Power transmission line icing thickness deduction and early warning method and system based on sar image

Abstract

The application discloses a power transmission line icing thickness deduction and early warning method and system based on SAR images, relates to the technical field of power transmission line icing monitoring, and aims at the problem that existing radar remote sensing icing monitoring can only qualitatively distinguish, cannot quantitatively and accurately calculate the icing thickness, and is difficult to predict the icing evolution trend. A background scattering reference vector is constructed by extracting the characteristics of a non-icing full-polarization SAR reference image. The characteristics of an icing monitoring image are extracted and compared with the background vector to determine the net icing characteristic vector. The standard icing characteristic vector is obtained based on the observation geometry parameter correction, and the icing dielectric parameter is determined. The forward mapping of the icing thickness and the theoretical echo response is established. The current icing thickness is obtained by substituting the measured echo response into the forward mapping and inversely optimizing. The evolution data are generated by driving the forward mapping with the current thickness as the initial state for time-space deduction. The vulnerability is determined according to the evolution data, and the grading early warning strategy is configured. The quantitative calculation, dynamic deduction and accurate early warning of the icing thickness under complex weather are realized.

Description

Technical Field

[0001] This invention relates to the field of transmission line icing monitoring technology, specifically to a method and system for extrapolating and warning of transmission line icing thickness based on SAR imagery. Background Technology

[0002] Icing on transmission lines is a significant hazard affecting the safe operation of power grids, and accurately obtaining information on ice thickness is crucial for de-icing scheduling and emergency response. Currently, monitoring of transmission line icing mainly relies on manual inspections, fixed video surveillance, and online sensors. These methods have limitations such as limited coverage, high maintenance costs, and difficulty in achieving large-scale synchronous monitoring. Radar and satellite remote sensing, due to their active imaging capabilities and immunity to cloud cover, fog, rain, and snow, offer a new technological approach for large-scale monitoring of transmission line icing.

[0003] However, existing radar remote sensing-based icing monitoring methods mainly rely on changes in the backscattering coefficient to determine icing. They compare the echo intensity before and after icing and set empirical thresholds to determine the presence of icing, achieving only qualitative icing identification and failing to quantitatively calculate ice thickness. Furthermore, because radar echoes are affected by multiple factors such as conductor orientation, incident angle, polarization, and the characteristics of the icing medium, relying solely on a single scattering intensity index is prone to misjudgment. In addition, spaceborne SAR satellites typically have revisit cycles of several days to over ten days; existing methods only provide static monitoring results at the satellite's transit time and cannot predict the dynamic evolution trend of ice thickness. Summary of the Invention

[0004] The purpose of this invention is to address the problems of existing radar remote sensing icing monitoring, which can only qualitatively identify icing thickness but cannot quantitatively and accurately calculate it, and is difficult to predict the icing evolution trend. This invention proposes a method and system for icing thickness estimation and early warning of transmission lines based on SAR imagery. By extracting the polarization echo characteristics of fully polarimetric SAR images to construct a background scattering benchmark and comparing it with the characteristics of the icing period, the scattering contribution of the conductor structure is removed to obtain the net icing polarization characteristics. Then, by combining observational geometric correction and dielectric parameter estimation, a forward modeling mapping between icing thickness and theoretical echo response is established. Inverse optimization is used to achieve quantitative inversion of the current icing thickness. Using the inversion result as the initial state, the forward modeling is iteratively derived using the temporal changes of meteorological environmental parameters to generate spatiotemporal evolution data of icing thickness. Based on this, the vulnerability of the transmission line and the early warning level are assessed, realizing quantitative perception and advanced early warning of icing thickness of transmission lines.

[0005] In a first aspect, one technical solution provided in this embodiment of the invention is: a method for extrapolating and warning of icing thickness on power transmission lines based on SAR imagery, comprising the following steps: The polarization echo features of the target line in the full polarimetric SAR reference image under non-icing conditions are extracted to construct the background scattering reference vector; The polarization echo features of the target line in the full polarization SAR monitoring image under icing conditions are extracted and compared with the background scattering reference vector to determine the net icing feature vector. The standard icing feature vector is obtained by correcting the net icing feature vector based on the observed geometric parameters, and the icing dielectric parameters are determined based on the standard icing feature vector and meteorological environmental parameters. The forward modeling mapping between ice thickness and theoretical echo response is determined based on the ice dielectric parameters and standard ice eigenvectors. The measured echo response is determined based on the standard icing feature vector, and the measured echo response is substituted into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line. In response to the temporal changes in meteorological environmental parameters, the forward modeling is driven by the current icing thickness as the initial state to perform spatiotemporal extrapolation of icing thickness, thereby generating spatiotemporal evolution data of icing thickness for the target line. The vulnerability of the target line is determined based on the spatiotemporal evolution data of icing thickness, and corresponding graded early warning strategies are configured for it.

[0006] As an optional approach, the steps for extracting polarimetric echo features from the target line in the full polarimetric SAR reference image under icing-free conditions to construct the background scattering reference vector are as follows: Acquire multi-temporal, non-icing, fully polarimetric SAR reference images, and extract the polarimetric echo features of the target line area in each of the fully polarimetric SAR reference images to construct the background polarimetric scattering matrix; Calculate the background polarization echo eigenvectors for each image based on the background polarization scattering matrix; The background polarization echo feature vectors corresponding to each scene are statistically fused pixel by pixel according to their spatial location to obtain the background scattering reference vector. The background polarization echo characteristic vector includes background co-polarization power, background cross-polarization power, background cross-polarization ratio, and background co-polarization phase difference.

[0007] As an optional approach, the step of extracting the polarimetric echo features from the fully polarimetric SAR monitoring image of the target line under icing conditions and comparing them with the background scattering reference vector to determine the net icing feature vector is as follows: Acquire the full polarimetric SAR monitoring images of the target line under icing conditions, and extract the polarimetric echo features of the same target line area in each full polarimetric SAR monitoring image to construct the polarimetric scattering matrix during the icing period. Calculate the eigenvector of the polarization echo during the icing period based on the polarization scattering matrix during the icing period; The net icing feature vector is determined by subtracting the polarization echo feature vector during the icing period from the background scattering reference vector at the same spatial location element by element. The polarization echo characteristic vector during the icing period includes the same polarization power during the icing period, the cross-polarization power during the icing period, the cross-polarization ratio during the icing period, and the same polarization phase difference during the icing period.

[0008] As an optional approach, the step of obtaining the standard icing feature vector by correcting the net icing feature vector based on the observed geometric parameters is as follows: Obtain the imaging azimuth angle and the traverse angle of the radar satellite, and determine the angle between the radar line of sight and the traverse axis based on the imaging azimuth angle and the traverse angle; Obtain the radar incident angle, and construct an observation geometry correction factor based on the included angle and the radar incident angle; The standard icing feature vector is obtained by normalizing the same polarization power and cross polarization power in the net icing feature vector according to the observation geometry correction factor.

[0009] As an optional approach, the steps for determining the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters are as follows: The icing type parameters are determined based on the ambient temperature and air humidity in the meteorological environmental parameters, and the liquid water content of the icing is estimated. Obtain the cross-polarization ratio and isopolarization phase difference from the standard icing feature vector; The icing dielectric parameter is determined based on the cross-polarization ratio, the same-polarization phase difference, the liquid water content, and the icing type parameter.

[0010] As an optional approach, the step of determining the forward mapping between icing thickness and theoretical echo response based on icing dielectric parameters and standard icing eigenvectors is as follows: Obtain the transmission conductor radius, icing dielectric parameters, and cross-polarization ratio and co-polarization phase difference in the standard icing eigenvector; The geometric scattering enhancement term is determined based on the conductor radius and ice thickness. The dielectric scattering contribution term is determined based on the ice dielectric parameters and ice thickness. The depolarization scattering enhancement term is determined based on the cross-polarization ratio and the icing thickness. The phase delay scattering contribution term is determined based on the same polarization phase difference; The dielectric-geometric cross-coupling term is determined based on the icing dielectric parameters, the conductor radius, and the icing thickness. The forward modeling is obtained by weighted summation of the geometric scattering enhancement term, dielectric scattering contribution term, depolarization scattering enhancement term, phase delay scattering contribution term, and dielectric-geometric cross-coupling term.

