Operating State Assessment via Graph Laplacian Factorization
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Solution Overview
Problem
Existing methods for assessing the operating state of technical systems are computationally intensive, especially when predicting characteristic variables that depend on complex relationships within the system, limiting the ability to optimize system design or predict potential issues in advance.
Innovation Solution
A method that uses an impact function to describe the interaction of basic variables within a technical system, factorizes this function into contributions depending on subsets of basic variables, and represents these interactions in a graph to assess the operating state through the extremal eigenvalue of the Laplace matrix of this graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If explicit evaluation of complex relationships is used to predict characteristic variables, then measurement precision is improved, but productivity deteriorates due to high computational effort
Solution Approach 1:
The patent segments the complex impact function into multiple factor functions, each depending on a subset of basic variables. This segmentation allows parallel computation of simpler factor functions instead of evaluating the complex whole function, thereby maintaining prediction accuracy while significantly improving computational efficiency and productivity.
2Manufacturing precision
If complex relationships are explicitly evaluated to optimize system design, then manufacturing precision is improved, but loss of time increases due to computational intensity
Solution Approach 1:
By dividing the complex impact function into multiple independent or partially independent factor functions, the patent enables parallel evaluation during system design optimization. This segmentation reduces the sequential computation time required to evaluate different design configurations, thereby decreasing loss of time while maintaining the precision needed for optimal design decisions.
Solution Approach 2:
The patent performs preliminary factorization of the impact function into manageable factor functions before the actual optimization process. This preliminary action prepares the computational structure in advance, allowing faster evaluation during the optimization iterations and reducing the overall time loss for design optimization.
3Reliability
If comprehensive evaluation of aggregate variables is performed, then reliability is improved, but device complexity increases due to computational requirements
Solution Approach 1:
The patent reduces device complexity by segmenting the comprehensive aggregate variable evaluation into multiple simpler factor function evaluations. Each factor function can be computed independently or with reduced interdependencies, simplifying the computational system architecture while maintaining comprehensive assessment capability through the combination of factor results.
Solution Approach 2:
The factor functions serve as intermediaries between the basic variables and the final aggregate variable. Instead of directly evaluating the complex relationship between basic variables and aggregate variables, the patent introduces factor functions as intermediate computational steps, thereby reducing the apparent complexity of the overall system while maintaining reliability.
Data Source
AI summary
A method for the assessment of the operating state of a technical system. The operating state is characterized by an aggregate variable whose value results through the interaction of basic variables according to the configuration of the technical system. In the method: an impact function, which indicates dependence of the aggregate variable on the basic variables is provided; the impact function is factorized to form a product of contributions, which depend on different subsets of the basic variables; a graph is formed, each node corresponding to a contribution, an edge extends in relation to each basic variable on which this contribution depends, at least one edge that corresponds to a basic variable on which two or more contributions depend connects two nodes corresponding to such contributions; the Laplace matrix of this graph is ascertained; an extremal eigenvalue of this Laplace matrix is ascertained as the assessment.