Investigation of likelihood and correlation in bayesian analysis with frequency response data

Through Bayesian system identification one learns model parameters through measurements of the system’s response. The underlying inverse problem is formulated in a probabilistic setting, and Bayes’ rule is applied to update a prior conjecture on the parameters. In this contribution, we consider linear, time-invariant dynamic systems of second order . Within the Bayesian formulation, the likelihood function expresses probabilistically the misfit between measurements and model response. We define the likelihood function based on the misfit of the complex valued frequency transformed measurement data and the model frequency response function. A crucial point is the selection of a probabilistic model for the various errors that contribute to this misfit. For complex valued model responses, standard distribution types, e.g. the lognormal distribution, are not generally suitable and one often resorts to the use of a complex Gaussian model. Despite its straightforward implementation, the Gaussian model is not well-suited for describing multiplicative errors. In our contribution, we investigate possibilities to include different likelihood models for such cases. Furthermore, we investigate the suitability of alternative correlation models for the different contributing errors in the spatial and frequency domain. In case of the model error, we specifically focus on models that allow for a periodicity of the correlation in the spatial domain. We apply the discussed likelihood and correlation models to beam- and plate-like structures, and discuss the influence of the model assumptions on the updating results.     «

Through Bayesian system identification one learns model parameters through measurements of the system’s response. The underlying inverse problem is formulated in a probabilistic setting, and Bayes’ rule is applied to update a prior conjecture on the parameters. In this contribution, we consider linear, time-invariant dynamic systems of second order . Within the Bayesian formulation, the likelihood function expresses probabilistically the misfit between measurements and model response. We define...     »