A physical mechanism constraint and multi-source data feature fusion power transmission line icing prediction method

Abstract

The application discloses a power transmission line icing prediction method based on physical mechanism constraint and multi-source data feature fusion, relates to the field of power transmission line icing prediction, and can effectively capture the dynamic change trend of the icing thickness by dynamically correcting key physical parameters as learnable latent variables, thereby providing a new approach with physical interpretability and data adaptability for power transmission line icing thickness prediction. Furthermore, by effectively coupling the global constraint of the physical equation and the local time sequence modeling advantage of the LSTM, the physical characteristic parameters and the data features are fully fused, and the accuracy and robustness of the power transmission line icing thickness prediction are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of transmission line icing prediction, specifically to a method for predicting transmission line icing by fusing physical mechanism constraints with multi-source data features. Background Technology

[0002] Under the threat of low temperatures, rain, snow, and freezing weather, the surface of power lines becomes covered with ice due to the collision and freezing of supercooled water droplets. This increases the mechanical load on the power lines and the sag, potentially leading to line galloping, insulator flashover, or even line breakage and tower collapse. Therefore, icing disasters on transmission lines are one of the core challenges threatening the safe and stable operation of the power grid.

[0003] Currently, transmission line icing prediction methods mainly fall into three categories: First, statistical correlation methods based on icing disaster-related parameters. These methods have low computational cost and good real-time performance, enabling rapid prediction. However, their nonlinear modeling capabilities are limited, and they are highly dependent on data quality, limiting their predictive performance under complex meteorological conditions. Second, physical process simulation methods considering environmental factors. These methods focus more on characterizing the icing mechanism, possessing strong interpretability and mechanistic support, and can adapt to complex environments. However, they suffer from low computational efficiency, poor adaptability to extreme meteorological conditions, and insufficient generalization ability, making them difficult to directly apply to large-scale transmission line icing thickness prediction. Third, data-driven modeling methods based on machine learning. These methods can effectively extract temporal features and improve prediction accuracy. However, they still have significant limitations in reflecting the nonlinear physical characteristics and mechanistic explanations of icing, and are sensitive to noise and lack robustness. Transmission line icing is a significant hazard threatening the safe operation of the power grid. Traditional methods for predicting icing thickness suffer from inaccuracy, poor adaptability, and limitations imposed by complex environmental factors. Summary of the Invention

[0004] One objective of this invention is to provide a method for predicting icing thickness of transmission lines by fusing physical mechanism constraints with multi-source data features. By dynamically correcting key physical parameters as learnable latent variables, this method can effectively capture the dynamic trend of icing thickness changes, providing a new approach for predicting icing thickness of transmission lines that combines physical interpretability and data adaptability. Furthermore, by effectively coupling the global constraints of physical equations with the local temporal modeling advantages of LSTM, this method fully integrates physical characteristic parameters and data features, effectively improving the accuracy and robustness of icing thickness prediction for transmission lines.

[0005] This objective is achieved using the following technical solution:

[0006] A method for predicting icing on transmission lines by fusing physical mechanism constraints with multi-source data features includes:

[0007] Step S1: Obtain ice thickness data and meteorological data, and preprocess the ice thickness data and meteorological data;

[0008] Step S2: Select features from the preprocessed meteorological data and filter out key features that conform to the physical laws of ice formation as input features of the PINN-LSTM model;

[0009] Step S3: Load the input features into the trained PINN-LSTM model. The trained PINN-LSTM model is used to dynamically correct physical parameters based on the input features to obtain the predicted icing thickness of the transmission line.

[0010] Among them, in the micro-topographic areas traversed by transmission lines, micro-topographic areas refer to local areas with a lateral spatial range typically ranging from several meters to hundreds of meters and a relative elevation difference ranging from centimeters to several meters, against the backdrop of mountains, hills, and other terrain features. Due to the local topographic undulations, the key attributes of local meteorological conditions in these areas deviate significantly from the average values ​​of the surrounding areas. Under the influence of local meteorological conditions, physical parameters such as the liquid water content in the air (…) ) and collision efficiency ( Parameters such as collision efficiency exhibit strong nonlinear fluctuation characteristics. Conventional meteorological monitoring equipment measures independent meteorological elements, such as temperature (T), wind speed (v), and relative humidity (RH). Physical parameters are the derivative results of the coupling effect of multiple meteorological elements and physical processes, and cannot be directly measured. Therefore, in the study of transmission line icing prediction, collision efficiency (…) is crucial. ), liquid water content ( ), surface emissivity ( ) and solar radiation absorptivity ( Key physical parameters such as icing are difficult to measure directly and accurately on-site using conventional meteorological monitoring equipment. Icing is a dynamic evolution process, and key physical parameters change in real time with time and icing status. However, the coefficients in fixed empirical formulas are static values ​​and cannot capture this time-varying characteristic. If fixed parameters are forcibly used, it will lead to the failure of physical constraints and even introduce systematic deviations, making it difficult to meet the actual engineering needs of icing early warning for transmission lines in micro-topographic areas.

[0011] This invention dynamically corrects key physical parameters that are difficult to measure directly. Key physical parameters refer to those core derived parameters that determine the icing physical process but cannot be directly read by conventional equipment and cannot be accurately described by fixed empirical formulas, such as collision efficiency. ), liquid water content ( ), surface emissivity ( ) and solar radiation absorptivity ( This allows key physical parameters to adaptively adjust with meteorological characteristics, enabling the physical equations to match real-time field conditions and ensuring the effectiveness of the model's physical constraints. Changes in the values ​​of key physical parameters directly correspond to the strength of the physical process, improving the physical interpretability of the prediction results. Icing is a dynamic, nonlinear evolutionary process; key physical parameters continuously change with time and icing status. Dynamic correction precisely matches this time-varying characteristic, improving prediction accuracy. Because the micro-topography and micro-meteorological differences between different tower locations on the same transmission line are significant, fixed parameters or empirical formulas cannot be adapted across scenarios. The dynamic correction mechanism perfectly solves this problem. The model only needs to input meteorological data for a new region to automatically generate key physical parameters adapted to the scenario, significantly improving the accuracy of icing prediction and the model's generalization ability to micro-topography and micro-meteorology. This makes the icing prediction model more aligned with the actual engineering needs of transmission line icing early warning. Meanwhile, the hybrid prediction model framework for transmission line micro-topography meteorological icing thickness based on the PINN-LSTM model aims to effectively couple the global constraints of physical equations with the local temporal modeling advantages of LSTM, fully integrating physical characteristic parameters and data features, thereby improving the accuracy of icing prediction. By adaptively inverting physical parameters and embedding them into PINN, physical parameters that are difficult to measure directly are treated as learnable latent variables. Monitoring data is used to drive the dynamic update of physical parameters, enhancing the model's robustness to extreme weather conditions and micro-topographic environments. On the other hand, by extracting the time-series dynamic features from the monitoring data through the LSTM module, the short-term fluctuation patterns of icing growth can be captured. Based on the gating memory mechanism adapted to time-series data, LSTM can identify the precursors of accelerated icing in advance through monitoring data at the minute or even second level, thereby improving the timeliness and accuracy of icing disaster early warning. The PINN-LSTM hybrid framework can achieve the fusion expression of multi-scale information by jointly optimizing the physical residual loss and sequence prediction loss, providing a new approach for predicting the icing thickness of transmission lines that combines physical interpretability and data adaptability.

