Coupling Chebyshev Collocation with TLBO to Optimal Control Problem of Reservoir Sedimentation: A Case Study on Golestan Dam, Gonbad Kavous City, Iran

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics Education, Farhangian university, Tehran, Iran.

2 Department of mathematics and statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University

3 Faculty of Natural Resources and Earth Sciences, Shahrekord University, Shahrekord, Iran

Abstract

‎In this paper‎, ‎an efficient and robust approach based on the Chebyshev collocation method and Teaching-Learning-Based Optimization (TLBO) is utilized to solve the Optimal Control Problem (OCP) of reservoir sedimentation on Golestan dam in Gonbad Kavous City‎, ‎Iran‎. ‎The discretized method employs Mth degree of Lagrange polynomial approximation for an unknown variable and Gauss-Legendre integration‎. ‎The OCP yields a nonlinear programming problem (NLP)‎, ‎and then this NLP is solved by TLBO‎. ‎Numerical implementations are given to demonstrate this approach yields more acceptable and the accurate results‎. ‎Furthermore‎, ‎it is found that filling the dam with sediment decreases the water storage‎, ‎increases dam maintenance costs‎, ‎and also decreases the stability of the dam over a period of 40 years‎. ‎Our results show that the Golestan dam will gain development with the construction of the new reservoir‎.

Keywords

Main Subjects

References

[1] E. Valizadegan, M. S. Bajestan and H. M. V. Samani, Control of sedimentation in reservoirs by optimal operation of reservoir releases, J. Food Agric.
Environ. 7 (2) (2009) 759 − 763.
[2] J. W. Nicklow and L. W. Mays, Optimal control of reservoir releases to minimize sedimentation in rivers and reservoirs, J. Am. Water Resour. Assoc. 37
(1) (2001) 197 − 211, https://doi.org/10.1111/j.1752-1688.2001.tb05486.x.
[3] J. Zhu, Q. Zeng, D. Guo and Z. Liu, Optimal control of sedimentation in navigation channels, J. Hydraul. Eng. 125 (7) (1999) 750 − 759,
https://doi.org/10.1061/(ASCE)0733-9429(1999)125:7(750).
[4] Y. Ding, M. Elgohry, M. S. Altinakar and S. S. Y. Wang, Optimal control of
flow and sediment in river and watershed, In Proceedings of 2013 IAHR
Congress, Tsinghua University Press, 2013, September, Chengdu, China
(Vol. 813).
[5] R. Huffaker and R. Hotchkiss, Economic dynamics of reservoir sedimentation management: optimal control with singularly perturbed equations of motion, J. Econ. Dyn. Control. 30 (12) (2006) 2553 − 2575,
https://doi.org/10.1016/j.jedc.2005.08.003.
[6] L. J. Alvarez-Vázquez, A. Martínez, C. Rodríguez and M. E.
Vázquez-Méndez, Sediment minimization in canals: an optimal
control approach, Math. Comput. Simul. 149 (2018) 109 − 122,
https://doi.org/10.1016/j.matcom.2018.02.007.
[7] Y. Ding, and S. S. Y. Wang, Optimal control of flood water with sediment transport in alluvial channel, Sep. Purif. Technol. 84 (2012) 85 − 94,
https://doi.org/10.1016/j.seppur.2011.06.019.
[8] R. V. Rao and V. D. Kalyankar, Parameter optimization of modern machining processes using teaching–learning-based optimization
algorithm, Eng. Appl. Artif. Intell. 26 (1) (2013) 524 − 531,
https://doi.org/10.1016/j.engappai.2012.06.007.
[9] R. Rao and V. Patel, An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems, Int. J. Ind.
Eng. Comput. 3 (4) (2012) 535 − 560.
[10] R. V. Rao, V. J. Savsani and D. P. Vakharia, Teaching–learning-based
optimization: a novel method for constrained mechanical design optimization problems, Comput. Aided Des. 43 (3) (2011) 303 − 315,
https://doi.org/10.1016/j.cad.2010.12.015.
[11] R. V. Rao, V. J. Savsani and D. P. Vakharia, Teaching–learning-based optimization: an optimization method for continuous non-linear large scale
problems, Inf. Sci. 183 (1) (2012) 1 − 15.
[12] R. Khanduzi, A. Ebrahimzadeh and M. R. Peyghami, A modified teaching–learning-based optimization for optimal control of
Volterra integral systems, Soft Comput. 22 (17) (2018) 5889 − 5899,
https://doi.org/10.1007/s00500-017-2933-8.
[13] R. D. Kundu, M. Mishra and D. Maity, Teaching–learning-based optimization algorithm for solving structural damage detection problem in frames
via changes in vibration responses, Archit. Struct. Constr. (2021) 1 − 20,
https://doi.org/10.1007/s44150-021-00009-6.
[14] J. Hays, A. Sandu, C. Sandu and D. Hong, Parametric design optimization
of uncertain ordinary differential equation systems, J. Mech. Des. 134 (8)
(2012) p. 081003, https://doi.org/10.1115/1.4006950.
[15] F. Valian, Y. Ordokhani and M. A. Vali, Numerical solution for a
class of fractional optimal control problems using the fractional-order
Bernoulli functions, Trans. Inst. Meas. Control. 44 (8) (2022) 1635 − 1648,
https://doi.org/10.1177/01423312211047033.
[16] F. Z. Lee, J. S. Lai and T. Sumi, Reservoir sediment management and downstream river impacts for sustainable water resources-case study of shihmen
reservoir, Water, 14 (3) (2022) p. 479.
[17] X. Chen, B. Xu, K. Yu and W. Du, Teaching-learning-based optimization with learning enthusiasm mechanism and its application in
chemical engineering, J. Appl. Math. 2018 (2018) Article ID 1806947,
https://doi.org/10.1155/2018/1806947.
[18] A. Kaveh, M. Kamalinejad, K. B. Hamedani and H. Arzani, Quantum
teaching-learning-based optimization algorithm for sizing optimization of
skeletal structures with discrete variables, Structures, 32 (2021) 1798−1819,
https://doi.org/10.1016/j.istruc.2021.03.046.
[19] M. Spence and D. Starrett, Most rapid approach paths in accumulation problems, Int. Econ. Rev. 16 (2) (1975) 388 − 403,
https://doi.org/10.2307/2525821.
[20] F. Fahroo and I. M. Ross, Direct trajectory optimization by a Chebyshev
pseudo spectral method, J. Guid. Control Dyn. 25 (1) (2002) 160 − 166,
https://doi.org/10.2514/2.4863.
Mathematics Interdisciplinary Research
Volume 8, Issue 2
August 2023
Pages 141-159

Files

Share

How to cite

Statistics