KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes
Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolm...
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2025-07-01
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| author | Zhongyuan Che Chong Peng Jikun Wang Rui Zhang Chi Wang Xinyu Sun |
| author_facet | Zhongyuan Che Chong Peng Jikun Wang Rui Zhang Chi Wang Xinyu Sun |
| author_sort | Zhongyuan Che |
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| description | Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners. |
| format | Article |
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| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-07-01 |
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| series | Applied Sciences |
| spelling | doaj-art-f770eb93b55940be8a139ab973afdb0a2025-08-20T03:32:24ZengMDPI AGApplied Sciences2076-34172025-07-011514803510.3390/app15148035KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning ProcessesZhongyuan Che0Chong Peng1Jikun Wang2Rui Zhang3Chi Wang4Xinyu Sun5School of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaSchool of Mechanical Engineering and Automation, Beihang University, Beijing 102206, ChinaTool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners.https://www.mdpi.com/2076-3417/15/14/8035Kolmogorov–Arnold Networks (KANs)tool wear modelinginterpretable machine learningCNC turning processeswhite-box mathematical modeling |
| spellingShingle | Zhongyuan Che Chong Peng Jikun Wang Rui Zhang Chi Wang Xinyu Sun KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes Applied Sciences Kolmogorov–Arnold Networks (KANs) tool wear modeling interpretable machine learning CNC turning processes white-box mathematical modeling |
| title | KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes |
| title_full | KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes |
| title_fullStr | KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes |
| title_full_unstemmed | KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes |
| title_short | KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes |
| title_sort | kan based tool wear modeling with adaptive complexity and symbolic interpretability in cnc turning processes |
| topic | Kolmogorov–Arnold Networks (KANs) tool wear modeling interpretable machine learning CNC turning processes white-box mathematical modeling |
| url | https://www.mdpi.com/2076-3417/15/14/8035 |
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