  Building a predictive model that rapidly adapts to real-time condition
monitoring (CM) signals is critical for engineering systems/units.
Unfortunately, many current methods suffer from a trade-off between
representation power and agility in online settings. For instance, parametric
methods that assume an underlying functional form for CM signals facilitate
efficient online prediction updates. However, this simplification leads to
vulnerability to model specifications and an inability to capture complex
signals. On the other hand, approaches based on over-parameterized or
non-parametric models can excel at explaining complex nonlinear signals, but
real-time updates for such models pose a challenging task. In this paper, we
propose a neural process-based approach that addresses this trade-off. It
encodes available observations within a CM signal into a representation space
and then reconstructs the signal's history and evolution for prediction. Once
trained, the model can encode an arbitrary number of observations without
requiring retraining, enabling on-the-spot real-time predictions along with
quantified uncertainty and can be readily updated as more online data is
gathered. Furthermore, our model is designed to incorporate qualitative
information (i.e., labels) from individual units. This integration not only
enhances individualized predictions for each unit but also enables joint
inference for both signals and their associated labels. Numerical studies on
both synthetic and real-world data in reliability engineering highlight the
advantageous features of our model in real-time adaptation, enhanced signal
prediction with uncertainty quantification, and joint prediction for labels and
signals.
