Overhead line freezing rain falling area icing thickness probability prediction method and model thereof
By constructing a probabilistic prediction model for icing thickness that integrates physical mechanisms and data-driven approaches, the uncertainty problem in icing thickness prediction in existing technologies has been solved, achieving more accurate and reliable icing thickness prediction and supporting risk assessment and prevention and control decisions in power systems.
Patent Information
- Application Number
- CN202610512119.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-17
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies lack physical mechanism constraints in predicting icing thickness, cannot quantify prediction uncertainties, and are difficult to support refined prevention and control decisions under risk warning conditions.
A probabilistic prediction model for icing thickness in freezing rain areas of overhead power lines is developed by integrating physical mechanisms and data-driven methods. This model is constructed by building a freezing rain event prediction model and an icing thickness probabilistic prediction model. It is trained using a long short-term memory network and a Gaussian process combined with a composite loss function. Non-negativity constraints on icing thickness, temperature constraints, and consistency constraints on icing growth are introduced to achieve probabilistic prediction and uncertainty quantification.
It improves the accuracy and reliability of icing thickness prediction, provides a basis for risk assessment of power systems, and helps to formulate more reasonable anti-icing and anti-icing measures.
Smart Images
Figure CN122047016A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system icing prediction technology, and more specifically, to a method and model for predicting the probability of icing thickness in the freezing rain zone of overhead lines. Background Technology
[0002] Freezing rain and snow disasters are among the natural disasters that seriously affect the safe and stable operation of power grids. Icing on transmission lines, especially rime ice caused by freezing rain, can drastically increase conductor load and seriously threaten the power supply reliability of the power system. Accurate prediction of icing thickness can provide decision-making reference for ice prevention and disaster reduction, and is of great significance and engineering application value for the safe operation of overhead transmission lines.
[0003] However, the icing formation process involves multi-scale coupling of microphysical phase transitions, complex topographic flow fields, and stochastic meteorological factors. Its uncertainties include both the accidental uncertainties of the physical processes and the cognitive uncertainties of the data-driven models themselves. Currently, most studies on icing thickness prediction are still limited to deterministic point prediction paradigms, lacking effective quantification of the uncertainty of prediction results, making it difficult to support refined prevention and control decisions under risk warning conditions.
[0004] Therefore, it is necessary to establish a probabilistic prediction model for the icing thickness of overhead lines by integrating mechanistic data, so as to realize the probabilistic prediction of the icing thickness of overhead lines and provide a reference basis with uncertainty quantification capability for risk perception and decision-making in power grid icing prevention and control. Summary of the Invention
[0005] This invention overcomes the shortcomings of existing icing thickness prediction methods, which lack physical mechanism constraints and cannot quantify prediction uncertainties. It provides a probabilistic prediction method and model for icing thickness in the freezing rain area of overhead lines. It can integrate the advantages of physical mechanisms and data-driven methods to achieve probabilistic prediction and uncertainty quantification of icing thickness, thereby improving prediction accuracy and reliability.
[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for probabilistically predicting the icing thickness in the freezing rain zone of overhead power lines includes the following steps: S1. Construct and train a freezing rain event prediction model to predict freezing rain events based on meteorological data. The prediction objects include the location and severity level of freezing rain. S2. Based on long short-term memory networks and Gaussian processes, construct a probabilistic prediction model for the icing thickness of overhead power lines; S3. Construct a composite loss function that integrates the mechanism penalty, and train the probability prediction model for icing thickness of overhead lines based on the composite loss function. S4. Based on step 1, identify areas with the risk of overhead line icing. Input the real-time micro-meteorological time series data of these areas into the overhead line icing thickness probability prediction model trained in step S3 to make predictions and achieve the prediction of icing thickness.
[0007] Preferably, step S1 includes the following steps: S11. Collect meteorological data for the study area; S12, Normalization process; S13. Employ synthetic minority oversampling techniques to enhance the characterization of freezing rain samples in meteorological data and generate sample data; S14. Construct a mild gradient boosting machine model, train and test the mild gradient boosting machine model with sample data, wherein the gradient boosting machine model extracts sample data as input through a preset feature vector table; S15. Set the division criteria, access real-time weather forecast data, and predict the location and severity of freezing rain events based on the prediction results.
