Power transmission overhead ice-coated multi-source information cooperative monitoring method

Abstract

The application provides a power transmission overhead icing multi-source information collaborative monitoring method, comprising: collecting the icing thickness and wind direction of the span between the power transmission towers in a preset time period, analyzing and extracting the icing thickness gradient characteristics, determining the icing distribution and local thickness peak value of the cable between the spans according to the icing thickness gradient characteristics; extracting the high-risk area characteristics of the risk distribution map, identifying the high-risk area, obtaining the wind direction disturbance and cable icing thickness of the high-risk area, and fusing to obtain the cable icing shedding probability; dividing the icing distribution of the cable in the span into grids, analyzing the icing thickness gradient map through spatial interpolation, and extracting the spatial distribution characteristics through feature extraction on the icing thickness gradient map; and fusing the spatial distribution characteristics and thickness change trend of the icing thickness gradient map, and extracting the cable icing thickness change rule and wind direction disturbance correlation.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method for collaborative monitoring of multi-source information on icing over overhead power transmission lines. Background Technology

[0002] Monitoring cable icing across transmission line spans is a critical area for ensuring the safe operation of the power grid. Its importance lies in preventing major accidents such as line breaks and tower collapses caused by icing, directly impacting the stability of power supply and the security of the social economy. Currently, most monitoring methods for overhead line icing rely on the assumption of uniform distribution or fixed-point sampling, neglecting the non-uniform distribution of icing weight within the span between transmission lines. These methods lack adaptability to complex environments, especially under dynamic conditions such as wind disturbances and temperature changes, making it difficult to capture the irregular changes in icing thickness along the span between transmission lines, leading to significant deviations between predicted and actual results. The core challenge lies in the dynamic changes in icing thickness gradient and its impact on the dynamic response of the line. Abnormal thickening of icing thickness in the middle of the span between transmission lines due to wind disturbances can cause local load imbalances, leading to stress concentration at the end nodes due to tension imbalances. This stress concentration further induces discontinuous switching of modal responses, complicating the line vibration characteristics. For example, within the span between transmission towers, frequent changes in wind direction lead to a rapid accumulation of ice thickness in the middle section, while micro-cracks appear at the end nodes due to a sudden increase in tension. Traditional monitoring methods struggle to capture this dynamic characteristic of nonlinear accumulation in real time and cannot accurately predict the risk of ice detachment. Therefore, how to dynamically optimize the extraction of ice thickness gradient features through adaptive spatial distribution modeling and improve the accuracy of ice detachment risk prediction has become a key issue. Summary of the Invention

[0003] This invention provides a multi-source information collaborative monitoring method for overhead power transmission line icing, mainly comprising:

[0004] The ice thickness and wind direction within the span between transmission racks are collected, and the ice thickness gradient characteristics are analyzed to determine the ice distribution and local thickness peaks of the cables within the span. The tension distribution state is determined based on the ice distribution and local thickness peaks, and the local load imbalance state is determined based on the tension distribution state. The stress distribution under tension imbalance is determined based on the local load imbalance state, and the magnitude of concentrated stress is obtained based on the stress distribution. The stress distribution is adjusted based on the magnitude of the concentrated stress to obtain the adjusted stress distribution. The modal response switching points are identified based on the adjusted stress distribution, and spectral analysis is performed on the modal response switching points to obtain the abnormal thickening characteristic distribution. The cable ice thickness gradient is determined based on the abnormal thickening characteristic distribution. The process involves extracting spatial gradient change features from the ice thickness gradient variation pattern, determining the cable ice shedding probability based on the abnormal thickening feature distribution and spatial gradient change features, and generating a risk distribution map based on the ice shedding probability. High-risk area features are extracted from the risk distribution map, and high-risk areas are identified based on these features. Wind direction disturbances and ice thickness in the high-risk areas are obtained and fused to obtain the ice shedding probability of the high-risk areas. The ice distribution is then gridded, and an ice thickness gradient map is obtained through spatial interpolation analysis. Spatial distribution features are extracted from the ice thickness gradient map. Finally, the spatial distribution features and thickness variation trends are fused to obtain the correlation between the cable ice thickness variation pattern and wind direction disturbance.

[0005] Furthermore, the ice thickness and wind direction within the span between the transmission towers are collected, and the ice thickness gradient characteristics are analyzed. Based on these ice thickness gradient characteristics, the ice distribution and local thickness peaks of the cables within the span are determined, including:

[0006] Ice thickness monitoring points are set at preset intervals within the span between transmission lines to obtain the distance value of the ice surface at each monitoring point. The ice thickness at each monitoring point is determined based on the difference between the original cable radius and the distance value. Wind direction sensors are deployed at the same locations to obtain wind direction angle and wind speed data, forming an ice thickness time series dataset and a wind direction time series dataset. Based on the ice thickness time series dataset, the time gradient is obtained by dividing the thickness difference between adjacent time points by the time interval, the spatial gradient is obtained by dividing the thickness difference between adjacent monitoring points by the spatial distance, and the thickness change rate is obtained by dividing the difference between the maximum and minimum thickness values ​​within a preset time window by the length of the time window. An ice thickness gradient feature matrix is ​​constructed based on the time gradient, spatial gradient, and thickness change rate. The ice thickness between monitoring points is processed by cubic spline interpolation to obtain a continuous ice distribution curve within the span. The first derivative of the ice distribution curve along the span direction is calculated, and the position where the derivative is zero is determined as a candidate point for local thickness peak. The effective local thickness peak is determined based on the ratio of the ice thickness at the candidate point to the average thickness of the adjacent area.

[0007] Furthermore, the process of determining the tension distribution state based on the icing distribution and local thickness peak, determining the local load imbalance state based on the tension distribution state, determining the stress distribution during tension imbalance based on the local load imbalance state, and obtaining the magnitude of concentrated stress based on the stress distribution includes:

[0008] The span is divided into multiple calculation units. The load value of each unit is calculated based on the icing distribution and local thickness peak. The vertical displacement and horizontal tension of each unit node are calculated, and the tension balance equations are solved to obtain the tension distribution state. Based on the tension distribution state, the ratio of the tension difference between adjacent units to the average tension is calculated as an imbalance index. The local load imbalance state is determined based on the imbalance index and load eccentricity. Based on the local load imbalance state, the additional bending moment generated by the load eccentricity is converted into bending stress of the conductor section. The axial tension of the conductor is divided by the cross-sectional area to obtain the axial tensile stress. The bending stress and axial tensile stress are superimposed to obtain the stress distribution when tension is unbalanced. The stress maximum point is extracted, and the ratio of the stress maximum value to the surrounding average stress is calculated as the stress concentration factor. The magnitude of the concentrated stress is determined based on the stress maximum value and the stress concentration factor.

[0009] Furthermore, the step of adjusting the stress distribution according to the magnitude of the concentrated stress to obtain an adjusted stress distribution, identifying modal response switching points based on the adjusted stress distribution, and performing spectral analysis on the modal response switching points to obtain an abnormal thickening characteristic distribution includes:

[0010] The stress adjustment coefficient is calculated based on the difference between the magnitude of the concentrated stress and the preset stress threshold. The stress value at each point in the stress distribution is multiplied by the stress adjustment coefficient to obtain the adjusted stress distribution. The stiffness change value of each segment of the conductor is calculated based on the adjusted stress distribution. The difference in stiffness change values ​​between adjacent segments is compared to determine the modal response switching point. Vibration signals are collected at the modal response switching point and at a preset distance before and after it. The vibration time-domain signal is converted into a frequency-domain signal. The amplitude and power spectral density of each frequency component are extracted. The frequency distribution is determined based on the proportion of the power spectral density to the total power. The peak frequency and amplitude are extracted based on the frequency distribution. The difference between adjacent peak frequencies and the rate of change of amplitude are calculated and combined to form an abnormal thickening feature distribution.

