ATD: Threat Detection Based on Simultaneous Monitoring of Complex Signals from Multiple Sources

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The chief question this research addresses is how to utilize information from many sources collectively, rather than from individual sources separately, in order to detect as soon as possible a threat to or disruption of their proper operation. For example, vehicles in a fleet of buses, trucks working in a mine, trains on the move or airplanes in flight emit complex signals with many components describing conditions of their operation. The data that motivate this research have complex structure, large volume, and velocity. The signals consist of many components, which are related in some way, but provide differently structured information and cannot be manipulated by usual algebraic operations. For example, one component may be the altitude of an aircraft, another may be temperature from a sensor placed in an engine, the third may be radiation measurement in the cabin. Complex data streams from a fleet of aircraft in flight must be processed in real time to detect a threat to one, some, or all aircraft. This project aims at developing statistical algorithms to detect a threat in such settings and their numerical implementations. The algorithms will be validated on real data from a fleet of heavy vehicles. However, this research will have a broad applicability as threat detection is crucial in an increasingly connected world consisting of cyber, physical, and human components. It will contribute to workforce development by training several PhD students in research at the intersection of statistics, computer science and engineering. Such expertise is in extremely high demand in private enterprise and government at all levels, from city to federal, as various groups attempt to interrupt the operation of our businesses, infrastructure and government.The state of a number of units being monitored will be quantified as a vector whose entries are complex data structures with non-comparable components. Such an abstract vector is observed at each time instant. The data to be monitored for a threat thus exhibit a complex structure with temporal and cross-sectional dependence. This research will develop algorithms to detect a sudden change in the system. This will be achieved by embedding the entries of the vector introduced above in a metric space, which is practically the most general space in which data can live. Since a metric space generally does not have a vector space structure, which cannot be imposed due to the nature of the data to be processed, the tools that will be developed will open directions of research in time series analysis that will be novel from both the theoretical and practical perspectives. Two classes of algorithms will be considered: 1) algorithms based on a general state space representation, 2) algorithms based on general invariance principles. The generality will be achieved by considering an abstract metric space on which specific conditions demanded by the algorithms will be imposed. The scope of the applicability and reliable performance of the algorithms will be analyzed by mathematical tools, that will lead to precise conditions and assumptions, and by numerical studies that will validate the algorithms on data streams from a fleet of heavy vehicles.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.