基于ISMA-Stacking集成建模和贝叶斯融合的全机结构试验可靠性评估

doi:10.7527/S1000-6893.2025.32365

Abstract

Abstract:

To address the issue of inaccurate reliability assessment in Full-Scale Structural Tests （FSST） under high-load conditions due to a limited sample size， a reliability assessment method integrating a surrogate model with Bayesian theory is proposed. First， based on the historical test data， the Stacking ensemble surrogate model is used to construct a prior model of the applied load distribution， and the applied load uncertainty is quantified through Bayesian theory. Then， combined with the field test data， the Stacking ensemble surrogate model is used to construct the constraint points load error prediction model， and the uncertainty of the constraint points load error is quantified through Monte Carlo simulation. Finally， the Copula function is used to achieve the reliability assessment of FSST with multiple constraint points load error failures. To enhance the predictive accuracy of the model， an Improved Slime Mould Algorithm （ISMA）， which incorporates a good point set and adaptive Cauchy-Gaussian variation strategy， is introduced to optimize the parameters of the Stacking integrated surrogate model synchronously， and an Improved Slime Mould Algorithm optimized Stacking ensemble modeling method （ISMA-Stacking） is proposed. The proposed method is applied to a certain type of FSST reliability assessment case， and the results show that compared with other methods， the Mean Absolute Error （MAE） of the applied load standard deviation prediction model and constraint points load error prediction models under 90% and 100% loading levels are reduced by 42.90%， 50.87% and 54.29%， respectively， and the accuracy of the reliability assessment under the 90% and 100% loading levels are as high as 99.87% and 99.77%， respectively. Therefore， the proposed method can provide theoretical and technical support for the reliability assessment of FSST.

Key words: full-scale structural test, reliability evaluation, uncertainty quantification, ensemble surrogate model, Bayesian, data fusion

CLC Number:

Yunwen FENG, Yuhang CUI, Qian HE, Xiaofeng XUE, Jun LU. Reliability evaluation of full-scale structural test based on ISMA-Stacking ensemble modeling and Bayesian fusion[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(21): 532365.

Figures/Tables 46

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Table 1

Table 2

Table 3

Table 4

Table 5

Load spectrum

加载级数/%	$F 1$ /N	$F 2$ /N	$F 3$ /N	$F 4$ /N	$F 5$ /N	$F 6$ /N	$F 7$ /N	$F 8$ /N	$F 9$ /N	$F 10$ /N	$F 11$ /N	$F 12$ /N
10	1 000	1 000	1 500	2 000	1 000	1 500	2 000	5 167	3 333	1 500	34 000	34 000
20	2 000	2 000	3 000	4 000	2 000	3 000	4 000	10 333	6 667	3 000	34 000	34 000
30	3 000	3 000	4 500	6 000	3 000	4 500	6 000	15 500	10 000	4 500	34 000	34 000
40	4 000	4 000	6 000	8 000	4 000	6 000	8 000	20 667	13 333	6 000	34 000	34 000
50	5 000	5 000	7 500	10 000	5 000	7 500	10 000	25 833	16 667	7 500	34 000	34 000
60	6 000	6 000	9 000	12 000	6 000	9 000	12 000	31 000	20 000	9 000	34 000	34 000
70	7 000	7 000	10 500	14 000	7 000	10 500	14 000	36 167	23 333	10 500	34 000	34 000
80	8 000	8 000	12 000	16 000	8 000	12 000	16 000	41 333	26 667	12 000	34 000	34 000
90	9 000	9 000	13 500	18 000	9 000	13 500	18 000	46 500	30 000	13 500	34 000	34 000
100	10 000	10 000	15 000	20 000	10 000	15 000	20 000	51 667	33 333	15 000	34 000	34 000

Table 5

Fig.7

Table 6

Sample data for modeling the uncertainty of applied load

样本编号	L/%	F/N	V/mm	$μ$ /N	$σ$ /N
1	20	4 335	24.2	4 289.09	6.56
2	20	1 889	24.0	1 848.97	8.20
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
655	150	7 272	9.5	7 271.53	11.91
656	150	4 000	7.6	3 998.72	12.68

