Graph-theoretic analysis of discrete-phase-space states for condition change detection and quantification of information
Data collected from devices and human condition may be used to forewarn of critical events such as machine/structural failure or events from brain/heart wave data stroke. By monitoring the data, and determining what values are indicative of a failure forewarning, one can provide adequate notice of the impending failure in order to take preventive measures. This disclosure teaches a computer-based method to convert dynamical numeric data representing physical objects (unstructured data) into discrete-phase-space states, and hence into a graph (structured data) for extraction of condition change.
1. A machine-readable non-transitory data storage device having a series of preprogrammed code which, when loaded on a computer apparatus, causes the computing apparatus to:
receive a stream of time-serial numeric data representing a physical object;
convert the data to structured data; and
analyze the structured network with graph-theoretic analysis to detect condition change in the time-serial numerical data and to quantify changes among phase-space dynamical states of the structured data, wherein the analysis of the structured network comprises:
partitioning the received data to define the plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-to-state transition represented as a link in the mathematical graph;
computing the dissimilarity measures between the mathematical graphs of the phase-space dynamical states;
establishing, using the phase-state dynamical states, a baseline state and obtaining average dissimilarity between each contiguous phase-space dynamical state and the baseline state;
classifying dynamical change based on a plurality of successive occurrences of phase-space dynamical states above a threshold; and
training the classification of dynamical change to minimize prediction distance.
2. The device of claim 1 , wherein the conversion of the data to structured data comprises:
performing quality check of the received data to obtain quality data;
filtering the quality data to remove artifacts from the quality data;
symbolizing the artifact-filtered data; and
partitioning the received data to define the plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-state transition represented as a link in the mathematical graph.
3. The device of claim 1 , wherein the training comprises:
choosing specific values for training parameters;
determining a smallest prediction distance by searching exhaustively over the successive phase-space dynamical states where the dissimilarity between the phase-space dynamical state and the baseline state is above a threshold; and
minimizing the prediction distance.
4. A machine-readable non-transitory data storage device having a series of preprogrammed code which, when loaded on a computer apparatus, causes the computing apparatus to:
receive a stream of time-serial numeric data representing a physical object and perform quality check of the received data to obtain quality data;
filter the quality data to remove artifacts from the quality data;
symbolize the artifact-filtered data;
partition the symbolized artifact-filtered data to define a plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-to-state transition represented as a link in the mathematical graph of the phase-space dynamical state;
compute the dissimilarity measures between the mathematical graphs of the phase-space dynamical states;
establish, using the phase-space dynamical states, a baseline state; and
analyze the network with graph-theoretic analysis to detect condition change in the time-serial numerical data and to quantify changes among the phase-space dynamical states, the analysis comprising computing a Laplacian matrix of the network, computing a plurality of eigenvalues of the Laplacian matrix and using the plurality of eigenvalues to detect condition change.
5. The device of claim 4 , wherein the condition change is detected when one or more of the eigenvalues is above a predetermined threshold.
6. The device of claim 4 , wherein the quality check is performed using one of proper number of data points test, intervals with unchanged amplitude test, saturation at high or low limits test, consistent amplitude across datasets test, adequate sampling rate test, excessive periodic content test, and excessive noise test.
7. The device of claim 4 , wherein the dissimilarity measures are based on summing the absolute value of differences between pairs of phase-space dynamical states.
8. A method for condition change detection, comprising:
receiving a stream of time-serial numeric data representing a physical object;
converting the data to structured data; and
analyzing the structured network with graph-theoretic analysis to detect condition change in the time-serial numerical data and to quantify changes among phase-space dynamical states of the structured data, wherein the analysis of the structured network comprises:
partitioning the received data to define the plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-to-state transition represented as a link in the mathematical graph;
computing the dissimilarity measures between the mathematical graphs of the phase-space dynamical states;
establishing, using the phase-state dynamical states, a baseline state;
obtaining average dissimilarity between each contiguous phase-space dynamical state and the baseline state;
classifying dynamical change based on a plurality of successive occurrences of phase-space dynamical states above a threshold; and
training the classification of dynamical change to minimize prediction distance.
9. The method of claim 8 , further comprising:
performing quality check of the received data to obtain quality data;
filtering the quality data to remove artifacts from the quality data;
symbolizing the artifact-filtered data; and
partitioning the received data to define the plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-to-state transition represented as a link in the mathematical graph.
10. The method of claim 8 , wherein the training comprises:
choosing specific values for training parameters;
determining a smallest prediction distance by searching exhaustively over the successive phase-space dynamical states where the dissimilarity between the phase-space dynamical state and the baseline state is above a threshold; and
minimizing the prediction distance.
11. A method for condition change detection comprising:
receiving a stream of time-serial numeric data representing a physical object and performing quality check of the received data to obtain quality data;
filtering the quality data to remove artifacts from the quality data;
symbolizing the artifact-filtered data;
partitioning the symbolized artifact-filtered data to define a plurality of phase-space dynamical states, for each phase-space dynamical state, each state represented as a node in a mathematical graph and each state-to-state transition represented as a link in the mathematical graph of the phase-space dynamical state;
computing the dissimilarity measures between the mathematical graphs of the phase-space dynamical states;
establishing, using the phase-space dynamical states, a baseline state; and
analyzing the network with graph-theoretic analysis to detect condition change in the time-serial numerical data and to quantify changes among the phase-space dynamical states, the analyzing comprising computing a Laplacian matrix of the network, computing eigenvalues of the Laplacian matrix and using the eigenvalues to detect condition change.
12. The method of claim 11 , wherein the quality check is performed using one of proper number of data points test, intervals with unchanged amplitude test, saturation at high or low limits test, consistent amplitude across datasets test, adequate sampling rate test, excessive periodic content test, and excessive noise test.
13. The method of claim 11 , wherein the dissimilarity measures are based on summing the absolute value of differences between pairs of phase-space dynamical states.