Supersaturated Design Matrix Generation for Active Factor Identification
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Solution Overview
Problem
Supersaturated designs in experiments are underutilized due to difficulties in identifying active factors with current model selection techniques, as they cannot estimate all factors simultaneously and require advanced correlation analysis.
Innovation Solution
A computer-program product generates a supersaturated design by selecting dimensions for a matrix Y, computing correlation between factors, and transposing matrices X and X* to output settings for test conditions, enabling the identification of active factors in experiments with more factors than test cases.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If supersaturated designs are used to investigate more factors than test cases, then the ability to study complex systems with multiple components is improved, but the difficulty of identifying active factors using current model selection techniques increases
Solution Approach 1:
The patent segments the analysis process into distinct phases: first generating a supersaturated design matrix to cover all factor combinations, then applying stepwise model selection to systematically identify active factors. This segmentation allows the complex problem of analyzing more factors than test cases to be broken into manageable steps, resolving the contradiction between studying complex systems and identifying active factors.
Solution Approach 2:
The patent performs preliminary actions by pre-generating the supersaturated design matrix and pre-calculating the design information matrix before actual experiment execution. This preliminary preparation enables more efficient factor identification during analysis, as the computational framework is already in place to handle the high-dimensional data structure.
2Adaptability or versatility
If the number of factors investigated is larger than the number of test cases, then the coverage of complex system options is improved, but the capability to estimate all factors simultaneously deteriorates
Solution Approach 1:
The patent applies partial action by using stepwise model selection to identify a subset of active factors from the complete set of factors investigated. Rather than attempting to estimate all factors simultaneously (which would require more test cases than factors), the method progressively adds factors to the model only when statistical criteria indicate they are active, thus achieving factor identification with fewer test cases than total factors.
Solution Approach 2:
The patent implements feedback through the iterative stepwise selection process, where the model evaluation continuously assesses which factors should be included or excluded based on statistical criteria. This feedback mechanism allows the analysis to adaptively identify active factors even when the number of factors exceeds the number of test cases, resolving the contradiction between factor coverage and estimation capability.
Data Source
AI summary
A computing device receives a request for a design of an experiment. The device generates a data representation of a matrix Y that defines a supersaturated design for the design of the experiment. The generating the data representation is by: generating a data representation of a matrix X according to an obtained design; computing an indication of correlation between effects of factors of a matrix Y; and generating, based on the indication of correlation, the data representation of the matrix Y that is the transposition of the matrix X or is the transposition of a matrix X*. The matrix X* is a first subset of the matrix X such that the transposition of the matrix X* represents a same number of factors as the transposition of the matrix X. The device outputs a setting for each test condition of the supersaturated design for the experiment.