A power transmission line icing monitoring method fusing GNSS perception and PI-KAN

Abstract

The application discloses a kind of fusion GNSS The power transmission line icing monitoring method of perception and PI-KAN Including:1.Using the way of "hanging point static calibration+observation point dynamic monitoring", the longitude-latitude-elevation coordinates of two hanging points and an observation point of power transmission line are collected, and the standardized input matrix is generated by coordinate transformation;2.The input matrix features of the network are extracted by fusing KAN And physical constraints PI-KAN The catenary differential equation residual is embedded as a physical constraint into the loss function, and the catenary physical parameters are output;3.A second-order numerical algorithm is designed to correct the physical parameters output by the network with high precision, and the optimal catenary physical parameters are obtained;4.Based on the optimal catenary physical parameters, the current conductor length is solved, the equivalent load is calculated by combining the thermal-mechanical coupling constitutive equation, and the icing thickness is calculated according to the geometric model.The application can significantly improve the calculation accuracy and efficiency of the conductor icing thickness, thereby providing reliable technical support for power transmission line icing monitoring and disaster warning.

Description

Technical Field

[0001] This invention belongs to the field of power transmission line safety monitoring, specifically a fusion GNSS Perception and PI-KAN Methods for monitoring icing on power transmission lines. Background Technology

[0002] As the core carrier of power transmission, the long-term safe operation of transmission lines is crucial to ensuring the stability of the power grid. Under complex meteorological conditions such as low temperature, high humidity, and high altitude, conductors are highly susceptible to icing. Icing overload can lead to major safety accidents such as increased conductor sag, phase-to-phase discharge, tower tilting, and even line breakage. Therefore, accurate and real-time monitoring of the icing status of transmission lines is of great engineering significance for power grid disaster prevention and mitigation.

[0003] Existing methods for monitoring icing on transmission lines mainly include mechanical sensor monitoring, image visual monitoring, electric field induction monitoring, and satellite positioning monitoring. Among them, mechanical sensor monitoring relies on strain and tension sensors to directly measure the load, but these sensors are prone to aging and drifting in harsh outdoor environments over long periods, making it difficult to guarantee stability and lifespan. Image visual monitoring is easily affected by weather conditions such as sunlight, rain, snow, and fog, and its recognition accuracy drops significantly at night or in severe weather, making it difficult to achieve stable monitoring around the clock. Electric field induction monitoring is sensitive to the on-site electromagnetic environment and is easily affected by the coupling of line load and meteorological factors, resulting in large errors in icing thickness inversion.

[0004] In recent years, based on GNSS Location-based, non-contact icing monitoring methods are widely used because they are not limited by weather conditions and can achieve long-distance dynamic sensing. However, existing methods... GNSS Most methods employ traditional catenary models for geometric fitting, failing to fully consider the coupling effect between the conductor's true mechanical properties and temperature deformation, resulting in limited accuracy in sag and icing load inversion. Furthermore, traditional data-driven models lack physical constraints, exhibit poor generalization ability and robustness, and are prone to overfitting and parameter instability under complex operating conditions. They struggle to simultaneously meet the high accuracy, strong stability, and engineering practicality requirements of icing monitoring, and cannot fully adapt to the demands of modern smart grids for refined monitoring of line conditions. Summary of the Invention

[0005] This invention aims to address the shortcomings of the existing technology by proposing a fusion method. GNSS Perception and PI- KAN The proposed method for monitoring icing on power transmission lines aims to achieve all-weather, high-precision, and robust monitoring of icing thickness, thereby effectively improving the early warning capability of power grid icing disasters and ensuring the safe, stable, and long-term operation of transmission lines under complex weather conditions.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: This invention is a fusion GNSS Perception and PI-KAN The characteristics of the transmission line icing monitoring method are as follows: Step 1: Collect the first suspension point of the transmission line. Static latitude-longitude coordinates Second suspension point Static latitude-longitude coordinates and observation points within the horizontal span exist Latitude, longitude and elevation coordinates of the moment The latitude, longitude, and elevation coordinates of the three points are then converted to station center coordinates. Spatial rectangular coordinates, thus forming a standardized input matrix. ; Step 2, Build PI-KAN Networks, including: layer KAN Hidden layers, output layers, and physical constraints are used to... The process is performed to obtain the catenary physical parameter vector. Thus, the total loss function is constructed. Used for training PI-KAN The network, and after training PI-KAN The optimal catenary physical parameter vector output by the model ; Step 3: Use a second-order numerical algorithm to obtain the optimal catenary physical parameter vector. High-precision correction is performed to obtain the corrected optimal catenary physical parameter vector. ; Step 4: Based on the corrected optimal physical parameter vector under the non-icing condition, establish and solve the thermo-mechanical coupled constitutive equation to obtain the icing thickness. .

