On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

Predictive maintenance planning in the presence of structural deterioration largely relies on stochastic deterioration models, which typically contain time-invariant uncertain parameters. Monitoring information obtained sequentially at different points in time can be utilized to update prior knowledge on the time invariant parameters within the Bayesian framework. In sequential settings, Bayesian parameter estimation can be performed either in an off-line (batch) or an on-line (recursive) framework. With a focus on the quantification of the full parameter uncertainty, we review, discuss and investigate selected methods for Bayesian inference: an on-line particle filter, an online iterated batch importance sampling filter, which performs Markov chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model is used to approximate the posterior distribution within the resampling process in all three filters. Two numerical examples serve as the basis for a comparative assessment of off-line and on-line Bayesian estimation of time-invariant deterioration model parameters. The first case study considers a low-dimensional probabilistic fatigue crack growth model that is updated with sequential crack monitoring measurements. The second high-dimensional case study employs a random field to model the spatially and temporally varying corrosion deterioration across a beam, which is updated with sequential measurements from sensors. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost. The investigated on-line particle filter proves competitive with MCMC-based filters. The effects of increasing problem dimensionality and sensor information amount on posterior estimates are demonstrated.