Not only can the icing coat on transmission line cause the electrical fault of gap discharge and icing flashover but also it will lead to the mechanical failure of tower, conductor, insulators, and others. It will bring great harm to the people’s daily life and work. Thus, accurate prediction of ice thickness has important significance for power department to control the ice disaster effectively. Based on the analysis of standard support vector machine, this paper presents a weighted support vector machine regression model based on the similarity (WSVR). According to the different importance of samples, this paper introduces the weighted support vector machine and optimizes its parameters by hybrid swarm intelligence optimization algorithm with the particle swarm and ant colony (PSO-ACO), which improves the generalization ability of the model. In the case study, the actual data of ice thickness and climate in a certain area of Hunan province have been used to predict the icing thickness of the area, which verifies the validity and applicability of this proposed method. The predicted results show that the intelligent model proposed in this paper has higher precision and stronger generalization ability.

Safe and reliable power supply is the security to ensure sound and rapid development of the national economy; as the main part of power transmission in the grid, normal and safe operation of transmission lines is an important guarantee for the grid to avoid a serious accident, while the icing on the transmission line will lead to excessive tension, conductor galloping, tripping, and break accident of transmission line. It will also cause the interruption of power supply, affecting the stability and security of power system operation seriously. Moreover, due to reverse distribution of China’s resources and productivity, our country needs to vigorously promote construction of outgoing channel of power base. It will increase the possibility of the icing when transmission lines go through extremely harsh complex area of the contamination, high altitude, snow, strong acid rain, and fog [

In the early 30s of last century, Britain, Japan, Canada, and American had some reports on transmission line ice coating, which had caused safety accident and brought the huge economic loss [

The standard SVM has the same punishment for deviation and accuracy requirements for different samples. However, in practical applications, we often find that some samples have large correlation degree which requires a smaller training error, while some has small correlation degree which has the permissible of relatively large error [

The basic theory of swarm intelligent optimization algorithm is to simulate exchanges and cooperation of the actual biological group lives between each individual, with a simple and limited individual behavior and intelligence to form the overall capability of the whole population of inestimable through interaction. Various organisms in a swarm intelligent optimization algorithm are handled by artificial, and individuals do not have the volume and quality of the actual biological. Its behavior has the necessary processing based on people’s needs to solve the problem [

Swarm intelligence optimization algorithm is a search of probability essentially. It does not need gradient information of questions and has the following characteristics which are different from the traditional optimization algorithm.

The interaction of individuals in the population is distributed, and there is no direct central control. Individual failure will not affect to solution of the problem. It has the strong robustness.

Each individual can only perceive the local information and the individual’s ability to follow the rules. So the swarm intelligence method is simple and convenient.

The computing time is less and the platform is easy to expand.

Self-organization, namely, the complex behavior of community is via a simple individual interaction which exhibits a high degree of intelligence.

Swarm intelligence optimization algorithm theory mainly aims to study the algorithm characteristics and improve the shortage and performance. The research mainly includes two aspects: one is to study its own characteristics of this algorithm to improve its performance; the other is to combine the swarm intelligence optimization with other algorithm to produce a new hybrid intelligent algorithm through the fusion of different algorithms.

Currently, the thinking of swarm intelligence is receiving increasing attention, which shows great characteristics in solving problems, especially optimization problems. There are many algorithms based on the group, such as genetic algorithm, differential evolution, ant colony optimization, particle swarm optimization, and evolutionary programming, which can be grouped into swarm intelligence algorithms. As the most commonly used swarm intelligence optimization algorithms, ant colony optimization and particle swarm optimization have greater optimization features. Ant colony optimization, which is the simulation of ant colony foraging process, has been successfully applied to many discrete optimization problems. Particle swarm optimization, which is the simulation of birds foraging process, is an efficient parallel search algorithm in continuous optimization field.

Ant colony optimization uses pheromone to transmit information, while particle swarm optimization uses three pieces of information of the information of its own, individual extreme information, and global extreme information to guide the particle to the next iteration. Using the organic combination of the positive feedback principle and some heuristic algorithms, ant colony optimization is easy to run into prematurity and fall into local optimum. The organic combination of those two algorithms can overcome the shortcomings of them effectively and improve the computational efficiency significantly. According to the mixing characteristics of ant colony optimization and particle swarm optimization, this paper proposes an improved ACO_PSO hybrid algorithm.

If the ant marked NO,

The method used by PSO to solve optimization problems is to initialize a group of random particles and find the optimal solution through several iterations (Figure

Movement of particles.

After obtaining individual extreme and global extreme in the process, each particle needs to update its velocity and position according to the following formulas:

In the process of particle swarm optimization algorithm, particle shares global extreme value to other particles within the group. This one-way flow of shared information and data makes the whole search process follow the group within the current optimal solution. Therefore, the initial particle swarm optimization algorithm has fast global convergence capability.

Researches show that the initial search process of ant colony optimization operates slowly because of lack of initial pheromone, and the set continuous parameters

The basic steps of ACO-PSO hybrid algorithm are shown in Figure

Flow chart of ACO-PSO hybrid intelligent optimization algorithm.

