Power transmission line icing thickness prediction method based on physical guidance FSLSTM-Mixup

Abstract

The invention discloses an overhead transmission line icing thickness prediction method based on physical guidance FSLSTM-Mixup, and aims to solve the problems that an existing icing thickness prediction model is low in prediction precision and generalization ability and neglects physical rules. A power transmission line mechanical static model is established, and the relation between lead icing and meteorological factors is analyzed; capturing local and global correlation of the icing data by using a Fourier transform segmented long-short term memory (FSLSTM) network; the generalization performance of the model is improved by combining a sample mixed data enhancement algorithm Mixup; wherein the FSLSTM extracts a main period of data through Fourier transform, and captures features in a segmented manner; the Mixup algorithm generates new data through linear combination of samples and labels, and expands a sample distribution space; by integrating the physical law and the data enhancement technology, the accuracy and authenticity of icing thickness prediction are remarkably improved, the method is suitable for ice resistance and disaster reduction work of the overhead transmission line, and early warning support is provided for decision making.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic disasters and protection of overhead transmission lines, and particularly to a method for predicting the ice coating thickness of transmission lines based on physically-guided FSLSTM-Mixup. Background Art

[0002] In recent years, extreme weather phenomena have occurred frequently, resulting in serious ice coating disasters on overhead transmission lines, which pose a major threat to the stable operation of the power system. These events have not only brought great inconvenience to people's daily lives but also caused huge economic losses.

[0003] To address this issue, the prediction technology of the ice coating thickness of overhead transmission lines is particularly important. Currently, the technologies in this field are mainly divided into three categories: physical mechanism models, machine learning algorithm models, and data-driven neural network models.

[0004] Physical mechanism models are based on the physical process of ice coating formation and predict the ice coating thickness through theoretical derivation and calculation. However, this method requires many parameters to be measured and is difficult to accurately obtain in practical applications. Therefore, it is difficult to construct a specific mapping function, and its practicality is greatly limited.

[0005] Machine learning algorithm models use statistical learning methods to predict the ice coating thickness through training on historical data. However, such methods are limited by the performance of the algorithms themselves, and the prediction accuracy is often not high, making it difficult to meet the requirements of practical applications.

[0006] In recent years, with the continuous development of neural network technology, data-driven neural network models have received extensive attention in the prediction of the ice coating thickness of overhead transmission lines. Common neural network models include BP neural networks, recurrent neural networks (RNNs), and convolutional neural networks (CNNs), etc. These models can automatically extract the features of input data and make predictions by simulating the learning process of the human brain. However, most existing ice coating prediction methods only consider the ice coating thickness itself and ignore the influence of meteorological factors on the ice coating thickness, resulting in low prediction accuracy. In addition, most of the existing prediction models use basic models, which are difficult to fully extract the non-static and non-temporal features during the ice coating growth process and ignore the physical laws of the ice coating on transmission lines, thus limiting the improvement of prediction performance.

[0007] Therefore, to solve the problems existing in the existing ice coating thickness prediction models, such as low prediction accuracy, weak generalization ability, inability to extract non-static and non-temporal features during the ice coating growth process, and ignoring the physical laws of transmission lines, it is urgent to establish an overhead transmission line ice coating prediction model with high accuracy and authenticity. This model can provide decision-making support such as early warning for the anti-icing and disaster reduction work of transmission lines and is of great significance for ensuring the stable operation of the power system. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for predicting the icing thickness of transmission lines based on physically-guided FSLSTM-Mixup, so as to solve the problems of low prediction accuracy, weak generalization ability, and inability to effectively extract non-static and non-temporal features in the process of ice growth in the field of overhead transmission line dynamic disasters and protection technologies, and to overcome the specific limitations such as the prediction model ignoring the physical laws of transmission lines, limited prediction accuracy, and insufficient generalization ability in the prior art.

[0009] To solve the above technical problems, the technical solution adopted by the present invention is as follows: an overhead transmission line icing thickness prediction method based on physically-guided FSLSTM-Mixup, comprising the following steps: Step1: Establish a mechanical static model of the transmission line, analyze the forces on the overhead transmission line, consider the self-weight of the conductor, the ice weight caused by icing, and the lateral load caused by wind pressure, and calculate the comprehensive specific load of the conductor according to the analysis results; Step2: Use Fourier transform to process the historical data of conductor icing, extract its main periodic components, segment the icing data according to this period, and construct a Fourier transform-based segmented long short-term memory network FSLSTM to capture local and global correlations respectively; Step3: Adopt the sample mixing enhancement algorithm Mixup. Based on the principle of minimizing the neighborhood risk, generate new samples and labels through the linear combination of samples and labels in the original dataset to expand the dataset scale and improve the model generalization ability; Step4: Use the processed historical icing data and related meteorological data as inputs, and train through the FSLSTM network to obtain an icing thickness prediction model; Step5: Input the real-time collected icing and related meteorological data of the overhead transmission line into the icing thickness prediction model, and output the predicted icing thickness.

