IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v170y2018icp175-190.html
   My bibliography  Save this article

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Author

Listed:
  • Palar, Pramudita Satria
  • Zuhal, Lavi Rizki
  • Shimoyama, Koji
  • Tsuchiya, Takeshi

Abstract

The presence of uncertainties is inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations is required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the low-fidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.

Suggested Citation

  • Palar, Pramudita Satria & Zuhal, Lavi Rizki & Shimoyama, Koji & Tsuchiya, Takeshi, 2018. "Global sensitivity analysis via multi-fidelity polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 175-190.
    • Handle: RePEc:eee:reensy:v:170:y:2018:i:c:p:175-190
    DOI: 10.1016/j.ress.2017.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016304872
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2017.10.013?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. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    2. Garcia-Cabrejo, Oscar & Valocchi, Albert, 2014. "Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 25-36.
    3. Bichon, Barron J. & McFarland, John M. & Mahadevan, Sankaran, 2011. "Efficient surrogate models for reliability analysis of systems with multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1386-1395.
    4. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    5. Crestaux, Thierry & Le Maıˆtre, Olivier & Martinez, Jean-Marc, 2009. "Polynomial chaos expansion for sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1161-1172.
    6. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    7. Buzzard, Gregery T., 2012. "Global sensitivity analysis using sparse grid interpolation and polynomial chaos," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 82-89.
    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. Yao, Wen & Zheng, Xiaohu & Zhang, Jun & Wang, Ning & Tang, Guijian, 2023. "Deep adaptive arbitrary polynomial chaos expansion: A mini-data-driven semi-supervised method for uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. 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).
    3. Thapa, Mishal & Missoum, Samy, 2022. "Uncertainty quantification and global sensitivity analysis of composite wind turbine blades," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    4. Du, Weiqi & Luo, Yuanxin & Wang, Yongqin, 2019. "Time-variant reliability analysis using the parallel subset simulation," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 250-257.

    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. 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.
    2. 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.
    3. Brown, S. & Beck, J. & Mahgerefteh, H. & Fraga, E.S., 2013. "Global sensitivity analysis of the impact of impurities on CO2 pipeline failure," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 43-54.
    4. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.
    5. Oladyshkin, Sergey & Nowak, Wolfgang, 2018. "Incomplete statistical information limits the utility of high-order polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 137-148.
    6. Oladyshkin, S. & Nowak, W., 2012. "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 179-190.
    7. Anstett-Collin, F. & Goffart, J. & Mara, T. & Denis-Vidal, L., 2015. "Sensitivity analysis of complex models: Coping with dynamic and static inputs," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 268-275.
    8. Alexanderian, Alen & Gremaud, Pierre A. & Smith, Ralph C., 2020. "Variance-based sensitivity analysis for time-dependent processes," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    9. Steiner, M. & Bourinet, J.-M. & Lahmer, T., 2019. "An adaptive sampling method for global sensitivity analysis based on least-squares support vector regression," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 323-340.
    10. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    11. Haro Sandoval, Eduardo & Anstett-Collin, Floriane & Basset, Michel, 2012. "Sensitivity study of dynamic systems using polynomial chaos," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 15-26.
    12. Daneshkhah, Alireza & Bedford, Tim, 2013. "Probabilistic sensitivity analysis of system availability using Gaussian processes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 82-93.
    13. Attar, Peter J. & Vedula, Prakash, 2013. "On convergence of moments in uncertainty quantification based on direct quadrature," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 119-125.
    14. Matieyendou Lamboni, 2020. "Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices," Statistical Papers, Springer, vol. 61(5), pages 1939-1970, October.
    15. Cheng, Kai & Lu, Zhenzhou, 2018. "Sparse polynomial chaos expansion based on D-MORPH regression," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 17-30.
    16. Gaspar, B. & Teixeira, A.P. & Guedes Soares, C., 2017. "Adaptive surrogate model with active refinement combining Kriging and a trust region method," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 277-291.
    17. Lambert, Romain S.C. & Lemke, Frank & Kucherenko, Sergei S. & Song, Shufang & Shah, Nilay, 2016. "Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 42-54.
    18. Deman, G. & Konakli, K. & Sudret, B. & Kerrou, J. & Perrochet, P. & Benabderrahmane, H., 2016. "Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 156-169.
    19. Turati, Pietro & Pedroni, Nicola & Zio, Enrico, 2017. "Simulation-based exploration of high-dimensional system models for identifying unexpected events," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 317-330.
    20. Pronzato, Luc, 2019. "Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 93-109.

    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:170:y:2018:i:c:p:175-190. 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.