Warped Gaussian processes for predicting the degradation of aerospace structures

Gaussian processes (GPs) can be used to predict future states of a system with credible intervals when considering multiple previous trajectories for training. For example, predicting the degradation of mechanical structures is one application in which they have shown their usefulness. In modeling the system output as a GP, the output is presumed to be normally distributed—assuming the predictions to be defined from negative to positive infinity. However, this assumption does not hold in many applications as, for example, crack lengths and damage indices can only assume positive values. Moreover, several degradation trajectories for training are rare in real-world applications, and the current state of a monitored system, which is used to update the prediction, can often be not directly measured. This paper presents an approach that utilizes warped GPs for treating data that is not normally distributed while considering multiple degradation trajectories for training. The approach is successfully applied to two different crack propagation examples: first, an analytically computed pre-cracked infinite plate, and second, two equally manufactured aluminum structures that resemble a lower section of a wing. For the investigated aerospace structures, we use finite element (FE) simulations to generate multiple degradation trajectories for training. To estimate their hidden degradation states, we infer the current crack length from strain measurements by using Bayesian inference. The results show that the approach of warped GPs provides more accurate predictions than using standard ones for non-normally distributed data, as is the case for crack growth problems. The approach enables quick training of warped GPs while considering multiple training trajectories. Additionally, the crack lengths estimated from strain measurements agree well with the visually inspected ones. Ultimately, the presented approach enables estimating the current and future degradation states with credible intervals that can be used to improve maintenance scheduling.