[0010] In a preferred solution, the specific steps for establishing the mechanical static model of the transmission line in Step1 include: Step1.1: Assume that the stress caused by the comprehensive load on the transmission line is within the maximum stress that the conductor can withstand and the conductor length remains unchanged, and calculate the self-weight specific load of the conductor: (1) In the formula, is the mass of the conductor per unit length; is the acceleration due to gravity; is the cross-sectional area of the overhead line; represents the self-weight specific load; Step1.2: Approximately assume that the ice-covered shape is circular, and calculate the specific load caused by the ice weight: (2) In the formula, is the ice thickness; is the conductor diameter; is the calculated cross-sectional area of the conductor; represents the specific load of ice covering when the ice thickness is and the wind speed is 0; The calculation formula for the total specific load in the vertical direction is: (3) In the formula, represents the total specific load in the vertical direction when the ice thickness is ; The calculation formula for the wind pressure specific load during ice covering is: (4) In the formula, is the wind load adjustment coefficient; is the wind speed non-uniformity coefficient; is the wind body shape coefficient; is the wind speed; is the angle between the wind direction and the conductor; is the ice-covered wind load increase coefficient; is the ice thickness of , and the wind speed is ; Step1.3: According to the specific load of the conductor self-weight and the specific load caused by the ice weight, calculate the comprehensive specific load during ice covering: (5) In the formula, represents the comprehensive specific load when the ice thickness is and the wind speed is ; Step1.4: Assume that the transmission line is an ideal flexible wire, the load on the overhead line is evenly distributed, and the overhead line is a completely elastic body with a constant elastic coefficient. According to the comprehensive specific load, obtain the state equation of the conductor: (6) In the formula, is the horizontal stress of the transmission line; is the elastic modulus; is the specific load of state 2; is the span; is the horizontal angle of the span; is the linear expansion coefficient; is the temperature; Step 1.5: During the training process, the model is corrected. The correction is achieved in the form of a comprehensive loss function. The predicted value of the ice thickness, wind speed, temperature, and tension monitoring data at the current moment of the model, as well as the true ice thickness, wind speed, temperature, and tension data at the previous moment, are substituted into Equation (6). The absolute value of the calculation result is defined as the degree of violation of physical laws, and the training process of the model is corrected accordingly to make it more conform to the actual wire icing process. At the same time, considering that some factors are ignored in the analysis process, a certain threshold value is set for the degree of violation of physical laws to increase the stability of the training process: Let the loss function formula during the model training process be: (7) In the formula, is the comprehensive loss function; is the model loss function; it represents the degree of closeness between the predicted value and the actual value; is the physical law loss function; represents weighting the physical law loss function; The model loss function adopts the mean square error, and its calculation formula is: (8) In the formula, is the model predicted value, is the actual ice thickness, is the number of samples; During the model training process, in order to make the prediction process of the prediction model as consistent as possible with the actual wire ice growth process, by substituting the predicted ice thickness, temperature, wind speed, tension at the current moment and the true ice thickness, temperature, wind speed, tension at the previous moment into the wire state equation, it is judged whether the predicted ice thickness of the model is consistent with the wire state equation, so as to obtain the physical law loss function, and its calculation equation is: (9) (10) In the formula, is a set positive threshold value.

[0011] In the preferred solution, the construction of the FSLSTM in Step 2 includes: obtaining the core period of the icing data through Fourier transform, segmenting the icing data according to this period, and using the segmented long short-term memory network to capture the local correlation and global correlation of each segment of data respectively.

[0012] In the preferred solution, the specific steps of the FSLSTM construction include: Step 2.1: Using the fast Fourier transform for the time series to make a transformation and obtain The frequency domain representation, and the calculation formula is: (11) In the formula, represents the time series to be processed, represents the fast Fourier transform, The subscript of represents the variable, and the superscript represents the period, is the time length, is the number of variables, is the time series; Step2.2: Calculate the average value of the Fourier transform result, and perform the same processing for each variable. The calculation formula is: (12) In the formula, represents the modulus function; represents the average function; represents the average value of the period to be obtained; Step2.3: Take the first values with the largest modulus to obtain the most effective components and their periods in the original time series. The calculation process is: (13) In the formula, represents the period represented by the first largest modulus values, represents the length of the time series, represents the obtained period; Step2.4: Based on the obtained periods, fill the time series with 0 so that it can be divisible by the period, and then divide it into segments with a length as the step , to obtain the th historical segment data of conductor icing. The calculation process is: (14) In the formula, is the original time series, is the th converted time series, is the filling function, is the conversion function; Step2.5: For the converted time series, the input at each time step is a matrix, and the cell state and the output at the previous time step are also For the matrix, a 1D convolutional layer is used to extract the time-dependent patterns within the current time step, that is, the local features within the segment; the time-iterative structure of the FSLSTM is used to extract the time-dependent patterns between different time steps, that is, the global features between segments: (15) (16) (17) (18) (19) In the formula, 、 、 and represent the 1D convolutional layer; represents the sigmoid function, represents the hyperbolic tangent function, represents the input at the current time step, represents the output of the previous time step, 、 、 、 、 、 represent the output of the forget gate, update gate output, candidate vector, cell state, cell state of the previous time step, and output.

[0013] In the preferred solution, the specific operation of the sample mixing enhancement algorithm Mixup in Step 3 is to generate virtual samples and virtual labels through the linear combination of samples and labels in the original dataset based on the principle of minimizing neighborhood risk. The mathematical expression is: (20) (21) In the formula, , and are the generated virtual samples and labels, 、 and 、 are the original samples and labels, , is responsible for controlling the interpolation trend, The closer The larger it is, the closer the generated virtual samples and labels are to the mean of the original samples and labels.

