大型运载火箭加筋圆柱壳混合整数序列近似优化方法

doi:10.7527/S1000-6893.2024.30189

Abstract

Abstract:

A Sequential Approximate Optimization method based on exploitation/exploration Competing Parallel Sampling strategy （SAOCPS） is proposed to conquer the difficulties of coupling multi-mixed-integer variables， high computational cost， and poor optimization convergence in the lightweight design of stiffened cylindrical shells for large launch vehicles. In this method， the Augmented Radial Basis Function （ARBF） approximate model of axial load-carrying capacity is constructed to improve the efficiency of post-buckling analysis for the stiffened cylindrical shells. A dual-elite population evolution-based exploitation strategy is developed to exploit the information in promising regions， thereby enhancing the local optimization performance of SAOCPS. Meanwhile， the new levels are determined according to the one-dimensional projection characteristics of discrete and continuous variables. The combination of element exchange and probabilistic transition is employed to enhance the performance of the permutation optimization method， achieving a uniform coverage of the exploration sample points to the discrete-continuous design space and enhancing the global optimization performance of SAOCPS. Ultimately， the exploration/exploitation competitive mechanism driven by performance gains is introduced for the balance between exploration and exploitation， thereby guiding the rapid convergence of the high-dimensional and time-consuming mixed-integer optimization problems. In applying the lightweight design of large-diameter stiffened cylindrical shells， the optimization results of SAOCPS are still comparable to those of the literature work， even if the initial sample points are greatly reduced by more than 90%. Furthermore， the weight is reduced by 279.8 kg compared with the classical PoF optimization method. The effectiveness and superiority of the proposed method are validated for the prospect of the engineering applications.

Key words: large-diameter stiffened cylindrical shells, mixed-integer optimization, element exchange and probabilistic transition, competitive parallel sampling mechanism, sequential approximate optimization method

CLC Number:

V214

Zhixiang WANG, Yongjun LEI, Dapeng ZHANG, Huiru CUI. Mixed-integer sequential approximate optimization method for stiffened cylindrical shells in large launch vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(10): 230189.

Figures/Tables 26

Fig.1

Fig.2

Fig.3

Table 1

Ranges of design variables in large-diameter stiffened cylindrical shells

变量	设计范围	变量	设计范围
$a E n d$ /mm	45~80	$h o u t$ /mm	10~30
$b E n d$ /mm	75~120	$t o u t$ /mm	2~15
$c E n d$ /mm	2~10	$n s$	85~105
$d E n d$ /mm	2~10	$t s k i n$ /mm	1.2~1.5
$θ E n d$ /（°）	4~5	$a M i d$ /mm	22~50
$w b o t$ /mm	50~100	$t 1 M i d$ /mm	2~10
$t b o t$ /mm	2~15	$b M i d$ /mm	80~150
$w u p$ /mm	20~50	$t 2 M i d$ /mm	2~10
$t u p$ /mm	2~15	$h 1$ /mm	400~600
$h f b$ /mm	50~150	$h 2$ /mm	800~1 200
$t f b$ /mm	2~15

Table 1

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Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

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Table 2

Comparisons of optimal design variables in large-diameter stiffened cylindrical shells

参数	SAOCPS		PoF	文献［16］
参数	“工”形	“几”形	“工”形	“几”形
$a E n d$ /mm	48.83	55.63	63.59	50.00
$b E n d$ /mm	75.15	77.41	92.09	75.00
$c E n d$ /mm	2.082	2.165	2.720	2.010
$d E n d$ /mm	5.122	2.319	5.870	3.020
$θ E n d$ /（°）	4.850	4.035	4.010	4.390
$w b o t$ /mm	94.95	100.00	98.63	97.80
$t b o t$ /mm	14.73	13.90	14.91	11.10
$w u p$ /mm	49.90	32.77	36.21	32.60
$t u p$ /mm	2.29	3.63	4.06	3.26
$h f b$ /mm	92.02	148.11	94.58	127.51
$t f b$ /mm	2.72	2.01	6.13	4.25
$h o u t$ /mm		21.11		21.45
$t o u t$ /mm		2.03		4.32
$n s$	100	85	85	95
$t s k i n$ /mm	1.41	1.20	1.41	27.34
$a M i d$ /mm	38.24	24.47	33.02	2.00
$t 1 M i d$ /mm	2.01	2.01	2.00	80.00
$b M i d$ /mm	100.10	93.27	129.61	2.58
$t 2 M i d$ /mm	4.24	2.20	6.04	404.7
$h 1$ /mm	403.55	595.67	486.50	965.60
$h 2$ /mm	1 187.10	1 197.90	1 199.60	1.26
$M$ /kg	3 410	3 357.10	3 689.70	3 321.65
$F c r$ /（10⁷ N）	7.02	7.01	7.02	7.04

Table 2

Table 3

Fig.20

Fig.21

Fig.22

Fig.23

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Mixed-integer sequential approximate optimization method for stiffened cylindrical shells in large launch vehicles

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项目	SAOCPS		PoF	文献［16］
项目	“工”形	“几”形	“工”形	“几”形
初始样本数量	200	200	200	2 400
迭代次数	200	200	143	150
每次迭代采样数量	11	11	11	11
总样本数量	2 400	2 400	1 773	4 050