Robust Stochastic Predictions of Dynamic Response During and Monitoring of Structures

This paper presents a general probabilistic framework for handling both modeling and excitation uncertainty when predicting structural response by using mathematical models. The fundamental probability models representing the structure's behavior are specified by the choice of a stochastic system model class which involves a set of input-output probability models for the structure and a prior probability distribution over this set. 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 candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes' Theorem. This higher-level application of Bayes' Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust analyses involve integrals over high-dimensional spaces that usually must be evaluated numerically by Laplace's method of asymptotic approximation or by Markov Chain Monte Carlo methods. (C) 2011 Published by Elsevier Ltd.