A hierarchical framework for complex networks robustness analysis to errors

Robustness analysis is concerned with the capability of a Complex Network, or System, to handle damaging events. It can consider errors or malicious attacks and is performed by simulating parts removals and quantifying such removals impact. Traditionally, errors are sampled with an assumption of equal failure probabilities for all susceptible system' parts. However, today engineered systems are becoming even more heterogeneous, with complex structure and dynamics. This paper introduces a hierarchical framework for robustness analysis to contemplate the structural complexity by respecting the different type of elements that constitute engineered systems. The proposed framework have two layers. The first is a Sampling Layer that uses models from Reliability Engineering to distinguish the process of failure for each type of element during random errors simulations. The second is a Performance Layer that uses the simulations from Sampling Layer to quantify the removals impacts. Samples from a Brazilian Power Distribution System are used as a test case to demonstrate the Hierarchical framework. The results are similar with the traditional robustness analysis when the relation between impact and removals is analyzed. In addition, a new analysis by considering the time variable added by the Sampling Layer is possible. By choosing a specific time window for comparing samples robustness, is possible to obtain different results. In our samples, the most vulnerable sample in a single day time window is a robust sample when considering only the impact versus removals. We conclude this manuscript with some aspects that should be explored in future research, as the use of covariates and rare events simulation techniques to focus on the low-probability high impact events.