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Optical elements machining error decomposition method based on the ICEEMDAN-CMPE.

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Title:	Optical elements machining error decomposition method based on the ICEEMDAN-CMPE.
Authors:	Cheng, Bohan¹ (AUTHOR), Guo, Yanjun¹ (AUTHOR), Yang, Xiaojing¹ (AUTHOR) xjyang@vip.sina.com, Luo, Shengyang² (AUTHOR), Deng, Guifang³ (AUTHOR), Yao, Tong¹ (AUTHOR), Lou, Fang¹ (AUTHOR), Miao, Wenhua¹ (AUTHOR)
Source:	Journal of Mechanical Science & Technology. Apr2026, Vol. 40 Issue 4, p2865-2881. 17p.
Subjects:	Optical elements, Entropy (Information theory), Error analysis in mathematics, Surface topography measurement, Statistical bias, Statistical errors
Abstract:	In this investigation, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) based on composite multi-scale permutation entropy (CMPE) for the optical elements machining error decomposition method is proposed. The proposed method employed the ICEEMDAN to decompose the surface measurement data containing multiple machining error components. This process can obtain different mode components and residual components. Subsequently, combined with the CMPE method, through analyzing CMPE values under different scale factors, components containing the systematic errors are filtered and reconstructed, and the machining error is decomposed into systematic and random errors. Finally, the simulated and experimental measurement data were employed to verified the performance of this method. The results show that the accuracy of ICEEMDANCMPE is more accurate than the other methods. The optimal values of mean, RMS, and variance values are 2.78 × 10−10 mm, 6.49 × 10−7 mm, and 4.21 × 10−13 mm, respectively. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	In this investigation, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) based on composite multi-scale permutation entropy (CMPE) for the optical elements machining error decomposition method is proposed. The proposed method employed the ICEEMDAN to decompose the surface measurement data containing multiple machining error components. This process can obtain different mode components and residual components. Subsequently, combined with the CMPE method, through analyzing CMPE values under different scale factors, components containing the systematic errors are filtered and reconstructed, and the machining error is decomposed into systematic and random errors. Finally, the simulated and experimental measurement data were employed to verified the performance of this method. The results show that the accuracy of ICEEMDANCMPE is more accurate than the other methods. The optimal values of mean, RMS, and variance values are 2.78 × 10−10 mm, 6.49 × 10−7 mm, and 4.21 × 10−13 mm, respectively. [ABSTRACT FROM AUTHOR]
ISSN:	1738494X
DOI:	10.1007/s12206-026-0239-4