Uncertainty of Resilience in Complex Networks With Nonlinear Dynamics

Abstract

Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behaviour well, our understanding of systems consisting of a large number of components is limited. Recent research in predicting the network level resilience pattern has advanced our understanding of the coupling relationship between global network topology and local nonlinear component dynamics. However, when there is uncertainty in the model parameters, our understanding of how this translates to uncertainty in resilience is unclear for a large-scale networked system. Here we develop a polynomial chaos expansion method to estimate the resilience for a wide range of uncertainty distributions. By applying this method to case studies, we not only reveal the general resilience distribution with respect to the topology and dynamics sub-models, but also identify critical aspects to inform better monitoring to reduce uncertainty.

Uncertainty quantification of multi-scale resilience in networked systems with nonlinear dynamics using arbitrary polynomial chaos

“…Uncertainty not only affects the macro-level resilience but also can affect individual nodes' , especially uncertainty may cause different effects on different nodes in a network. This can paint a different picture to that of the overall macro-scale network behavior found in previous work 15 . That is to say, a macro-scale resilient network may hide non-resilient behavior at the micro-scale, which if not addressed in time can cause long term issues.…”

“…We do so by defining arbitrary uncertainty distributions on system's parameters. A mean field estimation is used to approximate the network-level resilience and PCE is used to quantify the effect of uncertainty on network-level resilience as we have done in our previous work 15 . By this step, we can quantify the effect of uncertainty on network level.…”

“…Model uncertainty may stem directly from the incomplete information of the system or measurement noise of the initial data as well as from parameters of models whose values are not known exactly 13,14 . In order to know the effect of uncertain parameters on the network-level resilience, previous work introduced a polynomial chaos method 15 to understand network-level resilience loss with uncertainty. Uncertainty not only affects the macro-level resilience but also can affect individual nodes' , especially uncertainty may cause different effects on different nodes in a network.…”

“…When quantifying the uncertainty on the network-level resilience, mean field estimation and Central Limit Theorem (CLT) can be employed to make the system's equilibrium depend on a r.v. following Gaussian distribution 15 . So, the PCE methods can be directly used.…”

“…However, uncertainty, which may stem from incomplete information of the system or measurement noise of the initial data as well as parameters of model not known exactly, is widespread in practical problems in real world and affects performance of the system. To quantify the effects of uncertainty on the network-level resilience of the system, a specific network-based method with PCE is employed in 15 . However, it was not clear before our new paper:…”