Bayesian updating of nonlinear model predictions using Markov chain Monte Carlo simulation

The usual practice in system identification is to use system data to identify one model from a set of possible models and then to use this model for predicting system behavior. In contrast, the present robust predictive approach rigorously combines the predictions of all the possible models, appropriately weighted by their updated probabilities based on the data. This Bayesian system identification approach is applied to update the robust reliability of a dynamical system based on its measured response time histories. A Markov chain simulation method based on the Metropolis-Hastings algorithm and an adaptive scheme is proposed to evaluate the robust reliability integrals. An example for updating the reliability of a Duffing oscillator is given to illustrate the proposed method.