[0011] Furthermore, the step of determining the cable icing thickness gradient variation law based on the abnormal thickening feature distribution, extracting spatial gradient variation features from the icing thickness gradient variation law, determining the cable icing detachment probability based on the abnormal thickening feature distribution and the spatial gradient variation features, and generating a risk distribution map based on the icing detachment probability includes:

[0012] Based on the frequency distribution and amplitude variation in the abnormal thickening feature distribution, spectral feature parameters are arranged according to spatial location. The difference in feature parameters between adjacent monitoring points is calculated as the feature gradient. The ice thickness gradient variation function is obtained by fitting using the least squares method. The gradient direction is determined by calculating the angle between the gradient vector and the horizontal direction from the variation function. The rate of change is obtained by dividing the difference in gradient values ​​between adjacent points by the spatial interval. The location where the derivative is zero is determined as the local extreme point. These are combined to form the spatial gradient variation feature. Based on the abnormal thickening feature distribution and the spatial gradient variation feature, the probability of ice shedding is calculated using Bayesian inference. The historical shedding frequency is set as the prior probability, and the reciprocal of the Euclidean distance of the feature parameter is used as the likelihood to calculate the probability of ice shedding at each monitoring point. Based on the ice shedding probability, the span is divided into grid cells, the risk value of each cell is calculated, the risk level is divided and assigned a color, and a risk distribution map is generated.

[0013] Furthermore, the step of extracting high-risk area features from the risk distribution map, identifying high-risk areas based on these features, obtaining wind direction disturbances and icing thickness in the high-risk areas, and fusing them to obtain the icing shedding probability of the high-risk areas includes:

[0014] Grid cells with risk values ​​exceeding a preset high-risk threshold are extracted from the risk distribution map. Connecting regions formed by adjacent high-risk grids are identified, and the area of ​​the region is calculated by multiplying the number of grids in the connected region by the area of ​​a single grid cell. The risk level is determined based on the highest risk value within the region. Wind direction sensor data from monitoring points within the high-risk region are read, and the square root of the sum of the squares of the differences between the wind direction angle and the average wind direction angle is calculated by dividing by the number of monitoring points to obtain the standard deviation of wind direction disturbance. The weighted average value of icing thickness within the region is calculated. A fusion coefficient is determined by querying a fuzzy rule table based on the standard deviation of wind direction disturbance and the regional icing thickness. The detachment probability value of the region in the risk distribution map is multiplied by the fusion coefficient to obtain the fused icing detachment probability.

[0015] Furthermore, the step of dividing the ice distribution into grids, obtaining an ice thickness gradient map through spatial interpolation analysis, and extracting spatial distribution features based on the ice thickness gradient map includes:

[0016] The ice distribution is divided into grids, and an ice thickness gradient map is generated by cubic spline interpolation. The gradient direction and gradient magnitude of each grid point are extracted from the ice thickness gradient map. The gradient direction is determined by calculating the angle between the gradient vector and the horizontal direction. The rate of change is obtained by calculating the difference in gradient values ​​between adjacent grid points and dividing by the spatial interval. The local extreme points are determined by finding the position where the derivative is zero. These are combined to form the spatial distribution characteristics.

[0017] Furthermore, the fusion processing of the spatial distribution characteristics and thickness variation trends to obtain the cable icing thickness variation law and its correlation with wind direction disturbance includes:

[0018] Principal component analysis is performed on the gradient direction and gradient magnitude in the spatial distribution features. The principal component with the largest contribution to the variance is extracted as the main feature of the spatial distribution. The thickness change value is obtained by calculating the difference in ice thickness. The sequence of the main feature of the spatial distribution and the sequence of thickness change value are multiplied by matrix to obtain the spatiotemporal fusion feature matrix. The time series of ice thickness and wind direction angle are extracted. The thickness increment and wind direction change are calculated. The correlation value between the thickness increment and the wind direction change is calculated using the Pearson correlation coefficient. The periodic component is extracted by Fourier transform of the correlation value sequence through a sliding window. The ice thickness change law is obtained by fitting a quadratic function according to the periodic component. The correlation value is determined as the correlation of wind direction disturbance.

[0019] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0020] This invention discloses a multi-source collaborative monitoring method for icing on overhead power transmission lines. By collecting icing thickness and wind direction data within a preset time period, this invention extracts temporal and spatial gradient features and thickness change rates to construct an icing distribution model, accurately identifying local thickness peaks and tension distribution states, and further analyzing stress concentration and imbalance modes. When stress exceeds a threshold, this invention extracts abnormal thickening feature distributions through spectral analysis of modal response switching points, and combines this with spatial gradient change patterns to generate icing detachment probability and risk distribution maps, highlighting the fusion analysis of wind direction disturbances and thickness features in high-risk areas. Simultaneously, this invention generates icing thickness gradient maps through gridding and spatial interpolation, fusing spatial distribution features with the correlation of wind direction disturbances to reveal the icing thickness change patterns. This invention achieves dynamic monitoring and precise early warning of icing risks, significantly improving the safety and stability of transmission lines. Attached Figure Description

[0021] Figure 1 This is a flowchart of a multi-source information collaborative monitoring method for overhead power transmission icing according to the present invention.

[0022] Figure 2 This is a schematic diagram of a multi-source information collaborative monitoring method for overhead power transmission icing according to the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1-2 This embodiment of a multi-source information collaborative monitoring method for overhead power transmission line icing may specifically include:

[0025] S101. Collect the icing thickness and wind direction of the span between transmission racks within a preset time period, analyze and extract the icing thickness gradient characteristics, and determine the icing distribution and local thickness peak of the cables between spans based on the icing thickness gradient characteristics.

[0026] Icing thickness monitoring points are set at preset intervals within the span between transmission lines. Each monitoring point uses a laser rangefinder to acquire the distance to the icing surface. The icing thickness at each monitoring point is determined based on the difference between the original cable radius and the measured distance. Simultaneously, wind direction sensors are deployed at the same locations to record wind direction angle and wind speed data. These data are collected at preset collection frequencies to form icing thickness time-series datasets and wind direction time-series datasets. For the icing thickness time-series datasets, the temporal gradient is calculated by dividing the thickness difference between adjacent time points by the time interval, and the spatial gradient is obtained by dividing the thickness difference between adjacent monitoring points by the spatial distance. The temporal gradient represents the rate of change of icing thickness over time, and the spatial gradient represents the rate of change of icing thickness along the span direction. The thickness change rate is obtained by dividing the difference between the maximum and minimum thickness values ​​at each monitoring point within a preset time window by the length of the time window. An icing thickness gradient feature matrix is ​​constructed based on the time gradient, spatial gradient, and thickness change rate. Cubic spline interpolation is used to spatially interpolate the icing thickness between monitoring points. Cubic spline interpolation involves constructing a cubic polynomial function between adjacent monitoring points so that the curve passes through all monitoring points and maintains continuity of the second derivative, resulting in a continuous icing distribution curve within the span. The first derivative of the icing distribution curve is calculated along the span direction; points where the derivative is zero are identified as candidate points for local thickness peaks. If the icing thickness at a candidate point for a local thickness peak exceeds a preset multiple threshold of the average thickness of adjacent areas, it is determined as a valid local thickness peak. Based on the location coordinates and corresponding thickness value of the valid local thickness peak, combined with the icing thickness gradient feature matrix, the icing distribution and local thickness peaks of the cable across the span are determined.

