Flexible Space-Filling Design for Non-Rectangular Experimental Spaces
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Solution Overview
Problem
Existing methods face challenges in uniformly distributing design options across non-rectangular design spaces, particularly when categorical factors are involved, leading to inefficient experimentation and data analysis.
Innovation Solution
A computer-program product that generates representative points within a design space, determines primary and sub-clusters, allocates categorical factor levels, and modifies the design to increase separation between points, ensuring effective distribution and analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If representative points are generated and clusters are determined for non-rectangular design spaces with categorical factors, then the distribution of design points improves, but the complexity of the design generation process increases
Solution Approach 1:
The design space is segmented into multiple primary clusters based on categorical factors, and each primary cluster is further divided into sub-clusters. This hierarchical segmentation allows uniform distribution of design points across complex non-rectangular design spaces by breaking down the overall space into manageable regions, thereby improving distribution uniformity while managing process complexity through systematic division.
2Productivity
If design points are distributed uniformly across the design space, then experimentation efficiency improves, but the difficulty of allocating categorical factor levels uniformly increases
Solution Approach 1:
The method applies local quality by allocating categorical factor levels uniformly within each primary cluster and sub-cluster independently. This ensures that each local region maintains uniform distribution of factor levels, which contributes to overall experimentation efficiency while making the allocation process more manageable through localized uniformity rather than requiring global uniformity across the entire design space.
3Measurement precision
If separation between design points is increased, then measurement precision improves, but the number of design points that can be accommodated decreases
Solution Approach 1:
The hierarchical clustering approach introduces an additional dimensional structure by organizing design points into primary clusters and sub-clusters. This dimensional organization allows the system to maintain adequate separation between design points for measurement precision while accommodating a larger total number of design points through the multi-level cluster structure, effectively adding a organizational dimension to the design space.
Data Source
AI summary
A computing device generates representative points, each representing a potential design point for a design space. The computing device determines for the design space primary clusters, a categorical factor, and at least two levels for the categorical factor. The computing device, for each of the primary clusters, selects a design point from each sub-cluster of the respective primary cluster. The computing device, for each of the primary clusters, allocates the at least two levels of the categorical factor, such that a level of the at least two levels is allocated to each selected design point in the respective primary cluster. The computing device modifies an initial sub-design that represents the selected design points allocated a given level of the categorical factor by increasing separation between design points allocated a same level of the categorical factor. The computing device outputs to an output device a modified design for the design space.