Full Text:   <709>

Summary:  <243>

Suppl. Mater.: 

CLC number: 

On-line Access: 2023-02-24

Received: 2022-06-06

Revision Accepted: 2022-09-20

Crosschecked: 2023-02-24

Cited: 0

Clicked: 1406

Citations:  Bibtex RefMan EndNote GB/T7714


Guo-dong SA


-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2023 Vol.24 No.2 P.146-161


Reliability measure approach considering mixture uncertainties under insufficient input data

Author(s):  Zhenyu LIU, Yufeng LYU, Guodong SA, Jianrong TAN

Affiliation(s):  State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310058, China; more

Corresponding email(s):   sgd@zju.edu.cn

Key Words:  Insufficient data, Reliability index, Sensitivity analysis, Sparse variable, Uncertainty propagation

Zhenyu LIU, Yufeng LYU, Guodong SA, Jianrong TAN. Reliability measure approach considering mixture uncertainties under insufficient input data[J]. Journal of Zhejiang University Science A, 2023, 24(2): 146-161.

@article{title="Reliability measure approach considering mixture uncertainties under insufficient input data",
author="Zhenyu LIU, Yufeng LYU, Guodong SA, Jianrong TAN",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Reliability measure approach considering mixture uncertainties under insufficient input data
%A Zhenyu LIU
%A Yufeng LYU
%A Guodong SA
%A Jianrong TAN
%J Journal of Zhejiang University SCIENCE A
%V 24
%N 2
%P 146-161
%@ 1673-565X
%D 2023
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2200300

T1 - Reliability measure approach considering mixture uncertainties under insufficient input data
A1 - Zhenyu LIU
A1 - Yufeng LYU
A1 - Guodong SA
A1 - Jianrong TAN
J0 - Journal of Zhejiang University Science A
VL - 24
IS - 2
SP - 146
EP - 161
%@ 1673-565X
Y1 - 2023
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2200300

Reliability analysis and reliability-based optimization design require accurate measurement of failure probability under input uncertainties. A unified probabilistic reliability measure approach is proposed to calculate the probability of failure and sensitivity indices considering a mixture of uncertainties under insufficient input data. The input uncertainty variables are classified into statistical variables, sparse variables, and interval variables. The conservativeness level of the failure probability is calculated through uncertainty propagation analysis of distribution parameters of sparse variables and auxiliary parameters of interval variables. The design sensitivity of the conservativeness level of the failure probability at design points is derived using a semi-analysis and sampling-based method. The proposed unified reliability measure method is extended to consider p-box variables, multi-domain variables, and evidence theory variables. Numerical and engineering examples demonstrate the effectiveness of the proposed method, which can obtain an accurate confidence level of reliability index and sensitivity indices with lower function evaluation number.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]ChenJB, YangJS, JensenH, 2020. Structural optimization considering dynamic reliability constraints via probability density evolution method and change of probability measure. Structural and Multidisciplinary Optimization, 62(5):2499-2516.

[2]ChenWH, CuiJ, FanXY, et al., 2003. Reliability analysis of DOOF for Weibull distribution. Journal of Zhejiang University-SCIENCE, 4(4):448-453.

[3]ChoH, ChoiKK, GaulNJ, et al., 2016a. Conservative reliability-based design optimization method with insufficient input data. Structural and Multidisciplinary Optimization, 54(6):1609-1630.

[4]ChoH, ChoiKK, LeeI, et al., 2016b. Design sensitivity method for sampling-based RBDO with varying standard deviation. Journal of Mechanical Design, 138(1):011405.

[5]El HajAK, SoubraAH, 2021. Improved active learning probabilistic approach for the computation of failure probability. Structural Safety, 88:102011.

[6]FaesM, MoensD, 2020. Recent trends in the modeling and quantification of non-probabilistic uncertainty. Archives of Computational Methods in Engineering, 27(3):633-671.

[7]GanCB, WangYH, YangSX, 2018. Nonparametric modeling on random uncertainty and reliability analysis of a dual-span rotor. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 19(3):189-202.

