A dynamic importance function for accidental scenarios generation by RESTART in the computational risk assessment of cyber-physical infrastructures

The Computational Risk Assessment (CRA) of Cyber-Physical Systems (CPSs) calls for the analysis of accidental scenarios emerging from the complexities and interdependencies typical of CPSs. Generating these scenarios via crude Monte Carlo Simulation (MCS) is impractical due to the high computational demand of simulation codes of CPSs, considering the combinatorial number of possible scenarios. In this paper, we tailor the use of Repetitive Simulation Trials After Reaching Thresholds (RESTART), a rare-event simulation method of literature, to efficiently generate relevant accidental scenarios. The tailored RESTART is guided by a dynamic Importance Function (IF) originally introduced here to dynamically characterize the relevance of the scenarios with reference to the current topology of the CPS and the susceptibility of its components. Two case studies of increasing complexity are considered: a single power grid and a CPS consisting of an Integrated Power and Telecommunication (IP&TLC) infrastructure. Results show that RESTART mines out more relevant scenarios than crude MCS for a number of different IFs based on vulnerability metrics of literature, and thus particularly efficiently when the novel IF is adopted.