Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

摘要

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 multi-valuedudconditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. Theudfundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic udsystem model class: a set of input-output probability models for the structure and a prior probability distribution over this set udthat quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic udstructural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive udanalyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or ifudstructural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustnessudto modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidatesudweighted 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 data-fit of more udcomplex 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 udasymptotic approximation or Markov Chain Monte Carlo algorithms.