IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v219y2022ics0951832021006967.html
   My bibliography  Save this article

Probabilistic characterization of soil properties based on the maximum entropy method from fractional moments: Model development, case study, and application

Author

Listed:
  • Deng, Jian

Abstract

In probabilistic reliability analysis for geotechnical engineering applications, determining the underlying probability distributions of soil properties and corresponding parameters from observed data is a critical initial step because subsequent risk and reliability analyses depend upon these evaluations. Conventionally, the choice of probability distribution is dictated by subjective familiarity with a classical (e.g., normal or lognormal) distribution. This paper proposes an objective and unbiased method to estimate probability distributions of a soil property using the maximum entropy method from fractional moments of observed data. The probability distribution is based on the concept of maximum entropy and is free from the assumptions of classical distributions. A case study is presented for the undrained shear strength of soil in the Nipigon River landslide area, Ontario, Canada. The maximum entropy distributions of the soil property from fractional moments are compared to the frequency histogram, normal and lognormal distributions, and maximum entropy distributions from integral moments. The maximum entropy distribution with two-order fractional moments, almost equivalent to that with four-order integral moments, is verified with the chi-square goodness-of-fit test. Issues related to overfitting/underfitting, minimum sample size, fractional orders, negative moments, and limitations are discussed. Application of the method to geotechnical reliability analysis is illustrated.

Suggested Citation

  • Deng, Jian, 2022. "Probabilistic characterization of soil properties based on the maximum entropy method from fractional moments: Model development, case study, and application," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:reensy:v:219:y:2022:i:c:s0951832021006967
    DOI: 10.1016/j.ress.2021.108218
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832021006967
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2021.108218?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. El Masri, Maxime & Morio, Jérôme & Simatos, Florian, 2021. "Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. 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).
    3. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    4. Wang, Yuhao & Pang, Yutian & Chen, Oliver & Iyer, Hari N. & Dutta, Parikshit & Menon, P.K. & Liu, Yongming, 2021. "Uncertainty quantification and reduction in aircraft trajectory prediction using Bayesian-Entropy information fusion," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    5. Xiao, Sinan & Lu, Zhenzhou & Xu, Liyang, 2016. "A new effective screening design for structural sensitivity analysis of failure probability with the epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 1-14.
    6. Zarghami, Seyed Ashkan & Dumrak, Jantanee, 2021. "Unearthing vulnerability of supply provision in logistics networks to the black swan events: Applications of entropy theory and network analysis," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    7. 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.
    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. Oluwatuyi, Opeyemi E. & Ng, Kam & Wulff, Shaun S., 2023. "Improved resistance prediction and reliability for bridge pile foundation in shales through optimal site investigation plans," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    2. Yu Wang & Ganqiong Li & Shengwei Wang & Yongen Zhang & Denghua Li & Han Zhou & Wen Yu & Shiwei Xu, 2022. "A Comprehensive Evaluation of Benefit of High-Standard Farmland Development in China," Sustainability, MDPI, vol. 14(16), pages 1-13, August.
    3. Xu, Jun & Song, Jinheng & Yu, Quanfu & Kong, Fan, 2023. "Generalized distribution reconstruction based on the inversion of characteristic function curve for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

    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. Chiron, Marie & Genest, Christian & Morio, Jérôme & Dubreuil, Sylvain, 2023. "Failure probability estimation through high-dimensional elliptical distribution modeling with multiple importance sampling," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    2. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    3. Wen, Tao & Gao, Qiuya & Chen, Yu-wang & Cheong, Kang Hao, 2022. "Exploring the vulnerability of transportation networks by entropy: A case study of Asia–Europe maritime transportation network," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    4. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    5. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    6. Fabio Canova & Christian Matthes, 2021. "Dealing with misspecification in structural macroeconometric models," Quantitative Economics, Econometric Society, vol. 12(2), pages 313-350, May.
    7. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    8. Zhongqi Liang & Qihua Wang & Yuting Wei, 2022. "Robust model selection with covariables missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 539-557, June.
    9. HAEDO, Christian & MOUCHART , Michel & ,, 2013. "Specialized agglomerations with areal data: model and detection," LIDAM Discussion Papers CORE 2013060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Chen, Jun-Yu & Feng, Yun-Wen & Teng, Da & Lu, Cheng & Fei, Cheng-Wei, 2022. "Support vector machine-based similarity selection method for structural transient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    11. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    12. Schomaker Michael & Heumann Christian, 2011. "Model Averaging in Factor Analysis: An Analysis of Olympic Decathlon Data," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(1), pages 1-15, January.
    13. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    14. Tumala, Mohammed M & Olubusoye, Olusanya E & Yaaba, Baba N & Yaya, OlaOluwa S & Akanbi, Olawale B, 2017. "Forecasting Nigerian Inflation using Model Averaging methods: Modelling Frameworks to Central Banks," MPRA Paper 88754, University Library of Munich, Germany, revised Feb 2018.
    15. José Manuel Cordero Ferrera & Manuel Muñiz Pérez & Rosa Simancas Rodríguez, 2015. "The influence of socioeconomic factors on cognitive and non-cognitive educational outcomes," Investigaciones de Economía de la Educación volume 10, in: Marta Rahona López & Jennifer Graves (ed.), Investigaciones de Economía de la Educación 10, edition 1, volume 10, chapter 21, pages 413-438, Asociación de Economía de la Educación.
    16. Satoshi Hattori & Masayuki Henmi, 2014. "Stratified doubly robust estimators for the average causal effect," Biometrics, The International Biometric Society, vol. 70(2), pages 270-277, June.
    17. Naoya Sueishi & Arihiro Yoshimura, 2017. "Focused Information Criterion for Series Estimation in Partially Linear Models," The Japanese Economic Review, Japanese Economic Association, vol. 68(3), pages 352-363, September.
    18. Liao, Jun & Zou, Guohua, 2020. "Corrected Mallows criterion for model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Tune H Pers & Anders Albrechtsen & Claus Holst & Thorkild I A Sørensen & Thomas A Gerds, 2009. "The Validation and Assessment of Machine Learning: A Game of Prediction from High-Dimensional Data," PLOS ONE, Public Library of Science, vol. 4(8), pages 1-8, August.
    20. Miao Han & Liuquan Sun & Yutao Liu & Jun Zhu, 2018. "Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 523-547, July.

    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:219:y:2022:i:c:s0951832021006967. 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.