Mathematical Problems in Engineering

Volume 2015, Article ID 798325, 9 pages

http://dx.doi.org/10.1155/2015/798325

## The Weighted Support Vector Machine Based on Hybrid Swarm Intelligence Optimization for Icing Prediction of Transmission Line

Research Institute of Technology Economics Forecasting and Assessment, School of Economics and Management, North China Electric Power University, Beijing 102206, China

Received 22 December 2014; Revised 14 March 2015; Accepted 14 March 2015

Academic Editor: Alejandro Ortega-Moñux

Copyright © 2015 Xiaomin Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1, 2].

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 [3]. As one of the serious transmission line icing countries, the probability of occurrence of ice disaster accident of transmission line in China stays the forefront in the world [4]. Icing of transmission lines has become one of the important factors affecting the safe operation of power grid in the world. In view of great harm to the power system operation brought by icing, in recent years, the related research work on conductor icing has gradually become a hot research at home and abroad. And they have made certain achievements in the aspect of the formation mechanism of transmission line icing, ice prevention measures, Icing image monitoring, and conductor icing prediction model. The methods used for the icing prediction include empirical models, statistical refinement model [5, 6], and the intelligent models, such as neural network [7–9], support vector machine [10–13] and so on. The multivariate linear regression model is the most widely used in the statistical theory model. But the influence factors considered in the model are not comprehensive enough, and the model is required to meet the various statistical assumptions. There are restrictions on the types of influence factors, which limit the range of application [14]. Experience refined model is set out to establish a model from the physical essence of the ice cover and it is relatively simple; the generalization ability is weak. The outputs of different meteorological have high volatility [15]; neural network has the great ability of approaching nonlinearity but is easy to fall into local optimum and appear over learning situation. This model also has the disadvantages of low efficiency and poor generalization ability. It is difficult to guarantee the prediction accuracy of models [16]. 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 [17]. And the model has the advantages of repeated training and the faster speed of convergence [18]; it can solve practical problems of the small sample, nonlinearity, local extreme value, and so on. It is widely used in many fields such as machine control and speech recognition and has achieved good forecasting effects [19].

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 [20]. At this point, the traditional SVM cannot obtain an accurate prediction result [21]. In view of this problem, given comprehensive consideration of the factors of the environmental temperature, relative humidity, wind speed, wind direction, and elevation effects, combined with statistical prediction model and icing meteorological parameters model used for icing prediction, this paper proposes a weighted support vector (WSVR) regression algorithm for icing prediction [22]. We determine the weights of different samples by calculating the correlation coefficient between samples and optimize the parameters and using hybrid optimization algorithm of particle swarm and ant colony (PSO-ACO) to improve the model’s generalization ability. In the empirical analysis, ACO-SVM, BP neural network and linear regression methods are used for comparison. By contrast, the model proposed in this paper has higher precision and can accurately predict the ice thickness. The establishment of the model has practical significance for power department to effectively control the ice disaster and improve the safe and reliable operation of power grid [23].

#### 2. Basic Theories

##### 2.1. The Hybrid Cluster Intelligent Optimization

###### 2.1.1. Swarm Intelligence Optimization Algorithm

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 [24].

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.(1)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.(2)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.(3)The computing time is less and the platform is easy to expand.(4)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.

###### 2.1.2. Hybrid Swarm Intelligence Optimization Algorithm

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.

*(1) Ant Colony Optimization*. ACO is inspired by Italy scholar Dorigo M from the foraging behavior of real ant colony in nature. He found that an individual ant does not have much wisdom or master the nearby geographic information. But the colony can find an optimal path from nest to food sources. Established on the findings, Dorigo M and other researchers proposed ACO theory in 1991, attracting research enthusiasm of many scholars. The basic ACO model consists of the following three equations:

If the ant marked NO, passes by the path from to , where is the number of ants, is the number of iterations, is the position of ants, is the position where ants can reach, is the set of the position where ants can reach, is the heuristic information, which means the visibility of the path from to , named , is the objective function, is the pheromone intensity of the path from to , is the number of pheromone left by ants on the path from to , is the weight of the path, is the weight of the heuristic information, is the evaporation factor of the number of pheromone on the path, is coefficient of the pheromone quality, and denotes the transition probabilities of the NO ant moving from to .

*(2) Particle Swarm Optimization*. Particle swarm optimization (PSO) is a kind of evolutionary algorithm, derived from the observation of the birds’ behavior of searching for food. The conversion process of the motion of whole flock from disorderly to orderly comes from information shared by each individual bird in the flock, so as to find food [25].

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 1). In the process of iterations, each particle updates its direction and position constantly according to two extreme values. The first one is the optimal solution found by the particle itself, called individual extreme , and the other one is the current optimal solution found by the entire particle swarm, named global extreme . At the beginning of the iterations, the position of each initialized particle is the individual extreme, while the best position of the particle swarm is the global extreme. After all of the particles in the swarm complete the first iteration, we should compare the position front and rear of each particle and update the individual extreme with the optimal solution in this iteration if the new position is better than the previous one. Then, we need to get the optimal solution throughout individual extremes of all particles in the swarm as global extreme by comparison and update the global extreme if the new one is better than the old one. The final global extreme obtained through these cycle iteration operations determines the optimal solution [26].