数据驱动的曲面构件形状⁃拓扑协同优化方法

doi:10.7527/S1000-6893.2023.28806

Abstract

Abstract:

Due to the extreme lightweight requirements of surface components in compact design space， this paper proposed a data-driven shape-topology optimization method of curved shells， which consists of three stages， namely the offline stage， the online stage and the update stage. First， in the offline stage， the Latin hypercube sampling method is used to extract the sample points from the design space， and the mesh deformation technique is used for modeling to obtain the mesh model corresponding to the sample points. Then， topology optimization was carried out on the mesh models to obtain the optimized strain energy. Based on the sample data obtained in the above steps， the radial basis function surrogate model is trained， where the shape design variable is the input and the strain energy after topology optimization is the output. In the online stage， optimization is carried out based on the surrogate model obtained in the offline stage， and the covariance matrix adaptive evolution strategy is adopted to improve the optimization efficiency. In the update stage， the real response of optimization results of the surrogate model is calculated and added to the sample dataset to update the surrogate model. Finally， the algorithm is verified by a simply supported beam and a spacecraft cabin door. The results show that compared with the topology optimization with the fixed shape， the strain energy obtained by the proposed method can be reduced by 20.08% and 37.93%， respectively， indicating that the proposed method has better design capability.

Key words: shape-topology optimization, mesh deformation, data driven, curved shell, radial basis function

CLC Number:

V214.4

Tianhe GAO, Kuo TIAN, Lei HUANG, Shu ZHANG, Zengcong LI. Data⁃driven shape⁃topology optimization method for curved shells[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(2): 428806-428806.