[0012] Furthermore, the training process of the PINN-LSTM model in step S3 includes:

[0013] Step A1: Initialize the network weights and physical parameters of the PINN-LSTM model;

[0014] Step A2: Perform forward propagation based on the current physical parameters to obtain the predicted icing thickness, and calculate the total joint loss;

[0015] Step A3: Invert and update the physical parameters with the total joint loss value as the objective;

[0016] Step A4: Determine whether the physical parameter update amount and the total joint loss fluctuation value of N consecutive rounds are less than the preset threshold. If they are less than the threshold, convergence is determined and the iteration is terminated. Otherwise, the updated physical parameters are used as the current physical parameters and the iteration is returned to step A2.

[0017] Furthermore, the physical parameters are constrained within a numerical range that conforms to the physical definition by a nonlinear activation function. By applying soft constraints to the learnable physical parameters through the nonlinear activation function, it is possible to ensure that the parameters always fall within the range that conforms to the physical definition, avoid meaningless values, not disrupt PINN backpropagation, simplify the model structure, and improve training stability and prediction reliability.

[0018] Furthermore, in step A3, a weight decay coefficient is added to perform L2 regularization on the network weights of the PINN-LSTM model. Based on the total joint loss function including the L2 regularization term, the network weights and physical parameters of the PINN-LSTM model are updated by inversion with the goal of minimizing the total joint loss value. This can suppress overfitting and accelerate convergence, while ensuring the physical rationality of the parameters, improving the robustness and generalization ability of the model, and achieving synergistic optimization of data fitting and physical constraints.

[0019] Furthermore, the process for calculating the total joint loss in step A2 includes:

[0020] Step B1: Compare the predicted ice thickness calculated based on the PINN model and the predicted ice thickness calculated based on the LSTM model with the measured ice thickness, respectively, and calculate the data loss of the PINN model and the data loss of the LSTM model. Add the data loss of the PINN model and the data loss of the LSTM model to obtain the joint data loss.

[0021] Step B2: Integrate the equation characterizing the icing physical process into the PINN model, substitute the predicted icing thickness obtained from the PINN model into the equation, calculate the physical residual of the equation, and quantify the physical loss based on the physical residual.

[0022] Step B3: Add the physical loss and the joint data loss according to their weights to obtain the total joint loss.

[0023] The total joint loss can provide effective guidance for the model training process, ensuring that model optimization is driven by both physical accuracy and predictive performance, thus providing a solid guarantee for icing thickness prediction.

[0024] Furthermore, in step B1, when calculating the joint data loss, the smoothed L1 loss function is used to calculate the data loss of the PINN model and the LSTM model. When the error is small, the function is expressed as MSE. When the error exceeds a preset threshold, it switches to linear loss, which effectively controls the linear influence of outliers on the total loss and prevents extreme values ​​from dominating the adjustment of model parameters. At the same time, combined with the gradient penalty mechanism, a better balance between data fitting and physical loss is finally achieved.

[0025] Furthermore, the equation characterizing the icing physical process in step B2 is:

[0026] ;

[0027] In the formula, This refers to the thickness of the ice layer. For time; The density of ice; The latent heat of ice melting / freezing; The latent heat flux released when supercooled water droplets freeze upon impact with the conductor; The sensible heat flux generated by the supercooled water droplets impacting the conductor; For convective heat transfer flux; For evaporation / sublimation heat transfer flux; This represents the radiative heat transfer flux.

[0028] Physical loss incorporates physical equations into the PINN model, resulting in a loss when the neural network output does not satisfy physical laws. Its purpose is to enable the model to not only fit the data during the learning process but also satisfy physical constraints. Thus, in situations where data is scarce or expensive to acquire, physical characteristics can be used to guide learning, thereby improving the model's generalization ability and prediction accuracy.

[0029] Furthermore, the input features are a four-dimensional feature vector of temperature, humidity, wind speed, and air pressure. Temperature, humidity, and wind speed show a significant correlation with icing thickness, which highly matches the macroscopic meteorological conditions for icing formation. The statistical linear correlation between air pressure and icing thickness is relatively weak. In traditional pure data-driven prediction studies, such low-correlation features are often eliminated to reduce model complexity. However, this invention employs a physical information neural network framework, where feature selection must consider not only statistical correlations at the data level but also the completeness of physical mechanisms. In the fluid dynamics and thermodynamics equations governing icing growth, air pressure determines air density (…). The core state parameter of a collider is air density. Changes in air density directly alter the fluid's dynamic properties, thus affecting collision efficiency. ) and convective heat transfer coefficient ( If air pressure features are removed, the physical layer will be unable to accurately perceive air density fluctuations under micro-topography, leading to the failure of physical constraints. Therefore, the meteorological features selected in this invention ensure the rigor and closed-loop logic of the model in terms of physical mechanism.

[0030] Furthermore, the PINN-LSTM model is trained using the Adam optimizer. The Adam optimizer adaptively allocates personalized learning rates for different parameters, effectively mitigating the gradient explosion or vanishing problem caused by high-dimensional gradients. It significantly suppresses gradient decay caused by long-term LSTM dependence and gradient oscillations caused by residual calculations in the PINN physical equations. Combined with the ReduceLROnPlateau learning rate scheduler, which monitors performance metrics on the validation set in real time and automatically reduces the learning rate when metrics stagnate, the model helps escape local optima, accelerates the convergence process, and ultimately improves the overall performance of the model.

