Search for Author, Title, Keyword
RESEARCH PAPER
An efficient method for calculating system non-probabilistic reliability index
,
 
 
 
More details
Hide details
1
College of Medical Technology, Chengdu University of Traditional Chinese Medicine, No. 1166, Liutai Avenue, Wenjiang District, Chengdu 611137, China
 
2
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, China
 
 
Publication date: 2021-09-30
 
 
Eksploatacja i Niezawodność – Maintenance and Reliability 2021;23(3):498-504
 
HIGHLIGHTS
  • A method for calculating system non-probabilistic reliability index is proposed.
  • A refinement learning function is proposed to determine the best component.
  • Two important factors for non-probabilistic reliability index have been considered.
KEYWORDS
ABSTRACT
Collecting enough samples is difficult in real applications. Several interval-based non-probabilistic reliability methods have been reported. The key of these methods is to estimate system non-probabilistic reliability index. In this paper, a new method is proposed to calculate system non-probabilistic reliability index. Kriging model is used to replace time-consuming simulations, and the efficient global optimization is used to determine the new training samples. A refinement learning function is proposed to determine the best component (or performance function) during the iterative process. The proposed refinement learning function has considered two important factors: (1) the contributions of components to system nonprobabilistic reliability index, and (2) the accuracy of the Kriging model at current iteration. Two stopping criteria are given to terminate the algorithm. The system non-probabilistic index is finally calculated based on the Kriging model and Monte Carlo simulation. Two numerical examples are given to show the applicability of the proposed method.
 
REFERENCES (36)
1.
Ben-Haim Y. A non-probabilistic concept of reliability. Structural Safety, 1994; 14(4): 227-245, https://doi.org/10.1016/0167-4....
 
2.
Ben-Haim Y. A non-probabilistic measure of reliability of linear systems based on expansion of convex models. structural Safety 1995;17(2): 91-109,. https://doi.org/ 10.1016/0167-4730(95)00004-N.
 
3.
Bichon B J, Eldred M S, Swiler L P, et al. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal 2008; 46(10): 2459-2468, https://doi.org/10.2514/1.3432....
 
4.
Chen X Y, Fan J P, Bian X Y. Theoretical analysis of non-probabilistic reliability based on interval model. Acta Mechanica Solida Sinica 2017; 30: 638-646, https://doi.org/10.1016/j.cams....
 
5.
Dong L J, Sun D Y, Li X B, et al. Interval non-probabilistic reliability of surrounding jointed rock mass considering micro seismic loads in mining tunnels. Tunneling and Underground Space Technology 2018; 81: 326-335, https://doi.org/10.1016/j.tust....
 
6.
Du X. System reliability analysis with saddle-point approximation. Structural and Multidisciplinary Optimization 2010; 42: 193-208, https://doi.org/10.1007/s00158....
 
7.
Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011; 33: 145-154, https://doi.org/10.1016/j.stru....
 
8.
Elishakoff I, Elisseeff P, Glegg S A L. Non-probabilistic, convex-theoretic modeling of scatter in material properties. AIAA Journal 1995;32(4): 843-849, https://doi.org/10.2514/3.1206....
 
9.
Fauriat W, Gayton N. AK-SYS: An adaptation of the AK-MCS method for system reliability. Reliability Engineering and System Safety 2014; 123: 137-144, https://doi.org/10.1016/j.ress....
 
10.
Forrester A I J, Sóbester A, Keane A J. Engineering design via surrogate modelling. Chicheste: John Wiley & Sons, 2008.
 
11.
Grooteman F. Adaptive radial-based importance sampling method for structural reliability. Structural Safety 2008; 30: 533-542,https://doi.org/10.1016/j.stru....
 
12.
Guo S X, Lu Z Z, Feng Y S. A non-probabilistic model of structural reliability based on interval analysis. Chinese Journal of Computational Mechanics 2001; 18(1): 56-60. (In Chinese).
 
13.
Guo S X, Zhang L, Li Y. Procedures for computing the non-probabilistic reliability index of uncertain structures. Chinese Journal of Computational Mechanics, 2005; 22(2): 227-231. (In Chinese).
 
14.
Jiang C, Fu C, Ni B, et al. Interval arithmetic operations for uncertainty analysis with correlated interval variables. Acta Mechanica Sinica 2016; 32: 743-752, https://doi.org/10.1007/s10409....
 
15.
Jiang C, Han X, Lu G Y, et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Computer Methods in Applied Mechanics and Engineering 2011; 200(33-36): 2528-2546, https://doi.org/10.1016/j.cma.....
 
16.
Jiang C, Zhang Q F, Han X et al. A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model. Acta Mechanica 2014; 225: 383-395, https://doi.org/10.1108/MMMS-0....
 
17.
Jiang T, Chen J J, Xu Y L. A semi-analytic method for calculating non-probabilistic reliability index based on interval models. Applied Mathematical Modelling 2007; 31(7): 1362-1370, https://doi.org/10.1016/j.apm.....
 
18.
Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions. Journal of Global Optimization 1998;13: 455-492, https://doi.org/ 10.1023/A:1008306431147.
 
19.
Kumar V, Kumar G, Singh R K, et al. Degrading systems availability analysis: analytical semi-Markov approach. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2021; 23(1): 195-208, https://doi.org/10.17531/ein.2....
 
