Document Type : Original Article

Authors

1 Assistant Professor, Department of Water and hydraulic structures engineering, Faculty of Civil Engineering, semnan University

2 Semnan University

Abstract

The shape of the artificial channel sections and their optimal design by artificial intelligence methods can have significant effects on lowering the costs of constructions. In this study, an artificial channel with inverse cycloid and its optimal design by bat algorithm was introduced for the first time. Two schemes of sections were proposed: inverse cycloid without horizontal bed and inverse cycloid with horizontal bed. For optimal designing of proposed section, two scenarios were defined: channel with fixed freeboard and channel with variable freeboard. In both scenarios, Manning equation was used as a constraint and Horton equation was used for considering equivalent roughness. Based on sensitivity analysis, optimal parameters of the proposed algorithm were determined. Bat algorithm has been implemented randomly for each section and for each scenario for fifteen times, and coefficient of variation and speed of convergence were estimated. To find out the accuracy of bat algorithm in the global optimum determination, a comparison between solutions of bat algorithm and lingo software was made. Eventually, results from optimal design of proposed sections were compared with trapezoidal channel, parabolic with horizontal bed channel, ellipsoid channel, and general ellipsoid channel. Results from random runs of bat algorithm indicated that coefficient of variation for defined sections and scenarios were about 0.0002 to 0.0013. Convergence curves showed that the algorithm was convergence for all sections and scenarios in 1000 repetition. Findings of bat algorithm and lingo software also demonstrated high accuracy of mentioned algorithm in determination of global optimum. Furthermore, using proposed sections, compared with other common sections, led to 34.7 percent decrease in construction costs. Among sections and scenarios investigated here, the inverse cycloid under second scenario was found more economical, up to 17.15 percent.

Keywords

 
Ahmadianfar., I. Adib, A. and Salarijazi, M. 2015. Optimizing multireservoir operation: Hybrid of bat algorithm and differential evolution. J. Water Resour. Plann. Manage. 142(2): 05015010.
 
 Babaeyan-Koopaei, K., Valentine, E. M. and Swailes, D. C. 2000. Optimal design of parabolic-bottomed triangle canals. J. Irrig. Drain. Eng. 126(6): 408-411.
 
Bhattacharjya, R. K. 2006. Optimal design of open channel section incorporating critical flow condition. J. Irrig. Drain. Eng. 132(5): 513-518.
 
Bozorg-Haddad. O., Karimirad, I., Seifollahi-Aghmiuni, S. and Loáiciga, H. A. 2014. Development and application of the bat algorithm for optimizing the operation of reservoir systems. J. Water Resour. Plann. Manage. 141(8): 04014097.
 
Chahar, B. R. 2005. Optimal design of parabolic canal section. 2005. J. Irrig. Drain. Eng. 131(6): 546-554.
 
Chahar, B. R. 2007. Optimal Design of a Special Class of Curvilinear Bottomed Channel Section. J. Hydraul. Eng. 133(5): 571-576.
 
Das, A. 2000. Optimal channel cross section with composite roughness. J. Irrig. Drain. Eng. 126(1): 68-72.
 
Das, A. 2007a. Optimal design of channel having horizontal bottom and parabolic sides. J. Irrig. Drain. Eng. 133(2): 192-197.
 
Das, A. 2007b. Flooding probability constrained optimal design of trapezoidal channels. J. Irrig. Drain. Eng. 133(1): 53-60.
 
Easa, S. M. 2009.  Improved channel cross section with two-segment parabolic sides and horizontal bottom. J. Irrig. Drain. Eng. 135(3): 357-365.
 
Easa, S. M. 2011. New and improved channel cross section with piecewise linear or smooth sides. Can. J. Civil Eng. 38(6): 690-697.
 
Easa, S. M. 2016. Versatile general elliptic open channel cross section. KSCE. J. Civil Eng. 20(4): 1572-1581.
 
Easa, S. M. and Vatankhah, A. R. 2014. New open channel with elliptic sides and horizontal bottom. KSCE J. Civil Eng. 18(4): 1197-1204.
 
