Characterizing Uncertain Site-Specific Trend Function by Sparse Bayesian Learning
Publication: Journal of Engineering Mechanics
Volume 143, Issue 7
Abstract
This paper addresses the statistical uncertainties associated with the estimation of a depth-dependent trend function and spatial variation about the trend function using limited site-specific geotechnical data. Specifically, the statistical uncertainties associated with the following elements are considered: (1) the functional form (shape) of the trend function; (2) the parameters of the trend function (e.g., intercept and gradient); and (3) the random field parameters describing spatial variation about the trend function, namely standard deviation () and scale of fluctuation (). The problem is resolved with a two-step Bayesian framework. In Step 1, a set of suitable basis functions that parameterize the trend function is selected using sparse Bayesian learning. In Step 2, an advanced Markov chain Monte Carlo method is adopted for the Bayesian analysis. The two-step approach is shown to be consistent in the well-defined sense that the resulting 95% Bayesian confidence interval (or region) contains the actual trend (or actual and ) with a chance that is close to 0.95. Inconsistency can occur when the spatial variability has a large or a large relative to data record length.
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Acknowledgments
The authors gratefully acknowledge Kiso Jiban Consultant Co. Ltd. for providing the piezocone sounding at the eastern part of Singapore as a test example. The authors are also grateful for the valuable constructive review comments from the reviewers.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jul 20, 2016
Accepted: Nov 23, 2016
Published ahead of print: Feb 20, 2017
Published online: Feb 21, 2017
Published in print: Jul 1, 2017
Discussion open until: Jul 21, 2017
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