  Gaussian process regression is a powerful method for predicting states based
on given data. It has been successfully applied for probabilistic predictions
of structural systems to quantify, for example, the crack growth in mechanical
structures. Typically, predefined mean and covariance functions are employed to
construct the Gaussian process model. Then, the model is updated using current
data during operation while prior information based on previous data is
ignored. However, predefined mean and covariance functions without prior
information reduce the potential of Gaussian processes. This paper proposes a
method to improve the predictive capabilities of Gaussian processes. We
integrate prior knowledge by deriving the mean and covariance functions from
previous data. More specifically, we first approximate previous data by a
weighted sum of basis functions and then derive the mean and covariance
functions directly from the estimated weight coefficients. Basis functions may
be either estimated or derived from problem-specific governing equations to
incorporate physical information. The applicability and effectiveness of this
approach are demonstrated for fatigue crack growth, laser degradation, and
milling machine wear data. We show that well-chosen mean and covariance
functions, like those based on previous data, significantly increase look-ahead
time and accuracy. Using physical basis functions further improves accuracy. In
addition, computation effort for training is significantly reduced.