Table 6

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Table 7

Table 8

Table 9

Table 10

Fig.13

Fig.14

Fig.15

Fig.16

Table 11

Table 12

Fig.17

Fig.18

Table 13

Table 14

Fig.19

Fig.20

Table 15

Performance of applied load standard deviation model using different modeling methods

模型	SVR	BPNN	XGB	Stacking
MAE	1.440 4	1.009 6	0.883 8	0.866 2
MSE	3.652 5	1.706 0	1.189 9	1.159 7
$R 2$	0.825 2	0.918 1	0.943 1	0.944 6
模型	ISMA-SVR	ISMA-BPNN	ISMA-XGB	ISMA-Stacking
MAE	1.309 4	0.967 6	0.867 5	0.822 5
MSE	3.029 2	1.645 5	1.169 5	1.126 4
$R 2$	0.855 0	0.921 1	0.942 1	0.955 1

Table 15

Fig.21

Fig.22

Fig.23

Table 16

Prediction performance of constraint points load errors under 90% loading level using different modeling methods

模型	SVR	BPNN	XGB	Stacking
MMAE	1.784 5	1.246 5	0.998 6	0.926 4
MMSE	4.398 2	2.126 8	1.386 9	1.468 8
$M R 2$	0.966 4	0.984 1	0.987 5	0.989 2
模型	ISMA-SVR	ISMA-BPNN	ISMA-XGB	ISMA-Stacking
MMAE	1.668 9	1.115 2	0.952 1	0.876 8
MMSE	4.175 2	2.051 6	1.498 4	1.324 2
$M R 2$	0.974 5	0.987 2	0.988 3	0.991 0

Table 16

Table 17

Prediction performance of constraint points load errors under 100% loading level using different modeling methods

模型	SVR	BPNN	XGB	Stacking
MMAE	1.648 2	1.158 8	0.988 6	0.915 6
MMSE	4.264 8	1.985 6	1.386 9	1.347 9
$M R 2$	0.970 2	0.985 6	0.989 1	0.990 8
模型	ISMA-SVR	ISMA-BPNN	ISMA-XGB	ISMA-Stacking
MMAE	1.564 3	1.058 4	0.938 4	0.866 2
MMSE	3.985 6	1.864 5	1.355 7	1.275 6
$M R 2$	0.978 4	0.988 9	0.990 5	0.994 2

Table 17

Fig.24

Fig.25

Table 18

Table 19

Fig. 26

Fig.27

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约束点	i	j	k	x/mm	y/mm	z/mm
X1	-1	0	0	-3 000	0	5 070
X2	-1	0	0	-1 500	3 795	17 710
X3	-1	0	0	-1 500	-3 795	17 710
X4	0	0	1	-2 000	0	5 070
X5	0	-1	0	-2 000	0	5 070
X6	0	1	0	-1 500	3 795	17 710

加载点	x/mm	y/mm	z/mm
L1	2 000	0	3 000
L2	2 000	17 900	17 000
L3	2 000	9 950	17 000
L4	2 000	2 000	17 000
L5	2 000	-17 900	17 000
L6	2 000	-9 950	17 000
L7	2 000	-2 000	17 000
L8	-2 000	0	8 000
L9	-2 000	0	20 000
L10	-2 000	0	32 000
L11	2 000	0	2 000
L12	2 000	0	35 000

着力点	x/mm	y/mm	z/mm
H1	10 000	3 915	9 910
H2	10 000	17 900	17 000
H3	10 000	9 950	17 000
H4	10 000	-17 900	17 000
H5	10 000	-9 950	17 000
H6	10 000	2 000	17 000
H7	10 000	-2 000	17 000
H8	-4 000	0	8 000
H9	-4 000	0	20 000
H10	-4 000	0	32 000
H11	10 000	0	2 000
H12	10 000	0	35 000

