Regression Model For Noise With Its Application To Short-term Wind Speed Forecasting

Regression is an old topic in the domain of learning functions from a set of samples. Itprovides researchers and engineers with a powerful tool to extract hidden rules of data. Thetrained model is used to predict future events with the information of past or present events.Regression analysis is now successfully applied in nearly all fields of science and technology,including the social sciences, economics, finance, wind power prediction for grid operation.However, this domain is still attracting much attention from research and application domains.The main research contents of this work are as follows.The classical kernel ridge regression (KRR) and-Support vector regression (-SVR)techniques are aimed at discovering a linear or nonlinear structure hidden in original data.They make an assumption that the noise distribution is Gaussian. However, it is reported thatthe noise models in some real-world practical applications, such as wind power forecastingand direction of the direction-of-arrival of coherent electromagnetic waves impingingestimation problem, do not satisfy Gaussian distribution, but beta distribution, Laplaciandistribution, or other models. In these cases the current regression techniques are not optimal.Using Bayesian approach, we derive an optimal loss function for a general noise model. Wepropose a new framework of kernel ridge regression for the general noise mode (N KRR)and a novel-support vector regression model for the general noise model (N-SVR),respectively.The classical GN KRR and GN-SVRtechniques take an assumption that the noiseis Gaussian with zero mean and the same variance. However, it is found that the noise modelsin some practical applications satisfy Gaussian distribution with zero mean andheteroscedasticity, such as wind speed forecasting. In this case, the derived models are notoptimal. Using the optimal loss function for heteroscedastic noise model, propose a newframework of-SVRfor heteroscedastic noise model (HN-SVR).Two new rough-support vector regression models are proposed based on-supportvector regression, rough-support vector regression and rough set theory. Firstly, a roughboundary-insensitive tube is defined with fixed symmetrical boundary rough ε-insensitive loss function and the method of optimization and-support vector regressionmodel. Then we design a fixed symmetrical boundary rough-support vector regressionmodel (RFSM ε-SVR). Secondly, we extend the model to the case that asymmetrical lossfunction is considered. Finally, according to Karush-Kuhn-Tucker (KKT) conditions, wederive their dual problems by introducing the Lagrangian functional into rough-supportvector regression models.According to Karush-Kuhn-Tucker (KKT) conditions, we derive their dual problems byintroducing the Lagrangian functional into N-KRR, N-SVRand HN-SVR. The AugmentedLagrangian Multiplier (ALM) method is applied to solve the dual models of the modelsN-KRR and N-SVR. The Stochastic Gradient Descent (SGD) method is applied to solvethe model HGN-SVR. We test the proposed techniques to short-term wind speed prediction.Experimental results confirm the effectiveness of the proposed models.