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): 226667-226667.

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

References 33

1	王睿星, 王晓军, 王磊, 等. 几种结构非概率可靠性模型的比较研究[J]. 应用数学和力学, 2013, 34(8): 871-880.
	WANG R X, WANG X J, WANG L, et al. Comparisons of several non-probabilistic models for structural reliability[J]. Applied Mathematics and Mechanics, 2013, 34(8): 871-880 (in Chinese).
2	BEN-HAIM Y, ELISHAKOFF I. Preface[M]∥Convex models of uncertainty in applied mechanics. Amsterdam: Elsevier, 1990: xiii-xvii.
3	JIANG C, HAN X, LU G Y, et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(33-36): 2528-2546.
4	NI B Y, JIANG C, HAN X. An improved multidimensional parallelepiped non-probabilistic model for structural uncertainty analysis[J]. Applied Mathematical Modelling, 2016, 40(7-8): 4727-4745.
5	MENG Z, HU H, ZHOU H L. Super parametric convex model and its application for non-probabilistic reliability-based design optimization[J]. Applied Mathematical Modelling, 2018, 55: 354-370.
6	LIU J, YU Z B, ZHANG D Q, et al. Multimodal ellipsoid model for non-probabilistic structural uncertainty quantification and propagation[J]. International Journal of Mechanics and Materials in Design, 2021, 17(3): 633-657.
7	LIU X, WANG X Y, SUN L, et al. An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model[J]. Structural and Multidisciplinary Optimization, 2019, 59(6): 2189-2203.
8	檀中强. 基于椭球模型的不确定性量化与可靠性分析方法研究[D]. 杭州: 浙江理工大学, 2018.
	TAN Z Q. A study of uncertainty quantification and reliability analysis method based on ellipsoid model[D]. Hangzhou: Zhejiang Sci-Tech University, 2018 (in Chinese).
9	张卓辉. 可靠性精确建模分析及高效优化算法研究[D]. 合肥: 合肥工业大学, 2020.
	ZHANG Z H. Research on accurate reliability modeling and high performance optimization algorithm[D]. Hefei: Hefei University of Technology, 2020 (in Chinese).
10	张屹尚, 刘永寿, 赵彬, 等. 基于Kriging模型的充液管道共振非概率可靠性分析[J]. 振动工程学报, 2012, 25(2): 117-123.
	ZHANG Y S, LIU Y S, ZHAO B, et al. Non-probabilistic reliability analysis on resonance of fluid-filled pipeline based on Kriging model[J]. Journal of Vibration Engineering, 2012, 25(2): 117-123 (in Chinese).
11	辛腾达, 王华, 崔村燕, 等. 不确定条件下贮箱区间凸模型可靠性评估[J]. 北京航空航天大学学报, 2018, 44(11): 2380-2387.
	XIN T D, WANG H, CUI C Y, et al. Reliability evaluation of tank under uncertain conditions based on interval convex model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(11): 2380-2387 (in Chinese).
12	毕仁贵. 考虑相关性的不确定凸集模型与非概率可靠性分析方法[D]. 长沙: 湖南大学, 2015.
	BI R G. Non-probabilistic uncertainty convex model and reliability analysis method incorporating correlation[D]. Changsha: Hunan University, 2015 (in Chinese).
13	洪东跑, 马小兵, 赵宇, 等. 基于容差分析的结构非概率可靠性模型[J]. 机械工程学报, 2010, 46(4): 157-162.
	HONG D P, MA X B, ZHAO Y, et al. Non-probabilistic model for structural reliability based on tolerance analysis[J]. Journal of Mechanical Engineering, 2010, 46(4): 157-162 (in Chinese).
14	孙海龙, 姚卫星. 结构区间可靠性分析的可能度法[J]. 中国机械工程, 2008, 19(12): 1483-1488.
	SUN H L, YAO W X. Possibility degree method for structural interval reliability analysis[J]. China Mechanical Engineering, 2008, 19(12): 1483-1488 (in Chinese).
15	郭书祥, 吕震宙, 冯元生. 基于区间分析的结构非概率可靠性模型[J]. 计算力学学报, 2001, 18(1): 56-60.
	GUO S X, LU Z Z, FENG Y S. A non-probabilistic model of structural reliability based on interval analysis[J]. Chinese Journal of Computational Mechanics, 2001, 18(1): 56-60 (in Chinese).
16	CAO H J, DUAN B Y. Approach on the non-probabilistic reliability of structures based on uncertainty convex models[J]. Chinese Journal of Computational Mechanics, 2005, 22(5): 546-549+578.
17	罗阳军, 亢战, LI A. 基于凸模型的结构非概率可靠性指标及其求解方法研究[J]. 固体力学学报, 2011, 32(6): 646-654.
