A hierarchical output-only Bayesian approach for online vibration-based crack detection using parametric reduced-order models

This contribution presents a hierarchical Bayesian filter for recursive input, state and parameter estimation using spatially incomplete and noisy output-only vibration measurements. The problem at hand is tailored to a dual-layered scheme, whereby the sought-after parameters are treated as random variables with a finite number of evolving states. For each one of these states an output-only Bayesian filter is employed for estimating the state and unknown input, creating thus a bank of filters, which are recursively weighted upon assimilation of the measurement data. The dynamics of parameter states are governed by an evolution strategy, which enables exploration of the parameter space and subsequent identification of the target values. The proposed scheme is numerically tested on crack identification problems using parametric reduced-order models (pROMs). The latter is a key element of the methodology in that it provides a generator of computationally efficient models, which can be evaluated at different parameter configurations, using mesh morphing. The performance of the algorithm is tested by means of simulated realistic components encountered in aerospace applications.