[0031] Furthermore, in step S1, the preprocessing involves normalizing the meteorological data and then segmenting the normalized data using a sliding window method. The time series sliding window divides the time series data into multiple fixed-size windows, which can overlap or not. Starting from the beginning of the sequence, the window slides to every possible position of the data. Each time it slides, the content of the window changes. Ultimately, the time series of a single feature is transformed into a fixed number of observed and predicted values ​​for subsequent machine learning model training and prediction. This process mines the temporal correlation features of the meteorological data, generates time series input samples adapted to LSTM, and enables the model to effectively capture the meteorological time series evolution patterns related to icing. At the same time, the influencing factors in the model input features have different units of measurement. Considering the differences in units and magnitudes, the original data needs to be standardized before constructing the training set of the model.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] 1. The present invention provides a transmission line icing prediction method that integrates physical mechanism constraints and multi-source data features. By dynamically correcting key physical parameters as learnable latent variables, the parameters of the physical equations can be matched with the actual field conditions in real time, ensuring the effectiveness of the physical constraints of the model. The icing thickness prediction results can be traced back to the specific changes in key physical parameters and meteorological environmental factors, ensuring the physical interpretability of the icing thickness prediction results.

[0034] 2. The present invention provides a method for predicting icing of transmission lines by fusing physical mechanism constraints and multi-source data features. By generating key physical parameters for different tower locations of the transmission line that are adapted to the scenario, the physical parameters accurately correspond to the micro-topography and micro-meteorological features of the tower location. This enables the model prediction to adapt to the differences in micro-topography and micro-meteorological features at different locations, significantly improving the accuracy of icing prediction and the generalization ability of the model for micro-topography and micro-meteorological features.

[0035] 3. The present invention provides a transmission line icing prediction method that integrates physical mechanism constraints and multi-source data features. By effectively coupling the global constraints of physical equations with the local temporal modeling advantages of LSTM, it fully integrates physical characteristic parameters and data features. The LSTM module is used to extract the temporal dynamic features in the monitoring data, capture the short-term fluctuation pattern of icing growth, and ensure that the model maintains stable and accurate icing prediction capability under complex scenarios such as extreme weather changes and significant micro-topographic differences. This enhances the robustness of the model to icing prediction accuracy under extreme weather conditions and micro-topographic environments, and improves the timeliness and accuracy of icing disaster early warning. Attached Figure Description

[0036] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0037] Figure 1 This is a flowchart of the overall icing prediction process in the transmission line icing prediction method of the present invention, which integrates physical mechanism constraints and multi-source data features.

[0038] Figure 2 This is a schematic diagram of the overall steps of the transmission line icing prediction method that integrates physical mechanism constraints and multi-source data features according to the present invention.

[0039] Figure 3 These are Pearson correlation heatmaps of different key meteorological factors in embodiments of the present invention;

[0040] Figure 4 This is a schematic diagram of the training steps of the PINN-LSTM model in the transmission line icing prediction method that fuses physical mechanism constraints and multi-source data features according to the present invention.

[0041] Figure 5 This is a structural diagram of the PINN-LSTM model in the transmission line icing prediction method that integrates physical mechanism constraints and multi-source data features according to the present invention.

[0042] Figure 6 This is a schematic diagram of the total joint loss calculation steps in the transmission line icing prediction method of the present invention, which integrates physical mechanism constraints and multi-source data features.

[0043] Figure 7These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 1 in the transmission line of this embodiment of the invention.

[0044] Figure 8 These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 2 in the transmission line of this embodiment of the invention.

[0045] Figure 9 These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 3 in the transmission line of this embodiment of the invention.

[0046] Figure 10 These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 4 in the transmission line of this embodiment of the invention.

[0047] Figure 11 These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 5 in the transmission line of this embodiment of the invention.

[0048] Figure 12 These are the ice thickness prediction curves of five models (CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM) for line 6 in the transmission line of this embodiment of the invention.

[0049] Figure 13 This is a comparison chart of the MAE (mean absolute error) of six transmission lines under different prediction models according to an embodiment of the present invention;

[0050] Figure 14 This is a comparison chart of the RMSE (root mean square error) of six transmission lines under different prediction models in an embodiment of the present invention;

[0051] Figure 15 This is a comparison chart of R² (coefficient of determination) for six transmission lines under different prediction models in this embodiment of the invention;

[0052] Figure 16 This is a comparison diagram of the icing thickness prediction trajectories of the PINN-LSTM-Adaptive model and the PINN-LSTM-Fixed model in this embodiment of the invention;

[0053] Figure 17 These are the dominant hydrodynamic parameters in embodiments of the present invention ( ) Dynamic evolution diagram;

[0054] Figure 18 These are the auxiliary thermodynamic parameters of the embodiments of the present invention ( ) Dynamic evolution diagram;

[0055] Figure 19 This is a schematic diagram of the average predicted values ​​of five models under different noise disturbances in an embodiment of the present invention;

[0056] Figure 20 This is a schematic diagram of the mean change rate of different models in the embodiments of the present invention. Detailed Implementation

[0057] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0058] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0059] Example 1

[0060] A method for predicting icing on transmission lines by fusing physical mechanism constraints with multi-source data features, such as... Figure 2 As shown, it includes:

[0061] Step S1: Obtain ice thickness data and meteorological data, and preprocess the ice thickness data and meteorological data;

[0062] In some embodiments, the present invention employs a time-series sliding window method to preprocess meteorological data. This method divides the time series data into multiple fixed-size windows, which may overlap or not. Starting from the beginning of the sequence, the window is slid to every possible position of the data. Each time the window is slid, the content of the window changes. Finally, the time series of a single feature is transformed into a fixed number of observed and predicted values ​​for subsequent machine learning model training and prediction.

[0063] For the icing prediction process, it is assumed that there are a total of Data, in which Defined as The ice thickness value at time t is then the time series of the ice thickness is: Where n is the total length of the historical monitoring time series of icing thickness on transmission lines. It is a parameter characterizing the icing thickness of transmission lines, and its goal is to represent the length of the transmission line. Time series collection Convert into input-output data pairs This includes observations from the past [number] time steps, i.e., meteorological data, and target values ​​from the future [number] time steps, i.e., ice thickness values. For historical observation time steps, Input feature vectors to predict future time steps Includes the past Meteorological observation data at each time step, output target vector. Includes the future Ice thickness values ​​at each time step.

