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The Modeling and Optimization of a Multi-dam System

Received: 1 August 2024     Accepted: 24 August 2024     Published: 5 September 2024
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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.

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

Keywords

Optimization, Mathematical Programming, Modeling

References
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[4] Global Times. The Kariba Dam faces collapsing [R], 22-03-2014.
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[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.
[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.
[15] Xie, P., Yuan, Y. A new two-dimensional model-based subspace method for large-scale unconstrained derivative-free optimization: 2D-MoSub, 2023.
[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.
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[19] Xie, P. A derivative-free trust-region method for optimization on the ellipsoid, 2023. Journal of Physics: Conference Series, 2620: 012007.
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[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.
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  • 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

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    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

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    AMA 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

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  • @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}
    }
    

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    Y1  - 2024/09/05
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    N1  - https://doi.org/10.11648/j.acm.20241305.13
    DO  - 10.11648/j.acm.20241305.13
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    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  - 

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