	LUO Y J, KANG Z, LI A. Study on structural non-probabilistic reliability index under convex models and its solution methods[J]. Chinese Journal of Solid Mechanics, 2011, 32(6): 646-654 (in Chinese).
18	周凌, 安伟光, 贾宏光. 超椭球凸集合可靠性综合指标定义及求解方法[J]. 航空学报, 2011, 32(11): 2025-2035.
	ZHOU L, AN W G, JIA H G. Definition and solution of reliability comprehensive index of super-ellipsoid convex set[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(11): 2025-2035 (in Chinese).
19	王晓军, 邱志平, 武哲. 结构非概率集合可靠性模型[J]. 力学学报, 2007, 39(5): 641-646.
	WANG X J, QIU Z P, WU Z. Non-probabilistic set-based model for structural reliability[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(5): 641-646 (in Chinese).
20	乔心州, 仇原鹰, 孔宪光. 一种基于椭球凸集的结构非概率可靠性模型[J]. 工程力学, 2009, 26(11): 203-208.
	QIAO X Z, QIU Y Y, KONG X G. A non-probabilistic model of structural reliability based on ellipsoidal convex model[J]. Engineering Mechanics, 2009, 26(11): 203-208 (in Chinese).
21	MENG Z, WAN H P, SHENG Z L, et al. A novel study of structural reliability analysis and optimization for super parametric convex model[J]. International Journal for Numerical Methods in Engineering, 2020, 121(18): 4208-4229.
22	JIANG C, BI R G, LU G Y, et al. Structural reliability analysis using non-probabilistic convex model[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 254: 83-98.
23	魏娟, 张建国, 邱涛. 基于改进的动态Kriging模型的结构可靠度算法[J]. 北京航空航天大学学报, 2019, 45(2): 373-380.
	WEI J, ZHANG J G, QIU T. Structural reliability algorithm based on improved dynamic Kriging model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(2): 373-380 (in Chinese).
24	洪林雄, 李华聪, 彭凯, 等. 基于改进学习策略的Kriging模型结构可靠度算法[J]. 西北工业大学学报, 2020, 38(2): 412-419.
	HONG L X, LI H C, PENG K, et al. Structural reliability algorithms of kriging model based on improved learning strategy[J]. Journal of Northwestern Polytechnical University, 2020, 38(2): 412-419 (in Chinese).
25	王洪志. 基于距离约束策略的主动学习Kriging方法及其工程应用[D]. 大连: 大连理工大学, 2019.
	WANG H Z. Active learning Kriging method based on distance constraint strategy and its engineering application[D]. Dalian: Dalian University of Technology, 2019 (in Chinese).
26	张屹尚. 复杂结构的不确定性传递及重要性分析研究[D]. 西安: 西北工业大学, 2015.
	ZHANG Y S. Research on the propagation of stochastic uncertainty and importance measure for complex structures[D]. Xi'an: Northwestern Polytechnical University, 2015 (in Chinese).
27	XIAO N C, ZUO M J, ZHOU C N. A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis[J]. Reliability Engineering & System Safety, 2018, 169: 330-338.
28	SHI L J, SUN B B, IBRAHIM D S. An active learning reliability method with multiple kernel functions based on radial basis function[J]. Structural and Multidisciplinary Optimization, 2019, 60(1): 211-229.
29	HONG L X, LI H C, PENG K. A combined radial basis function and adaptive sequential sampling method for structural reliability analysis[J]. Applied Mathematical Modelling, 2021, 90: 375-393.
30	JING Z, CHEN J Q, LI X. RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis[J]. Reliability Engineering & System Safety, 2019, 189: 42-57.
31	罗阳军, 亢战. 超椭球模型下结构非概率可靠性指标的迭代算法[J]. 计算力学学报, 2008, 25(6): 747-752.
	LUO Y J, KANG Z. An iteration approach for structural non-probabilistic reliability analysis based on hyper-ellipsoidal models[J]. Chinese Journal of Computational Mechanics, 2008, 25(6): 747-752 (in Chinese).
32	KLEIJNEN J, BEERS W. Application-driven sequential designs for simulation experiments: Kriging metamodeling[J]. Journal of the Operational Research Society, 2004, 55:876-883
33	ZHAO H L, YUE Z F, LIU Y S, et al. An efficient reliability method combining adaptive importance sampling and Kriging metamodel[J]. Applied Mathematical Modelling, 2015, 39(7): 1853-1866.

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

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