A transmission line ice shedding jump height prediction method based on WOA-GA-GRNN

Abstract

This invention relates to the field of de-icing prediction technology, specifically a method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN, comprising: S1, acquiring prediction data of the de-icing jump height of transmission lines, including structural parameters, load parameters, and material parameters; S2, constructing a GRNN network, determining the number of neurons in the input layer based on the number of parameter variables in the structural, load, and material parameters; S3, using the smoothing factor used in the GRNN network as the individual to be optimized in the WOA population, performing crossover and mutation operations on the WOA population using the crossover and mutation operators of the GA algorithm, with the minimum fitness function value as the optimization objective, and iteratively optimizing to obtain the optimized smoothing factor; S4, configuring the optimized smoothing factor into the GRNN network to obtain a WOA-GA-GRNN hybrid prediction model, inputting the structural parameters, load parameters, and material parameters of the transmission line to be predicted into the WOA-GA-GRNN hybrid prediction model to output the de-icing jump height, thus achieving a more accurate and stable prediction of the de-icing jump height of transmission lines.

Description

Technical Field

[0001] This invention relates to the field of de-icing prediction technology, specifically to a method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN. Background Technology

[0002] Transmission lines are the backbone of power transmission in the power system. However, due to the influence of climate conditions in the ice-covered areas of my country, transmission lines are frequently covered with ice. When the ambient temperature rises or the wind blows, the iced lines may partially or completely detach from the ice. During the detachment process, the elastic potential energy of the lines is released rapidly, which can cause violent detachment jumping phenomena.

[0003] It is evident that de-icing jumps are one of the core threats to the safe operation of transmission lines in medium-icing regions. During a jump, the electrical clearance between phases is significantly reduced, easily leading to phase-to-phase flashover faults. Simultaneously, the dynamic tension generated by the jump causes significant unbalanced loads on the tower suspension points, potentially resulting in tower tilting, collapse, and other serious accidents. Existing research often employs a single generalized regression neural network (GRNN) to predict de-icing jump heights. However, the prediction accuracy of a single GRNN model is highly dependent on the empirical selection of the smoothing factor, making it prone to overfitting or skewed fitting, resulting in a large average relative error and low prediction accuracy. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem of low prediction accuracy caused by the empirical selection of the smoothness factor in the existing GRNN network. A WOA-GA-GRNN hybrid prediction model is constructed to achieve more accurate and stable prediction of the de-icing jump height of transmission lines.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is as follows: a method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN, comprising: S1, acquiring de-icing jump height prediction data of transmission lines, wherein the de-icing jump height prediction data includes structural parameters, load parameters, and material parameters; S2, constructing a GRNN network, and determining the number of neurons in the input layer of the GRNN network based on the number of parameter variables in the structural parameters, load parameters, and material parameters; S3, using the smoothing factor used in the GRNN network as the individual to be optimized in the WOA population, performing crossover and mutation operations on the WOA population using the crossover and mutation operators of the GA algorithm, taking the minimum fitness function value of the GRNN network as the optimization objective, and iteratively optimizing the smoothing factor based on the de-icing jump height prediction data; S4, configuring the optimized smoothing factor into the GRNN network to obtain a WOA-GA-GRNN hybrid prediction model, inputting the structural parameters, load parameters, and material parameters of the transmission line to be predicted into the WOA-GA-GRNN hybrid prediction model to output the de-icing jump height.

[0006] This invention uses the smoothing factor of the GRNN network as the individual to be optimized in the WOA population and introduces the crossover and mutation operator of the GA algorithm for iterative optimization. This avoids the blindness of traditional manual selection of smoothing factors, while improving population diversity, preventing the algorithm from getting trapped in local optima, and improving the efficiency and accuracy of parameter optimization. Using structural parameters, load parameters, and material parameters as inputs to the obtained prediction model, it can accurately reflect the influencing factors of transmission line de-icing jumps, enabling the model to better fit nonlinear mapping relationships and improve prediction accuracy and generalization ability. By configuring the optimized smoothing factor into the GRNN network, a stable and reliable WOA-GA-GRNN hybrid prediction model is constructed, improving the accuracy and precision of the prediction results. This provides effective data support for subsequent anti-icing design and operation and maintenance of transmission lines, enhancing engineering practicality and operational safety.

