Bayesian Learning and Model Class Selection for Complex Dynamic Systems

Abstract

A huge amount of data is available almost every second nowadays due to fast development of technology. This provides a perfect opportunity to improve mathematical modeling using measured data for understanding and predicting behaviors of dynamic systems, but at the same time it also poses a challenge on how to effectively and efficiently extract information from a large amount of data, because it means that a large computational power is required. This paper addresses the problem of identifying mathematical models of large-scale complex dynamic systems in civil engineering based on measured data. This problem is especially challenging in practice because identifying a mathematical model in high-dimensional parameter space is time-consuming (sometimes the model is unidentifiable), and the information contained in data is always incomplete and there are uncertainties. The identification problem is formulated as a Bayesian learning problem where the plausible models and the associated uncertainties are learned by identifying the posterior PDF of the model of a dynamic system. Bayesian model class selection is also discussed, i.e., how to select an appropriate model class that is not too simple and not too complicated based on the same set of data. Because conventional methods are not applicable in the current case, an efficient Markov chain Monte Carlo method is proposed to sample from the posterior PDF in a complex high-dimensional parameter space. The proposed Bayesian method is applied on a full-scale building.KeywordsBayesian learningBayesian model class selectionMarkov chain Monte CarloUncertainty quantification