参数可靠性全局灵敏度高效分析的代理模型法

doi:10.7527/S1000-6893.2022.27670

Abstract

Abstract:

To give an efficient analysis of parameter reliability global sensitivity， this paper proposes a method by integrating the single-loop importance sampling technique and the adaptive Kriging model. First， a single-loop importance sampling algorithm for estimating the parameter reliability global sensitivity is constructed based on the Bayes theorem， Metropolis-Hastings algorithm and Edgeworth expansion， which unifies the analyses of reliability and parameter reliability global sensitivity. Based on the proposed single-loop importance sampling algorithm， the estimation of the parameter reliability global sensitivity is converted into the identification of states （failure or safety） of all unconditional importance sampling samples， so that each parameter reliability global sensitivity can be evaluated by repeatedly using the unconditional importance sampling samples. Secondly， the Kriging model surrogating the performance function is adaptively constructed to approximate the optimal importance sampling Probability Density Function （PDF） and then generate the corresponding importance samples. Finally， the Kriging model used to construct the approximately optimal importance sampling PDF is continuously updated among the candidate sampling pool of the generated importance samples until the states of all importance samples are accurately identified by the Kriging model. Based on the accurately identified states of all importance samples， parameter global reliability sensitivity of each uncertain distribution parameter is assessed.Results of a numerical example and a missile wing structure verify the efficiency and accuracy of the proposed method.

Key words: parameter reliability global sensitivity analysis, Bayes theorem, surrogate model, Metropolis-Hastings algorithm, importance sampling, Edgeworth expansion

CLC Number:

V215.7

Wanying YUN, Zhenzhou LYU. An efficient surrogate method for analyzing parameter global reliability sensitivity[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 227670-227670.

Figures/Tables 8

Table 1

Results of parameter global reliability sensitivity indices of numerical example

方法	$S 1 θ$	$S 2 θ$	$S 3 θ$	CSP	$N c a l l$	计算时间/s
所提方法	0.004 4^{［0.029 8］}	0.001 7^{［0.071 3］}	0.002 4^{［0.048 1］}	200	24.10	0.74
	0.004 4^{［0.020 7］}	0.001 7^{［0.039 9］}	0.002 5^{［0.036 1］}	500	24.10	1.46
	0.004 4^{［0.009 7］}	0.001 7^{［0.029 1］}	0.002 5^{［0.023 0］}	1 000	24.32	6.62
文献［9］方法	0.003 3^{［0.059 0］}	0.001 4^{［0.057 9］}	0.002 0^{［0.055 8］}	65 536	17.45	2.85
	0.003 3^{［0.055 9］}	0.001 4^{［0.048 1］}	0.002 1^{［0.049 8］}	131 072	19.50	6.50
	0.003 9^{［0.025 5］}	0.001 6^{［0.034 7］}	0.002 3^{［0.031 2］}	262 144	21.60	14.69
	0.004 2^{［0.015 6］}	0.001 7^{［0.018 5］}	0.002 4^{［0.026 1］}	524 288	22.30	30.52
3层MCS	0.004 4	0.001 7	0.002 5		$≈ 1.6 × 1012$	$3.456 × 105$

Table 1

Fig. 1

Fig. 2

Table 2

Distribution types and distribution parameters of variables

随机变量	分布类型	均值	标准差
$E$ /MPa	正态分布	$μ E$	1 176
$ν$	正态分布	$μ ν$	0.003
$P$ $/ k N$	正态分布	$μ P$	0.008
$t s k$ /mm	正态分布	$μ t s k$	0.016
$t r s$ /mm	正态分布	$μ t r s$	0.060

Table 2

Table 3

Distribution types and distribution parameters of means of variables

随机变量均值	分布类型	均值	标准差
$μ E$ /MPa	正态分布	117 600	3 528
$μ ν$	正态分布	0.3	0.009 0
$μ P$ $/ k N$	正态分布	016	0.004 8
$μ t s k$ /mm	正态分布	0.8	0.024 0
$μ t r s$ /mm	正态分布	3	0.090 0

Table 3

Fig. 3

Table 4

Computational cost of proposed method and method in Ref.［9］ with different sizes of candidate sampling pool

