Time series analysis and prediction on complex dynamical behavior observed in a blast furnace

Physica D: Nonlinear Phenomena

Volumn 135, Issue 3-4, 2000, Pages 305-330

  Miyano, T ^a,c   Kimoto, S ^b   Shibuta, H ^a   Nakashima, K ^a   Ikenaga, Y ^a   Aihara, K ^b  

^a Sumitomo Metal Industries Ltd   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

^c HIROSAKI UNIVERSITY   (Japan)

Author keywords

KM2O Langevin equation; RBF networks; Time series prediction

Indexed keywords

EID: 0346057281     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00135-9     Document Type: Article

References (28)

1. A.S. Lapedes, R. Farber, Nonlinear signal processing using neural networks: prediction and system modeling, Technical Report LA-UR-87-2662 (1987), Los Alamos National Laboratory.
2. M. Casdagli, Nonlinear prediction of chaotic time series, Physica D 35 (1989) 335.
3. P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractor, Phys. Rev. Lett. 31 (1983) 346.
4. D. Ruelle, Deterministic chaos; the science and the fiction, Proc. Roy. Soc. London A 427 (1990) 241.
5. A.R. Osborne, A. Provenzale, A search for chaotic behavior in large and mesoscale motions in the pacific ocean, Physica D 35 (1989) 357.
6. J.D. Farmer, J.J. Sidorowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (1987) 845.
7. G. Sugihara, R.M. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature 344 (1990) 734.
8. A.A. Tsonis, J.B. Elsner, Nonlinear prediction as a way of distinguishing chaos from random fractal sequences, Nature 358 (1992) 217.
9. T. Miyano, Time series analysis of complex dynamical behavior contaminated with observational noise, Int. J. Bifur. Chaos 6 (1996) 2031.
10. D.T. Kaplan, L. Glass, Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos, Physica D 64 (1993) 431.
11. R. Wayland, D. Bromley, D. Pickett, A. Passamante, Recognizing determinism in a time series, Phys. Rev. Lett. 70 (1993) 580.
12. Y. Okabe, On Stochastic Difference Equations for the Multi-Dimensional Weakly Stationary Time Series, Prospect of Algebraic Analysis, Academic Press, New York, 1988, p. 601.
13. 2O-Langevin equations to the linear prediction problem for the multi-dimensional weakly stationary time series, J. Math. Soc. Jpn. 45 (1993) 277.
14. 2O-Langevin equations, Hokkaido Math. J. 22 (1993) 199.
15. 2O-Langevin equations and its applications to data analysis (I): Stationary analysis, Hokkaido Math. J. 20 (1991) 45.
16. 2O-Langevin equations and its applications to data analysis (II): causal analysis, Nagoya Math. J. 134 (1994) 1.
17. 2O-Langevin equations and its applications to the nonlinear prediction problem for the one-dimensional strictly stationary time series, J. Math. Soc. Jpn. 47 (1995) 349.
18. S. Kimoto, T. Ikeguchi, T. Matozaki, K. Aihara, In: M. Yamaguti (Ed.), Deterministic Chaos and its Stationary Analysis, Towards the Harnessing of Chaos, Elsevier, Amsterdam, 1994, p. 373.
19. M. Casdagli, D. des Jardins, S. Eubank, J.D. Farmer, J. Gibson, N. Hunter, J. Theiler, Nonlinear modeling of chaotic time series; theory and applications, Technical Report LA-UR-91-1637, Los Alamos National Laboratory, 1991.
20. H. Akaike, T. Nakagawa, Statistical Analysis and Control for a Dynamical System, Science Company, 1973, in Japanese.
21. T. Poggio, F. Girosi, Networks for approximation and learning, Proc. IEEE 78 (1990) 1481.
22. F. Girosi, M. Jones, T. Poggio, Regularization theory and neural networks architectures, Neural Computation 7 (1995) 219.
23. G. Wahba, Spline Models for Observational Data, Series in Applied Mathematics, vol. 59, SIAM, Philadelphia, 1990.
24. T. Miyano, F. Girosi, Forecasting global temperature variations by neural networks, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, A. I. Memo No. 1447 (1994).
25. T. Miyano, H. Morita, A. Shintani, T. Kanda, M. Hourai, Characterization of complexities in Czochralski crystal growth by nonlinear forecasting, J. Appl. Phys. 76 (1994) 2681.
26. J.H. Friedman, W. Stuetzle, Projection pursuit regression, J. Am. Statist. Assoc. 76 (1981) 817.
27. P. Niyogi, F. Girosi, On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, A. I. Memo, No. 1467 (1994).
28. T. Miyano, K. Aihara, Forecasting complex time series by bell-shaped regularization networks, Proceedings of International Symposium on Artificial Life and Robotics (AROB'97), 1997, p. 150.