[0027] For example, in one implementation, the icing monitoring system between transmission lines achieves accurate measurement of icing thickness by arranging multiple monitoring points within the span. The laser rangefinder works by emitting laser pulses and receiving reflected signals, calculating the target distance based on the speed of light and round-trip time. When icing forms on the cable surface, the laser beam strikes the outer surface of the icing, and the difference between the measured distance and the original cable radius is the icing thickness at that point. The wind direction sensor uses ultrasonic principles, determining the wind direction angle by measuring the time difference of sound wave propagation in different directions, while the wind speed is measured by the rotational speed of the wind cup.

[0028] It should be noted that the spacing between monitoring points needs to be optimized based on the span length and terrain conditions. In mountainous transmission lines, the uneven wind field distribution due to undulating terrain necessitates closer spacing between monitoring points; while in plains areas, where the wind field is relatively uniform, the spacing between monitoring points can be appropriately increased. The sampling frequency setting needs to comprehensively consider the icing growth rate and data storage capacity, increasing the sampling frequency during periods of high icing incidence and decreasing it during normal periods to achieve dynamic adjustment.

[0029] Specifically, the temporal gradient reflects the dynamic changes in ice thickness over time. At a given monitoring point, if the ice thickness is h1 at time t1 and h2 at time t2, the temporal gradient is (h2-h1) / (t2-t1). The spatial gradient describes the distribution of ice thickness along the span direction. If the ice thicknesses of adjacent monitoring points P1 and P2 are H1 and H2 respectively, and the spatial distance is D, then the spatial gradient is (H2-H1) / D. The temporal gradient reflects the rate of ice accumulation; a positive value indicates increasing ice thickness, while a negative value indicates melting or detachment of ice. The spatial gradient reflects the non-uniformity of ice distribution; a larger gradient indicates a more uneven ice distribution. The thickness change rate is obtained by finding the maximum and minimum thickness values ​​within a preset time window, and dividing the difference between them by the time window length. This index comprehensively reflects the degree of fluctuation in ice thickness.

[0030] In one possible implementation, the ice thickness gradient feature matrix is ​​constructed by using the temporal gradient, spatial gradient, and thickness change rate of each monitoring point as the three components of the feature vector. The feature vectors of all monitoring points are arranged in spatial order to form a feature matrix. Each row of this matrix corresponds to a monitoring point, and each column corresponds to a gradient feature. Abnormal areas of ice distribution can be quickly identified through matrix operations.

[0031] Preferably, the application of cubic spline interpolation in icing distribution modeling ensures the smoothness and continuity of the interpolation curve. Cubic spline interpolation involves constructing a cubic polynomial function between every two adjacent monitoring points, ensuring that the entire curve not only passes through all monitoring points but also maintains continuity of the first and second derivatives at the connection points. This interpolation method is particularly suitable for describing the continuous distribution of icing thickness because the physical formation process of icing determines that its thickness distribution will not undergo abrupt changes. In practical applications, the coefficients of the cubic polynomial for each segment are obtained by solving a system of linear equations, thereby obtaining an estimate of the icing thickness at any location within the entire span.

[0032] For example, in the monitoring of a 500 kV transmission line with a span of 400 meters, 21 monitoring points were set up. During a cold wave, a wind speed convergence zone formed in the middle of the span due to topographic factors, resulting in a significantly thicker icing layer in this area compared to the ends. By differentiating the interpolated icing distribution curve, it was found that the derivative was zero at the 180-meter and 220-meter spans, indicating the existence of two local thickness peaks. Further analysis revealed that the peak at 180 meters was due to icing accumulation caused by changes in wind direction, while the peak at 220 meters was due to the location being at a valley wind gap, where cold air converged.

[0033] For example, determining local thickness peaks requires considering the average thickness of adjacent areas as a reference. The average ice thickness of all monitoring and interpolation points within a 50-meter radius before and after the candidate peak is calculated. If the thickness of the candidate point exceeds a preset multiple threshold of this average, it is confirmed as a valid peak. This method effectively distinguishes between genuine concentrated ice areas and spurious peaks caused by measurement noise.

[0034] S102. Determine the tension distribution state based on the cable's icing distribution and local thickness peak, determine the local load imbalance state based on the tension distribution state, determine the stress distribution when the tension is unbalanced based on the local load imbalance state, and obtain the magnitude of the concentrated stress based on the stress distribution when the tension is unbalanced.

[0035] Based on the cable's icing distribution and local peak thickness, the span is divided into multiple calculation units. The load value of each unit is the sum of the conductor's self-weight and the weight of the icing. The vertical displacement and horizontal tension of each unit node are calculated using the catenary equation, which is the curve equation formed by the conductor under its own weight. A set of tension balance equations for each node is established based on the torque balance principle, and the tension distribution state at each point along the span direction is obtained. Based on the tension distribution state, the ratio of the tension difference between adjacent calculation units to the average tension is calculated as an imbalance index. If the imbalance index exceeds a preset threshold, a local load imbalance is determined. The load eccentricity is obtained by accumulating the product of the load of each unit in the imbalance section and its distance from the midpoint of the span, then dividing by the total load. The local load imbalance state is determined based on the imbalance index and the load eccentricity. For the aforementioned local load imbalance state, the additional bending moment generated by the load eccentricity is converted into bending stress of the conductor section according to beam bending theory. The bending stress is equal to the ratio of the bending moment to the section bending modulus. The axial tension of the conductor is divided by the cross-sectional area to obtain the axial tensile stress. The bending stress and the axial tensile stress are superimposed to obtain the stress distribution under tension imbalance. The stress maximum point is extracted from the stress distribution. The stress gradient is obtained by calculating the stress difference between the maximum point and the adjacent points and dividing by the distance. The ratio of the maximum stress to the surrounding average stress is used as the stress concentration factor. The product of the maximum stress and the stress concentration factor is determined as the magnitude of the concentrated stress.

[0036] For example, in one implementation, the tension distribution calculation of the iced conductor is based on the catenary theory. The catenary equation describes the natural curve shape formed by the flexible conductor under its own weight and icing load; its physical essence is the geometry of the conductor at which it reaches mechanical equilibrium under gravity. The division of calculation cells is adaptively adjusted according to the gradient of icing thickness variation. In areas with drastic changes in icing thickness, the calculation cells are more densely divided, while in areas with uniform icing distribution, the calculation cells are relatively sparse. The load of each calculation cell includes two parts: the conductor's own weight and the weight of the icing. The conductor's own weight is calculated by multiplying the mass per unit length by the gravitational acceleration, while the weight of the icing is determined based on the cross-sectional area of ​​the icing, the density of the ice, and the gravitational acceleration.

[0037] It should be noted that the application of the torque balance principle in tension calculation is reflected at each node. For any node, the torque generated by the conductor segment to its left is equal to the torque generated by the conductor segment to its right. By establishing the torque balance equation of the node and combining it with the geometric constraints of the conductor, a nonlinear equation system is formed. The tension value of each node is obtained by solving the system using the Newton-Raphson iterative method.

