Stochastic Fuzzy Neural Network: Case Study of Optimal Reservoir Operation
Publication: Journal of Water Resources Planning and Management
Volume 133, Issue 6
Abstract
Reservoirs play an important role within the water resources management framework. Among the available techniques for reservoir optimal operation, the most well known one is stochastic dynamic programming (SDP). In recent years, artificial intelligence techniques such as genetic algorithms (GA) and artificial neural networks have arisen as an alternative to overcome some of the limitations of traditional methods. Some of these limitations are related to the difficulty in combining SDP with other simulation and prediction models, the curse of dimensionality due to the increase in the number of decision and state variables, and the error resulting from the rough discretization of these variables. Here, we introduce a new approach for system optimization and operation, named stochastic fuzzy neural network (SFNN), which can be defined as a neuro-fuzzy system that is stochastically trained (optimized) by a GA model to represent the system operational strategy. Moreover, to deal with imprecision originated by the discretization of inflow intervals (events) in calculating the transition probabilities, we applied the method based on the conditional probability of a fuzzy event. To investigate the applicability and efficiency of the proposed method, the Barra Bonita Reservoir, Brazil, is stochastically optimized and operated. The results found by the SFNN method were compared to the results of other available dynamic programming models, showing success in developing and applying the proposed method to optimal reservoir operation.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bellman, R. (1959). Dynamic programming, Princeton University Press, Princeton, N.J.
Butcher, W. (1971). “Stochastic dynamic programming for optimum reservoir operation.” Water Resour. Bull., 7(1), 115–123.
Cancelliere, A., Giuliano, G., Ancarani, A., and Rossi, G. (2002). “A neural networks approach for deriving irrigation reservoir operating policies.” Water Resour. Manage., 16(1), 71–88.
Chandramouli, V., and Raman, H. (2001). “Multireservoir modeling with dynamic programming and neural networks.” J. Water Resour. Plann. Manage., 127(2), 89–98.
Chang, L. C., and Chang, F. J. (2001). “Intelligent control for modeling of real-time reservoir operation.” Hydrolog. Process., 15(9), 1621–1634.
Chang, Y. T., Chang, L. C., and Chang, F. J. (2005). “Intelligent control for modeling of real-time reservoir operation. II: Artificial neural network with operating rule curves.” Hydrolog. Process., 19(7), 1431–1444.
Chaves, P., and Kojiri, T. (2004). “Reservoir optimization through stochastic dynamic programming with fuzzy conditional probability.” Proc., 2004 Annual Conf. of the Japanese Society of Hydrology and Water Resources, Hokkaido, Japan, 32–33.
Chaves, P., Kojiri, T., and Yamashiki, Y. (2003). “Optimization of storage reservoir considering water quantity and quality.” Hydrolog. Process., 17(14), 2769–2793.
Chaves, P., Tsukatani, T., and Kojiri, T. (2004). “Operation of storage reservoir for water quality by using optimization and artificial intelligence techniques.” Math. Comput. Simul., 67(4-5), 419–432.
Esogbue, A. O. (1989). Dynamic programming for optimal water resources systems analysis, Prentice-Hall, Englewood Cliffs, N.J.
Fontane, D. G., Gates, T. K., and Moncada, E. (1997). “Planning reservoir operations with imprecise objectives.” J. Water Resour. Plann. Manage., 123(3), 154–162.
Galvao, C. O., and Valenca, M.S. (1999). Sistemas inteligentes: Aplicações a recursos hídricos e ciências ambientais (Intelligent systems: Applications to water resources and environmental science), ABRH, Brazil (in Portuguese).
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning, Addison-Wesley, Reading, Mass.
Goulter, I. C., and Tai, F. K. (1985). “Practical implication in the use of stochastic dynamic programming for reservoir operation.” Water Resour. Bull., 2(1), 65–74.
Hagan, M. T., Demuth, H. B., Beale, M. H., and Demuth, B. H. (1995). Neural network design, PWS, Boston.
Hori, T., and Takasao, T. (1997). “Drought control under the interaction between uncertainty of inflow prediction and the fuzziness of decision criteria.” Proc., Int. Conf. On Large Scale Water Resources Development in Developing Countries: New Dimensions of Prospects and Problems, 53–60.
Howard, R. A. (1960). Dynamic programming and markov process, MIT Press, Cambridge, Mass.
Jang, S. R., and Sun, T. (1993). “Functional equivalence between radial basis functions and fuzzy inference system.” IEEE Trans. Neural Netw., 4(1), 156–158.
Jang, S. R., and Sun, T. (1995). “Neuro-fuzzy modeling and control.” Proc. IEEE, 83, 378–405.
Jin, Y. (2003). Advanced fuzzy systems design and applications, Physica, New York.
Kacprzyk, J. (1997). Multistage fuzzy control: A model based approach to fuzzy control and decision making, Wiley, Chichester, U.K.
Kaufmann, A. (1975). Introduction to the theory of fuzzy subsets, Vol. I, Fundamental theoretical elements, Academic, Orlando, Fla.
Kelman, J., and Stendinger, J. R. (1990). “Sampling stochastic dynamic programming applied to reservoir operation.” Water Resour. Res., 26(3), 447–454.
Kojiri, T., Sugiyama, Y., and Paudyal, G. N. (1993). “Fuzzy reservoir operation with multi-objective and few monitoring data.” Proc., Int. Conf. on Environment Sound Water Resources Utilization, Bangkok, Thailand.
Labadie, J. W. (2004). “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage., 130(2), 93–111.
Mousavi, S. J., Karamouz, M., and Menhadj, M. B. (2004). “Fuzzy-state stochastic dynamic programming for reservoir operation.” J. Water Resour. Plann. Manage., 130(6), 460–470.
Ponnambalam, K., Karray, F., and Mousavi, S. J. (2003). “Minimizing variance of reservoir system operations benefits using soft computing tools.” Fuzzy Sets Syst., 139(2), 451–461.
Raman, H., and Chandramouli, V. (1996). “Deriving a general operating policy for reservoirs using neural network.” J. Water Resour. Plann. Manage., 122(5), 342–347.
Torabi, M., and Mobasheri, F. (1973). “A stochastic dynamic programming model for the optimum operation of a multi-purpose reservoir.” Water Resour. Bull., 9(6), 1089–1099.
Yakowitz, S. (1982). “Dynamic programming applications in water resource.” Water Resour. Res., 18(4), 673–696.
Yao, X. (1999). “Evolving artificial neural networks.” Proc. IEEE, 87(9), 1423–1447.
Zadeh, L. A. (1968). “Probability measures of fuzzy events.” J. Mathematical Analysis and Applications, 23, 421–427.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 133 • Issue 6 • November 2007
Pages: 509 - 518
Copyright
© 2007 ASCE.
History
Received: Aug 5, 2005
Accepted: Jan 22, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
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.