20.
Lemaire M. Structural reliability. Hoboken: John Wiley & Sons, 2009.
 
21.
Meng Z, Zhang Z, Zhang D, et al. An active learning method combining Kriging and accelerated chaotic single loop approach (AKACSLA) for reliability-based design optimization. Computer Methods in Applied Mechanics and Engineering 2019; 357: 112570, https://doi.org/10.1016/j.cma.....
 
22.
Nie X B, Li H B. A direct integration-based structural reliability analysis method using non-probabilistic convex model. Journal of Mechanical Science and Technology 2018; 32(11): 5063-5068, https://doi.org/10.1007/s12206....
 
23.
Schöbi R, Sudret B. Structural reliability analysis for p-boxes using multi-level meta-models. Probabilistic Engineering Mechanics 2017; 48: 27-38, https://doi.org/10.1016/ j.probengmech.2017.04.001.
 
24.
Teixeira R, Nogal M, Connor A O, et al. Reliability assessment with density scanned adaptive kriging. Reliability Engineering and System Safety 2020; 199: 106908, https://doi.org/10.1016/j.ress....
 
25.
Wang C, Matthies H G. Epistemic uncertainty-based reliability analysis for engineering system with hybrid evidence and fuzzy variables. Computer Methods in Applied Mechanics and Engineering 2019; 355: 438-455, https://doi.org/10.1016/j.cma.....
 
26.
Wang L, Kodiyalam S. An efficient method for probabilistic and robust design with non-normal distributions. In Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, 22–25, April, 2002.
 
27.
Wang Z, Shafieezadeh A. On confidence intervals for failure probability estimates in kriging-based reliability analysis. Reliability Engineering and System Safety 2020; 196: 106758, https://doi.org/10.1016/j.ress....
 
28.
Xiao M, Zhang J H, Gao L, et al. An efficient kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability. Structural and Multidisciplinary Optimization 2019; 59(6): 2077-2029, https://doi.org/10.1007/s00158....
 
29.
Xiao M, Zhang J H, Gao L. A system active learning Kriging method for system reliability-based design optimization with a multiple response model. Reliability Engineering and System Safety 2020; 199: 106935, https://doi.org/10.1016/j.ress....
 
30.
Xiao N C, Huang H Z, Li Y F, et al. Non-probabilistic reliability sensitivity analysis of the model of structural systems with interval variables whose state of dependence is determined by constraints. Journal of Risk and Reliability 2013; 227(5): 491-498, https://doi.org/10.1177/174800....
 
31.
Xiao N C, Yuan K, Zhou C N. Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables. Computer Methods in Applied Mechanics and Engineering 2020; 359:112649, https://doi.org/10.1016/ j.cma.2019.112649.
 
32.
Xiao N C, Zuo M J, Zhou C. A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis. Reliability Engineering and System Safety 2018; 169: 330-338, https://doi.org/10.1016/j.ress....
 
33.
Yang Z M, Zhang Y J, Meng W J, et al. A convex model approach for structure non-probabilistic reliability analysis. Journal of Risk and Reliability 2017; 231(5): 508-515, https://doi.org/10.1177/174800....
 
34.
Zhang D Q, Zhang N, Ye N, et al. Hybrid learning algorithm of radial basis function networks for reliability analysis. IEEE Transaction on Reliability 2020; https://doi.org/10.1109/TR.202....
 
35.
Zhang X F, Wang L, Sørensen J D. REIF: A novel active learning function toward adaptive kriging surrogate models for structural reliability analysis. Reliability Engineering and System Safety 2019; 185: 440-454, https://doi.org/10.1016/j.ress....
 
36.
Zhou C, Xiao N C, Zuo M, et al. AK-PDF: an active learning method combining kriging and probability density function for efficient reliability analysis. Journal of Risk and Reliability 2020; 234(3): 536-549, https://doi.org/10.1177/174800....
 
 
CITATIONS (6):
1.
Hybrid active learning method for non-probabilistic reliability analysis with multi-super-ellipsoidal model
Linxiong Hong, Huacong Li, Jiangfeng Fu, Jia Li, Kai Peng
Reliability Engineering & System Safety
 
2.
A novel safety measure with random and fuzzy variables and its solution by combining Kriging with truncated candidate region
Xiaoyu Huang, Pan Wang, Huanhuan Hu, Haihe Li, Lei Li
Aerospace Science and Technology
 
3.
Non-Probabilistic Reliability Bounds Method for Series Structural Systems Considering Redundant Failure Modes
Xinzhou Qiao, Fan Zhang, Jiangbin Zhao, Xiurong Fang
Applied Sciences
 
4.
A non-probabilistic convex polyhedron model for reliability analysis of structures with multiple failure modes and correlated uncertainties based on limited data
Zhiping Qiu, Haijun Tang, Bo Zhu
Acta Mechanica Sinica
 
5.
Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion
Yi‐Chuan Fang, Yong‐Juan Wang, Jin‐Long Sha, Tong‐Guang Gu
Quality and Reliability Engineering International
 
6.
Evaluation of a reliability index for steel trusses to the deflection criterion with interval uncertainty of data
Sergey Solovev, Alexander Inkov, Anastasia Soloveva
Structural Mechanics of Engineering Constructions and Buildings
 
eISSN:2956-3860
ISSN:1507-2711
Journals System - logo
Scroll to top