[0064] Starting from the beginning of the sequence, each time step is slid to extract the continuous sequence. A historical value is used as input, corresponding to its subsequent... Each value is used as an output sample, resulting in the first input sample sequence. The first output sample sequence is And so on, the... The input samples are , No. The output samples are , For the first A sequence of input samples, consisting of continuous... The ice thickness values ​​at each time point constitute the historical time-series features used to provide the model. For the first The start time step of each input sample. No. A sequence of output samples, composed of input samples Corresponding continuity The ice thickness values ​​at future moments constitute the model's prediction target, and are related to... One-to-one correspondence.

[0065] The final sample set can be represented as , The total number of samples in the final sample set is determined by the total length of the time series. Input window length and output window length We jointly decide to ensure that the time steps of all samples are within the valid range [1, n]. The final input-output sample set, constructed based on the sliding window method, is the core data for model training or validation.

[0066] Among them, the influencing factors in the input features have different units of measurement. Considering the differences in dimensions and magnitudes, the original data needs to be standardized before constructing the training set of the model. The input data is scaled between [0, 1] by the normalization equation shown in the formula.

[0067] ;

[0068] In the formula, The first characteristic variable represents the... The result after transforming the data. , The total number of data samples, This represents the minimum value of the feature variable across all samples. This represents the maximum value of the feature variable across all samples.

[0069] Step S2: Select features from the preprocessed meteorological data and filter out key features that conform to the physical laws of ice formation as input features of the PINN-LSTM model;

[0070] In some embodiments, the Pearson correlation analysis method is used to analyze the correlation between ice thickness and meteorological factors in the monitoring data of six transmission lines during a cold wave in a certain region of southwest China.

[0071] like Figure 3 The image shows a Pearson correlation coefficient heatmap, used to illustrate the linear correlation between ice thickness and environmental factors such as temperature, humidity, wind speed, and pressure. Pearson1 is the legend label, representing the Pearson correlation coefficient. The numbers in the cells are the Pearson correlation coefficients for the corresponding variables, ranging from [−1, 1]. Figure 3 The darker the color, the closer the Pearson correlation coefficient is to -1; the lighter the color, the closer the Pearson correlation coefficient is to 1. Figure 3The data shows that temperature has the most significant impact on icing, and it is negatively correlated with icing thickness, indicating that a decrease in temperature significantly promotes icing formation. Wind speed and humidity have the next most significant impact, while air pressure has the least. There are interrelationships among various meteorological factors; for example, temperature and humidity are strongly negatively correlated. During icing formation, this correlation may lead to mutual constraints or promotion among meteorological factors, thus affecting the final state of icing. Therefore, to study icing more accurately, key meteorological factors need to be analyzed in combination. In the formation mechanism of icing thickness, different meteorological factors play specific roles in the process of icing thickness change, influencing icing thickness to a certain extent. Among them, temperature, humidity, and wind speed show significant correlations with icing thickness, while the statistical linear correlation between air pressure and icing thickness is relatively weak. In traditional pure data-driven prediction studies, such low-correlation features are often eliminated to reduce model complexity. This invention adopts a physical information neural network framework. Feature selection not only needs to consider statistical correlations at the data level but also needs to follow the completeness of the physical mechanism. Furthermore, in the fluid dynamics and thermodynamic equations for icing growth, air pressure determines air density (…). The core state parameters of a collider. Changes in air density directly alter the dynamic properties of the fluid, thus affecting collision efficiency. ) and convective heat transfer coefficient ( If air pressure features are removed, the physical layer will be unable to accurately perceive air density fluctuations under micro-topography, leading to the failure of physical constraints. In order to ensure the rigor and closed-loop logic of the model in terms of physical mechanism, the input features of the model are determined to be a combination of four-dimensional vectors of temperature, humidity, wind speed and air pressure. All input features have been normalized by normalization equations before being fed into the model to eliminate the influence of dimensional differences on the convergence speed of gradient descent.

[0072] Step S3: Load the input features into the trained PINN-LSTM model. The trained PINN-LSTM model is used to dynamically correct physical parameters based on the input features to obtain the predicted icing thickness of the transmission line.

[0073] like Figure 4 and Figure 1 As shown, the training process of the PINN-LSTM model in step S3 includes:

[0074] Step A1: Initialize the network weights and physical parameters of the PINN-LSTM model;

[0075] Step A2: Perform forward propagation based on the current physical parameters to obtain the predicted icing thickness, and calculate the total joint loss;

[0076] Step A3: Invert and update the physical parameters with the goal of minimizing the total joint loss value;

[0077] Step A4: Determine whether the physical parameter update amount and the total joint loss fluctuation value of N consecutive rounds are less than the preset threshold. If they are less than the threshold, convergence is determined and the iteration is terminated. Otherwise, the updated physical parameters are used as the current physical parameters and the iteration is returned to step A2.

[0078] Subsequently, based on the engineering requirements for icing prediction and the model training patterns, a threshold for the physical parameter update amount was set. Threshold for total joint loss fluctuation over 10 consecutive rounds If the physical parameter update amount is less than the threshold at the same time The total combined loss fluctuation value is less than the threshold for 10 consecutive rounds. If the model converges, the iteration is terminated immediately. If any index fails to meet the threshold, the updated physical parameters in step A3 are used as the current parameters for the next iteration, and the iteration returns to step A2.

[0079] In some embodiments, the PINN-LSTM model is trained using the Adam optimizer with a learning rate of 0.001. It can calculate a personalized learning rate for each parameter and use the ReduceLROnPlateau learning rate scheduler to monitor the performance metrics on the validation set in real time. When the metrics stagnate, the learning rate is automatically reduced, which helps the model escape local optima, accelerates the convergence process, and ultimately improves the overall performance of the model.

[0080] While PINN can provide physical constraints for the model, ensuring that the predicted icing thickness of transmission lines conforms to objective physical characteristics, its ability to capture dependencies on long-term series data such as icing monitoring data is insufficient. Figure 5 The diagram shows the structure of the PINN-LSTM hybrid prediction model for icing thickness. By integrating the gating mechanism and long-term memory capability of LSTM with the strong nonlinear fitting ability of the PINN model, the physical parameter inversion update captures the intrinsic physical laws of icing evolution, improving the robustness and reliability of the prediction model in scenarios with scarce or out-of-distribution data. At the same time, it deeply mines the temporal dependencies of historical icing data, thereby more accurately capturing the dynamic characteristics of icing thickness changes over time. Ultimately, it achieves an effective combination of data-driven and physical constraints, improving prediction accuracy and generalization ability.