Figures/Tables 15

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References 48

1	李增聪，田阔，赵海心. 面向多级加筋壳的高效变保真度代理模型［J］. 航空学报， 2020， 41（7）： 623435.
	LI Z C， TIAN K， ZHAO H X. Efficient variable-fidelity models for hierarchical stiffened shells［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（7）： 623435 （in Chinese）.
2	TIAN K， LAI P， SUN Y， et al. Efficient buckling analysis and optimization method for rotationally periodic stiffened shells accelerated by Bloch wave method［J］. Engineering Structures， 2023， 276： 115395.
3	TIAN K， HUANG L， YANG M， et al. Concurrent numerical implementation of vibration correlation technique for fast buckling load prediction of cylindrical shells under combined loading conditions［J］. Engineering with Computers， 2022， 38（4）： 3269-3281.
4	YUAN S. Fundamentals and processes of fluid pressure forming technology for complex thin-walled components［J］. Engineering， 2021， 7（3）： 358-366.
5	李玉海，王成波，陈亮，等. 先进战斗机寿命设计与延寿技术发展综述［J］. 航空学报， 2021， 42（8）： 525791.
	LI Y H， WANG C B， CHEN L， et al. Overview on development of advanced fighter life design and extension technology［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（8）： 525791 （in Chinese）.
6	ZHU J H， ZHANG W H， XIA L. Topology optimization in aircraft and aerospace structures design［J］. Archives of Computational Methods in Engineering， 2016， 23（4）： 595-622.
7	STEGMANN J， LUND E. Nonlinear topology optimization of layered shell structures［J］. Structural and Multidisciplinary Optimization， 2005， 29（5）： 349-360.
8	PARK K S， YOUN S K. Topology optimization of shell structures using adaptive inner-front （AIF） level set method［J］. Structural and Multidisciplinary Optimization， 2008， 36（1）： 43-58.
9	ZHANG W， ZHAO L， GAO T， et al. Topology optimization with closed B-splines and Boolean operations［J］. Computer Methods in Applied Mechanics and Engineering， 2017， 315： 652-670.
10	WANG B， ZHOU Y， TIAN K， et al. Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter［J］. Structural and Multidisciplinary Optimization， 2020， 62（4）： 2091-2100.
11	FENG S， ZHANG W， MENG L， et al. Stiffener layout optimization of shell structures with B-spline parameterization method［J］. Structural and Multidisciplinary Optimization， 2021， 63（6）： 2637-2651.
12	WU Z， WANG S， XIAO R， et al. A local solution approach for level-set based structural topology optimization in isogeometric analysis［J］. Journal of Computational Design and Engineering， 2020， 7（4）： 514-526.
13	张卫红，章胜冬，高彤. 薄壁结构的加筋布局优化设计［J］. 航空学报， 2009， 30（11）： 2126-2131.
	ZHANG W H， ZHANG S D， GAO T. Stiffener layout optimization of thin walled structures［J］. Acta Aeronautica et Astronautica Sinica， 2009， 30（11）： 2126-2131 （in Chinese）.
14	ZHOU Y， ZHU J， ZHAN H， et al. A bio-inspired B-spline offset feature for structural topology optimization［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 386： 114081.
15	DONG X， DING X， LI G， et al. Stiffener layout optimization of plate and shell structures for buckling problem by adaptive growth method［J］. Structural and Multidisciplinary Optimization， 2020， 61： 301-318.
16	HU T， DING X， ZHANG H， et al. Geometry and size optimization of stiffener layout for three-dimensional box structures with maximization of natural frequencies［J］. Chinese Journal of Aeronautics， 2023， 36（1）： 324-341.
17	ANSOLA R， CANALES J， TARRAGO J A， et al. Combined shape and reinforcement layout optimization of shell structures［J］. Structural and Multidisciplinary Optimization， 2004， 27（4）： 219-227.
18	NGUYEN T T， BRENTZEN J A， SIGMUND O， et al. Efficient hybrid topology and shape optimization combining implicit and explicit design representations［J］. Structural and Multidisciplinary Optimization， 2020， 62（3）： 1061-1069.
19	CAI S， ZHANG W. An adaptive bubble method for structural shape and topology optimization［J］. Computer Methods in Applied Mechanics and Engineering， 2020， 360： 112778.
20	ANSOLA R， CANALES J， TARRAGO J A， et al. An integrated approach for shape and topology optimization of shell structures［J］. Computers & Structures， 2002， 80（5-6）： 449-458.
21	SHIMODA M， NAKAYAMA H， SUZAKI S， et al. A unified simultaneous shape and topology optimization method for multi-material laminated shell structures［J］. Structural and Multidisciplinary Optimization， 2021， 64（6）： 3569-3604.
22	范俊，尹泽勇，王建军，等. 轮盘概念设计中拓扑和形状同时优化方法［J］. 北京航空航天大学学报，2015，41（3）：456-465.
	FAN J， YIN Z Y， WANG J J， et al. Simultaneous topology and shape optimization method in conceptual design of disk［J］. Journal of Beijing University of Aeronautics and Astronautics， 2015， 41（3）： 456-465 （in Chinese）.
23	张卫红，杨军刚，朱继宏. 压力载荷下的结构拓扑-形状协同优化［J］. 航空学报，2009， 30（12）： 2335-2341.
	ZHANG W H， YANG J G， ZHU J H. Simultaneous topology and shape optimization of pressure load structures［J］. Acta Aeronautica et Astronautica Sinica， 2009， 30（12）： 2335-2341 （in Chinese）.
24	DU X， HE P， MARTINS J R R A. Rapid airfoil design optimization via neural networks-based parameterization and surrogate modeling［J］. Aerospace Science and Technology， 2021， 113： 106701.
25	CHANDRASEKHAR A， SURESH K. TOuNN： topology optimization using neural networks［J］. Structural and Multidisciplinary Optimization， 2021， 63（3）： 1135-1149.
26	TIAN K， LI H， HUANG L， et al. Data-driven modelling and optimization of stiffeners on undevelopable curved surfaces［J］. Structural and Multidisciplinary Optimization， 2020， 62（6）： 3249-3269.
27	HUANG L， LI H， ZHENG K， et al. Shape optimization method for axisymmetric disks based on mesh deformation and smoothing approaches［J］. Mechanics of Advanced Materials and Structures， 2023，30（12）： 2532-2555.
28	李增聪，陈燕，李红庆，等. 面向集中力扩散的回转曲面加筋拓扑优化方法［J］. 航空学报， 2021， 42（9）： 224616.
	LI Z C， CHEN Y， LI H Q， et al. Topology optimization method for concentrated force diffusion on stiffened curved shell of revolution［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（9）： 224616 （in Chinese）.
29	张智超，高太元，张磊，等. 基于径向基神经网络的气动热预测代理模型［J］. 航空学报， 2021， 42（4）： 524167.
	ZHANG Z C， GAO T Y， ZHANG L， et al. Aeroheating agent model based on radial basis function neural network［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（2）： 524167 （in Chinese）.
30	LI Z， TIAN K， LI H， et al. A competitive variable-fidelity surrogate-assisted CMA-ES algorithm using data mining techniques［J］. Aerospace Science and Technology， 2021， 119： 107084.
31	LI Z， GAO T， TIAN K， et al. Elite-driven surrogate-assisted CMA-ES algorithm by improved lower confidence bound method［J］. Engineering with Computers， 2022： 1-21.
32	MENG D， LI Y， HE C， et al. Multidisciplinary design for structural integrity using a collaborative optimization method based on adaptive surrogate modelling［J］. Materials & Design， 2021， 206： 109789.
33	BRAIBANT V， FLEURY C. Shape optimal design using B-splines［J］. Computer Methods in Applied Mechanics and Engineering， 1984， 44（3）： 247-267.
34	BENDSOE M P， SIGMUND O. Topology optimization： theory， methods， and applications［M］. 2003.
35	ZHOU M， FLEURY R， SHYY Y K， et al. Progress in topology optimization with manufacturing constraints［C］∥ 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. 2002： 5614.
36	MIKI M， HIROYASU T， KANEKO M， et al. A parallel genetic algorithm with distributed environment scheme［C］∥ IEEE International Conference on Systems. 1999： 695-700.
37	HELTON J C， DAVIS F J. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems［J］. Reliability Engineering & System Safety， 2003， 81（1）： 23-69.
38	XU S， LIU H， WANG X， et al. A robust error-pursuing sequential sampling approach for global metamodeling based on Voronoi diagram and cross validation［J］. Journal of Mechanical Design， 2014， 136（7）： 071009.
39	FUHG J N， FAU A， NACKENHORST U. State-of-the-art and comparative review of adaptive sampling methods for kriging［J］. Archives of Computational Methods in Engineering， 2021， 28： 2689-2747.
40	HUSSLAGE B G M， RENNEN G， VAN DAM E R， et al. Space-filling Latin hypercube designs for computer experiments［J］. Optimization and Engineering， 2011， 12（4）： 611-630.
41	文谦，杨家伟，武泽平，等. 快速交叉验证改进的运载火箭近似建模方法［J］. 航空学报， 2022， 43（9）： 225967.
	WEN Q， YANG J W， WU Z P， et al. An approximation modeling method of launch vehicles improved by fast cross-validation［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（9）： 225967 （in Chinese）.
42	BAJER L， PITRA Z， REPICKÝ J， et al. Gaussian process surrogate models for the CMA evolution strategy［J］. Evolutionary Computation， 2019， 27（4）： 665-697.
43	WANG Y J， HUANG J Q， ZHOU W X， et al. Neural network-based model predictive control with fuzzy-SQP optimization for direct thrust control of turbofan engine［J］. Chinese Journal of Aeronautics， 2022， 35（12）： 59-71.
44	韩忠华，许晨舟，乔建领，等. 基于代理模型的高效全局气动优化设计方法研究进展［J］. 航空学报， 2020， 41（5）： 623344.
	HAN Z H， XU C Z， QIAO J L， et al. Recent progress of efficient global aerodynamic shape optimization using surrogate-based approach［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（5）： 623344 （in Chinese）.
45	HAN Z H. SurroOpt： a generic surrogate-based optimization code for aerodynamic and multidisciplinary design［C］∥Proceedings of ICAS 2016. 2016： 2016-0281.
46	FANG K， ZHOU Y C， MA P. An adaptive sequential experiment design method for model validation［J］. Chinese Journal of Aeronautics， 2020， 33（6）： 1661-1672.
47	JIN R， CHEN W， SIMPSON T W. Comparative studies of metamodelling techniques under multiple modelling criteria［J］. Structural and Multidisciplinary Optimization， 2001， 23： 1-13.
48	RAKIĆ T， KASAGIĆ-VUJANOVIĆ I， JOVANOVIĆ M， et al. Comparison of full factorial design， central composite design， and box-behnken design in chromatographic method development for the determination of fluconazole and its impurities［J］. Analytical Letters， 2014， 47（8）： 1334-1347.