[0008] Preferably, step S2 includes the following steps: S21. Construct a long short-term memory network to map variable-length meteorological time series inputs into fixed-dimensional feature vectors; S22. Construct a Gaussian process and use the feature vectors extracted by the Long Short-Term Memory network as input to the Gaussian process for Bayesian inference.
[0009] As a preferred option, the composite loss function is a weighted sum of the basic loss term, the mechanism loss term, and the L2 regularization term, wherein the mechanism loss term and the L2 regularization term are weighted by adjusting the mechanism loss coefficient and the regularization coefficient, respectively.
[0010] As a preferred option, the mechanistic loss term includes: a non-negative constraint on icing thickness, and the loss term is constructed to penalize predictions where the icing thickness is negative.
[0011] As a preferred option, the mechanistic loss term includes: a temperature constraint, which is used to construct a loss term to penalize the predicted icing growth at temperatures above a preset temperature.
[0012] As a preferred option, the mechanistic loss term includes: an ice growth consistency constraint, which is used to construct the loss term to penalize predictions that violate the Makkonen mechanistic model.
[0013] Preferably, the Gaussian inference process of S22 includes a mean function and a covariance function, wherein the mean function... For constant functions, radial basis functions are chosen for the covariance function.
[0014] As preferred options, the training evaluation metrics for a mild gradient booster model include area under the curve, accuracy, precision, recall, and F-score; the training evaluation metrics for a long short-term memory network include root mean square error, mean absolute error, and coefficient of determination; and the training evaluation metrics for a Gaussian process include the prediction interval coverage reliability index and the prediction interval average width.
[0015] A probabilistic prediction model for icing thickness in freezing rain zones of overhead power lines includes: The freezing rain event prediction module predicts freezing rain events based on meteorological data, including the location and severity of freezing rain. The overhead power line icing thickness probability prediction module includes a long short-term memory network and a Gaussian process; And a composite loss function module that incorporates mechanism penalties.
[0016] Compared with the prior art, the beneficial effects of the present invention are: (1) By introducing non-negative constraints on icing thickness, temperature constraints and consistency constraints on icing growth through a composite loss function, the prediction results are ensured to conform to physical laws, thereby improving the accuracy and reliability of the prediction.
[0017] (2) The Gaussian process was used to realize the probability prediction and uncertainty quantification of ice thickness, which provided a basis for risk assessment of power system operation and helped to formulate more reasonable anti-icing measures. Attached Figure Description
[0018] Figure 1 This is a schematic diagram of the model architecture of the present invention; Figure 2 This is a visualization of the prediction results from the freezing rain event prediction model of this invention; Figure 3 This is a visualization of the overhead line icing thickness probability prediction model of the present invention; Figure 4 This is a comparison chart of the prediction and actual measurement of the overhead line icing thickness probability prediction model of the present invention. Detailed Implementation
[0019] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.
[0020] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0021] Example: like Figure 1 As shown, a method for probabilistically predicting the icing thickness in the freezing rain zone of overhead power lines includes the following steps: S1. Construct and train a freezing rain event prediction model to predict freezing rain events based on meteorological data. The prediction objects include the location and severity level of freezing rain. S2. Based on long short-term memory networks and Gaussian processes, construct a probabilistic prediction model for the icing thickness of overhead power lines; S3. Construct a composite loss function that integrates the mechanism penalty, and train the probability prediction model for icing thickness of overhead lines based on the composite loss function. S4. Based on step 1, identify areas with the risk of overhead line icing. Input the real-time micro-meteorological time series data of these areas into the overhead line icing thickness probability prediction model trained in step S3 to make predictions and achieve the prediction of icing thickness.
[0022] The prediction process utilizes two models: first, a freezing rain event prediction model, which predicts the location and severity of freezing rain; and second, a probability prediction model for overhead power line icing thickness, which predicts the icing thickness of overhead power lines based on more detailed micro-meteorological time-series data. The freezing rain event prediction model provides a coarse screening, while the overhead power line icing thickness probability prediction model provides a finer screening, adhering to the physical laws of icing formation (ice rain is required for icing to form on overhead power lines), thus reducing the computational power requirements.
[0023] Step S1, which involves building and training a freezing rain event prediction model, specifically includes the following steps: S11. Collect meteorological data for the study area; S12, Normalization process; S13. Employ synthetic minority oversampling techniques to enhance the characterization of freezing rain samples in meteorological data and generate sample data; S14. Construct a mild gradient boosting machine model, train and test the mild gradient boosting machine model with sample data, wherein the gradient boosting machine model extracts sample data as input through a preset feature vector table; S15. Set the division criteria, access real-time weather forecast data, and predict the location and severity of freezing rain events based on the prediction results.