[0007] A fusion described in this invention GNSS Perception and PI-KAN The characteristic of the transmission line icing monitoring method is that step 1 includes the following steps: Step 1.1, , , any observation point in the middle The latitude-longitude coordinates are as follows , ,in, They represent the observation points respectively. Geodetic longitude, geodetic latitude, and geodetic elevation; Step 1.2: Based on Earth ellipsoid parameters, including: semi-major axis eccentricity Using equation (1), a geodetic coordinate to geocentric rectangular coordinate transformation operator is constructed. : (1) In equation (1), For observation point The radius of curvature of the ellipsoidal vertex at that location; Step 1.3: Select the center point of the horizontal span of the transmission line as the reference station, and let the geodetic longitude, geodetic latitude, and geodetic elevation of the reference station be respectively... Thus, the station center is constructed using equation (2). Coordinate system rotation matrix : (2) Step 1.4: Obtain the observation point using equation (3). Spatial rectangular coordinate vector Thus obtain : (3) In equation (3), This is the translation vector of the reference station center.

[0008] Furthermore, step 2 includes the following steps: Step 2.1, Current KAN The hidden layer number is and initialize ; Initialize the first layer KAN Hidden layer output layer feature vector ; Define the first layer KAN The number of nodes in the hidden layer is ; Step 2.2: Calculate the first step using equation (4). layer KAN The first hidden layer The node feature values ​​output by each node Thus, the first layer KAN Hidden layer output layer feature vector , Indicates transpose; (4) In equation (4), Indicates the first layer KAN The first hidden layer The node feature values ​​output by each node. Indicates the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The activation function for each node is: (5) In equation (5), for Activation function For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The linear branch weights of each node to be learned for Step The basis function vector formed by spline basis functions. For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The spline branch of each node is a vector of control coefficients to be learned. Represents the inner product in Euclidean space. These are the balance weights for the spline branches; Step 2.3, take in sequence Assignment After that, return to step 2.2 and execute sequentially until... Until then, thus obtaining the first layer KAN Hidden layer output layer feature vector ; Step 2.4, the output layer uses equation (6) to... Perform a linear transformation to obtain the catenary physical parameter vector. ,in, The horizontal tension coefficient of the catenary. The normalized position of the horizontal span of the sag point. Elevation of the sag point of the traverse line: (6) In equation (6), The weight matrix to be learned for the output layer. The bias vector to be learned for the output layer; Step 2.5: Construct the total loss function using equation (7). : (7) In equation (7), for A defined vertical shape function for the conductor. The x-coordinate of the conductor on the horizontal span. For observation point Theoretical elevation, For observation point The measured elevation, The regularization weight coefficients for the physical constraint loss are... It is a second-order nonlinear differential residual operator. , , The suspension points are respectively Suspension point Observation points Horizontal coordinates; Step 2.6: Minimize the total loss function Iterative updates to achieve the goal. PI-KAN All the parameters to be learned from the network are used to obtain the trained network. PI-KAN The model is generated and the optimal catenary physical parameter vector is output. ,in, This represents the optimal value for the horizontal tension coefficient. This represents the optimal value for the normalized position of the sag point. This represents the optimal value for the elevation of the sag point.

[0009] Furthermore, step 3 includes the following steps: Step 3.1: Set the current iteration count to... and initialize ; Define the first Catenary physical parameter vector under the next iteration ;in, For the first The horizontal tension coefficient of the catenary in the next iteration For the first Normalized position of the horizontal span of the sag point in the next iteration For the first Elevation of the sag point in the next iteration; and initialize ; Step 3.2: Construct the first equation using equation (8). Non-convex residual objective function under the next iteration : (8) In equation (8), for A defined vertical morphological function for the conductor; Step 3.3: Using equation (9), obtain the catenary of the transmission line at the first... Physical parameter vector under the next iteration : (9) In equation (9), For the objective function exist The approximate Hessian matrix at that location, For the objective function exist The gradient vector at that point, For the iterative damping factor, A matrix of the same order; superscript This represents finding the inverse of a matrix. Step 3.4, when When that happens, stop the iteration and... As the corrected optimal physical parameter vector Otherwise, Assign to Then, return to step 3.2, where, The preset high-precision threshold; where, This represents the corrected optimal catenary horizontal tension coefficient. This indicates the normalized position of the corrected optimal sag point horizontal span. This indicates the corrected optimal sag point elevation.

