A SET-BASED SYSTEM FOR ELIMINATING INFEASIBLE DESIGNS IN ENGINEERING PROBLEMS DOMINATED BY UNCERTAINTY

This paper gives an overview of a system which eliminates infeasible designs from engineering design problems dominated by multiple sources of uncertainty. It outlines methods for representing constraints on sets of values for design parameters using quantified relations, a special class of predicate logic expressions which express some of the causal information inherent in engineering systems. The paper extends constraint satisfaction techniques and describes elimination algorithms that operate on quantified relations and catalogs of toleranced or adjustable parts. It demonstrates the utility of these tools on a simple electronic circuit, and describes their implementation and test in a prototype software tool. 1.0 INTRODUCTION This work addresses classes of design problems in which uncertainty complicates the design, manufacture, and operation of engineering systems. Uncertainty enters design processes from many sources, including: manufacturing variations, environmental changes, operator adjustment, and uncertainty in the decisions of other engineers. In electronic design, for example, component tolerances are often critical to a design’s success. Compared with (Ward, 89) this approach offers greater expressive power, a clearer semantics, and closer ties to well-established ideas in computer science. A result of including uncertainty in design processes is that precise values are no longer sufficient to describe the attributes of engineering systems. Electronic engineers, for example, rarely describe resistors solely by nominal values, typically using toleranced values (e.g. 100 ohms ±10%) instead. For resistors, this representation is more expressive than a single value; it constrains information about possible manufacturing variations. Several representations have been proposed for including variations in engineering analysis and design. Probability distributions, e.g. normal curves, often describe variations resulting from stochastic processes. (Wood and Antonsson, 89) and (Wood, et. al, 92) use fuzzy set representations to encode and propagate imprecision through engineering equations. (Ward, 89) uses closed and labeled intervals to represent sets of possible and required values for parameters. (Habib and Ward, 91) then extend this approach to arbitrary sets. In the approach described in this paper, closed intervals describe many types of design variation; however, new propagation operations replace conventional interval mathematics. The remainder of this section briefly discusses the Set-Based Paradigm for design processes and formulates a design problem for a simple electronic circuit. The following sections describe each component of the system and apply it to the design example. Finally, these ideas are integrated into a software tool that reduces the size of design spaces by eliminating infeasible designs. 1.1 Set-Based Design This approach is most readily understood within the framework of the Set-Based Design paradigm. Set-Based Design is a term coined by Ward describing a process in which “designers...must draw inferences about sets of artifacts (physical objects) under sets of operating conditions; they cannot simply simulate or analyze single, completely specified designs” (Ward, 89). This contrasts iterative, or p int-to-point , approaches which synthesize a single solution and then evolve the design through a series of analyses, evaluations and modifications (see for example Shigley and Mitchell, 83). An example, adapted from (Lee, 96), illustrates how set-based reasoning efficiently finds answers to some types of