Technical Papers
Nov 10, 2018

Constructing Site-Specific Multivariate Probability Distribution Model Using Bayesian Machine Learning

Publication: Journal of Engineering Mechanics
Volume 145, Issue 1

Abstract

This study proposes a novel data-driven Bayesian machine learning method for constructing site-specific multivariate probability distribution models in geotechnical engineering. There is a trade-off for constructing a site-specific model: a model developed from generic data may not be fully applicable to a local site, but a model purely developed from limited site-specific data may be very imprecise due to significant statistical uncertainty. The proposed method is based on the hybridization between site-specific and generic data in the way that it is governed by site-specific data when site-specific data are abundant and by generic data when site-specific data are sparse. This method broadly follows how an engineer currently estimates design soil parameters from limited site-specific information. The proposed method admits incomplete multivariate data, so it can handle missing data that are commonly encountered in site investigation. It is a Bayesian method, so uncertainties are rigorously quantified. Actual case studies are used to demonstrate the usefulness of the proposed method. Analysis results show that the proposed method can effectively capture the correlation behaviors in site-specific data and, moreover, can make meaningful predictions even when site-specific data are very sparse.

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Acknowledgments

The authors would like to thank the members of the TC304 Committee on Engineering Practice of Risk Assessment and Management of the International Society of Soil Mechanics and Geotechnical Engineering for developing Database 304dB (ISSMGE 2018) used in this study and making it available for scientific inquiry.