[0038] Specifically, the calculation process of the imbalance index involves a comparative analysis of local tension and overall tension. Under normal icing conditions, the tension difference between adjacent calculation units is small. However, when abnormal thickening of local icing occurs, the tension in that area increases significantly, leading to a larger tension difference with adjacent areas. The imbalance index is defined as the ratio of the tension difference between adjacent units to the average tension of the two units. This dimensionless processing eliminates the influence of absolute tension magnitude, providing a unified standard for imbalance judgment across different spans and conductor types. The preset threshold is determined based on historical operating data and the safety factor of the conductor material, typically set between 0.15 and 0.25. Exceeding this threshold indicates a local load imbalance. The calculation of load eccentricity reflects the degree of asymmetry in the distribution of icing loads. By calculating the sum of the moments of each unit load about the midpoint of the span and then dividing by the total load, the equivalent eccentricity is obtained. A larger eccentricity indicates a more uneven load distribution.

[0039] In one possible implementation, the mechanism of the additional bending moment is closely related to load eccentricity. When the ice distribution is uneven, the conductor, in addition to bearing axial tensile force, will also undergo bending deformation. The product of the load eccentricity and the total load forms the additional bending moment, which induces bending stress in the conductor. The application of beam bending theory here takes into account the bending stiffness characteristics of the conductor; the bending stress is equal to the bending moment divided by the section modulus of bending, where the section modulus of bending is related to the geometry and material properties of the conductor.

[0040] Preferably, the stress superposition process follows the superposition principle of mechanics of materials. Axial tensile stress is obtained by dividing the conductor tension by the conductor's cross-sectional area, and this stress is uniformly distributed across the entire cross-section. Bending stress is linearly distributed across the cross-section, with tensile stress on the outside of the bend and compressive stress or a smaller tensile stress on the inside. The algebraic superposition of the two stresses yields the combined stress distribution, with the maximum stress typically occurring on the outside of the bend.

[0041] For example, during icing monitoring of a 220 kV transmission line, an abnormally thickened local icing layer was observed 180 meters midway through the span, reaching a thickness of 25 mm, while the icing thickness at both ends was only 10 mm. Tension calculations revealed that the tension in the abnormal area was 35% higher than in the normal area, with an imbalance index of 0.28, exceeding the preset threshold. The calculated load eccentricity was 12 meters, resulting in an additional bending moment that led to a maximum bending stress of 45 MPa.

[0042] For example, determining the stress concentration factor requires analyzing the local characteristics of the stress distribution. By extracting the stress values ​​at the point of maximum stress and several points around it, the stress gradient is calculated, which is the amount of stress change per unit distance. The larger the stress gradient, the more severe the stress concentration. The stress concentration factor is defined as the ratio of the maximum stress to the average stress in the surrounding area; this factor reflects the degree of stress concentration. By multiplying the maximum stress by the stress concentration factor, the equivalent stress considering the stress concentration effect is obtained. This value is compared with the yield strength of the conductor material to determine whether the conductor is at risk of breakage. When the concentrated stress approaches or exceeds 70% of the material's yield strength, de-icing measures or adjustments to the line operation mode are required.

[0043] S103. If the magnitude of the concentrated stress exceeds the preset stress threshold, the stress distribution during tension imbalance is adjusted according to the magnitude of the concentrated stress. The modal response switching point is identified through the adjusted stress distribution, and the abnormal thickening characteristic distribution is obtained by performing spectral analysis on the modal response switching point.

[0044] If the magnitude of the concentrated stress exceeds a preset stress threshold, the difference between the concentrated stress and the preset stress threshold is calculated. A stress adjustment coefficient is determined based on the proportion of this difference to the threshold. The stress value at each point in the stress distribution under tension imbalance is multiplied by this stress adjustment coefficient to obtain the adjusted stress distribution. The adjusted stress distribution reflects the actual stress state after considering the influence of stress concentration. The stiffness change of each segment of the conductor is calculated based on the adjusted stress distribution. The stiffness change value of each segment is obtained by dividing the difference between the adjusted stress and the initial stress by the Young's modulus of the conductor material. When the difference in stiffness change values ​​between adjacent segments exceeds a preset stiffness difference threshold, this location is determined as a modal response switching point. The modal response switching point characterizes the location where the conductor's vibration characteristics undergo a sudden change. For each modal response switching point, accelerometers are placed at the switching point location and at preset distances before and after it to collect vibration signals. The vibration time-domain signal is converted into a frequency-domain signal using a fast Fourier transform. The amplitude of each frequency component is extracted from the frequency-domain signal, and the power spectral density of each frequency component is calculated. The proportion of the power spectral density to the total power is determined as the energy proportion of that frequency, thus obtaining the frequency distribution. Based on the frequency distribution, identify the frequency value and amplitude corresponding to the spectral peak, calculate the difference between the frequencies of adjacent spectral peaks as the frequency interval, divide the difference between the current amplitude and the amplitude at the previous moment by the time interval to obtain the amplitude change rate, and combine the spectral peak frequency, frequency interval, spectral peak amplitude and amplitude change rate to form an abnormal thickening feature distribution.

[0045] For example, in one implementation, the stress adjustment coefficient is determined based on the safety factor theory of materials mechanics. When the concentrated stress exceeds a preset stress threshold, it indicates that the conductor material is approaching its elastic limit, at which point the conductor's mechanical properties begin to exhibit nonlinear changes. The stress adjustment coefficient is determined by calculating the deviation of the actual stress from the threshold; the greater the deviation, the smaller the adjustment coefficient, thereby reducing the calculated stress value and reflecting the decrease in the material's actual load-bearing capacity under high stress conditions. The adjusted stress distribution more accurately describes the true stress state of the conductor under uneven icing conditions.

[0046] It should be noted that the preset stress threshold takes into account the yield strength and safety margin of the conductor material. For steel-cored aluminum stranded wire, the threshold is usually set to 60% to 70% of the yield strength. This range ensures the safe operation of the conductor while making full use of the material's load-bearing capacity.

[0047] Specifically, the calculation of stiffness variation involves the fundamental mechanical parameter of the material, Young's modulus. Young's modulus reflects the ratio of stress to strain within the elastic deformation range of a material. For aluminum alloys commonly used in power transmission conductors, the Young's modulus is approximately 70 gigapascals. When the stress on a section of the conductor changes, the stiffness of that section also changes accordingly. The stiffness variation value is obtained by dividing the difference between the adjusted stress and the initial stress by the Young's modulus. This value characterizes the degree of change in the local elastic properties of the conductor. The difference in stiffness variation values ​​between adjacent sections reflects the continuity of the conductor's vibration characteristics. When the difference exceeds a preset threshold, it indicates a qualitative change in the conductor's vibration mode at that location, i.e., a modal response switch has occurred. The physical significance of the modal response switch point lies in the fact that the conductor exhibits different vibration modes on either side of that point. One side may be dominated by lower-order modes, while the other side may excite higher-order modes. This modal switch is often accompanied by a redistribution of vibration energy and a concentration of local stress.

[0048] In one possible implementation, the acquisition and processing of vibration signals are crucial for identifying abnormal thickening features. Accelerometers are positioned at and before / after the modal response switching point, and the sensor's sampling frequency needs to satisfy the Nyquist sampling theorem, i.e., at least twice the highest vibration frequency of the conductor. For transmission lines, the vibration frequency range is typically between 0.1 Hz and 100 Hz, therefore the sampling frequency is set to above 250 Hz.

