Multi-step-ahead model error prediction using time-delay neural networks combined with chaos theory

Summary This paper presents a time series prediction scheme using time-delay neural networks combined with chaos theory. To achieve reliable multi-step-ahead prediction, the optimal architecture of networks is determined by average mutual information and false nearest neighbors analyses in chaos theory. The networks are applied to predict the model errors at four measurement stations in the Singapore Regional Model domain, with five prediction horizons ranging from 2 h to 96 h. It is found that the combined scheme significantly improves the accuracy of tidal prediction, with more than 70% of the root mean square errors removed for 2 h tidal forecast and more than 50% for 96 h tidal forecast.

[1]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[2]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

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

[4]  Dulakshi S. K. Karunasinghe,et al.  Chaotic time series prediction with a global model: Artificial neural network , 2006 .

[5]  Vladan Babovic,et al.  Applying local model approach for tidal prediction in a deterministic model , 2009 .

[6]  Vladan Babovic,et al.  Local model approximation in the real time wave forecasting , 2005 .

[7]  J. C Mason,et al.  Algorithms for approximation : based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data held at the Royal Military College of Science, Shrivenham, July 1985 , 1987 .

[8]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[9]  Yen-Ming Chiang,et al.  Multi-step-ahead neural networks for flood forecasting , 2007 .

[10]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[11]  V. Babovic,et al.  Forecasting of River Discharges in the Presence of Chaos and Noise , 2000 .

[12]  G. Williams.  Chaos theory tamed , 1997 .

[13]  J. Sprott.  Chaos and time-series analysis , 2001 .

[14]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[15]  Wei-Zhen Lu,et al.  Using Time-Delay Neural Network Combined with Genetic Algorithms to Predict Runoff Level of Linshan Watershed, Sichuan, China , 2007 .

[16]  Vladan Babovic,et al.  Error correction of a predictive ocean wave model using local model approximation , 2005 .

[17]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[18]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[19]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[20]  Geoffrey E. Hinton,et al.  Learning representations of back-propagation errors , 1986 .

[21]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Gregory B. Pasternack,et al.  Does the river run wild? Assessing chaos in hydrological systems , 1999 .

[23]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[24]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[25]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[26]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[27]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[28]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[29]  Vladan Babovic,et al.  Efficient data assimilation method based on chaos theory and Kalman filter with an application in Singapore Regional Model , 2009 .

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

[31]  Zhong Shi-sheng,et al.  Time series prediction using wavelet process neural network , 2008 .

[32]  R. S. Govindaraju,et al.  Artificial Neural Networks in Hydrology , 2010 .

[33]  Kevin J. Lang.  A time delay neural network architecture for speech recognition , 1989 .

[34]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[35]  S. Lallahem,et al.  Evaluation and forecasting of daily groundwater outflow in a small chalky watershed , 2003 .

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

[37]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[38]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[39]  A. Soldati,et al.  Artificial neural network approach to flood forecasting in the River Arno , 2003 .

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

[41]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[42]  B. S. Thandaveswara,et al.  A non-linear rainfall–runoff model using an artificial neural network , 1999 .