Speaker
Description
Evaluating the integrity measure of safe basins is a critical task in engineering, as it provides insight into the robustness of operational states in various machines and systems. A classical local approach involves determining the largest radius hypersphere (or, in a suitably scaled context, a hyperellipsoid) fully contained within the safe region. However, in high-dimensional spaces, even infinitesimal discrepancies between the basin boundary and the shape of the l² hypersphere lead to a drastic reduction in its relevance. As the number of dimensions n grows, a fixed-radius l² hypersphere occupies an increasingly negligible portion of the basin’s hypervolume, rendering the conventional l²-based measure less meaningful. In this work, we elucidate the fundamental inadequacy of the standard l² measure in high-dimensional settings. To overcome this shortcoming, we propose an alternative approach for identifying the optimal l^p-norm that best aligns with the basin geometry, thereby minimizing the volume loss at the basin’s boundary. By analyzing a set of high-dimensional escape problems, we show that an appropriately chosen lᵖ-based measure offers a more robust and consistent framework for quantifying safe basins, ultimately enhancing the reliability of safety evaluations in engineering applications.
