IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v172y2018icp12-24.html
   My bibliography  Save this article

Bayesian model updating with summarized statistical and reliability data

Author

Listed:
  • VanDerHorn, Eric
  • Mahadevan, Sankaran

Abstract

The accuracy of model-based reliability analysis is affected by the uncertainty regarding the model parameters used to predict the behavior of the engineering system. The uncertainty in the model parameters can be reduced by combining prior knowledge about the parameters with observed data regarding system inputs and outputs. In some cases, the information about the observations is only available as abstracted data, where the original raw data have been reduced to a summarized representation. Common forms of abstracted data include summary statistics, such as the mean and variance for continuous variables and observed frequencies for discrete variables. In the context of reliability analysis, a common form of available information is summarized reliability data for various mechanical components (e.g., failure rates or failure probabilities) instead of detailed actual test data. This paper presents a methodology for updating the model parameters using these abstracted data forms through a Bayesian network. First, the concept of a statistics function is developed and linked to the abstracted data forms. The concept of arc reversal is then exploited to transform the Bayesian network to a form that can be used to incorporate the statistics function and thereby enable the updating of the model parameters. Several numerical examples are used to demonstrate the applicability and generality of the proposed method for several different forms of abstracted data.

Suggested Citation

  • VanDerHorn, Eric & Mahadevan, Sankaran, 2018. "Bayesian model updating with summarized statistical and reliability data," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 12-24.
    • Handle: RePEc:eee:reensy:v:172:y:2018:i:c:p:12-24
    DOI: 10.1016/j.ress.2017.11.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017303903
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2017.11.023?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. Nunes Matthew A & Balding David J, 2010. "On Optimal Selection of Summary Statistics for Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, September.
    2. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    3. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    4. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 814-824.
    5. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    6. Ross D. Shachter, 1988. "Probabilistic Inference and Influence Diagrams," Operations Research, INFORMS, vol. 36(4), pages 589-604, August.
    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. Zhang, Caiping & Wang, Yubin & Gao, Yang & Wang, Fang & Mu, Biqiang & Zhang, Weige, 2019. "Accelerated fading recognition for lithium-ion batteries with Nickel-Cobalt-Manganese cathode using quantile regression method," Applied Energy, Elsevier, vol. 256(C).
    2. Liu, Yushan & Li, Luyi & Chang, Zeming, 2023. "Efficient Bayesian model updating for dynamic systems," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    3. Greco, Salvatore F. & Podofillini, Luca & Dang, Vinh N., 2021. "A Bayesian model to treat within-category and crew-to-crew variability in simulator data for Human Reliability Analysis," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    4. Wang, Yuhao & Liu, Yongming, 2020. "Bayesian entropy network for fusion of different types of information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    5. Zheng, Yi-Xuan & Xiahou, Tangfan & Liu, Yu & Xie, Chaoyang, 2021. "Structure function learning of hierarchical multi-state systems with incomplete observation sequences," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    6. Zhou, Daoqing & He, Jingjing & Du, Yi-Mu & Sun, C.P. & Guan, Xuefei, 2021. "Probabilistic information fusion with point, moment and interval data in reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    7. Lee, Seulbi & Choi, Minji & Lee, Hyun-Soo & Park, Moonseo, 2020. "Bayesian network-based seismic damage estimation for power and potable water supply systems," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    8. Tohme, Tony & Vanslette, Kevin & Youcef-Toumi, Kamal, 2020. "A generalized Bayesian approach to model calibration," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. 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. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
    2. Florian Maire & Nial Friel & Pierre ALQUIER, 2017. "Informed Sub-Sampling MCMC: Approximate Bayesian Inference for Large Datasets," Working Papers 2017-40, Center for Research in Economics and Statistics.
    3. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    4. Christopher C. Drovandi & Anthony N. Pettitt, 2013. "Bayesian Experimental Design for Models with Intractable Likelihoods," Biometrics, The International Biometric Society, vol. 69(4), pages 937-948, December.
    5. Baey, Charlotte & Smith, Henrik G. & Rundlöf, Maj & Olsson, Ola & Clough, Yann & Sahlin, Ullrika, 2023. "Calibration of a bumble bee foraging model using Approximate Bayesian Computation," Ecological Modelling, Elsevier, vol. 477(C).
    6. Jonathan U Harrison & Ruth E Baker, 2020. "An automatic adaptive method to combine summary statistics in approximate Bayesian computation," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-21, August.
    7. Prangle Dennis & Fearnhead Paul & Cox Murray P. & Biggs Patrick J. & French Nigel P., 2014. "Semi-automatic selection of summary statistics for ABC model choice," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 67-82, February.
    8. Buzbas, Erkan O. & Rosenberg, Noah A., 2015. "AABC: Approximate approximate Bayesian computation for inference in population-genetic models," Theoretical Population Biology, Elsevier, vol. 99(C), pages 31-42.
    9. Soubeyrand Samuel & Carpentier Florence & Guiton François & Klein Etienne K., 2013. "Approximate Bayesian computation with functional statistics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 17-37, March.
    10. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
    11. Creel, Michael & Kristensen, Dennis, 2016. "On selection of statistics for approximate Bayesian computing (or the method of simulated moments)," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 99-114.
    12. Wilkinson Richard David, 2013. "Approximate Bayesian computation (ABC) gives exact results under the assumption of model error," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(2), pages 129-141, May.
    13. Nakagome Shigeki & Fukumizu Kenji & Mano Shuhei, 2013. "Kernel approximate Bayesian computation in population genetic inferences," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 667-678, December.
    14. Michael Stocks & Mathieu Siol & Martin Lascoux & Stéphane De Mita, 2014. "Amount of Information Needed for Model Choice in Approximate Bayesian Computation," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-13, June.
    15. Soubeyrand, Samuel & Haon-Lasportes, Emilie, 2015. "Weak convergence of posteriors conditional on maximum pseudo-likelihood estimates and implications in ABC," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 84-92.
    16. Silk Daniel & Filippi Sarah & Stumpf Michael P. H., 2013. "Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 603-618, October.
    17. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    18. Grazzini, Jakob & Richiardi, Matteo G. & Tsionas, Mike, 2017. "Bayesian estimation of agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 26-47.
    19. Camilo Alberto Cárdenas-Hurtado & Aaron Levi Garavito-Acosta & Jorge Hernán Toro-Córdoba, 2018. "Asymmetric Effects of Terms of Trade Shocks on Tradable and Non-tradable Investment Rates: The Colombian Case," Borradores de Economia 1043, Banco de la Republica de Colombia.
    20. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 171-181.

    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:172:y:2018:i:c:p:12-24. 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.