Bayesian Inference for Dynamic Systems under Model Uncertainty

Matteo Pozzi, Dennis Bernal

This project investigates the use of probabilistic graphical models for performing inference on dynamic systems, as vibrating structures, instrumented with sensors. Specifically, we focus on time-invariant linear dynamic systems exposed to Gaussian noise, whose model parameters are unknown. We have proposed to use the Gibbs Sampling approach, and it is able to generate a set of samples of models and state variable trajectories according to the posterior distribution of these quantities conditional to the observed measurements. Generation of samples of state trajectories is related to Kalman Filter algorithm. By post-processing the outcome of the sampling procedure, one can consistently estimate the probability of failure or damage events.

We use the Bayesian framework to assess consistently relevant features, as probability of damage, computing the posterior probability density of the model parameters given the observations.

Probabilistic graphical model for a linear Gaussian model with uncertain parameters.

Pozzi, M., Bernal, D.Gibbs sampling for inference and reliability assessment in dynamic systems,” 7th International Conference on Structural Health Monitoring of Intelligent Infrastructure, Torino July 1-3 2015.