[0010] Furthermore, step 4 includes the following steps: Step 4.1: Measure the conductor temperature under non-icing conditions using a temperature sensor. Obtain suspension points through the route design ledger. The baseline length of the conductors and the load per unit length of conductor under non-icing conditions ; The input matrix corresponding to the non-icing condition Input after training PI-KAN After processing in the model, the results are then subjected to second-order numerical correction according to step 3 to obtain the corrected optimal physical parameter vector under the non-icing condition. And calculate the horizontal tension under the non-icing condition. ;in, The corrected optimal catenary horizontal tension coefficient under non-icing conditions. This represents the normalized position of the optimal sag point horizontal span under non-icing conditions. The corrected optimal sag point elevation of the traverse line under non-icing conditions; Step 4.2, based on the first suspension point Spatial rectangular coordinate vector Second suspension point Spatial rectangular coordinate vector According to equation (10), the conductor at the suspension point A With suspension point B Integrating the arc lengths between the arcs yields the conductor length under the current operating conditions. : (10) In equation (10), For the reason The derived horizontal x-coordinate of the sag point To account for the geometric correction factors for elevation differences and coordinate rotation, and we have: (11) (12) Step 4.3: Real-time acquisition of conductor temperature under current operating conditions. And the thermo-mechanical coupling constitutive equation is established using equation (13): (13) In equation (13), The elastic modulus of the conductor. The cross-sectional area of ​​the conductor. The coefficient of thermal expansion; The horizontal tension under the current working conditions; Step 4.4: Solve the thermo-mechanical coupling constitutive equation to obtain the horizontal tension under the current operating condition. Thus, the equivalent unit load norm is calculated. ; Step 4.5: Based on the icing geometry model, obtain the icing thickness using equation (14). : (14) In equation (14), Let the radius be the conductor. This represents the density of the ice layer.

[0011] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in performing the method described therein, and the processor is configured to execute the program stored in the memory.

[0012] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program is executed by a processor to perform the steps of the method described thereon.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention adopts GNSS The non-contact mode eliminates the need for easily malfunctioning mechanical sensors and is unaffected by environmental factors such as light, rain, snow, and nighttime. It overcomes the problems of poor stability and inability to work around the clock that are traditional monitoring methods, and enables long-term reliable sensing of the status of power transmission lines.

[0014] 2. This invention constructs a system with embedded physical constraints of catenary differential equations. PI-KAN The network, combined with second-order numerical algorithms for parameter optimization, solves the shortcomings of traditional models such as low accuracy and pure data-driven approach, and significantly improves the inversion accuracy of catenary parameters and conductor sag, as well as the robustness of the model.

[0015] 3. This invention eliminates the influence of temperature deformation by using thermo-mechanical coupling constitutive equations, accurately calculates the equivalent load of icing, effectively reduces calculation errors caused by environmental factors, and significantly improves the accuracy of icing thickness monitoring. It can provide efficient and accurate technical support for disaster prevention, mitigation and safe operation of transmission lines. Attached Figure Description

[0016] Picture 1 This is a schematic diagram illustrating an application scenario of the present invention; Picture 2 This is a flowchart of the main program of the present invention; Picture 3 for PI-KAN Network architecture schematic diagram. Detailed Implementation

[0017] In this embodiment, a fusion GNSS Perception and PI-KAN The method for monitoring icing on power transmission lines is through GNSS Satellite positioning technology enables non-contact perception of the spatial morphology of transmission lines. Relying on physically constrained neural networks and numerical optimization algorithms, it accurately inverts conductor mechanical parameters. Combined with a thermo-mechanical coupling model to remove temperature influences and calculate icing thickness, this not only ensures all-weather adaptability and computational accuracy for icing monitoring but also achieves stable, reliable, and real-time characterization of conductor icing conditions. This provides scientific and effective technical support for early warning of icing disasters, safety operation assessment, and risk prevention and control of transmission lines. Specifically, for example... Picture 2 As shown, the method includes the following steps: Step 1, as follows Picture 1 As shown, the first suspension point of the transmission line is collected. Static latitude-longitude coordinates Second suspension point Static latitude-longitude coordinates and observation points within the horizontal span exist Latitude, longitude and elevation coordinates of the moment The latitude, longitude, and elevation coordinates of the three points are then converted to station center coordinates. Spatial rectangular coordinates, thus forming a standardized input matrix. .

