LSSVR Model of G-L Mixed Noise-Characteristic with Its Applications

Due to the complexity of wind speed, it has been reported that mixed-noise models, constituted by multiple noise distributions, perform better than single-noise models. However, most existing regression models suppose that the noise distribution is single. Therefore, we study the Least square SVR of the Gaussian–Laplacian mixed homoscedastic (GLM−LSSVR) and heteroscedastic noise (GLMH−LSSVR) for complicated or unknown noise distributions. The ALM technique is used to solve model GLM−LSSVR. GLM−LSSVR is used to predict short-term wind speed with historical data. The prediction results indicate that the presented model is superior to the single-noise model, and has fine performance.

[1]  Yuyang Gao,et al.  A Hybrid Method Based on Singular Spectrum Analysis, Firefly Algorithm, and BP Neural Network for Short-Term Wind Speed Forecasting , 2016 .

[2]  Arthur E. Hoerl,et al.  Application of ridge analysis to regression problems , 1962 .

[3]  M. Negnevitsky,et al.  Innovative short-term wind generation prediction techniques , 2006, 2006 IEEE Power Engineering Society General Meeting.

[4]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[5]  Bernhard Schölkopf,et al.  Experimentally optimal v in support vector regression for different noise models and parameter settings , 2004, Neural Networks.

[6]  J. Torres,et al.  Forecast of hourly average wind speed with ARMA models in Navarre (Spain) , 2005 .

[7]  Yunqian Ma,et al.  Practical selection of SVM parameters and noise estimation for SVM regression , 2004, Neural Networks.

[8]  Lin Sun,et al.  Feature selection using neighborhood entropy-based uncertainty measures for gene expression data classification , 2019, Inf. Sci..

[9]  Yuhua Qian,et al.  Neighborhood multi-granulation rough sets-based attribute reduction using Lebesgue and entropy measures in incomplete neighborhood decision systems , 2020, Knowl. Based Syst..

[10]  L. Völgyesi,et al.  Application of kernel ridge regression to network levelling via Mathematica , 2005 .

[11]  Chao Chen,et al.  A hybrid statistical method to predict wind speed and wind power , 2010 .

[12]  Wei Chu,et al.  Bayesian support vector regression using a unified loss function , 2004, IEEE Transactions on Neural Networks.

[13]  Yan Jiang,et al.  Short-term wind speed prediction: Hybrid of ensemble empirical mode decomposition, feature selection and error correction , 2017 .

[14]  A. Llombart,et al.  Statistical Analysis of Wind Power Forecast Error , 2008, IEEE Transactions on Power Systems.

[15]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[16]  Francesco Orabona,et al.  Solving Ridge Regression using Sketched Preconditioned SVRG , 2016, ICML.

[17]  Jing Shi,et al.  Fine tuning support vector machines for short-term wind speed forecasting , 2011 .

[18]  Rob Law,et al.  The forecasting model based on modified SVRM and PSO penalizing Gaussian noise , 2011, Expert Syst. Appl..

[19]  Jing Shi,et al.  On comparing three artificial neural networks for wind speed forecasting , 2010 .

[20]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[21]  Sancho Salcedo-Sanz,et al.  Short term wind speed prediction based on evolutionary support vector regression algorithms , 2011, Expert Syst. Appl..

[22]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machine Classifiers , 1999, Neural Processing Letters.

[23]  R. Rockafellar Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[24]  Patrick Gallinari,et al.  SGD-QN: Careful Quasi-Newton Stochastic Gradient Descent , 2009, J. Mach. Learn. Res..

[25]  S. Sathiya Keerthi,et al.  Improvements to the SMO algorithm for SVM regression , 2000, IEEE Trans. Neural Networks Learn. Syst..

[26]  P. Dokopoulos,et al.  Short-term forecasting of wind speed and related electrical power , 1998 .

[27]  Qinghua Hu,et al.  Transfer learning for short-term wind speed prediction with deep neural networks , 2016 .

[28]  Jiucheng Xu,et al.  Feature Selection Using Fuzzy Neighborhood Entropy-Based Uncertainty Measures for Fuzzy Neighborhood Multigranulation Rough Sets , 2021, IEEE Transactions on Fuzzy Systems.

[29]  Ali Akbar Abdoos,et al.  A new intelligent method based on combination of VMD and ELM for short term wind power forecasting , 2016, Neurocomputing.

[30]  J.T. Kwok,et al.  Linear Dependency betweenand the Input Noise in -Support Vector Regression , 2001 .

[31]  Jianzhou Wang,et al.  A corrected hybrid approach for wind speed prediction in Hexi Corridor of China , 2011 .

[32]  Yun Wang,et al.  Approaches to wind power curve modeling: A review and discussion , 2019 .

[33]  Jianzhou Wang,et al.  Research and application of a novel hybrid forecasting system based on multi-objective optimization for wind speed forecasting , 2017 .

[34]  Licheng Jiao,et al.  Fast Sparse Approximation for Least Squares Support Vector Machine , 2007, IEEE Transactions on Neural Networks.

[35]  Johan A. K. Suykens,et al.  Weighted least squares support vector machines: robustness and sparse approximation , 2002, Neurocomputing.

[36]  Farid Melgani,et al.  Kernel ridge regression with active learning for wind speed prediction , 2013 .

[37]  Qi Wu,et al.  A hybrid-forecasting model based on Gaussian support vector machine and chaotic particle swarm optimization , 2010, Expert Syst. Appl..

[38]  Lei Wu,et al.  Wind speed forecasting based on the hybrid ensemble empirical mode decomposition and GA-BP neural network method , 2016 .

[39]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.

[40]  Wentao Mao,et al.  ν-Support Vector Regression Model Based on Gauss-Laplace Mixture Noise Characteristic for Wind Speed Prediction , 2019, Entropy.

[41]  R. Kavasseri,et al.  Day-ahead wind speed forecasting using f-ARIMA models , 2009 .

[42]  Zhihua Zhang,et al.  Regularized Discriminant Analysis, Ridge Regression and Beyond , 2010, J. Mach. Learn. Res..

[43]  A. Fabbri,et al.  Assessment of the cost associated with wind generation prediction errors in a liberalized electricity market , 2005, IEEE Transactions on Power Systems.