设计点	R²	RRMSE	a/mm	b/mm	质量/g	应变能/mJ
设计上限			15	5	1.4	0.020 7
设计下限			-15	-5	1.4	0.056 6
初始设计（仅拓扑优化）			0	0	1.4	0.024 9
形状⁃拓扑协同优化设计Ⅰ （15 代理模型样本+5 优化加点）	0.956 5	0.201 5	-7.838 6	1.610 1	1.4	0.019 9
形状-拓扑协同优化设计Ⅱ （19 代理模型样本+1 精细校核）	0.995 0	0.068 7	-5.891 5	1.610 1	1.4	0.020 7
形状-拓扑协同优化设计Ⅲ （无代理模型，20 CMA-ES迭代点）			11.533 6	1.707 7	1.4	0.024 3
形状-拓扑协同优化设计Ⅳ （15 代理模型FF样本+5 优化加点）	0.984 3	0.120 9	-12.226 9	1.610 1	1.4	0.019 6
形状-拓扑协同优化设计Ⅴ （无代理模型，100 CMA-ES迭代点）			5.634 1	1.796 8	1.4	0.021 7

结构	密度/（g·cm^-3）	弹性模量/GPa	泊松比
门体	1.780	42.2	0.3
门框	2.640	68.0	0.3

设计点	R²	RRMSE	c/mm	n	应变能/mJ
设计上限			100	3.000 0	15 040.0
设计下限			60	1.000 0	14 038.0
初始设计（仅拓扑优化）			80	2.000 0	11 983.0
形状⁃拓扑协同优化设计I （30 代理模型样本+15 优化加点）	0.931 0	0.674 3	100	1.465 4	7 437.4
形状-拓扑协同优化设计II （44 代理模型样本+1 精细校核）	0.937 8	0.774 7	100	1.381 2	7 519.4
形状-拓扑协同优化设计III （无代理模型，45 CMA-ES迭代点）			100	1.314 4	7 818.2

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Data⁃driven shape⁃topology optimization method for curved shells

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