In this paper, we present a maintenance plan for the Kariba Dam in Africa. The Kariba Dam, a double curvature concrete arch dam in Zambia's capital, is crucial for regional energy and water management. Ensuring its safety and functionality is essential. This study provides a comprehensive analysis and maintenance plan to safeguard the dam's long-term viability. Our mathematical analysis begins with a threshold evaluation of three proposed options, considering costs such as relocation, dam removal, construction of new dams, repairs, and ecological damage, as well as benefits like energy generation, flood prevention, employment, tourism, and ecological protection. The data-driven analysis indicates that our option is the most economically viable. We assess water management capabilities, using them as a safety coefficient for the dams. We selected 30 seed points along the riverbank to establish dams. Our recommendation is to increase the number of dams and ensure their strategic distribution. An assessment model based on the analytic hierarchy process was then developed, focusing on three factors: safety, economy, and population. We determined the weights of each factor. The optimal scheme was identified through this model, and the sensitivity of the results was also evaluated. The greatest impact under extreme conditions was found. This paper provides the details of the theoretical analysis and the numerical experiments, which include the use of modeling, optimization, mathematical programming, and so on.
| Published in | Applied and Computational Mathematics (Volume 13, Issue 5) |
| DOI | 10.11648/j.acm.20241305.13 |
| Page(s) | 140-152 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Optimization, Mathematical Programming, Modeling
| [1] | Zou, S. Study on the dam collapse and numerical model of dam break flood [D], Guangxi University, Nanning, 2009. |
| [2] | Chow, V. T. Open-Channel Hydraulics. New York: McGraw-Hill, 1959. https://doi.org/10.1016/B978-0-7506-6857-6.X5000-0 |
| [3] | China News. The Kariba dam is facing collapsed crisis. Africa urgently carries out maintenance engineering [R], 26-3-2014. |
| [4] | Global Times. The Kariba Dam faces collapsing [R], 22-03-2014. |
| [5] | International Dam Commission. Classification criteria for size dams [S], 2014. |
| [6] | Nugent. To The Victoria Falls Formation of the Victoria Falls The Formation of the Zambezi [R], 1990. |
| [7] | Taji, K., Matsumoto, K. Inverse sensitive analysis of pairwise comparison matrices [R], Journal of Operations Research Society of Japan, 2006, Vol. 49, No. 4, 332-341, 25-6-2006. https://doi.org/10.15807/jorsj.49.332 |
| [8] | Moore, A. E., Cotterill, F. P. D. (Woody), Main, M. P. L., Williams, H. B. The Zambezi River [D]. |
| [9] | Fread, D. L. Transient hydraulic simulation: Breaches earth dams [D], University of Missouri-Rolla, 1971. |
| [10] | Mossa, R., Bocquillon, C. Approximation zones of the Saint-Venant equations for the flood routing with overbank flow [J], Hydrology and Earth System Sciences, 2000, 4(2): 251-261. https://doi.org/10.5194/hess-4-251-2000 |
| [11] | Shen, D. Research and application of dam collapse test [J], Jianghuai Water Resources Science and Technology, 2009 (5). |
| [12] | Huang, J., He, X. Unified two-dimensional mathematical model for dam break flood [J], Journal of Hydraulic Engineering, 2006, 37(2): 222-226. |
| [13] | Zhao, K. Mathematical model of one-dimensional unsteady flow in natural river [J], Journal of Water Resources and Water Engineering, 2004, 15(1): 38-41. |
| [14] | Zhang, Q., Xie, P. On the Relationship between Λ-poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor, 2024. arXiv: 2407.17529. https://doi.org/10.48550/arXiv.2407.17529 |
| [15] | Xie, P., Yuan, Y. A new two-dimensional model-based subspace method for large-scale unconstrained derivative-free optimization: 2D-MoSub, 2023. https://doi.org/10.48550/arXiv.2309.14855 |
| [16] | Xie, P., Yuan, Y. Derivative-free optimization with transformed objective functions (DFOTO) and the algorithm based on the least Frobenius norm updating quadratic model, 2023. Journal of the Operations Research Society of China. https://doi.org/10.1007/s40305-023-00532-x |
| [17] | Xie, P., Yuan, Y. Least H2 norm updating quadratic interpolation model function for derivative-free trust-region algorithms, 2023. arXiv: 2302.12017. https://doi.org/10.48550/arXiv.2302.12017 |
| [18] | Xie, P., Yuan, Y. A derivative-free optimization algorithm combining line-search and trust-region techniques, 2023. Chinese Annals of Mathematics, Series B, 44(5): 719-734. https://doi.org/10.1007/s11401-023-0040-y |
| [19] | Xie, P. A derivative-free trust-region method for optimization on the ellipsoid, 2023. Journal of Physics: Conference Series, 2620: 012007. https://doi.org/10.1088/1742-6596/2620/1/012007 |
