Research on multi-fidelity surrogate modeling method for non-hierarchical low-fidelity analysis model problem

Table 1. Prediction accuracy comparison of different MFS modeling methods
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Table 1. Prediction accuracy comparison of different MFS modeling methods
方法 e_MAE e_RMSE
VWS-MFS 1.411 2 0.441 8
VWS-HK 3.654 5 1.495 6
LR-MFS 2.315 2 0.702 1
MLMF-CK 7.418 6 2.552 6
IHK 5.788 3 2.208 8

Table 2. Features of eight numerical examples

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Table 2. Features of eight numerical examples

序号	维度	低精度分析模型数目	非线性程度	样本点配置
1	d=1	2	低	5H/10L₁/10L₂
2	d=2	2	低	10H/20L₁/20L₂
3	d=2	3	低	10H/30L₁/30L₂
4	d=4	2	高	20H/30L₁/30L₂
5	d=4	3	低	40H/80L₁/80L₂/80L₃
6	d=6	3	高	60H/120L₁/120L₂/120L₃
7	d=8	2	低	150H/300L₁/300L₂
8	d=10	3	高	200H/400L₁/400L₂/400L₃

Table 3. Prediction accuracy comparison of different MFS modeling methods

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Table 3. Prediction accuracy comparison of different MFS modeling methods

算例序号	参数	VWS-MFS	VWS-HK	LR-MFS	MLMF-CK
1	e_MAE	0.193	1.027	2.975	1.792
1	e_RMSE	0.049	0.350	0.945	1.278
2	e_MAE	2.224	4.432	4.819	25.066
2	e_RMSE	0.711	1.120	0.969	6.605
3	e_MAE	0.003	0.015	0.091	0.150
3	e_RMSE	0.001	0.003	0.106	0.040
4	e_MAE	0.498	0.558	1.102	6.453
4	e_RMSE	0.078	0.095	0.199	1.211
5	e_MAE	16 169.535	35 696.463	102 872.464	96 953.487
5	e_RMSE	2 704.872	4 534.145	19 979.142	20 271.358
6	e_MAE	1.020	2.622	8.165	11.309
6	e_RMSE	0.197	0.299	2.184	2.047
7	e_MAE	619.427	726.884	840.149	4 987.921
7	e_RMSE	58.820	69.501	91.237	191.103
8	e_MAE	8.501×10⁷	3.300×10⁸	7.128×10⁹	6.028×10¹¹
8	e_RMSE	7.851×10⁶	3.157×10⁷	8.909×10⁷	6.972×10¹⁰

Table 4. Value ranges of design variables
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Table 4. Value ranges of design variables
设计变量物理意义取值范围/m
X₁ 斜臂长度L [0.015 0, 0.020 0]
X₂ 竖梁厚度T_h [0.005 0, 0.010 0]
X₃ 斜梁厚度T_l [0.003 5, 0.010 0]

Table 5. Relevance between HF/LF analysis models
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Table 5. Relevance between HF/LF analysis models
性能分析模型相关度
HF-LF₁ HF-LF₂
最大应变 0.998 3 0.998 7

Table 6. Prediction accuracy comparison of different MFS models
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Table 6. Prediction accuracy comparison of different MFS models
方法 e_MAE e_RMSE
VWS-MFS 0.013 1 0.002 6
VWS-HK 0.016 0 0.005 1
LR-MFS 0.024 5 0.008 3
MLMF-CK 0.041 3* 0.012 2*

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Meng CHENG, Qi ZHOU, Xiao WEI, Jian WANG, Wei CHEN. Research on multi-fidelity surrogate modeling method for non-hierarchical low-fidelity analysis model problem[J]. Chinese Journal of Ship Research, 2024, 19(6): 82

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