估计GM(1,1)模型中参数的LS-SVM方法及其在负荷预测中的应用

Estimation of GM(1,1) Model Parameter Based on LS-SVM Algorithm and Application in Load Forecasting

摘要: 为克服利用传统最小二乘法估计GM(1,1)模型参数的缺陷，改善GM(1,1)模型在中长期负荷预测中的精度，提出了基于LS-SVM算法估计GM(1,1)模型中参数的方法。该方法根据GM(1,1)灰色差分方程的特点，构造以背景值序列和原始序列为训练样本的灰色LS-SVM，将GM(1,1)模型参数的估计问题转化为灰色LS-SVM的参数估计问题，依据LS-SVM算法求得灰色LS-SVM的参数，进而得到GM(1,1)模型的参数估计。利用本文方法估计GM(1,1)模型的参数，方法上遵循了结构风险最小化原则，算法实现上具有速度快，稳健性强的优点，适合GM(1,1)小样本建模的特点。将本文方法应用于中长期负荷预测，通过与传统的GM(1,1)模型预测效果的对比分析，验证了该模型的有效性和优越性。

Abstract: In order to overcome the defects of traditional parameters estimation method in GM(1,1) model by means of least square procedure and enhance the forecasting accuracy of GM(1,1) in medium and long-term load forecasting precision, an improvement GM(1,1) model based on LS-SVM algorithm is presented. This method constructs the grey LS-SVM with background value and raw data series as the training sample ac-cording to the character of grey difference equation, converts the GM(1,1) model parameter estimation prob-lem into a grey LS-SVM parameter estimation problem, then the regression parameters in the grey LS-SVM are solved based on the LS-SVM algorithm and the GM(1,1) model parameters estimation are also obtained. Using this method in this paper to estimate the GM(1,1) model, the method follows structural risk minimiza-tion principles, algorithm has the advantage of fast speed, strong robustness, suitable for GM(1,1) model of small samples. This method is applied to long-term load forecasting, compared with forecasting effect analy-sis of traditional GM(1,1) model to prove the validity and the superiority of the model.