[0018] Step 1.1, , , any observation point in the middle The latitude-longitude coordinates are as follows , ,in, They represent the observation points respectively. Geodetic longitude, geodetic latitude, and geodetic elevation; Step 1.2: Based on Earth ellipsoid parameters, including: semi-major axis eccentricity Using equation (1), a geodetic coordinate to geocentric rectangular coordinate transformation operator is constructed. : (1) In equation (1), For observation point The ellipsoidal radius of curvature at that location; geocentric rectangular coordinates facilitate spatial vector calculations and are essential for subsequent implementation. The basis for this transformation is to eliminate systematic biases caused by geographical location differences.

[0019] Step 1.3: Construct based on the center of the gear gap A local coordinate system can more intuitively reflect the displacement changes of the conductor in the horizontal and vertical directions, improving the stability of sag and icing load inversion. Therefore, the center point of the horizontal span of the transmission line is selected as the reference station, and the geodetic longitude, geodetic latitude, and geodetic elevation of the reference station are respectively... Thus, the station center is constructed using equation (2). Coordinate system rotation matrix : (2) Step 1.4: Obtain the observation point using equation (3). Spatial rectangular coordinate vector Thus obtain : (3) In equation (3), This is the translation vector of the reference station center.

[0020] Step 2, as follows Picture 3 As shown, construct PI-KANNetworks, including: layer KAN Hidden layers, output layers, and physical constraints are used to... The process is performed to obtain the catenary physical parameter vector. Thus, the total loss function is constructed. Used for training PI-KAN The network, and after training PI-KAN The optimal catenary physical parameter vector output by the model .

[0021] In construction PI-KAN Before establishing the network, the geometric model of the transmission line and the physical parameters to be inverted must first be defined. The geometric model of the transmission line is described by the classical catenary equation: ;in, Let x be the x-coordinate of the traverse point on the horizontal span. Let be the lateral coordinates of the traverse point perpendicular to the horizontal span direction. These are the vertical elevation coordinates corresponding to the traverse points. The horizontal tension coefficient of the catenary. Let x be the x-coordinate of the lowest point of the conductor on the horizontal span. Let be the lateral coordinate of the lowest point of the conductor, perpendicular to the horizontal span direction. The equation contains the vertical elevation coordinates corresponding to the lowest point of the traverse line. , , , Four unknowns; Environmental wind field speed Under the quasi-static assumption, the geometry of the traverse degenerates into a two-dimensional planar curve, and the lateral offset of the lowest point of the traverse is negligible. A normalized scaling parameter is introduced. Parametrically segmenting the horizontal clearance reduces the four-dimensional parameter space to three dimensions, resulting in the following unknowns: , , .

[0022] Step 2.1, Current KAN The hidden layer number is and initialize ; Initialize the first layer KAN Hidden layer output layer feature vector ; Define the first layer KAN The number of nodes in the hidden layer is ; Step 2.2: Calculate the first step using equation (4). layer KAN The first hidden layer The node feature values ​​output by each node Thus, the first layer KAN Hidden layer output layer feature vector , Indicates transpose; (4) In equation (4), Indicates the first layer KAN The first hidden layer The node feature values ​​output by each node. Indicates the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The activation function for each node is: (5) In equation (5), for Activation functions, characterized by smoothness and absence of hard saturation, can effectively alleviate the gradient vanishing problem during network training. For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The linear branch weights of each node to be learned for Step The basis function vector formed by spline basis functions can ensure that the feature fitting curve is continuous and smooth, matching the smooth geometric properties of the catenary itself. For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The spline branch of each node is a vector of control coefficients to be learned. Represents the inner product in Euclidean space. represents the spline branch balancing weight coefficient.

[0023] Step 2.3, take in sequence Assign to Then, return to step 2.2 and execute sequentially until... Until then, thus obtaining the first layer KAN Hidden layer output layer feature vector The shallow network mainly extracts basic features such as single-point coordinates and relative positions of points, while the deep network integrates and abstracts these basic features to uncover the deep correlation between coordinate changes and the overall shape and mechanical state of the conductor.