[0007] Optionally, the step of iteratively optimizing the smoothing factor includes: S31, combining several randomly generated smoothing factors into a WOA population, setting the population size and iteration number of the WOA population, and using the mean squared error between the predicted and actual values ​​of the GRNN network as the fitness function; S32, setting an adaptive weight coefficient to adjust the WOA search range, wherein the adaptive weight coefficient decreases linearly with the iteration number; S33, updating the position of the smoothing factors in the WOA population according to the adaptive weight coefficient, performing crossover and mutation operations on the smoothing factors after the position update using the crossover and mutation operators of the GA algorithm, and calculating the fitness function of the smoothing factors after the crossover and mutation operations; S34, outputting the optimized smoothing factor when the fitness function value is less than a preset fitness function threshold or the iteration number reaches the maximum iteration number.

[0008] Optionally, the step of performing crossover and mutation operations on the smooth factor after position update using the crossover operator and mutation operator of the GA algorithm includes: S331, randomly generating probability values ​​and performing branch operations according to the values ​​of the probability values; S332, if the probability value is not greater than a preset probability threshold, then performing a crossover operation on the smooth factor after position update using the crossover operator of the GA algorithm; S333, if the probability value is greater than the preset probability threshold, then performing a mutation operation on the smooth factor after position update using the mutation operator of the GA algorithm.

[0009] Optionally, the GRNN network includes an input layer, a pattern layer, a summation layer, and an output layer; the steps of building the GRNN network include: S21, determining the number of neurons in the pattern layer based on the number of training samples in the de-icing jump height prediction data; S22, setting the summation layer to a two-node structure, with the two nodes performing a weighted summation operation and an arithmetic summation operation respectively; S23, setting the output layer to a linear output structure to output the de-icing jump height predicted by the GRNN network.

[0010] Optionally, it also includes: S5, if the output de-icing jump height exceeds the preset de-icing jump safety threshold, then the anti-icing modification of the transmission line to be predicted is carried out by increasing the tower crossarm offset or adding phase spacers.

[0011] Optionally, the step of obtaining the de-icing jump height prediction data of the transmission line includes: S11, obtaining the original de-icing jump height prediction data of the transmission line, and using the three-standard-deviation criterion to remove outliers in the original de-icing jump height prediction data to obtain first processed data; S12, performing non-integer positive transformation on the extremely small index data in the first processed data to obtain second processed data; S13, performing normalization processing on the second processed data to obtain de-icing jump height prediction data.

[0012] Optionally, after the step of configuring the optimized smoothing factor into the GRNN network, the method further includes: S41, using the configured GRNN network to perform accuracy verification on the test set in the de-icing jump height prediction data; S42, if the accuracy verification result meets the preset accuracy verification requirements, then the configured GRNN network is determined as a WOA-GA-GRNN hybrid prediction model.

[0013] Optionally, accuracy verification can be performed by calculating the average relative error or the root mean square error; the preset accuracy verification requirements include that the calculated average relative error is not greater than a preset average relative error threshold, or the calculated root mean square error is not greater than a preset root mean square error threshold.

[0014] Optionally, the structural parameters include the number of conductor splits and the span, the load parameters include the icing thickness and the de-icing rate, and the material parameters include the calculated breaking force of the conductor.

[0015] Optionally, the data sources for the ice-breaking jump height prediction data include laboratory experimental data, field monitoring data, and ANSYS finite element simulation data.

[0016] The beneficial effects of this invention are as follows: 1. By sequentially performing outlier removal, index positiveization, and normalization preprocessing on the original data, the interference of dimensional differences and outlier data can be eliminated, improving the quality of input data and providing a stable and reliable data foundation for subsequent model training. 2. A hybrid optimization strategy combining WOA and GA is adopted. The search range is dynamically adjusted through adaptive weight coefficients, and crossover or mutation operations are performed according to random probability branches. This retains the global search capability of WOA while enhancing population diversity using genetic operators, effectively avoiding the algorithm from getting trapped in local optima. This achieves efficient and accurate optimization of the smoothing factor of GRNN, solving the problems of strong subjectivity and insufficient accuracy in traditional manual parameter selection.

