Identifiability of Geotechnical Site-Specific Trend Functions
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 3, Issue 4
Abstract
This paper investigates the possibility of consistently identifying a site-specific geotechnical trend function in the presence of spatial variability , where denotes depth. The trend function is represented as the linear combination of prescribed basis functions (BFs), whereas is modeled as a zero-mean stationary Gaussian stochastic process with unknown standard deviation and scale of fluctuation. It is found that can be unidentifiable if the single exponential (SExp) autocorrelation model is adopted for . Two mechanisms, overfit and poor fit, that cause unidentifiability are explored. The overfit happens when part of is falsely fitted by the BFs, whereas the poor fit happens when part of is erroneously interpreted as spatial variability. Nonetheless, identifiability is also affected by the sounding depth (or data record length) and the number of (statistically independent) soundings. An important feature for the SExp autocorrelation model is that it produces rough realizations with local jitters. If an autocorrelation model that produces smooth realizations is adopted, the trend function can become identifiable. The reason the identifiability for is related to the smoothness of the realizations is explored. Finally, it is found that the sparse Bayesian learning framework can effectively alleviate overfit but cannot alleviate poor fit.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first author would like to acknowledge the gracious support from the Ministry of Science and Technology (MOST) of the Republic of China (Research Grant 105-2918-I-002-001). He also appreciates that the California Institute of Technology hosted his sabbatical leave from July 2016 to January 2017. The authors also gratefully acknowledge Kiso Jiban Consultant Co. Ltd. for providing the piezocone sounding at the eastern part of Singapore as an illustrative example.
References
Beck, J., and Yuen, K. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 192–203.
Ching, J., and Chen, Y. C. (2007). “Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection and model averaging.” J. Eng. Mech., 816–832.
Ching, J., and Phoon, K. K. (2015). “Constructing multivariate distributions for soil parameters.” Chapter 1, Risk and reliability in geotechnical engineering, K. K. Phoon and J. Ching, eds., Taylor & Francis, Boca Raton, FL.
Ching, J., and Phoon, K. K. (2017). “Characterizing uncertain site-specific trend function by sparse Bayesian learning.” J. Eng. Mech., 04017028.
Ching, J., Phoon, K. K., and Wu, S. H. (2016a). “Impact of statistical uncertainty on geotechnical reliability estimation.” J. Eng. Mech., 04016027.
Ching, J., and Wang, J. S. (2016). “Application of the transitional Markov chain Monte Carlo to probabilistic site characterization.” Eng. Geol., 203, 151–167.
Ching, J., Wang, J. S., Juang, C. H., and Ku, C. S. (2015). “CPT-based stratigraphic profiling using the wavelet transform modulus maxima.” Can. Geotech. J., 52(12), 1993–2007.
Ching, J., Wu, S. H., and Phoon, K. K. (2016b). “Statistical characterization of random field parameters using frequentist and Bayesian approaches.” Can. Geotech. J., 53(2), 285–298.
Fenton, G. A. (1999a). “Estimation for stochastic soil models.” J. Geotech. Geoenviron. Eng., 470–485.
Fenton, G. A. (1999b). “Random field modeling of CPT data.” J. Geotech. Geoenviron. Eng., 486–498.
Geman, S., and Geman, D. (1984). “Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images.” IEEE Trans. Pattern Anal. Mach. Intell., 6(6), 721–741.
Gilks, W. R., Spiegelhalter, D. J., and Richardson, S. (1996). Markov chain Monte Carlo in practice, Chapman and Hill, London.
Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, 57(1), 97–109.
Huang, Y., and Beck, J. L. (2015). “Hierarchical sparse Bayesian learning for structural health monitoring with incomplete modal data.” Int. J. Uncertainty Quantif., 5(2), 139–169.
Huang, Y., Beck, J. L., Wu, S., and Li, H. (2014). “Robust Bayesian compressive sensing for signals in structural health monitoring.” Comput. Aided Civil Infrastruct. Eng., 29(3), 160–179.
Jaksa, M. B., Brooker, P. I., and Kaggwa, W. S. (1997). “Inaccuracies associated with estimating random measurement errors.” J. Geotech. Geoenviron. Eng., 393–401.