[0081] like Figure 6 As shown, the process for calculating the total joint loss in step A2 includes:

[0082] Step B1: Compare the predicted ice thickness calculated based on the PINN model and the predicted ice thickness calculated based on the LSTM model with the measured ice thickness, respectively, and calculate the data loss of the PINN model and the data loss of the LSTM model. Add the data loss of the PINN model and the data loss of the LSTM model to obtain the joint data loss.

[0083] The smoothed L1 loss function is used to calculate the data loss of the PINN and LSTM models. When the error is small, this function exhibits MSE; when the error exceeds a preset threshold, it switches to linear loss. The data losses of the PINN and LSTM parts are denoted as follows: and The data loss of PINN and LSTM is calculated by comparing the predictions with the measured values.

[0084] The total data loss is obtained by summing the data losses from PINN and LSTM predictions with the measured values. This joint data loss captures the model's prediction accuracy from both physical information and the deep learning process, thereby evaluating the model's performance. Based on this, the joint data loss can be expressed as:

[0085] ;

[0086] In the formula, Indicates joint data loss. This represents the data loss of the PINN model. This represents the data loss of the LSTM model.

[0087] Step B2: Integrate the equation characterizing the icing physical process into the PINN model, substitute the predicted icing thickness obtained from the PINN model into the equation, calculate the physical residual of the equation, and quantify the physical loss based on the physical residual.

[0088] Among them, physical loss is to incorporate the equations characterizing the physical process of icing into the PINN model. Physical loss is obtained by calculating the residual quantification of the physical equations, ensuring that the model prediction results strictly follow the objective physical laws of icing growth. Its role is to enable the model to not only fit the data during the learning process, but also meet the physical constraints. Thus, in the case of scarce data or high acquisition costs, physical characteristics are used to guide learning, thereby improving the model's generalization ability and prediction accuracy.

[0089] In some embodiments, the equation characterizing the icing physical process in step B2 is:

[0090] ;

[0091] In the formula, ( ( ) represents the thickness of the ice layer. ( ( ) represents time; ( ( ) represents the density of ice, taken as 900-920. , The latent heat of ice melting / freezing, The latent heat flux released when supercooled water droplets freeze upon impact with a conductor ( ), The sensible heat flux from the supercooled water droplets impacting the conductor ( ), For convective heat transfer flux ( ), For evaporation / sublimation heat transfer flux ( ), For radiative heat transfer flux ( ).

[0092] Assuming the surface temperature of the ice layer The ice cover growth is 0. (273.15 (), during ablation, the ambient temperature or 0 .

[0093] (1) Effective diameter for:

[0094] ;

[0095] In the formula, The initial diameter of the conductor is the diameter of the conductor before it becomes icy.

[0096] (2) Reynolds number for:

[0097] ;

[0098] In the formula, air density, Aerodynamic viscosity, For incoming wind speed.

[0099] (3) Nusselt number for:

[0100] ;

[0101] In the formula, and Let be an empirical constant, and take . , , The Prandtl number is approximately 0.71 for air.

[0102] (4) Convection heat transfer coefficient for:

[0103] ;

[0104] In the formula, is the thermal conductivity of air.

[0105] (5) Mass transfer coefficient for:

[0106] ;

[0107] In the formula, It is a Lewis number, so we take 0.85. This is the specific heat capacity of air at constant pressure.

[0108] (6) Saturated vapor pressure and environmental water vapor pressure for:

[0109] ,

[0110] ;

[0111] In the formula, The ambient thermodynamic temperature, Relative humidity is the ratio of the actual water vapor pressure in the air to the saturated water vapor pressure at the same temperature. This refers to the air temperature, which is the thermodynamic temperature of the air when calculating the ambient water vapor pressure.

[0112] In the above expression, the various heat fluxes involved can be further decomposed and specifically expressed as follows: latent heat of freezing of impacting water droplets for:

[0113] ;

[0114] In the formula, Collision efficiency represents the proportion of water droplets that collide with the conductor, and is affected by factors such as droplet size, wind speed, and conductor diameter. To ensure its physical meaning... This paper defines it as a learnable parameter constrained by the Sigmoid activation function, i.e. ; The liquid water content in the air represents the mass concentration of supercooled water droplets in the air. To ensure the conservation of quality ( The Softplus activation function is used to define it as a non-negative learnable parameter, i.e. ; For the incoming wind speed ( This refers to the air velocity relative to the conductor or ice surface. The latent heat of ice melting / freezing ( ).

[0115] Sensitive heat from impacting water droplets for:

[0116] ;

[0117] In the formula, The specific heat capacity of water ( ), This refers to the ice surface temperature, i.e., the surface temperature of the conductor / ice surface.

[0118] Convection heat transfer for:

[0119] ;

[0120] In the formula, This refers to the surface temperature of the ice.

[0121] Evaporation / sublimation heat exchange for:

[0122] ;

[0123] In the formula, The latent heat of vaporization of water is approximately 2.5. .

[0124] Radiative heat transfer for:

[0125] ;

[0126] In the formula, For surface emissivity, also treated as a learnable parameter, a sigmoid constraint is introduced to ensure... ; It is the Stefan-Boltzmann constant; The sky temperature can usually be approximated as... arrive ; Solar radiation absorptivity, as a learnable parameter, is defined as follows: ; Solar radiation intensity ( ).

[0127] The combination of the above physical equations with the PINN-LSTM model first uses PINN to automatically differentiate the predicted icing thickness to obtain the time derivative of the icing thickness. Then, it combines meteorological data and learnable physical parameters to calculate the net heat flux term on the right side of the equation. Subsequently, it solves for the difference between the left and right sides of the equation to obtain the physical residuals. The mean square error of the residuals for the entire sample is then calculated to obtain the physical loss. .

[0128] Step B3: Add the physical loss and the joint data loss according to their weights to obtain the total joint loss.

[0129] The total joint loss is:

[0130] ;

[0131] In the formula, Indicates the total joint loss, For physical loss, For joint data loss; and These are the weights for physical loss and data loss, respectively.

[0132] In some embodiments, the physical parameters are constrained within a reasonable physical range using a nonlinear activation function; specifically, for collision efficiency... and solar radiation absorption To prevent non-physical phenomena such as probability overflow, a sigmoid activation function is introduced and its value is strictly limited to the (0, 1) interval. This is relevant for liquid water content. The Softplus activation function is introduced to ensure that it is always non-negative, which conforms to the law of conservation of mass.