The principle of SVM is to transform the samples which cannot be separated in linear low-dimensional space to high dimensional feature space by nonlinear mapping algorithm to make the samples linearly separable and then analyze linearly the samples transformed. SVM regression is to create a nonlinear mapping and map the data to high dimensional feature space for the linear regression work later [

Assuming that the samples are

According to the theory of statistics, we define SVM regression function based on the target of minimization and build the following goal programming:

By using Lagrange method to solve the constrained optimization problems described above, the original problem can be converted to its dual problem:

The SVM regression function is shown as follows:

The traditional support vector machine algorithm applies to the cases where the sample data obeys identically distribution and the samples are independent of each other, and it has same punishment for penalty parameters and error request parameters of different sample. In this case, the model can ensure an accuracy result. However, the actual data is more complex and we often find that some important samples demand lower training error while others allow a certain size of training error. Therefore, to get a more accurate regression estimate, we should assign different error requirements and penalty coefficients to each sample data when describing the optimization problem. To solve this problem, the weighted support vector machine regression algorithm [

Assume that the variance of random error term has the following properties:

In circumstances of different

The basic idea of gray correlation degree is to determine the degree of association according to similarities between curves. Therefore, to determine the weights, this paper introduces gray correlation degree to calculate the similarities between samples. The gray correlation degree is calculated as follows:

The gray correlation degree

The weight

Among the numerous factors influencing the ice coating on the transmission line, meteorological conditions are the most important factor, including temperature, humidity, wind speed, wind direction and other external climate. A lot of scholars have studied the impact factors preliminary. Literature [

On this basis, a pole called “Fuwaixian” in Hunan province is as a case study to demonstrate the effectiveness of the proposed approach. The historical meteorological data and ice thickness data from January 10, 2008, to March 21, 2008, are taken as data base. The forecasting model is solved through Matlab on a single core of a 32-bit Lenovo workstation running on Windows7 with 2 dual-core 2.60 GHz CPU and 4.0 GB of RAM. We extract rules from the past information to forecast the ice thickness. The main factors considered here are average temperature, relative humidity, wind speed, choosing average temperature, relative humidity and wind speed of forecasting day, the ice thickness, temperature, and relative humidity of the day before as input factors of support vector machine to predict the ice thickness of the transmission line. The original data chart is shown in Figure

Original data chart of temperature, relative humidity, wind’s speed, and ice thickness.

Before training samples, we must screen and normalize the raw data, deleting the cases of small relative humidity, high temperature, and small wind speed which lead to ice thickness close to 0. Finally, we retain 289 groups of data, of which the first 200 groups are the training set and the latter 90 groups are a test set, to prove the validity of the model.

The formula of normalization is as follows:

After normalization, the values of each variable are between

As the climate factors have the characteristics of greater volatility and randomness, SVM can take comprehensive consideration of multiple factors of ice thickness and has better ability of nonlinear mapping and generalization. As the selection of kernel parameter

This paper will adopt PSO-ACO hybrid cluster intelligent optimization algorithm to optimize the parameters

This paper selects the average percentage error of predictive value and the actual value as the objective function to search for the target of the minimum value of the objective function. The optimal solution of ant colony corresponding to the global minimum is the parameters

Figure

Process of optimization iterative convergence of PSO-ACO parameters.

Forecasting curve of WSVR based on PSO-ACO hybrid optimization.

In order to assess the reasonableness of the model proposed in this paper, we select support vector machine optimized by ant colony (ACO-SVM), SVM model, and linear regression model as the model for comparison. The prediction results of the three algorithms are shown in Figure

Comparison of the prediction results of different algorithms.

The error distribution of different algorithms.

This paper selects the mean absolute percentage error index as quantitative evaluation of the result of prediction:

Error distributions of different methods are shown in Figure

It can be seen from comparison of the prediction curve and the actual load curve that the results of four algorithms of ice thickness have approximation to actual curve. Among them, weighted support vector machine regression (WSVR) based on PSO-ACO hybrid intelligent optimization has the best fitting effect, and the mean absolute percentage error prediction result of this proposed method is 2.533% while ACO-SVM, the traditional SVM and linear regression method are 6.47%, 10.62%, 12.24%. The error is much higher than the method proposed in this paper. Error evaluation results show that weighted support vector machine optimized by the hybrid algorithm has a higher prediction accuracy than the single optimization SVM algorithm, the hybrid optimization algorithm makes up for the defects of single algorithm, and weighted support vector machine makes full use of the sample information, which improve the accuracy and the generalization ability of the model and make better prediction effect. Compared with other methods, the proposed method has obvious advantages and can be used for the ice thickness prediction of transmission line.

This paper proposes an intelligent model of weighted support vector machine (WSVR) based on PSO-ACO hybrid optimization. It is used to predict the ice thickness of transmission line, which has extremely important realistic meaning for the power sector to control ice coating effectively. This intelligent model is combined with the advantages of dealing with small samples, nonlinearity, and local optimum of SVM. The PSO-ACO hybrid optimization algorithm can overcome shortcomings of the local optimum in particle swarm algorithm and lack of pheromone in ant colony algorithm; at the same time, weighted support vector machine can make full use of sample information, which improves the generalization ability of the mode and promote the actual application scope of the prediction model. During the process of thickness forecasting, we give full consideration of the impact factors of climate and select the key factors, which makes the model more credible and scientific. This paper selects the icing data of “Fuwaixian” tower in a certain region of Hunan province from January 10, 2008, to March 21, 2008, for calculation. Empirical results show that the accuracy and generalization ability of improved model are improved.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by Natural Science Foundation of China (Project nos. 71471059 and 7107152). The authors would like to thank the anonymous reviewers for their valuable comments, which greatly helped them to clarify and improve the contents of the paper.