Strange Attractors and Chaos in Wastewater Flow
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Abstract
This study investigates the complexity of wastewater flow phenomena using state‐of‐the‐art chaos analysis. Techniques used are power spectrum, correlation exponent, and Lyapunov exponent analyses. These techniques are general and can be used for other dynamic systems. The analyses provide a qualitative description of the irregular behavior of wastewater flow. Flow time series of three Ohio wastewater treatment plants are investigated. Among other things, the results indicate the presence of underlying strange attractors, which qualify the investigated flows as chaotic. These findings indicate that the structure of wastewater flow data can be very complex and that accurate prediction using stochastic models may be invalid. The procedures employed in this study can be used to evaluate flow models normally used in process control studies.
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References
1.
Benettin, G. L., Galgani, A. G., and Strelcyn, J. M. (1980). “Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: theory.” Meccanica, 15, 9.
2.
Essex, C., Lookman, T., and Nerenberg, M. A. H. (1987). “The climate attractor over short timescales.” Nature, 326, 64–66.
3.
Farmer, J. D., Ott, E., and Yorke, J. A. (1983). “The dimension of chaotic attractors.” Physica, 7D, 153–180.
4.
Grebogi, C., Ott, E., Pelikan, S., and Yorke, J. A. (1984). “Strange attractors that are not chaotic.” Physica, 13D, 261–268.
5.
Grassberger, P., and Prococcia, I. (1983). “Measuring the strangeness of strange attractors.” Physica, 9D, 189–208.
6.
Kurths, J., and Herzel, H. (1987). “An attractor in a solar time series.” Physica, 25D, 165–172.
7.
Malraison, B., Atten, P., Berge, P., and Dubuois, M. (1983). “Dimension of strange attractors: an experimental determination of the chaotic regime of two convective systems.” J. Physique‐Lettres, Paris, France, 44, 897–902.
8.
Mane, R. (1981). “On the dimension of the compact invariant sets of certain nonlinear maps.” Lecture notes in mathematics 898, D. A. Rand and L. S. Young, eds., Springer, Berlin, Germany, 230–242.
9.
Moon, F. C. (1988). Experiments in chaotic dynamics: chaotic motions in nonlinear dynamical systems. Springer‐Verlag, New York, N.Y.
10.
Osborne, A. R., and Provenzale, A. (1989). “Finite correlation dimension for stochastic systems with power‐law spectra.” Physica, 35D, 357–381.
11.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1986). “Fourier transform spectral methods.” Numerical Recipes. Cambridge University Press, Cambridge, Mass.
12.
Rodriguez‐Iturbe, I., De Power, B. F., Sharafi, M. B., and Georgakakos, K. P.(1989). “Chaos in rainfall.” Water Resour. Res., 25(7), 1667–1675.
13.
Roux, J. C., Simoyi, R. H., and Swinney, H. L. (1983). “Observation of a strange attractor.” Physica, 8D, 257–266.
14.
Ruelle, D. (1979). “Sensitive dependence on initial conditions and turbulent behavior of dynamical systems.” Annu. N.Y. Acad. of Sci., New York, N.Y.
15.
Shaw, R. (1981). “Strange attractors, chaotic behavior, and information flow.” Z. Naturforsh, 36A.
16.
Takens, F. (1981). “Detecting strange attractors in turbulence.” Lecture notes in Mathematics 898, D. A. Rand and L. S. Young, eds, Springer, Berlin, Germany, 366.
17.
Tsonis, A. A., and Elsner, J. B. (1989). “Chaos, strange attractors, and weather.” Bull. American Meterological Soc., 70(1), 14–23.
18.
Wilcox, B. P., Seyfried, M. S., Blackburn, W. H., and Matison, T. H. (1990). “Chaotic characteristics of snowmelt runoff: a preliminary study.” Watershed planning and analysis in action, ASCE, New York, N.Y., 125–134.
19.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A. (1985). “Determining Lyapunov exponents from a time series.” Physica, 16D, 285–317.
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Copyright © 1994 American Society of Civil Engineers.
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Received: Feb 27, 1991
Published online: Jan 1, 1994
Published in print: Jan 1994
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