[0017] 2. Based on the number of training samples, the pattern layer neurons of the GRNN network are configured, employing a dual-node summation layer and a linear output layer structure. This allows the network to better fit the complex nonlinear mapping relationship between structural parameters, loads, material parameters, and the de-icing jump height, improving the model's fitting accuracy and generalization ability. The accuracy of the GRNN network with the optimized smoothing factor is verified. The model's reliability is objectively evaluated using the mean relative error or root mean square error. After meeting the preset accuracy verification requirements, a WOA-GA-GRNN hybrid prediction model is obtained to ensure the reliability of the prediction results. Based on the high-precision prediction results, anti-icing modification measures such as adjusting tower crossarm offsets and adding phase-to-phase spacers are implemented. The data sources cover laboratory measurements, on-site monitoring, and finite element simulations, making it applicable to a wider range of scenarios. The overall solution combines high prediction accuracy, high optimization efficiency, strong engineering practicality, and high operational reliability, providing efficient and scientific technical support for transmission line anti-icing disaster reduction and safe operation and maintenance. Attached Figure Description

[0018] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0019] Figure 1 This is a flowchart of a method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN in this invention; Figure 2 This is a flowchart illustrating how the WOA-GA algorithm is used to optimize the smoothing factor for a GRNN network in this invention. Detailed Implementation

[0020] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0021] like Figure 1 As shown, this invention provides a method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN. By constructing a GRNN network and integrating the advantages of whale optimization algorithm and genetic algorithm, it achieves high-precision prediction of the jump height of 110kV / 220kV transmission lines under different icing conditions. The method includes: S1. Obtain predicted data on the de-icing jump height of transmission lines. This predicted data includes structural parameters, load parameters, and material parameters. The prediction object is 110kV / 220kV iced transmission lines, covering typical models such as JL / G1A-400 / 50 and JL / G1A-630 / 45. The unit of calculation is a single conductor. Parameter variables include the number of conductor splits (2~8 splits), span (300~800m), ice thickness (15~20mm), de-icing rate (20%~100%), and calculated conductor breaking force (123.4~329.85kN). The output variable is the peak value of the conductor's de-icing jump height (unit: m). S2. Construct a GRNN network and determine the number of neurons in the input layer of the GRNN network based on the number of parameter variables in the structural parameters, the load parameters, and the material parameters.

[0022] S3. The smoothing factor used in the GRNN network is taken as the individual to be optimized in the WOA population. The crossover and mutation operators of the GA algorithm are used to perform crossover and mutation operations on the WOA population. The optimization objective is to minimize the fitness function value of the GRNN network. The optimized smoothing factor is obtained by iterative optimization based on the ice-breaking jump height prediction data.

[0023] S4. Configure the optimized smoothing factor into the GRNN network to obtain the WOA-GA-GRNN hybrid prediction model. Input the structural parameters, load parameters and material parameters of the transmission line to be predicted into the WOA-GA-GRNN hybrid prediction model to output the de-icing jump height.

[0024] It should be noted that the de-icing jump height refers to the maximum upward jump displacement of the transmission line caused by the release of elastic potential energy at the moment of ice removal. The smoothing factor is a core parameter in the Generalized Regressive Neural Network (GRNN), used to control the smoothness of the kernel function of the network's pattern layer, directly affecting the model's fitting accuracy and generalization ability. In this application, it is determined through optimization using a WOA-GA hybrid algorithm. The number of parameter variables refers to the total number of feature parameters input to the GRNN network, specifically including the number of parameter types such as structural parameters, load parameters, and material parameters, used to determine the number of neurons in the GRNN network's input layer. In the Whale Optimization Algorithm (WOA), each GRNN smoothing factor to be optimized is treated as an independent individual, and several individuals constitute the initial population of the algorithm. The optimal individual is selected through iterative evolution. The crossover operator and mutation operator are basic operations of the Genetic Algorithm (GA). The crossover operator is used for information exchange and combination among individuals in the population, while the mutation operator is used to randomly perturb individual parameters. Both together improve the algorithm's global search capability and avoid getting trapped in local optima. The fitness function value is a quantitative indicator used to evaluate the quality of each individual during the algorithm iteration process. In this application, the mean squared error between the predicted value and the actual value of the GRNN network is used as the fitness function, and minimizing the fitness function value is the optimization objective. Iterative optimization refers to the process of continuously updating the position of individuals in the population through the WOA-GA hybrid optimization algorithm, repeatedly executing the steps of position update, crossover, mutation, and fitness calculation, and gradually approaching and determining the optimal GRNN smoothing factor. The WOA-GA-GRNN hybrid prediction model refers to the prediction model obtained by optimizing the smoothing factor of the GRNN network using the WOA-GA hybrid algorithm, which combines the whale optimization algorithm and the genetic algorithm, and is used to achieve accurate prediction of the de-icing jump height of transmission lines.

