Structural optimization for dynamic stability of a plane-grating monochromator

doi:10.1007/s10483-026-3416-6

Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (8): 1789-1810.doi: https://doi.org/10.1007/s10483-026-3416-6

收稿日期:2026-02-28 修回日期:2026-05-19 出版日期:2026-07-31 发布日期:2026-07-31

Structural optimization for dynamic stability of a plane-grating monochromator

Guanghui HAN¹, Xinyu LIAN²^,³, Jixia YI¹, Huaxia DENG²^,⁴(), Mengchao MA¹, Xiang ZHONG¹, Xinglong GONG²^,⁵

^1.School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Hefei 230009, China
^2.CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
^3.Anhui Weiwei Rubber Parts Group Co., Ltd., Tongcheng 231460, Anhui Province, China
^4.The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
^5.State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China

Received:2026-02-28 Revised:2026-05-19 Online:2026-07-31 Published:2026-07-31
Contact: Huaxia DENG E-mail:hxdeng@ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 12372187, 12402228, 12427802, 52321003, and 12132016), the Fundamental Research Funds for the Central Universities of China (Nos. WK2480000010 and WK2090250095), the China Postdoctoral Science Foundation (No. 2024M753103), the Chinese Academy of Sciences (CAS) Talent Introduction Program (No. KJ2090007006), the Anhui Provincial Natural Science Foundation of China (No. 2408085QA014), and the National Synchrotron Radiation Laboratory Joint Foundation of China (Nos. KY2090000901, KY2090000097, and KY2090000124)

摘要/Abstract

Abstract:

A structural optimization framework integrating the receptance method (RM) is developed to enhance the dynamic stability of a plane-grating monochromator (PGM). Three vertical geometric dimensions are selected as physically interpretable design variables. The plane-mirror angular vibration under ambient ground excitation is minimized directly in the geometric design space, so resonance and antiresonance features are modified implicitly, without prescribing modal targets. The meta-model of optimal prognosis (MOP) surrogates, selected using the coefficient of prognosis (CoP), enables global sensitivity analysis (SA) and surrogate-assisted multi-objective evolutionary optimization with a limited number of finite element (FE) evaluations. The SA identifies D₂ as the dominant driver of the mirror angular response, with D₃ providing secondary tuning and D₁ remaining nearly neutral within the investigated range. In the FE simulations, the optimized geometry reduces the peak angular vibration by 19.8% and the root mean square (RMS) angular vibration by 37.5%. Under identical ground microvibration excitations, laser Doppler vibrometer (LDV) measurements show a 22.8% reduction in the RMS. Receptance comparisons further confirm suppressed resonance peaks and a lower high-frequency response envelope after optimization. These results provide a practical and physically transparent method for improving the dynamic stability of complex optical systems.

Key words: receptance method (RM), microvibration, plane-grating monochromator (PGM), multi-objective evolutionary optimization, global sensitivity analysis (SA)

中图分类号:

TH113.1

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1789-1810.

Guanghui HAN, Xinyu LIAN, Jixia YI, Huaxia DENG, Mengchao MA, Xiang ZHONG, Xinglong GONG. Structural optimization for dynamic stability of a plane-grating monochromator[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1789-1810.

图/表 9

Peak displacement response	$C CoP (D 1)$	$C CoP (D 2)$	$C CoP (D 3)$	Total $C CoP$
$w 1, pk$	0.1%	91.3%	21.0%	99.8%
$w 2, pk$	0.1%	91.8%	16.1%	99.9%

Parameter	IS/mm	VS/mm	Relative change/%
D₁	510	665	$+ 30.39$
D₂	192	172	$− 10.42$
D₃	340	300	$− 11.76$

Metrics	Simulation			Experiment
Metrics	Sim-IS	Sim-VS	$R ed$ /%	Test-IS	Test-VS	$R ed$ /%
$w 1,pk$ /nm	368.34	363.96	1.2	416.36	173.33	58.4
$w 2,pk$ /nm	399.91	374.54	6.3	466.63	204.79	56.1
Angle peak/nrad	605.41	485.77	19.8	1 083.79	849.25	21.6
$w 1$ RMS/nm	134.68	134.35	0.2	148.94	71.79	51.8
$w 2$ RMS/nm	139.90	138.29	1.2	158.23	81.82	48.3
Angle RMS/nrad	226.29	141.49	37.5	429.23	331.46	22.8
Here, $R ed$ denotes the percentage reduction of the VS results relative to the IS

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Structural optimization for dynamic stability of a plane-grating monochromator

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Parameter	Initial value/mm	Lower bound/mm	Upper bound/mm
D₁	510	500	670
D₂	192	170	214
D₃	340	300	360