Managing Epistemic Uncertainty in Design Models through Type-2 Fuzzy Logic Multidisciplinary Optimization

Humans have a natural ability to operate in dynamic environments and perform complex tasks with little perceived effort. An experienced ship designer can intuitively understand the general consequences of design choices and the general attributes of a good vessel. A person's knowledge is often ill-structured, subjective, and imprecise, but still incredibly effective at capturing general patterns of the real-world or of a design space. Computers on the other hand, can rapidly perform a large number of precise computations using well-structured, objective mathematical models, providing detailed analyses and formal evaluations of a specfic set of design candidates. In ship design, which involves generating knowledge for decision-making through time, engineers interactively use their own mental models and information gathered from computer-based optimization tools to make decisions which steer a vessel's design. In recent decades, the belief that large synthesis codes can help achieve cutting-edge ship performance has led to an increased popularity of optimization methods, potentially leading to rewarding results. And while optimization has proven fruitful to structural engineering and the aerospace industry, its applicability to early-stage design is more limited for three main reasons. First, mathematical models are by definition a reduction which cannot properly describe all aspects of the ship design problem. Second, in multidisciplinary optimization, a low-fidelity model may incorrectly drive a design, biasing the system level solution. Finally, early-stage design is plagued with limited information, limiting the designer's ability to develop models to inform decisions. This research extends previously done work by incorporating type-2 fuzzy logic into a human-centric multidisciplinary optimization framework. The original framework used type-1 fuzzy logic to incorporate human expertise into optimization models through linguistic variables. However, a type-1 system does not properly account for the uncertainty associated with linguistic terms, and thus does not properly represent the uncertainty associated with a human mental model. This limitation is corrected with the type-2 fuzzy logic multidisciplinary optimization presented in this work, which more accurately models a designer's ability to "communicate, reason and make rational decisions in an environment of imprecision, uncertainty, incompleteness of information and partiality of truth" (Mendel et al., 2010). It uses fuzzy definitions of linguistic variables and rule banks to incorporate "human intelligence" into design models, and better handles the linguistic uncertainty inherent to human knowledge and communication. A general mathematical optimization proof of concept and a planing craft case study are presented in this dissertation to show how mathematical models can be enhanced by incorporating expert opinion into them. Additionally, the planing craft case study shows how human mental models can be leveraged to quickly estimate plausible values of ship parameters when no model exists, increasing the designer's ability to run optimization methods when information is limited.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145891/1/doriancb_1.pd