Uncertainty Characterization in the Design of Flow Diversion Structure Profiles Using Genetic Algorithm and Fuzzy Logic
Publication: Journal of Irrigation and Drainage Engineering
Volume 139, Issue 2
Abstract
Flow diversion head works are constructed across rivers to divert flow into irrigation, navigation, or power generation channels. Hydraulic structures, such as weirs or barrages, are integral parts of these diversion head works. The optimal design of these hydraulic structures is generally obtained by considering the deterministic values of hydrogeological parameters. However, there is a high degree of local soil variability and imprecision in the determination of soil parameters, such as the safe exit gradient. The seepage head also exhibits a high degree of variability, depending on complex hydrological and metrological factors. This work considers the hydrogeological parameters safe exit gradient and seepage head as imprecise or uncertain. An optimization-based methodology is presented to incorporate uncertainty in the safe exit gradient and seepage head in the optimization formulation and obtain the optimum structural dimensions that minimize the total cost. The subsurface flow consideration is embedded in the optimization formulation. The nonlinear optimization formulation (NLOF) solution procedure using a genetic algorithm (GA) is implemented to demonstrate the characterization of uncertainty in design and hence, overall cost from the uncertain safe exit gradient and seepage head. The limited evaluation shows the potential applicability of the proposed methodology.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abebe, A. J., Guinot, V., and Solomatine, D. P. (2000). “Fuzzy alpha-cut vs. Monte Carlo techniques in assessing uncertainty in model parameters.” Proc., 4th Int. Conf. Hydroinformatics, International Association for Hydro-Environment Engineering and Research (IAHR), Madrid, Spain.
Anoop, M. B., Rao, K. B., and Gopalakrishnan, S. (2006). “Conversion of probabilistic information into fuzzy sets for engineering decision analysis.” Compos. Struct., 84, 141–155.
Apostolakis, G. (1990). “The concept of probability in safety assessments of technological systems.” Sci., 250(4986), 1359–1364.
Asawa, G. L. (2005). Irrigation and water resources engineering, New Age International (P) Limited Publishers, New Delhi, India.
Bellman, R. E., and Zadeh, L. A. (1970). “Decision-making in a fuzzy environment.” Manage. Sci., 17, 141–164.
Bureau of Indian Standards. (1989). “Indian standard hydraulic design of barrages and weirs—Guidelines.” IS 6966 (Part 1), Reaffirmed 2001, New Delhi, India.
Cho, H. N., Choi, H.-H., and Kim, Y. B. (2002). “A risk assessment methodology for incorporating uncertainties using fuzzy concepts.” Reliab. Eng. Syst. Saf., 78(2), 173–183.
Choquet, G. (1954). “Theory of capacities.” Ann. Inst. Fourier, 5, 131–295.
De Jong, K. A. (1975). “An analysis of the behavior of a class of genetic adaptive systems.” Ph.D. dissertation, Univ. of Michigan, Ann Arbor, MI.
de Lima, B. S. L. P., and Ebecken, N. F. F. (2000). “A comparison of models for uncertainty analysis by the finite element method.” Finite Elem. Anal. Des., 34(2), 211–232.
Dong, W., and Wong, F. (1987). “Fuzzy weighted averages and implementation of the extension principle.” Fuzzy Set Syst., 21(2), 183–199.
Dubois, D., and Prade, H. (1988). Possibility theory: An approach to computerized processing of uncertainty, Plenum Press, New York.
Ganoulis, J. (1996). “Modeling hydrologic phenomena.” Rev. Sci. Eau, 9(4), 421–434.
Garg, N. K., Bhagat, S. K., and Asthana, B. N. (2002). “Optimal barrage design based on subsurface flow considerations.” J. Irrig. Drain. Eng., 128(4), 253–263.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning, Kluwer Academic Publishers, Boston, MA.
Gueorguieva, I., Nestorov, I., and Rowland, M. (2004). “Fuzzy simulation of pharmacokinetic models: Case study of whole body physiologically based model of diazepam.” J. Pharmacokinet Phar., 11, 577–593.
Haestad, M., et al. (2003). Advanced water distribution modeling and management, Haestad Press, Waterbury, CT.
Hanss, A. M. (2002). “The transformation method for the simulation and analysis of systems with uncertain parameters.” Fuzzy Sets Syst., 130(3), 277–289.
Hanss, M., and Willner, K. (1999). “On using fuzzy arithmetic to solve problems with uncertain model parameters.” Proc., Euromech 405 Colloquium, European Mechanics Society, Udine, Italy, 85–92.
Helton, J. C., Johnson, J. D., and Oberkampf, W. L. (2004). “An exploration of alternative approaches to the representation of uncertainty in model predictions.” Reliab. Eng. Syst. Safety, 85(1–3), 39–71.
Helton, J. C., and Oberkampf, W. L. (2004). “Alternative representations of epistemic uncertainty.” Reliab. Eng. Syst. Safety, 85(1–3), 1–10.
Hofer, E., Kloos, M., Krzykacz-Hausmann, B., Peschke, J., and Woltereck, M. (2002). “An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties.” Reliab. Eng. Syst. Safety, 77(3), 229–238.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, MI.
