actual scalar electric field strength value obtained from the airborne Pockels electric field sensor at each actual measurement location point is acquired. The three-dimensional spatial coordinates of each ideal measurement location point. Subtract the corresponding three-dimensional spatial coordinates of the actual measured location point That is, to obtain the three-dimensional spatial position difference between the three-dimensional spatial coordinates of each ideal measurement location point and the corresponding three-dimensional spatial coordinates of the actual measurement location point. As shown in the following formula:

[0082]

[0083] when When the value is 0, it is determined that the actual measured position point has not deviated from the corresponding ideal measured position point. When the value is not 0, it can be determined that the corresponding actual measurement position point deviates from the corresponding ideal measurement position point.

[0084] When deviations exist, based on the posterior mean vector obtained in step 2, the predicted scalar electric field strength along the sensor's sensitive axis is calculated for each actual measurement location and the corresponding ideal measurement location obtained in step 2 using the electrostatic physics learning model. Then, the predicted scalar electric field strength along the sensor's sensitive axis is subtracted from the predicted scalar electric field strength along the sensor's sensitive axis for each actual measurement location with deviation, yielding the environmental field distortion difference for each actual measurement location with deviation. As shown in the following formula:

[0085]

[0086] In the formula: Represents the mathematical expectation operation; This represents the predicted scalar electric field strength along the sensor's sensitive axis at each actual measurement location point where deviations exist, as indicated by the electrostatic physics learning model. This represents the predicted scalar electric field strength along the sensor's sensitive axis at the ideal measurement position corresponding to each actual measurement position point with deviation, as indicated by the electrostatic physics learning model. This represents the electric field observation matrix for each actual measurement location point where deviations exist; This represents the electric field observation matrix for each actual measurement location point corresponding to the ideal measurement location point where deviations exist. This represents the posterior mean vector obtained in step 2.

[0087] Then, the actual scalar electric field strength value at each actual measurement location point with deviation is... Subtract the difference in environmental field strength distortion at the actual measurement location. This will perfectly represent the actual scalar electric field strength value that deviates from the given value. The compensation is projected onto the preset ideal measurement location point, thereby calculating the actual scalar electric field strength value at each actual measurement location point that deviates from the target value. Corrected to the pure scalar electric field strength value at the corresponding ideal measurement location. As shown in the following formula:

[0088]

[0089] For actual scalar electric field strength values ​​at actual measurement locations without deviation, they are directly regarded as pure scalar electric field strength values ​​at the corresponding ideal measurement locations.

[0090] Finally, the pure scalar electric field intensity values ​​at each ideal measurement location point form a sequence of pure scalar electric field intensity. ,in The pure scalar electric field strength values ​​are the values ​​at the 1st to Mth ideal measurement locations.

[0091] Step 4: After preprocessing the pure scalar electric field intensity sequence obtained in Step 3, wavelet analysis is performed to obtain the scalar electric field intensity distribution curve. Then, based on the higher-order derivative characteristics of the scalar electric field intensity distribution curve, it is determined whether there is a zero-value insulator fault in the high-voltage insulator string.

[0092] In this embodiment, the pure scalar electric field intensity sequence The preprocessing includes outlier removal and interpolation repair. The preprocessing process is as follows:

[0093] (B1) Outlier Removal

[0094] During the acquisition and spatial coordinate compensation of electric field signals, data noise mainly originates from the random electronic noise of the Pockels electric field sensor, pulsed electromagnetic interference from the high-voltage environment, and slight spatial alignment residuals. According to the central limit theorem, the overall distribution of these unsystematic noises can be regarded as an approximate normal distribution, and the 3σ criterion is applicable to eliminate abnormal jump points that seriously deviate from physical logic.

[0095] When using the 3σ criterion for elimination, the first step is to select a pure scalar electric field intensity sequence. Set a fixed-length sliding window, and select a fixed number of items each time. A series of continuous sampling points are used as a local interval for static statistical analysis.

[0096] Then, starting from the beginning of the sequence, the window is gradually slid forward (each sliding step is 1 sampling point) until the window completely covers the entire data sequence.

