0
Research Papers: Design Automation

A Radial-Based Centralized Kriging Method for System Reliability Assessment

[+] Author and Article Information
Yao Wang

China Academy of Launch Vehicle Technology,
Beijing 100076, China
e-mail: wangyao87@hotmail.com

Dongpao Hong

China Academy of Launch Vehicle Technology,
Beijing 100076, China
e-mail: dp_hong@hotmail.com

Xiaodong Ma

China Academy of Launch Vehicle Technology,
Beijing 100076, China
e-mail: ma_xiaodong@hotmail.com

Hairui Zhang

China Academy of Launch Vehicle Technology,
Beijing 100076, China
e-mail: zhang_hairui@hotmail.com

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 16, 2017; final manuscript received April 1, 2018; published online May 11, 2018. Assoc. Editor: Xiaoping Du.

J. Mech. Des 140(7), 071403 (May 11, 2018) (11 pages) Paper No: MD-17-1694; doi: 10.1115/1.4039919 History: Received October 16, 2017; Revised April 01, 2018

System reliability assessment is a challenging task when using computationally intensive models. In this work, a radial-based centralized Kriging method (RCKM) is proposed for achieving high efficiency and accuracy. The method contains two components: Kriging-based system most probable point (MPP) search and radial-based centralized sampling. The former searches for the system MPP by progressively updating Kriging models regardless of the nonlinearity of the performance functions. The latter refines the Kriging models with the training points (TPs) collected from pregenerated samples. It concentrates the sampling in the important high-probability density region. Both components utilize a composite criterion to identify the critical Kriging models for system failure. The final Kriging models are sufficiently accurate only at those sections of the limit states that bound the system failure region. Its efficiency and accuracy are demonstrated via application to three examples.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lin, Y. H. , Li, Y. F. , and Zio, E. , 2016, “ A Reliability Assessment Framework for Systems With Degradation Dependency by Combining Binary Decision Diagrams and Monte Carlo Simulation,” IEEE Trans. Syst. Man Cybern. Syst., 46(11), pp. 1556–1564. [CrossRef]
Huang, B. , and Du, X. , 2008, “ Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation,” Reliab. Eng. Syst. Saf., 93(2), pp. 325–336. [CrossRef]
Hu, Z. , and Du, X. , 2014, “ Lifetime Cost Optimization With Time-Dependent Reliability,” Eng. Optim., 46(10), pp. 1389–1410. [CrossRef]
Li, D. Q. , Jiang, S. H. , Wu, S. B. , Zhou, C. B. , and Zhang, L. M. , 2013, “ Modeling Multivariate Distributions Using Monte Carlo Simulation for Structural Reliability Analysis With Complex Performance Function,” Proc. Inst. Mech. Eng., Part O: J. Risk Reliab., 227(2), pp. 109–118.
Du, X. , and Hu, Z. , 2012, “ First Order Reliability Method With Truncated Random Variables,” ASME J. Mech. Des., 134(9), p. 091005. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ First Order Reliability Method for Time-Variant Problems Using Series Expansions,” Struct. Multidiscip. Optim., 51(1), pp. 1–21. [CrossRef]
Lee, I. , Noh, Y. , and Yoo, D. , 2012, “ A Novel Second-Order Reliability Method (SORM) Using Noncentral or Generalized Chi-Squared Distributions,” ASME J. Mech. Des., 134(10), p. 100912. [CrossRef]
Jin, R. , Chen, W. , and Simpson, T. W. , 2001, “ Comparative Studies of Metamodelling Techniques Under Multiple Modelling Criteria,” Struct. Multidiscip. Optim., 23(1), pp. 1–13. [CrossRef]
Wang, Y. , Zeng, S. , and Guo, J. , 2013, “ Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos,” J. Appl. Math., 2013, p. 513261.
Du, X. , and Sudjianto, A. , 2004, “ First Order Saddlepoint Approximation for Reliability Analysis,” AIAA J., 42(6), pp. 1199–1207. [CrossRef]
Bichon, B. J. , Eldred, M. S. , Swiler, L. P. , Mahadevan, S. , and McFarland, J. M. , 2008, “ Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions,” AIAA J., 46(10), pp. 2459–2468. [CrossRef]
Jones, D. R. , Schonlau, M. , and Welch, W. J. , 1998, “ Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492. [CrossRef]
Echard, B. , Gayton, N. , and Lemaire, M. , 2011, “ AK-MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation,” Struct. Saf., 33(2), pp. 145–154. [CrossRef]
Bucher, C. G. , 1988, “ Adaptive Sampling—An Iterative Fast Monte Carlo Procedure,” Struct. Saf., 5(2), pp. 119–126. [CrossRef]
Bichon, B. J. , McFarland, J. M. , and Mahadevan, S. , 2011, “ Efficient Surrogate Models for Reliability Analysis of Systems With Multiple Failure Modes,” Reliab. Eng. Syst. Saf., 96(10), pp. 1386–1395. [CrossRef]
