  This manuscript outlines an automated anomaly detection framework for jet
engines. It is tailored for identifying spatial anomalies in steady-state
temperature measurements at various axial stations in an engine. The framework
rests upon ideas from optimal transport theory for Gaussian measures which
yields analytical solutions for both Wasserstein distances and barycenters. The
anomaly detection framework proposed builds upon our prior efforts that view
the spatial distribution of temperature as a Gaussian random field. We
demonstrate the utility of our approach by training on a dataset from one
engine family, and applying them across a fleet of engines -- successfully
detecting anomalies while avoiding both false positives and false negatives.
Although the primary application considered in this paper are the temperature
measurements in engines, applications to other internal flows and related
thermodynamic quantities are made lucid.