加载点	F/N	V/mm	加载点	F/N	V/mm
L1	9 000	0	L7	13 500	1.03
L2	9 000	28.61	L8	46 500	0
L3	13 500	11.57	L9	30 000	0
L4	13 500	1.03	L10	13 500	0
L5	9 000	28.61	L11	34 000	0
L6	13 500	11.57	L12	34 000	0

加载点	F/N	V/mm	加载点	F/N	V/mm
L1	10 000	0	L7	15 000	1.03
L2	10 000	28.61	L8	51 667	0
L3	15 000	11.57	L9	33 333	0
L4	15 000	1.03	L10	15 000	0
L5	10 000	28.61	L11	34 000	0
L6	15 000	11.57	L12	34 000	0

Reliability evaluation of full-scale structural test based on ISMA-Stacking ensemble modeling and Bayesian fusion

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加载点	均值	标准差	加载点	均值	标准差
L1	8 997.28	12.54	L7	13 498.54	12.26
L2	9 001.65	11.95	L8	46 486.02	11.18
L3	13 493.89	10.62	L9	29 993.37	12.20
L4	13 498.90	12.28	L10	13 496.88	10.69
L5	8 997.32	10.70	L11	33 989.77	11.88
L6	13 494.52	11.48	L12	33 990.43	12.11

加载点	均值	标准差	加载点	均值	标准差
L1	9 997.99	11.32	L7	14 998.66	12.05
L2	9 996.85	11.85	L8	51 664.9	11.84
L3	14 998.54	12.39	L9	33 334.67	12.11
L4	14 994.06	11.35	L10	14 998.60	11.15
L5	9 997.87	12.01	L11	34 000.99	12.07
L6	14 995.22	11.46	L12	33 995.68	12.36

变量	分布类型	均值	标准差	变量	分布类型	均值	标准差
F₁	正态分布	8 997.28	12.54	x₂	正态分布	4 572.88	15.52
F₂	正态分布	9 001.65	11.95	y₂	正态分布	17 128.13	5.00
F₃	正态分布	13 493.89	10.62	x₃	正态分布	3 043.74	9.69
F₄	正态分布	13 498.90	12.28	y₃	正态分布	9 648.91	2.09
F₅	正态分布	8 997.32	10.70	x₄	正态分布	2 092.27	1.07
F₆	正态分布	13 494.52	11.48	y₄	正态分布	1 973.98	0.09
F₇	正态分布	13 498.54	12.26	x₅	正态分布	4 577.97	17.44
F₈	正态分布	46 486.02	11.18	y₅	正态分布	-17 125.99	5.13
F₉	正态分布	29 993.37	12.20	x₆	正态分布	3 041.40	9.04
F₁₀	正态分布	13 496.88	10.69	y₆	正态分布	-9 648.54	2.04
F₁₁	正态分布	33 989.77	11.88	x₇	正态分布	2 092.01	0.92
F₁₂	正态分布	33 990.43	12.11	y₇	正态分布	-1 974.01	0.08

约束点	分布类型	均值	标准差
X1	正态分布	2 433.68	29.79
X2	正态分布	2 852.58	53.26
X3	正态分布	2 875.19	52.29
X4	正态分布	156.14	7.66
X5	正态分布	107.56	5.12
X6	正态分布	175.51	13.52

约束点	分布类型	均值	标准差
X1	正态分布	2 916.59	30.06
X2	正态分布	2 863.71	57.25
X3	正态分布	2 861.64	57.03
X4	正态分布	173.19	7.00
X5	正态分布	120.12	4.74
X6	正态分布	136.74	15.97

方法	可靠度	方法	可靠度
SVR	0.990 3	ISMA-SVR	0.990 9
BPNN	0.991 9	ISMA-BPNN	0.992 3
XGB	0.992 4	ISMA-XGB	0.992 9
Stacking	0.993 8	ISMA-Stacking	0.994 2

方法	可靠度	方法	可靠度
SVR	0.952 2	ISMA-SVR	0.958 9
BPNN	0.965 8	ISMA-BPNN	0.969 5
XGB	0.967 2	ISMA-XGB	0.972 5
Stacking	0.975 4	ISMA-Stacking	0.980 8

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