Design as a Sequential Decision Process: A Method for Reducing Set Space Using Models to Bound Objectives
Open Access
- Author:
- Miller, Simon W
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 01, 2017
- Committee Members:
- Timothy W Simpson, Dissertation Advisor/Co-Advisor
Timothy W Simpson, Committee Chair/Co-Chair
Mary Frecker, Committee Member
Michael A Yukish, Committee Member
Gordon Warn, Outside Member
Mark Traband, Committee Member - Keywords:
- design
decision-making
sequential decision
bounding model
interval dominance
discriminatory
model
set-based design
fidelity - Abstract:
- Complex engineered systems rely heavily on simulation models for design. Designing such systems typically involves a sequential decision process that increases the modeling and engineering analysis detail while simultaneously decreasing the space of alternatives considered. This space of alternatives is called the tradespace, and in a decision theoretic framework, low-fidelity models help decision-makers identify regions of interest in the tradespace and cull others prior to constructing more computationally-expensive higher fidelity models to further discriminate alternatives in support of a model-based systems engineering process. Previous work has shown that multi-fidelity modeling can aid in rapid optimization of the design space when higher fidelity models \emph{are coupled with} lower fidelity models, i.e., it is assumed that both models are available, and the two are used as a computational ``trick'' to speedup optimization routines. This dissertation introduces and motivates the sequential process of design through a formal model. The formal model seeks to answer (1) what structure models of varying fidelities should have relative to one another, (2) a linkage between decisions made from each modeling effort, and (3) a method for selecting a sequence of computational models and analyses when considering design as a \emph{sequential decision process}. The method presented herein demonstrates design as a sequence of finite decision epochs through a tradespace defined by the extent of the set of designs under consideration, modeling characteristics, and the level of analytic fidelity subjected to each design. This work introduces a method for constructing cost-optimal sequences of models of increasing fidelity by reducing the design set size under the guarantee that the optimal solution remains in the consideration set at each epoch. A summary of relevant literature in design sciences, social sciences, and engineering optimization communities is given to scope the research. The formal model is presented with its assumptions, definitions, and applications as well as a method for applying the model to an engineering system. The method is applied to several examples including 1D and 2D finite element analysis and a bi-level optimization problem with a combinatorial kernel based on a 2D bin packing problem. It is demonstrated that by treating design as a sequential decision process, significant savings (e.g., time, money) can be obtained.