[0025] This invention uses the smoothing factor of the GRNN network as the individual to be optimized in the WOA population and introduces the crossover and mutation operator of the GA algorithm for iterative optimization. This avoids the blindness of traditional manual selection of smoothing factors, while improving population diversity, preventing the algorithm from getting trapped in local optima, and improving the efficiency and accuracy of parameter optimization. Using structural parameters, load parameters, and material parameters as inputs to the obtained prediction model, it can accurately reflect the influencing factors of transmission line de-icing jumps, enabling the model to better fit nonlinear mapping relationships and improve prediction accuracy and generalization ability. By configuring the optimized smoothing factor into the GRNN network, a stable and reliable WOA-GA-GRNN hybrid prediction model is constructed, improving the accuracy and precision of the prediction results. This provides effective data support for subsequent anti-icing design and operation and maintenance of transmission lines, enhancing engineering practicality and operational safety.

[0026] The steps for iteratively optimizing the smoothing factor include: S31, combining several randomly generated smoothing factors into a WOA population, setting the population size and iteration number of the WOA population, and using the mean squared error between the predicted and actual values ​​of the GRNN network as the fitness function.

[0027] S32. Set an adaptive weight coefficient to adjust the WOA search range. The adaptive weight coefficient decreases linearly with the number of iterations, and the weight ω decreases linearly from 0.9 to 0.4 with the number of iterations, so as to optimize the population position and avoid local optima. In the formula, Indicates the adaptive weighting coefficient. Indicates the current iteration number. This indicates the maximum number of iterations.

[0028] S33. Update the position of the smoothing factor in the WOA population according to the adaptive weight coefficient, and perform crossover and mutation operations on the smoothing factor after the position update using the crossover and mutation operators of the GA algorithm, and calculate the fitness function of the smoothing factor after the crossover and mutation operations.

[0029] S34. Under the condition that the fitness function value is less than the preset fitness function threshold or the number of iterations reaches the maximum number of iterations, the optimized smoothing factor is output. The preset fitness function threshold can be 0.01.

[0030] As is understandable, a Generalized Regressive Neural Network (GRNN) is a neural network model based on a Probabilistic Neural Network (PNN), primarily used for regression problems. A GRNN consists of four layers: an input layer, a pattern layer, a summation layer, and an output layer. Input Layer: The number of nodes in the input layer equals the dimension of the input variables; each node receives one input variable. Pattern Layer: Each node in the pattern layer corresponds to a training sample, calculating the Euclidean distance between the input sample and the training samples, and converting the distance into a similarity using a Gaussian radial basis function. Summation Layer: This layer has two nodes: a weighted summation layer and an arithmetic summation layer. Output Layer: The number of nodes in the output layer equals the dimension of the output variables; each node calculates the final predicted value.

[0031] It is important to note the value of the smoothing factor. While generalized regression neural networks (GRNNs) do not require training, the smoothing factor significantly impacts network performance and needs optimization. GRNNs use the same smoothing factor for the basis functions of all hidden layer neurons, and the training process only requires one-dimensional optimization. If the smoothing factor is very large, d(x, x) approaches zero, and y(x) approximates the average of all sample dependent variables. If the smoothing factor approaches zero, y(x) is very close to the value of the training samples. When the point to be predicted is in the training samples, the calculated predicted value is very close to the expected output in the samples. However, once a new input is given, the prediction effect deteriorates sharply, causing the network to lose its generalization ability; this phenomenon is called overlearning. Based on this, this invention uses a WOA-GA hybrid algorithm to optimize and determine a suitable smoothing factor value.

[0032] As one implementation method, it further includes: S5, if the output de-icing jump height exceeds a preset de-icing jump safety threshold, then the transmission line to be predicted is modified to increase the tower crossarm offset or add phase spacers for anti-icing modification. Anti-icing modification refers to engineering measures (such as increasing the tower crossarm offset or adding phase spacers) taken to improve the anti-icing safety performance of the transmission line in the case of de-icing jump height exceeding the standard.

[0033] The steps of performing crossover and mutation operations on the smoothing factor after position update using the crossover and mutation operators of the GA algorithm include: S331, randomly generating probability values, and performing branch operations according to the values ​​of the probability values.

[0034] S332. If the probability value is not greater than a preset probability threshold, then the crossover operation is performed on the smoothing factor after position update using the crossover operator of the GA algorithm. This combines the advantageous features of different individuals in the WOA population to generate new optimized individuals, thereby improving population diversity and preventing the algorithm from getting trapped in local optima. The crossover probability is 0.6~0.8. In the formula, For individuals after crossover, The parent individuals before the crossover. It is a random number in the range [0,1].

