On the quantification of robustness and its thresholds

Structural systems need to be safe enough against foreseeable loads, but they also need to be robust enough against unforeseeable or abnormal loading. In this paper, a novel entropy-based robustness index for arbitrary perturbations is derived for coherent path-dependent systems, which is consistent with information-theoretic and thermodynamic principles. Using a reliability-based robustness index and the entropy-based robustness index, quantitative robustness thresholds are derived that enable the explicit classification of <em>low</em>, <em>medium</em>, and <em>high</em> robustness based on the sensitivity of the system to arbitrary perturbations. Furthermore, relations between the entropy- and reliability- and risk-based robustness indices are explored, where thresholds for the risk-based robustness indices are provided based on the novel entropy-based robustness index. The use of the various robustness indices and the thresholds are exemplified in three case studies, involving a redundant system subjected to various degrees of damage, damage propagation in frame structures, and a network. For the first time, quantitative thresholds for the robustness of coherent path-dependent systems are provided, which can be applied to structures, networks, and more. This paves the way for providing quantitative guidance on acceptable degrees of robustness in such systems, which may lead to more economic and rational systems with an appropriate degree of robustness.