[0097] Next, within each current window, calculate the mean value of all electric field intensities within that local interval of the current window. with standard deviation As shown in the following formula:

[0098]

[0099] In the formula: A sequence of pure scalar electric field strengths The value of the electric field intensity of the i-th pure scalar in the equation; This represents the total number of pure scalar electric field strength values ​​contained within the current window.

[0100] Finally, for any i-th pure scalar electric field intensity value in the current window If its measured value deviates significantly from the mean and meets the following conditions: Then determine the value of the pure scalar electric field strength. For "abnormal isolated points" that are affected by instantaneous strong electromagnetic pulses or severe jitter, physical removal of the abnormal data points should be performed immediately.

[0101] Therefore, by using the 3σ criterion, these sequences are eliminated from the pure scalar electric field intensity sequence. Remove outlier data points.

[0102] (B2) Interpolation Repair

[0103] Because outlier removal leads to a pure scalar electric field intensity sequence Since some data is missing or broken, this embodiment uses a robust linear interpolation method to repair the time / space sequence.

[0104] Specifically, firstly, on the horizontal coordinate interval of the pure scalar electric field intensity sequence after removing outliers (i.e., the spatial position of the axis or the sampling order on the ideal measurement path), find the first valid sampling point immediately to the left and right of the missing block as the known data endpoint.

[0105] Then, a continuous local linear interpolation function is constructed using the known data endpoints. As shown in the following formula:

[0106]

[0107] In the formula: , These represent the abscissas of the spatial positions of adjacent valid sampling points on both sides of the missing block along the ideal path. , These are the pure scalar electric field strength values ​​corresponding to these two valid sampling points.

[0108] Finally, the above formula is used to locate all the removed missing points. The sequence is calculated and repaired one by one to fill the gaps and obtain a spatially continuous pure scalar electric field intensity sequence. It is then strictly arranged in ascending order according to its spatial coordinates on the ideal axis of the high-voltage insulator string, so that it is absolutely consistent with the physical spatial distribution of the high-voltage insulator string from the high-voltage end to the grounding end.

[0109] In this embodiment, after preprocessing the pure scalar electric field intensity sequence, the preprocessed complete pure scalar electric field intensity sequence is used as the input for wavelet analysis. Utilizing the excellent time-frequency localization characteristics of wavelet analysis, high-frequency spikes are removed while retaining the sharp edge features caused by zero-value insulators, resulting in the scalar electric field intensity distribution curve. The wavelet analysis process is as follows:

[0110] (C1) First, perform multi-scale decomposition:

[0111] The Daubechies wavelet (db4 or db5 is preferred in engineering) with approximate symmetry and compact support is selected as the wavelet basis function to perform multi-scale orthogonal decomposition on the pure scalar electric field intensity values ​​in the processed pure scalar electric field intensity sequence.

[0112] In engineering applications, selecting 3 to 5 layers for wavelet multi-scale decomposition can balance denoising effect and feature preservation. Too few layers will result in noise residue, while too many layers will make the curve too smooth, thereby weakening the characteristic peaks of zero-value insulators.

[0113] (C2) Then perform a separation approximation and obtain the detail coefficients:

[0114] In the multi-scale decomposition process, the pure scalar electric field intensity sequence is projected and decomposed into low-frequency approximation coefficients and high-frequency detail coefficients. The low-frequency part reflects the macroscopic overall physical trend of the electric field intensity along the longitudinal direction of the high-voltage insulator string, while the high-frequency part mainly corresponds to random glitches and electrical noise introduced by various high-frequency abrupt changes.

[0115] (C3) Next, non-linear shrinkage thresholding is performed:

[0116] For the high-frequency detail coefficients obtained from each decomposition layer, a globally unified threshold is determined based on the principle of statistical noise estimation. A soft thresholding function is used to nonlinearly shrink the detail coefficients, weakening or eliminating high-frequency interference components. Threshold The calculation formula is as follows:

[0117]

[0118]

[0119] In the formula: To determine the high-frequency detail coefficients of the first layer The noise standard deviation estimate is made from the median. This represents the total length of the signal.

