A Formal Two-Phase Method for Decomposition of Complex Design Problems

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.