Predicate Logic Representations For Set-Based Design Constraints On Uncertainty

Dr. William W. Finch
Center for Innovation in Product Development
Massachusetts Institute of Technology

Colloquium & AIRG/AIDG Presentation
Thursday, November 20, 1997
11 a.m.
Salisbury Labs 121

In this work, predicate logic is used in conjunction with algebraic constraints to mathematically represent engineering problems dominated by causally related variations in parameter values. Uncertainty enters design processes from many sources, including: manufacturing variations, environmental changes, operator adjustments, and uncertainty in the decisions of engineers. These variations complicate design processes in a wide variety of product domains. Conventional approaches to including uncertainty in engineering analysis and design, interval propagation for example, ignore how and when different variations affect system parameters. This can lead to incorrect inferences. Recent research solves the problem of including this missing information about uncertainty in engineering calculations.

The approach combines elements from predicate logic, constraint satisfaction, and Ward's Set-Based Design paradigm into a collection of tools for automating calculations about design variations. First, causal tables and graphs represent the causality of engineering systems, that is how and when variations affect the precise value of system parameters. These models help engineers understand complex interactions of multiple sources of variation. Second, quantified relations are predicate logic constraints on design, manufacturing, adjustment, and other variations. Construction of their patterns of quantified variables is guided by causal table entries. Third, two new theorems constitute an inference mechanism which operates on quantified relations involving monotonic, asymptote- free equations. It makes correct inferences about sets of variations in many cases where conventional methods fail. In isolation, however, the inference mechanism is not very useful for design automation.

New, set-based algorithms, based on conventional arc consistency techniques, eliminate provably infeasible variation sets, simplifying engineers' tasks by reducing the size of design spaces. This requires extension of existing constraint satisfaction techniques to variables that are assigned sets. This research may subsume Ward's prior work on the Label Interval Calculus (LIC), extending the approach to a wider range of engineering design problems. These algorithms have been implemented in a prototype software tool. Its application to three small example problems provides evidence that this work may lead to the development of useful automated design tools.

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