[0035] S333. If the probability value is greater than a preset probability threshold, then the mutation operation is performed on the smoothing factor after the position update using the mutation operator of the GA algorithm, randomly perturbing the individuals in the population to enrich population diversity and ensure that the algorithm can explore a better smoothing factor value. The mutation probability is 0.01~0.05. In the formula, For the mutated individual, For the mutated individual, A random number in the range [0,1]. The variable asynchronous length is 0.1~0.3.

[0036] A GRNN network comprises an input layer, a pattern layer, a summation layer, and an output layer; the steps for constructing a GRNN network include: S21. Determine the number of neurons in the pattern layer based on the number of training samples in the ice-breaking jump height prediction data.

[0037] S22. Set the summation layer to a two-node structure, with the two nodes performing weighted summation and arithmetic summation operations respectively.

[0038] S23. Set the output layer to a linear output structure to output the ice-breaking jump height predicted by the GRNN network.

[0039] The steps for obtaining predicted data on the de-icing jump height of transmission lines include: S11, obtaining the original predicted data on the de-icing jump height of transmission lines from laboratory experimental data, field monitoring data, or ANSYS finite element simulation data. The predicted de-icing jump height data includes structural parameters, load parameters, and material parameters. Structural parameters include the number of conductor splits and span; load parameters include ice thickness and de-icing rate; and material parameters include the calculated breaking force of the conductor. The calculated breaking force of the conductor is determined by the conductor type parameters, specifically: 123.4 kN for JL / G1A-400 / 50 conductor, 148.7 kN for JL / G1A-630 / 45 conductor, and 329.85 kN for JL1 / G2A-1250 / 100 conductor, used to quantify the influence of conductor type on the ice jump height. Outliers in the original predicted de-icing jump height data are removed using a three-standard-deviation criterion to obtain the first processed data.

[0040] Specifically, measured and simulated data corresponding to the input variables were collected. The measured data came from on-site monitoring of transmission lines in the medium-icing area and laboratory de-icing tests. The simulated data was obtained by ANSYS finite element simulation of the de-icing dynamic response under different working conditions, covering more than 100 sets of valid samples. The 3σ criterion was used to remove extreme data (such as abnormal samples with ice thickness > 30 mm), and more than 95 sets of valid samples were retained.

[0041] S12. Perform non-integer positive transformation on the extremely small index data in the first processed data, and perform non-integer positive transformation on extremely small indexes such as conductor breaking force (the smaller the value, the greater the ice jump height) to obtain the second processed data, and perform non-integer positive transformation using the following formula: Integer numbers (such as split numbers) are converted to their inverses and then forwarded. S13. Normalize the second processed data to obtain the predicted jump height data. Map all variables to the [0,1] interval to eliminate the influence of dimensional differences on model convergence. Normalize using the following formula: Following the step of configuring the optimized smoothing factor into the GRNN network, the method further includes: S41, dividing the de-icing jump height prediction data into training and test sets using 4-fold cross-validation. 100 samples are randomly divided into 90 training sets and 10 test sets, and the validation is repeated four times to eliminate data partitioning bias. The configured GRNN network is then used to verify the accuracy of the test set in the de-icing jump height prediction data, and the mean relative error (MRE) or root mean square error (RMSE) is calculated. In the formula, MRE is the mean relative error, and RMSE is the root mean square error. The number of samples in the test set. For the first The predicted value for each sample, For the first The actual value of each sample.

[0042] S42. If the accuracy verification result meets the preset accuracy verification requirements, the preset accuracy verification requirements include that the calculated average relative error is not greater than the preset average relative error threshold, which can be 15%, or the calculated root mean square error is not greater than the preset root mean square error threshold, then the configured GRNN network is determined as the WOA-GA-GRNN hybrid prediction model.

[0043] As one implementation method, this embodiment selects finite element simulation data from 12 typical working conditions, covering long-span / large elevation difference lines and uniform / non-uniform icing patterns, to fully demonstrate the execution flow of the prediction method. In practical engineering applications, the sample size can be expanded to further improve the model's generalization ability, such as by adding on-site monitoring data.

[0044] Step 1: Determine the prediction object and variable system, including the following steps: Step 11: The prediction object in this embodiment is a 110kV isolated span JL / G1A-400 / 50 conductor. The basic parameters include: the calculated breaking force of the conductor is 123.4kN; the number of conductor splits is 2; the target working conditions include long span lines without elevation difference (span length 500m) and long span lines with large elevation difference (span length 500m, elevation difference 50m); the de-icing rate is 100% (same-span whole span de-icing).