References

Alvarez, I., J. Niemi, and M. Simpson. 2014. “Bayesian inference for a covariance matrix.” In Proc., 26th Annual Conf. on Applied Statistics in Agriculture. Manhattan, KS: Kansas State Univ.
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).
Cao, Z., and Y. Wang. 2014. “Bayesian model comparison and characterization of undrained shear strength.” J. Geotech. Geoenviron. Eng. 140 (6): 04014018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001108.
Cao, Z., Y. Wang, and D. Li. 2016. “Quantification of prior knowledge in geotechnical site characterization.” Eng. Geol. 203: 107–116. https://doi.org/10.1016/j.enggeo.2015.08.018.
CEN (European Committee for Standardization). 2004. Eurocode 7: Geotechnical design—Part 1: General rules. EN 1997-1. Brussels, Belgium: CEN.
Ching, J. 2018. “What does the soil parameter estimated from a transformation model really mean?” J. GeoEng. 13 (3): 105–113. https://doi.org/10.6310/jog.201809_13(3).2.
Ching, J., K. H. Li, K. K. Phoon, and M. C. Weng. 2018a. “Generic transformation models for some intact rock properties.” Can. Geotech. J. in press. https://doi.org/10.1139/cgj-2017-0537.
Ching, J., G. H. Lin, J. R. Chen, and K. K. Phoon. 2017a. “Transformation models for effective friction angle and relative density calibrated based on a multivariate database of coarse-grained soils.” Can. Geotech. J. 54 (4): 481–501. https://doi.org/10.1139/cgj-2016-0318.
Ching, J., G. H. Lin, K. K. Phoon, and J. R. Chen. 2017b. “Correlations among some parameters of coarse-grained soils—The multivariate probability distribution model.” Can. Geotech. J. 54 (9): 1203–1220. https://doi.org/10.1139/cgj-2016-0571.
Ching, J., and K. K. Phoon. 2012. “Value of geotechnical site investigation in reliability-based design.” Adv. Struct. Eng. 15 (11): 1935–1945. https://doi.org/10.1260/1369-4332.15.11.1935.
Ching, J., and K. K. Phoon. 2014a. “Correlations among some clay parameters—The multivariate distribution.” Can. Geotech. J. 51 (6): 686–704. https://doi.org/10.1139/cgj-2013-0353.
Ching, J., and K. K. Phoon. 2014b. “Transformations and correlations among some parameters of clays: The global database.” Can. Geotech. J. 51 (6): 663–685. https://doi.org/10.1139/cgj-2013-0262.
Ching, J., K. K. Phoon, K. H. Li, and M. C. Weng. 2018b. “Multivariate probability distribution for some intact rock properties.” Can. Geotech. J. in press.
Ching, J., K. K. Phoon, and J. W. Yu. 2014. “Linking site investigation efforts to final design savings with simplified reliability-based design methods.” J. Geotech. Geoenviron. Eng. 140 (3): 04013032. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001049.
Ching, J., K.-K. Phoon, and Y.-C. Chen. 2010. “Reducing shear strength uncertainties in clays by multivariate correlations.” Can. Geotech. J. 47 (1): 16–33. https://doi.org/10.1139/T09-074.
D’Ignazio, M., K. K. Phoon, S. A. Tan, and T. Lansivaara. 2016. “Correlations for undrained shear strength of Finnish soft clays.” Can. Geotech. J. 53 (10): 1628–1645. https://doi.org/10.1139/cgj-2016-0037.
Djoenaidi, W. J. 1985. “A compendium of soil properties and correlations.” M.Eng. thesis, School of Civil and Mining Engineering, Univ. of Sydney.
Doucet, A., N. de Freitas, and N. Gordon. 2001. Sequential Monte Carlo methods in practice. New York: Springer.
Feng, X., and R. Jimenez. 2014. “Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength.” Eng. Geol. 173: 32–40. https://doi.org/10.1016/j.enggeo.2014.02.005.
Feng, X., and R. Jimenez. 2015. “Estimation of deformation modulus of rock masses based on Bayesian model selection and Bayesian updating approach.” Eng. Geol. 199: 19–27. https://doi.org/10.1016/j.enggeo.2015.10.002.
Gelman, A. 2006. “Prior distributions for variance parameters in hierarchical models.” Bayesian Anal. 1 (3): 515–534. https://doi.org/10.1214/06-BA117A.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. 3rd ed. Boca Raton, FL: Chapman and Hall/CRC.
Geman, S., and D. Geman. 1984. “Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images.” IEEE Trans. Pattern Anal. Machine Intell. 6 (6): 721–741. https://doi.org/10.1109/TPAMI.1984.4767596.
Gilks, W. R., D. J. Spiegelhalter, and S. Richardson. 1996. Markov chain Monte Carlo in practice. London: Chapman and Hill.
Hastings, W. K. 1970. “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika 57 (1): 97–109. https://doi.org/10.1093/biomet/57.1.97.
Heckerman, D., D. Geiger, and D. M. Chickering. 1995. “Learning Bayesian networks: The combination of knowledge and statistical data.” Mach. Learn. 20 (3): 197–243. https://doi.org/10.1023/A:1022623210503.
Huang, A., and M. P. Wand. 2013. “Simple marginally noninformative prior distributions for covariance matrices.” Bayesian. Anal. 8 (2): 439–452. https://doi.org/10.1214/13-BA815.
ISSMGE (International Society of Soil Mechanics and Geotechnical Engineering). 2018. “Database 304dB.” TC304 Engineering Practice of Risk Assessment and Management. Accessed October 6, 2017. http://140.112.12.21/issmge/tc304.htm?=6.
James, A. 1964. “Distributions of matrix variates and latent roots derived from normal samples.” Ann. Math. Stat. 35 (2): 475–501. https://doi.org/10.1214/aoms/1177703550.
Johnson, N. L. 1949. “Systems of frequency curves generated by methods of translation.” Biometrika 36 (1/2): 149–176. https://doi.org/10.2307/2332539.
Kulhawy, F. H. and P. W. Mayne. 1990. Manual on estimating soil properties for foundation design. Palo Alto, CA: Electric Power Research Institute.
Li, D. Q., S. B. Wu, C. B. Zhou, and K. K. Phoon. 2012. “Performance of translation approach for modeling correlated non-normal variables.” Struct. Saf. 39 (2): 52–61. https://doi.org/10.1016/j.strusafe.2012.08.001.
