Nonlinear characterization of pressure fluctuations in fluidized beds

Industrial and Engineering Chemistry Research

Volumn 47, Issue 23, 2008, Pages 9497-9507

  Zarghami, Reza ^a   Mostoufi, Navid ^a   Sotudeh Gharebagh, Rahmat ^a  

^a UNIVERSITY OF TEHRAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; FLUID DYNAMICS; FLUIDIZATION; FORECASTING; REGRESSION ANALYSIS; TIME SERIES ANALYSIS;

AUTO REGRESSIONS; BUBBLE REGIMES; CHAOTIC BEHAVIORS; CORRELATION DIMENSIONS; DYNAMIC INVARIANTS; EMBEDDING DIMENSIONS; FLUIDIZED SYSTEMS; LINEAR METHODS; NEAREST NEIGHBORS; NONLINEAR CHARACTERIZATIONS; NONLINEAR DYNAMICS; NONLINEAR TIME-SERIES ANALYSIS; PREDICTION METHODS; PRESSURE FLUCTUATION SIGNALS; PRESSURE FLUCTUATIONS; PRESSURE SIGNALS; QUALITY OF PREDICTIONS; RECONSTRUCTED STATE SPACES; STATE SPACES; TIME- DELAYS;

FLUIDIZED BEDS;

EID: 57949096251     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie800460f     Document Type: Article

References (28)

1. Van den Bleek, C. M.; Schouten, J. C. Deterministic chaos: a new tool in fluidized bed design and operation. Chem. Eng. J. 1993, 53, 75.
2. Van der Stappen, M. L. M.; Schouten, J. C.; van den Bleek, C. M. Application of deterministic chaos theory in understanding the fluid dynamic behaviour of gas-solids fluidization. AIChE Symp. Ser. 1993, 89 (296), 91-02.
3. Van der Stappen, M. L. M. Chaotic hydrodynamics of fluidized beds. Thesis, Delft University Press, Delft, 1996.
4. Tam, S. W., Devine, M. K. Is there a strange attractor in a fluidized bed? In Measures of Complexity and Chaos; Abraham, N. B., Albano, A. M., Passamante, A., Rapp, P. E., Eds.; Plenum: New York, 1989; pp 193-197.
5. Letaief, N.; Roze, C.; Gouesbet, G. Noise/chaos distinction applied to the study of a fluidized bed. J. Phys. II Fr. 1995, 5, 1883-1899.
6. Takens, F. Detecting strange attractors in turbulence. In Proceedings of Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898; Rand, D. A., Yong, L. S., Eds.; Springer Verlag: Berlin, 1981; pp 366-381.
7. Johnsson, F.; Zijerveld, R. C.; Schouten, J. C.; van den Bleek, C. M.; Leckner, B. Characterization of fluidization regimes by time-series analysis of pressure fluctuations. Int. J. Multiphase Flow 2000, 26, 663.
8. Kantz, H.; Schreiber, T. Nonlinear time series analysis, 2nd ed.; Cambridge University Press: New York, 2003.
9. Addison, P. S. Fractals and Chaos: An Illustrated Course; IOP Publishing Ltd.: London, UK, 2005.
10. Fraser, A.; Swinney, H. Independent coordinates for strange attractors from mutual information. Phys. Rev. A 1986, 33, 1134.
11. Kennel, M. B.; Isabelle, S. Method to distinguish possible chaos from colored noise and to determine embedding parameters. Phys. Rev. A 1992, 46, 3111.
12. Grassberger, P.; Procaccia, I. Characterization of strange attractors. Phys. Rev. Lett. 1983, 50, 346.
13. Grassberger, P.; Procaccia, I. Measuring the strangeness of strange attractors. Physica D 1983, 9, 189.
14. Schouten, J. C.; Takens, F.; van den Bleek, C. M. Estimation of the dimension of a noisy attractor. Phys. Rev. E 1994, 50, 3.
15. Van Ommen, J. R.; Coppens, M.; van den Bleek, C. M. Early warning of agglomeration in fluidized beds by attractor comparison. AIChE J. 2000, 46, 2183.
16. McNames, J. A nearest trajectory strategy for time series prediction. Proceedings of the International Workshop on Advanced Black-box Techniques for Nonlinear Modeling, Katholieke Universiteit, Leuven, Belgium, July 1998; pp 112-128.
17. Casdagli, M.; Des Jardins, D.; Eubank, S.; Doyne Farmer, J.; Gibson, J.; Theiler, J. Nonlinear modeling of chaotic time series: Theory and applications. In Applied Chaos; Kim, J. H., Stringer, J., Eds.; John Wiley & Sons Inc.: New York, 1992; pp 335-380.
18. Liu, Z.; Ren, X.; Zhu, Z. Equivalence between different local prediction methods of chaotic time series. Phys. Let. A 1997, 227, 37.
19. Grassberger, P.; Procaccia, I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys. Rev. A 1983, 28, 2591.
20. Grassberger, P.; Procaccia, I. Dimensions and entropies of strange attractors from a fluctuating dynamics approach. Physica D 1984, 13, 34.
21. Grassberger, P. Estimating the fractal dimensions and entropies of strange attractors. In Chaos-Nonlinear Science: Theory and Applications; Holden, A. V., Ed.; Manchester University Press: Manchester, 1986; pp 291-311.
22. Schouten, J. C.; Takens, F.; van den Bleek, C. M. Maximum likelihood estimation of the entropy of an attractor. Phys. Rev. E 1994, 49, 126.
23. Breeden, J. L.; Packard, N. H. A learning algorithm for optimal representation of experimental data. Int. J. Bif. Chaos 1994, 4, 311.
24. Broomhead, D. S.; King, G. P. Extracting qualitative dynamics from experimental data. Physica D 1986, 20, 217.
25. Whitney, H. Differentiable manifolds. Ann. Math. 1936, 37, 645.
26. Saure, T.; Yorke, J. A.; Casdagli, M. Embedology. J. Stat. Phys. 1991, 65, 578.
27. Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J. D. Testing for nonlinearity in time series: the method of surrogate data. Physica D 1992, 58, 77.
28. Provenzale, A.; Smith, L. A.; Vio, R.; Murante, G. Distinguishing between low dimensional dynamics and randomness in measured time series. Physica D 1992, 58, 31.