[0014] In a preferred solution, when training the FSLSTM network in Step 3, the mean square error is used as the loss function, and the model parameters are adjusted through an optimization algorithm until a preset training termination condition is reached. Finally, the mean square error , the mean absolute error and the mean absolute percentage error are used as model evaluation indicators to evaluate the performance of the model: (22) (23) (24) In the formula, is the model prediction value, is the actual ice coating thickness, is the number of samples.

[0015] In a preferred solution, the method further includes a data preprocessing step, which cleans the monitoring data, eliminates abnormal data, uses linear interpolation to complete missing data, and normalizes the data: (25) In the formula, is the sequence value before normalization, is the maximum value of the entire sequence, is the minimum value of the entire sequence, is the sequence value after normalization.

[0016] In a preferred solution, the method is applied to the ice coating prediction of overhead transmission lines in actual projects, improving the prediction accuracy and the generalization ability of the model.

[0017] The overhead transmission line ice coating thickness prediction method based on physics-guided FSLSTM-Mixup provided by the present invention has the following beneficial effects: 1. The present invention solves the problems of low prediction accuracy and weak generalization ability in the field of overhead transmission line dynamic disaster and protection technology, especially the problem of being unable to effectively mine non-static and non-temporal features in the ice coating growth process, and overcomes the specific limitations of the existing prediction models, such as ignoring the physical laws of transmission lines, limited prediction accuracy, and insufficient generalization ability; 2. The present invention combines the mechanical static model of overhead transmission lines and the conductor state equation, and introduces physical laws into the loss function on the basis of the conductor ice coating prediction model with meteorological factors as input features, making the prediction process more real and accurate; 3. The present invention combines Fourier transform and LSTM to construct a prediction model. By extracting the main periods of the input data, it captures local patterns first and then global patterns at multiple scales, realizing the comprehensive feature modeling of icing data at different scales. This model has a stronger modeling ability for the time dependence of icing and higher prediction accuracy. 4. The present invention uses data augmentation algorithms (including the Mixup algorithm) to expand the sample distribution space and improve the overall generalization performance of the model. When the training samples are few, the Mixup algorithm is used for data augmentation, which improves the generalization performance of the model. 5. The present invention establishes a neural network model based on monitoring data. The acquisition method of sample data is more convenient and the application maturity is higher. It is effectively applied to the actual engineering icing prediction, overcoming the shortcomings of traditional mathematical and physical models, with good flexibility and strong generality. 6. Compared with the traditional icing prediction model, the present invention combines physical laws and neural networks to improve the prediction accuracy. By incorporating physical laws into the loss function, the prediction process of the model is more in line with the actual process of icing formation, thus providing more realistic prediction results. 7. The present invention extracts the main periods of the input data through Fourier transform and processes them in segments at different scales, enabling the model to capture local and global correlations respectively, and improving the modeling ability for the time dependence of icing. 8. By combining physical laws and neural networks, and using Fourier transform segmented processing and the Mixup algorithm for data augmentation, the prediction model proposed by the present invention has significantly improved prediction accuracy. 9. In the aspect of predicting the icing thickness of overhead transmission lines, the present invention combines physical laws, mechanical models, neural networks, Fourier transform and data augmentation algorithms to improve the prediction accuracy and generalization ability, having significant technical advantages and practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be further described below in conjunction with the drawings and embodiments: Figure 1 is the overall flowchart of the present invention; Figure 2 is the static mechanical model of the transmission line of the present invention; Figure 3 is the structural diagram of the comprehensive loss function of the present invention; Figure 4 is the structural diagram of FSLSTM of the present invention; Figure 5 is the comparison diagram of the prediction effects of different models in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The technical solutions in the present invention will be further described below in conjunction with the accompanying drawings and embodiments: Embodiment 1 As Figures 1 to 5 shown, an overhead transmission line ice thickness prediction method based on physically-guided FSLSTM-Mixup includes the following steps: Step1: Establish a mechanical static model of the transmission line, conduct a force analysis on the overhead transmission line, consider the self-weight of the conductor, the ice weight caused by icing, and the lateral load caused by wind pressure, and calculate the comprehensive specific load of the conductor according to the analysis results; Step2: Use Fourier transform to process the historical data of conductor icing, extract its main periodic components, segment the icing data according to this period, construct a segmented long short-term memory network FSLSTM based on Fourier transform, and capture local and global correlations respectively; Step3: Adopt the sample mixing enhancement algorithm Mixup, based on the principle of minimizing neighborhood risk, generate new samples and labels through the linear combination of samples and labels in the original dataset to expand the dataset scale and improve the model generalization ability; Step4: Use the processed historical icing data and relevant meteorological data as inputs, train through the FSLSTM network, and obtain an ice thickness prediction model; Step5: Input the real-time collected overhead transmission line icing and relevant meteorological data into the ice thickness prediction model, and output the predicted ice thickness.