[0024] Step 2.4, the output layer uses equation (6) to... Perform a linear transformation to obtain the catenary physical parameter vector. ,in, The horizontal tension coefficient of the catenary. The normalized position of the horizontal span of the sag point. Elevation of the sag point of the traverse line: (6) In equation (6), The weight matrix to be learned for the output layer. This is the bias vector to be learned for the output layer.

[0025] Step 2.5: Construct the total loss function using equation (7). : (7) In equation (7), for A defined vertical shape function for the conductor. Let x be the x-coordinate of the traverse point on the horizontal span. For observation point Theoretical elevation, For observation point The measured elevation, The regularization weight coefficients for the physical constraint loss are... It is a second-order nonlinear differential residual operator. , , The suspension points are respectively Suspension point Observation points The horizontal coordinates; the total loss function consists of two parts. The first part is the fitting error term of the observation point elevation, which is used to ensure that the theoretical elevation calculated by the parameters output by the network is consistent with the measured elevation. The second part is the residual term of the catenary differential equation, which is also the core embodiment of physical constraints, constraining the shape of the entire traverse interval to satisfy the catenary mechanical equation.

[0026] Step 2.6: Minimize the total loss function Iterative updates to achieve the goal. PI-KAN All the parameters to be learned from the network are used to obtain the trained network. PI-KAN The model is generated and the optimal catenary physical parameter vector is output. ,in, This represents the optimal value for the horizontal tension coefficient. This represents the optimal value for the normalized position of the sag point. This represents the optimal value for the elevation of the sag point.

[0027] Step 3 PI-KAN Network output Although it possesses good physical rationality and basic accuracy, it still exhibits slight deviations due to factors such as network fitting errors and minor measurement noise, making it difficult to meet accuracy requirements. Therefore, a second-order numerical algorithm is used to obtain the optimal catenary physical parameter vector. High-precision correction is performed to obtain the corrected optimal catenary physical parameter vector.

[0028] Step 3.1: Set the current iteration count to... and initialize ; Define the first Catenary physical parameter vector under the next iteration ;in, For the first The horizontal tension coefficient of the catenary in the next iteration For the first Normalized position of the horizontal span of the sag point in the next iteration For the first Elevation of the sag point in the next iteration; and initialize .

[0029] Step 3.2: Construct the first equation using equation (8). Non-convex residual objective function under the next iteration : (8) In equation (8), for A defined vertical morphology function for the conductor.

[0030] Step 3.3: Using equation (9), obtain the catenary of the transmission line at the first... Physical parameter vector under the next iteration : (9) In equation (9), For the objective function exist The approximate Hessian matrix at a given point represents the second derivative information of the objective function, reflecting the curvature of the function surface. For the objective function exist The gradient vector at that point, For the iterative damping factor, A matrix of the same order; superscript This represents finding the inverse of a matrix.

[0031] Step 3.4, when When that happens, stop the iteration and... As the corrected optimal physical parameter vector Otherwise, Assign to Then, return to step 3.2, where, The preset high-precision threshold; where, This represents the corrected optimal catenary horizontal tension coefficient. This indicates the normalized position of the corrected optimal sag point horizontal span. This indicates the corrected optimal sag point elevation.

[0032] Step 4: Calculate the ice thickness; Step 4.1: Measure the conductor temperature under non-icing conditions using a temperature sensor. Obtain suspension points through the route design ledger. The baseline length of the conductors and the load per unit length of conductor under non-icing conditions .

[0033] The input matrix corresponding to the non-icing condition Input after training PI-KAN After processing in the model, the results are then subjected to second-order numerical correction according to step 3 to obtain the corrected optimal physical parameter vector under the non-icing condition. And calculate the horizontal tension under the non-icing condition. ;in, The corrected optimal catenary horizontal tension coefficient under non-icing conditions. This represents the normalized position of the optimal sag point horizontal span under non-icing conditions. The corrected elevation of the optimal sag point of the traverse line under non-icing conditions.

