Algorithms for Bayesian Model Class Selection of Higher-dimensional Dynamic Systems

Abstract

n recent years, Bayesian model updating techniques based on measured data have been applied in structural health monitoring. Often we are faced with the problem of how to select the `best' model from a set of competing candidate model classes for the system based on data. To tackle this problem, Bayesian model class selection is used, which provides a rigorous Bayesian updating procedure to give the probability of different candidate classes for a system, based on the data from the system. There may be cases where more than one model class has significant probability and each of these will give different predictions. Bayesian model class averaging provides a coherent mechanism to incorporate all the considered model classes in the probabilistic predictions for the system. However, both Bayesian model class selection and Bayesian model class averaging require the calculation of the evidence of the model class which requires the nontrivial computation of a multi-dimensional integral. In this paper, several methods for solving this computationally challenging problem of model class selection are presented, proposed and compared. The efficiency of the proposed methods is illustrated by an example involving a structural dynamic system.

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