[0011] As an optional approach, the steps of determining the measured echo response based on the standard icing feature vector and substituting the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line are as follows: Obtain the normalized homopolarization power, normalized cross-polarization power, cross-polarization ratio, and homopolarization phase difference from the standard icing feature vector; The measured echo response is obtained by weighting and summing the normalized co-polarization power, the normalized cross-polarization power, the cross-polarization ratio, and the co-polarization phase difference. Using ice thickness as the independent variable, an objective function is constructed by minimizing the difference between the measured echo response and the theoretical output value of the forward modeling. Solving the objective function yields the current ice thickness of the target line.

[0012] As an optional approach, the steps for generating the spatiotemporal evolution data of the icing thickness of the target line by driving forward modeling to extrapolate the icing thickness in response to the temporal changes of meteorological environmental parameters, using the current icing thickness as the initial state, are as follows: Obtain the environmental temperature forecast sequence, air humidity forecast sequence, and precipitation intensity forecast sequence for future time periods; Based on the environmental temperature prediction sequence and the air humidity prediction sequence, determine the prior values ​​of the icing dielectric parameters and icing thickness for each future time point; Using the current icing thickness as the initial state, the ambient temperature, air humidity, precipitation intensity, and the corresponding icing dielectric parameters and the prior value of the icing thickness at each future moment are sequentially input into the forward modeling to iteratively deduce the icing thickness of the target line at each future moment. The spatiotemporal evolution data of icing thickness is obtained by integrating the current icing thickness with the icing thickness at each future time.

[0013] As an optional approach, the steps of determining the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and configuring a corresponding graded early warning strategy for it are as follows: The target line is divided into several sections according to a preset spatial interval; Based on the spatiotemporal evolution data of ice thickness, the inversion values ​​of ice thickness at each location point in each segment are statistically analyzed to determine the upper limit and lower limit of ice thickness in each segment. Obtain the ice thickness threshold and ice thickness calculation confidence for each section, and construct the vulnerability index for each section based on the upper limit, lower limit, threshold and calculation confidence of ice thickness. The warning levels are divided according to the vulnerability index of each section, and a graded warning strategy is configured for each warning level.

[0014] As an optional approach, the steps of obtaining the ice thickness threshold and ice thickness calculation confidence level for each segment, and constructing the vulnerability index for each segment based on the upper limit, lower limit, threshold, and calculation confidence level of the ice thickness are as follows: The severity of icing in a given section is determined by the ratio of the upper limit of icing thickness to the threshold of icing thickness. The icing unevenness of the corresponding section is determined by the ratio of the difference between the upper and lower limits of icing thickness to the icing thickness threshold. The vulnerability of each section is obtained by weighted summation of the icing severity component, the icing unevenness component, and the solution confidence. The solution confidence level is determined by the product of the response residual factor, the polarization feature stability factor, and the observation geometry correction factor. The response residual factor is determined based on the residual between the measured echo response and the theoretical output value of the forward modeling at the optimal icing thickness. The polarization feature stability factor is determined based on the degree of dispersion of each polarization feature in the standard icing feature vector. The observation geometry correction factor is determined based on the angle between the radar line of sight and the conductor axis and the radar incident angle.

[0015] As an optional approach, the steps of classifying warning levels based on the vulnerability index of each segment and configuring tiered warning strategies for each warning level are as follows: When the vulnerability is less than the first preset threshold, the corresponding segment is determined to be at the normal level; When the vulnerability is greater than or equal to the first preset threshold and less than the second preset threshold, the corresponding segment is determined to be of concern level. When the vulnerability index is greater than or equal to the second preset threshold and less than the third preset threshold, the corresponding section is determined to be at the warning level. When the vulnerability index is greater than or equal to the third preset threshold, the corresponding segment is determined to be at the alarm level.

[0016] Secondly, an embodiment of the present invention also provides a technical solution: a transmission line icing thickness prediction and early warning system, applicable to the method described in the first aspect, comprising: The background construction module is used to extract polarization echo features from the full polarimetric SAR reference image of the target line under non-icing conditions to construct the background scattering reference vector. The net feature extraction module is used to extract the polarization echo features in the full polarization SAR monitoring image of the target line under icing conditions, and compare them with the background scattering reference vector to determine the net icing feature vector. The feature correction module is used to correct the net icing feature vector based on the observed geometric parameters to obtain the standard icing feature vector, and to determine the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters. The forward modeling module is used to determine the forward modeling mapping between ice thickness and theoretical echo response based on the icing dielectric parameters and the standard icing eigenvector. The thickness inversion module is used to determine the measured echo response based on the standard icing feature vector, and to substitute the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line. The spatiotemporal simulation module is used to respond to the temporal changes of meteorological environmental parameters, drive forward modeling with the current icing thickness as the initial state to perform spatiotemporal simulation of icing thickness, and generate spatiotemporal evolution data of icing thickness of the target line. The early warning decision module is used to determine the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and to configure corresponding graded early warning strategies for it.

[0017] The present invention has at least the following substantial beneficial effects: This application constructs a background scattering reference vector by extracting the polarization echo features of fully polarimetric SAR images and compares it element-by-element with the polarization scattering matrix during the icing period. It removes the scattering contribution of the conductor's background structure to extract the net icing polarization features, effectively overcoming the interference of the conductor's own structure, surface roughness, and terrain background on the radar echo. On this basis, it combines observation geometry correction to eliminate systematic deviations caused by different imaging conditions, and estimates the icing dielectric parameters based on the correlation between polarization features and dielectric properties. Finally, it establishes a forward mapping between icing thickness and theoretical echo response and substitutes the measured echo response into it for inverse optimization, so that the inversion of icing thickness no longer depends on empirical threshold discrimination but is transformed into a quantitative solution based on a physical model, which significantly improves the calculation accuracy of icing thickness.

[0018] This application uses the current icing thickness obtained through reverse optimization as the initial state, and continuously inputs the time-series prediction sequences of ambient temperature, air humidity, and precipitation intensity as driving factors into the forward modeling for iterative deduction. This enables the icing thickness inversion to form a continuous recursive chain in the time dimension, extending the monitoring capability of icing thickness from discrete satellite transit times to a continuous time axis that includes future periods. This achieves the autonomous generation of spatiotemporal evolution data of icing thickness, effectively making up for the deficiency of not being able to predict the development trend of icing during the satellite revisit cycle.

[0019] This application divides the line into several sections according to preset spatial intervals. By statistically analyzing the deviation of the upper and lower limits of icing thickness in each section from the design threshold and calculating the confidence level, a vulnerability index is constructed that simultaneously reflects the severity, unevenness, and reliability of icing. Based on the vulnerability index, each section is divided into four differentiated levels: normal, attention, early warning, and alarm, and corresponding handling strategies are configured. This shifts the operation and maintenance decision-making from a broad assessment of the entire line to a precise positioning of specific sections, effectively improving the pertinence and timeliness of emergency response to icing disasters.

[0020] The above description of the invention is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0021] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0022] Figure 1 This is a flowchart of the method for extrapolating and warning of icing thickness on power transmission lines based on SAR imagery, according to an embodiment of the present invention.

[0023] Figure 2 This is a flowchart illustrating the net icing feature vector generation process according to an embodiment of the present invention.

[0024] Figure 3 This is a flowchart illustrating the forward mapping construction process according to an embodiment of the present invention.

[0025] Figure 4 This is a flowchart illustrating the spatiotemporal extrapolation of icing thickness according to an embodiment of the present invention.

[0026] Figure 5 This is a block diagram of a spatiotemporal simulation and early warning system for icing thickness of power transmission lines according to an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only one preferred embodiment of this invention and are only used to explain this invention. They do not limit the scope of protection of this invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0028] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the operations (or steps) as sequential processes, many of the operations (or steps) can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but it may also have additional steps not included in the figures; the process may correspond to a method, function, procedure, subroutine, subroutine, etc.

[0029] Example 1: As Figure 1 As shown, one technical solution provided in this embodiment of the invention is: a method for extrapolating and warning of icing thickness on transmission lines based on SAR images, which executes steps as shown in S100~S700.

[0030] S100, extract the polarization echo features from the full polarization SAR reference image of the target line under non-icing conditions to construct the background scattering reference vector.

[0031] Understandably, fully polarimetric SAR baseline imagery can be acquired via satellite platforms equipped with fully polarimetric synthetic aperture radar, such as ALOS-2, PALSAR-2, and SAOCOM, which possess fully polarimetric imaging capabilities. This allows for imaging of the target line area in strip or spotlight mode, acquiring complex scattering data including four polarimetric channels: HH, HV, VH, and VV. The icing-free condition typically refers to historical images acquired during the non-icing season or image data from periods when the same area was not icy. The background scattering baseline vector is used to characterize the inherent electromagnetic scattering characteristics of the transmission line's structure, surface roughness, and surrounding terrain background in the icing-free state. Constructing this baseline provides a stable reference map for subsequent icing monitoring, thus establishing a foundation for eliminating environmental background interference at the data processing source. It should be understood that the acquisition method for background scattering data is not limited to a specific time window; it only needs to accurately reflect the scattering characteristics of the target line in the icing-free state.

