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Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice

Author

Listed:
  • Alena Vagaská

    (Department of Natural Sciences and Humanities, Faculty of Manufacturing Technologies with a Seat in Prešov, The Technical University of Košice, 080 01 Presov, Slovakia)

  • Miroslav Gombár

    (Department of Management, Faculty of Management and Business, University of Prešov, 080 01 Presov, Slovakia)

  • Ľuboslav Straka

    (Department of Automobile and Manufacturing Technologies, Faculty of Manufacturing Technologies with a Seat in Prešov, The Technical University of Košice, 080 01 Presov, Slovakia)

Abstract

Engineering optimization is the subject of interest for many scientific research teams on a global scale; it is a part of today’s mathematical modelling and control of processes and systems. The attention in this article is focused on optimization modelling of technological processes of surface treatment. To date, a multitude of articles are devoted to the applications of mathematical optimization methods to control technological processes, but the situation is different for surface treatment processes, especially for anodizing. We perceive their lack more, so this state has stimulated our interest, and the article contributes to filling the gap in scientific research in this area. The article deals with the application of non-linear programming (NLP) methods to optimise the process of anodic oxidation of aluminium using MATLAB toolboxes. The implementation of optimization methods is illustrated by solving a specific problem from engineering practice. The novelty of this article lies in the selection of effective approaches to the statement of optimal process conditions for anodizing. To solve this complex problem, a solving strategy based on the design of experiments approach (for five factors), exploratory data analysis, confirmatory analysis, and optimization modelling is proposed. The original results have been obtained through the experiment (performed by using the DOE approach), statistical analysis, and optimization procedure. The main contribution of this study is the developed mathematical-statistical computational (MSC) model predicting the thickness of the resulting aluminium anodic oxide layer (AOL). Based on the MSC model, the main goal has been achieved—the statement of optimal values of factors acting during the anodizing process to achieve the thickness of the protective layer required by clients, namely, for 5, 7, 10, and 15 [μm].

Suggested Citation

  • Alena Vagaská & Miroslav Gombár & Ľuboslav Straka, 2022. "Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice," Energies, MDPI, vol. 15(6), pages 1-22, March.
  • Handle: RePEc:gam:jeners:v:15:y:2022:i:6:p:2205-:d:773495
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    References listed on IDEAS

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    1. Thuy Vi Tran & Myungbok Kim & Kyeong-Hwa Kim, 2019. "Frequency Adaptive Current Control Scheme for Grid-connected Inverter without Grid Voltage Sensors Based on Gradient Steepest Descent Method," Energies, MDPI, vol. 12(22), pages 1-27, November.
    2. Oscar Danilo Montoya & Walter Gil-González & Andrés Arias-Londoño & Arul Rajagopalan & Jesus C. Hernández, 2020. "Voltage Stability Analysis in Medium-Voltage Distribution Networks Using a Second-Order Cone Approximation," Energies, MDPI, vol. 13(21), pages 1-15, November.
    3. Rongjie Wang & Yiju Zhan & Haifeng Zhou, 2015. "Application of Artificial Bee Colony in Model Parameter Identification of Solar Cells," Energies, MDPI, vol. 8(8), pages 1-19, July.
    4. Ramadhani, F. & Hussain, M.A. & Mokhlis, H. & Hajimolana, S., 2017. "Optimization strategies for Solid Oxide Fuel Cell (SOFC) application: A literature survey," Renewable and Sustainable Energy Reviews, Elsevier, vol. 76(C), pages 460-484.
    5. Askhat Diveev & Elena Sofronova & Ivan Zelinka, 2020. "Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm," Mathematics, MDPI, vol. 8(12), pages 1-18, November.
    6. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    7. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    8. Francisco G. Montoya & Raúl Baños & Alfredo Alcayde & Francisco Manzano-Agugliaro, 2019. "Optimization Methods Applied to Power Systems," Energies, MDPI, vol. 12(12), pages 1-8, June.
    9. Suiling Wang & Zhiqiang Jiang & Yi Liu, 2022. "Dimensionality Reduction Method of Dynamic Programming under Hourly Scale and Its Application in Optimal Scheduling of Reservoir Flood Control," Energies, MDPI, vol. 15(3), pages 1-17, January.
    10. Ximing Wang & Hongwen He & Fengchun Sun & Jieli Zhang, 2015. "Application Study on the Dynamic Programming Algorithm for Energy Management of Plug-in Hybrid Electric Vehicles," Energies, MDPI, vol. 8(4), pages 1-20, April.
    11. Pablo T. Rodriguez-Gonzalez & Vicente Rico-Ramirez & Ramiro Rico-Martinez & Urmila M. Diwekar, 2019. "A New Approach to Solving Stochastic Optimal Control Problems," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
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    Cited by:

    1. Alena Vagaská, 2023. "Mathematical–Statistical Nonlinear Model of Zincing Process and Strategy for Determining the Optimal Process Conditions," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    2. Alena Vagaská & Miroslav Gombár & Antonín Korauš, 2022. "Mathematical Modeling and Nonlinear Optimization in Determining the Minimum Risk of Legalization of Income from Criminal Activities in the Context of EU Member Countries," Mathematics, MDPI, vol. 10(24), pages 1-25, December.

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