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

Journal of Hydrology

Volumn 395, Issue 1-2, 2010, Pages 109-116

  Sun, Yabin ^a   Babovic, Vladan ^a   Chan, Eng Soon ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Chaos theory; Model error prediction; Time delay neural networks

Indexed keywords

AVERAGE MUTUAL INFORMATION; FALSE NEAREST NEIGHBOR; MODEL ERROR PREDICTION; MODEL ERRORS; MULTI-STEP; OPTIMAL ARCHITECTURE; PREDICTION HORIZON; REGIONAL MODEL; ROOT MEAN SQUARE ERRORS; SINGAPORE; TIME DELAY NEURAL NETWORKS; TIME SERIES PREDICTION;

FORECASTING; MEASUREMENT ERRORS; NEURAL NETWORKS; TIME DELAY; TIME SERIES;

CHAOS THEORY;

CHAOS THEORY; ERROR ANALYSIS; REGIONAL PATTERN; TIDAL MODELING; TIME SERIES;

SINGAPORE [SOUTHEAST ASIA];

EID: 78349305293     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2010.10.020     Document Type: Article

References (43)

1. Alligood K., Sauer T., Yorke J.A. CHAOS: An Introduction to Dynamical Systems 1997, Spring-Verlag, New York.
2. Babovic, V., Keijzer, M., 1999. Forecasting of river discharges in the presence of chaos and noise. In Coping with Floods: Lessons Learned from Recent Experiences, Kluwer, Dordrecht, pp. 405-420.
3. Babovic V., Sannasiraj S.A., Chan E.S. Error correction of a predictive ocean wave model using local model approximation. Journal of Marine Systems 2005, 53(1-4):1-17.
4. Box G.E.P., Jenkins G.M. Time Series Analysis: Forecasting and Control 1976, Holden-Day, San Francisco.
5. Campolo M., Soldati A., Andreussi P. Artificial neural network approach to flood forecasting in the River Arno. Hydrological Sciences Journal 2003, 48(3):381-398.
6. Chang F.J., Chiang Y.M., Chang L.C. Multi-step-ahead neural networks for flood forecasting. Hydrological Sciences Journal 2007, 52(1):114-130.
7. Cybenko G. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems 1989, 2(4):303-314.
8. Ding G., Zhong S.S., Li Y. Time series prediction using wavelet process neural network. Chinese Physics B 2008, 17(6):1998-2003.
9. Fraser A.M., Swinney H.L. Independent coordinates for strange attractors from mutual information. Physical Review A 1989, 33(2):1134-1140.
10. Gallager R.G. Information Theory and Reliable Communication 1968, John Wiley and Sons, New York.
11. Govindaraju R.S., Rao A.R. Artificial Neural Networks in Hydrology 2000, Kluwer, Dordrecht.
12. Grassberger P., Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal. Physical Review A 1983, 28(4):2591-2593.
13. Grassberger P., Procaccia I. Characterization of strange attractors. Physical Review Letters 1983, 50(5):346-349.
14. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D 1983, 9(1-2):189-208.
15. Haykin S. Neural Networks: A Comprehensive Foundation 1999, Prentice Hall, New Jersey.
16. Hopfield J.J. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America 1982, 79:2554-2558.
17. Hydrographic Department of Singapore, 1999. Singapore Tide Tables. ISSN: 0129-0282, Singapore.
18. Kantz H., Schreiber T. Nonlinear Time Series Analysis 2004, Cambridge University Press, Cambridge.
19. Karunasinghe D.S.K., Liong S.Y. Chaotic time series prediction with a global model: artificial neural network. Journal of Hydrology 2006, 323(1-4):92-105.
20. Kennel M.B., Brown R., Abarbanel H.D.I. Determining minimum embedding dimension using a geometrical construction. Physical Review A 1992, 45(6):3403-3411.
21. Kernkamp, H., Zijl, F., 2004. Further Hydraulic Model Studies for Pulau Ubin & Pulau Tekong Reclamation Scheme. Interim Report on Hydrodynamic Modelling - Model Set-up and Calibration. Delft Hydraulics, Delft, The Netherlands.
22. Kohonen T. Self-organized formation of topologically correct feature maps. Biological Cybernetics 1982, 43(1):59-69.
23. Lallahem S., Mania J. Evaluation and forecasting of daily groundwater outflow in a small chalky watershed. Hydrological Processes 2003, 17(8):1561-1577.
24. Lang, K., Hinton, G., 1988. A Time-Delay Neural Network Architecture for Speech Recognition. Technical Report CMU-CS-88-152, Carnegie Mellon University, Pittsburgh, PA.
25. McCulloch W.S., Pitts W. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 1943, 5:115-133.
26. Minsky M.L., Papert S.A. Perceptrons 1969, MIT Press, Cambridge, MA.
27. Ott E. Chaos in Dynamical Systems 1993, Cambridge University Press, Cambridge.
28. Pasternack G.B. Does the river run wild? Assessing chaos in hydrological systems. Advances in Water Resources 1999, 23(3):253-260.
29. Powell, M.J.D., 1985. Radial basis functions for multivariable interpolation: a review. In: Proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, Shrivenham.
30. Rosenblatt F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review 1958, 65(6):386-408.
31. Rumelhart D.E., McClelland J.L. Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1986, MIT Press, Cambridge, MA.
32. Rumelhart D.E., Hinton G.E., Williams R.J. Learning representations of back-propagation errors. Nature 1986, 323:533-536.
33. Sajikumar N., Thandaveswara B.S. A non-linear rainfall-runoff model using an artificial neural network. Journal of Hydrology 1999, 216(1):32-55.
34. Sannasiraj S.A., Babovic V., Chan E.S. Local model approximation in the real time wave forecasting. Coastal Engineering 2005, 52(3):221-236.
35. Schreiber T., Schmitz A. Improved surrogate data for nonlinearity tests. Physical Review Letters 1996, 77(4):635-638.
36. Sprott J.C. Chaos and Time-Series Analysis 2003, Oxford University Press, Oxford.
37. Sun, Y.B., Sisomphon, P., Babovic, V., Chan E.S., 2008. Applying local model approach for tidal prediction in a deterministic model. International Journal for Numerical Methods in Fluids, Published online in Wiley InterScience, doi: 10.1002/fld.1910.
38. Sun Y.B., Sisomphon P., Babovic V., Chan E.S. Efficient data assimilation method based on chaos theory and Kalman filter with an application in Singapore Regional Model. Journal of Hydro-environment Research 2009, 3(2):85-95.
39. Takens F. Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, Lecture Notes in Mathematics 1981, vol. 898:366-381. Springer-Verlag, Berlin.
40. Vapnik V.N. The Nature of Statistical Leaning Theory 1995, Springer-Verlag, New York.
41. Wang X.K., Lu W.Z., Cao S.Y., Fang D. Using time-delay neural network combined with genetic algorithms to predict runoff level of Linshan Watershed, Sichuan, China. Journal of Hydrologic Engineering 2007, 12(2):231-236.
42. Werbos, P.J., 1974. Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. Ph.D. Thesis, Harvard University, Cambridge, MA.
43. Williams G.P. Chaos Theory Tamed 1997, Taylor & Francis, London.