Ismail, S. S., and Aziz, M. (2005). “Toshika spillway barrages stability analysis.” Proc., Ninth Int. Water Technology Conf., IWTC9, Sharm El-Sheikh, Egypt, 527–540.
Kentel, E., and Aral, M. M. (2004). “Probabilistic-fuzzy health risk modeling.” Stochastic Environ. Res. Risk Assess. (SERRA), 18(5), 324–338.
Khosla, A. N. (1932). “Pressure pipe observations at Panjnad weir.”, Punjab Engineering Congress, Mufid-I-’Am Press, Lahore, Pakistan.
Khosla, A. N., Bose, N. K., and Taylor, E. M. (1936). “Design of weirs on permeable foundations.”, Central Board of Irrigation and Power (CBIP), New Delhi, India.
Khrisnapuram, R. (1998). “Membership function elicitation and learning.” Handbook of fuzzy computation, E. H. Ruspini, P. P. Bonissone, and W. Pedrryez, eds., Institute of Physics, Dirac House, Temple Bath, Bristol, UK.
Klir, G. J. (1995). “Principles of uncertainty: What are they? Why do we need them?” Fuzzy Sets Syst., 74(1), 15–31.
Lane, E. W. (1935). “Security from Under-Seepage-Masonry Dams on Earth Foundations.” Trans. ASCE, 100(1), 1235–1272.
Leliavsky, S. (1979). Irrigation engineering: Canals and barrages, Oxford and IBH, New Delhi, India.
Mauris, G., Lasserre, V., and Foulloy, L. (2001). “A fuzzy approach for the expression of uncertainty in measurement.” Measurement, 29(3), 165–177.
Modi, P. N. (2008). Irrigation water resources and water power engineering, Standard Book House, Rajsons Publications, Delhi, India.
Oberkampf, W. L., Helton, J. C., Joslyn, C. A., Wojtkiewicz, S. F., and Ferson, S. (2004). “Challenge problems: Uncertainty in system response given uncertain parameters.” Reliab. Eng. Syst. Safety, 85(1–3), 11–19.
O’Hagan, A., and Oakley, J. E. (2004). “Probability is perfect, but we can’t elicit it properly.” Reliab. Eng. Syst. Safety, 85(1–3), 239–248.
Passino, K. M. (2005). Biomimicry for optimization, control, and automation, Springer-Verlag, London, UK.
Ross, J. L., Ozbek, M. M., and Pinder, G. F. (2009). “Aleatoric and epistemic uncertainty in groundwater flow and transport simulation.” Water Resour. Res., 45, W00B15.
Schuhmacher, M., Meneses, M., Xifro, A., and Domingo, J. L. (2001). “The use of Monte-Carlo simulation techniques for risk assessment: Study of a municipal waste incinerator.” Chemosphere, 43(4–7), 787–799.
Seng, K.-Y., Nestorov, I., and Vicini, P. (2007). “Simulating pharmacokinetic and pharmacodynamic fuzzy-parameterized models: A comparison of numerical methods.” J. Pharmacokinet Phar., 34(5), 595–621.
Shafer, G. (1976). A mathematical theory of evidence, Princeton University Press, Princeton, NJ.
Singh, R. M. (2007). “Optimal design of barrages using genetic algorithm.” Proc. National Conf. on Hydraulics and Water Resources: Hydro-2007, Elite Publishing House Pvt Ltd, New Delhi, India, 623–631.
Singh, R. M. (2011). “Design of barrages with genetic algorithm based embedded simulation optimization approach.” Water Resour. Manage., 25(2), 409–429.
Singh, R. M., and Datta, B. (2006). “Identification of unknown groundwater pollution sources using genetic algorithm based linked simulation optimization approach.” J. Hydrol. Eng., 11(2), 101–109.
Skutch, J. (1997). “Minor irrigation design DROP—Design manual hydraulic analysis and design of energy-dissipating structures.”, HR Wallingford, Wallingford, UK.
Srinivasan, G., Tartakovsky, D. M., Robinson, B. A., and Aceves, A. B. (2007). “Quantification of uncertainty in geochemical reactions.” Water Resour. Res., 43(12), W12415.
Swamee, P. K., Mishra, G. C., and Salem, A. S. (1996). “Optimal design of sloping weir.” J. Irrig. Drain. Eng., 122(4), 248–255.
Terzaghi, K., and Peck, R. B. (1967). Soil Mechanics in Engineering Practice, John Wiley & Sons, New York.
Varshney, R. S., Gupta, S. C., and Gupta, R. L. (2007). Theory and design of irrigation structures, Vol. 2, Nem Chand and Bros, Roorkee (U.A.), India.
Zadeh, L. A. (1965). “Fuzzy sets.” Inf. Control, 8(3), 338–353.
Zadeh, L. A. (1968). “Fuzzy algorithms.” Inf. Control, 12(2), 94–102.
Zadeh, L. (1978). “Fuzzy sets as a basis for a theory of possibility.” Fuzzy Sets Syst., 1(1), 3–28.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 139 • Issue 2 • February 2013
Pages: 145 - 157
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Apr 27, 2011
Accepted: Jul 12, 2012
Published online: Jul 27, 2012
Published in print: Feb 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.