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

• Published in: Proceedings in applied mathematics and mechanics Vol. 18; no. 1
• Main Authors: Vogt, Marc Eric, Duddeck, Fabian, Harbrecht, Helmut, Stutz, Florian, Wahle, Martin, Zimmermann, Markus
• Format: Journal Article
• Language: English
• Published: Berlin WILEY‐VCH Verlag 01.12.2018
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201800103

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 [7].