Comparison of Different Model Classes for Bayesian Updating and Robust Predictions using Stochastic State-Space System Models

Abstract

A stochastic system-based framework for Bayesian model updating of dynamic systems was presented in Beck and Katafygiotis (1998). One key concept in this framework is a stochastic system model class which consists of probabilistic predictive input-output models for a system together with a prior probability distribution over this set that quantifies the initial relative plausibility of each predictive model. Past applications of this framework focus on model classes which consider an uncertain prediction error as the difference between the real system output and the model output and model it probabilistically using Jaynes' Principle of Maximum Information Entropy. In this paper, in addition to these model classes, we also consider an extension of such model classes to allow more flexibility in treating modeling uncertainties when updating state space models and making robust predictions; this is done by introducing prediction errors in the state vector equation in addition to those in the system output vector equation. The extended model classes allow for interactions between the model parameters and the prediction errors in both the state vector equation and the system output equation to give more robust predictions at unobserved DOFs. Bayesian model class selection is used to evaluate the posterior probability of model classes for the comparison of the extended model classes and the original one. To make predictions robust to model uncertainties, Bayesian model averaging is used to combine the predictions of these model classes. State-of- the-art algorithms (Cheung & Beck 2007, 2008; Ching & Chen 2007) are used to solve the computational problems involved. The importance and effectiveness of the proposed method is illustrated with examples for robust reliability updating of structural systems.

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