[0045] Step 12: Determine the predictor variable system. The input variables are conductor split number (2), span (500m), icing thickness (equivalent icing thickness corresponding to different working conditions, such as the equivalent thickness of uniform icing in working condition L0 and the maximum icing thickness of 30mm at the midpoint of the span in working condition L5), de-icing rate (100%), and conductor calculated breaking force (123.4kN). The output variable is the maximum de-icing jump height of the conductor.

[0046] Step 2, Data Acquisition and Preprocessing, includes the following steps: Step 21: Sample Data Collection. In this embodiment, the training / test samples are derived from finite element simulation data of conductor de-icing and jumping characteristics analysis under different icing conditions. A total of 16 valid samples were collected: For long-span, zero-elevation-difference railway lines: the maximum de-icing jump height and corresponding parameters for L0 (uniform icing) and L1-L5 (non-uniform icing) conditions are shown in Table 1.

[0047] Table 1. Schematic diagram of maximum ice-removing jump height and corresponding parameters for long-span, zero-elevation-difference railway tracks. For lines with large elevation differences: the maximum de-icing jump height and corresponding parameters for the H1-H5 (non-uniform icing) and H01-H05 (corresponding to uniform icing) conditions are shown in Table 2.

[0048] Table 2. Schematic diagram of maximum ice-removal jump height and corresponding parameters for lines with large elevation differences. Step 22, data preprocessing, including: Outlier removal: The samples in this embodiment are finite element simulation data, which have no extreme outliers, so 16 sets of samples are directly retained.

[0049] The index is positiveized, and the calculated breaking force of the conductor is a very small index (non-integer). After positiveizing with the formula, the value is 1.

[0050] Normalization maps the gear distance (300~800m) and icing thickness (20~35mm) to the [0,1] interval. For example, the icing thickness of 30mm in L5 condition is normalized to 0.667.

[0051] Step 3: Construct a WOA-GA-GRNN hybrid prediction model, including the following steps: Step 31: Initialize the GRNN model. Number of neurons in the input layer: 5 (to match the number of input variables); Number of neurons in the pattern layer: 14 (corresponding to 14 sets of training samples); Summation layer: set up two nodes for weighted summation and arithmetic summation; Optimization objective: smoothness factor σ of GRNN.

[0052] Step 32: Optimize the smoothing factor σ using the WOA-GA hybrid algorithm, as per attached... Figure 2The detailed steps are as follows, and the overall process is as follows: 1) Parameter initialization: WOA population size 40, number of iterations 50, fitness function is the mean squared error (MSE) between predicted and simulated values; 2) Probability-triggered operation: randomly generate probability p. When p>0.5, perform mutation operation (mutate asynchronous length 0.2); when p≤0.5 and |A|<1, perform crossover operation (crossover probability 0.7). 3) Adaptive weight update, the weight ω decreases linearly from 0.9 to 0.4 with each iteration; 4) Converging output: After 35 iterations, the fitness function value converges to 0.008, and the output optimal smoothness factor σ=0.62.

[0053] Step 4: Model Training and Accuracy Validation Step 41: Dataset partitioning. Using 4-fold cross-validation, the 16 samples are divided into a training set of 14 groups (including the large gear gap L0-L4 and the large elevation difference H1-H4+ corresponding to the H01-H04 working conditions); and a test set of 2 groups (the large gear gap L5 working condition and the large elevation difference H5+ corresponding to the H05 working condition). Step 42: Model training. Substitute the optimal σ=0.62 into the GRNN model and use the training set to complete parameter fitting. The model fit reaches 0.98.

[0054] Step 43, accuracy verification: The comparison results of the predicted values ​​of the test set with the simulation values ​​of the conductor de-icing and jumping characteristics under different icing conditions are shown in Table 3. The calculated average relative error (MRE) of the test set is 1.24%, which meets the qualified standard of "MRE≤15%".

[0055] Table 3. Schematic diagram of results comparison Step 5: Output the prediction results. Taking the 600m span L1 condition (maximum icing at 50m span) as an example, the input variables are "splitting number 2, span 600m, icing thickness 25mm, de-icing rate 100%, calculated breaking force 123.4kN". After substituting these into the trained model, the predicted maximum de-icing jump height is 15.82m. Based on the analysis of conductor de-icing jump characteristics under different icing conditions (the larger the span, the linearly larger the ice jump height), this predicted value deviates from the simulated value of 15.782m for condition L1 (600m span) in the table by only 0.24%, verifying the effectiveness of the method. If the phase-to-phase safety gap threshold for this line is 6.3m, and the predicted value > the threshold, an early warning will be triggered. It is recommended to adopt anti-icing modification measures such as "installing phase-to-phase spacers at 3 / 8, 1 / 2, and 5 / 8 of the span".

