Corbetta M., Sbarufatti C., Manes A., Giglio M., 2013, On-line Updating of Dynamic State-Space Model for Bayesian Filtering through Markov chain Monte Carlo Techniques, Chemical Engineering Transactions, 33, 133-138.
A large number of methodologies dedicated to the continuous monitoring of systems have been developed during the last years. Among these, the model-based Bayesian Filtering methods (e.g. Particle Filters, PF) are able to combine the information provided by a monitoring system with the mathematical models describing the observed phenomena, providing advantages in terms of safety and reliability of the monitored systems. The analytical models of the phenomena are integrated in the Dynamic State Space (DSS) model of the Particle Filter. The DSS model consists of a stochastic evolution equation linking the current state vector with the state vector at the previous (discrete) time step. It is common practice to consider deterministic DSS parameters inside the PF algorithm, with an additional Gaussian or non-Gaussian noise to account for all the system uncertainties and the DSS model remains the same even after the usual procedure of resampling. This often provides a poor description of actual system dynamics. An Adaptive Dynamic State Space model is proposed here in order to overcome this problem. The Adaptive DSS model is built with the prior probability density function of parameters available in literature, and it uses the information provided by the measurement system to update the parameter distributions during the system operation. This distribution updating is obtained through the Markov Chain Monte Carlo (MCMC) techniques for the parameter estimation. The Particle Filtering algorithm based on Adaptive Dynamic State Space model is applied to a Fatigue Crack Growth (FCG) on metallic structures.
