## 1 Introduction
For example, paper [6] presented a short-term icing prediction model based on a three layer BP neural network, and the results showed that the BP forecasting model is accurate for transmission lines of different areas. Paper [7] presented an ice thickness prediction model based on fuzzy neural network, the tested result demonstrated its forecasting abilities of better learning and mapping. However, the single BP model easily falls into the local optimum, and cannot always reach the expected accuracy. For this problem, some scholars adopted optimization algorithms to optimize the parameters of BP neural network, thereby improving the prediction accuracy. For instance, [PERSON] and [PERSON] _et al._ used Genetic Algorithm (GA) to optimize BP network and built the GA-BP ice thickness prediction model [8], and this model proved that the GA-BP model was more effective than the BP model in ice thickness prediction for transmission lines. Although this combination model could improve the prediction accuracy of BP neural networks, some scholars started to use SVM to build the icing forecasting model for transmission lines due to its slow calculating speed and overall poor performance. SVM can establish the non-linear relationship between various factors and ice thickness, and has better nonlinear mapping ability and generalization ability. In addition, SVM has a strong learning ability and can quickly approach the target value through continuous repetitive learning. Therefore, theSVM model is more widely used in transmission line research. For example, paper [9; 10; 11] introduced the icing forecasting model based on the Support Vector Regression learning algorithm, and obtained the ideal results. As is known, the standard SVM uses a Gaussian kernel function to solve the support vector by quadratic programming, and the quadratic programming will involve the calculation of an \(m\) order matrix (\(m\) is sample number). When \(m\) is bigger, the processing ability of the Gaussian function is more unsatisfactory. It will take much computing time, thereby seriously affecting the learning accuracy and predictive accuracy of the algorithm. In transmission line icing forecasting, there are many influencing factors, so a large amount of input data will make the SVM algorithm become unfeasible using the traditional Gaussian kernel for such a large-scale training sample. In view of this problem, this paper will replace the Gaussian kernel function with the wavelet kernel function, and establishes the wavelet support vector machine (w-SVM) for icing forecasting. Using wavelet kernel function in place of the Gaussian kernel is mainly based on the following considerations [12]: (1) the wavelet kernel function has the fine characteristic of progressively describing the data, and using the SVM of the wavelet kernel function can approximate any function with high accuracy while the traditional Gaussian kernel function cannot; (2) the wavelet kernel functions are orthogonal or nearly orthogonal, and the traditional Gaussian kernel functions are relevant, even redundant; (3) the wavelet kernel function has multi-resolution analyzing ability for wavelet signals, so the nonlinear processing capacity of the wavelet kernel function is better than that of Gaussian kernel function, which can improve the generalization ability of the support vector machine regression model. The forecasting performance of the w-SVM model largely depends on the values of its parameters; however, most researchers choose the parameters of SVM only by subjective judgment or experience. Therefore, the parameters values of SVM need to be optimized by meta-heuristic algorithms. Currently, several algorithms have been successfully applied to determine the control parameters of SVM, such as genetic algorithms [13], particle swarm optimization [14], differential evolution [15] and so on.