[0056] As one implementation method, refer to Figure 2This paper provides a process for optimizing the smoothness factor of a GRNN network using the WOA-GA algorithm, including: Algorithm startup: Start process.

[0057] Data preprocessing: The data related to the de-icing and jumping of transmission lines are segmented and normalized.

[0058] Parameter initialization: Complete the parameter initialization of the GA and WOA algorithms, and set the fitness value to the training error MSE.

[0059] Record the best individual: Record the fitness value and position of the best individual in the current population.

[0060] Random probability judgment: Generate a random probability value p. If p > 0.5, perform a mutation operation; if p ≤ 0.5, proceed to the WOA branch for judgment.

[0061] WOA Branch Decision: Determine if the absolute value of the WOA algorithm coefficient A, |A|, is less than 1. If yes, perform the crossover operation; otherwise, randomly select a new individual to replace the current individual.

[0062] Update global optimum: Compare the fitness of individuals after the operation, and select the optimum as the current global optimum.

[0063] Termination condition judgment: If the termination condition is not met (such as not reaching the maximum number of iterations or fitness not meeting the target), return to the "Record the optimal individual extreme value and position" step and repeat; if the termination condition is met, output the GRNN optimal smoothing factor.

[0064] Model prediction: Substitute the optimal smoothness factor into the GRNN network to perform the prediction of the de-icing jump height, and the process ends.

[0065] This invention achieves high-precision and strong generalization prediction of the de-icing jump height of transmission lines by constructing a multi-dimensional variable system and optimizing the GRNN model with a WOA-GA hybrid algorithm. Prediction accuracy is significantly improved: the average relative error is only 12.9%, a 54.4% reduction compared to the traditional design code formula (28.3%), and a 30.3% reduction compared to the single GRNN model (18.5%). The root mean square error is only 1.45m, meeting the core requirement of "error <15%" in engineering projects. It has strong generalization ability: adaptable to different 110kV / 220kV conductor types (JL / G1A-400 / 50, JL / G1A-630 / 45, etc.) and different split numbers (2~8 splits), with prediction deviations of <8% for different spans and icing thicknesses. Algorithm efficiency is optimized: the WOA-GA hybrid algorithm, through crossover mutation operators and adaptive weight updates, reduces the convergence iterations to 35 times, a 16.7% improvement compared to single WOA optimization, making it suitable for rapid engineering evaluation. High engineering practicality: Data sources cover on-site monitoring, laboratory tests, and finite element simulation. The model can be embedded into the transmission line operation and maintenance system, and the output results directly guide the design of phase-to-phase safety gaps and the formulation of anti-icing modification measures, providing accurate data support for the safe operation of transmission lines in medium-icing areas.

[0066] The beneficial effects of the present invention include at least the following: 1. By sequentially preprocessing the original data with outlier removal, index positiveization, and normalization, the interference of dimensional differences and outlier data can be eliminated, improving the quality of input data and providing a stable and reliable data foundation for subsequent model training. A hybrid optimization strategy combining WOA and GA is adopted. The search range is dynamically adjusted through adaptive weight coefficients, and crossover or mutation operations are performed based on random probability branches. This retains the global search capability of WOA while enhancing population diversity using genetic operators, effectively avoiding the algorithm from getting trapped in local optima. This achieves efficient and accurate optimization of the smoothing factor for GRNN, solving the problems of strong subjectivity and insufficient accuracy in traditional manual parameter selection.

[0067] 2. Based on the number of training samples, the pattern layer neurons of the GRNN network are configured, employing a dual-node summation layer and a linear output layer structure. This allows the network to better fit the complex nonlinear mapping relationship between structural parameters, loads, material parameters, and the de-icing jump height, improving the model's fitting accuracy and generalization ability. The accuracy of the GRNN network with the optimized smoothing factor is verified. The model's reliability is objectively evaluated using the mean relative error or root mean square error. After meeting the preset accuracy verification requirements, a WOA-GA-GRNN hybrid prediction model is obtained to ensure the reliability of the prediction results. Based on the high-precision prediction results, anti-icing modification measures such as adjusting tower crossarm offsets and adding phase-to-phase spacers are implemented. The data sources cover laboratory measurements, on-site monitoring, and finite element simulations, making it applicable to a wider range of scenarios. The overall solution combines high prediction accuracy, high optimization efficiency, strong engineering practicality, and high operational reliability, providing efficient and scientific technical support for transmission line anti-icing disaster reduction and safe operation and maintenance.

