Computing solution-compensation spaces using an enhanced Fourier-Motzkin algorithm

Vogt, Marc Eric and Duddeck, Fabian and Harbrecht, Helmut and Stutz, Florian and Wahle, Martin and Zimmermann, Markus. (2018) Computing solution-compensation spaces using an enhanced Fourier-Motzkin algorithm. Proceedings in applied mathematics and mechanics, 18 (1). e201800103.

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Official URL: https://edoc.unibas.ch/67342/

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In complex system design, design variables can be divided into two groups, early‐ and late‐decision variables. Early‐decision variables are equipped with tolerance regions which are specified during the early stages of the development process. Tolerance is necessary to account for changes of design variable values due to later and therefore unknown, design restrictions. In this sense, early‐decision variables are subject to lack‐of‐knowledge uncertainty. Tolerance regions for early‐decision variables can be significantly increased by the use of late‐decision variables. The latter are not equipped with tolerance regions and, by contrast, have to be arbitrarily well adjustable within their design intervals. The values of late‐decision variables are chosen in a later development phase when further design restrictions are known. Late‐decision variables then may compensate for the choice of early‐decision variables. Solution‐compensation spaces are regions of early‐ and late‐decision variables where for all values of early‐decision variables values for late‐decision variables from their associated intervals exist such that all design requirements are satisfied. A new approach to compute solution‐compensation spaces for linear systems is introduced. It is based on an enhanced Fourier‐Motzkin‐Elimination algorithm which uses H‐redundancy removal. The new algorithm is applied to a design problem from vehicle dynamics and we show that it outperforms the so‐called basic projection algorithm presented in [ Vogt M. E., Duddeck F., Wahle M., Zimmermann M. "Optimizing tolerance to uncertainty in systems design with early-and late-decision  variables." IMA Journal of Management Mathematics].
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Stutz, Florian
Item Type:Article
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:15 Sep 2020 07:04
Deposited On:15 Sep 2020 07:04

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