Katafygiotis, L. S., and Beck, J. L. (1998). “Updating models and their uncertainties II: Model identifiability.” J. Eng. Mech., 463–467.
Kulatilake, P. H. S. W. (1991). “Closure to ‘Probabilistic potentiometric surface mapping’ by Pinnaduwa H. S. W. Kulatilake.” J. Geotech. Eng., 1458–1459.
Li, K. S. (1991). “Discussion of ‘Probabilistic potentiometric surface mapping’ by Pinnaduwa H. S. W. Kulatilake.” J. Geotech. Eng., 1457–1458.
MacKay, D. J. C. (1992). “Bayesian interpolation.” Neural Comput., 4(3), 415–447.
MacKay, D. J. C. (1998). “Introduction to Gaussian processes.” Neural networks and machine learning, Vol. 168, Springer, Berlin.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equation of state calculations by fast computing machines.” J. Chem. Phys., 21, 1087–1092.
Mu, H. Q., and Yuen, K. V. (2016). “Ground motion prediction equation development by heterogeneous Bayesian learning.” Comput. Aided Civil Infrastruct. Eng., 31, 761–776.
Neal, R. M. (1997). “Monte Carlo implementation of Gaussian process models for Bayesian regression and classification.”, Dept. of Computer Science, Univ. of Toronto, Toronto.
Phoon, K. K., and Kulhawy, F. H. (1999). “Characterization of geotechnical variability.” Can. Geotech. J., 36(4), 612–624.
Phoon, K. K., Quek, S. T., and An, P. (2003). “Identification of statistically homogeneous soil layers using modified Bartlett statistics.” J. Geotech. Geoenviron. Eng., 649–659.
Robertson, P. K. (2009). “Interpretation of cone penetration tests—A unified approach.” Can. Geotech. J., 46, 1337–1355.
Stein, M. L. (1999). Interpolation of spatial data: Some theory for Kriging, Springer, New York.
Tipping, M. E. (2001). “Sparse Bayesian learning and the relevance vector machine.” J. Mach. Learn. Res., 1, 211–244.
Uzielli, M., Vannucchi, G., and Phoon, K. K. (2005). “Random field characterisation of stress-normalised cone penetration testing parameters.” Geotechnique, 55(1), 3–20.
Vanmarcke, E. H. (1977). “Probabilistic modeling of soil profiles.” J. Geotech. Eng., GT11, 1227–1246.
Wang, Y., and Aladejare, A. E. (2015). “Selection of site-specific regression model for characterization of uniaxial compressive strength of rock.” Int. J. Rock Mech. Min. Sci., 75, 73–81.
Wang, Y., and Zhao, T. (2016a). “Interpretation of soil property profile from limited measurement data: A compressive sampling perspective.” Can. Geotech. J., 53(9), 1547–1559.
Wang, Y., and Zhao, T. (2016b). “Statistical interpretation of soil property profiles from sparse data using Bayesian compressive sampling.” Geotechnique, 67(6), 523–536.
Williams, C. K. I., and Rasmussen, C. E. (1996). “Gaussian processes for regression.” Advances in neural information processing systems, Vol. 8, MIT Press, London.
Wu, B., Huang, Y., Chen, X., Krishnaswamy, S., and Li, H. (2016). “Guided-wave signal processing by the sparse Bayesian learning approach employing Gabor pulse model.” Struct. Health Monit., 16(3), 347–362.
Yan, W. M., Yuen, K. V., and Yoon, G. L. (2009). “Bayesian probabilistic approach for the correlations of compression index for marine clays.” J. Geotech. Geoenviron. Eng., 1932–1940.
Yuen, K.-V. (2010a). Bayesian methods for structural dynamics and civil engineering, Wiley, New York.
Yuen, K.-V. (2010b). “Recent developments of Bayesian model class selection and applications in civil engineering.” Struct. Saf., 32(5), 338–346.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 10, 2017
Accepted: Apr 24, 2017
Published online: Jul 22, 2017
Published in print: Dec 1, 2017
Discussion open until: Dec 22, 2017
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.