Methodical Extensions for Decomposition of Matrix-Based Design Problems

The two-phase method is a matrix-based approach for system decomposition, in which a system is represented by a rectangular matrix to capture dependency relationships of two sets of system elements. While the two-phase method has its own advantages in problem decomposition, this paper focuses on two methodical extensions to improve the method’s capability. The first extension is termed nonbinary dependency analysis, which can handle nonbinary dependency information, in addition to just binary information, of the model. This extension is based on the formal analysis of a resemblance coefficient to quantify the couplings among the model’s elements. The second extension is termed heuristic partitioning analysis, which allows the method to search for a reasonably good decomposition solution with less computing effort. This extension can be viewed as an alternative to the original partitioning approach that uses an enumerative approach to search for an optimal solution. At the end, the relief valve redesign example is applied to illustrate and justify the newly developed method components.