[0049] Preferably, the Fast Fourier Transform (FFT) converts the time-domain vibration signal to the frequency domain for analysis. The FFT is an efficient algorithmic implementation of the Discrete Fourier Transform (DFT). Through decomposition and recursive operations, it decomposes the time-domain signal into a superposition of different frequency components. The resulting frequency-domain signal contains the amplitude and phase information of each frequency component, where the amplitude reflects the contribution of that frequency component to the vibration.

[0050] For example, in the monitoring of an icing transmission line, the modal response switching point is located at 195 meters of the span. The vibration signal collected by the accelerometer at this point, after Fast Fourier Transform (FFT), shows distinct spectral peaks at 0.8 Hz, 2.3 Hz, and 5.7 Hz. Power spectral density calculations indicate that the energy proportion of the 0.8 Hz frequency component reaches 45%, corresponding to the first-order transverse vibration mode of the conductor; the energy proportion of the 2.3 Hz frequency component is 30%, corresponding to the second-order vibration mode; and the energy proportion of the 5.7 Hz frequency component is 15%, corresponding to a higher-order vibration mode.

[0051] For example, the calculation of amplitude variation rate reflects the evolution of vibration intensity over time. By continuously monitoring the amplitude of the same frequency component at different times, the difference in amplitude between adjacent times is calculated and divided by the time interval to obtain the amplitude variation rate for that frequency. A positive amplitude variation rate indicates enhanced vibration, which may indicate continued icing accumulation; a negative amplitude variation rate indicates weakened vibration, which may indicate the beginning of icing detachment or dissipation of vibration energy.

[0052] Understandably, the construction of the abnormal thickening feature distribution integrates multiple dimensions of information from frequency domain analysis. The peak frequency reflects the vibration modal characteristics of the conductor, the frequency interval reflects the coupling relationship between different modes, the peak amplitude reflects the excitation degree of each mode, and the amplitude change rate reflects the dynamic evolution trend of the vibration.

[0053] S104. Determine the gradient variation law of cable icing thickness based on the abnormal thickening feature distribution, extract the spatial gradient variation features of the abnormal thickening feature distribution from the cable icing thickness gradient variation law, determine the probability of cable icing detachment based on the abnormal thickening feature distribution and the spatial gradient variation features, and generate a risk distribution map based on the probability of cable icing detachment.

[0054] Based on the frequency distribution and amplitude variation data in the abnormal thickening feature distribution, the spectral feature parameters of each monitoring point are arranged according to spatial location. The difference between the feature parameters of adjacent monitoring points is calculated as the feature gradient. The relationship between the feature gradient and spatial location is fitted using the least squares method to obtain the ice thickness gradient variation function. This variation function characterizes the distribution law of the ice thickness gradient along the span. From the ice thickness gradient variation function, the angle between the gradient vector of each point and the horizontal direction is calculated to determine the gradient direction. The rate of change is obtained by dividing the difference of the gradient values ​​of adjacent points by the spatial interval. The first derivative of the variation function is calculated and set to zero to identify the location of local extrema. The gradient direction, rate of change, and location of local extrema are combined to form the spatial gradient variation feature. Based on the abnormal thickening feature distribution and spatial gradient variation feature, Bayesian inference is used to calculate the ice shedding probability. The prior probability is set as the historical shedding frequency of the same period. The reciprocal of the Euclidean distance between the current feature parameter and the historical shedding feature parameter is used as the likelihood. The ice shedding probability of each monitoring point is calculated using the Bayesian formula. The span is divided into grid cells based on the ice shedding probability. The risk value of each grid cell is calculated by the distance-weighted average of the shedding probability of the monitoring points within the cell. The weight is the reciprocal of the distance from the monitoring point to the center of the grid. The risk values ​​are divided into high, medium and low risk levels according to a preset threshold and assigned corresponding colors to generate an ice shedding risk distribution map.

[0055] For example, in one implementation, the ice thickness gradient variation function is constructed based on the spatial distribution of spectral characteristic parameters. The spectral characteristic parameters for each monitoring point include the dominant frequency, frequency interval, peak amplitude, and amplitude variation rate. These parameters are arranged according to the actual location of the monitoring point within the span. The characteristic gradient is calculated by the difference between corresponding parameters of adjacent monitoring points; this difference reflects the degree of spatial variation in the ice accretion characteristics.

[0056]

[0057] This is the formula for calculating the feature gradient, where P represents the gradient of the spectral characteristic parameters at the i-th monitoring point. i+1 and P i-1 x represents the spectral characteristic parameter values ​​of adjacent monitoring points, respectively. i+1 and x i-1 This formula represents the spatial coordinates of adjacent monitoring points within the span, and calculates the degree of spatial variation using the parameter differences between adjacent monitoring points. The least squares method is used to fit the functional relationship between the feature gradient and spatial location. This method solves for the coefficients of the fitted function by minimizing the sum of squared errors between the measured gradient values ​​and the fitted function values.

[0058]

[0059] This is the least squares fitting objective function, where m represents the total number of monitoring points, and G... k f(x) represents the measured gradient value at the k-th monitoring point. k ) indicates at position x k The fitted function value at the specified location. This formula solves for the coefficients of the fitted function by minimizing the sum of squared errors between the measured gradient value and the fitted function value. The fitted function is typically a quadratic or cubic polynomial, capable of describing the continuous distribution of the icing thickness gradient over the entire span.

[0060]

[0061] This is the polynomial expression of the ice thickness gradient variation function, where T(x) represents the ice thickness gradient value at position x, a0, a1, a2, and a3 represent the coefficients of the cubic polynomial, and x represents the spatial coordinates within the span. This function can describe the continuous distribution pattern of the ice thickness gradient throughout the entire span.

[0062] It should be noted that the choice of the least squares method is based on its robustness to measurement errors. In actual monitoring, due to environmental interference and measurement accuracy limitations, characteristic parameters inevitably contain noise, and the least squares method can obtain stable fitting results even in the presence of noise.

[0063] Specifically, the extraction of spatial gradient variation characteristics involves three key dimensions. The gradient direction is obtained by calculating the angle between the gradient vector and the horizontal direction. This angle reflects the dominant direction of ice thickness increase; a positive angle indicates upward thickening, and a negative angle indicates downward thickening. The rate of change describes how quickly the gradient changes spatially, calculated by dividing the difference in gradient values ​​between adjacent points by the spatial interval. A larger rate of change indicates a more uneven ice distribution. The identification of local extrema is achieved by taking the first derivative of the variation function and finding points where the derivative is zero. These extrema correspond to the peak or valley locations of the ice thickness gradient and are areas with high stress concentration and a high risk of ice detachment. These three feature dimensions together constitute the spatial gradient variation characteristics, comprehensively describing the spatial distribution pattern of ice.

[0064] In one possible implementation, Bayesian inference is used to calculate the probability of ice shedding, the core of which lies in integrating prior knowledge and current observational data. The prior probability is set based on historical ice shedding statistics for the same period, reflecting the basic probability of ice shedding under similar meteorological conditions. The likelihood is calculated using the reciprocal of the Euclidean distance, which measures the similarity between the current feature parameter vector and the feature parameter vector of historical shedding events. The smaller the distance, the more similar the current state is to the historical shedding state, and the greater the likelihood.

[0065] Preferably, the application of Bayes' theorem is as follows: the posterior probability equals the likelihood multiplied by the prior probability and then divided by the normalization constant. The normalization constant ensures that the sum of the posterior probabilities of all possible states is 1. The calculated posterior probability is the probability of ice shedding at each monitoring point, with a probability value between 0 and 1; the closer to 1, the higher the risk of shedding.