[0032] As an optional embodiment, the steps for extracting polarimetric echo features from the full polarimetric SAR reference image of the target line under icing-free conditions to construct the background scattering reference vector are shown in S101~S103: S101, acquire multi-temporal, non-icing full-polarization SAR reference images, and extract the polarization echo features of the target line area in each full-polarization SAR reference image to construct the background polarization scattering matrix. S102, calculate the background polarization echo feature vector corresponding to each image based on the background polarization scattering matrix; S103, the background polarization echo feature vectors corresponding to each scene image are statistically fused pixel by pixel according to spatial location to obtain the background scattering reference vector. The background polarization echo characteristic vector includes background co-polarization power, background cross-polarization power, background cross-polarization ratio, and background co-polarization phase difference.

[0033] Understandably, to overcome the inherent speckle noise of spaceborne SAR images and the random fluctuations in the scattering of the conductor itself, it is usually necessary to acquire multi-temporal, non-icing, fully polarimetric SAR reference images, such as 3 to 5 high-resolution images from before the icing season or from the same period in historical years. For each image, the polarimetric echo features of the target line area are extracted to construct the background polarimetric scattering matrix, and the background polarimetric echo feature vector corresponding to each image is calculated accordingly. Subsequently, the background polarimetric echo feature vectors corresponding to each image are statistically fused pixel by pixel according to spatial location, for example, by using mean filtering or median filtering algorithms, to obtain a high signal-to-noise ratio background scattering reference vector. Furthermore, the multi-temporal statistical fusion method can effectively smooth random noise and establish a stable reference benchmark that can accurately characterize the inherent scattering characteristics of the conductor's metal core and the background environment, laying the foundation for stripping the non-icing signal in step S200.

[0034] Specifically, the background polarization echo eigenvector The form is: ;in, This represents the complex scattering coefficient of a horizontally transmitted, horizontally received polarized channel. This represents the complex scattering coefficient of the horizontally transmitted, vertically received polarized channel. This represents the complex scattering coefficient of the vertically transmitted, horizontally received polarized channel. This represents the complex scattering coefficient of the vertical transmission and vertical reception polarization channel.

[0035] Specifically, the form of the background polarization echo eigenvector is as follows: Background horizontal isopolarization power The background vertical same polarization power is expressed as: Background cross-polarization power Background cross-polarization ratio: Background co-polarization phase difference ; where |·|² represents taking the square of the modulus of the complex scattering coefficient to obtain the power value of the corresponding polarization channel, and arg(·) represents taking the phase angle of the complex scattering coefficient.

[0036] S200: Extract the polarization echo features from the full polarization SAR monitoring image of the target line under icing conditions, and compare them with the background scattering reference vector to determine the net icing feature vector.

[0037] Understandably, since radar echoes are the result of the combined effect of the conductor and the icing layer, directly using images from the icing period for inversion would introduce significant errors. This embodiment, by comparing the icing period characteristics with the background scattering reference vector, can effectively deduct the scattering components of the conductor's metallic core and background features, thereby separating the scattering increment purely caused by the icing medium, i.e., the net icing feature vector. This differential processing mechanism significantly improves the sensitivity of subsequent inversion to icing signals.

[0038] As an alternative embodiment, such as Figure 2 As shown, the steps of extracting the polarimetric echo features from the fully polarimetric SAR monitoring image of the target line under icing conditions and comparing them with the background scattering reference vector to determine the net icing feature vector are as shown in S201~S204: S201, acquire the full polarization SAR monitoring image of the target line under icing conditions, and extract the polarization echo features of the same target line area in each full polarization SAR monitoring image to construct the polarization scattering matrix during the icing period. S202, Calculate the eigenvector of the polarization echo during the icing period based on the polarization scattering matrix during the icing period; S203, the net icing feature vector is determined by subtracting the polarization echo feature vector during the icing period from the background scattering reference vector at the same spatial location element by element. S204, the polarization echo characteristic vector during the icing period includes the same polarization power during the icing period, the cross-polarization power during the icing period, the cross-polarization ratio during the icing period, and the same polarization phase difference during the icing period.

[0039] Understandably, when the target line is iced, full-polarization SAR monitoring images for the corresponding time period are acquired. After radiometric calibration and geometric registration, polarization echo characteristics of the same target line area are extracted to construct the icing-period polarization scattering matrix, and the icing-period polarization echo feature vector is calculated. This vector also includes the icing-period co-polarization power, the icing-period cross-polarization power, the icing-period cross-polarization ratio, and the icing-period co-polarization phase difference. Since the total echo received by the radar is a linear superposition of the conductor's own scattering and the scattering of the ice layer, directly using the icing-period data for inversion would introduce significant structural errors. Therefore, this embodiment subtracts the icing-period polarization echo feature vector element-by-element from the background scattering reference vector at the same spatial location to determine the net icing feature vector. Its physical essence is to remove the structural scattering contribution of the conductor itself from the mixed signal, retaining only the pure scattering increment caused by the icing medium, ensuring the purity and relevance of the input to the subsequent inversion model.

[0040] The process of determining the net icing feature vector by subtracting elements one by one is expressed as follows: ;in, For spatial location The net icing feature vector at the location, This represents the characteristic vector of polarization echoes during the glacial period. This represents the baseline scattering vector at the same spatial location. It includes four components: net icing co-polarization power, net icing cross-polarization power, net icing cross-polarization ratio, and net icing co-polarization phase difference. Each component is obtained by subtracting the background reference value from the corresponding characteristic value during the icing period.

[0041] S300, based on the observed geometric parameters, the net icing feature vector is corrected to obtain the standard icing feature vector, and the icing dielectric parameters are determined according to the standard icing feature vector and meteorological environmental parameters.

[0042] Understandably, the observation response of spaceborne SAR to linear targets is highly dependent on the relative geometric relationship between the radar line of sight and the axis of the guide wire. Correction based on observation geometric parameters aims to eliminate echo intensity fluctuations caused by differences in satellite orbit direction, incident angle, and guide wire alignment, making features acquired under different observation conditions comparable and thus obtaining standardized feature vectors. Meanwhile, the electromagnetic properties of icing are not constant but dynamically change with meteorological conditions such as temperature and humidity. Determining the dielectric parameters of icing by combining meteorological environmental parameters can accurately characterize the physical state of the icing layer (such as liquid water content and density).

[0043] As an optional embodiment, the step of obtaining the standard icing feature vector by correcting the net icing feature vector based on the observed geometric parameters is shown in S301~S303: S301, acquire the imaging azimuth angle and the guide wire direction angle of the radar satellite, and determine the angle between the radar line of sight direction and the guide wire axis based on the imaging azimuth angle and the guide wire direction angle; S302, Obtain the radar incident angle, and construct an observation geometry correction factor based on the included angle and the radar incident angle; S303, the same polarization power and cross polarization power in the net icing feature vector are normalized according to the observation geometry correction factor to obtain the standard icing feature vector.

[0044] It should be noted that, in a preferred implementation, the observation geometry correction factor can be expressed as the product of the square of the sine of the included angle and the cosine of the incident angle, reflecting the comprehensive modulation law of the effective projected area and specular reflection component of a linear target in a specific observation direction. It should be understood that the specific mathematical expression of the observation geometry correction factor is not limited to the example above; any functional form that can characterize the influence of the relative relationship between the radar line of sight and the conductor axis on the echo intensity is applicable. Furthermore, through geometric normalization, echo intensity fluctuations caused by differences in satellite orbit direction, imaging angle, and trajectory are eliminated, ensuring that characteristic data acquired at different times and in different sections have uniform physical dimensions and comparability, significantly improving the model's generalization ability.

[0045] Specifically, the angle between the radar line-of-sight direction and the axis of the guide wire is expressed as: ;in, This indicates the angle between the radar line-of-sight direction and the axis of the conductor. Indicates the imaging azimuth angle of the radar satellite. Indicates the angle of the conductor's direction.