[0020] In this embodiment, the specific steps of establishing the mechanical static model of the transmission line in Step1 include: Step1.1: Assume that the stress caused by the comprehensive load on the transmission line is within the maximum stress that the conductor can withstand and the conductor length remains unchanged, and calculate the specific self-weight load of the conductor: (1) In the formula, is the mass of the conductor per unit length; is the acceleration due to gravity; is the cross-sectional area of the overhead line; represents the specific self-weight load; Step1.2: Approximately consider the icing shape as circular, and calculate the specific load caused by the icing weight: (2) In the formula, is the ice thickness; is the conductor diameter; is the calculated cross-sectional area of the conductor; represents the icing specific load when the ice thickness is and the wind speed is 0; The calculation formula for the total specific load in the vertical direction is as follows: (3) In the formula, represents the total specific load in the vertical direction when the ice thickness is ; The calculation formula for the wind pressure specific load during icing is as follows: (4) In the formula, is the wind load adjustment coefficient; is the wind speed non-uniformity coefficient; is the wind load shape coefficient; is the wind speed; is the angle between the wind direction and the conductor; is the increased coefficient of wind load during icing; is the ice thickness of , and the wind speed is ; Step1.3: Calculate the comprehensive specific load during icing according to the specific load caused by the self-weight of the conductor and the weight of the ice coating: (5) In the formula, represents the comprehensive specific load when the ice thickness is and the wind speed is ; Step1.4: Assume that the transmission line is an ideal flexible wire, the load on the overhead line is evenly distributed, and the overhead line is a completely elastic body with a constant elastic coefficient. According to the comprehensive specific load, obtain the state equation of the conductor: (6) In the formula, is the horizontal stress of the transmission line; is the elastic modulus; is the specific load at state 2; is the span; is the horizontal angle of the span; is the linear expansion coefficient; is the temperature; Step1.5: During the training process, correct the model. The correction is achieved in the form of a comprehensive loss function. Substitute the predicted value of the ice coating thickness, wind speed, temperature, and tension monitoring data at the current moment of the model and the true ice coating thickness, wind speed, temperature, and tension data at the previous moment into formula (6). Define the absolute value of the calculation result as the degree of violation of physical laws, and use this to correct the training process of the model to make it more conform to the actual conductor icing process. At the same time, considering that some factors are ignored in the analysis process, set a certain threshold value for the degree of violation of physical laws to increase the stability of the training process: Let the loss function formula during model training be as follows: (7) In the formula, is the comprehensive loss function; is the model loss function; it represents the degree of closeness between the predicted value and the actual value; is the physical law loss function; represents weighting the physical law loss function; The model loss function adopts the mean square error, and its calculation formula is: (8) In the formula, is the model predicted value, is the actual ice coating thickness, is the number of samples; During the model training process, to make the prediction process of the prediction model as consistent as possible with the actual wire ice coating growth process, by substituting the predicted ice coating thickness, temperature, wind speed, tension at the current moment and the true ice coating thickness, temperature, wind speed, tension at the previous moment into the wire state equation, it is judged whether the predicted ice coating thickness of the model is consistent with the wire state equation, so as to obtain the physical law loss function, and its calculation equation is: (9) (10) In the formula, is a set positive threshold value.

[0021] Furthermore, the construction of the FSLSTM in Step 2 includes: obtaining the core period of the ice coating data through Fourier transform, segmenting the ice coating data according to this period, and using the segmented long short-term memory network to capture the local correlation and global correlation of each segment of data respectively.

[0022] Furthermore, the specific steps of the FSLSTM construction include: Step 2.1: Using the fast Fourier transform to transform the time series to obtain the frequency domain representation of , and the calculation formula is: (11) In the formula, represents the time series to be processed, represents the fast Fourier transform, The subscript of represents the variable, and the superscript represents the period, is the time length, is the number of variables, is the time series; Step2.2: Calculate the average value of the Fourier transform results, and perform the same processing for each variable. The calculation formula is: (12) In the formula, represents the modulus function; represents the average function; represents the average value of the period to be calculated; Step2.3: Take the first values with the largest modulus to obtain the most effective components and their periods in the original time series. The calculation process is as follows: (13) In the formula, represents the periods represented by the first moduli with the largest values, represents the length of the time series, represents the calculated period; Step2.4: Based on the obtained periods, fill the time series with 0 so that it can be divisible by the period, and then divide it into segments with a length of as the step size to obtain the th segment data of the historical icing of the conductor. The calculation process is as follows: (14) In the formula, is the original time series, is the th converted time series, is the filling function, is the conversion function; Step2.5: For the converted time series, the input at each time step is a matrix of . The cell state and the output at the previous time step are also matrices of . Use a 1D convolutional layer to extract the time-dependent patterns within the current time step, that is, the local features within the segment; use the time iteration structure of FSLSTM to extract the time-dependent patterns between different time steps, that is, the global features between segments: (15) (16) (17) (18) (19) In the formula, , , and represent 1D convolutional layers; represents the sigmoid function, represents the hyperbolic tangent function, represents the input at the current time step, represents the output of the previous time step, 、 、 、 、 、 represent the output of the forget gate, the output of the update gate, the candidate vector, the cell state, the cell state of the previous time step, and the output.

[0023] Furthermore, the specific operation of the sample mixing and augmentation algorithm Mixup in Step 3 is to generate virtual samples and virtual labels through the linear combination of samples and labels in the original dataset based on the principle of minimizing neighborhood risk. The mathematical expression is: (20) (21) In the formula, , and are the generated virtual samples and labels, , and , are the original samples and labels, , is responsible for controlling the trend of interpolation, the closer it is to 0, the closer the generated virtual samples and labels are to the original samples and labels, the larger it is, the closer the generated virtual samples and labels are to the mean of the original samples and labels.

