Before revision:  In order to quantify resilience uncertainty across the network resolutions (macro to micro), we develop an arbitrary polynomial chaos (aPC) expansion method  to estimate the resilience subject to parameter uncertainties with arbitrary distributions.
After revision:  In order to quantify resilience uncertainty across the network resolutions (macro to micro), we develop an arbitrary polynomial chaos (aPC) expansion method is developed in this paper to estimate the resilience subject to parameter uncertainties with arbitrary distributions.