Abstract
The consideration of uncertainty is especially important for the design of complex systems. Because of high complexity, the total system is normally divided into subsystems, which are treated in a hierarchical and ideally independent manner. In recent publications, e.g., (Zimmermann, M., and von Hoessle, J. E., 2013, “Computing Solution Spaces for Robust Design,” Int. J. Numer. Methods Eng., 94(3), pp. 290–307; Fender, J., Duddeck, F., and Zimmermann, M., 2017, “Direct Computation of Solution Spaces,” Struct. Multidiscip. Optim., 55(5), pp. 1787–1796), a decoupling strategy is realized via first the identification of the complete solution space (solutions not violating any design constraints) and second via derivation of a subset, a so-called box-shaped solution space, which allows for decoupling and therefore independent development of subsystems. By analyzing types of uncertainties occurring in early design stages, it becomes clear that especially lack-of-knowledge uncertainty dominates. Often, there is missing knowledge about overall manufacturing tolerances like limitations in production or subsystems are not even completely defined. Furthermore, flexibility is required to handle new requirements and shifting preferences concerning single subsystems arising later in the development. Hence, a set-based approach using intervals for design variables (i.e., interaction quantities between subsystems and the total system) is useful. Because in the published approaches, no uncertainty consideration was taken into account for the computation of these intervals, they can possibly have inappropriate size, i.e., being too narrow. The work presented here proposes to include these uncertainties related to design variables. This allows now to consider lack-of-knowledge uncertainty specific for early phase developments in the framework of complex systems design. An example taken from a standard crash load case (frontal impact against a rigid wall) illustrates the proposed methodology.