[0024] Furthermore, when training the FSLSTM network in Step 3, the mean squared error is used as the loss function, and the model parameters are adjusted through an optimization algorithm until the preset training termination condition is reached. Finally, the mean squared error , the mean absolute error and the mean absolute percentage error are used as model evaluation indicators to evaluate the performance of the model: (22) (23) (24) In the formula, is the model predicted value, is the actual ice coating thickness, is the number of samples.

[0025] Furthermore, the method further includes a data preprocessing step of cleaning the monitoring data, removing abnormal data, complementing the missing data by using linear interpolation method, and normalizing the data: (25) In the formula, is the sequence value before normalization, is the maximum value of the whole sequence, is the minimum value of the whole sequence, is the sequence value after normalization.

[0026] Furthermore, the method is applied to the ice coating prediction of overhead transmission lines in actual engineering to improve the prediction accuracy and the generalization ability of the model.

[0027] Embodiment 2 In another preferred embodiment, on the basis of the above Embodiment 1, as Figures 1 to 5 shown, the following will detail the method of the present invention through specific embodiments. In this embodiment, we will introduce in detail the specific implementation steps of the ice coating thickness prediction method for overhead transmission lines based on Physics-Informed - FSLSTM (Fourier Transform Segmented Long Short-Term Memory network) - Mixup (Sample Mixing Data Augmentation).

[0028] Step 1: Establish a mechanical static model of the transmission line First, conduct a force analysis on the overhead transmission line. The overhead transmission line is usually subjected to three types of loads in the external environment, namely the self-weight of the conductor, the ice weight caused by ice coating, and the lateral load caused by wind pressure. Assuming that the stress caused by the combined load on the transmission line is within the maximum stress that the conductor can withstand and the length of the conductor remains unchanged, we can calculate the relevant specific loads according to the following formula: Calculation formula for the self-weight specific load: (1) Calculation formula for the ice coating specific load (simplified calculation, approximately assuming that the ice coating shape is circular): (2) The calculation formula for the total specific load in the vertical direction is: (3) In the formula, represents the total specific load in the vertical direction when the ice thickness is ; The calculation formula for the wind pressure specific load during ice coating is: (4) The comprehensive specific load during ice coating: (5) Next, we assume that the transmission line is an ideal flexible line, the load on the overhead line is evenly distributed, and the overhead line is a perfectly elastic body with a constant elastic coefficient. Based on these assumptions, we can obtain the state equation of the conductor for subsequent model correction.

[0029] During the training process, we substitute the predicted value of the ice coating thickness, wind speed, temperature, and tension monitoring data at the current moment of the model, and the true ice coating thickness, wind speed, temperature, and tension data at the previous moment into the conductor state equation to calculate the degree of violation of physical laws, and based on this, correct the training process of the model. The calculation equation for the degree of violation of physical laws is as follows: (9) (10).

[0030] Step 2: Construct the FSLSTM model For a time series with a time length of and a variable number of , we first use the fast Fourier transform to transform the time series to obtain the frequency domain representation of ; then, we find the average value of the Fourier transform results and perform the same processing for each variable. Next, we take the first values with the largest modulus to obtain the most effective components and their periods in the original time series.

[0031] Based on the obtained periods, we fill the time series with 0 so that it can be divisible by the period, and then divide it into segments with a length of the period and a step size of the period. In this way, we can obtain the segmented representation of the ice coating historical data for input to the FSLSTM model.

[0032] The structure of the FSLSTM model includes multiple 1D convolutional layers (One-Dimensional Convolutional Layer) and LSTM (Long Short-Term Memory). By extracting the main period of the input data, it first captures the local pattern at multiple scales and then captures the global pattern, thereby realizing comprehensive feature modeling of ice cover data at different scales.

[0033] Step 3: Sample Mixing Enhancement Algorithm Due to the high difficulty of collecting icing data on overhead transmission lines and related meteorological data, it is difficult to obtain relevant data and the icing data on transmission lines is incomplete. Therefore, under the condition of fewer training samples, we use the data enhancement Mixup algorithm to expand the sample distribution space and improve the overall generalization performance of the model.

[0034] The Mixup algorithm is based on the principle of neighborhood risk minimization. It generates new samples and labels through the linear combination of samples and labels in the original data set. Its mathematical model is: (20) (twenty one).

[0035] Example 3 Based on Example 2, we further explain the specific application of the present invention in detail.

[0036] In this neural network training example, we selected the ambient temperature, relative humidity, wind speed, light, air pressure, ice thickness and tension in the test records as input features. The data collection time interval is 20 minutes, with a total of 539 sets of sample data. First, we normalize the data to between 0 and 1.

[0037] Then, we used the first 70% of the monitoring data as the training set and the last 30% as the test set to test the performance of the model. For abnormal data (such as data with a temperature above 5°C), we chose to remove it and use linear interpolation to fill in the missing data.

[0038] Next, we calculated the comprehensive specific load of the conductor according to the formula of the static model of conductor mechanics, and used it as a part of the physical law loss function for model correction.

[0039] In the process of building the FSLSTM model, we first use Fourier transform to extract the main cycle of the input historical data and adaptively segment the ice cover historical data according to the cycle. Then, we use FSLSTM to capture local correlation and global correlation respectively to achieve accurate prediction of ice cover thickness.

