Computations with Imprecise Parameters in Engineering Design: Background and Theory

Abstract

A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineer­ ing design. This imprecision is represented using the fuzzy calculus. Calculations can be performed using this method, to produce (imprecise) performance parameters from imprecise (input) design parameters. The Fuzzy Weighted Average technique is used to perform these calculations. A new metric, called the y-level measure, is in­ troduced to determine the relative coupling between imprecise inputs and outputs. The background and theory supporting this approach are presented, along with one example. Engineering design, both in practice and research, is evolv­ ing rapidly, especially in the development of computer-base d tools. Emphasis is moving from the later stages of design, to computational tools for preliminary design. In an earlier paper [35], a general approach to computational tools in preliminary engineering design and a model of the design pro­ cess was described. The primary aim of this model is to pro­ vide a structure for the development of tools to assist the designer in: managing the large amount of information en­ countered in the design process; determining a design's func­ tional requirements and constraints; evaluating the coupling between the design parameters; and carrying out the process of choosing between alternative design concepts. We are particularly interested in developing tools to assist the designer in the. preliminary phase of engineering design, by making more information available on the performance of design alternatives than is available using conventional design techniques. The most important design decisions (and poten­ tially the most costly, if wrong) are made at the preliminary stage. Our hypothesis is that increased information, over what is available by traditional design methods, will enable these decisions to be made with greater confidence and reduced risk. The effect will be greater, the earlier in the design cycle addi­ tional information can be made available. The preliminary phase of the engineering design process is one that embodies many functions: concept generation; evaluation of imprecise descriptions of simplified versions of the design; judgment of design feasibility; etc. [14, 15, 28]. The concept generation and simplification processes will not be addressed by the research reported here; rather our aim is to provide a technique for representing, manipulating, and evaluating the approximate, or imprecise, parametric descrip­ tions of the (preliminary) design artifact.