| [20] | Xie, P. Sufficient conditions for error distance reduction in the l2-norm trust region between minimizers of local nonconvex multivariate quadratic approximates, 2025. Journal of Computational and Applied Mathematics, 453: 116146. https://doi.org/10.1016/j.cam.2024.116146 |
| [21] | Li, S., Xie, P., Zhou, Z., et al. Simulation of interaction of folded waveguide space traveling wave tubes with derivative-free mixed-integer based NEWUOA algorithm, 2021. 7th International Conference on Computer and Communications (ICCC), pp. 1215--1219. https://ieeexplore.ieee.org/document/9674410. https://doi.org/10.1109/ICCC54389.2021.9674410 |
| [22] | Xie, P., Tao, M. Parametric resonant control of macroscopic behaviors of multiple oscillators, 2019. American Control Conference (ACC), pp. 1898--1905. https://doi.org/10.23919/ACC.2019.8814709 |
APA Style
Xie, P. (2024). The Modeling and Optimization of a Multi-dam System. Applied and Computational Mathematics, 13(5), 140-152. https://doi.org/10.11648/j.acm.20241305.13
ACS Style
Xie, P. The Modeling and Optimization of a Multi-dam System. Appl. Comput. Math. 2024, 13(5), 140-152. doi: 10.11648/j.acm.20241305.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20241305.13,
author = {Pengcheng Xie},
title = {The Modeling and Optimization of a Multi-dam System},
journal = {Applied and Computational Mathematics},
volume = {13},
number = {5},
pages = {140-152},
doi = {10.11648/j.acm.20241305.13},
url = {https://doi.org/10.11648/j.acm.20241305.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241305.13},
abstract = {In this paper, we present a maintenance plan for the Kariba Dam in Africa. The Kariba Dam, a double curvature concrete arch dam in Zambia's capital, is crucial for regional energy and water management. Ensuring its safety and functionality is essential. This study provides a comprehensive analysis and maintenance plan to safeguard the dam's long-term viability. Our mathematical analysis begins with a threshold evaluation of three proposed options, considering costs such as relocation, dam removal, construction of new dams, repairs, and ecological damage, as well as benefits like energy generation, flood prevention, employment, tourism, and ecological protection. The data-driven analysis indicates that our option is the most economically viable. We assess water management capabilities, using them as a safety coefficient for the dams. We selected 30 seed points along the riverbank to establish dams. Our recommendation is to increase the number of dams and ensure their strategic distribution. An assessment model based on the analytic hierarchy process was then developed, focusing on three factors: safety, economy, and population. We determined the weights of each factor. The optimal scheme was identified through this model, and the sensitivity of the results was also evaluated. The greatest impact under extreme conditions was found. This paper provides the details of the theoretical analysis and the numerical experiments, which include the use of modeling, optimization, mathematical programming, and so on.},
year = {2024}
}
TY - JOUR T1 - The Modeling and Optimization of a Multi-dam System AU - Pengcheng Xie Y1 - 2024/09/05 PY - 2024 N1 - https://doi.org/10.11648/j.acm.20241305.13 DO - 10.11648/j.acm.20241305.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 140 EP - 152 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20241305.13 AB - In this paper, we present a maintenance plan for the Kariba Dam in Africa. The Kariba Dam, a double curvature concrete arch dam in Zambia's capital, is crucial for regional energy and water management. Ensuring its safety and functionality is essential. This study provides a comprehensive analysis and maintenance plan to safeguard the dam's long-term viability. Our mathematical analysis begins with a threshold evaluation of three proposed options, considering costs such as relocation, dam removal, construction of new dams, repairs, and ecological damage, as well as benefits like energy generation, flood prevention, employment, tourism, and ecological protection. The data-driven analysis indicates that our option is the most economically viable. We assess water management capabilities, using them as a safety coefficient for the dams. We selected 30 seed points along the riverbank to establish dams. Our recommendation is to increase the number of dams and ensure their strategic distribution. An assessment model based on the analytic hierarchy process was then developed, focusing on three factors: safety, economy, and population. We determined the weights of each factor. The optimal scheme was identified through this model, and the sensitivity of the results was also evaluated. The greatest impact under extreme conditions was found. This paper provides the details of the theoretical analysis and the numerical experiments, which include the use of modeling, optimization, mathematical programming, and so on. VL - 13 IS - 5 ER -
Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, United States
Information