Stochastic Model Updating and Model Class Selection for Quantification of Different Types of Uncertainties

Abstract

Stochastic model updating has been increasingly utilized in various engineering applications to quantify parameter uncertainty from multiple measurement datasets. We have recently developed a stochastic updating framework, in which the parameter distributions are approximated by staircase density functions (SDFs). This framework is applicable without any prior knowledge of the distribution formats; thus, it can be considered as a distribution-free approach. On the other hand, measurement uncertainty should also be considered in model updating since the measurement is typically performed under hard-to-control randomness. However, in model updating, it is difficult to distinguish different types of uncertainties in the measurement datasets, and measurement uncertainty is often embedded in parameter uncertainty. To address this issue, this study employs the Bayesian model class selection framework, in which different types of probabilistic models are used to represent different types of uncertainties and the most appropriate model is determined based on the associated evidence. In this sense, the proposed framework does not require any prior knowledge about the sources of uncertainty in the measurement datasets. Simple numerical examples are used to demonstrate the proposed framework.