[0024] The meteorological data used is high-precision ERA5 meteorological data for the study area. While introducing meteorological data from outside the study area might increase the model's generalization ability, the typical regional nature of meteorological data means that pursuing high generalization could lead to dimensionality explosion in the model. Therefore, only meteorological data from the study area is used for model training and prediction. The study area refers to a set of regions with similar climatic characteristics. The data includes relative humidity, absolute humidity, temperature, vertical wind speed, rainfall type, longitude, and latitude at the surface and multiple pressure levels, with a time resolution of 1 hour and a horizontal resolution of 31 kilometers.
[0025] The normalization expression is as follows:
[0026] In the formula, For normalized meteorological elements, As the original meteorological elements, for The minimum value, for The maximum value. Normalize the data and scale it proportionally to the range of 0-1 to ensure that the normalization process has no impact on the model's training and prediction results.
[0027] Next, synthetic minority oversampling was used to enhance the representational ability of freezing rain samples in meteorological data, forming sample data. Since freezing rain is an extreme weather event, the number of freezing rain samples in the sample data is relatively small (less than 1%). In order for the prediction model to capture the characteristics of freezing rain climate during training, synthetic minority oversampling was used to expand the number of freezing rain climate samples, thereby strengthening the representational ability of freezing rain as a minority sample.
[0028] The sample data is divided into training set and test set according to a preset ratio. In some embodiments, the ratio is 80%:20%.
[0029] Next, model construction is performed. This application employs the Light Gradient Boosting Machine (LightGBM) model. For categorical features in meteorological data (such as weather type), the LightGBM model does not require one-hot encoding and directly processes categorical features, simplifying the feature engineering process. Based on this, a feature variable table is set up according to the formation principle of freezing rain. Sample data is input into the LightGBM in the format of the feature variable table to reduce data dimensionality, improve training efficiency and generalization ability, and avoid the model learning spurious associations. The feature variable table is shown in the table below:
[0030] The mild gradient booster was evaluated using a test set after training. Specifically, Area Under the Curve (AUC), Accuracy (ACC), Precision, Recall, and F-Score (F) were selected as evaluation metrics to assess model performance from multiple dimensions. AUC, the area under the receiver operating characteristic curve, measures the model's overall performance in terms of true positive and false positive rates at different thresholds; ACC is the proportion of correctly predicted samples to the total number of samples, reflecting the model's overall classification accuracy; and the F-score is a weighted average of recall and precision, used to balance the model's ability to capture minority classes with its prediction accuracy.
[0031] For a light gradient booster that has completed training and passed the training index acceptance, it is connected to the weather forecast data for the next few days provided by numerical weather prediction, and automated prediction is achieved by connecting to the pipeline.
[0032] Finally, the classification criteria are set, and freezing rain events are divided into different levels based on the duration and predicted probability of freezing rain, such as light freezing rain, weak freezing rain, moderate freezing rain, heavy freezing rain, and extremely heavy freezing rain. In some embodiments, the specific classification criteria are shown in the table below:
[0033] Based on the aforementioned classification criteria, the results of the predictions made by the mild gradient lift machine on the input meteorological data are classified to obtain the location and severity level of freezing rain events.
[0034] In some embodiments, based on the prediction results, the data is classified according to the classification criteria and then visualized using a visualization component in conjunction with a map.
[0035] In this step, we can exclude a large number of non-freezing rain weather events, as well as icing rain events that are insufficient to affect overhead lines, thereby saving the model's computational power.
[0036] If a freezing rain event sufficient to affect overhead lines is detected, such as freezing rain of severe freezing rain level or above, the next step of processing the line icing probability prediction will be carried out.
[0037] The process is as follows: S21. Construct a long short-term memory network to map variable-length meteorological time series inputs into fixed-dimensional feature vectors; S22. Construct a Gaussian process and use the feature vectors extracted by the Long Short-Term Memory network as input to the Gaussian process for Bayesian inference.
