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1- Zhou, S.L., Mcmohon, T.A., Walton, A., and Lewis, J. (2000). “Forecasting daily urban water demand: A case study
supply zone.” J. Hydrology, 259, 189-202. $4
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5- Milot, J., Rodriguez, M.J., and Sérodes, J.B. (2002). “Contribution of neural networks for modeling trihalomethanes occurrence in drinking water.” J. of Water Resources Planning and Management, 128(5), 370-376, 6- Michaelides, S.C., Pattichis, C.S., and Kleovoulou, G. (2001). “Classification of rainfall variability by using artificial
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neural networks.” International J. of Climatology, 21, 1401-1414. 7- Stark, H.L., Stanley, S.J. and Buchanan, I.D. (2000). “The application of artificial neural networks to water demand modeling.” Annual Conference Abstracts of Canadian Society for Civil Engineering, 139 8-Jain, A., Joshi, U.C., and Varshney, A.K. (2000). “Short-term water demand forecasting using artificial neural networks: IIT Kanpur experience.” In Proceedings of International Conference on Pattern Recognition, 15(2), 459-462. 9- Jain, A., Varshney, A.K., and Joshi, U.C. (2001). “Short-term water demand forecast modeling at IIT Kanpur using artificial neural networks.” Water Resources Management, 15(5), 299-321. 10- Liu, J., Savenije, H.G., and Xu, J. (2003). “Forecast of water demand in Weinan City in China using WDF-ANN model.” Physics and Chemistry of the Earth, 28(4-5), 219-224 11- Yu, T-C, Zhang, T. Q., Mao, G. H., and Wu, X, G. (2004). “Study of artificial neural network model for forecasting urban water demand.” J. of Zhejiang University (Engineering Science), 38(9), 1156-1161.
94
www.SID.ir
12- Bougadis, J., Adamowski, K.B., and Diduch, R. (2005). “Short-term municipal water demand forecasting.” Hydrological Processes, 19(1), 137-148. 13- Adamowski, J.F. (2008). “Peak daily water demand forecast modeling using artificial neural networks.” J. of Water Resources Planning and Management, 134(2), 119-128. 14- Chang, N.B., and Makkeasorn, A. (2007). “Water demand analysis in urban region by neural network models.” In Proceedings of the 8th Annual Water Distribution Systems Analysis Symposium, 48. 15- Msiza, I.S., Nelwamondo, F.V., and Marwala, T. (2007). “Water demand forecasting using multi-layer perceptron and radial basis functions.” In Proceedings of the IEEE International Conference on Neural Networks, Article, 13-18. 16- Zhang, J., Song, R., Bhaskar, N. R., and French, M.N. (2007). “Short-term water demand forecasting: A case study.” In Proceedings of the 8th Annual Water Distribution Systems Analysis Symposium , 49. 17- Ghiassi, G. A, Zimbra, D. K. B., and Saidane, H.C. (2008). “Urban water demand forecasting with a dynamic
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artificial neural network model.” J. of Water Resources Planning and Management, 134(2), 138-146. 18-Yurdusev, M.A., Firat, M., Mermer, M., and Turan, M.E. (2009). “Water use prediction by radial and feed-forward neural nets.” In Proceedings of the Institution of Civil Engineers: Water Management, 162(3), 179-188. '6B(
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Engineering, 121(3), 232-246. 23- Buchberger, G., and Wells, G.J. (1996). “Intensity, duration and frequency of residential water demands.” J. of Water Resources Planning and Management, 122(11), 11-18. 24- Haykin, S. (1999). Neural networks: a comprehensive foundation, Prentice Hall, New Jersey, USA. > x %$B+ k" 02
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