Liu, P. L., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Liu, S., H. Zou, G. Cai, B. V. Bheemasetti, A. J. Puppala, and J. Lin. 2016. “Multivariate correlation among resilient modulus and cone penetration test parameters of cohesive subgrade soils.” Eng. Geol. 209: 128–142. https://doi.org/10.1016/j.enggeo.2016.05.018.
MacKay, D. J. C. 1995. “Probable networks and plausible predictions: A review of practical Bayesian methods for supervised neural networks.” Network: Comput. Neural Syst. 6 (3): 469–505. https://doi.org/10.1088/0954-898X_6_3_011.
MacKay, D. J. C. 1998. “Introduction to Monte Carlo methods.” In Learning in graphical models, edited by M. Jordan. Cambridge, MA: MIT Press.
Mardia, K. V., J. T. Kent, and J. M. Bibby. 1979. Multivariate analysis. London: Academic Press.
Mayne, P. W., Christopher, B. R., and DeJong, J. 2001. Manual on subsurface investigations. Washington, DC: Federal Highway Administration.
Mesri, G., and N. Huvaj. 2007. “Shear strength mobilized in undrained failure of soft clay and silt deposits.” In Advances in measurement and modeling of soil behavior (GSP 173), edited by D. J. DeGroot, C. Vipulanandan, J. A. Yamamuro, V. N. Kaliakin, P. V. Lade, M. Zeghal, U. El Shamy, N. Lu, and C. R. Song, 1–22. Reston, VA: ASCE.
Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. “Equation of state calculations by fast computing machines.” J. Chem. Phys. 21 (6): 1087–1092. https://doi.org/10.1063/1.1699114.
Ng, I. T., K. V. Yuen, and L. Dong. 2017. “Estimation of undrained shear strength in moderately OC clays based on field vane test data.” Acta Geotech. 12 (1): 145–156. https://doi.org/10.1007/s11440-016-0433-0.
Ng, I. T., K. V. Yuen, and C. H. Lau. 2015. “Predictive model for uniaxial compressive strength for Grade III granitic rocks from Macao.” Eng. Geol. 199: 28–37. https://doi.org/10.1016/j.enggeo.2015.10.008.
Ou, C. Y., and J. T. Liao. 1987. Geotechnical engineering research report. GT96008. Taipei, Taiwan: National Taiwan Univ. of Science and Technology.
Phoon, K. K., and F. H. Kulhawy. 1999a. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Phoon, K. K., and F. H. Kulhawy. 1999b. “Evaluation of geotechnical variability.” Can. Geotech. J. 36 (4): 625–639. https://doi.org/10.1139/t99-039.
Rasmussen, C. E., and C. K. Williams. 2006. Gaussian processes for machine learning. Cambridge, MA: MIT Press.
Tan, T. S., K. K. Phoon, D. W. Hight, and S. Leroueil. 2003a. Vol. 1 of Characterisation and engineering properties of natural soils. Rotterdam, Netherlands: A.A. Balkema.
Tan, T. S., K. K. Phoon, D. W. Hight, and S. Leroueil. 2003b. Vol. 2 of Characterisation and engineering properties of natural soils. Rotterdam, Netherlands: A.A. Balkema.
Tan, T. S., K. K. Phoon, D. W. Hight, and S. Leroueil. 2006a. Vol. 3 of Characterisation and engineering properties of natural soils. London: Taylor & Francis.
Tan, T. S., K. K. Phoon, D. W. Hight, and S. Leroueil. 2006b. Vol. 4 of Characterisation and engineering properties of natural soils. London: Taylor & Francis.
Tipping, M. E. 2001. “Sparse Bayesian learning and the relevance vector machine.” J. Mach. Learn. Res. 1: 211–244.
Tokuda, T., B. Goodrich, I. Van Mechelen, and A. Gelman. 2011. “Visualizing distributions of covariance matrices.” Accessed August 3, 2017. http://www.stat.columbia.edu/∼gelman/research/unpublished/Visualization.pdf.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. 103 (11): 1227–1246.
Wang, H., and D. Y. Yeung. 2016. “Towards Bayesian deep learning: A framework and some existing methods.” IEEE Trans. Knowl. Data Eng. 28 (12): 3395–3408. https://doi.org/10.1109/TKDE.2016.2606428.
Wang, Y., and O. V. Akeju. 2016. “Quantifying the cross-correlation between effective cohesion and friction angle of soil from limited site-specific data.” Soils Found. 56 (6): 1055–1070. https://doi.org/10.1016/j.sandf.2016.11.009.
Wang, Y., and A. E. Aladejare. 2015. “Selection of site-specific regression model for characterization of uniaxial compressive strength of rock.” Int. J. Rock Mech. Min. Sci. 75: 73–81. https://doi.org/10.1016/j.ijrmms.2015.01.008.
Wang, Y., and A. E. Aladejare. 2016. “Bayesian characterization of correlation between uniaxial compressive strength and Young’s modulus of rock.” Int. J. Rock Mech. Min. Sci. 85: 10–19. https://doi.org/10.1016/j.ijrmms.2016.02.010.
Wang, Y., and Z. J. Cao. 2013. “Probabilistic characterization of Young’s modulus of soil using equivalent samples.” Eng. Geol. 159: 106–118. https://doi.org/10.1016/j.enggeo.2013.03.017.
Yan, W. M., K. V. Yuen, and G. L. Yoon. 2009. “Bayesian probabilistic approach for the correlations of compression index for marine clays.” J. Geotech. Geoenviron. Eng. 135 (12): 1932–1940. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000157.
Yuen, K. V. 2010. “Recent developments of Bayesian model class selection and applications in civil engineering.” Struct. Saf. 32 (5): 338–346. https://doi.org/10.1016/j.strusafe.2010.03.011.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 145Issue 1January 2019

History

Received: Dec 6, 2017
Accepted: Jun 13, 2018
Published online: Nov 10, 2018
Published in print: Jan 1, 2019
Discussion open until: Apr 10, 2019

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Authors

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Jianye Ching, M.ASCE [email protected]
Professor, Dept. of Civil Engineering, National Taiwan Univ., Taipei 106, Taiwan (corresponding author). Email: [email protected]
Kok-Kwang Phoon, F.ASCE
Professor, Dept. of Civil and Environmental Engineering, National Univ. of Singapore, Singapore 119077, Singapore.

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