基于多重保真度的复杂空间缩减与优化方法

doi:10.7527/S1000-6893.2024.30583

Abstract

Abstract:

Aerospace structural optimization often faces the problems of complex design space and high nonlinearity characteristic. However， the optimization based on high-fidelity model is time-consuming， making it difficult to complete the optimization design in the tight research and development cycle. A complex space reduction and optimization method based on multiple fidelity model is proposed. Firstly， the high-fidelity， medium-fidelity analysis models are constructed. Then， the variable-fidelity surrogate model is constructed based on the low-fidelity and medium-fidelity data by sampling in the original design space， and the clustering is carried out based on Fuzzy-C means to obtain the initial reduction space. Then， the high-fidelity sample points are sampled in the initial reduction space， and the variable fidelity surrogate model is constructed based on the medium-fidelity and high-fidelity data. Finally， the optimization was carried out and the reduced space was moved according to the position of the sample points with the best response value， and the optimal solution was obtained through optimization iteration. To verify the effectiveness of the proposed method， the test function example and an engineering example of the hierarchical stiffened shells are carried out. The example results show that the relative errors of the optimal solution and the global optimal solution obtained by the proposed method is reduced by 68.4% and 44.4%， compared with the traditional high-fidelity and variable-fidelity surrogate optimization methods. For the engineering examples， the collapse load optimized by the proposed method is improved by 9.0% and 14.7%， compared with the high-fidelity and variable-fidelity surrogate optimization methods. At the same time， compared with the variable-fidelity static reduction space method proposed in previous work， the calculation time is reduced by 41.5% when reaching the same collapse load. In summary， the proposed optimization method can make full use of multiple fidelity data， and has the advantages of high optimization efficiency and strong global optimization ability for complex and time-consuming aerospace structural engineering optimization problems.

Key words: structural optimization, space reduction, multiple fidelity model, hierarchical stiffened shells, fuzzy clustering

CLC Number:

V214.4

Shu ZHANG, Kuo TIAN, Cong GUO. Complex space reduction and optimization method based on multiple fidelity model[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1): 730583.

Figures/Tables 11

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优化方法	x	y	相对误差/%	耗时（LFM样本点数目）
10高+5加点	1.110 5	-0.145 7	83.23	150
8高+20低+5加点	1.351 8	-0.353 9	59.27	150
5高+9中+20低+5加点动态缩减空间	0.531 6	-0.740 1	14.83	150
5高+9中+20低+20加点动态缩减空间	0.548 0	-0.868 9	00.02	300

参数	高保真度模型	中保真度模型	低保真度模型
样本点数量	25	200	2 000
R²	0.93	0.90	0.62
耗时/h	41.7	16.7	3.3

优化方法	h_j/mm	h_n/mm	N_aj	N_an	N_cj	N_cn	t_rj/mm	t_rn/mm	t_s/mm	P_cr/kN	质量/kg	耗时/h
设计变量下限	15.0	6.0	20	1	3	1	3.0	3.0	2.5
设计变量上限	30.0	15.0	50	4	9	4	12.0	12.0	5.5
20高+5加点	30.0	14.8	33	1	8	1	6.6	10.8	4.2	22 820	355.0	41.7
20高+500低+5加点	30.0	15.0	45	1	4	3	6.7	9.9	3.9	21 681	354.8	42.5
10高+150中+1 000低+5加点静态缩减空间	27.0	14.6	48	1	7	1	9.1	9.1	3.6	22 182	355.0	39.2
10高+150中+1 000低+5加点动态缩减空间	30.0	14.4	49	1	5	1	11.4	6.7	3.4	24 870	355.0	39.2
25高+200中+5加点静态缩减空间^［23］	29.9	10.6	47	2	8	1	9.6	3.2	3.8	25 032	355.0	67.0

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Complex space reduction and optimization method based on multiple fidelity model

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