Updating models and their uncertainties

24-Nov-2014 22:30 by 6 Comments

Updating models and their uncertainties

The Bayesian interpretation of probability does not distinguish between these two categories, since all uncertainties are seen as epistemic uncertainties [13,14].

The topic of model updating has been in the focus of intensive research for over four decades and it continues to be a topic of high importance for the accurate prediction of structural performance of dynamic systems [1–3].

A numerical example involving different degrees of nonlinearity will be used for demonstrating how this type of uncertainty is considered within the Bayesian updating procedure.► In this study, the consideration of model uncertainties is investigated.

► The study focuses on the field of Bayesian model updating.

The potential of Bayesian analysis has led to the development and enhancement of various Bayesian methods (see e.g. Finally, in Section 4, a linear beam model is updated where the reference data derives from nonlinear models involving different degrees of nonlinearity.

[15,16]) and to applications in various fields, such as natural sciences, economics and engineering, where in case of the latter the areas of structural dynamics (e.g. This provides a means for investigating quantitatively the effect of model uncertainties.

Model updating procedures are applied in order to improve the matching between experimental data and corresponding model output. improved, finite element (FE) model can be used for more reliable predictions of the structural performance in the target mechanical environment.

The discrepancies between the output of the FE-model and the results of tests are due to the uncertainties that are involved in the modeling process.

Based on the available data, the initial knowledge of the range of the unknown parameters is updated, making some parameter ranges more plausible if the data provide the necessary information.

This embedment of the deterministic model in a model class is performed by the use of Bayes’ Theorem which is given by and expresses the probability of the data conditional on the structural parameters, i.e. This term describes the discrepancies between model output and measurement through the prediction error, which is introduced in order to bridge the gap between model output and measurements and which will be discussed in Section 3. The evidence is used for performing model class comparison and selection, where posterior probabilities are assigned to a set of competing model classes [24–26].

in a frequentist interpretation of probability (see [6,7]).

Another way to treat model uncertainties is given by the non-parametric approach [8,9].

Several approaches have been proposed for taking model uncertainties into consideration, where the focus of this manuscript will be set on the updating procedure within the Bayesian statistical framework.