[0133] In some embodiments, in step A3, a weight decay coefficient is added to perform L2 regularization on the network weights of the PINN-LSTM model. A sum of squares penalty term for the weights is added to the original total joint loss function to form the total joint loss function. Based on the total joint loss function containing the L2 regularization term, the network weights and physical parameters of the PINN-LSTM model are synchronously updated by inversion with the goal of minimizing the total joint loss value. This limits the excessive growth of the network weights of the PINN-LSTM model, reduces the model complexity, avoids overlearning on training data noise, effectively prevents overfitting, and improves the model's predictive generalization ability on unknown data.

[0134] Example 2

[0135] Based on Example 1, in order to comprehensively evaluate the predictive performance and physical consistency of the PINN-LSTM model of the present invention, a horizontal comparison was made with the mainstream benchmark icing thickness prediction model, using actual monitoring data of six transmission lines in a typical micro-topographic region in Southwest China as a basis.

[0136] The resolution of meteorological and icing data for transmission lines during cold waves is 25 minutes. During the data partitioning process, 70% of the data is selected as the training set, and the remaining 30% of the data is used for prediction. In this embodiment, four classic models, namely CNN-LSTM, PINN, LSTM, and SVM, are selected for comparative analysis with the PINN-LSTM model.

[0137] The icing prediction results of the five models for the above six transmission lines are as follows: Figures 7 to 12 As shown, the horizontal axis represents TimeSteps, which is the time series sequence of ice thickness monitoring or prediction, ranging from 0 to 500. Each step corresponds to a discrete time point, used to show the evolution of the ice accumulation process over time. It not only shows the comparison between the predicted values ​​of each model and the actual monitored values, but also presents the trend of the two changing with time or other related variables.

[0138] like Figures 7 to 12 As shown, the PINN-LSTM model exhibits excellent predictive performance. In terms of the fit between the predicted and monitored values, the PINN-LSTM model's ice thickness prediction curve highly overlaps with the ice thickness monitoring curve. At each key time point or variable value point, the deviation between the predicted and monitored values ​​is controlled within a very small range.

[0139] In contrast, the four models—CNN-LSTM, PINN, LSTM, and SVM—all exhibit some degree of prediction bias, with significant deviations even occurring during critical phases of trend changes. For example, the LSTM model's prediction performance for Route 4 showed a lag in responding to changes in ice thickness during periods of rapid increase or melting, leading to a significant deviation between the predicted curve and the actual observed values.

[0140] To quantitatively evaluate the PINN-LSTM model's performance in predicting icing under micro-topographic and micro-meteorological conditions, and to conduct a fair comparison with other comparative models, this paper uses the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (CDE). The accuracy of the prediction results is evaluated using this as a core evaluation indicator, and its expression is:

[0141] ,

[0142] ,

[0143] ;

[0144] In the formula, The total number of data; This is the predicted value for icing. These are the icing monitoring values, i.e., the actual values; This is the average of the true values.

[0145] Evaluation metrics for the icing thickness prediction results of five models: CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM are as follows: Figures 13 to 15 As shown in Table 1, Figures 13 to 15 The horizontal axis represents different transmission line numbers (1-6). Figure 13 The vertical axis represents the MAE value, which indicates the mean absolute error of the model's predictions. Figure 14 The vertical axis represents the RMSE value, which indicates the root mean square of the model's prediction error. It also reflects prediction accuracy but is more sensitive to extreme errors. Figure 15 The vertical axis represents the R² value, which indicates the model's ability to explain the changes in measured ice thickness data. The value ranges from 0 to 1, with a value closer to 1 indicating a better fit.

[0146] Table 1 Evaluation Indicators of Prediction Results for Six Routes under Different Prediction Models

[0147]

[0148] In the table, MAE represents the mean absolute error, which is the average absolute error between the model's predicted values ​​and the measured values, directly reflecting the average magnitude of the prediction error. RMSE represents the root mean square error, reflecting the overall dispersion of the prediction error. The coefficient of determination represents the explanatory power of the model's predicted values ​​for changes in the measured values, that is, the proportion of the measured data changes that the model can fit.

[0149] As shown in Table 1, the average values ​​of the five models—PINN-LSTM, CNN-LSTM, PINN, LSTM, and SVM—are 0.0349, 0.0613, 0.1120, 0.1614, and 0.1898, respectively. Compared to the other four models, PINN-LSTM's prediction error decreased by 43.07%, 68.84%, 78.38%, and 81.61%, respectively, demonstrating higher prediction accuracy.

[0150] like Figures 13 to 15As shown, except for the prediction error value of line 4 which is lower than that of the PINN-LSTM model, the PINN-LSTM model outperforms the other four models in terms of prediction results for the other lines. This difference is particularly evident in the average value of each model. This significant difference fully demonstrates that the physical constraints added to the LSTM model in this embodiment play a crucial role in the improvement.

[0151] Furthermore, CNN-LSTM, also a composite model, performed well in prediction, with average scores of 0.0613, 0.1314, and 0.9701, respectively. The prediction results of the PINN-LSTM model were 43.07% and 28.23% lower than those of CNN-LSTM, respectively, representing an improvement of 1.67%. Introducing physical constraints allows the model to better adhere to physical characteristics during training, thereby improving its ability to model the dynamic behavior of complex systems and significantly enhancing prediction accuracy.

[0152] Example 3

[0153] Based on Examples 1 and 2, ablation experiments using a physical parameter adaptive mechanism were conducted to analyze in depth the model's dynamic inversion capability and mechanism effectiveness for key parameters such as liquid water content and collision efficiency during the rapid ice growth phase.

[0154] In traditional models of icing growth mechanisms on transmission lines, fluid dynamics and thermodynamic parameters often rely on empirical formulas or are simplified to fixed constants. However, in micro-topographic and micro-meteorological environments, airflow is affected by topographic lifting or canyon effects, leading to changes in the collision efficiency of water droplets in the air. With liquid water content Key physical parameters exhibit strong spatiotemporal heterogeneity and nonlinear fluctuations. Using fixed parameters makes it difficult to accurately describe the icing physical process under complex working conditions.

