Trajectory Boundary Modeling of Time Series for Anomaly Detection

We address the problem of online detection of unanticipated modes of mechanical failure given a small set of time series under normal conditions, with the requirement that the anomaly detection model be manually verifiable and modifiable. We specify a set of time series features, which are linear combinations of the current and past values, and model the allowed feature values by a sequence of minimal bounding boxes containing all of the training trajectories. The model can be constructed in O(n log n) time. If there are at most three features, the model can be displayed graphically for verification, otherwise a table is used. Test time is O(n) with a guaranteed upper bound on computation time for each test point. The model compares favorably with anomaly detection algorithms based on Euclidean distance and dynamic time warping on the Space Shuttle Marrotta fuel control valve data set.