[0066] For example, in a certain icing monitoring operation, the span was divided into a 20×10 grid, totaling 200 grid cells. A certain grid cell contained three monitoring points with detachment probabilities of 0.65, 0.72, and 0.58, respectively. The distances from each monitoring point to the grid center were 2.5 meters, 1.8 meters, and 3.2 meters, with corresponding weights of 0.4, 0.556, and 0.313. Calculated using a distance-weighted average, the risk value for this grid cell was 0.654.

[0067] For example, a three-tier system is used to classify risk levels. Areas with a risk value below 0.3 are classified as low-risk and are marked with a green label; areas with a risk value between 0.3 and 0.7 are classified as medium-risk and are marked with a yellow label; and areas with a risk value above 0.7 are classified as high-risk and are marked with a red label.

[0068] Understandably, the distance-weighted average calculation method ensures that the grid cell risk value reflects the overall risk level of localized icing detachment. Monitoring points that are closer together contribute more to the grid risk value, which aligns with the principle of spatial correlation—points that are spatially close share similar physical characteristics. Furthermore, the risk distribution map is visualized using a color gradient, displaying not only discrete risk levels but also subtle differences in risk values ​​through continuous variations in color intensity. The risk distribution map also includes annotations of key information, such as the specific locations of high-risk areas, the maximum risk value, and their corresponding monitoring point numbers, providing maintenance personnel with an intuitive basis for decision-making when developing de-icing plans.

[0069] S105. Extract the features of high-risk areas from the risk distribution map, identify high-risk areas, obtain the wind direction disturbance and cable icing thickness in high-risk areas, and fuse them to obtain the probability of cable icing falling off.

[0070] Grid cells with risk values ​​exceeding a preset high-risk threshold are extracted from the risk distribution map. Connected regions formed by four- or eight-neighbor high-risk grids are identified using connected component markers. The area of ​​each region is calculated by multiplying the number of grids in each region by the area of ​​a single grid. The risk level is determined based on the highest risk value within the region. The region area and risk level are combined to form a high-risk region feature. For the high-risk region, wind direction sensor data from all monitoring points within the region boundary are read. The square root of the sum of the squares of the differences between the wind direction angle at each monitoring point and the average wind direction angle is calculated and divided by the number of monitoring points to obtain the standard deviation of wind direction disturbance. The measured icing thickness at each monitoring point within the region is obtained. A weighted average is calculated using the reciprocal of the distance from the monitoring point to the center of the region as the weight to obtain the regional icing thickness. Based on the standard deviation of wind direction disturbance and the regional icing thickness, a fusion coefficient is determined by querying a preset fuzzy rule table. The fuzzy rule table is preset based on the combination of wind direction disturbance degree and icing thickness level. The detachment probability value of the region in the aforementioned risk distribution map is multiplied by the fusion coefficient to obtain the fused cable icing detachment probability.

[0071] For example, in one implementation, a connected component labeling algorithm is used to identify high-risk clusters in a risk distribution map. Four-neighbor connectivity refers to the connectivity between the current grid cell and its four adjacent grid cells (up, down, left, and right), while eight-neighbor connectivity includes the four grid cells along the diagonal. For icing monitoring applications, using eight-neighbor connectivity can more accurately identify diagonally extending high-risk areas, which typically correspond to uneven icing distribution caused by wind tilt.

[0072] It should be noted that the high-risk threshold is set based on historical icing accident statistics, and is usually set at 0.7 or higher, indicating that areas with a detachment probability of more than 70% need to be closely monitored.

[0073] Specifically, the calculation of the standard deviation of wind direction disturbance reflects the degree of wind direction turbulence within the region. In stable wind fields, the wind direction angles at each monitoring point are similar, resulting in a smaller standard deviation; however, under the influence of turbulence or eddies, wind direction changes drastically, leading to a larger standard deviation. Wind direction disturbance directly affects the adhesion strength and distribution uniformity of icing; the greater the disturbance, the higher the uncertainty of icing detachment. The weighting in the weighted average uses the inverse distance method, with monitoring points closer to the region's center receiving a larger weight. This weighting allocation method conforms to the attenuation law of spatial influence, making the regional icing thickness more representative of the actual situation at the center.

[0074] Preferably, the fuzzy rule table is designed based on expert experience and historical data analysis. The rule table categorizes wind direction disturbances into three levels: low, medium, and high, and icing thickness into three levels: thin, medium, and thick, resulting in nine possible combinations. Each combination corresponds to a fusion coefficient, which ranges from 0.8 to 1.2.

[0075] For example, when the standard deviation of wind direction disturbance is 15 degrees, which is considered a moderate disturbance, and the regional icing thickness is 20 mm, which is also considered a moderate thickness, the fusion coefficient obtained from the table is 1.05. If the original detachment probability of this area in the risk distribution map is 0.75, and the detachment probability after fusion is 0.75 × 1.05, it indicates that the detachment risk is increased after considering wind direction disturbance and actual icing thickness.

[0076] S106. The icing distribution of the cable within the span is divided into grids, and the icing thickness gradient map is obtained through spatial interpolation analysis. The spatial distribution features are obtained by feature extraction from the icing thickness gradient map.

[0077] Based on the required span length between transmission lines and monitoring accuracy, a non-uniform grid partitioning scheme was constructed. A dense grid was used in areas prone to icing accumulation, while a sparse grid was used in areas with relatively stable icing, resulting in a grid structure containing node coordinates. The inverse distance weighted interpolation method was used to calculate the icing thickness at each node in the grid structure. Based on the measured icing thickness values ​​of neighboring monitoring points and the distance weighting coefficient, the interpolation results for the icing thickness of each grid node were determined, generating a complete icing thickness distribution field. The Sobel operator was used to calculate the gradient of the icing thickness distribution field, extracting the gradient magnitude and gradient direction angle of each grid point. If the gradient magnitude exceeded a preset threshold, it was marked as a region of abrupt change in icing thickness, resulting in a spatial distribution feature set containing gradient direction, rate of change, and local extrema.

[0078] For example, in one implementation, the non-uniform grid partitioning scheme is constructed based on historical icing data and meteorological condition analysis.

[0079] Specifically, by analyzing the topographic relief and wind field distribution characteristics along the transmission line, areas prone to icing accumulation are identified. These areas are typically located on windward slopes, in valleys, and in areas with drastic elevation changes. Higher grid density is set in these icing-prone areas, with grid spacing less than a preset first threshold. In areas with gentle terrain and relatively uniform historical icing, the grid spacing is greater than a preset second threshold, thus forming a grid structure with varying density.

[0080] For example, the application process of the inverse distance weighted interpolation method in calculating ice thickness includes: first, determining the search radius of the grid node to be interpolated, and selecting all measured monitoring points within the search radius; then, calculating the Euclidean distance from each monitoring point to the node to be interpolated, with the distance weighting coefficient in the form of a power of the reciprocal of the distance, and the power value determined according to the spatial correlation of the ice distribution; finally, obtaining the ice thickness interpolation result of the grid node by weighted average calculation.

[0081] It should be noted that when the number of monitoring points around a certain grid node is insufficient, the search radius is dynamically expanded until the minimum number of monitoring points is met, ensuring the reliability of the interpolation results. The ice thickness distribution field is essentially a two-dimensional numerical matrix, where each element corresponds to the ice thickness value of a grid node.

