A method for the representation and manipulation of uncertainties in preliminary engineering design

Citation

Wood, Kristin Lee (1990) A method for the representation and manipulation of uncertainties in preliminary engineering design. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/g1hs-p655. https://resolver.caltech.edu/CaltechETD:etd-11152007-080746

Abstract

Each stage of the engineering design process, and particularly the preliminary phase, includes imprecision, stochastic uncertainty, and possibilistic uncertainty. A technique is presented by which the various levels of imprecision (where imprecision is: "uncertainty in choosing among alternatives") in the description of design elements may be represented and manipulated. The calculus of Fuzzy Sets provides the foundation of the approach. An analogous method to representing and manipulating imprecision using probability calculus is presented and compared with the fuzzy calculus technique. Extended Hybrid Numbers are then introduced to combine the effects of imprecision with stochastic and possibilistic uncertainty. Using the results, a preliminary set of metrics is proposed by which a designer can make decisions among alternative configurations in preliminary design.

In general, the hypothesis underlying the techniques described above is that making more information available than conventional approaches will enhance the decision-making capability of the designer in preliminary design. A number of elemental concepts toward this hypothesis have been formulated during the evolution of this work: • Imprecision is a hallmark of preliminary engineering design. To carry out decisions based on the information available to the designer and on basic engineering principles, the imprecise descriptions of possible solution technologies must be formalized and quantified in some way. The application of the fuzzy calculus along with a fundamental interpretation provides a new and straight-forward means by which imprecision can be represented and manipulated. • Besides imprecision, other uncertainties, categorized as stochastic and possibilistic, are prevalent in design, even in the early stages of the design process. Providing a method by which these uncertainties can be represented in the context of the imprecision is an important and necessary step when considering the evaluation of a design's performance. Extended Hybrid Numbers have been introduced in this work in order to couple the stochastic and possibilistic components of uncertainty with imprecision such that no information is lost in the process. • Because of the size, coupling, and complexity of the functional requirement space in any realistic design, it is difficult to make decisions with regard to the performance of a design, even with an Extended Hybrid Number representation. Defining and utilizing metrics (or figures of merit) in the evaluation of how well a design meets the functional requirements reduces the complexity of this process. Such metrics also have merit when we begin to think of languages of design and adding the necessary pragmatics of "will a generated or proposed design satisfy the performance requirements with respect to the ever-present and unavoidable uncertainties?". These concepts form the central focus of this work. The mathematical methods presented here were developed to support and formalize these ideas.

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