Multi-Dimensional Mapping of Design Imprecision

Manuscript prepared for submission to the ASME 1996 Design Theory and Methodology Conference.

William S. Law
Engineering Design Research Laboratory
California Institute of Technology
Pasadena, California 91125
law@design.caltech.edu

Erik K. Antonsson
Engineering Design Research Laboratory
Division of Engineering and Applied Science
California Institute of Technology
Pasadena, California 91125

Preliminary design information is characteristically imprecise or fuzzy: specifications and requirements are subject to change, and the design description is vague and incomplete. Precise information about the final design is usually not available. Yet many powerful evaluation tools, including finite element models, expect precisely specified data. Thus it is common for engineers to evaluate promising designs one by one. Alternatively, optimization may be used to search for the single ``best'' design. But these approaches focus on individual, precisely specified points in the design space and provide limited information about the full range of possible designs under consideration. An alternative approach would be to evaluate sets of designs and hence explicitly model design imprecision.

The Method of Imprecision uses the mathematics of fuzzy sets to represent and manipulate imprecise preliminary design information, enabling the designer to better understand the full range of designs and performances that satisfy an imprecise set of specifications and requirements. Imprecision is represented by quantifying the customer's preferences in the context of relevant aspects of design performance. Functional requirements model the customer's direct preference on performance variables. Design preferences model the customer's anticipated preference on design variables. These preferences are aggregated separately on the design variable space (DVS) and the performance variable space (PVS). A key step is to map design preferences from the DVS to the PVS, a step that requires the mapping of sets as opposed to individual points. The extended methods introduced in this paper map design preference level sets from n design variables to q performance variables. These methods attempt to minimize the number of function evaluations required while retaining an appropriate level of accuracy. This is achieved by using optimization to obtain extremal points for each performance variable and selectively applying a linear approximation for the mapping from the DVS to the PVS to interpolate between extremal points. This linear approximation is constructed using regression techniques adapted from experiment design.