A combined framework for automated diagnosis and prognosis based on surrogate modelling and a particle filter

Abstract

Bayesian approaches have proven to be successful in prognostic health monitoring, especially for inverse problem solutions, such as the estimation of damage evolution model parameters from some damage dependent observations. In practice, they stem from the evaluation of the posterior distribution of a vector of parameters of interest conditioned on the observation of some signal features, which relies on the direct calculation of the observation likelihood, i.e. a measure of the probability that the observations are associated to some realizations of the system parameter vector. However, for realistic structures, a numerical simulation might be required for the evaluation of each sample likelihood, which can make the whole procedure for posterior pdf estimation computationally unfeasible.

In this work, this problem is addressed by leveraging on surrogate modelling. Particle filter is used as a general framework for the combined health state estimation and prognosis of a skin panel subject to fatigue crack growth, while observing the strain field pattern acquired at some specific locations. A surrogate model consisting of an artificial neural network, trained on a set of analytical simulations, is used to predict the strain as a function of the crack position and length, thus allowing a fast calculation of the strain observation likelihood. The algorithm is tested with an analytic case study of a crack propagating in an infinite plate, allowing for a simultaneous diagnosis of the crack position and length, as well as a real-time updating of the evolution model parameters and system prognosis.