[0034] Step 4.2, based on the first suspension point Spatial rectangular coordinate vector Second suspension point Spatial rectangular coordinate vector According to equation (10), the conductor at the suspension point A With suspension point B Integrating the arc lengths between the arcs yields the conductor length under the current operating conditions. : (10) In equation (10), For the reason The derived horizontal x-coordinate of the sag point To account for the geometric correction factors for elevation differences and coordinate rotation, and we have: (11) (12) Step 4.3: Real-time acquisition of conductor temperature under current operating conditions. And the thermo-mechanical coupling constitutive equation is established using equation (13): (13) In equation (13), The elastic modulus of the conductor. The cross-sectional area of ​​the conductor. The coefficient of thermal expansion; This represents the horizontal tension under the current operating conditions.

[0035] Step 4.4: Solve the thermo-mechanical coupling constitutive equation to obtain the horizontal tension under the current operating condition. Thus, the equivalent unit load norm is calculated. ; Step 4.5: Based on the icing geometry model, obtain the icing thickness using equation (14). : (14) In equation (14), Let the radius be the conductor. This represents the density of the ice layer.

[0036] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0037] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A fusion GNSS Perception and PI-KAN A method for monitoring icing on power transmission lines, characterized in that, Includes the following steps: Step 1: Collect the first suspension point of the transmission line. Static latitude-longitude coordinates Second suspension point Static latitude-longitude coordinates and observation points within the horizontal span exist Latitude, longitude and elevation coordinates of the moment The latitude, longitude, and elevation coordinates of the three points are then converted to station center coordinates. Spatial rectangular coordinates are used to form a standardized input matrix. ; Step 2, Build PI-KAN Networks, including: layer KAN Hidden layers, output layers, and physical constraints are used to... The process is performed to obtain the catenary physical parameter vector. Thus, the total loss function is constructed. Used for training PI-KAN The network, and after training PI-KAN The optimal catenary physical parameter vector output by the model ; Step 3: Use a second-order numerical algorithm to obtain the optimal catenary physical parameter vector. High-precision correction is performed to obtain the corrected optimal catenary physical parameter vector. ; Step 4: Based on the corrected optimal physical parameter vector under the non-icing condition, establish and solve the thermo-mechanical coupled constitutive equation to obtain the icing thickness. .

2. A fusion according to claim 1 GNSS Perception and PI-KAN A method for monitoring icing on power transmission lines, characterized in that, Step 1 includes the following steps: Step 1.1, , , any observation point in the middle The latitude-longitude coordinates are as follows , ,in, They represent the observation points respectively. Geodetic longitude, geodetic latitude, and geodetic elevation; Step 1.2: Based on Earth ellipsoid parameters, including: semi-major axis eccentricity Using equation (1), a geodetic coordinate to geocentric rectangular coordinate transformation operator is constructed. : (1) In equation (1), For observation point The radius of curvature of the ellipsoidal vertex at that location; Step 1.3: Select the center point of the horizontal span of the transmission line as the reference station, and let the geodetic longitude, geodetic latitude, and geodetic elevation of the reference station be respectively... Thus, the station center is constructed using equation (2). Coordinate system rotation matrix : (2) Step 1.4: Obtain the observation point using equation (3). Spatial rectangular coordinate vector Thus obtain : (3) In equation (3), This is the translation vector of the reference station center.

3. A fusion according to claim 2 GNSS Perception and PI-KAN A method for monitoring icing on power transmission lines, characterized in that, Step 2 includes the following steps: Step 2.1, Current KAN The hidden layer number is and initialize ; Initialize the first layer KAN Hidden layer output layer feature vector ; Define the first layer KAN The number of nodes in the hidden layer is ; Step 2.2: Calculate the first step using equation (4). layer KAN The first hidden layer The node feature values ​​output by each node Thus, the first layer KAN Hidden layer output layer feature vector , Indicates transpose; (4) In equation (4), Indicates the first layer KAN The first hidden layer The node feature values ​​output by each node. Indicates the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The activation function for each node is: (5) In equation (5), for Activation function For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The linear branch weights of each node to be learned for Step The basis function vector formed by spline basis functions. For the first layer KAN The first hidden layer The node to the first layer KAN The first hidden layer The spline branch of each node is a vector of control coefficients to be learned. Represents the inner product in Euclidean space. These are the balance weights for the spline branches; Step 2.3, take in sequence Assign to Then, return to step 2.2 and execute sequentially until... Until then, thus obtaining the first layer KAN Hidden layer output layer feature vector ; Step 2.4, the output layer uses equation (6) to... Perform a linear transformation to obtain the catenary physical parameter vector. ,in, The horizontal tension coefficient of the catenary. The normalized position of the horizontal span of the sag point. Elevation of the sag point of the traverse line: (6) In equation (6), The weight matrix to be learned for the output layer. The bias vector to be learned for the output layer; Step 2.5: Construct the total loss function using equation (7). : (7) In equation (7), for A defined vertical shape function for the conductor. The x-coordinate of the conductor on the horizontal span. For observation point Theoretical elevation, For observation point The measured elevation, The regularization weight coefficients for the physical constraint loss are... It is a second-order nonlinear differential residual operator. , , The suspension points are respectively Suspension point Observation points Horizontal coordinates; Step 2.6: Minimize the total loss function Iterative updates to achieve the goal. PI-KAN All the parameters to be learned from the network are used to obtain the trained network. PI-KAN The model is generated and the optimal catenary physical parameter vector is output. ,in, This represents the optimal value for the horizontal tension coefficient. This represents the optimal value for the normalized position of the sag point. This represents the optimal value for the elevation of the sag point.