[0068] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN, characterized in that, include: S1. Obtain the predicted data of the de-icing jump height of the transmission line, wherein the predicted data of the de-icing jump height includes structural parameters, load parameters and material parameters; S2. Construct a GRNN network, and determine the number of neurons in the input layer of the GRNN network based on the number of parameter variables in the structural parameters, the load parameters, and the material parameters; S3. The smoothing factor used in the GRNN network is taken as the individual to be optimized in the WOA population. The crossover and mutation operators of the GA algorithm are used to perform crossover and mutation operations on the WOA population. The optimization objective is to minimize the fitness function value of the GRNN network. The optimized smoothing factor is obtained by iterative optimization based on the ice-breaking jump height prediction data. S4. Configure the optimized smoothing factor into the GRNN network to obtain the WOA-GA-GRNN hybrid prediction model. Input the structural parameters, load parameters and material parameters of the transmission line to be predicted into the WOA-GA-GRNN hybrid prediction model to output the de-icing jump height.

2. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, The step of iteratively optimizing the smoothness factor includes: S31. Combine several randomly generated smoothing factors into a WOA population, set the population size and number of iterations of the WOA population, and use the mean square error between the predicted value and the actual value of the GRNN network as the fitness function. S32. Set an adaptive weight coefficient for adjusting the WOA search range, wherein the adaptive weight coefficient decreases linearly with the number of iterations. S33. Update the position of the smoothing factor in the WOA population according to the adaptive weight coefficient, and perform crossover and mutation operations on the smoothing factor after the position update using the crossover and mutation operators of the GA algorithm, and calculate the fitness function of the smoothing factor after the crossover and mutation operations. S34. Under the condition that the fitness function value is less than the preset fitness function threshold or the number of iterations reaches the maximum number of iterations, the optimized smoothing factor is output.

3. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 2, characterized in that, The step of performing crossover and mutation operations on the smoothing factor after position update using the crossover and mutation operators of the GA algorithm includes: S331. Randomly generate probability values, and perform branch operations based on the values ​​of the probability values; S332. If the probability value is not greater than the preset probability threshold, then the crossover operation is performed on the smoothing factor after the position update using the crossover operator of the GA algorithm. S333. If the probability value is greater than the preset probability threshold, then the mutation operation is performed on the smoothing factor after the position update using the mutation operator of the GA algorithm.

4. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, The GRNN network includes an input layer, a pattern layer, a summation layer, and an output layer; the steps for constructing the GRNN network include: S21. Determine the number of neurons in the pattern layer based on the number of training samples in the ice-breaking jump height prediction data; S22. Set the summation layer to a two-node structure, with the two nodes performing weighted summation and arithmetic summation operations respectively; S23. Set the output layer to a linear output structure to output the ice-breaking jump height predicted by the GRNN network.

5. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, Also includes: S5. If the output de-icing jump height exceeds the preset de-icing jump safety threshold, then the anti-icing modification of the transmission line to be predicted is carried out by increasing the tower crossarm offset or adding phase spacers.

6. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, The step of obtaining the predicted data of the de-icing jump height of the transmission line includes: S11. Obtain the original de-icing jump height prediction data of the transmission line, and use the three-standard-deviation criterion to remove outliers in the original de-icing jump height prediction data to obtain the first processed data. S12. Perform non-integer positive transformation on the extremely small index data in the first processed data to obtain the second processed data; S13. Normalize the second processed data to obtain the predicted height of the ice-breaking jump.

7. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, After the step of configuring the optimized smoothing factor into the GRNN network, the method further includes: S41. The accuracy of the test set in the de-icing jump height prediction data is verified using the configured GRNN network. S42. If the accuracy verification result meets the preset accuracy verification requirements, then the configured GRNN network is determined as a WOA-GA-GRNN hybrid prediction model.

8. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 7, characterized in that, Accuracy verification is performed by calculating the average relative error or the root mean square error; the preset accuracy verification requirements include that the calculated average relative error is not greater than a preset average relative error threshold, or the calculated root mean square error is not greater than a preset root mean square error threshold.

9. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, The structural parameters include the number of conductor splits and the span; the load parameters include the icing thickness and the de-icing rate; and the material parameters include the calculated breaking force of the conductor.

10. The method for predicting the de-icing jump height of transmission lines based on WOA-GA-GRNN according to claim 1, characterized in that, The data sources for the predicted de-icing jump height include laboratory experimental data, field monitoring data, and ANSYS finite element simulation data.

Images