CYBER SECURITY
Systems and methods that use probabilistic grammatical inference and statistical data analysis techniques to characterize the behavior of systems in terms of a low dimensional set of summary variables and, on the basis of these models, detect anomalous behaviors are disclosed. The disclosed information-theoretic system and method exploit the properties of information to deduce a structure for information flow and management. The properties of information can provide a fundamental basis for the decomposition of systems and hence a structure for the transmission and combination of observations at the desired levels of resolution (e.g., component, subsystem, system).
1 . A computer implemented method for detecting cyber physical system behavior, comprising:
utilizing one or more processors and associated memory storing one or more programs for execution by the one or more processors, the one or more programs including instructions for:
receiving data from a plurality of sensors associated with the cyber physical system;
constructing a metrization of the data utilizing a data structuring;
determining at least one ensemble and at least one summary variable from the metrized data, wherein the summary variable is based on automata model utilizing a probabilistic grammatical inference that includes discovering common subtrees of a string parse tree via a nonparametric Bayesian clustering method including a Dirichlet Process or a Beta Process a diffusion map technique;
applying a thermodynamic formalism to the at least one summary variable to classify a plurality of system behaviors;
identifying the plurality of system behaviors based at least in part on the classified plurality of system behaviors;
obtaining, by the one or more processors, a baseline of the system behavior associated with the classified plurality of systems behaviors; and
detecting an anomalous condition based on a deviation of the plurality of system behaviors from the baseline.
2 . The method for detecting cyber physical system behavior of claim 1 , wherein determining at least one summary variable includes a symbolic encoding of the metrized data.
3 . The method for detecting cyber physical system behavior of claim 1 , wherein the probabilistic grammatical inference comprises an ϵ-Machine Reconstruction statistical machine learning technique that includes describing a system trajectory as a string of symbols and describing system dynamics in terms of shift dynamics of the associated symbol string.
4 . The method for detecting cyber physical system behavior of claim 3 , including identifying cycles in strings of symbols utilizing pumping lemmas.
5 . The method for detecting cyber physical system behavior of claim 1 further comprising:
generating an output indicating the identified plurality of system behaviors or the anomalous condition.
6 . The method for detecting cyber physical system behavior of claim 1 , wherein the at least one ensemble is determined empirically.
7 . The method for detecting cyber physical system behavior of claim 1 , wherein applying a thermodynamic formalism includes applying thermodynamic techniques to the sensor data.
8 . The method for detecting cyber physical system behavior of claim 1 , wherein the data structuring includes a manifold learning technique comprising at least one of a Diffusion Mapping, a bijective mapping or a spectral graph analysis.
9 . The method for detecting cyber physical system behavior of claim 1 , wherein the at least one summary variable is determined by forming a derivative of a natural variable.
10 . The method for detecting cyber physical system behavior of claim 1 , wherein receiving data includes receiving time series data from a plurality of sensors monitoring a cyber-physical system.
11 . The method for detecting cyber physical system behavior of claim 10 , wherein the cyber-physical system is an electrical power grid system.
12 . The method for detecting cyber physical system behavior of claim 1 , wherein detecting an anomalous condition includes at least one of predicting or detecting the presence of an Improvised Explosive Device.
13 . A system for detecting cyber physical system behavior, comprising:
a processor and memory coupled to the processor, the processor executes the following executable components:
a data collection component that receives encoded information from a plurality of sensors associated with the cyber physical system;
a data assimilation component for decoding the encoded information, via a spectral graph analysis process comprising a diffusion mapping technique, by applying a manifold learning technique to the information to identify system features including at least one summary variable, wherein the data assimilation component applies a thermodynamic formalism to the at least one summary variable to obtain an indication of system behavior; and
an operational component for receiving the indication of system behavior and for detecting an anomalous system behavior.
14 . The system for detecting cyber physical system behavior of claim 13 , wherein the encoded information includes at least one of continuous, discrete or transactional cyber physical system dynamics.
15 . The system for detecting cyber physical system behavior of claim 13 , wherein the operational component provides an output indicating the anomalous system behavior.
16 . The system for detecting cyber physical system behavior of claim 13 , wherein the data assimilation component utilizes the spectral graph analysis process that includes integrating data across at least one of a continuous physical domain or a discrete physical domains and at least one of a computational cyber domain or a transactional cyber domain.
17 . The system for detecting cyber physical system behavior of claim 16 , wherein the operational component is further configured to generate an output indicating the identified anomalous system behavior.
18 . The system for detecting cyber physical system behavior of claim 13 , wherein the data assimilation component utilizes a bijective mapping technique.
19 . A tangible computer readable medium, comprising computer executable instructions that when executed by a processor perform operations, comprising:
receiving data from a plurality of sensors associated with the cyber physical system;
constructing a metrization of the data utilizing a data structuring;
determining at least one ensemble and at least one summary variable from the metrized data, wherein the summary variable is based on automata model utilizing a probabilistic grammatical inference that includes discovering common subtrees of a string parse tree via a nonparametric Bayesian clustering method including a Dirichlet Process or a Beta Process a diffusion map technique;
applying a thermodynamic formalism to the at least one summary variable to classify a plurality of system behaviors;
identifying the plurality of system behaviors based at least in part on the classified plurality of system behaviors;
obtaining, by the one or more processors, a baseline of the system behavior associated with the classified plurality of systems behaviors; and
detecting an anomalous condition based on a deviation of the plurality of system behaviors from the baseline.
20 . The tangible computer readable medium of claim 19 , wherein the determining at least one summary variable includes a symbolic encoding of the metrized data and wherein the probabilistic grammatical inference comprises an ϵ-Machine Reconstruction statistical machine learning technique that includes describing a system trajectory as a string of symbols and describing system dynamics in terms of shift dynamics of the associated symbol string.