State Evolution Determination via Degree of Freedom Similarity
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Real systems with a large number of degrees of freedom are difficult to calculate due to interacting degrees of freedom, requiring significant computational effort and resources.
Innovation Solution
A method that selects a subset of degrees of freedom based on similarity analysis, reducing the complexity of state evolution determination by considering only those degrees of freedom with similar temporal developments, thereby reducing computational demands.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all degrees of freedom are considered in the calculation, then the accuracy of state evolution determination is improved, but the computational effort and complexity increase significantly
Solution Approach 1:
The patent extracts and selects only the most relevant degrees of freedom for calculation by determining similarity measures between different degrees of freedom. Degrees of freedom with high similarity to the selected one are included in the reduced set, while less similar ones are excluded, thereby reducing computational complexity while maintaining sufficient accuracy.
Solution Approach 2:
The patent segments the complete set of degrees of freedom into a reduced subset based on similarity criteria. By dividing the full set into relevant and irrelevant portions, the method enables efficient computation focusing only on the segmented relevant subset while excluding less relevant degrees of freedom.
2Reliability
If all degrees of freedom are considered in the calculation, then the completeness of system characterization is improved, but the computational resources required increase significantly
Solution Approach 1:
The patent extracts and removes less relevant degrees of freedom from the complete set, retaining only those with high similarity to the selected degree of freedom. This extraction reduces the computational resource requirement while maintaining reliable system characterization through the preserved relevant subset.
Solution Approach 2:
The patent changes the parameter of degree of freedom selection from considering all possible degrees to selecting based on similarity thresholds. This parameter change enables computational resource efficiency while maintaining characterization reliability by dynamically adjusting which degrees of freedom are included based on their similarity measures.
3Measurement precision
If similarity analysis is performed for all degrees of freedom, then the accuracy of degree selection is improved, but the computational effort increases
Solution Approach 1:
The patent applies partial action by performing similarity analysis only for degrees of freedom that are potentially relevant, rather than exhaustively analyzing all degrees. By using a systematic approach to identify and analyze only the necessary subset, the method achieves accurate selection without the full computational burden of complete analysis.
Data Source
AI summary
The invention relates to a method for determining a state evolution of a real system with a plurality N of degrees of freedom, comprising the following steps: determining states for each of the plurality N of degrees of freedom up to a time t0, wherein the determining of states for each of the plurality N of degrees of freedom is carried out by measuring corresponding state variables of the real system; selecting a degree of freedom f from the plurality N of degrees of freedom; determining a measure of similarity between the selected degree of freedom f and each other degree of freedom of the plurality N of degrees of freedom of the real system for the determined states; determining a selection M of degrees of freedom from the plurality N of degrees of freedom based on the measure of similarity; and determining the state evolution of measured states for the selected degree of freedom f based on the selection M of degrees of freedom.