Warped Gaussian Processes for Prognostic Health Monitoring

Gaussian process regression is a powerful method for predicting states associated with uncertainty. A common application field is to predict damage states of structural systems. Recently, Gaussian processes became very popular as they deliver credible intervals for the predicted states. However, one major disadvantage of Gaussian processes is that they assume a normal distribution. This is not justified when the relevant variables can only assume positive values, such as crack lengths or damage states. This paper presents a way to bypass this problem by using warped Gaussian processes: We (1) transform the data with a warping function, (2) apply Gaussian process regression in the latent space, and (3) transform the results back by using the inverse of the warping function. The method is applied to a crack growth example. The paper shows how to integrate prior knowledge into warped Gaussian processes in order to increase prediction accuracy and that warped Gaussian processes lead to better and more plausible results.