[0038] In step S21, long-term time-series data in the form of micrometeorological data (temperature, wind speed, humidity, etc., change dynamically over time, directly affecting the growth / melting of icing) is used as the model input. Traditional recurrent neural networks (RNNs) suffer from the vanishing gradient problem and cannot capture the dependencies in long-term time-series data; while long short-term memory networks (LSTMs), through gating mechanisms of input gates, forget gates, and output gates, can selectively retain key information in time-series data and forget irrelevant information, effectively solving the vanishing gradient problem and accurately capturing the long-term dependencies and dynamic changes in micrometeorological time-series data during the icing process. LSTM maps variable-length micrometeorological time-series inputs (such as temperature, wind, and humidity data from five consecutive monitoring times) to fixed-dimensional feature vectors, extracting the core information from the time-series data and providing high-quality, highly concentrated feature inputs for the subsequent probability prediction of the GP layer.
[0039] In some embodiments, the input to the Long Short-Term Memory (LSTM) network also includes the physical orientation of the overhead line, including its position, angle, tension, and tilt angle. This data, along with time-series data and icing thickness data, is input into the LTM network after normalization.
[0040] Specifically, the aforementioned micro-meteorological time-series data is transformed into corresponding input features. This application provides an input feature table as an example, as shown in the table below:
[0041] Specifically, the real-time micro-meteorological time-series data of the aforementioned freezing rain weather with a severity level of 3 or higher will be used. The input is fed into a long short-term memory network to extract a fixed-dimensional feature vector. The process is as follows:
[0042] In the formula, This is the parameter vector of the Long Short-Term Memory network; model training involves optimizing these parameters.
[0043] In step S22, the Gaussian process (GP) is fully defined by the mean function and the covariance function, where the mean function... The mean function is a constant, and the covariance function uses a radial basis function kernel. Setting the mean function directly as a constant helps simplify the model while ensuring the robustness of Bayesian inference, avoiding the introduction of additional model errors by complex mean functions. As a smooth nonlinear kernel function, the radial basis function can accurately characterize the complex nonlinear relationship between LSTM feature vectors and ice thickness, and can also calculate the covariance matrix between any two input features, providing a foundation for Bayesian inference. Through Bayesian inference, the GP layer outputs a probability distribution of ice thickness (rather than a single value) based on the input LSTM features, laying the theoretical foundation for subsequent output point predictions and prediction intervals at different confidence levels.
[0044] Specifically, the inference process expression of GP is as follows:
[0045] in, For the output of GP, Let be the mean function of a Gaussian process. Let covariance function be used. For input variables.
[0046] Next, the probability prediction model for icing thickness of overhead power lines, composed of a long short-term memory network and a Gaussian process, is trained. The core of this model lies in the definition of the loss function.
[0047] The loss function has a built-in mechanistic loss term, which constrains the model by setting a penalty term, thereby ensuring the consistency between the model and the actual physical phenomenon.
[0048] Specifically, the composite loss function is a weighted sum of the basic loss term, the mechanistic loss term, and the L2 regularization term. The mechanistic loss term and the L2 regularization term are weighted by adjusting the mechanistic loss coefficient and the regularization coefficient, respectively. The expression is as follows:
[0049] in, For composite loss function, Basic loss term, For mechanism loss term, This is an L2 regularization term.
[0050] Considering the Gaussian process model, the basic loss term is expressed as a negative marginal log-likelihood, which measures the likelihood of the model given the data.
[0051] Where x is the feature vector extracted from the selected high-risk micro-meteorological time series information through a long short-term memory network, and y is the measured value of the corresponding icing thickness.
[0052] The mechanistic loss term includes one or more of the following: non-negativity constraint on icing thickness, temperature constraint, and consistency constraint on icing growth. Preferably, it includes three terms, and this application uses three mechanistic loss terms as an example.
[0053]
[0054] in, Assuming a non-negative constraint on icing thickness, For temperature constraints, To ensure consistency in icing growth, Constraints on the consistency of ice melting.
[0055] The principle behind the non-negativity constraint on icing thickness is that the predicted probability result indicates the icing thickness generated by the model might be negative. To avoid negative values, a penalty term is set to constrain the model, and its expression is:
[0056] In the formula, Let be the ice thickness predicted by the model for i samples. This represents the sample size. When the predicted value is negative, this loss value generates a positive loss, thus guiding the model to adjust its parameters to reduce negative predictions; otherwise, a reward is given.
