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

本研究所要解决的主要问题是如何集体利用来自多个来源的信息，而不是单独利用来自各个来源的信息，以便尽快发现对其正常运作的威胁或破坏。例如，公共汽车车队中的车辆、在矿井中工作的卡车、移动中的火车或飞行中的飞机发出复杂的信号，其中有许多组件描述其操作条件。 激发本研究的数据具有结构复杂、体积大、速度快等特点。信号由许多分量组成，这些分量以某种方式相关，但提供不同结构的信息，并且不能通过通常的代数运算进行操作。例如，一个分量可以是飞行器的高度，另一个分量可以是来自放置在发动机中的传感器的温度，第三个分量可以是机舱中的辐射测量。必须真实的处理来自飞行中的一组飞机的复杂数据流，以检测对一个、一些或所有飞机的威胁。该项目旨在开发统计算法，以检测这种环境中的威胁及其数值实现。这些算法将在重型车辆车队的真实的数据上进行验证。然而，这项研究将具有广泛的适用性，因为威胁检测在由网络、物理和人类组成的日益互联的世界中至关重要。它将通过在统计、计算机科学和工程的交叉领域培训几名博士生，为劳动力发展做出贡献。从城市到联邦，私营企业和各级政府对这种专业知识的需求非常高，因为各种团体试图中断我们的企业、基础设施和政府的运作。被监控的许多单位的状态将被量化为一个向量，其条目是具有不可比较组件的复杂数据结构。这样一个抽象的向量在每个时刻都被观察到。因此，要针对威胁监视的数据呈现出具有时间和横截面依赖性的复杂结构。这项研究将开发算法来检测系统中的突然变化。这将通过将上面介绍的向量的条目嵌入度量空间中来实现，度量空间实际上是数据可以存在的最一般的空间。由于度量空间通常不具有向量空间结构，由于要处理的数据的性质，无法强加向量空间结构，因此将开发的工具将开辟时间序列分析的研究方向，从理论和实践角度来看，这将是新颖的。将考虑两类算法：1）基于一般状态空间表示的算法，2）基于一般不变性原理的算法。一般性将通过考虑一个抽象的度量空间来实现，在该度量空间上将施加算法所需的特定条件。算法的适用范围和可靠性能将通过数学工具进行分析，这将导致精确的条件和假设，并通过数值研究，将验证算法的数据流从一个车队的重型车辆。该奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的智力价值和更广泛的影响审查标准。

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.