A Formal Two-Phase Method for Decomposition of Complex Design Problems
Bibliographic record
Abstract
This paper presents a formal two-phase decomposition method for complex design problems that are represented in an attribute-component incidence matrix. Unlike the conventional approaches, this method decouples the overall decomposition process into two separate, autonomous function components: dependency analysis and matrix partitioning, which are algorithmically achieved by an extended Hierarchical Cluster Analysis (HCA) and a Partition Point Analysis (PPA), respectively. The extended HCA (Phase 1) is applied to convert the (input) incidence matrix, which is originally unorganized, into a banded diagonal matrix. The PPA (Phase 2) is applied to further transform this matrix into a block-angular matrix according to a given set of decomposition criteria. This method provides both flexibility in the choice of the different settings on the decomposition criteria, and diversity in the generation of the decomposition solutions, both taking place in Phase 2 without resort to Phase 1. These features essentially make this decomposition method effective, especially in its application to re-decomposition. A powertrain design example is employed for illustration and discussion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".