[0057] The principle of temperature constraint is that when the ambient temperature is significantly higher than the freezing point of water, liquid water cannot freeze on the surface of the conductor to form icing, and existing ice layers will begin to melt. Therefore, the model should not predict the growth of icing thickness under high-temperature environments. Its expression is:
[0058] In the formula, Let i be the ambient temperature of the i-th sample. This is the threshold temperature; the temperature at which frost forms is between -3 and 0 degrees Celsius, and it is set to 2 degrees Celsius here. This represents the icing thickness predicted by the model for the i-th sample. Let represent the change in ice thickness for the i-th sample. When the ambient temperature is significantly higher than the freezing point, this loss value generates a positive loss, thereby guiding the model to adjust its parameters to reduce the prediction of ice growth under high-temperature conditions; otherwise, a reward is given.
[0059] The principle of the consistency constraint on the direction of icing growth is as follows: The icing process is a phase change mechanism driven by meteorological conditions. Its growth or melting direction is synergistically controlled by key factors such as temperature, humidity, wind speed, and precipitation. Icing growth and melting is a continuous process, and its direction of change should be consistent with meteorological conditions. In analyzing the wet growth mechanism of rime ice, Makkonen used the previously established icing theory model, as shown in the following equation:
[0060] In the formula, M is the icing mass per unit length of conductor, V is the current wind speed, R is the conductor radius, and L is the conductor length. Angular frequency, This is the collision rate of the liquid water droplets at this moment. For liquid water droplet capture rate, The freezing rate of liquid water droplets.
[0061] When the model predicts a significant increase in icing, the icing thickness should not decrease:
[0062] When the model predicts significant melting of the ice cover, the ice thickness should not increase:
[0063] In the formula, Let be the predicted icing growth rate for the t-th sample. Let be the predicted value for the t-th sample. is the threshold, and N is the time length sequence.
[0064] The L2 regularization term is used to prevent the model from degrading its generalization performance due to overfitting the training data. Its expression is:
[0065] In the formula, It is the first in the model A weight matrix.
[0066] The load loss function was used as the objective function to train an overhead power line icing thickness probability prediction model composed of a Long Short-Term Memory (LSTM) network and a Gaussian process. The network parameters of the LSTM and the hyperparameters of the Gaussian process were simultaneously optimized by maximizing the predicted log-likelihood of the training data.
[0067] The log-likelihood function is:
[0068] pass Fit the data to measure the deviation between the predicted and actual values; through Complexity penalty is used to measure the uncertainty of a model and balance the goodness of fit. As a constant term.
[0069] The model is trained using the above process and sample data. The model is then evaluated. For deterministic training of Long Short-Term Memory (LSTM) networks, the evaluation metrics include root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). For uncertain training of Gaussian processes, the evaluation metrics include prediction interval coverage (PICP), reliability index (RI), and average prediction interval width (AIW).
[0070] In some embodiments, the model's predictions are analyzed through visualization analysis, which combines visualization with maps.
[0071] Verification example: This application uses ERA5 meteorological data from 2008, 2013, and 2016 as samples, dividing the dataset into a training set (first 70% of the time series data) and a test set (last 30% of the time series data) to train and evaluate the freezing rain event prediction model. The model will be validated in February 2024.
[0072] Since this is a probabilistic prediction model for the thickness of ice accretion on overhead power lines, the sample used is a sample set consisting of ice rain climate and ice accretion thickness pairs. The first 70% of the time series data in the dataset is used as the training set, and the last 30% of the time series data is used as the test set.
[0073] The actual ice thickness data of an overhead transmission line in Huzhou City, Zhejiang Province, in February 2024 was selected for verification. This tower is located in Anji County, Huzhou City, within an area experiencing severe freezing rain. The dataset contains complete synchronous monitoring records of meteorological elements and ice thickness, with a time resolution of 10 minutes, covering the key development stages of the entire freezing rain process. The first 70% of the time-series data was used as the training set, and the last 30% as the test set. Feature data from five consecutive monitoring times, totaling 40 minutes, were used as input to predict the ice thickness three hours later.
[0074] The evaluation metrics for the final mild gradient booster model are shown in the table below:
[0075] The final deterministic evaluation index of the long short-term memory network corresponding to the probabilistic prediction model for icing thickness of overhead power lines is shown in the table below:
[0076] The uncertainty indices of the corresponding Gaussian process at different confidence levels are shown in the table below:
[0077] Based on the model described above, a 3-hour advance prediction of the freezing rain duration is made, and the resulting visualization is shown below. Figure 2As shown in Figure 4, the actual ice thickness detected and the model prediction are compared. The visualization of the ice thickness prediction for each region is shown in Figure 5. Figure 3 As shown.
