Online Prognostics of Remaining Useful Properties for Cross-Ply Composites in Early Fatigue Life

Abstract

High performance continuous fiber-reinforced composites are becoming increasingly important in the aerospace industry. In these structures, internal damage is often created and propagated throughout the lifetime, having a negative impact on the structural properties. In order to allow for condition-based maintenance, there is a need for reliable prognostics to predict future damage states. Therefore, a model-based machine learning approach is developed in this thesis to perform prognostics of the remaining useful life (RUL) and remaining useful properties (RUP) of cross-ply composites to end-of-early-fatigue-life (EOEFL). In-situ transverse matrix crack density and dynamic stiffness data are available, as well as offline delamination ratio and damage induced stiffness degradation data. To account for the multicausality and non-linearity in stiffness degradation, the evolution of cracks and delaminations is modeled using separate phenomenological relations that are pre-trained with high variance using non-linear least squares (NLS) on a separate training set. These damage properties are then combined into a normalized stiffness prediction using NLS pre-trained phenomenological relations that express the induced stiffness degradation for each of the aforementioned properties. A particle filter (PF) trains the model parameters, initialized in a high variance uniform distribution, for the phenomenological models in real-time (i.e. online). This is done with the in-situ crack density and normalized stiffness measurements of the testing specimen only. A random walk on the model parameters, which declines towards EOEFL with a given rate of convergence, is added to allow for continuous adaptivity. By propagating each particle to future states beyond the online time step in the PF, the prognostics are obtained. This encompasses the RUP and RUL to EOEFL using a weighted sum of the particles. After applying this methodology to the case study data, it is concluded that the potential of PF to offer adaptivity required for RUP prognostics of composites is identified, definitely for damage properties showing early characteristic behavior. However, reliable RUL estimation to EOEFL with the methodology set out in this thesis remains difficult. Especially the stiffness degradation model and the failure criterion for EOEFL generate difficulties. Therefore, a promising recommendation would be to combine similar phenomenological relations to end-of-life for crack and delamination growth with an alternative stiffness model. A feasible approach would be to train a surrogate model on synthetic data generated with finite element modeling simulations. Finally, a sensitivity analysis is done on three PF hyperparameters: sample size, threshold effective sample size, and rate of convergence. The first shows that a minimum sample size can be distinguished after which no improvement occurs when the sample size increases. The second indicates a 'sweet spot' that balances the sample impoverishment and weight degeneracy drawbacks. The latter makes it plausible that a moderate rate of convergence is preferable.