IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v233y2019i3p487-502.html
   My bibliography  Save this article

A sparse surrogate model for structural reliability analysis based on the generalized polynomial chaos expansion

Author

Listed:
  • Qian Liu
  • Xufang Zhang
  • Xianzhen Huang

Abstract

The reliability analysis of a structural system is typically evaluated based on a multivariate model that describes the underlying mechanistic relationship between the system’s input and output random variables. This is the need to develop an effective surrogate model to mimic the input–output relationship as the Monte Carlo simulation–based on the mechanistic model might be computationally intensive. In this regard, the article presents a sparse regression method for structural reliability analysis based on the generalized polynomial chaos expansion. However, results from the global sensitivity analysis have justified that it is unnecessary to contain all polynomial terms in the surrogate model, instead of comprising a rather small number of principle components only. One direct benefit of the sparse approximation allows utilizing a small number of training samples to calibrate the surrogate model, bearing in mind that the required sample size is positively proportional to the number of unknowns in regression analysis. Therefore, by utilizing the standard polynomial chaos basis functions to constitute an explanatory dictionary, an adaptive sparse regression approach characterized by introducing the most significant explanatory variable in each iteration is presented. A statistical approach for detecting and excluding spuriously explanatory polynomials is also introduced to maintain the high sparsity of the meta-modeling result. Combined with a variety of low-discrepancy schemes in generating training samples, structural reliability and global sensitivity analysis of originally true but computationally demanding models are alternatively realized based on the sparse surrogate method in conjunction with the brutal Monte Carlo simulation method. Numerical examples are carried out to demonstrate the applicability of the sparse regression approach to structural reliability problems. Results have shown that the proposed method is an effective, non-intrusive approach to deal with uncertainty analysis of various structural systems.

Suggested Citation

  • Qian Liu & Xufang Zhang & Xianzhen Huang, 2019. "A sparse surrogate model for structural reliability analysis based on the generalized polynomial chaos expansion," Journal of Risk and Reliability, , vol. 233(3), pages 487-502, June.
    • Handle: RePEc:sae:risrel:v:233:y:2019:i:3:p:487-502
    DOI: 10.1177/1748006X18804047
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X18804047
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X18804047?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Qyyum, Muhammad Abdul & Duong, Pham Luu Trung & Minh, Le Quang & Lee, Sanggyu & Lee, Moonyong, 2019. "Dual mixed refrigerant LNG process: Uncertainty quantification and dimensional reduction sensitivity analysis," Applied Energy, Elsevier, vol. 250(C), pages 1446-1456.
    3. Jung, WoongHee & Taflanidis, Alexandros A., 2023. "Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    4. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    5. Sudret, B. & Mai, C.V., 2015. "Computing derivative-based global sensitivity measures using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 241-250.
    6. Li, Chenzhao & Mahadevan, Sankaran, 2016. "An efficient modularized sample-based method to estimate the first-order Sobol׳ index," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 110-121.
    7. Zhang, Xufang & Wang, Lei & Sørensen, John Dalsgaard, 2019. "REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 440-454.
    8. Wei, Pengfei & Song, Jingwen & Lu, Zhenzhou & Yue, Zhufeng, 2016. "Time-dependent reliability sensitivity analysis of motion mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 107-120.
    9. Wu, Zeping & Wang, Wenjie & Wang, Donghui & Zhao, Kun & Zhang, Weihua, 2019. "Global sensitivity analysis using orthogonal augmented radial basis function," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 291-302.
    10. Wang, Zhenqiang & Jia, Gaofeng, 2023. "Extended sample-based approach for efficient sensitivity analysis of group of random variables," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    11. Konakli, Katerina & Sudret, Bruno, 2016. "Global sensitivity analysis using low-rank tensor approximations," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 64-83.
    12. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    13. Wang, Lei & Zhang, Xufang & Zhou, Yangjunjian, 2018. "An effective approach for kinematic reliability analysis of steering mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 62-76.

    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:sae:risrel:v:233:y:2019:i:3:p:487-502. 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: SAGE Publications (email available below). General contact details of provider: .

    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.