  Fatigue-induced damage is still one of the most uncertain failures in
structural systems. Prognostic health monitoring together with surrogate models
can help to predict the fatigue life of a structure. This paper demonstrates
how to combine data from previously observed crack evolutions with data from
the currently observed structure in order to predict crack growth and the total
fatigue life. We show the application of one physics-based model, which is
based on Paris' law, and four mathematical surrogate models: recurrent neural
networks, Gaussian process regression, k-nearest neighbors, and support vector
regression. For a coupon test, we predict the time to failure and the crack
growth with confidence intervals. Moreover, we compare the performance of all
proposed models by the mean absolute error, coefficient of determination, mean
of log-likelihood, and their confidence intervals. The results show that the
best mathematical surrogate models are Gaussian process regression and
recurrent neural networks. Furthermore, this paper shows that the mathematical
surrogate models tend to have conservative confidence intervals, whereas the
physics-based model exhibits overly optimistic (too small) confidence
intervals.