[0046] Specifically, the observation geometry correction factor is expressed as: ;in, Indicates the observation geometry correction factor. Indicates the radar incident angle. The term reflects the effective projected area of ​​a linear target in a specific observation direction, i.e., when the radar line of sight is perpendicular to the axis of the conductor ( The echo is strongest when parallel ( ) The echo is weakest at ) time; The term reflects the modulation effect of the incident angle on the specular reflection component; that is, the smaller the incident angle (the closer to perpendicular incidence), the greater the contribution of specular reflection. The product of the two terms comprehensively characterizes the modulation law of the observation geometry on the intensity of the conductor echo.

[0047] Furthermore, the polarization powers in the net icing eigenvector are normalized according to the observed geometric correction factor, specifically in the following form: ;in, , , These are the normalized horizontal co-polarization power, vertical co-polarization power, and cross-polarization power, respectively. , , This represents the original polarization power value corresponding to the net icing feature vector, i.e., the icing scattering contribution retained after background differential processing. For observation geometry correction factor; The stability constant (typically 10) -6 (magnitude), used to avoid when The value becomes unstable when it approaches zero due to division by zero.

[0048] Furthermore, a standard icing feature vector is constructed after normalization. ,in and Since these are ratio and phase quantities, they are not affected by the scaling of the geometric correction factor, so no normalization is required.

[0049] As an optional embodiment, the step of determining the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters is shown in S311~S313: S311, Determine the icing type parameters based on the ambient temperature and air humidity in the meteorological environmental parameters, and estimate the liquid water content of the icing. S312, obtain the cross-polarization ratio and the same-polarization phase difference in the standard icing feature vector; S313, determine the icing dielectric parameter based on the cross-polarization ratio, the same-polarization phase difference, the liquid water content, and the icing type parameter.

[0050] It should be noted that the dielectric constant of icing is not a constant value, but rather changes dynamically with its physical state. This embodiment first determines the icing type parameters (such as rime, glaze, or mixed rime) based on ambient temperature and air humidity from meteorological environmental parameters. Then, it estimates the liquid water content of the icing using the combined relationship between temperature and humidity, as liquid water content is the dominant factor determining the dielectric loss of icing in the microwave frequency band. Simultaneously, it obtains the cross-polarization ratio and co-polarization phase difference from the standard icing feature vector. These two polarization features are sensitive to the roughness of the icing surface, non-uniform structure, and wave propagation delay within the medium, respectively, and can reflect the dielectric properties of icing from remote sensing observations. Finally, the icing dielectric parameters are determined by combining the cross-polarization ratio, co-polarization phase difference, liquid water content, and icing type parameters. This embodiment employs a joint estimation strategy that integrates prior meteorological information and radar polarization observation information, overcoming the limitation of a single data source in accurately distinguishing between dry and wet ice or different types of icing.

[0051] Furthermore, the dielectric parameters of the icing layer can be expressed as: ;in, It represents the equivalent dielectric constant of the icing medium, reflecting the overall electromagnetic response characteristics of the icing layer to radar waves; This represents the basic dielectric constant of dry ice (approximately 3.15 in the microwave band), serving as a benchmark term for dielectric estimation. This represents the cross-polarization ratio. The larger the value, the rougher the ice-covered surface or the more uneven the interior, which corresponds to higher dielectric loss. It represents the absolute value of the phase difference between the same polarizations, reflecting the degree to which the icing medium shell alters the radar wave propagation path; This represents the liquid water content of the ice layer. Since the dielectric constant of liquid water is much higher than that of ice, this term makes the most significant contribution to the equivalent dielectric constant. The parameter indicates the icing type and is used to distinguish the essential dielectric differences between different icing types such as rime (low density, high air gap), rain rime (high density, dense), and mixed rime. , , , The dielectric parameter estimation coefficients are obtained through artificial climate chamber calibration experiments or offline electromagnetic simulation.

[0052] Furthermore, liquid water content Estimate based on ambient temperature and air humidity: ;in, Indicates ambient temperature. This indicates the reference temperature for the ice-water phase transition (usually taken as 0℃). Ensure that the contribution of liquid water is zero when the ambient temperature is below the freezing point, and that a liquid water film can only appear in the ice when the temperature is above the freezing point; This indicates air humidity; a high humidity environment is conducive to the maintenance and adsorption of liquid water on ice-covered surfaces. This is the temperature-water content coupling coefficient, which reflects the incremental contribution of each 1°C increase in temperature to the liquid water content. The humidity-water content coupling coefficient reflects the positive correlation between air humidity and the liquid water content in ice.

[0053] As a further supplement to the above-described net icing feature vector generation process, this embodiment also introduces polarimetric coherence features as an additional dimension to the net icing feature vector. Specifically, the polarimetric coherence amplitude and polarimetric coherence phase are extracted by utilizing the polarimetric coherence between the full polarimetric SAR monitoring image during the icing period and the immediately preceding full polarimetric SAR image (which can be from the initial icing period or the ice-free period). The polarimetric coherence amplitude reflects the stability of the scattering mechanism of the guide target between two observations. That is, when the ice layer grows steadily, the scattering mechanism changes little, and the coherence amplitude is high; when the ice layer detaches, melts, or undergoes drastic morphological changes, the scattering mechanism changes significantly, and the coherence amplitude decreases sharply. The polarimetric coherence phase is sensitive to subwavelength changes in ice thickness and can be used to detect thin ice growth or minute melting processes that are difficult to capture with traditional intensity features.

[0054] In a preferred implementation, the coherence amplitudes of the three polarization combinations—HH-VV coherence, HH-HV coherence, and VV-HV coherence—can be calculated separately to form a polarization coherence feature vector, which is then appended to the standard icing feature vector. The introduction of this polarization coherence feature means that the feature system not only includes the scattering intensity and polarization information from a single observation but also incorporates scattering stability information over time, providing additional criteria for distinguishing between steadily growing icing and dynamically changing icing.

[0055] S400 determines the forward mapping between icing thickness and theoretical echo response based on icing dielectric parameters and standard icing eigenvectors.

[0056] Understandably, the forward modeling relationship is constructed based on the electromagnetic scattering mechanism, describing the theoretical radar echo response values ​​corresponding to different ice thicknesses under specific icing dielectric parameters and geometric conditions. Unlike traditional empirical regression models, the forward modeling in this embodiment can more accurately reflect the modulation law of radar signals caused by changes in ice thickness.

[0057] As an alternative embodiment, such as Figure 3 As shown, the steps for determining the forward mapping between the icing thickness and the theoretical echo response based on the icing dielectric parameters and the standard icing eigenvector are as shown in S401~S407: S401, obtain the transmission conductor radius, icing dielectric parameters, and cross-polarization ratio and co-polarization phase difference in the standard icing eigenvector; S402, determine the geometric scattering enhancement term based on the conductor radius and icing thickness; S403, determine the dielectric scattering contribution term based on the ice-covering dielectric parameters and ice-covering thickness; S404, Depolarization scattering enhancement term is determined based on the cross-polarization ratio and icing thickness; S405, determine the phase delay scattering contribution term based on the same polarization phase difference; S406, Determine the dielectric-geometric cross-coupling term based on the icing dielectric parameters, the conductor radius, and the icing thickness; S407, the forward modeling is obtained by weighted summation of the geometric scattering enhancement term, dielectric scattering contribution term, depolarization scattering enhancement term, phase delay scattering contribution term, and dielectric-geometric cross-coupling term.

[0058] It can be understood that the forward modeling in this embodiment is not a simple numerical fitting curve, but a physical model constructed based on the electromagnetic scattering mechanism. It is obtained by weighted summation of five components with clear physical meanings. Among them, the geometric scattering enhancement term characterizes the specular reflection cross-section enhancement effect caused by the increase of the equivalent outer diameter of the conductor as the ice thickness increases; the dielectric scattering contribution term characterizes the volume scattering energy caused by the dielectric properties of the ice, which is directly related to the material properties and thickness accumulation of the ice; the depolarization scattering enhancement term characterizes the depolarization scattering caused by the surface roughness and non-uniform structure of the ice; the phase delay scattering contribution term characterizes the scattering contribution corresponding to the phase delay caused by the ice dielectric shell; and the dielectric-geometric cross-coupling term describes the modulation effect of the dielectric constant on the geometric scattering cross-section. The forward modeling is obtained by weighted summation of the above five components. It should be emphasized that this weighted summation is based on the power domain superposition principle in the radar equations. Each component represents the contribution of different physical mechanisms in the total backscattered power, so its combination has strict physical interpretability.

