A matrix-based clustering approach for the decomposition of design problems

In matrix-based modeling, a design problem is represented by a rectangular matrix that captures the dependency relationships between design functions and parameters. To decompose such a matrix-based design problem, the two-phase method, which adapts hierarchical cluster analysis, has been proposed in literature. Yet, the clustering strategy in general is still challenging since the decomposition of design problems requires simultaneous clustering of two types of objects (i.e., design functions and parameters). In this paper, the notion of coupling is advanced by characterizing the coupling between two objects of different types. Accordingly, the two-phase method is revised via two methodical components: coupling-based dependency analysis and tree-based partitioning analysis. While the coupling-based dependency analysis concatenates different types of coupling for organizing the dependency structure, the tree-based partitioning analysis utilizes the coupling information from dependency analysis to identify design sub-problems and their interactions. Due to a better understanding of the coupling notion, the revised approach is able to simplify the algorithmic procedure and narrow down the solution search space without compromising the solution quality. Two examples (i.e., a relief valve system and a powertrain system) are used to demonstrate and justify the utility of the revised method.