Technische Universität München

Numerical Optimization of Solution Spaces for Complex Systems Design (PhD)

Aplications by October 26th 2021

Dividing large technical systems, such as airplanes or vehicles, into several smaller and more manageable parts or components is a common technique to reduce design complexity. This can be accomplished by formulating component requirements that help to align separated and independent design work towards an overall system design goal. Good component requirements guarantee – when satisfied – that the system of interacting components reaches the overall design goal. In addition, they are just as restrictive as absolutely necessary and, thus, provide maximum design freedom. This is difficult to accomplish for complex systems, where non-linear component interaction with a large number of combinations of possible component properties is to be taken into account.

Existing approaches compute so-called solution spaces that are the Cartesian product of permissible regions for component properties. They rely on special adaptions of numerical optimization algorithms. Approaches that can treat arbitrary non-linear systems are unfortunately limited to one-dimensional permissible regions, i.e., interval-type requirements for only one component property each. However, even when maximized, interval-type requirements may be unnecessarily restrictive. When a component possesses several relevant properties, requirements for each of them will be in total more restrictive than (or at least as restrictive as) one requirement for all of them. The goal of this project is to compute and maximize generalized component solution spaces: they are the largest high-dimensional (or possibly infinite-dimensional) permissible regions for all relevant properties of one component. If properties of all components are realized within their respective component solution spaces, the overall design goal will be reached with maximum design freedom. Numerical Tools to be used range from numerical optimization to modern machine learning algorithms.

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