Chaos theory applied to input space representation of autonomous neural network-based short-term load forecasting models

After 1991, the literature on load forecasting has been dominated by neural network based proposals. However, one major risk in using neural models is the possibility of excessive training, i.e., data overfitting. The extent of nonlinearity provided by neural network based load forecasters, which depends on the input space representation, has been adjusted using heuristic procedures. The empirical nature of these procedures makes their application cumbersome and time consuming. Autonomous modeling including automatic input selection and model complexity control has been proposed recently for short-term load forecasting. However, these techniques require the specification of an initial input set that will be processed by the model in order to select the most relevant variables. This paper explores chaos theory as a tool from non-linear time series analysis to automatic select the lags of the load series data that will be used by the neural models. In this paper, Bayesian inference applied to multi-layered perceptrons and relevance vector machines are used in the development of autonomous neural models.

[1]  Carlos E. Pedreira,et al.  Neural networks for short-term load forecasting: a review and evaluation , 2001 .

[2]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[3]  R. Ramanathan,et al.  Short-run forecasts of electricity loads and peaks , 1997 .

[4]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[5]  Malik Magdon-Ismail,et al.  No Free Lunch for Early Stopping , 1999, Neural Computation.

[6]  A. Atiya,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[7]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[8]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[9]  Michael E. Tipping.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001, J. Mach. Learn. Res..

[10]  Ming-Wei Chang,et al.  Load Forecasting Using Support Vector Machines: A Study on EUNITE Competition 2001 , 2004, IEEE Transactions on Power Systems.

[11]  William E. Griffiths,et al.  Learning and Practicing Econometrics , 1993 .

[12]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[13]  Geoffrey E. Hinton,et al.  Bayesian Learning for Neural Networks , 1995 .

[14]  T. Senjyu,et al.  Several-hours-ahead electricity price and load forecasting using neural networks , 2005, IEEE Power Engineering Society General Meeting.

[15]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[16]  A.P. Alves da Silva,et al.  Toward Estimating Autonomous Neural Network-Based Electric Load Forecasters , 2007, IEEE Transactions on Power Systems.

[17]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[18]  Ming-Wei Chang,et al.  Load forecasting using support vector Machines: a study on EUNITE competition 2001 , 2004, IEEE Transactions on Power Systems.

[19]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[20]  Isabelle Guyon,et al.  An Introduction to Variable and Feature Selection , 2003, J. Mach. Learn. Res..

[21]  Vitor Hugo Ferreira,et al.  Automatic Kernel Based Models for Short Term Load Forecasting , 2009, 2009 15th International Conference on Intelligent System Applications to Power Systems.

[22]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Klaus-Robert Müller,et al.  Statistical Theory of Overtraining - Is Cross-Validation Asymptotically Effective? , 1995, NIPS.

[24]  D. Mackay,et al.  Bayesian methods for adaptive models , 1992 .

[25]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .