Axiomatic approach to the modeling of product conceptual design processes using set theory

This thesis presents an axiomatic approach to the modeling of product conceptual design processes using set theory. It can be divided into three parts: the axiomatic system, the nature of the design problem and design processes, and applications. The first part aims to establish the theory whereas the latter two test and justify the theory.; The axiomatic system consists of two axioms: axiom of bounded rationality and axiom of object structuring. The axiom of bounded rationality states that human recognition is not perfect while the axiom of object structuring indicates what should be a full picture of an object. These two axioms deal with human and natural parts in the design process respectively. Set theory is used as the language to represent axioms, theorems, and facts appearing in the theory. Based on this theory, formal models of the product-environment system, design requirements, and the design process are derived following logical steps. These formal models are characterized by: the dynamic and evolving nature of product descriptions and product performances, the uniform representation of design requirements, and an environment decomposition-based conceptual design process. These three parts constitute an integral formal model of product state to the concrete and specific.; A design governing equation, which captures the ill-structured nature of design problem, is obtained from the axiomatic system. This equation implies that design problem solving is a process looking for fixed points under the design function, which is nonlinear in nature. This associates designing to nonlinear dynamics and leads to an explanation of design creativity. In this way, the randomness and uncertainty of design creativity could have a position in a scientific framework with determined laws. These are the three routes to creative designs presented in the thesis. To illustrate and test the ideas in this theory, a rivet setting tool design case study is used throughout the thesis.; This thesis also presents a mechanism design software developed based on the principles implied in the established theory. The software automatically generates multiple design concepts for changing straight-line motions merely with the performance knowledge. This software prototype demonstrates the usefulness of the theory in the development of conceptual design tools in aiding design engineers.