[0059] Specifically, the icing thickness is defined as... The theoretical radar response at that time is: ;in, Indicates the ice thickness as The theoretical radar response at that time (i.e., the forward modeling expression of this application); Indicates the radius of the conductor; Indicates the dielectric parameter of icing; X Indicates the cross-polarization ratio; Indicates the phase difference of co-polarization; , , , , These are the coefficients of the forward mapping model. The physical meanings of each term in the model are as follows: First term The first term represents the geometric scattering enhancement, characterizing the increased specular reflection cross-section resulting from the increased equivalent outer diameter of the conductor due to the increased ice thickness; the second term... The third term is the contribution term for dielectric scattering, characterizing the volume scattering energy caused by the dielectric properties of icing; The fourth term represents the depolarization scattering enhancement term, characterizing the depolarization scattering caused by the roughness and inhomogeneity of the icy surface; The fifth term represents the phase delay scattering contribution, characterizing the scattering contribution corresponding to the phase delay caused by the icy medium shell. This is a dielectric-geometric cross-coupling term that describes the modulation effect of the dielectric constant on the geometric scattering cross section.

[0060] S500: Determine the measured echo response based on the standard icing feature vector, and substitute the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line.

[0061] Understandably, this embodiment uses standardized measured echo responses as input to search or iteratively calculate within the solution space defined by the forward modeling, seeking the ice thickness value that minimizes the difference between the theoretical and measured responses. This inverse optimization strategy fully utilizes the physical constraints of the forward modeling, avoids the ambiguity of single-index judgment, and achieves high-precision quantitative calculation of ice thickness under complex meteorological conditions.

[0062] As an optional embodiment, the steps of determining the measured echo response based on the standard icing feature vector and substituting the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line are shown in S501~S503: S501, obtain the normalized homopolarization power, normalized cross-polarization power, cross-polarization ratio, and homopolarization phase difference from the standard icing feature vector; S502, the normalized same-polarization power, the normalized cross-polarization power, the cross-polarization ratio and the same-polarization phase difference are weighted and summed to obtain the measured echo response; S503, with ice thickness as the independent variable, construct an objective function by minimizing the difference between the measured echo response and the theoretical output value of the forward modeling, and solve the objective function to obtain the current ice thickness of the target line.

[0063] Understandably, to transform multi-dimensional radar observation information into scalars comparable to the forward modeling, the normalized co-polarization power, normalized cross-polarization power, cross-polarization ratio, and co-polarization phase difference from the standard icing feature vector are first obtained. These four features are then weighted and summed to obtain the measured echo response. The weights of each feature can be dynamically adjusted based on their sensitivity to changes in icing thickness. For example, the cross-polarization ratio and co-polarization phase difference are typically more sensitive to icing conditions and can be assigned higher weights. Subsequently, using icing thickness as the independent variable, an objective function is constructed to minimize the difference between the measured echo response and the theoretical output value of the forward modeling. The essence of this objective function is to find the optimal solution under physical constraints, maximizing the approximation of the actual observation value by the theoretical prediction. During the solution process, numerical optimization algorithms such as grid search, the golden section method, or gradient descent can be used to search within a pre-defined reasonable range for icing thickness. The thickness at which the objective function is minimized is the current icing thickness of the target line. This embodiment, through this reverse optimization strategy, not only makes full use of the physical laws inherent in the forward mapping model, but also effectively avoids the multiple solutions or ambiguity problems that may exist in single feature inversion, ensuring the uniqueness and accuracy of the ice thickness calculation results under complex meteorological conditions.

[0064] Specifically, the measured echo response is obtained by weighted summation of each feature in the standard icing feature vector, in the following form: ;in, This represents the measured echo response; , , These are the normalized horizontal co-polarization power, vertical co-polarization power, and cross-polarization power, respectively, reflecting the normalized scattering intensity of the icing conductor under different polarization channels; , , , , To observe the response weighting coefficients, they can be set based on the sensitivity analysis results of each polarization feature to changes in ice thickness. Features with higher sensitivity are assigned greater weights. Initial values ​​can be set according to... : : The ratio setting is 1:1:2:4:2, which is the cross-polarization ratio. Assign it the highest weight.

[0065] Specifically, the objective function for icing thickness inversion is expressed as: ;in, This represents the objective function for icing thickness inversion; the smaller the value, the higher the degree of matching between theoretical predictions and actual observations. This represents the ice thickness to be determined; This represents the theoretical output value of the forward mapping; This is the data fitting term, which measures the squared residual between the measured echo response and the theoretical radar response, driving the inversion results to approximate the actual observations. μ represents the prior constraint weight, which controls the balance between the data fitting term and the prior constraint term. The larger μ is, the more the inversion result depends on prior information, and the smaller μ is, the more it depends on radar observation data. This represents the prior value of the icing thickness; This is a priori constraint term used to avoid jumps in inversion results when radar noise is high or local target scattering is unstable, thus ensuring the numerical stability of the inversion.

[0066] Furthermore, the prior value of the icing thickness is estimated based on meteorological conditions, specifically in the following form: ; Indicates precipitation intensity. Indicates the duration of low temperature. Indicates air humidity. Indicates ambient temperature. This indicates the central value of the temperature range most prone to icing (typically -3°C to -5°C, where icing growth is most active). This indicates the degree to which the current temperature deviates from the temperature most prone to icing; the greater the deviation, the more unfavorable the conditions for icing growth. , , The prior thickness estimation coefficients are obtained through regression fitting of historical icing observation data. It is understandable that the prior icing thickness value serves as a stability constraint term in the objective function, used to avoid jumps in the inversion results when radar noise is high or local target scattering is unstable. Ultimately, the icing thickness is still determined by the matching results of the radar observation response and the forward modeling.

[0067] In a preferred implementation, based on the aforementioned forward mapping and inverse optimization, this embodiment further introduces an adaptive forward model selection mechanism to enhance the model's adaptability to different types of icing. Specifically, before constructing the forward mapping, the current icing is first classified as at least one of hoarfrost, rime ice, mixed rime ice, or wet ice based on the cross-polarization ratio and co-polarization phase difference in the standard icing feature vector, combined with the ambient temperature and precipitation type in the meteorological environmental parameters, using a pre-trained icing type classifier. Different types of icing correspond to different forward model structure configurations: for hoarfrost with a loose structure and low dielectric constant, the weights of the dielectric scattering contribution term and the dielectric-geometric cross-coupling term can be appropriately reduced; for dense rime ice or wet ice with high water content, the weights of the dielectric scattering contribution term and the dielectric-geometric cross-coupling term need to be strengthened to accurately reflect the strong body scattering and significant coupling effect under high dielectric constant conditions.

[0068] In one alternative implementation, the icing type classifier can employ machine learning models such as support vector machines or random forests, using polarization features and meteorological parameters of historical icing samples as training data, and manually determined icing types as labels for offline training. This strategy of adaptively adjusting the model structure based on icing type enables the forward mapping to more accurately match the scattering mechanisms under different icing physical states, avoiding the systematic bias that may arise when a single fixed model structure handles multiple icing types.

[0069] S600, in response to the temporal changes of meteorological environmental parameters, drives forward modeling with the current icing thickness as the initial state to perform spatiotemporal extrapolation of icing thickness, and generates spatiotemporal evolution data of icing thickness for the target line.

[0070] Understandably, to address the pain points of long satellite revisit cycles and the difficulty in capturing real-time dynamic changes in icing, this embodiment introduces a time-dimensional extrapolation mechanism. Starting with the thickness retrieved at the current moment, it continuously drives the forward modeling using meteorological forecast sequences for future periods, simulating the accumulation or melting process of icing as environmental conditions change. This not only fills the monitoring gap between two satellite passes but also enables advance prediction of icing development trends, transforming passive monitoring into proactive forecasting.

[0071] As an alternative embodiment, such as Figure 4 As shown, the steps of generating the spatiotemporal evolution data of the icing thickness of the target line by driving forward modeling to extrapolate the icing thickness in response to the temporal changes of meteorological environmental parameters, using the current icing thickness as the initial state, are as follows: S601, obtain the environmental temperature prediction sequence, air humidity prediction sequence, and precipitation intensity prediction sequence for the future time period; S602, Based on the ambient temperature prediction sequence and the air humidity prediction sequence, determine the prior values ​​of the icing dielectric parameters and icing thickness corresponding to each future time. S603, taking the current icing thickness as the initial state, the ambient temperature, air humidity, precipitation intensity, and the corresponding icing dielectric parameters and the prior value of the icing thickness at each future time are sequentially input into the forward modeling to iteratively deduce the icing thickness of the target line at each future time. S604, integrate the current icing thickness with the icing thickness at each future moment to obtain spatiotemporal evolution data of icing thickness.