方法	CSP	$N c a l l$	代理模型训练时间/s
所提方法	1 000	44.44	6.48
	2 000	46.70	13.00
	3 000	49.58	17.70
	4 000	51.02	22.78
	5 000	51.40	28.76
文献［9］	262 144	34.08	18.66
	524 288	38.90	47.12
	1 048 576	43.98	117.42
	2 097 152	51.88	321.28

Table 4

Fig. 4

References 24

1	SALTELLI A. Sensitivity analysis for importance assessment［J］. Risk Analysis， 2002， 22（3）： 579-590.
2	POHYA A A， WICKE K， KILIAN T. Introducing variance-based global sensitivity analysis for uncertainty enabled operational and economic aircraft technology assessment［J］. Aerospace Science and Technology， 2022， 122： 107441.
3	YUN W Y， LU Z Z， JIANG X. An efficient sampling approach for variance-based sensitivity analysis based on the law of total variance in the successive intervals without overlapping［J］. Mechanical Systems and Signal Processing， 2018， 106： 495-510.
4	BORGONOVO E. A new uncertainty importance measure［J］. Reliability Engineering & System Safety， 2007， 92（6）： 771-784.
5	ZHANG F， XU X Y， CHENG L， et al. Global moment-independent sensitivity analysis of single-stage thermoelectric refrigeration system［J］. International Journal of Energy Research， 2019， 43（15）： 9055-9064.
6	PAPAIOANNOU I， STRAUB D. Variance-based reliability sensitivity analysis and the FORM α-factors［J］. Reliability Engineering & System Safety， 2021， 210： 107496.
7	张磊刚，吕震宙，陈军. 基于失效概率的矩独立重要性测度的高效算法［J］. 航空学报， 2014， 35（8）： 2199-2206.
	ZHANG L G， LYU Z Z， CHEN J. An efficient method for failure probability-based moment-independent importance measure［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（8）： 2199-2206 （in Chinese）.
8	WANG P， LU Z Z， TANG Z C. An application of the Kriging method in global sensitivity analysis with parameter uncertainty［J］. Applied Mathematical Modelling， 2013， 37（9）： 6543-6555.
9	YUN W Y， LU Z Z， HE P F， et al. Parameter global reliability sensitivity analysis with meta-models： A probability estimation-driven approach［J］. Aerospace Science and Technology， 2020， 106： 106040.
10	LIU P L， DER KIUREGHIAN A. Multivariate distribution models with prescribed marginals and covariances［J］. Probabilistic Engineering Mechanics， 1986， 1（2）： 105-112.
11	DOBRIC J， SCHMID F. A goodness of fit test for copulas based on Rosenblatt’s transformation［J］. Computational Statistics & Data Analysis， 2007， 51（9）： 4633-4642.
12	DENG J. Probabilistic characterization of soil properties based on the maximum entropy method from fractional moments： Model development， case study， and application［J］. Reliability Engineering & System Safety， 2022， 219： 108218.
13	张洪铭，顾晓辉，邸忆. 基于树形马氏链模型的可靠性分析方法［J］. 航空学报， 2019， 40（5）： 222643.
	ZHANG H M， GU X H， DI Y. Reliability analysis method based on Tree Markov Chain model［J］. Acta Aeronautica et Astronautica Sinica， 2019， 40（5）： 222643 （in Chinese）.
14	PERNINGE M. Stochastic optimal power flow by multi-variate Edgeworth expansions［J］. Electric Power Systems Research， 2014， 109： 90-100.
15	METROPOLIS N， ROSENBLUTH A W， ROSENBLUTH M N， et al. Equation of state calculations by fast computing machines［J］. The Journal of Chemical Physics， 1953， 21（6）： 1087-1092.
16	HASTINGS W K. Monte Carlo sampling methods using Markov chains and their applications［J］. Biometrika， 1970， 57（1）： 97-109.
17	DUBOURG V， SUDRET B， DEHEEGER F. Metamodel-based importance sampling for structural reliability analysis［J］. Probabilistic Engineering Mechanics， 2013， 33： 47-57.
18	KLEIJNEN J P C. Regression and Kriging metamodels with their experimental designs in simulation： A review［J］. European Journal of Operational Research， 2017， 256（1）： 1-16.
19	LI Y H， SHI J J， YIN Z F， et al. An improved high-dimensional kriging surrogate modeling method through principal component dimension reduction［J］. Mathematics， 2021， 9（16）： 1985.
20	AFSHARI S S， ENAYATOLLAHI F， XU X， et al. Machine learning-based methods in structural reliability analysis： A review［J］. Reliability Engineering & System Safety， 2022， 219： 108223.
21	RIDLEY G， FORGET B. A simple method for rejection sampling efficiency improvement on SIMT architectures［J］. Statistics and Computing， 2021， 31（3）： 30.
22	SIVULA T， MAGNUSSON M， VEHTARI A. Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance［J/OL］. Communications in Statistics-Theory and Methods （2022-02-03）［2022-06-22］. .
23	ECHARD B， GAYTON N， LEMAIRE M. AK-MCS： An active learning reliability method combining Kriging and Monte Carlo Simulation［J］. Structural Safety， 2011， 33（2）： 145-154.
24	SOBOL IM. On quasi-Monte Carlo integrations［J］. Mathematics and Computers in Simulation， 1998， 47： 103-112.