[0120] (C4) Finally, perform inverse wavelet transform reconstruction:

[0121] The low-frequency approximation coefficients representing the background trend of the electric field strength are fully preserved, and the high-frequency detail coefficients of each layer after thresholding and shrinking are also substituted into the curve. The signal is then reconstructed using inverse wavelet transform, and finally a smoothed, high-fidelity scalar electric field intensity distribution curve is obtained. ,in This refers to the spatial location point of the axis on the ideal measurement path of the high-voltage insulator string.

[0122] In this embodiment, based on the first and second derivative characteristics of the scalar electric field intensity distribution curve obtained by wavelet analysis, it is determined whether there is a zero-value insulator fault in the high-voltage insulator string. The process is as follows:

[0123] (D1) First, compare the scalar electric field intensity distribution curve. Perform higher-order derivative calculations:

[0124] For the smoothed high-fidelity scalar electric field intensity distribution curve Calculate the first derivative along the path coordinates. With the second derivative As shown in the following formula:

[0125]

[0126] Wherein, the first derivative Curve reflecting scalar electric field intensity distribution The slope change is used to characterize the rising and falling trend of the electric field strength as the physical location moves. Second derivative Curve reflecting scalar electric field intensity distribution The changes are used to deeply reveal the inflection points of the curve and the characteristics of abrupt changes in the electric field. This embodiment introduces the second derivative. To assist the first derivative By extracting feature points, while ensuring extreme sensitivity to field strength distortion, it can effectively eliminate misjudgments and omissions caused by small fluctuations in the smooth section, and significantly improve the accuracy of identifying real physical inflection points.

[0127] (D2) Next, extract the inflection points and extreme value feature points:

[0128] Finding the first derivative by solving a system of simultaneous equations Extreme points where the value is zero and the second derivative The inflection points where the electric field intensity is zero are marked as scalar electric field intensity distribution curves. feature point set ,in These are the 1st to the nth feature points, respectively.

[0129] (D3) Then, calculate the rate of change of electric field intensity in the characteristic interval:

[0130] At two adjacent feature points (Location Field strength )and (Location Field strength Between ), calculate two adjacent feature points. rate of change of electric field intensity :

[0131]

[0132] (D4) Finally, perform fault diagnosis and determination for zero-value insulators:

[0133] According to the typical laws of electrostatic fields in power systems, when a normal high-voltage insulator string moves from the high-voltage end to the middle, the field strength decay curve should be smooth and gradual.

[0134] If adjacent feature points are captured within a certain continuous sub-interval... The rate of change of electric field intensity calculated between It exhibits a negative mutation, and absolute value If the electric field strength change rate abruptly drops significantly above the average attenuation level in the same spatial location range of a normal high-voltage insulator string, and the physical width of the abrupt range precisely falls within the typical physical height / thickness range of a single insulator in the high-voltage insulator string, it is confirmed that the precipitous drop in electric field occurs within the thickness space of a single insulator in the high-voltage insulator string. Furthermore, if a positive peak value of the second derivative of an adjacent healthy insulator due to excessive voltage occurs at a immediately adjacent location, then the insulator corresponding to the abrupt range of electric field strength change rate is diagnosed as a zero-value insulation fault with conduction breakdown. The precise defect number of the insulator is automatically output based on the coordinates of the ideal measurement location point.

[0135] The following examples illustrate the practical application of this embodiment.

[0136] by Figure 2 Taking the spatial distribution of the electric field at the z=0.5 plane as an example, the dataset comes from the Kaggle pyGDMNear-field Electromagnetic Database. Based on the trained GP model, a 20×20 grid (400 prediction points) is constructed on the insulator surface at a fixed height z=0.5 plane to predict the three-dimensional electric field on this plane. The results are shown in two sub-figures: (a) a heatmap, which maps the predicted electric field amplitude |E| to color for quick identification of the field strength distribution; (b) a vector graph, which uses arrows to represent the Ex and Ey components for easy observation of the direction of the electric field flow. This graph is used to verify whether the GP model captures a reasonable electric field topology in spatial extrapolation.