4. A fusion according to claim 3 GNSS Perception and PI-KAN A method for monitoring icing on power transmission lines, characterized in that, Step 3 includes the following steps: Step 3.1: Set the current iteration count to... and initialize ; Define the first Catenary physical parameter vector under the next iteration ;in, For the first The horizontal tension coefficient of the catenary in the next iteration For the first Normalized position of the horizontal span of the sag point in the next iteration For the first Elevation of the sag point in the next iteration; and initialize ; Step 3.2: Construct the first equation using equation (8). Non-convex residual objective function under the next iteration : (8) In equation (8), for A defined vertical morphological function for the conductor; Step 3.3: Using equation (9), obtain the catenary of the transmission line at the first... Physical parameter vector under the next iteration : (9) In equation (9), For the objective function exist The approximate Hessian matrix at that location, For the objective function exist The gradient vector at that point, For the iterative damping factor, A matrix of the same order; superscript This represents finding the inverse of a matrix. Step 3.4, when When that happens, stop the iteration and... As the corrected optimal physical parameter vector Otherwise, Assign to Then, return to step 3.2, where, The preset high-precision threshold; where, This represents the corrected optimal catenary horizontal tension coefficient. This indicates the normalized position of the corrected optimal sag point horizontal span. This indicates the corrected optimal sag point elevation.

5. A fusion according to claim 3 GNSS Perception and PI-KAN A method for monitoring icing on power transmission lines, characterized in that, Step 4 includes the following steps: Step 4.1: Measure the conductor temperature under non-icing conditions using a temperature sensor. Obtain suspension points through the route design ledger. The baseline length of the conductors and the load per unit length of conductor under non-icing conditions ; The input matrix corresponding to the non-icing condition Input after training PI-KAN After processing in the model, the results are then subjected to second-order numerical correction according to step 3 to obtain the corrected optimal physical parameter vector under the non-icing condition. And calculate the horizontal tension under the non-icing condition. ;in, The corrected optimal catenary horizontal tension coefficient under non-icing conditions. This represents the normalized position of the optimal sag point horizontal span under non-icing conditions. The corrected optimal sag point elevation of the traverse line under non-icing conditions; Step 4.2, based on the first suspension point Spatial rectangular coordinate vector Second suspension point Spatial rectangular coordinate vector According to equation (10), the conductor at the suspension point A With suspension point B Integrating the arc lengths between the arcs yields the conductor length under the current operating conditions. : (10) In equation (10), For the reason The derived horizontal x-coordinate of the sag point To account for the geometric correction factors for elevation differences and coordinate rotation, and we have: (11) (12) Step 4.3: Real-time acquisition of conductor temperature under current operating conditions. And the thermo-mechanical coupling constitutive equation is established using equation (13): (13) In equation (13), The elastic modulus of the conductor. The cross-sectional area of ​​the conductor. The coefficient of thermal expansion; The horizontal tension under the current working conditions; Step 4.4: Solve the thermo-mechanical coupling constitutive equation to obtain the horizontal tension under the current operating condition. Thus, the equivalent unit load norm is calculated. ; Step 4.5: Based on the icing geometry model, obtain the icing thickness using equation (14). : (14) In equation (14), Let the radius be the conductor. This represents the density of the ice layer.

6. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-5, the processor being configured to execute the program stored in the memory.

7. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the method according to any one of claims 1-5.

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