[0082] Preferably, the Sobel operator uses convolution kernels in two directions to calculate the gradient components in the horizontal and vertical directions, respectively, in the calculation of the icing thickness gradient. The horizontal convolution kernel detects the change in icing thickness along the longitudinal direction of the transmission line, while the vertical convolution kernel detects the change in icing thickness perpendicular to the line. By performing convolution operations on the icing thickness distribution field, the gradient magnitude and gradient direction angle of each grid point are obtained, where the gradient magnitude reflects the rate of change of icing thickness, and the gradient direction angle indicates the direction in which the icing thickness increases the fastest.

[0083] In one embodiment, the marking process for regions with abrupt changes in ice thickness employs an adaptive threshold determination, dynamically adjusting the threshold based on the statistical characteristics of the ice thickness gradient across the entire monitoring area. When the gradient magnitude of a grid point exceeds this adaptive threshold, that point is marked as a mutation point, and consecutive mutation points constitute a mutation region. The spatial distribution feature set not only includes the gradient direction and rate of change but also identifies local extreme points through local window scanning. These extreme points often correspond to ice accumulation centers or weak points in ice accumulation.

[0084] S107. The spatial distribution characteristics and thickness variation trend of the icing thickness gradient map are fused to extract the variation law of cable icing thickness and the correlation of wind direction disturbance.

[0085] Principal component analysis (PCA) is performed on the gradient direction and magnitude of each grid point in the icing thickness gradient map. The principal component with the largest contribution to variance is extracted as the spatial distribution principal feature. The difference between the current icing thickness and the previous icing thickness is calculated to obtain the thickness change value. The spatial distribution principal feature and the sequence of thickness change values ​​are multiplied by a matrix to obtain a spatiotemporal fusion feature matrix. Based on the spatiotemporal fusion feature matrix, the icing thickness time series and wind direction angle time series are extracted from the monitoring data. The difference between the icing thickness and the previous icing thickness at each moment is calculated as the thickness increment, and the difference between the wind direction angle and the previous icing thickness is calculated as the wind direction change. The Pearson correlation coefficient is used to calculate the correlation value between the thickness increment and the wind direction change. Fourier transform is performed on the correlation value sequence through a sliding window of preset length to extract the periodic component. Based on the periodic components, the main period of icing change is determined. The spatiotemporal fusion feature matrix is ​​segmented according to this period. The least squares method is used to fit the quadratic function of icing thickness with time and spatial location in each segment to obtain the variation law of cable icing thickness. The Pearson correlation coefficient between the thickness increment and the wind direction change is determined as the wind direction disturbance correlation.

[0086] For example, in one implementation, principal component analysis is used to extract the main spatial distribution patterns of the ice thickness gradient map. Each grid point in the gradient map contains two attributes: gradient direction and gradient magnitude. The attribute values ​​of all grid points constitute the original data matrix. By calculating the eigenvalues ​​and eigenvectors of the covariance matrix, the eigenvector with the largest variance contribution rate is selected as the first principal component. This principal component represents the main spatial pattern of ice distribution and reflects the overall distribution trend of ice over the span.

[0087] It should be noted that the purpose of spatiotemporal fusion is to combine spatial distribution characteristics with temporal evolution processes. The formation of icing not only has spatial heterogeneity but also temporal cumulative characteristics, and the fusion of the two can comprehensively describe the dynamic evolution process of icing.

[0088] Specifically, matrix multiplication achieves the fusion of spatial features and temporal series. The dimension of the spatial distribution principal feature vector corresponds to the number of spatial grid points, while the dimension of the thickness variation value sequence corresponds to the number of temporal sampling points. The spatiotemporal fusion feature matrix obtained by multiplying the two represents the intensity of icing change at a specific spatial location at a specific time. This fusion method preserves the integrity of the spatial pattern while introducing dynamic information in the temporal dimension.

[0089] Preferably, the Pearson correlation coefficient is calculated using standardized data. The thickness increment series and wind direction change series are first standardized to zero mean to eliminate dimensional effects. Then, the covariance of the two series is calculated by dividing the product of their respective standard deviations to obtain the correlation coefficient. The closer the absolute value of the correlation coefficient is to 1, the stronger the correlation between wind direction change and icing thickness change.

[0090] For example, in the monitoring of a certain transmission line, Fourier transform revealed two main cycles for icing changes: a 24-hour cycle and a 72-hour cycle. The 24-hour cycle corresponds to the cycle of icing melting and accumulation caused by diurnal temperature differences, while the 72-hour cycle corresponds to the influence cycle of weather systems passing through. Data was segmented based on these two cycles, and the icing changes within each segment exhibited a relatively stable pattern.

[0091] Understandably, the quadratic function obtained by least squares fitting can describe the spatial and temporal variation trend of icing thickness. The coefficient of the first term reflects the linear growth rate, the coefficient of the quadratic term reflects the acceleration or deceleration trend, and the constant term represents the initial icing thickness. This function can be used to predict the icing distribution over a certain period, providing decision support for power grid dispatching and de-icing operations.

[0092] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within this application. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for multi-source collaborative monitoring of overhead power transmission line icing, characterized in that, include: The process involves collecting data on icing thickness and wind direction within the span between transmission towers, analyzing the icing thickness gradient characteristics, determining the icing distribution and local thickness peaks of the cable within the span based on these gradient characteristics, determining the tension distribution state based on the icing distribution and local thickness peaks, determining the local load imbalance state based on the tension distribution state, determining the stress distribution under tension imbalance based on the local load imbalance state, and obtaining the magnitude of concentrated stress based on the stress distribution. The stress distribution is then adjusted based on the magnitude of the concentrated stress to obtain an adjusted stress distribution. Modal response switching points are identified based on the adjusted stress distribution, and spectral analysis is performed on these switching points to obtain an abnormal thickening characteristic distribution. The cable icing thickness gradient variation law is determined based on the abnormal thickening characteristic distribution, spatial gradient variation characteristics are extracted from the icing thickness gradient variation law, and the probability of cable icing detachment is determined based on the abnormal thickening characteristic distribution and spatial gradient variation characteristics. Finally, a risk distribution map is generated based on the icing detachment probability. High-risk area features are extracted from the risk distribution map, high-risk areas are identified based on the high-risk area features, wind direction disturbance and icing thickness of the high-risk areas are obtained, and the icing detachment probability of the high-risk areas is obtained by fusing them. The ice distribution is divided into grids, and an ice thickness gradient map is obtained through spatial interpolation analysis. Spatial distribution features are then extracted based on the ice thickness gradient map. The spatial distribution characteristics and thickness variation trends are fused to obtain the variation law of cable icing thickness and its correlation with wind direction disturbance.

2. The method for multi-source collaborative monitoring of overhead power transmission icing according to claim 1, characterized in that, The ice thickness and wind direction within the span between transmission towers are collected, and the ice thickness gradient characteristics are analyzed. Based on these ice thickness gradient characteristics, the ice distribution and local thickness peaks of the cables within the span are determined, including: Ice thickness monitoring points are set at preset intervals within the span between transmission lines to obtain the distance value of the ice surface at each monitoring point. The ice thickness at each monitoring point is determined based on the difference between the original cable radius and the distance value. Wind direction sensors are deployed at the same locations to obtain wind direction angle and wind speed data, forming an ice thickness time series dataset and a wind direction time series dataset. Based on the ice thickness time series dataset, the time gradient is obtained by dividing the thickness difference between adjacent time points by the time interval, the spatial gradient is obtained by dividing the thickness difference between adjacent monitoring points by the spatial distance, and the thickness change rate is obtained by dividing the difference between the maximum and minimum thickness values ​​within a preset time window by the length of the time window. An ice thickness gradient feature matrix is ​​constructed based on the time gradient, spatial gradient, and thickness change rate. The ice thickness between monitoring points is processed by cubic spline interpolation to obtain a continuous ice distribution curve within the span. The first derivative of the ice distribution curve along the span direction is calculated, and the position where the derivative is zero is determined as a candidate point for local thickness peak. The effective local thickness peak is determined based on the ratio of the ice thickness at the candidate point to the average thickness of the adjacent area.