[0137] like Figure 3 The diagram shows the spatial distribution of the compensated electric field amplitude at the detection points. The compensated electric field amplitude E_c of 60 actual detection points P_actual is mapped to spatial locations, where: the scatter coordinates are the projections of P_actual onto the xy plane; the color intensity represents the magnitude of |E_c|, using plasma color bars: light colors represent high compensation amplitudes, and dark colors represent low compensation amplitudes; circles mark the points with the highest compensation values, i.e., the detection locations with the largest |E_c|, through Top-K (k=1).

[0138] like Figure 4The figure shows the scalar electric field intensity distribution curve (Processed Curve) corresponding to a normal high-voltage insulator string measured by the Pockles sensor. By calculating the first and second derivatives of this curve, each feature point (i.e., the red key points in the figure) is extracted, and the rate of change of electric field intensity between adjacent feature points is calculated (i.e., the numerical labels between two points in the figure). It can be seen that in a normal high-voltage insulator string, as the electric field intensity decreases from the high-voltage end to the ground end, the rate of change of electric field intensity between adjacent feature points is uniformly distributed, without any local negative abrupt changes.

[0139] like Figure 5 The figure shows the scalar electric field intensity distribution curves (the fourth plate is the zero-value plate) of a high-voltage insulator string with a zero-value fault, as measured by a Pockles sensor. Figure 5 It can be clearly observed that within a certain continuous sub-interval corresponding to the x-axis (i.e., the physical spatial location of the 4th insulator), the rate of change of electric field intensity between adjacent feature points exhibits a significant negative abrupt change. At this point, the absolute value of the rate of change of electric field intensity at this abrupt change is significantly higher than... Figure 4 The average attenuation level within the same spatial location range of a normal high-voltage insulator string. Simultaneously, the physical width of this spatial range where the rate of change of electric field intensity abruptly changes falls precisely within the typical physical height range of a single insulator piece in a high-voltage insulator string. Therefore, through... Figure 5 The characteristic values ​​successfully diagnosed and identified the insulator corresponding to the spatial interval as a zero-value fault insulator with conduction breakdown.

[0140] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0141] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation, characterized in that, The process is as follows: Step 1: Establish a mathematical model of the relationship between the scalar electric field strength output by the UAV-borne Pockels electric field sensor and the latent space electrostatic potential function when the sensing axis of the Pockels electric field sensor coincides with the spatial geometric axis of the high-voltage insulator string; assign a zero-mean Gaussian process prior distribution to the latent space electrostatic potential function; then, perform a low-rank approximation on the Gaussian process prior distribution to obtain multiple eigenvalues ​​and characteristic basis functions in the bounded region; based on each eigenvalue and characteristic basis function, approximate the latent space electrostatic potential function in continuous space as a finite linear set. Step 2: Command the UAV to fly over the clearance area around the high-voltage insulator string and measure the scalar electric field intensity observations at multiple sampling points in the clearance area using the airborne Pockels electric field sensor; then concatenate the scalar electric field intensity observations at each sampling point into an observation vector. Then, based on the three-dimensional absolute coordinates of the sampling location point corresponding to each sample, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in step 1, the electric field observation matrix corresponding to the sampling location point is constructed. Then, combined with the observation vector, the low-rank linear Gaussian closed-form solution of the finite linear combination of the latent space electrostatic potential function obtained in step 1 is solved to obtain the posterior mean vector of the prior distribution of the feature basis function weights in the confined region around the high-voltage insulator string. Thus, the electrostatic physics learning model of the confined region around the high-voltage insulator string is constructed. Step 3: The UAV is instructed to fly along the preset ideal measurement path around the high-voltage insulator string, and the actual scalar electric field strength value at each actual measurement location point during the flight is obtained by the airborne Pockels electric field sensor. Determine whether each actual measurement location point deviates from the corresponding ideal measurement location point. If there is a deviation, based on the posterior mean vector and electrostatic physics learning model obtained in step 2, correct the actual scalar electric field intensity value of each actual measurement location point with deviation to the pure scalar electric field intensity value of the corresponding ideal measurement location point. The actual scalar electric field intensity value of the actual measurement location point without deviation is regarded as the pure scalar electric field intensity value of the corresponding ideal measurement location point, and the pure scalar electric field intensity values ​​of each ideal measurement location point form a pure scalar electric field intensity sequence. Step 4: Perform wavelet analysis on the pure scalar electric field intensity sequence to obtain the scalar electric field intensity distribution curve, and then determine whether there is a zero-value insulator fault in the high-voltage insulator string based on the scalar electric field intensity distribution curve.

2. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 1, the kernel function in the prior distribution of the Gaussian process is the squared exponential covariance function.

3. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation as described in claim 1, characterized in that, In step 1, during the low-rank approximation, an air domain is extended outward by a predetermined distance from the approximate center point of the high-voltage insulator string, thereby defining a cubic boundary region around the high-voltage insulator string; then, multiple eigenvalues ​​and characteristic basis functions are solved within the boundary region.

4. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 2, the three-dimensional absolute coordinates of each sampling location point are obtained by the trilateration method.

5. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 2, the electric field observation matrix corresponding to each sampling location point is constructed based on the three-dimensional absolute coordinates of each sampling location point, the corresponding sensor sensitive axis direction, and the multiple feature basis functions obtained in step 1; the electric field observation matrices of all sampling locations are vertically spliced ​​together to form a global single-axis electric field observation matrix. Based on the global uniaxial electric field observation matrix, the low-rank linear Gaussian closed-form solution of the finite linear combination of latent space electrostatic potential functions obtained in step 1 is solved to obtain the posterior covariance matrix of the prior distribution of characteristic basis function weights in the confined region around the high-voltage insulator string; then, based on the posterior covariance matrix and the observation vector, the posterior mean vector of the prior distribution of characteristic basis function weights in the confined region around the high-voltage insulator string is solved.

6. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 3, based on the three-dimensional spatial position difference between the three-dimensional spatial coordinates of each actual measurement location point and the three-dimensional spatial coordinates of the corresponding ideal measurement location point, it is determined whether each actual measurement location point deviates from the corresponding ideal measurement location point.

7. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 3, if there is a deviation, the environmental field strength distortion difference between the predicted scalar electric field strength at each actual measurement location point and the corresponding ideal measurement location point is calculated based on the posterior mean vector obtained in step 2. Based on the environmental field strength distortion difference at each actual measurement location point with deviation, the actual scalar electric field strength value at each actual measurement location point with deviation is corrected to the pure scalar electric field strength value at the corresponding ideal measurement location point.

8. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 4, the pure scalar electric field intensity sequence is preprocessed before wavelet analysis is performed. The preprocessing includes outlier removal and interpolation repair.

9. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 4, during wavelet analysis, the pure scalar electric field intensity values ​​in the pure scalar electric field intensity sequence are first decomposed into a multi-scale orthogonal decomposition. During the multi-scale decomposition, the pure scalar electric field intensity sequence is decomposed into low-frequency approximation coefficients and high-frequency detail coefficients. Then, the high-frequency detail coefficients obtained from each decomposition layer are nonlinearly shrunk using a soft threshold function based on a globally unified threshold. Finally, the low-frequency approximation coefficients representing the background trend of the electric field strength are fully preserved, and the high-frequency detail coefficients of each layer after thresholding and shrinking are substituted into the curve. The signal is reconstructed using wavelet inverse transform to obtain the scalar electric field strength distribution curve.

10. The method for detecting zero-value insulator faults in high-voltage insulator strings based on UAV and spatial electric field model compensation according to claim 1, characterized in that, In step 4, the first and second derivatives of the scalar electric field intensity distribution curve are calculated; the extreme points where the first derivative is zero and the inflection points where the second derivative is zero are taken as the characteristic points of the scalar electric field intensity distribution curve, and the rate of change of electric field intensity between two adjacent characteristic points is calculated. If a negative abrupt change in the rate of change of electric field intensity between adjacent feature points is detected within a certain continuous sub-interval, and the absolute value of the rate of change of electric field intensity is higher than the average attenuation level of the same spatial location interval of a normal high-voltage insulator string, and the spatial physical width of the abrupt change interval of electric field intensity falls within the typical physical height / thickness range of a single insulator in a high-voltage insulator string, the insulator corresponding to the abrupt change interval of electric field intensity is diagnosed as a zero-value insulator fault with conduction breakdown.

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