  Prognostics is concerned with predicting the future health of the equipment
and any potential failures. With the advances in the Internet of Things (IoT),
data-driven approaches for prognostics that leverage the power of machine
learning models are gaining popularity. One of the most important categories of
data-driven approaches relies on a predefined or learned health indicator to
characterize the equipment condition up to the present time and make inference
on how it is likely to evolve in the future. In these approaches, health
indicator forecasting that constructs the health indicator curve over the
lifespan using partially observed measurements (i.e., health indicator values
within an initial period) plays a key role. Existing health indicator
forecasting algorithms, such as the functional Empirical Bayesian approach, the
regression-based formulation, a naive scenario matching based on the nearest
neighbor, have certain limitations. In this paper, we propose a new `generative
+ scenario matching' algorithm for health indicator forecasting. The key idea
behind the proposed approach is to first non-parametrically fit the underlying
health indicator curve with a continuous Gaussian Process using a sample of
run-to-failure health indicator curves. The proposed approach then generates a
rich set of random curves from the learned distribution, attempting to obtain
all possible variations of the target health condition evolution process over
the system's lifespan. The health indicator extrapolation for a piece of
functioning equipment is inferred as the generated curve that has the highest
matching level within the observed period. Our experimental results show the
superiority of our algorithm over the other state-of-the-art methods.