[0072] Understandably, spaceborne SAR satellites typically have revisit cycles of several days to over ten days, making it difficult to capture the rapid accumulation or dissipation of icing between two transits. This embodiment introduces a time-dimensional extrapolation mechanism. First, it acquires the predicted sequences of ambient temperature, air humidity, and precipitation intensity for future time periods. These meteorological data can be derived from numerical weather prediction products or extrapolated data from micro-weather stations. Next, based on the ambient temperature and air humidity prediction sequences, it determines the prior values ​​of icing dielectric parameters and icing thickness for each future time period. The dielectric parameters are dynamically updated with temperature and humidity conditions to reflect changes in the physical state of icing, while the prior values ​​provide trend constraints on thickness changes based on a meteorological accumulation model. Subsequently, using the current icing thickness as the initial state, the ambient temperature, air humidity, precipitation intensity, and corresponding prior values ​​of icing dielectric parameters and icing thickness for each future time period are sequentially input into the aforementioned forward modeling to iteratively extrapolate the icing thickness of the target line at each future time period. In this iterative process, the extrapolation results of the previous time period can serve as physical constraints for the next time period, thereby ensuring the continuity of the time series. Finally, by integrating the current ice thickness with the ice thickness at various future moments, we obtain spatiotemporal evolution data of ice thickness. This extrapolation mechanism not only achieves a leap from static snapshots to dynamic processes, but also enables the early warning system to predict the development trend of ice accumulation in advance, thus gaining a valuable window of opportunity for ice melting scheduling.

[0073] Specifically, let's assume the current time... The ice thickness is At the k-th future moment The ice thickness was obtained through iterative deduction, and the mathematical expression of the spatiotemporal deduction process is as follows: ;in, This represents the optimal solution for the icing thickness at the k-th future time. This represents the thickness d within a reasonable range of ice thickness values ​​that minimizes the objective function within the curly braces; The measured echo response at time k is... Forward mapping, The prior constraint weights at that moment. This is based on the prior value of the icing thickness at time k. The spatiotemporal evolution data of the icing thickness are represented as follows: Where K is the total number of simulation moments. The current ice thickness obtained from the inversion is taken as the initial state.

[0074] The S700 determines the vulnerability of target lines based on spatiotemporal evolution data of icing thickness and configures corresponding graded early warning strategies for them.

[0075] Understandably, the risk of icing depends not only on the absolute thickness but also on the unevenness of spatial distribution and the reliability of the data. Vulnerability assessment takes into account these factors comprehensively, enabling a more complete characterization of the safety status of the lines. Based on this, the tiered early warning strategy can trigger differentiated response measures according to different risk levels, such as routine inspections, key monitoring, ice melting scheduling, or emergency repairs. This tiered decision-making mechanism effectively avoids the problems of missed or false alarms caused by single threshold alarms, improving the accuracy and efficiency of power grid disaster prevention and mitigation.

[0076] As an optional embodiment, the steps of determining the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and configuring a corresponding graded early warning strategy for it are as shown in S701~S704: S701, the target line is divided into several segments according to a preset spatial interval; S702, based on the spatiotemporal evolution data of ice thickness, statistically analyze the ice thickness inversion values ​​at each location point in each segment, and determine the upper limit and lower limit of ice thickness for each segment; S703, obtain the ice thickness threshold and ice thickness calculation confidence of each section, and construct the vulnerability index of each section based on the ice thickness upper limit, ice thickness lower limit, ice thickness threshold and calculation confidence. S704, classify the warning level according to the vulnerability index of each section, and configure a graded warning strategy for each warning level.

[0077] It is understandable that the safety risks of transmission lines depend not only on the absolute ice thickness at a single point, but also on the spatial uniformity of ice distribution within that section and the reliability of monitoring data. Therefore, this embodiment first divides the target line into several sections according to preset spatial intervals, such as by tower span or by a fixed length (e.g., 100 meters), to adapt to the line management needs of different voltage levels and terrain conditions. Next, based on the spatiotemporal evolution data of ice thickness, the inversion values ​​of ice thickness at each location point within each section are statistically analyzed to determine the upper and lower limits of ice thickness for each section. These upper and lower limits are not simple extreme values, but rather confidence boundaries determined by statistical methods (e.g., mean plus or minus several times the standard deviation) or quantile methods, used to characterize the fluctuation range and potential extreme values ​​of ice thickness in that section. Subsequently, the ice thickness threshold and ice thickness calculation confidence level for each section are obtained, and a vulnerability index for each section is constructed based on the upper and lower limits of ice thickness, the ice thickness threshold, and the calculation confidence level. Finally, the warning levels are divided according to the vulnerability index of each section, and a graded warning strategy is configured for each warning level. This assessment method based on the statistical characteristics of the sections effectively overcomes the random errors that may exist in single-point inversion and can better reflect the mechanical load risks that may exist in the entire line.

[0078] Furthermore, the upper limit of the icing thickness can be expressed as: The lower limit of icing thickness can be expressed as: ;in, It is the arithmetic mean of the ice thickness inversion values ​​at each location point in the section, reflecting the overall ice level of the section; The standard deviation reflects the spatial dispersion of ice thickness within this section. The larger the value, the more uneven the ice distribution. and A coefficient (typical value) adjusted according to the importance of the line and the design ice thickness. =1.0, =1.5~2.0), Value greater than This reflects a conservative estimation strategy for the lower limit, that is, giving a greater safety margin when assessing the minimum icing thickness.

[0079] As an optional embodiment, the steps of obtaining the ice thickness threshold and ice thickness calculation confidence of each section, and constructing the vulnerability index of each section based on the upper limit, lower limit, threshold and calculation confidence of ice thickness are as shown in S7031~S7033: S7031, the icing severity of the corresponding section is determined based on the ratio of the upper limit of icing thickness to the threshold of icing thickness; S7032, The icing unevenness of the corresponding section is determined by the ratio of the difference between the upper limit and the lower limit of icing thickness to the icing thickness threshold. S7033, the icing severity component, the icing unevenness component, and the solution confidence are weighted and summed to obtain the vulnerability of each section; The solution confidence level is determined by the product of the response residual factor, the polarization feature stability factor, and the observation geometry correction factor. The response residual factor is determined based on the residual between the measured echo response and the theoretical output value of the forward modeling at the optimal icing thickness. The polarization feature stability factor is determined based on the degree of dispersion of each polarization feature in the standard icing feature vector. The observation geometry correction factor is determined based on the angle between the radar line of sight and the conductor axis and the radar incident angle.

[0080] Understandably, the vulnerability index is obtained by weighted summation of three components. The first component is the severity of icing, determined by the ratio of the upper limit of icing thickness to the icing thickness threshold, reflecting how close the mechanical load borne by the line under the most unfavorable condition is to the design safety margin. The second component is the icing unevenness, determined by the ratio of the difference between the upper and lower limits of icing thickness to the icing thickness threshold. This component characterizes the spatial variability of icing distribution within a section; excessive unevenness may lead to conductor tension imbalance, increased galloping, or insulator string misalignment, and may even cause faults even if the average thickness does not exceed the standard. The third component is the solution confidence level; the lower the value, the greater the data uncertainty, and it should be considered as a risk assessment factor. This involves identifying potential risk sources. Specifically, the confidence level is determined by the product of the response residual factor, the polarization characteristic stability factor, and the observation geometry correction factor. The response residual factor is determined based on the residual between the measured echo response and the theoretical output value of the forward model at the optimal icing thickness. A smaller residual indicates a better match between the physical model and actual observations, leading to more reliable inversion results. The polarization characteristic stability factor is determined based on the dispersion of each polarization characteristic in the standard icing characteristic vector. Low dispersion indicates stable radar echo signals and a high signal-to-noise ratio. The observation geometry correction factor is determined based on the angle between the radar line-of-sight direction and the conductor axis, as well as the radar incident angle. When the observation angle is nearly perpendicular and the incident angle is moderate, the conductor imaging quality is optimal, resulting in the highest confidence level. Incorporating these three factors into the vulnerability calculation allows the early warning system to automatically upgrade the risk level when data quality is poor, avoiding missed detections due to blindly trusting low-quality data.