[0040] Finally, we adopt the mean squared error (Mean Squared Error), mean absolute error (Mean Absolute Error), and mean absolute percentage error (Mean Absolute Percentage Error) as the model evaluation indicators to evaluate the performance of the model. Through comparative experiments with other ice thickness prediction models, such as BP (Back Propagation Neural Network), RNN (Recurrent Neural Network), LSTM, TCN (Temporal Convolutional Networks), CNN-LSTM (Convolutional Neural Network-Long Short-Term Memory combined model), etc., we found that the physically guided FSLSTM-Mixup prediction model proposed in the present invention has relatively higher prediction accuracy, the ice coverage prediction output is significantly closer to the actual ice thickness, the fitting effect of the model is better, and the prediction performance is superior to other models.

[0041] Example 4 In another preferred embodiment, based on the above Embodiments 1, 2, and 3, please refer to the attached Figure 1 Overall flowchart. The specific implementation steps of the overhead transmission line ice thickness prediction method based on physical guidance-FSLSTM (Fourier piecewise long short-term memory network)-Mixup (sample mixing data augmentation) are as follows: In this neural network training example, the environmental temperature, relative humidity, wind speed, light, air pressure, ice thickness, and tension in the test records are selected. The time interval for data collection is 20 minutes, and a total of 539 sets of sample data are obtained.

[0042] Normalize according to the following formula to normalize the data between 0 and 1. Some of the normalized data is shown in Table 1: (25).

[0043]

[0044] Use the first 70% of the monitoring data as the training set and the last 30% as the test set to test the performance of the model. The monitoring data may be abnormal or missing due to equipment failures, maintenance, etc. Therefore, abnormal data (such as data with a temperature above 5°C) is selected for deletion, and the missing data is filled in using the linear interpolation method.

[0045] The overall process of the prediction model is as follows Figure 1 As shown, for the input icing historical data, first expand the distribution space of the training set according to the following formula: (20) (21) The mechanical static model of the conductor is as follows Figure 2 As shown, calculate the comprehensive specific load of the conductor according to the following formula: The calculation formula of the dead weight specific load: (1) The calculation formula of the icing specific load (simplified calculation, approximately considering the icing shape as circular): (2) The calculation formula of the total specific load in the vertical direction is: (3) In the formula, represents the total specific load in the vertical direction when the ice thickness is ; The calculation formula of the wind pressure specific load during icing is: (4) The comprehensive specific load during icing: (5) The loss function introducing physical laws is as follows Figure 3 As shown, calculate according to the following formula: (9) (10) (11) (12) The structure of FSLSTM is as follows Figure 4 As shown, first use Fourier transform to extract the main period of the input historical data, segment the icing historical data adaptively according to this period, and then use FSLSTM to capture local correlation and global correlation respectively.

[0046] To better demonstrate the excellent performance of the present invention, prediction models such as BP neural network, RNN, LSTM, TCN, and CNN-LSTM are selected for comparison. They are trained for the same number of epochs on the same dataset, with the training batch size set to 32, the learning rate to 0.002, the model optimizer to Adam, trained for 300 epochs under the same conditions, and , and are calculated on the test set to compare the performance of each model.

[0047] The present invention uses some metrics for evaluating sequence prediction problems to display the results, namely the mean square error , the mean absolute error and the mean absolute percentage error , and their mathematical models are respectively: (22) (23) (24) The comparison of the evaluation metrics of each model is shown in Table 2 below. The predicted curves of the ice thickness of overhead transmission lines for each model are as Figure 5 shown. According to the following table and Figure 5 , it can be seen that compared with other ice thickness prediction models, the prediction accuracy of the physically-guided FSLSTM-Mixup prediction model proposed by the present invention is relatively higher, the predicted output of ice cover is significantly closer to the actual ice thickness, the fitting effect of the model is better, the prediction performance is superior to the other two models, and the generalization performance is the best.

[0048]

[0049] Compared with the traditional ice cover prediction model, the prediction error of the model in this paper is the smallest and the model performance is the best. Compared with other models, its mean square error is reduced by 0.675 - 0.796, the mean absolute error is reduced by 0.413 - 0.531, and the mean absolute percentage error is reduced by 8.61% - 11.29%. Therefore, the experimental results further prove that the prediction model proposed by the present invention can further reduce the prediction error and improve the prediction accuracy.

[0050] The above four embodiments fully demonstrate the effectiveness and superiority of the present invention in predicting the ice thickness of overhead transmission lines. By combining physical laws, Fourier transform, LSTM, and data augmentation techniques, the present invention can achieve accurate prediction of ice thickness and provide strong decision-making support for the anti-icing and disaster reduction work of transmission lines.

[0051] In a preferred solution, the construction of FSLSTM in Step 2 includes: obtaining the core period of the ice cover data through Fourier transform, segmenting the ice cover data according to this period, and using the segmented long short-term memory network to capture the local correlation and global correlation of each segment of data respectively; the above settings can significantly improve the prediction accuracy and generalization ability of the model for ice cover data. In addition, the attention mechanism is used to weight and fuse the features of each segment, further optimizing the performance of FSLSTM in processing non-stationary ice cover data.

[0052] In the preferred solution, the specific operation of the sample mixing enhancement algorithm Mixup in Step 3 is to generate virtual samples and virtual labels through linear combinations of samples and labels in the original data set based on the principle of neighborhood risk minimization; the above settings effectively expand the diversity of the training set and enhance the generalization ability of the model. During the model training process, these virtual samples and real samples jointly participate in the calculation of the loss function, further optimizing the decision boundary of the model.

