We describe a multi-dimensional time series anomaly detection method in which each point in a test series is required to match the value, slope, and curvature of a point seen in training (with an optional sequential constraint), and a method of generating a model in the form of concise, human-comprehensible, and editable rules. Training time complexity is O(n log n), and testing is O(n). The method generalizes to multiple training series by allowing test points to fall within the range bounded by the training data. We use this approach to detect test failures in Marotta fuel control valves used on the Space Shuttle.
Mahoney, M.V., Chan, P.K. (2005). Learning rules for time series anomaly detection (CS-2005-04). Melbourne, FL. Florida Institute of Technology.