Matroid Graph Cycle Decomposition for System Evaluation
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Solution Overview
Problem
Current mathematical tools are inadequate for fully evaluating complex systems, particularly in modeling and controlling nonlinear systems, as they can be time/cost prohibitive and provide misleading results due to round-off errors, and struggle with analyzing the impact of multiple simultaneous perturbations.
Innovation Solution
A unique data processing technique that represents a network as a graphical data structure corresponding to a matroid, decomposes closed pathways into a minimal cycle set using a spanning tree representation, and identifies fundamental cycles, allowing for the complete characterization and control of both linear and nonlinear systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing mathematical tools are used to evaluate complex systems, then the evaluation process can be completed, but it becomes time/cost prohibitive and may provide misleading results due to round-off errors
Solution Approach 1:
The patent segments the system evaluation process by decomposing the system representation into fundamental cycles. This allows complex system behaviors to be analyzed through simpler, discrete cycle components rather than treating the entire system as a monolithic complex structure, thereby reducing computational time while maintaining evaluation accuracy.
Solution Approach 2:
The patent changes the mathematical parameters used in system evaluation by transitioning from traditional continuous mathematical models to a discrete cycle-based representation. This parameter transformation enables more efficient computation and reduces round-off errors by working with integer-based cycle decompositions rather than floating-point continuous values.
2Adaptability or versatility
If existing mathematical tools are used to analyze system behaviors, then basic evaluation can be performed, but they struggle with analyzing the impact of multiple simultaneous perturbations
Solution Approach 1:
The patent segments perturbation analysis into individual cycle evaluations. By decomposing the system into fundamental cycles, each perturbation can be independently tracked through specific cycles, enabling accurate analysis of multiple simultaneous perturbations without the computational burden of analyzing the entire complex system at once.
Solution Approach 2:
The patent introduces fundamental cycles as intermediary structures between perturbations and system responses. These cycles serve as mediators that translate perturbation inputs into systematic cycle-based representations, making it easier to analyze and predict the impacts of multiple simultaneous perturbations on system behavior.
Data Source
AI summary
One embodiment of the present invention includes a computer operable to represent a physical system with a graphical data structure corresponding to a matroid. The graphical data structure corresponds to a number of vertices and a number of edges that each correspond to two of the vertices. The computer is further operable to define a closed pathway arrangement with the graphical data structure and identify each different one of a number of fundamental cycles by evaluating a different respective one of the edges with a spanning tree representation. The fundamental cycles each include three or more of the vertices.