Ehteram, M., Mousavi, S. F., Karami, H., Farzin, S., Singh, V. P., Wing, K. and El-Shafie, A. 2017. Reservoir operation based on evolutionary algorithms and multi-criteria decision-making under climate change and uncertainty. J. Hydroinform. 20(2): 332-355.
 
Ehteram, M., Karami, H., Mousavi, S. F., Farzin, S., Sarkamaryan, V. P., Wing, K. and
El-Shafie, A. 2018. Evaluation of the performance of bat algorithm in optimization of nonlinear Muskingum model parameters for flood routing. J. Hydroinform. 4(4):
1025-1032.
 
Froehlich, D. C. 1994. Width and depth-constrained best trapezoidal section. J. Irrig. Drain. Eng. 120(4): 828-835.
 
Gupta, S. K., Mishra, U., Datta, D. and Singh, V. P. 2017. Fish shoal optimization for identification of the most suitable revetment stone for design of minimum cost earthen canals carrying sediment-laden flow. ISH J. Hydraul. 23(1): 1-18.
 
Han, Y. C. 2015. Horizontal bottomed semi-cubic parabolic channel and best hydraulic section. Flow. Meas. Instrum. 45: 56-61.
 
Han, Y. C. and Easa, S. M. 2017. New and improved three and one-third parabolic channel and most efficient hydraulic section. Can. J. Civil Eng. 44(5): 387-391.
 
Horton, R. E. 1933. Separate roughness coefficients for channel bottom and sides. Eng.
News-Rec. 111(22): 652-653.
 
Jain, A., Bhattacharjya, R. K. and Sanaga, S. 2004. Optimal design of composite channels using genetic algorithm. J. Irrig. Drain. Eng. 130(4): 286-295.
 
Jayabarathi, T., Raghunathan, T. and Gandomi, A. H. 2018. The Bat Algorithm, Variants and Some Practical Engineering Applications. In: Yang, X. S. (Ed) Nature-Inspired Algorithms and Applied Optimization.  Springer, Cham.
 
Karami, H., Ehteram, M., Mousavi, S. F., Farzin, S., Kisi, O. and El-Shafie, A. 2018. Optimization of energy management and conversion in the water systems based on evolutionary algorithms. Neural Comput. Appl. doi.org/10.1007/s00521-018-3412-6.
 
 Laycock, A. 2007. Irrigation Systems: Design, Planning and Construction. CABI.
 
Loganathan, G. V. Optimal design of parabolic canals. 1991. J. Irrig. Drain. Eng. 117(5):
716-735.
 
Mironenko, A. P., Willardson., L. S. and Jenab, S. A. 1984. Parabolic canal design and analysis. J. Irrig. Drain. Eng. 110(2): 241-246.
 
Monadjemi, P. 1994. General formulation of best hydraulic channel section. J. Irrig. Drain. Eng. 120(1): 27-35.
 
Niknam, T., Sharifinia, S. and Azizipanah-Abarghooee, R. 2013. A new enhanced bat-inspired algorithm for finding linear supply function equilibrium of GENCOs in the competitive electricity market. Energy Convers. Manage. 76, 1015-1028.
 
Orouji, H., Mahmoudi, N., Fallah-Mehdipour., E, Pazoki, M. and Biswas, A. 2016. Shuffled frog-leaping algorithm for optimal design of open channels.  J. Irrig. Drain. Eng. 142(10): 06016008.
 
Reddy, M. and Adarsh, S. 2010. Chance constrained optimal design of composite channels using meta-heuristic techniques. J. Water Resour. Plan. Manage. 10(24): 2221-2235.
 
Swamee, P. K. 1995. Optimal irrigation canal sections.  J. Irrig. Drain. Eng. 121(6): 467-469.
 
Swamee, P. K., Mishra, G. C. and Chahar, B. R. 2002. Design of minimum water-loss canal sections. J. Hydraul. Res. 40(2): 215-220.
 
Yang, X. S. 2010. A New Metaheuristic Bat-Inspired Algorithm. In: González, J. R., Pelta, D. A., Cruz, C., Terrazas, G. and Krasnogor, N. (Eds.) Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). Studies in Computational Intelligence, Vol 284. Springer, Berlin, Heidelberg.