Filtering and Uncertainty Propagation Methods for Model-Based Prognosis of Fatigue Crack Growth in Unidirectional Fiber-Reinforced Composites

Abstract

Prognosis aims at calculating the remaining useful life (RUL) of a system by estimating its current health state and then predicting its future behavior. In this paper, the prediction of fatigue crack growth in structural elements made of unidirectional fiber-reinforced composites is considered. Model uncertainty and measurement uncertainty are included, as well as future loading uncertainty. Both cases of constant amplitude loading and variable amplitude loading (block loading) are examined. The analytical model that describes the fatigue crack growth is highly nonlinear and contains fixed model parameters that depend on material and loading parameters that may vary or not, depending on the applied load. Thus, because of its ability to handle uncertainties and high nonlinearities, but also to perform joint parameter-state estimation, a particle filter is used. In the first part, fatigue crack growth prognosis under constant amplitude loading is realized. The loading parameters are constant and known a priori, while the model parameters are jointly estimated along with the crack length. In the second part, fatigue crack growth prognosis under variable amplitude loading is performed. This time, the loading parameters are unknown and change abruptly at unknown time steps in accordance with the applied variable block loading. The two-sided cumulative sum (CUSUM) algorithm is implemented to detect abrupt load variations and help the particle filter to adapt and learn new loading parameters values. With the combination of these two techniques, the prognosis module could be informed of the sudden crack length increase and correct the predicted remaining useful life. In both case studies, real data from fatigue tests on unidirectional fiber-reinforced titanium matrix composites are used.