Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T01:12:09.419Z Has data issue: false hasContentIssue false

Generalized set-propagation operations over relations of more than three variables

Published online by Cambridge University Press:  27 February 2009

William W. Finch
Affiliation:
Mechanical Engineering and Applied Mechanics Department, 2250 G.G. Brown Lab, University of Michigan, Ann Arbor, Ml 48109–2125
Allen C. Ward
Affiliation:
Mechanical Engineering and Applied Mechanics Department, 2250 G.G. Brown Lab, University of Michigan, Ann Arbor, Ml 48109–2125

Abstract

This paper extends previously developed generalized set propagation operations to work over relationships among an arbitrary number of variables, thereby expanding the domain of engineering design problems the theory can address. It then narrows its scope to a class of functions and sets useful to designers solving engineering problems: monotonic algebraic functions and closed intervals of real numbers, proving formulas for computing the operations under these conditions. The work is aimed at the automated optimal design of electro-mechanical systems from catalogs of parts; an electronic example illustrates.

Type
Articles
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alefeld, G., & Herzberger, J. (1983). Introduction to Interval Computations. Academic Press, New York.Google Scholar
Bains, N., & Ward, A. (1993). Multiple-type interval propagations through non-monotonic equations. Submitted to ASME Journal of Mechanical Design.Google Scholar
Borowski, E., & Borwein, J. (1991). The Harper Collins Dictionary of Mathematics. Harper Perennial, New York.Google Scholar
Chen, R., & Ward, A. (1993). Generalizing interval matrix operations for design. Submitted to ASME Journal of Mechanical Design.Google Scholar
Habib, W., & Ward, A. (1991). In pursuit of a design mathematics: Generalizing the labeled interval calculus. 1991 ASME DTM Conference, Miami Beach, pp. 279284.Google Scholar
Liker, J., Sobek, D., Ward, A., & Cristiano, J. (1994). Communicating requirements to auto parts suppliers in the U.S. and Japan: Evidence for the set-based hypothesis in concurrent engineering. IEEE Journal of Engineering Management (in press).Google Scholar
Papalambros, P., & Wilde, D. (1991). Principles of Optimal Design, Modeling and Computation. Cambridge University Press, Cambridge.Google Scholar
Ward, A. (1989). A Theory of Quantitative Inference for Artifact Sets, Applied to a Mechanical Design Compiler. Ph.D. Thesis. Massachusetts Institute Of Technology, Cambridge.Google Scholar
Ward, A. (1990a). A recursive model for managing the design process. 1990 ASME Conference on Design Theory and Methodology, Chicago, IL.Google Scholar
Ward, A., Lozano-Perez, T., & Seering, W. (1990). Extending the constraint propagation of intervals. AI EDAM, 4 (1), 4754.Google Scholar
Ward, A., Liker, J., Sobek, D., & Cristiano, J. (1994). The second Toyota paradox: How delaying decisions can make better cars faster. Submitted to The Sloan Management Review.Google Scholar