[0078] Based on this, a probabilistic prediction model for icing thickness in freezing rain zones of overhead power lines is also provided, including: The freezing rain event prediction module predicts freezing rain events based on meteorological data, including the location and severity of freezing rain. The overhead power line icing thickness probability prediction module includes a long short-term memory network and a Gaussian process; And a composite loss function module that incorporates mechanism penalties.
[0079] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Other variations and modifications may be made without departing from the technical solutions described in the claims.
Claims
1. A method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines, characterized in that, Includes the following steps: S1. Construct and train a freezing rain event prediction model to predict freezing rain events based on meteorological data. The prediction objects include the location and severity level of freezing rain. S2. Based on long short-term memory networks and Gaussian processes, construct a probabilistic prediction model for the icing thickness of overhead power lines; S3. Construct a composite loss function that integrates the mechanism penalty, and train the probability prediction model for icing thickness of overhead lines based on the composite loss function. S4. Based on step 1, identify areas with the risk of overhead line icing. Input the real-time micro-meteorological time series data of these areas into the overhead line icing thickness probability prediction model trained in step S3 to make predictions and achieve the prediction of icing thickness.
2. The method for predicting the probability of icing thickness in the freezing rain zone of overhead power lines according to claim 1, characterized in that, Step S1 includes the following steps: S11. Collect meteorological data for the study area; S12, Normalization process; S13. Employ synthetic minority oversampling techniques to enhance the characterization of freezing rain samples in meteorological data and generate sample data; S14. Construct a mild gradient boosting machine model, train and test the mild gradient boosting machine model with sample data, wherein the gradient boosting machine model extracts sample data as input through a preset feature vector table; S15. Set the division criteria, access real-time weather forecast data, and predict the location and severity of freezing rain events based on the prediction results.
3. The method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines according to claim 1, characterized in that, Step S2 includes the following steps: S21. Construct a long short-term memory network to map variable-length meteorological time series inputs into fixed-dimensional feature vectors; S22. Construct a Gaussian process and use the feature vectors extracted by the Long Short-Term Memory network as input to the Gaussian process for Bayesian inference.
4. The method for predicting the probability of icing thickness in the freezing rain zone of overhead power lines according to claim 1, characterized in that, The composite loss function is a weighted sum of the basic loss term, the mechanism loss term, and the L2 regularization term, where the mechanism loss term and the L2 regularization term are weighted by adjusting the mechanism loss coefficient and the regularization coefficient, respectively.
5. The method for predicting the probability of icing thickness in the freezing rain zone of an overhead power line according to claim 4, characterized in that, The mechanism loss term includes: non-negative constraint on icing thickness, and the loss term is constructed to penalize the prediction results when the icing thickness is negative.
6. The method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines according to claim 4, characterized in that, The mechanistic loss term includes: temperature constraint, which is used to penalize the predicted icing growth at temperatures above the preset temperature.
7. The method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines according to claim 4, characterized in that, The mechanistic loss term includes: icing growth consistency constraints, which are used to penalize predictions that violate the Makkonen mechanistic model.
8. The method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines according to claim 3, characterized in that, Gauss's inference process in S22 includes the mean function and the covariance function, where the mean function... For constant functions, radial basis functions are chosen for the covariance function.
9. The method for probabilistic prediction of icing thickness in freezing rain zones of overhead power lines according to claim 2, characterized in that, The training evaluation metrics for a mild gradient booster model include area under the curve, accuracy, precision, recall, and F-score; the training evaluation metrics for a long short-term memory network include root mean square error, mean absolute error, and coefficient of determination; and the training evaluation metrics for a Gaussian process include prediction interval coverage, reliability index, and average prediction interval width.
10. A probabilistic prediction model for icing thickness in freezing rain zones along overhead power lines, characterized in that, include: The freezing rain event prediction module predicts freezing rain events based on meteorological data, including the location and severity of freezing rain. The overhead power line icing thickness probability prediction module includes a long short-term memory network and a Gaussian process; And a composite loss function module that incorporates mechanism penalties.