3. The method for multi-source collaborative monitoring of overhead power transmission icing according to claim 1, characterized in that, The process of determining the tension distribution state based on the icing distribution and local thickness peak, determining the local load imbalance state based on the tension distribution state, determining the stress distribution during tension imbalance based on the local load imbalance state, and obtaining the magnitude of concentrated stress based on the stress distribution includes: The span is divided into multiple calculation units. The load value of each unit is calculated based on the icing distribution and local thickness peak. The vertical displacement and horizontal tension of each unit node are calculated, and the tension balance equations are solved to obtain the tension distribution state. Based on the tension distribution state, the ratio of the tension difference between adjacent units to the average tension is calculated as an imbalance index. The local load imbalance state is determined based on the imbalance index and load eccentricity. Based on the local load imbalance state, the additional bending moment generated by the load eccentricity is converted into bending stress of the conductor section. The axial tension of the conductor is divided by the cross-sectional area to obtain the axial tensile stress. The bending stress and axial tensile stress are superimposed to obtain the stress distribution when tension is unbalanced. The stress maximum point is extracted, and the ratio of the stress maximum value to the surrounding average stress is calculated as the stress concentration factor. The magnitude of the concentrated stress is determined based on the stress maximum value and the stress concentration factor.

4. The method for multi-source collaborative monitoring of overhead power transmission line icing according to claim 1, characterized in that, The process of adjusting the stress distribution according to the magnitude of the concentrated stress to obtain an adjusted stress distribution, identifying modal response switching points based on the adjusted stress distribution, and performing spectral analysis on the modal response switching points to obtain an abnormal thickening characteristic distribution includes: The stress adjustment coefficient is calculated based on the difference between the magnitude of the concentrated stress and the preset stress threshold. The stress value at each point in the stress distribution is multiplied by the stress adjustment coefficient to obtain the adjusted stress distribution. The stiffness change value of each segment of the conductor is calculated based on the adjusted stress distribution. The difference in stiffness change values ​​between adjacent segments is compared to determine the modal response switching point. Vibration signals are collected at the modal response switching point and at a preset distance before and after it. The vibration time-domain signal is converted into a frequency-domain signal. The amplitude and power spectral density of each frequency component are extracted. The frequency distribution is determined based on the proportion of the power spectral density to the total power. The peak frequency and amplitude are extracted based on the frequency distribution. The difference between adjacent peak frequencies and the rate of change of amplitude are calculated and combined to form an abnormal thickening feature distribution.

5. The method for multi-source collaborative monitoring of overhead power transmission line icing according to claim 1, characterized in that, The process of determining the cable icing thickness gradient variation law based on the abnormal thickening feature distribution, extracting spatial gradient variation features from the icing thickness gradient variation law, determining the cable icing detachment probability based on the abnormal thickening feature distribution and spatial gradient variation features, and generating a risk distribution map based on the icing detachment probability includes: Based on the frequency distribution and amplitude variation in the abnormal thickening feature distribution, spectral feature parameters are arranged according to spatial location. The difference in feature parameters between adjacent monitoring points is calculated as the feature gradient. The ice thickness gradient variation function is obtained by fitting using the least squares method. The gradient direction is determined by calculating the angle between the gradient vector and the horizontal direction from the variation function. The rate of change is obtained by dividing the difference in gradient values ​​between adjacent points by the spatial interval. The location where the derivative is zero is determined as the local extreme point. These are combined to form the spatial gradient variation feature. Based on the abnormal thickening feature distribution and the spatial gradient variation feature, the probability of ice shedding is calculated using Bayesian inference. The historical shedding frequency is set as the prior probability, and the reciprocal of the Euclidean distance of the feature parameter is used as the likelihood to calculate the probability of ice shedding at each monitoring point. Based on the ice shedding probability, the span is divided into grid cells, the risk value of each cell is calculated, the risk level is divided and assigned a color, and a risk distribution map is generated.

6. The method for multi-source collaborative monitoring of overhead power transmission line icing according to claim 1, characterized in that, The process of extracting high-risk area features from the risk distribution map, identifying high-risk areas based on these features, obtaining wind direction disturbances and icing thickness in the high-risk areas, and fusing them to obtain the icing shedding probability of the high-risk areas includes: Grid cells with risk values ​​exceeding a preset high-risk threshold are extracted from the risk distribution map. Connecting regions formed by adjacent high-risk grids are identified, and the area of ​​the region is calculated by multiplying the number of grids in the connected region by the area of ​​a single grid cell. The risk level is determined based on the highest risk value within the region. Wind direction sensor data from monitoring points within the high-risk region are read, and the square root of the sum of the squares of the differences between the wind direction angle and the average wind direction angle is calculated by dividing by the number of monitoring points to obtain the standard deviation of wind direction disturbance. The weighted average value of icing thickness within the region is calculated. A fusion coefficient is determined by querying a fuzzy rule table based on the standard deviation of wind direction disturbance and the regional icing thickness. The detachment probability value of the region in the risk distribution map is multiplied by the fusion coefficient to obtain the fused icing detachment probability.

7. The method for multi-source collaborative monitoring of overhead power transmission line icing according to claim 1, characterized in that, The process of dividing the ice distribution into grids, obtaining an ice thickness gradient map through spatial interpolation analysis, and extracting spatial distribution features based on the ice thickness gradient map includes: The ice distribution is divided into grids, and an ice thickness gradient map is generated by cubic spline interpolation. The gradient direction and gradient magnitude of each grid point are extracted from the ice thickness gradient map. The gradient direction is determined by calculating the angle between the gradient vector and the horizontal direction. The rate of change is obtained by calculating the difference in gradient values ​​between adjacent grid points and dividing by the spatial interval. The local extreme points are determined by finding the position where the derivative is zero. These are combined to form the spatial distribution characteristics.

8. The method for multi-source collaborative monitoring of overhead power transmission line icing according to claim 1, characterized in that, The process of fusing the spatial distribution characteristics and thickness variation trends to obtain the cable icing thickness variation law and its correlation with wind direction disturbance includes: Principal component analysis is performed on the gradient direction and gradient magnitude in the spatial distribution features. The principal component with the largest contribution to the variance is extracted as the main feature of the spatial distribution. The thickness change value is obtained by calculating the difference in ice thickness. The sequence of the main feature of the spatial distribution and the sequence of thickness change value are multiplied by matrix to obtain the spatiotemporal fusion feature matrix. The time series of ice thickness and wind direction angle are extracted. The thickness increment and wind direction change are calculated. The correlation value between the thickness increment and the wind direction change is calculated using the Pearson correlation coefficient. The periodic component is extracted by Fourier transform of the correlation value sequence through a sliding window. The ice thickness change law is obtained by fitting a quadratic function according to the periodic component. The correlation value is determined as the correlation of wind direction disturbance.

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