[0155] This embodiment designed a set of ablation experiments, and the experiments set up two comparative models:

[0156] 1. PINN-LSTM-Adaptive model: This model improves collision efficiency ( ), liquid water content ( ), surface emissivity ( ) and solar radiation absorptivity ( The parameters are defined as learnable latent variables in a neural network. The model dynamically inverts these parameters based on the input meteorological characteristics and constrains them within a reasonable physical range using Sigmoid and Softplus activation functions. Specifically, for collision efficiency... and solar radiation absorptivity To prevent non-physical phenomena such as probability overflow, a sigmoid activation function is introduced and its value is strictly limited to the (0, 1) interval. This is relevant for liquid water content. The Softplus activation function is introduced to ensure that it is always non-negative, which conforms to the law of conservation of mass.

[0157] 2. PINN-LSTM-Fixed Model: The four physical parameters mentioned above are set to fixed constants and do not participate in the dynamic update of the gradient. To ensure the fairness of the comparative experiments and avoid the baseline model's performance being too low due to unreasonable parameter settings, this embodiment adopts the "posterior mean initialization" strategy, that is, taking the statistical mean of the parameters obtained by inverting the PINN-LSTM-Adaptive model on the training set as the fixed parameter values ​​of PINN-Fixed. In this experiment, the following settings are used: ; ; ; .

[0158] The prediction performance of the two models on the test set is compared in Table 2:

[0159] Table 2 Comparison of ablation experimental results using the physical parameter adaptive mechanism

[0160]

[0161] In the table, MAE represents the mean absolute error, which is the average absolute error between the model's predicted values ​​and the measured values, directly reflecting the average magnitude of the prediction error. RMSE represents the root mean square error, reflecting the overall dispersion of the prediction error. The coefficient of determination represents the explanatory power of the model's predicted values ​​for changes in the measured values, that is, the proportion of the measured data changes that the model can fit.

[0162] As shown in Table 2, after introducing the physical parameter adaptive mechanism, the PINN-LSTM-Adaptive model significantly outperforms the PINN-LSTM-Fixed model in all evaluation metrics. Specifically, Decreased by 21.6%. A decrease of 29.7%, An increase of 6.68% was observed. This demonstrates that transforming physical parameters from fixed constants into learnable latent variables can significantly correct the systematic bias of simple physical equations in micro-topographical environments. Meanwhile, the performance improvement varies significantly across different routes. Taking Route 3 as an example, the PINN-LSTM-Fixed model exhibits a large prediction error, indicating that this area may be located in extremely complex micro-topography, rendering commonly used empirical parameters completely ineffective. However, the PINN-LSTM-Adaptive model, which can be dynamically modified to physical parameters, performs better on this route. The value dropped significantly to 0.1056, a decrease of over 50%, indicating that the corrective role of physical parameter adaptive inversion becomes more crucial in extremely complex environments where empirical parameters are difficult to cover.

[0163] The TimeSteps100-150 test set for Route 3 was selected as the typical analysis period. During this period, the route experienced a highly representative continuous icing process (a surge from 0 mm to 4.77 mm), with a significant abrupt change in the initial stage. This effectively validates the model's adaptive inversion performance under complex micro-topography and continuous adverse conditions. Figures 16 to 18 As shown, the dynamic evolution of the model-predicted trajectory and four inversion parameters of Line 3 during a typical period of rapid increase in icing is illustrated.

[0164] like Figure 16 As shown, Figure 16 This is a comparison chart of the predicted trajectories of different models for icing thickness, used to visually compare the fitting effects of different prediction methods with the actual icing process. The horizontal axis represents time steps, and the vertical axis represents icing thickness. During the explosive increase in icing thickness from 1.0 mm to 4.8 mm, the PINN-LSTM-Fixed model, limited by its fixed parameters, exhibits significant prediction lag. In contrast, the PINN-LSTM-Adaptive model, benefiting from its dynamic parameter adjustment capabilities, shows a prediction trajectory that closely matches the actual observations, effectively eliminating time-series errors. This improvement in accuracy is directly attributed to… Figure 17 The revealed dominant parameter-driven mechanism, Figure 17 The dominant fluid dynamics parameter (liquid water content) Collision efficiency The dynamic evolution diagram shows the horizontal axis as the time step and the vertical axis as the liquid water content. With collision efficiency , Figure 17 This indicates the liquid water content obtained through inversion. With collision efficiency It did not remain constant, but rather showed a high positive correlation with the rate of icing growth, rapidly climbing to a high level during the acceleration period, accurately reflecting the surge in supercooled water droplet flux under severe weather conditions. Meanwhile, Figure 18 For auxiliary parameters, surface emissivity and solar radiation absorptivity A schematic diagram of dynamic evolution, where the horizontal axis represents the time step and the vertical axis represents the surface emissivity. and solar radiation absorptivity This confirms the excellent physical consistency of the model, and the auxiliary parameter surface emissivity and solar radiation absorptivity Throughout the entire process, the model consistently converged to the vicinity of the physical empirical value without any non-physical oscillations, which fully demonstrates that the model is not simply a data fit, but has successfully captured the intrinsic physical laws of icing evolution.

[0165] Example 4

[0166] Based on Examples 1 to 3, multiple sets of experiments were designed using the constructed dataset and feature engineering results. The effectiveness of the PINN-LSTM model was verified and comprehensively evaluated from three dimensions: prediction accuracy, physical parameter adaptation mechanism, and model robustness.

[0167] In actual power grid operation environments, meteorological observation data are often affected by factors such as measurement errors, sensor failures, and communication interference, resulting in unavoidable noise disturbances in the input signals.

[0168] This embodiment constructs test datasets with different signal-to-noise ratios (SNR) based on Gaussian noise perturbation (mean 0, variance adjustable) to conduct robustness experiments on PINN-LSTM and contrasting models. By analyzing the prediction error variation patterns of five models—CNN-LSTM, PINN, LSTM, SVM, and PINN-LSTM—under different noise conditions, the performance degradation is analyzed to evaluate the reliability and generalization ability of the models in noisy environments.

[0169] The prediction results after adding noise perturbation are as follows Figure 19 As shown in Table 3, Figure 19 A line graph comparing the average predicted values ​​of five models under different noise disturbances is presented. The horizontal axis represents the signal-to-noise ratio, and the vertical axis represents the average predicted value of each model, which is used to quantify the performance of the models under different noise conditions.

[0170] Table 3. Average prediction values ​​of the five models under different signal-to-noise ratios.

