Dealing with Nonlattice Data in Three-Dimensional Probabilistic Site Characterization
Publication: Journal of Engineering Mechanics
Volume 147, Issue 5
Abstract
In site investigation, it is common to conduct some soundings to explore greater depths that are not explored by remaining soundings. This produces the scenario of nonlattice data, meaning that not all soundings measure identical depths. Recently in 2020, the first and third authors of the current paper developed a probabilistic site characterization method based on sparse Bayesian learning (SBL). This SBL method assumes lattice data (all soundings measure identical depths) to take advantage of the Kronecker-product derivations. These Kronecker-product derivations significantly improve computation efficiency, so the resulting SBL method can be scaled up to address full-scale three-dimensional problems. However, this SBL method is not applicable to nonlattice data, which are common in practice. The purpose of the current paper is to modify the SBL method developed in 2020 to accommodate nonlattice data, while retaining the crucial computational advantage of the Kronecker-product derivations. One real-world case study of underground stratification is used to demonstrate the usefulness of the modified method.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All codes of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors thank the members of the ISSMGE TC304 Committee for developing the database 304dB (http://140.112.12.21/issmge/Database_2010.htm) used in this study. The first author thanks the Ministry of Science and Technology (Taiwan) (106-2221-E-002-084-MY3).
References
Beck, J. L., and K. V. Yuen. 2004. “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech. 130 (2): 192–203. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(192).
Betz, W., I. Papaioannou, and D. Straub. 2016. “Transitional Markov Chain Monte Carlo: Observations and improvements.” J. Eng. Mech. 142 (5): 04016016. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001066.
Celeux, G., and J. Diebolt. 1986. “The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem.” Comput. Stat. Q. 2 (1): 73–82.
Ching, J., and Y. C. Chen. 2007. “Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection and model averaging.” J. Eng. Mech. 133 (7): 816–832. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(816).
Ching, J., W. H. Huang, and K. K. Phoon. 2020. “3D probabilistic site characterization by sparse Bayesian learning.” J. Eng. Mech. 146 (12): 04020134. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001859.
Ching, J., and K. K. Phoon. 2017. “Characterizing uncertain site-specific trend function by sparse Bayesian learning.” J. Eng. Mech. 143 (7): 04017028. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001240.
Ching, J., K. K. Phoon, A. W. Stuedlein, and M. Jaksa. 2019. “Identification of sample path smoothness in soil spatial variability.” Struct. Saf. 81 (Nov): 101870. https://doi.org/10.1016/j.strusafe.2019.101870.
Crisp, M. P., M. B. Jaksa, Y. L. Kuo, G. A. Fenton, and D. V. Griffiths. 2019. “A method for generating virtual soil profiles with complex, multi-layer stratigraphy.” Georisk 13 (2): 154–163. https://doi.org/10.1080/17499518.2018.1554817.
Firouzianbandpey, S., D. V. Griffiths, L. B. Ibsen, and L. V. Anderson. 2014. “Spatial correlation length of normalized cone data in sand: Case study in the north of Denmark.” Can. Geotech. J. 51 (8): 844–857. https://doi.org/10.1139/cgj-2013-0294.
Guttorp, P., and T. Gneiting. 2006. “Studies in the history of probability and statistics XLIX on the Matérn correlation family.” Biometrika 93 (4): 989–995. https://doi.org/10.1093/biomet/93.4.989.
Liu, W. F., Y. F. Leung, and M. K. Lo. 2017. “Integrated framework for characterization of spatial variability of geological profiles.” Can. Geotech. J. 54 (1): 47–58. https://doi.org/10.1139/cgj-2016-0189.
Lloret-Cabot, M., G. A. Fenton, and M. A. Hicks. 2014. “On the estimation of scale of fluctuation in geostatistics.” Georisk 8 (2): 129–140.
Neilsen, S. F. 2000. “The stochastic EM algorithm: Estimation and asymptotic results.” Bernoulli 6 (3): 457–489.
Nishimura, S., T. Shibata, T. Shuku, and K. Imaide. 2017. “Geostatistical analysis for identifying weak soil layers in dikes.” In Proc., Geotechnical Risk Assessment and Management, 529–538. Reston, VA: ASCE.
Robertson, P. K. 1990. “Soil classification using the cone penetration test.” Can. Geotech. J. 27 (1): 151–158. https://doi.org/10.1139/t90-014.
Robertson, P. K., and C. E. Wride. 1998. “Evaluating cyclic liquefaction potential using the cone penetration test.” Can. Geotech. J. 35 (3): 442–459. https://doi.org/10.1139/t98-017.
Shuku, T., and J. Ching. 2020. “Case studies on 2D/3D subsurface modeling using spare machine learning.” Int. J. Geoeng. Case Hist.
Shuku, T., K. K. Phoon, and I. Yoshida. 2020. “Trend estimation and layer boundary detection in depth-dependent soil data using sparse Bayesian lasso.” Comput. Geotech. 128 (Dec): 103845. https://doi.org/10.1016/j.compgeo.2020.103845.
Tipping, M. E. 2001. “Sparse Bayesian learning and the relevance vector machine.” J. Mach. Learn. Res. 1 (Jun): 211–244.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. 103 (11): 1227–1246.
Wang, H., X. Wang, J. F. Wellmann, and R. Y. Liang. 2018. “Bayesian stochastic soil modeling framework using Gaussian–Markov random fields.” J. Risk Uncertainty Eng. Syst. 4 (2): 04018014. https://doi.org/10.1061/AJRUA6.0000965.
Wang, Y., and T. Zhao. 2017. “Statistical interpretation of soil property profiles from sparse data using Bayesian compressive sampling.” Géotechnique 67 (6): 523–536. https://doi.org/10.1680/jgeot.16.P.143.
Wei, G. C. G., and M. A. Tanner. 1990. “A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithm.” J. Am. Stat. Assoc. 85 (411): 699–704. https://doi.org/10.1080/01621459.1990.10474930.
Xiao, T., D. Q. Li, Z. J. Cao, and L. M. Zhang. 2018. “CPT-based probabilistic characterization of three-dimensional spatial variability using MLE.” J. Geotech. Geoenviron. Eng. 144 (5): 04018023. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001875.
Yoshida, I., Y. Tasaki, and S. Nishimura. 2019. “Basic study on conditional random field with sparse modeling.” In Proc., 7th Int. Symp. on Geotechnical Safety and Risk (ISGSR), 541–546. Singapore: Research Publishing.
Yoshida, I., Y. Tasaki, Y. Otake, and S. Wu. 2018. “Optimal sampling placement in a Gaussian random field based on value of information.” J. Risk Uncertainty Eng. Syst. 4 (3): 04018018. https://doi.org/10.1061/AJRUA6.0000970.
Zhao, T., and Y. Wang. 2020. “Non-parametric simulation of non-stationary non-Gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo.” Reliab. Eng. Syst. Saf. 203 (Nov): 107087. https://doi.org/10.1016/j.ress.2020.107087.
Zhao, T., L. Xu, and Y. Wang. 2020. “Fast non-parametric simulation of 2D multi-layer cone penetration test (CPT) data without pre-stratification using Markov Chain Monte Carlo simulation.” Eng. Geol. 273 (May): 105670. https://doi.org/10.1016/j.enggeo.2020.105670.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 147 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 9, 2020
Accepted: Nov 24, 2020
Published online: Feb 23, 2021
Published in print: May 1, 2021
Discussion open until: Jul 23, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.