Beck, James L. (2011) Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response. In: Proceedings of the 8th European Conference on Structural Dynamics, EURODYN 2011. K VIV Royal Flemish Society of Engineers , Antwerp, Belguim. ISBN 9789076019314. https://resolver.caltech.edu/CaltechAUTHORS:20120831111433299

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Abstract
A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multivalued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of inputoutput probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the datafit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms.
Item Type:  Book Section  

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Subject Keywords:  Structural modeling; Robust stochastic analysis; System identification; Bayesian updating; Ockham’s razor  
Record Number:  CaltechAUTHORS:20120831111433299  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:20120831111433299  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  33770  
Collection:  CaltechAUTHORS  
Deposited By:  Carmen NemerSirois  
Deposited On:  05 Sep 2012 18:45  
Last Modified:  03 Oct 2019 04:13 
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