Seminar in Numerical Analysis: Markus Zimmermann (Technische Universität München)

Solution Spaces in Complex Systems Design

Solution spaces are sets of engineering solutions, i.e., designs that satisfy all engineering requirements. Seeking solution spaces rather than just one possibly optimal solution is numerically challenging, but it can significantly simplify the development of systems in the presence of uncertainty and complexity. For different system components, solution spaces are decomposed into independent target regions that enable distributed development work and encompass uncertainty without particular underlying uncertainty model. A basic stochastic algorithm to maximize so-called box-shaped solution spaces is presented. Two recent extensions are discussed: first, representations as Cartesian product of two- and higher-dimensional spaces and, second, so-called solution-compensation spaces, where design variables are grouped according to the order in which they need to be specified. Applications to vehicle development for crash and driving dynamics are presented.

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