Ditlevsen, O. , 1979, “ Narrow Reliability Bounds for Structural Systems,” J. Struct. Mech., 7(4), pp. 453–472. [CrossRef]
Song, J. , and Der Kiureghian, A. , 2003, “ Bounds on System Reliability by Linear Programming,” J. Eng. Mech., 129(6), pp. 627–636. [CrossRef]
Wang, P. , Hu, C. , and Youn, B. D. , 2011, “ A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis,” ASME J. Mech. Des., 133(7), p. 071003. [CrossRef]
Youn, B. D. , and Wang, P. , 2009, “ Complementary Intersection Method for System Reliability Analysis,” ASME J. Mech. Des., 131(4), p. 041004. [CrossRef]
Wang, Z. , and Wang, P. , 2015, “ An Integrated Performance Measure Approach for System Reliability Analysis,” ASME J. Mech. Des., 137(2), p. 021406. [CrossRef]
Fauriat, W. , and Gayton, N. , 2014, “ AK-SYS: An Adaptation of the AK-MCS Method for System Reliability,” Reliab. Eng. Syst. Saf., 123, pp. 137–144. [CrossRef]
Zhu, Z. , and Du, X. , 2016, “ Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions,” ASME J. Mech. Des., 138(12), p. 121403. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis,” AMSE J. Mech. Des., 138(6), p. 061406. [CrossRef]
Martin, J. D. , and Simpson, T. W. , 2005, “ Use of Kriging Models to Approximate Deterministic Computer Models,” AIAA J., 43(4), pp. 853–863. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 137(5), p. 051401. [CrossRef]
Gablonsky, J. , 1998, “ An Implementation of the DIRECT Algorithm,” North Carolina State University, Raleigh, NC, Technical Report No. CRSC-TR98-29.
Echard, B. , Gayton, N. , Lemaire, M. , and Relun, N. , 2013, “ A Combined Importance Sampling and Kriging Reliability Method for Small Failure Probabilities With Time-Demanding Numerical Models,” Reliab. Eng. Syst. Saf., 111(2), pp. 232–240. [CrossRef]
Au, S. K. , and Beck, J. L. , 1999, “ A New Adaptive Importance Sampling Scheme for Reliability Calculations,” Struct. Saf., 21(2), pp. 135–158. [CrossRef]
Harbitz, A. , 1986, “ An Efficient Sampling Method for Probability of Failure Calculation,” Struct. Saf., 3(2), pp. 109–115. [CrossRef]
Grooteman, F. , 2008, “ Adaptive Radial-Based Importance Sampling Method for Structural Reliability,” Struct. Saf., 30(6), pp. 533–542. [CrossRef]
Lophaven, S. , Nielsen, H. , and Sondergaard, J. , 2002, “ DACE, a Matlab Kriging Toolbox, Version 2.0,” Technical University of Denmark, Lyngby, Denmark, Technical Report No. IMM-TR-2002-12. http://orbit.dtu.dk/en/publications/dace--a-matlab-kriging-toolbox-version-20(4988653d-4fc7-4ecb-a82e-62bfe44b0fd1)/export.html
McAllister, C. D. , and Simpson, T. W. , 2003, “ Multidisciplinary Robust Design Optimization of an Internal Combustion Engine,” ASME J. Mech. Des., 125(1), pp. 124–130. [CrossRef]
Liang, J. , Mourelatos, Z. P. , and Nikolaidis, E. , 2007, “ A Single-Loop Approach for System Reliability-Based Design Optimization,” ASME J. Mech. Des., 129(12), pp. 1215–1224. [CrossRef]
Nguyen, T. H. , Song, J. , and Paulino, G. H. , 2009, “ Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications,” ASME J. Mech. Des., 132(1), p. 011005. [CrossRef]
Du, X. , and Chen, W. , 2004, “ Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design,” ASME J. Mech. Des., 126(2), pp. 225–233. [CrossRef]
Youn, B. D. , Choi, K. K. , Yang, R. J. , and Gu, L. , 2003, “ Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact,” Struct. Multidiscip. Optim., 26(3–4), pp. 272–283.

Figures

Grahic Jump Location
Fig. 1

Iterations of the Kriging-based MPP searching for system reliability

Grahic Jump Location
Fig. 2

Illustration of the radial-based centralized sampling approach

Grahic Jump Location
Fig. 3

Limit state contours and multiple MPPs of example 1: (a) c = 3, (b) c = 4, (c) c = 5

Grahic Jump Location
Fig. 4

Resulting Kriging models and TPs for case 1 (c = 3). The solid lines represent the Kriging models that are the approximations of the dashed limit state contours for the two performance functions.

Grahic Jump Location
Fig. 5

Resulting Kriging models and TPs for case 2 (c = 4). The solid lines represent the Kriging models that are the approximations of the dashed limit state contours for the two performance functions.

Grahic Jump Location
Fig. 6

Resulting Kriging models and TPs for case 3 (c = 5). The solid lines represent the Kriging models that are the approximations of the dashed limit state contours for the two performance functions.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In