[1]	Zhuangzhuang CUI, Xin YUAN, Guoqing ZHAO, Simeng JING, Qijun ZHAO. Influence of control strategy on forward flight performance of coaxial rigid rotor high⁃speed helicopters [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529256-529256.
[2]	Jiaqi LIU, Rongqian CHEN, Jinhua LOU, Xu HAN, Hao WU, Yancheng YOU. Aerodynamic shape optimization of high-speed helicopter rotor airfoil based on deep learning [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529828-529828.
[3]	Yuhan LI, Baoyu YANG, Yinong WU, Qiang ZHANG, Xiao TANG. Research on parameters correction method for thermal model of satellite optomechanical load [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 628814-628814.
[4]	Shusheng CHEN, Cong FENG, Zhaokang ZHANG, Ke ZHAO, Xinyang ZHANG, Zhenghong GAO. Aerodynamic design of wide-speed-range waverider-wing configuration based on global & gradient optimization method [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 629596-629596.
[5]	Huan ZHAO, Zhenghong GAO, Lu XIA. Novel multi-fidelity surrogate model assisted many-objective optimization method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(6): 126962-126962.
[6]	Huan ZHAO, Zhenghong GAO, Lu XIA. Aerodynamic shape design optimization method based on novel high⁃dimensional surrogate model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 126924-126924.
[7]	Zhiyang ZHENG, Yang ZHANG, Zhao ZHANG, Baohai WU, Ying ZHANG. Layout optimization of auxiliary support for thin-walled blade based on GA-SVR [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 426805-426805.
[8]	Ting YU, Luyi LI, Yushan LIU, Zeming CHANG. Efficient Bayesian updating method under observation uncertainty and its application in wing structure [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(24): 228592-228592.
[9]	Qian YANG, Xiaofeng GUO, Qin LI, Wei DONG. Hot air anti-icing performance estimation method based on POD and surrogate model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 626992-626992.
[10]	Junjie NIU, Weimin SANG, Dong LI, Lian HAO, Zelin WANG. Icing test flight area determination method based on surrogated model of water droplet collection [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 627697-627697.
[11]	Qilei GUO, Weimin SANG, Junjie NIU, Ye YUAN. UAV flight strategy considering icing risk under complex meteorological conditions [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 627518-627518.
[12]	CHEN Zhiyuan, LI Luyi. Efficient methods for reliability sensitivity analysis of inputs with distribution parameter uncertainty [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 325881-325881.
[13]	LUO Zexiong, QU Guoyuan, YAN Long, TANG Xueqian. A scheduling table generation method for time-triggered flows based on importance sampling [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 325209-325209.
[14]	LI Haiquan, CHEN Xiaoqian, ZUO Linxuan, ZHAO Zhuolin. Surrogate model for flight load analysis based on random forest [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 225640-225640.
[15]	YE Nianhui, LONG Teng, WU Yufei, TANG Yifan, SHI Renhe. Kriging-assisted constrained differential evolution algorithm [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(6): 324580-324580.

An efficient surrogate method for analyzing parameter global reliability sensitivity

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 8

References 24

Related Articles 15

Recommended Articles

Metrics

Comments