Pi Number Inverse Transformation for Variable Quantity Analysis
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Solution Overview
Problem
Existing data analysis methods struggle to transform pi number data vectors into variable quantity data vectors without adding conditions to close equations between variable quantities and pi numbers, especially when multiple variable quantities are involved in a phenomenon.
Innovation Solution
A data analysis method that performs inverse transformation on pi number data vectors using pi number transformation information to obtain variable quantity data vectors, setting the range of numerical data within a particular variable quantity region to facilitate the transformation without requiring additional conditions to close equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If assumptions are introduced to fix part of the physical quantities, then the equations are closed and a particular solution can be obtained, but the transformation becomes restricted to specific conditions
Solution Approach 1:
The patent inverts the traditional transformation approach by using inverse transformation to convert pi number data vectors into variable quantity data vectors. Instead of transforming variable quantities to pi numbers and requiring assumptions to close equations, the method transforms from the simplified pi number representation back to the original variable quantities, eliminating the need for closing assumptions while maintaining transformation validity.
Solution Approach 2:
The patent changes the parameter representation from variable quantities to pi numbers for data processing, then uses inverse transformation to convert back to variable quantities. This parameter change allows the system to handle multiple variable quantities without requiring equation closure assumptions, as the pi number transformation information preserves the relationships between variables.
2Device complexity
If multiple variable quantities are involved in a phenomenon, then the pi number representation reduces complexity, but the equations cannot be closed without additional conditions
Solution Approach 1:
The patent applies inverse transformation to convert pi number data vectors into variable quantity data vectors. This inversion process eliminates the need for closing assumptions by directly transforming the simplified pi number representation back to the original variable quantities, maintaining the relationships between multiple variable quantities without requiring additional conditions.
Solution Approach 2:
The patent extracts the essential transformation relationships between variable quantities and pi numbers through the pi number transformation information matrix. By extracting this transformation information, the system can work with reduced complexity pi number representations and then reconstruct the original variable quantities through inverse transformation, separating the complexity reduction function from the equation closure requirement.
Data Source
AI summary
[PROBLEM TO BE SOLVED] Provided is a data analysis method which can transform a pi number data vector, which is numerical data of pi numbers, into a variable quantity data vector, which is numerical data of variable quantities, without adding a condition for closing equations between the variable quantities and the pi numbers.[SOLUTIONS TO THE PROBLEMS] A pi number inverse transformation processing in a data analysis method inversely transforms the pi number data vector π, composed of pi number data that is numerical data of the pi numbers, into the variable quantity data vector (q), composed of variable quantity data that is numerical data of the variable quantities, based on pi number transformation information (P) which determines, by an exponent of variable quantities included in the pi numbers, a relationship between a variable quantity set composed of a plurality of the variable quantities observed in the predetermined phenomenon and a pi number set composed of one or a plurality of pi numbers configured to be transformed from the variable quantities. In the performing of the inverse transformation includes performing a numerical analysis in which a range of the numerical data in the variable quantity data vector (q) is set to a particular variable quantity region D, and performing pi number inverse transformation processing which inversely transforms the pi number data vector n into the variable quantity data vector (q) existing in the variable quantity region D.