[0171]

[0172] In the table, the mean change rate represents the relative increase in the mean prediction error of each model relative to the initial state (SNR=100) when the signal-to-noise ratio (SNR) decreases from 100 to 50. It is used to quantify the degree of degradation in the prediction performance of the model under increased noise.

[0173] from Figure 19As shown in Table 3, with the gradual increase of noise intensity (the smaller the SNR, the higher the noise intensity), the prediction accuracy of the five models all decreased to varying degrees. Compared with the CNN-LSTM, PINN, LSTM, and SVM models, the PINN-LSTM model showed better overall robustness, and the error growth on lines 1, 2, 4, 5, and 6 was significantly lower than that of other models, indicating that its physical constraints had a certain suppressive effect on noise disturbances. Specifically, the RMSE value of line 3 increased from 0.1056 at SNR=100 to 0.374 at SNR=50, indicating that high noise interference weakens the model's prediction accuracy. However, the overall error change of the PINN-LSTM model was still lower than that of the CNN-LSTM, PINN, LSTM, and SVM models. Furthermore, CNN-LSTM exhibits strong robustness in low-noise environments, but its prediction accuracy drops significantly under high noise levels. Additionally, in lines 2, 3, and 4, the RMSE decreases slightly with increasing noise, which may be related to the noise regularization effect. Moderate noise can mitigate overfitting to some extent, resulting in smoother predictions. Overall, the CNN-LSTM model maintains relatively stable prediction performance under high noise conditions, demonstrating good anti-interference capabilities and generalization stability.

[0174] like Figure 20 The bar chart comparing the rate of change of the mean prediction error for each model is used to visually demonstrate the relative increase in the mean prediction error of different models under increased noise, thereby assessing the model's noise resistance. The horizontal axis represents the five different prediction models, and the vertical axis represents the relative increase in the mean prediction error of each model. The larger the value, the more significant the error increase and the worse the noise resistance. It can be seen that the PINN-LSTM model's RMSE change rate under different signal-to-noise ratio conditions is 65.53%, with a relatively large overall amplitude. This is mainly due to the significant increase in prediction error under high noise conditions on line 3, leading to a higher overall mean. Apart from this line, the RMSE changes for lines 1, 2, 4, 5, and 6 are relatively stable, with the change rate controlled at around 30%, indicating that the model maintains good stability on most lines. This result shows that the robustness of the PINN-LSTM model varies among different lines, but its overall anti-interference performance is still better than the comparative models, demonstrating the suppressive effect of physical constraints on noise disturbances.

[0175] The PINN-LSTM model of this invention effectively overcomes the prediction lag problem caused by the rigidity of traditional empirical parameters by adaptively adjusting key physical parameters such as liquid water content and collision efficiency. Experimental results show that the PINN-LSTM model can effectively capture the dynamic evolution characteristics of ice thickness, and its overall prediction performance is significantly better than the comparison method. Furthermore, it exhibits strong stability and anti-interference ability under different complex environments.

[0176] This invention not only improves the robustness and adaptability of the ice thickness prediction model, reveals the physical driving mechanism of ice growth under micro-topography, and verifies the effectiveness of machine learning methods under complex micro-meteorological conditions, but also demonstrates that the method has strong engineering application potential and can provide strong support for ice monitoring and early warning.

[0177] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0178] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for predicting icing on transmission lines by fusing physical mechanism constraints with multi-source data features, characterized in that, include: Step S1: Obtain ice thickness data and meteorological data, and preprocess the ice thickness data and meteorological data; Step S2: Select features from the preprocessed meteorological data and filter out key features that conform to the physical laws of ice formation as input features of the PINN-LSTM model; Step S3: Load the input features into the trained PINN-LSTM model. The trained PINN-LSTM model is used to dynamically correct physical parameters based on the input features to obtain the predicted icing thickness of the transmission line. The physical parameters include: collision efficiency, liquid water content, surface emissivity, and solar radiation absorptivity; The training process of the PINN-LSTM model includes: Step A1: Initialize the network weights and physical parameters of the PINN-LSTM model; Step A2: Perform forward propagation based on the current physical parameters to obtain the predicted icing thickness, and calculate the total joint loss; Step A3: Invert and update the physical parameters with the total joint loss value as the objective; Step A4: Determine whether the physical parameter update amount and the total joint loss fluctuation value of N consecutive rounds are less than the preset threshold. If they are less than the threshold, convergence is determined and the iteration is terminated. Otherwise, the updated physical parameters are used as the current physical parameters and the iteration is returned to step A2. The calculation process for the total joint loss includes: Step B1: Compare the predicted ice thickness calculated based on the PINN model and the predicted ice thickness calculated based on the LSTM model with the measured ice thickness, respectively, and calculate the data loss of the PINN model and the data loss of the LSTM model. Add the data loss of the PINN model and the data loss of the LSTM model to obtain the joint data loss. Step B2: Integrate the equation characterizing the icing physical process into the PINN model, substitute the predicted icing thickness obtained from the PINN model into the equation, calculate the physical residual of the equation, and quantify the physical loss based on the physical residual. Step B3: Add the physical loss and the joint data loss according to their weights to obtain the total joint loss.

2. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, The physical parameters are constrained to a numerical range that conforms to the physical definition by a nonlinear activation function.

3. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, In step A3, a weight decay coefficient is added to perform L2 regularization on the network weights of the PINN-LSTM model. Based on the total joint loss function containing the L2 regularization term, the network weights and physical parameters of the PINN-LSTM model are updated by inversion with the goal of minimizing the total joint loss value.

4. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, When calculating the joint data loss in step B1, the smoothed L1 loss function is used to calculate the data loss of the PINN model and the LSTM model.

5. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, The equation characterizing the icing physical process in step B2 is: ； In the formula, h is the ice thickness; t is the time; ρ i L is the density of ice. f The latent heat of ice melting / freezing; Q imp The latent heat flux released when supercooled water droplets freeze upon impact with the conductor; Q sens The sensible heat flux from the supercooled water droplets impacting the conductor; Q conv Q is the convective heat transfer flux; evap For evaporation / sublimation heat transfer flux; Q rad This represents the radiative heat transfer flux.

6. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, The input features are a four-dimensional feature vector of temperature, humidity, wind speed, and air pressure.

7. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, The PINN-LSTM model is trained using the Adam optimizer.

8. The method for predicting icing on transmission lines by fusing physical mechanism constraints and multi-source data features according to claim 1, characterized in that, In step S1, the preprocessing involves normalizing the meteorological data and then segmenting the normalized data using a sliding window method.

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