Information-Theoretic Methods for Modularity in Engineering Design

Abstract

Due to their many advantages, modular structures commonly exist in artificial and natural systems, and the concept of modular product design has recently received extensive attention from the engineering research community. Although some work has been done on modularity, most of it is qualitative and exploratory in nature, and little is quantitative. One reason for this gap is the lack of a clear definition of modularity. This thesis begins with a detailed discussion on the concepts of “modularity” and “module.” Based on the background presented here, a mutual information-based method is proposed to quantify modularity. The method is based on the view that coupling is information flow instead of real physical interactions. Information flow can be quantified by mutual information, which is based on randomness (or uncertainty). Since most engineering products can be modeled as stochastic systems and therefore have randomness, the mutual information-based method can be applied in very general cases, and it is shown that the commonly existing linkage counting modularity measure is a special case of the mutual information-based modularity measure. The mutual information-based method is applicable to final design products. But at the early stage of the engineering design process, there are generally only function diagrams. To exploit the benefits of modularity as early as possible, a minimal description length principle-based modularity measure is proposed to determine the modularity of graph structures, which can represent function diagrams. The method is used as criteria to hierarchically decompose abstract graph structures and the real function structure of an HP printer by evolutionary computation. Due to the specialty of genome representations in evolutionary computation, new genetic operators are developed to determine optimal hierarchical decompositions. This quantitative modularity measure has been developed to synthesize modular engineering products, especially by evolutionary design. There are many factors affecting evolving modular structures, such as genome representation, fitness function, learning, and task structure. The thesis preliminarily studies the effects of the modularity of tasks on the modularity of products in evolutionary computation. Using feed-forward neural networks as examples, the results show that the effects are task-dependent and rely on the amount of resources available for the tasks.