可靠性分析改进元模型重要抽样算法

doi:10.7527/S1000-6893.2024.30738

Abstract

Abstract:

To give an efficient analysis of structural reliability， an enhanced metamodel-based importance sampling method is proposed in this paper by introducing an error-based stopping criterion for updating the Kriging model. Firstly， an analytical relationship of the relative error between the estimate of failure probability by the metamodel-based importance sampling method and the true value obtained by the actual limit state function is established. Secondly， an approximate relationship between the upper bound of the relative error between the estimate of failure probability and the true value and the prediction accuracy of the Kriging model is derived. By ensuring that the relative error between the estimate of failure probability by the metamodel-based importance sampling method and the true value obtained by the actual limit state function does not exceed a predefined accuracy， an error-based stopping criterion for updating the Kriging model is established to improve the efficiency of the existing metamodel-based importance sampling method. Finally， the proposed method is applied to numerical examples and engineering examples of reliability analysis of turbine shaft fatigue life. The results verify the efficiency and accuracy of the proposed method.

Key words: reliability analysis, metamodel-based, importance sampling method, Kriging model, error-based stopping criterion

CLC Number:

Wanying YUN, Fengyuan LI, Bo HUANG, Siyu WANG, Yunfei JIAO, Xinyu BAI, Xueqi HUANG. Enhanced metamodel-based importance sampling method for reliability analysis[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 230738.

Figures/Tables 11

Fig.1

Fig.2

Table 1

Reliability analysis results of numerical example

方法	停止准则	$ε r (m a x)$	$ε r (t h r)$	$ε r$	$P ̂ f$	$C O V P ̂ f$	$N c a l l$
MCS					0.003 43	0.017 0	10⁶
AK-MCS	$m i n (U) ≥ 2$				0.003 44	0.017 0	156
Meta-IS-AK	$m i n (U) ≥ 2$				0.003 47	0.024 4	105
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.062 3	0.10	0.002 88	0.003 46	0.023 8	67
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.033 5	0.05	0.002 88	0.003 48	0.024 4	72
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.011 4	0.02	0	0.003 47	0.024 3	83

Table 1

Fig.3

Table 2

Distribution parameters of input variables of bracket structure

输入变量	分布类型	均值	变异系数
$σ S / M P a$	Lognormal	225	0.08
$P / k N$	Gumbel	100	0.15
$E / G P a$	Gumbel	200	0.08
$ρ /$ （kg·m^-3）	Weibull	7 860	0.10
$t / m m$	Normal	269	0.05
$L / m$	Normal	5	0.05
$ω A B / m m$	Normal	61	0.05
$ω C D / m m$	Normal	202	0.05

Table 2

Table 3

Reliability analysis results of bracket structure

方法	停止准则	$ε r (m a x)$	$ε r (t h r)$	$ε r$	$P ̂ f$	$C O V P ̂ f$	$N c a l l$
MCS					0.002 13	0.015 3	2×10⁶
AK-MCS	$m i n (U) ≥ 2$				0.002 13	0.015 3	249
Meta-IS-AK	$m i n (U) ≥ 2$				0.002 12	0.020 9	165
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.097 3	0.10	0	0.002 12	0.020 7	101
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.047 6	0.05	0	0.002 12	0.020 7	125
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.016 6	0.02	0	0.002 12	0.020 9	146

Table 3

Fig.4

Table 4

Fig.5

Table 5

Distribution parameters of input variables of turbine shaft

输入变量	分布类型	均值	变异系数
$r / m m$	Normal	1.5	0.02
$h / m m$	Normal	4	0.02
$E / G P a$	Normal	146	0.03
$ν$	Normal	0.325	0.02
$T 1 /$ （N·m）	Normal	1 800	0.03
$T 2$ /（N·m）	Normal	1 650	0.03
$n 1 /$ （r·s^-1）	Normal	1 124	0.03
$n 2 /$ （r·s^-1）	Normal	1 006	0.03

Table 5

Table 6

Reliability analysis results of turbine shaft fatigue life

方法	停止准则	$ε r (m a x)$	$ε r (t h r)$	$ε r$	$P ̂ f$	$C O V P ̂ f$	$N c a l l$
AK-MCS	$m i n (U) ≥ 2$				0.007 91	0.015 8	182
Meta-IS-AK	$m i n (U) ≥ 2$				0.007 76	0.017 6	70
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.050 3	0.10	0.001 3	0.007 77	0.016 1	36
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.030 2	0.05	0	0.007 76	0.016 6	37
改进Meta-IS-AK	$ε r (m a x) ≤ ε r (t h r)$	0.011 1	0.02	0	0.007 76	0.017 2	39

Table 6

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工作载荷类型	转速/（r·s^-1）	循环次数
启动-最大转速-启动	0-1 124-0	1 128
巡航-最大转速-巡航	1 006-1 124-1 006	23 046

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Enhanced metamodel-based importance sampling method for reliability analysis

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