Graph-Theoretic Analysis for Condition Change Detection
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Solution Overview
Problem
Existing methods for condition change analysis and event forewarning in data from physical processes or human conditions fail to effectively convert unstructured numeric data into structured data for timely detection of critical events like machine failures or health anomalies.
Innovation Solution
A computer-based method that converts time-serial numeric data into structured data using graph-theoretic analysis, including Laplacian matrix computation and time-delay-embedding techniques to represent dynamical states as nodes and transitions as links in a graph, allowing for topologically-invariant measures and dissimilarity analysis to detect significant changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If unstructured numeric data is analyzed directly using traditional methods, then analysis can be performed quickly, but detection precision of condition changes is insufficient
Solution Approach 1:
The patent segments unstructured numeric data into structured representations by dividing the data stream into discrete segments or windows, then constructing phase-space representations for each segment. This segmentation transforms continuous unstructured data into discrete analyzable units, improving detection precision while managing complexity through systematic division
Solution Approach 2:
The patent applies dimensionality transformation by converting one-dimensional time-series data into multi-dimensional phase-space representations using time-delay embedding. This creates a structured graph where nodes represent phase-space states and edges represent transitions, enabling precise detection of condition changes through topological analysis of the expanded dimensional structure
2Measurement precision
If graph-theoretic analysis with Laplacian matrix computation is applied, then condition change detection precision is improved, but computational complexity increases
Solution Approach 1:
The patent performs preliminary actions by pre-computing the Laplacian matrix and its eigenvalues from the structured graph representation of the data. This pre-computation enables efficient subsequent analysis of condition changes without repeatedly performing complex matrix operations, reducing real-time computational power requirements while maintaining high detection precision
Solution Approach 2:
The patent utilizes parameter changes in the spectral properties of the Laplacian matrix (eigenvalues and eigenvectors) to detect condition changes in the underlying system. By monitoring how these spectral parameters evolve as the system transitions between states, the method achieves high detection precision with computationally efficient parameter tracking rather than full matrix recomputation
3Reliability
If topologically-invariant measures are used for analysis, then reliability of condition detection is improved, but difficulty of detecting and measuring increases
Solution Approach 1:
The patent introduces topologically-invariant graph measures as intermediary quantities that bridge the raw structured data and the final condition detection. These measures (such as spectral properties of the Laplacian) serve as reliable intermediaries that capture essential system characteristics independent of specific coordinate systems or representations, ensuring reliable condition detection while providing a systematic framework that manages analytical complexity
Data Source
AI summary
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.