[0081] Specifically, vulnerability can be expressed as: ;in, This represents the vulnerability index of a section; the higher the value, the higher the risk of icing in that section. This is the upper limit of the ice thickness. This is the lower limit of the ice thickness. The ice thickness threshold for this section is usually determined by the line design ice thickness or operating procedures, representing the maximum ice thickness that the conductor structure can safely withstand; Conf is the confidence level for ice thickness calculation. , , Let be the weighting coefficient, satisfying The normalization constraints reflect the influence weights of absolute icing severity, icing unevenness, and data reliability, respectively. The first term... The severity of icing is indicated by a value closer to or exceeding 1, signifying that the upper limit thickness is approaching or exceeding the design safety margin; the second item... The value represents the icing unevenness; a higher value indicates greater differences in icing distribution within a section, potentially leading to mechanical risks such as uneven tension, galloping, or insulator string misalignment. (Item 3) This reflects the reliability of the data; the lower the confidence level, the greater the contribution of this item, enabling the early warning system to automatically raise the risk level to avoid missed reports.

[0082] Specifically, the confidence level is determined by the product of three factors, as follows: ;in, This represents the confidence level of the ice thickness calculation, with a value range of (0, 1]. A larger value indicates a more reliable inversion result. In response to the residual factor, the factor is 1 when the residual is zero, and the larger the residual, the closer the factor is to zero; This is the polarization characteristic stability factor. The lower the dispersion, the more stable the radar echo signal and the higher the signal-to-noise ratio. The larger the value; To observe the geometric correction factor, when the radar line of sight is nearly perpendicular to the axis of the conductor and the incident angle is moderate. The maximum value indicates the best imaging quality for the conductor.

[0083] As an optional embodiment, the steps of classifying the warning level according to the vulnerability index of each segment and configuring a graded warning strategy for each warning level are as shown in S7041~S7044: S7041, when the vulnerability is less than the first preset threshold, the corresponding segment is determined to be at the normal level; S7042, when the vulnerability is greater than or equal to the first preset threshold and less than the second preset threshold, the corresponding segment is determined to be of concern level; S7043, when the vulnerability index is greater than or equal to the second preset threshold and less than the third preset threshold, the corresponding section is determined to be at the warning level; S7044: When the vulnerability index is greater than or equal to the third preset threshold, the corresponding segment is determined to be at the alarm level.

[0084] Understandably, this embodiment sets up a four-level early warning mechanism to achieve refined management. When the vulnerability is less than the first preset threshold, the corresponding section is determined to be at the normal level, indicating that the line is in a safe operating state and the monitoring data is reliable, and routine inspections are sufficient. When the vulnerability is greater than or equal to the first preset threshold and less than the second preset threshold, the corresponding section is determined to be at the attention level, possibly due to a slight increase in icing, slightly uneven distribution, or a slight decrease in data confidence, prompting maintenance personnel to strengthen monitoring or arrange for drone verification. When the vulnerability index is greater than or equal to the second preset threshold and less than the third preset threshold, the corresponding section is determined to be at the early warning level, indicating that icing has approached the design limit or there is significant unevenness, or the data quality is too low to rule out high risks, at which point de-icing preparations should be initiated or the operating mode adjusted. When the vulnerability index is greater than or equal to the third preset threshold, the corresponding section is determined to be at the alarm level, meaning that icing has seriously exceeded the standard or the risk is extremely high, and emergency de-icing, load transfer, or even shutdown and risk avoidance measures must be taken immediately.

[0085] It should be understood that the specific values ​​of the above thresholds can be flexibly set according to the importance of the line, historical icing patterns, and operation and maintenance strategies. This hierarchical early warning strategy is different from the simple alarm mode in existing technologies that only rely on a single thickness threshold. It incorporates the reliability of the data itself as a risk factor into the decision-making closed loop, which avoids frequent false alarms caused by data noise and prevents underestimation of risk due to model mismatch or poor observation conditions. This significantly improves the scientific nature and effectiveness of transmission line icing disaster prevention.

[0086] Example 2, an embodiment of the invention also provides an implementation scheme: a transmission line icing thickness prediction and early warning system, applicable to the method described in Example 1, such as... Figure 5 As shown, it includes: The background construction module 001 is used to extract polarization echo features from the full polarization SAR reference image of the target line under non-icing conditions to construct the background scattering reference vector. The net feature extraction module 002 is used to extract the polarization echo features in the full polarization SAR monitoring image of the target line under icing conditions, and compare them with the background scattering reference vector to determine the net icing feature vector. Feature correction module 003 is used to correct the net icing feature vector based on the observed geometric parameters to obtain the standard icing feature vector, and to determine the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters. Forward modeling module 004 is used to determine the forward modeling mapping between ice thickness and theoretical echo response based on ice dielectric parameters and standard ice eigenvectors. Thickness inversion module 005 is used to determine the measured echo response based on the standard icing feature vector, and substitute the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line. The spatiotemporal simulation module 006 is used to respond to the temporal changes of meteorological environmental parameters, drive forward modeling with the current icing thickness as the initial state to perform spatiotemporal simulation of icing thickness, and generate spatiotemporal evolution data of icing thickness of the target line. The early warning decision module 007 is used to determine the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and to configure corresponding graded early warning strategies for it.

[0087] In this embodiment, the system uses the intrinsic scattering benchmark of the conductor extracted by the background construction module as a reference. The net feature extraction module separates the scattering contribution of the conductor's bulk structure by comparing the polarization characteristics of the icing period and the ice-free period element-wise, and extracts the pure icing polarization information from the background scattering as the pure signal input for subsequent quantitative inversion. The feature correction module performs observation geometric normalization on the signal to eliminate the systematic bias introduced by the satellite imaging attitude, and calculates the icing dielectric parameters based on the correlation between polarization characteristics and dielectric properties, so that the input signal completes the standardized transformation from the original observation to physical parameters. The forward modeling module uses the standardized parameters to establish a quantitative mapping model between the icing thickness and the theoretical echo response. The thickness inversion module substitutes the measured echo response into the mapping to perform inverse solving and output the current thickness. At this time, the thickness inversion result drives the spatiotemporal extrapolation module to take the current thickness as the initial state, input the meteorological environmental parameter time series prediction sequence into the mapping and perform iterative extrapolation, so that the thickness inversion continuously updates along the time axis from the static value at discrete time, generating spatiotemporal evolution data covering the current state and the future state. The early warning decision module finally constructs the vulnerability index of each section and configures the differentiated early warning level based on the data, and transforms the quantitative perception result into hierarchical decision information output. It overcomes the inherent limitations of traditional icing monitoring methods in terms of coverage, quantitative capability and timeliness, and realizes quantitative perception and early warning of icing thickness of transmission lines.

[0088] Through the above description of the embodiments, those skilled in the art will understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the specific device can be divided into different functional modules to complete all or part of the functions described above.

[0089] In the embodiments provided in this application, it should be understood that the disclosed structures and methods can be implemented in other ways. For example, the structural embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another structure, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between structures or units, and may be electrical, mechanical, or other forms.

[0090] The units described as separate components may or may not be physically separate. A component shown as a unit can be one or more physical units; that is, it can be located in one place or distributed in multiple different locations. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0091] Furthermore, in the embodiments of this application, the functional units can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0092] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0093] The specific embodiments described above are preferred embodiments of the method and system for estimating and warning the icing thickness of transmission lines based on SAR images of the present invention. They are not intended to limit the specific scope of the present invention. The scope of the present invention includes, but is not limited to, these specific embodiments. All equivalent changes made in accordance with the shape and structure of the present invention are within the protection scope of the present invention.

Claims

1. A method for extrapolating and warning of icing thickness on power transmission lines based on SAR imagery, characterized in that, The steps include the following: The polarization echo features of the target line in the full polarimetric SAR reference image under non-icing conditions are extracted to construct the background scattering reference vector; The polarization echo features of the target line in the full polarization SAR monitoring image under icing conditions are extracted and compared with the background scattering reference vector to determine the net icing feature vector. The standard icing feature vector is obtained by correcting the net icing feature vector based on the observed geometric parameters, and the icing dielectric parameters are determined based on the standard icing feature vector and meteorological environmental parameters. The forward modeling mapping between ice thickness and theoretical echo response is determined based on the ice dielectric parameters and standard ice eigenvectors. The measured echo response is determined based on the standard icing feature vector, and the measured echo response is substituted into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line. In response to the temporal changes in meteorological environmental parameters, the forward modeling is driven by the current icing thickness as the initial state to perform spatiotemporal extrapolation of icing thickness, thereby generating spatiotemporal evolution data of icing thickness for the target line. The vulnerability of the target line is determined based on the spatiotemporal evolution data of icing thickness, and corresponding graded early warning strategies are configured for it.

2. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for extracting polarimetric echo features from the target line in the full polarimetric SAR reference image under non-icing conditions to construct the background scattering reference vector are as follows: Acquire multi-temporal, non-icing, fully polarimetric SAR reference images, and extract the polarimetric echo features of the target line area in each of the fully polarimetric SAR reference images to construct the background polarimetric scattering matrix; Calculate the background polarization echo eigenvectors for each image based on the background polarization scattering matrix; The background polarization echo feature vectors corresponding to each scene are statistically fused pixel by pixel according to their spatial location to obtain the background scattering reference vector. The background polarization echo characteristic vector includes background co-polarization power, background cross-polarization power, background cross-polarization ratio, and background co-polarization phase difference.

3. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for extracting the polarization echo features from the fully polarimetric SAR monitoring image of the target line under icing conditions and comparing them with the background scattering reference vector to determine the net icing feature vector are as follows: Acquire the full polarimetric SAR monitoring images of the target line under icing conditions, and extract the polarimetric echo features of the same target line area in each full polarimetric SAR monitoring image to construct the polarimetric scattering matrix during the icing period. Calculate the eigenvector of the polarization echo during the icing period based on the polarization scattering matrix during the icing period; The net icing feature vector is determined by subtracting the polarization echo feature vector during the icing period from the background scattering reference vector at the same spatial location element by element. The polarization echo characteristic vector during the icing period includes the same polarization power during the icing period, the cross-polarization power during the icing period, the cross-polarization ratio during the icing period, and the same polarization phase difference during the icing period.

4. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for obtaining the standard icing feature vector by correcting the net icing feature vector based on observed geometric parameters are as follows: Obtain the imaging azimuth angle and the traverse angle of the radar satellite, and determine the angle between the radar line of sight and the traverse axis based on the imaging azimuth angle and the traverse angle; Obtain the radar incident angle, and construct an observation geometry correction factor based on the included angle and the radar incident angle; The standard icing feature vector is obtained by normalizing the same polarization power and cross polarization power in the net icing feature vector according to the observation geometry correction factor.

5. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 4, characterized in that, The steps for determining the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters are as follows: The icing type parameters are determined based on the ambient temperature and air humidity in the meteorological environmental parameters, and the liquid water content of the icing is estimated. Obtain the cross-polarization ratio and isopolarization phase difference from the standard icing feature vector; The icing dielectric parameter is determined based on the cross-polarization ratio, the same-polarization phase difference, the liquid water content, and the icing type parameter.

6. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for determining the forward mapping between ice thickness and theoretical echo response based on ice dielectric parameters and standard ice eigenvectors are as follows: Obtain the transmission conductor radius, icing dielectric parameters, and cross-polarization ratio and co-polarization phase difference in the standard icing eigenvector; The geometric scattering enhancement term is determined based on the conductor radius and ice thickness. The dielectric scattering contribution term is determined based on the ice dielectric parameters and ice thickness. The depolarization scattering enhancement term is determined based on the cross-polarization ratio and the icing thickness. The phase delay scattering contribution term is determined based on the same polarization phase difference; The dielectric-geometric cross-coupling term is determined based on the icing dielectric parameters, the conductor radius, and the icing thickness. The forward modeling is obtained by weighted summation of the geometric scattering enhancement term, dielectric scattering contribution term, depolarization scattering enhancement term, phase delay scattering contribution term, and dielectric-geometric cross-coupling term.

7. The method for extrapolating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for determining the measured echo response based on the standard icing feature vector, and then substituting the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line are as follows: Obtain the normalized homopolarization power, normalized cross-polarization power, cross-polarization ratio, and homopolarization phase difference from the standard icing feature vector; The measured echo response is obtained by weighting and summing the normalized co-polarization power, the normalized cross-polarization power, the cross-polarization ratio, and the co-polarization phase difference. Using ice thickness as the independent variable, an objective function is constructed by minimizing the difference between the measured echo response and the theoretical output value of the forward modeling. Solving the objective function yields the current ice thickness of the target line.

8. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for generating the spatiotemporal evolution data of the icing thickness of the target line by responding to the temporal changes of meteorological environmental parameters, using the current icing thickness as the initial state to drive forward modeling for spatiotemporal extrapolation of icing thickness, are as follows: Obtain the environmental temperature forecast sequence, air humidity forecast sequence, and precipitation intensity forecast sequence for future time periods; Based on the environmental temperature prediction sequence and the air humidity prediction sequence, determine the prior values ​​of the icing dielectric parameters and icing thickness for each future time point; Using the current icing thickness as the initial state, the ambient temperature, air humidity, precipitation intensity, and the corresponding icing dielectric parameters and the prior value of the icing thickness at each future moment are sequentially input into the forward modeling to iteratively deduce the icing thickness of the target line at each future moment. The spatiotemporal evolution data of icing thickness is obtained by integrating the current icing thickness with the icing thickness at each future time.

9. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 1, characterized in that, The steps for determining the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and configuring a corresponding graded early warning strategy for it are as follows: The target line is divided into several sections according to a preset spatial interval; Based on the spatiotemporal evolution data of ice thickness, the inversion values ​​of ice thickness at each location point in each segment are statistically analyzed to determine the upper limit and lower limit of ice thickness in each segment. Obtain the ice thickness threshold and ice thickness calculation confidence for each section, and construct the vulnerability index for each section based on the upper limit, lower limit, threshold and calculation confidence of ice thickness. The warning levels are divided according to the vulnerability index of each section, and a graded warning strategy is configured for each warning level.

10. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 9, characterized in that, The steps for obtaining the ice thickness threshold and ice thickness calculation confidence level for each segment, and constructing the vulnerability index for each segment based on the upper limit, lower limit, threshold, and calculation confidence level of ice thickness are as follows: The severity of icing in a given section is determined by the ratio of the upper limit of icing thickness to the threshold of icing thickness. The icing unevenness of the corresponding section is determined by the ratio of the difference between the upper and lower limits of icing thickness to the icing thickness threshold. The vulnerability of each section is obtained by weighted summation of the icing severity component, the icing unevenness component, and the solution confidence. The solution confidence level is determined by the product of the response residual factor, the polarization feature stability factor, and the observation geometry correction factor. The response residual factor is determined based on the residual between the measured echo response and the theoretical output value of the forward modeling at the optimal icing thickness. The polarization feature stability factor is determined based on the degree of dispersion of each polarization feature in the standard icing feature vector. The observation geometry correction factor is determined based on the angle between the radar line of sight and the conductor axis and the radar incident angle.

11. The method for estimating and warning of icing thickness on transmission lines based on SAR imagery according to claim 10, characterized in that, The steps for classifying early warning levels based on the vulnerability index of each segment and configuring tiered early warning strategies for each level are as follows: When the vulnerability is less than the first preset threshold, the corresponding segment is determined to be at the normal level; When the vulnerability is greater than or equal to the first preset threshold and less than the second preset threshold, the corresponding segment is determined to be of concern level. When the vulnerability index is greater than or equal to the second preset threshold and less than the third preset threshold, the corresponding section is determined to be at the warning level. When the vulnerability index is greater than or equal to the third preset threshold, the corresponding segment is determined to be at the alarm level.

12. A transmission line icing thickness prediction and early warning system, applicable to the method described in any one of claims 1 to 11, characterized in that, include: The background construction module is used to extract polarization echo features from the full polarimetric SAR reference image of the target line under non-icing conditions to construct the background scattering reference vector. The net feature extraction module is used to extract the polarization echo features in the full polarization SAR monitoring image of the target line under icing conditions, and compare them with the background scattering reference vector to determine the net icing feature vector. The feature correction module is used to correct the net icing feature vector based on the observed geometric parameters to obtain the standard icing feature vector, and to determine the icing dielectric parameters based on the standard icing feature vector and meteorological environmental parameters. The forward modeling module is used to determine the forward modeling mapping between ice thickness and theoretical echo response based on the icing dielectric parameters and the standard icing eigenvector. The thickness inversion module is used to determine the measured echo response based on the standard icing feature vector, and to substitute the measured echo response into the forward modeling to perform inverse optimization to obtain the current icing thickness of the target line. The spatiotemporal simulation module is used to respond to the temporal changes of meteorological environmental parameters, drive forward modeling with the current icing thickness as the initial state to perform spatiotemporal simulation of icing thickness, and generate spatiotemporal evolution data of icing thickness of the target line. The early warning decision module is used to determine the vulnerability of the target line based on the spatiotemporal evolution data of icing thickness and to configure corresponding graded early warning strategies for it.

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