Coupling Chebyshev Collocation with TLBO to Optimal Control Problem of Reservoir Sedimentation: A Case Study on Golestan Dam, Gonbad Kavous City, Iran
نویسندگان
1 Department of Mathematics Education, Farhangian university, Tehran, Iran.
2 Faculty of Natural Resources and Earth Sciences, Shahrekord University, Shahrekord, Iran
3 Department of mathematics and statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University
doi
10.22052/mir.2023.247434.1370چکیده
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.
