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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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    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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