[0053] In the preferred solution, when training the FSLSTM network in Step 3, the mean square error is used As the loss function, the model parameters are adjusted through the optimization algorithm until the preset training termination condition is reached, and finally the mean square error is used , mean absolute error and mean absolute percentage error As a model evaluation indicator to evaluate the performance of the model; the above settings are designed to ensure the stability and accuracy of the FSLSTM network in time series prediction tasks. In addition, an early stopping strategy is introduced to avoid overfitting, and after the training is completed, the model is cross-validated to further verify its generalization ability.

[0054] The preferred scheme also includes a data preprocessing step to clean the monitoring data, eliminate abnormal data, use linear interpolation to fill in missing data, and normalize the data; the above settings can significantly improve the accuracy and efficiency of data analysis, ensure the quality of input data during model training, thereby enhancing the reliability of prediction results and providing a solid foundation for subsequent decision-making.

[0055] In summary, the proposed physical-guided FSLSTM-Mixup method for predicting the icing thickness of overhead transmission lines has made remarkable progress in the field of dynamic disaster and protection technology of overhead transmission lines: This method effectively solves the problems existing in the existing icing thickness prediction models of transmission lines, such as low prediction accuracy, weak generalization ability, and the inability to effectively mine non-static and non-temporal features in the icing growth process. Compared with previous technologies, the innovation of this invention lies in the first combination of the physical laws of transmission line icing with neural network models. It not only makes full use of the powerful data fitting ability of neural networks but also incorporates the guidance of physical laws, making the prediction results closer to the actual situation and significantly improving the prediction accuracy. Traditional prediction models often only focus on the icing thickness itself, ignoring the non-static, non-temporal features in its growth process and the influence of meteorological factors such as temperature, humidity, and wind speed, resulting in limited prediction accuracy. However, by constructing an advanced FSLSTM neural network model, this invention can deeply mine these features and their correlations with the icing thickness, making the prediction results more comprehensive and accurate. In addition, this method also processes the icing data through Fourier transform, segments it by period, and constructs an FSLSTM model for prediction. This segmented processing method can better capture the local and global correlations of icing data, further improving the prediction performance. In short, by using physical laws as an important guidance for neural network models and combining advanced data processing technologies and neural network architectures, this invention achieves accurate prediction of the icing thickness of overhead transmission lines, providing strong decision-making support for the anti-icing and disaster reduction work of transmission lines. The successful application of this technology marks a new level in the disaster prevention and mitigation technology of transmission lines in China, not only ensuring the safe and stable operation of the power grid but also providing a solid technical guarantee for energy supply under extreme weather conditions.

Claims

1. A method for predicting ice thickness of overhead transmission lines based on physics-guided FSLSTM-Mixup, characterized in that: The following steps are involved: Step 1: Establish a static mechanical model of the transmission line, perform a force analysis on the overhead transmission line, consider the conductor's deadweight, ice weight caused by icing, and lateral load caused by wind pressure, and calculate the comprehensive load ratio of the conductor based on the analysis results; Step 2: Use Fourier transform to process the historical data of conductor ice coverage, extract its main periodic components, segment the ice coverage data according to the period, and construct a segmented long short-term memory network FSLSTM based on Fourier transform to capture local correlation and global correlation respectively; Step 3: Using the sample mixing enhancement algorithm Mixup, based on the principle of neighborhood risk minimization, new samples and labels are generated through linear combinations of samples and labels in the original data set to expand the data set size and improve the generalization ability of the model; Step 4: Use the processed historical ice data and related meteorological data as input, train the FSLSTM network, and obtain the ice thickness prediction model; Step 5: Input the real-time collected overhead transmission line icing and related meteorological data into the icing thickness prediction model, and output the predicted icing thickness.

2. According to claim 1, the method for predicting ice thickness of overhead transmission lines based on FSLSTM-Mixup guided by physics is characterized in that: The specific steps of establishing the transmission line mechanical static model in Step 1 include: Step 1.1: Assuming that the stress caused by the combined load on the transmission line is within the maximum stress range that the conductor can withstand and the conductor length remains unchanged, calculate the conductor deadweight load ratio: （1）； In the formula, is the mass of the conductor per unit length; is the acceleration due to gravity; is the cross-sectional area of ​​the overhead line; Indicates the deadweight load; Step 1.2: Assume that the shape of the ice is approximately circular, and calculate the specific load caused by the weight of the ice: （2）； In the formula, is the ice thickness; is the wire diameter; Calculate the cross-sectional area for the conductor; The ice thickness is , ice load ratio at wind speed 0; The calculation formula for the total specific load in the vertical direction is: （3）； In the formula, The ice thickness is Total specific load in vertical direction; The calculation formula of wind pressure load ratio when ice is applied is: （4）； In the formula, is the wind load adjustment factor; is the wind speed unevenness coefficient; is the wind body shape coefficient; is the wind speed; is the angle between wind direction and conductor; is the ice-covered wind load enhancement factor; The ice thickness is , wind speed is Wind pressure load ratio at time; Step 1.3: Calculate the comprehensive specific load when ice is applied based on the specific load caused by the conductor’s own weight and the specific load caused by ice coverage: （5）； In the formula, The ice thickness is , wind speed is The comprehensive load ratio at that time; Step 1.4: Assuming that the transmission line is an ideal flexible line, the load on the overhead line is evenly distributed, and the overhead line is a completely elastic body with its elastic coefficient remaining unchanged, the state equation of the conductor is obtained according to the comprehensive load ratio: （6）； In the formula, is the horizontal stress of the transmission line; is the elastic modulus; is the specific load of state 2; is the gear spacing; is the horizontal angle of the gear pitch; is the linear expansion coefficient; is temperature; Step 1.5: During the training process, the model is corrected. The correction is implemented in the form of a comprehensive loss function. The model's current prediction of ice thickness, wind speed, temperature, and tension monitoring data and the actual ice thickness, wind speed, temperature, and tension data at the previous moment are substituted into formula (6). The absolute value of the calculation result is defined as the degree of violation of physical laws. This is used to correct the model training process to make it more consistent with the actual conductor icing process. At the same time, considering that some factors are ignored in the analysis process, a certain threshold value is set for the degree of violation of physical laws to increase the stability of the training process: Assume that the loss function formula during model training is: （7）； In the formula, is the comprehensive loss function; Is the model loss function; it indicates the closeness between the predicted value and the actual value; is the physical law loss function; Indicates weighting of the physical law loss function; The model loss function uses mean square error, and its calculation formula is: （8）； In the formula, is the model prediction value, is the actual ice thickness, is the number of samples; In the process of model training, in order to make the prediction process of the prediction model and the actual conductor ice growth process as consistent as possible, the predicted ice thickness, temperature, wind speed, tension at the current moment and the actual ice thickness, temperature, wind speed, and tension at the previous moment are substituted into the conductor state equation to determine whether the model's predicted ice thickness is consistent with the conductor state equation, thereby obtaining the physical law loss function, whose calculation equation is: （9）； （10）； In the formula, is the positive threshold value set.

