A Graph Theory Based Method for Functional Decoupling of a Design With Complex Interaction Structure

The primary objective in design is to achieve the target value of the design’s functional requirement. In design with multiple functional requirements, one way a design fails is the inability to converge to the multiple target values in spite of iterative adjustment of the design parameters. This is symptom of a design that fails to perform in the presence of functional coupling. Functional coupling occurs when two or more functional requirements are affected by a common set of design parameters. It is particularly difficult to identify and break when it involves inter-relation loops created among large number of functional requirements, typical of a large complex system. This paper presents a structured method based on the graph theory to effectively identify and eliminate functional couplings in a design. Use of the graph theory in this context is natural by the fact that inter-relations among functional requirements and design parameters can be represented by a digraph. Each inter-relation corresponds to an arc of the digraph, and functional coupling is equivalent to a cycle in it. The proposed method consists of: 1) represent interactions among functional requirements and design parameters as a digraph, 2) construct the cycle matrix for the digraph, 3) identify those candidate sets of arcs that, if removed, will destroy all cycles in the digraph, and 4) examine engineering feasibility of the candidate solutions. Once target interactions, i.e. arcs, are determined, the design parameters responsible for those interactions are modified to implement the solution. To demonstrate the effectiveness of the proposed method, we apply it to a large complex system, the car door to body, involving 28 functional requirements and design parameters.