[8]HongLX, LiHC, GaoN, et al., 2021. Random and multi-super-ellipsoidal variables hybrid reliability analysis based on a novel active learning Kriging model. Computer Methods in Applied Mechanics and Engineering, 373:113555.

[9]KangYJ, LimOK, NohY, 2016. Sequential statistical modeling method for distribution type identification. Structural and Multidisciplinary Optimization, 54(6):‍1587-1607.

[10]KeshtegarB, HaoP, 2018. Enhanced single-loop method for efficient reliability-based design optimization with complex constraints. Structural and Multidisciplinary Optimization, 57(4):1731-1747.

[11]LeeI, ChoiKK, NohY, et al., 2011. Sampling-based stochastic sensitivity analysis using score functions for RBDO problems with correlated random variables. Journal of Mechanical Design, 133(2):021003.

[12]LeeI, ChoiKK, NohY, et al., 2013. Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information. Structural and Multidisciplinary Optimization, 47(2):175-189.

[13]LiuXX, ElishakoffI, 2020. A combined importance sampling and active learning Kriging reliability method for small failure probability with random and correlated interval variables. Structural Safety, 82:101875.

[14]LiuY, JeongHK, ColletteM, 2016. Efficient optimization of reliability-constrained structural design problems including interval uncertainty. Computers & Structures, 177:1-11.

[15]LiuZY, XuHC, SaGD, et al., 2022. A comparison of sensitivity indices for tolerance design of a transmission mechanism. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 23(7):527-542.

[16]McFarlandJ, DeCarloE, 2020. A Monte Carlo framework for probabilistic analysis and variance decomposition with distribution parameter uncertainty. Reliability Engineering & System Safety, 197:106807.

[17]NiBY, JiangC, HuangZL, 2018. Discussions on non-probabilistic convex modelling for uncertain problems. Applied Mathematical Modelling, 59:54-85.

[18]OberkampfWL, HeltonJC, JoslynCA, et al., 2004. Challenge problems: uncertainty in system response given uncertain parameters. Reliability Engineering & System Safety, 85(1-3):11-19.

[19]PengX, LiJQ, JiangSF, 2017. Unified uncertainty representation and quantification based on insufficient input data. Structural and Multidisciplinary Optimization, 56(6):‍‍‍1305-1317.

[20]SankararamanS, MahadevanS, 2013. Distribution type uncertainty due to sparse and imprecise data. Mechanical Systems and Signal Processing, 37(1-2):182-198.

[21]SankararamanS, MahadevanS, 2015. Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems. Reliability Engineering & System Safety, 138:194-209.

[22]SolazziL, 2022. Reliability evaluation of critical local buckling load on the thin walled cylindrical shell made of composite material. Composite Structures, 284:115163.

[23]Tostado-VélizM, Icaza-AlvarezD, JuradoF, 2021. A novel methodology for optimal sizing photovoltaic-battery systems in smart homes considering grid outages and demand response. Renewable Energy, 170:884-896.

[24]Tostado-VélizM, KamelS, AymenF, et al., 2022. A stochastic-IGDT model for energy management in isolated microgrids considering failures and demand response. Applied Energy, 317:119162.

[25]WakjiraTG, IbrahimM, EbeadU, et al., 2022. Explainable machine learning model and reliability analysis for flexural capacity prediction of RC beams strengthened in flexure with FRCM. Engineering Structures, 255:113903.

[26]WangC, LiQW, PangL, et al., 2016. Estimating the time-dependent reliability of aging structures in the presence of incomplete deterioration information. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 17(9):677-688.

[27]WeiPF, SongJW, BiSF, et al., 2019. Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis. Mechanical Systems and Signal Processing, 126:227-247.

[28]YunWY, LuZZ, JiangX, et al., 2020. AK-ARBIS: an improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability. Structural Safety, 82:101891.

[29]ZhangZ, WangJ, JiangC, et al., 2019. A new uncertainty propagation method considering multimodal probability density functions. Structural and Multidisciplinary Optimization, 60(5):1983-1999.

[30]ZhaoYG, ZhangXY, LuZH, 2018. Complete monotonic expression of the fourth-moment normal transformation for structural reliability. Computers & Structures, 196:186-199.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE