Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness
Application of computational methods in engineering and science constantly increases, which is also visible in sector of material science, often with promising results. In following paper, authors would like to propose fractal dimension, a mathematical method of quantifying self-similarity and compl...
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| Format: | Article |
| Language: | English |
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Lublin University of Technology
2022-11-01
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| Series: | Advances in Sciences and Technology |
| Subjects: | |
| Online Access: | http://www.astrj.com/Fractal-Dimension-as-Robust-Estimate-of-Low-Carbon-Steels-Hardness,155799,0,2.html |
| _version_ | 1811326030470709248 |
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| author | Krzysztof Zając Karolina Płatek Paweł Wachel Leszek Łatka |
| author_facet | Krzysztof Zając Karolina Płatek Paweł Wachel Leszek Łatka |
| author_sort | Krzysztof Zając |
| collection | DOAJ |
| description | Application of computational methods in engineering and science constantly increases, which is also visible in sector of material science, often with promising results. In following paper, authors would like to propose fractal dimension, a mathematical method of quantifying self-similarity and complexity of spatial patterns, as robust method of hardness estimation of low carbon steels. A dataset of microstructure images and corresponding Vickers hardness measurements of S235JR steel under different delivery conditions was created. Then, three different computational methods for evaluation of materials hardness based on microstructure image were tested. In this paper those methods are called: (i) Otsu-based index, (ii) fractal dimension index and (iii) vision transformer index. The results were compared with method used in literature for similar problems. Comparison showed that fractal dimension performs better than other evaluated methods, in terms of median absolute error, which value was equal to 4.12 HV1, which is significantly lower than results achieved by Otsu-based index and vision transformer index, which were 4.49 HV1 and 5.07 HV1 respectively. Those results can be attributed to the relative robustness of fractal dimension index, when compared to other methods. Robust estimation is preferable, due to the high amount of noise in the dataset, which is a consequence of the nature of used material. |
| first_indexed | 2024-04-13T14:42:43Z |
| format | Article |
| id | doaj.art-83dee553a15646e790fc2b443204d419 |
| institution | Directory Open Access Journal |
| issn | 2080-4075 2299-8624 |
| language | English |
| last_indexed | 2024-04-13T14:42:43Z |
| publishDate | 2022-11-01 |
| publisher | Lublin University of Technology |
| record_format | Article |
| series | Advances in Sciences and Technology |
| spelling | doaj.art-83dee553a15646e790fc2b443204d4192022-12-22T02:42:51ZengLublin University of TechnologyAdvances in Sciences and Technology2080-40752299-86242022-11-0116533534410.12913/22998624/155799155799Fractal Dimension as Robust Estimate of Low Carbon Steels HardnessKrzysztof Zając0Karolina Płatek1Paweł Wachel2https://orcid.org/0000-0002-7353-2310Leszek Łatka3https://orcid.org/0000-0002-5236-5349Faculty of Microsystem Electronics and Photonics, Wrocław University of Science and Technology, ul. Janiszewskiego 11, 50-372 Wrocław, PolandFaculty of Mechanical Engineering, Wrocław University of Science and Technology, ul. Łukasiewicza 5, 50-371 Wrocław, PolandFaculty of Information and Communication Technology, Wroclaw University of Science and Technology, ul. Janiszewskiego 11, 50-372 Wrocław, PolandDepartment of Metal Forming, Welding and Metrology, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, ul. Łukasiewicza 5, 50-371 Wroclaw, PolandApplication of computational methods in engineering and science constantly increases, which is also visible in sector of material science, often with promising results. In following paper, authors would like to propose fractal dimension, a mathematical method of quantifying self-similarity and complexity of spatial patterns, as robust method of hardness estimation of low carbon steels. A dataset of microstructure images and corresponding Vickers hardness measurements of S235JR steel under different delivery conditions was created. Then, three different computational methods for evaluation of materials hardness based on microstructure image were tested. In this paper those methods are called: (i) Otsu-based index, (ii) fractal dimension index and (iii) vision transformer index. The results were compared with method used in literature for similar problems. Comparison showed that fractal dimension performs better than other evaluated methods, in terms of median absolute error, which value was equal to 4.12 HV1, which is significantly lower than results achieved by Otsu-based index and vision transformer index, which were 4.49 HV1 and 5.07 HV1 respectively. Those results can be attributed to the relative robustness of fractal dimension index, when compared to other methods. Robust estimation is preferable, due to the high amount of noise in the dataset, which is a consequence of the nature of used material.http://www.astrj.com/Fractal-Dimension-as-Robust-Estimate-of-Low-Carbon-Steels-Hardness,155799,0,2.htmllinear regressionimage processingfractal dimensionrobust hardness estimationlow carbon steels |
| spellingShingle | Krzysztof Zając Karolina Płatek Paweł Wachel Leszek Łatka Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness Advances in Sciences and Technology linear regression image processing fractal dimension robust hardness estimation low carbon steels |
| title | Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness |
| title_full | Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness |
| title_fullStr | Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness |
| title_full_unstemmed | Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness |
| title_short | Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness |
| title_sort | fractal dimension as robust estimate of low carbon steels hardness |
| topic | linear regression image processing fractal dimension robust hardness estimation low carbon steels |
| url | http://www.astrj.com/Fractal-Dimension-as-Robust-Estimate-of-Low-Carbon-Steels-Hardness,155799,0,2.html |
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