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

Abstract

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

CLC Number:

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.

Figures/Tables 15

Fig. 1

Fig. 2

Fig. 3

Table 1

Evaluation results of Example 1

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

Table 1

Fig. 4

Fig. 5

Fig. 6

Table 2

Uncertain variables for roof truss

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	$[1.88 × 1010, 2.12 × 1010]$

Table 2

Table 3

Evaluation results of Example 2

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

Table 3

Fig. 7

Fig. 8

Fig. 9

Table 4

Uncertain variables for sliding bearings

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）	$[6 900,7 100]$
$η I$ /（ $P a ⋅ s$ ）	$[9.341 2 × 10 - 4, 9.978 8 × 10 - 4]$
$e I$	$[0.77,0.83]$

Table 4

Table 5

Evaluation results of Example 3

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

Table 5

Fig. 10

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

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