Uncertainty Quantification of Multi-Scale Resilience in Nonlinear Complex Networks using Arbitrary Polynomial Chaos

Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network considering interactions between components is limited. Even though, recent research in macro and micro resilience pattern has developed analytical tools to analyze the relationship between topology and dynamics across network scales. The effect of uncertainty in a large-scale networked system is not clear, especially when uncertainties cascade between connected nodes. In order to quantify resilience uncertainty across the network resolutions (macro to micro),an arbitrary polynomial chaos (aPC) expansion method is developed in this paper to estimate the resilience subject to parameter uncertainties with arbitrary distributions. For the first time and of particular importance, is our ability to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk. We test this using a generic networked bi-stable system and this will aid practitioners to both understand macro-scale behaviour and make micro-scale interventions.