3. According to claim 1, the method for predicting ice thickness of overhead transmission lines based on FSLSTM-Mixup guided by physics is characterized in that: The construction of FSLSTM in Step 2 includes: obtaining the core period of ice cover data through Fourier transform, segmenting the ice cover data according to the period, and using the segmented long short-term memory network to capture the local correlation and global correlation of each segment data respectively.

4. According to claim 3, the method for predicting ice thickness of overhead transmission lines based on FSLSTM-Mixup guided by physics is characterized in that: The specific steps of constructing the FSLSTM include: Step 2.1: Using Fast Fourier Transform For time series Convert to get The frequency domain representation of is: （11）； In the formula, represents the time series to be processed, represents the fast Fourier transform, The subscripts represent variables, and the superscripts represent periods. is the length of time, is the number of variables, is a time series; Step 2.2: Find the average value of the Fourier transform results. Perform the same treatment on each variable. The calculation formula is: （12）； In the formula, represents the modulus value function; represents the averaging function; represents the desired period average value; Step 2.3: Take the first value with the largest modulus value values, and get the most effective The components and their periods are calculated as follows: （13）； In the formula, Indicates the maximum front The period represented by the modulus value, represents the length of the time series, represents the obtained period; Step 2.4: Based on the obtained Periods, fill the time series with 0 to make it divisible by the period, and then use the length as the step length , divide it into segments, and get The historical segmented data of conductor ice coverage is calculated as follows: （14）； In the formula, is the original time series, For the The transformed time series, is the filling function, is the conversion function; Step 2.5: For the converted time series, the input of each time step is yes Matrix, cell state and the output of the previous time step Too The 1D convolutional layer is used to extract the time-dependent pattern in the current time step, that is, the local features in the segment; the time-iterative structure of FSLSTM is used to extract the time-dependent pattern between different time steps, that is, the global features between segments: （15）； （16）； （17）； （18）； （19）； In the formula, , , and Represents a 1D convolutional layer; represents the sigmoid function, represents the hyperbolic tangent function, represents the input of the current time step, represents the output of the previous time step, 、 、 、 、 、 Represents the output of the forget gate, the update gate output, the candidate vector, the cell state, the cell state at the previous time step, and the output.

5. According to claim 1, the method for predicting ice thickness of overhead transmission lines based on FSLSTM-Mixup guided by physics is characterized in that: The specific operation of the sample mixing enhancement algorithm Mixup in Step 3 is to generate virtual samples and virtual labels through the linear combination of samples and labels in the original data set based on the principle of minimizing neighborhood risk. The mathematical expression is: （20）； （21）； In the formula, , and are the generated virtual samples and labels, , and , are the original samples and labels, , Responsible for controlling the interpolation trend, The closer it is to 0, the closer the generated virtual samples and labels are to the original samples and labels. The larger it is, the closer the generated virtual samples and labels are to the mean of the original samples and labels.

6. According to claim 1, the method for predicting ice thickness of overhead transmission lines based on FSLSTM-Mixup guided by physics is characterized in that: When training the FSLSTM network in Step 3, the mean square error is used As the loss function, the model parameters are adjusted through the optimization algorithm until the preset training termination condition is reached, and finally the mean square error is used. , mean absolute error and mean absolute percentage error As model evaluation indicators to evaluate the performance of the model: （22）； （23）； （24）； In the formula, is the model prediction value, is the actual ice thickness, is the number of samples.

7. The method for predicting ice thickness of overhead power transmission lines based on physics-guided FSLSTM-Mixup according to claim 1 is characterized in that: It also includes data preprocessing steps to clean the monitoring data, remove abnormal data, use linear interpolation to fill in missing data, and normalize the data: （25）； In the formula, is the sequence value before normalization, is the maximum value of the entire sequence, is the minimum value of the entire sequence, is the normalized sequence value.

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