IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v173y2018icp105-115.html
   My bibliography  Save this article

Generalized Reliability Importance Measure (GRIM) using Gaussian mixture

Author

Listed:
  • Kim, Taeyong
  • Song, Junho

Abstract

In structural reliability analysis, it is often desirable to evaluate the relative contributions of random variables to the variability of the limit-state function in the failure domain. Based on the relative contributions, one can effectively reduce the dimension of the reliability problem or obtain useful insight and information. However, existing reliability importance measures, which are available as a by-product of reliability analysis by first-order reliability method (FORM), may not capture the contributions of random variables accurately when the limit-state surface shows a large curvature around the design point or multiple critical subdomains exist in the failure domain. To address the issue, this paper proposes a Generalized Reliability Importance Measure (GRIM) that can deal with multiple critical failure regions, large curvatures of limit-state surfaces and the correlation between the input random variables. By introducing Gaussian mixture and the regional participation factor, the failure domain is divided into several subdomains, and the relative contributions of random variables in each critical domain are evaluated. To facilitate the computations of GRIMs, the cross-entropy-based adaptive importance sampling technique (CE-AIS-GM) is employed to identify the locations of critical subdomains, their relative contributions and corresponding importance vectors. Eight numerical examples covering a variety of component and system reliability problems demonstrate the proposed method and its merits. The test results confirm robust performance against the number of important regions or the dimension. The proposed GRIMs and computational procedure are expected to provide more reliable measures for a wide range of component and system reliability problems. The supporting source code and data are available for download at https://github.com/TyongKim/GRIM.

Suggested Citation

  • Kim, Taeyong & Song, Junho, 2018. "Generalized Reliability Importance Measure (GRIM) using Gaussian mixture," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 105-115.
    • Handle: RePEc:eee:reensy:v:173:y:2018:i:c:p:105-115
    DOI: 10.1016/j.ress.2018.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017308384
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2018.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    2. Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.
    3. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    4. Zhang, Z. & Jiang, C. & Wang, G.G. & Han, X., 2015. "First and second order approximate reliability analysis methods using evidence theory," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 40-49.
    5. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    6. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    7. Bansal, Sahil & Cheung, Sai Hung, 2017. "On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 583-594.
    8. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    9. Liu, Wang-Sheng & Cheung, Sai Hung, 2017. "Reliability based design optimization with approximate failure probability function in partitioned design space," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 602-611.
    10. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
    11. Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Papaioannou, Iason & Straub, Daniel, 2021. "Variance-based reliability sensitivity analysis and the FORM α-factors," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    2. Straub, Daniel & Ehre, Max & Papaioannou, Iason, 2022. "Decision-theoretic reliability sensitivity," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    3. Wang, Jinsheng & Xu, Guoji & Yuan, Peng & Li, Yongle & Kareem, Ahsan, 2024. "An efficient and versatile Kriging-based active learning method for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    4. Ye, Zhenggeng & Yang, Hui & Cai, Zhiqiang & Si, Shubin & Zhou, Fuli, 2021. "Performance evaluation of serial-parallel manufacturing systems based on the impact of heterogeneous feedstocks on machine degradation," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Lyu, Dong & Si, Shubin, 2020. "Dynamic importance measure for the K-out-of-n: G system under repeated random load," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    6. Yadong Zhang & Chao Zhang & Shaoping Wang & Rentong Chen & Mileta M. Tomovic, 2022. "Performance Degradation Based on Importance Change and Application in Dissimilar Redundancy Actuation System," Mathematics, MDPI, vol. 10(5), pages 1-15, March.
    7. Lyu, Dong & Si, Shubin, 2021. "Importance measure for K-out-of-n: G systems under dynamic random load considering strength degradation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Ehre, Max & Papaioannou, Iason & Straub, Daniel, 2020. "A framework for global reliability sensitivity analysis in the presence of multi-uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    9. Zhao, Jiangbin & Si, Shubin & Cai, Zhiqiang & Guo, Peng & Zhu, Wenjin, 2020. "Mission success probability optimization for phased-mission systems with repairable component modules," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    10. Cheng, Jin & Wang, Jian & Wu, Xuezhou & Wang, Shuo, 2019. "An improved polynomial-based nonlinear variable importance measure and its application to degradation assessment for high-voltage transformer under imbalance data," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 175-191.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tatsuya Sakurahara & Seyed Reihani & Ernie Kee & Zahra Mohaghegh, 2020. "Global importance measure methodology for integrated probabilistic risk assessment," Journal of Risk and Reliability, , vol. 234(2), pages 377-396, April.
    2. Ehre, Max & Papaioannou, Iason & Straub, Daniel, 2020. "Global sensitivity analysis in high dimensions with PLS-PCE," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    3. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Margins associated with loss of assured safety for systems with multiple weak links and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. Wei, Pengfei & Liu, Fuchao & Tang, Chenghu, 2018. "Reliability and reliability-based importance analysis of structural systems using multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 183-195.
    5. Zhai, Qingqing & Yang, Jun & Xie, Min & Zhao, Yu, 2014. "Generalized moment-independent importance measures based on Minkowski distance," European Journal of Operational Research, Elsevier, vol. 239(2), pages 449-455.
    6. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.
    7. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    8. Shang, Xiaobing & Su, Li & Fang, Hai & Zeng, Bowen & Zhang, Zhi, 2023. "An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    9. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    10. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    11. Zio, E. & Pedroni, N., 2012. "Monte Carlo simulation-based sensitivity analysis of the model of a thermal–hydraulic passive system," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 90-106.
    12. Hou, Tianfeng & Nuyens, Dirk & Roels, Staf & Janssen, Hans, 2019. "Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    13. Yun, Wanying & Lu, Zhenzhou & Jiang, Xian, 2019. "An efficient method for moment-independent global sensitivity analysis by dimensional reduction technique and principle of maximum entropy," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 174-182.
    14. Tang, Zhang-Chun & Zuo, Ming J. & Xiao, Ningcong, 2016. "An efficient method for evaluating the effect of input parameters on the integrity of safety systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 111-123.
    15. Emanuele Borgonovo & Gordon B. Hazen & Elmar Plischke, 2016. "A Common Rationale for Global Sensitivity Measures and Their Estimation," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1871-1895, October.
    16. McFarland, John & DeCarlo, Erin, 2020. "A Monte Carlo framework for probabilistic analysis and variance decomposition with distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    17. Jiang, Chen & Qiu, Haobo & Yang, Zan & Chen, Liming & Gao, Liang & Li, Peigen, 2019. "A general failure-pursuing sampling framework for surrogate-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 47-59.
    18. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    19. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    20. Zhang, Kaichao & Lu, Zhenzhou & Cheng, Kai & Wang, Laijun & Guo, Yanling, 2020. "Global sensitivity analysis for multivariate output model and dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 204(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:173:y:2018:i:c:p:105-115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.