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A Formal Representational Theory for Engineering Design

Kevin N. Otto

Ph.D. Thesis, California Institute of Technology
(May 1992).

Abstract

In the design of engineered artifacts, it is hypothesized that computations must be performed. Informal specifications must be converted into formal functional requirements and informal descriptions must be converted into formal parameterizations, so that performance can be computed. Such performance evaluations are developed for general set based mappings. The development includes, for example, functional relations, differential equations, simple experimentation, and even subjective questioning. When this level of formalization is complete, the design is not determined; it is only parameterized. A designer must specify levels of the various performances desired, and how the various performances should be simultaneously considered in an overall determination. also must specify the simultaneous consideration of the performances in an overall determination.

An axiomatically based methodology is presented to formalize such decisions. Each decision variable is equipped with a preference specification, whose determination is made from techniques similar to utility theory. A design strategy for resolving these different aspects of a design is developed to produce an overall rating. For example, a designer may rate a design by the worst case performance. Alternatively, a designer may rate a design by a compensation among the goals.

In addition to decision representation, other parameters in a formalization reflect phenomena which the designer cannot control. A methodology for accommodating confounding noise influences is developed. Random measurement noise is represented, as well as the possibility of other decision makers in a design process. Convolutions of these methods are developed. For example, designer decision-making is developed for a decision which must be made in light of random errors (such as manufacturing). Designer decision-making is further developed for the case when a manufacturing engineer can subsequently tune a design (a possibilistic uncertainty) to eliminate such random error effects. Ensuring against failure is also discussed, with respect to the measured noise.

Given this development, a methodology is constructed in which a designer can incompletely specify performance requirements on a design. The incomplete specification can be induced across the design, to determine any restrictions imposed on the portions of the design where no specifications have been made. Thus, an iterative design process of specification, calculation, observation, and re-specification is given formal foundation.