Dynamic evolution sequence set-assisted machine tool interval analysis

Xindi Wei; Jin Deng; Shizhong Liang; Yu Ye; Xindi Wei; Jin Deng; Shizhong Liang; Yu Ye

doi:10.3934/math.2025840

AIMS Mathematics

2025, Volume 10, Issue 8: 18801-18823. doi: 10.3934/math.2025840

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Dynamic evolution sequence set-assisted machine tool interval analysis

1.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China
2.
Yunnan Branch of China Academy of Machinery Co., Ltd., Yunnan Provincial Key Laboratory of Mechatronics Application Technology, 309 Hongling Road, Wuhua District, Kunming City, Yunnan, China
^† These authors contributed equally to this work and are co-first authors

Received: 09 April 2025 Revised: 01 July 2025 Accepted: 15 July 2025 Published: 19 August 2025
MSC : 65C05, 74P10, 90C29

This paper investigates the uncertainty of machine tools and proposes an efficient interval uncertainty analysis framework for machine tools. This problem involves interval analysis and the calculation of machine tool response. The traditional analysis method has drawbacks, including low computational efficiency and the need to collect a large amount of sample information. In this paper, the intelligent optimization algorithm is used to analyze the interval of the machine tool, and the interval analysis results can be obtained by using less sample information, which improves the efficiency of the interval analysis. The dynamic evolution sequence (DES) is used to optimize the search sequence of the artificial bee colony (ABC) algorithm to improve the computational efficiency and accuracy of the optimization algorithm. To address the problem of the high computational cost of the finite element model, the Kriging surrogate model is used to replace complex finite element calculations. To achieve better calculation accuracy, this paper utilizes the DES to optimize the Kriging model, resulting in a significant improvement in the calculation accuracy of the improved Kriging model (DES-Kriging). Combining DES-ABC and DES-Kriging, this paper proposes a new interval uncertainty analysis framework and verifies the accuracy and efficiency of this interval analysis framework by numerical experiments.
- uncertainty analysis,
- intelligent optimization algorithm,
- dynamic evolution sequence,
- Kriging surrogate model,
- machine tool stability
Citation: Xindi Wei, Jin Deng, Shizhong Liang, Yu Ye. Dynamic evolution sequence set-assisted machine tool interval analysis[J]. AIMS Mathematics, 2025, 10(8): 18801-18823. doi: 10.3934/math.2025840

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Abstract

This paper investigates the uncertainty of machine tools and proposes an efficient interval uncertainty analysis framework for machine tools. This problem involves interval analysis and the calculation of machine tool response. The traditional analysis method has drawbacks, including low computational efficiency and the need to collect a large amount of sample information. In this paper, the intelligent optimization algorithm is used to analyze the interval of the machine tool, and the interval analysis results can be obtained by using less sample information, which improves the efficiency of the interval analysis. The dynamic evolution sequence (DES) is used to optimize the search sequence of the artificial bee colony (ABC) algorithm to improve the computational efficiency and accuracy of the optimization algorithm. To address the problem of the high computational cost of the finite element model, the Kriging surrogate model is used to replace complex finite element calculations. To achieve better calculation accuracy, this paper utilizes the DES to optimize the Kriging model, resulting in a significant improvement in the calculation accuracy of the improved Kriging model (DES-Kriging). Combining DES-ABC and DES-Kriging, this paper proposes a new interval uncertainty analysis framework and verifies the accuracy and efficiency of this interval analysis framework by numerical experiments.

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