Optimizing the Cross-section of Diversion Dams Using Particle Swarm Optimization Algorithm
Subject Areas : Hydrology, hydraulics, and water transfer buildingsShahab Naderi 1 , Saeid Shabanlou 2 , Mohammad Reza Javaheri Tafti 3 , Behrouz Yaghoubi 4
1 - Ph.D. Candidate, Department of Civil Engineering, Taft Branch, Islamic Azad University, Taft, Iran.
2 - Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
3 - Department of Civil Engineering, Taft Branch, Islamic Azad University, Taft, Iran
4 - Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
Keywords: particle swarm optimization, stability, Nazelian diversion dam,
Abstract :
Introduction: The hydraulic design of diversion dams is traditionally very complicated and time-consuming and it is necessary for the designer to change the used assumptions several times in order to achieve a stable design with a suitable concreting volume. In today's advanced and competitive world, due to the lack of raw materials and the need for better efficiency, design engineers are forced to design more economically and optimally. Therefore, it is necessary to reduce the cost of concrete in the design of these dams and at the same time ensure the stability of the dam. In this research, the application of a meta-heuristic algorithm has been investigated in order to minimize the weight function of the diversion dam and, as a result, the cost of concreting the dam at the same time as providing the functions related to the dam's stability.
Methods: The algorithm used in this research is the particle swarm optimization (PSO) algorithm. According to the nature of this algorithm and the research problem, it is necessary to make changes in the execution steps of the algorithm. Therefore, by making changes in the PSO algorithm, this algorithm was developed to solve the dam weight optimization problem by considering the limitations of this problem. These changes include controlling the speed of searcher particles and normalizing the position of particles in the feasible space of the problem. The diversion dam studied in this research is the Nazelian dam located in Kermanshah province. The decision variables in the optimization problem include the height of the upstream and downstream dam cutoff walls, the length and thickness of the concrete apron at upstream and the thickness of the detention pond. In order to optimize these dimensions, by performing sensitivity analysis, the parameters with the greatest impact on the performance of the algorithm were identified.
Results and Discussion: In this research, based on the results of the sensitivity measurement of the number of particles or the population size of the PSO algorithm, the number of 20 particles was chosen for the size of the population of particles. According to the convergence graph of the PSO algorithm in different executions, to ensure finding the optimal global response and avoid additional calculations and evaluations, the number of iterations of the algorithm was equal to 1000. According to the best implementation of the PSO algorithm, the weight of the studied dam in the optimal response of this algorithm was equal to 52.80 tons per unit of dam width. The best answer to the problem of optimal design of the dam has dimensions of 7.6 meters for the length of the upstream apron, 0.6 meters for the thickness of the upstream apron, 0.6 meters for the thickness of the detention pond, 1 meter for the height of the upstream cutoff and 1.1 meters for the height of the downstream cutoff.
Conclusion: In general, the result of the present research indicates the optimal performance and speed of the PSO algorithm in finding the optimal solution to the problem of designing a diversion dam with the least weight of the dam along with the observance of stability indicators. Using this algorithm in order to find the optimal parameters for the design of diversion dams can provide useful information to the executives to provide the best and most optimal design with minimum cost and very little time while observing the safety factors of the stability of diversion dams. The program developed in this research provides the necessary and sufficient conditions for the optimal design of the cross-section of diversion dams and is reliable in terms of general and practical validity, but it has limitations. Among the limitations of this method is that the cross-section obtained based on the code developed in this study must be adjusted later for different stress criteria (using the finite element method) and be tested for specific conditions that are different in each project (earthquake, flood, sedimentation, etc.).
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