基于RBF和主动学习的非概率可靠度求解方法

doi:10.7527/S1000-6893.2022.26667

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基于RBF和主动学习的非概率可靠度求解方法

姜峰, 李华聪(), 符江锋, 洪林雄

西北工业大学动力与能源学院，西安　710072

收稿日期:2021-11-15 修回日期:2021-12-23 接受日期:2022-01-17 出版日期:2023-01-25 发布日期:2022-01-26
通讯作者: 李华聪 E-mail:lihuacong@nwpu.edu.cn
基金资助:
国家科技重大专项(2017-V-0013-0065)

A RBF and active learning combined method for structural non-probabilistic reliability analysis

Feng JIANG, Huacong LI(), Jiangfeng FU, Linxiong HONG

School of Power and Energy，Northwestern Polytechnical University，Xi’an 710072，China

Received:2021-11-15 Revised:2021-12-23 Accepted:2022-01-17 Online:2023-01-25 Published:2022-01-26
Contact: Huacong LI E-mail:lihuacong@nwpu.edu.cn
Supported by:
National Science and Technology Major Project(2017-V-0013-0065)

摘要/Abstract

摘要：

进行结构非概率可靠性分析时，对于失效域与超椭球不确定域发生干涉的情况，非概率可靠度相较于非概率可靠度指标更具有适用性。为了提高超椭球模型下结构非概率可靠度的求解效率，本文提出一种求解非概率可靠度问题的高效主动学习方法。首先，结合交叉验证和jackknifing方法推导了RBF模型在未知点处的jackknifing方差以评估模型预测的不确定性，并根据该方差基于RBF的主动学习函数对非概率可靠度进行求解。其次，提出有效收敛准则来终止非概率可靠性分析的主动学习过程。最后，3个算例表明该方法能够在较少功能函数调用次数下得到精确的非概率可靠度估计值，具有良好的工程应用价值。

关键词: 非概率可靠性分析, 超椭球模型, RBF模型, 交叉验证, 主动学习

Abstract:

When the failure domain and the hyper-ellipsoid uncertainty domain interfere with each other in non-probabilistic reliability analysis， non-probabilistic reliability is more applicable than the non-probabilistic reliability index. To improve the solution efficiency of structural non-probabilistic reliability of the hyper-ellipsoid model， this paper proposes an active learning method to solve non-probabilistic reliability problems. The jackknifing variance of the Radial Basis Function （RBF） model at the unknown point is derived by combining the cross-validation and the jackknifing methods， so as to estimate the uncertainty of the predicted values. To solve the non-probabilistic reliability， the is employed which is based on the variance. Based on the jackknifing variance， non-probabilistic reliability is solved using the active learning function of RBF. An effective convergence criterion is then proposed to terminate the process of active learning of non-probabilistic reliability analysis. Three numerical examples reveal that this method proposed can estimate the exact non-probabilistic reliability value under the condition of less calculation of the limit state function， and has strong applicability in structural non-probabilistic reliability analysis.

Key words: non-probabilistic reliability analysis, hyper-ellipsoidal model, Radial Basis Function (RBF) model, cross-validation, active learning

中图分类号:

姜峰, 李华聪, 符江锋, 洪林雄. 基于RBF和主动学习的非概率可靠度求解方法[J]. 航空学报, 2023, 44(2): 226667.

Feng JIANG, Huacong LI, Jiangfeng FU, Linxiong HONG. A RBF and active learning combined method for structural non-probabilistic reliability analysis[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 226667.

图/表 15

图 1

图 2

图 3

表 1

算例1的计算结果对比

方法		$N c a l l$	$R ̂ c$	$ς$ /%
MCS		1×10⁶	0.638 0	0
ERF		12+110	0.638 3	0.047 02
本文的方法	Case1	12+80	0.638 5	0.078 37
	Case2	12+83	0.638 3	0.047 02
	Case3	12+79	0.638 2	0.031 35
	Case4	12+69	0.638 5	0.078 37

表 1

图 4

图 5

图 6

表 2

屋顶桁架的不确定变量参数

变量	边缘区间
$q I$ /（N·m^-1）	$[16 400,23 600]$
$l I$ /m	$[10.8,13.2]$
$A s I$ /m²	$[8.838 × 10 - 4, 10.802 × 10 - 4]$
$A c I$ /m²	$[0.035 2,0.044 8]$
$E s I$ /Pa	$[0.9 × 1011, 1.1 × 1011]$
$E c I$ /Pa	$[1.88 × 1010, 2.12 × 1010]$

表 2

表 3

算例2的计算对比

方法		$N c a l l$	$R ̂ c$	$ς$ /%
MCS		1×10⁶	0.721 2	0
ERF		12+41	0.719 8	0.194 10
本文的方法	Case1	12+24	0.721 1	0.013 87
	Case2	12+29	0.721 0	0.027 73
	Case3	12+31	0.721 0	0.027 73
	Case4	12+32	0.721 1	0.013 87

表 3

图 7

图 8

图 9

表 4

航空齿轮泵滑动轴承的不确定变量参数

变量	边缘区间
$B I$ /m	$[28 × 10 - 3, 32 × 10 - 3]$
$R I$ /m	$[9.94 × 10 - 3, 10 × 10 - 3]$
$C I$ /m	$[0.03 × 10 - 3, 0.05 × 10 - 3]$
$n I$ /（r·min^-1）	$[6 900,7 100]$
$η I$ /（ $P a ⋅ s$ ）	$[9.341 2 × 10 - 4, 9.978 8 × 10 - 4]$
$e I$	$[0.77,0.83]$

表 4

表 5

算例3的计算对比

方法		$N c a l l$	$R ̂ c$	$ς$ /%
MCS		1×10⁶	0.837 0	0
ERF		12+32	0.836 6	0.047 79
本文的方法	Case1	12+26	0.836 5	0.059 74
	Case2	12+25	0.836 6	0.047 79
	Case3	12+27	0.836 9	0.011 95
	Case4	12+30	0.836 9	0.011 95

表 5

图 10

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基于RBF和主动学习的非概率可靠度求解方法

A RBF and active learning combined method for structural non-probabilistic reliability analysis

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