A Systematic Approach of Global Sensitivity Analysis and Its Application to a Model for the Quantification of Resilience of Interconnected Critical Infrastructures

Abstract

We consider a model for the resilience analysis of interconnected critical infrastructures (ICIs) that describes the dependencies among the subsystems within the ICIs and their time-varying behavior. The model response is a function of uncertain inputs comprising ICIs design parameters and failure magnitudes of vulnerable elements in the system, etc. In this methodological paper, we present a systematic approach based on an innovative blend of methods to perform a sensitivity analysis for identifying the most relevant variables affecting the system resilience at different stages, during a disruptive event. The methods considered include the following: the use of the graphical representation of Cusunoro curves for a visualization of the impact of an input on the resilience metric and an understanding of whether the associated dependence is monotonic, increasing, or decreasing; the introduction of an ensemble of indicators related to different properties of the resilience metric to allow the prioritization of variable importance and avoid false negatives, meaning to regard a variable as non-influential when, instead, it plays a relevant role in the determination of the model response; the calculation of first-order variance-based sensitivity indices to have an appreciation on the relevance of interactions when inputs are independent; and a data approach to visually identify relevant second-order interactions. All the sensitivity methods considered are performed on a provided sample, and do not require additional model evaluations. They allow the analyst to post-process the data to extract, simultaneously, several desirable insights. The systematic approach proposed to apply these methods allows us to identify the model input variables and parameters that are not very relevant, while it enables the identification of the relevant ones which allows prioritizing interventions on the vulnerable elements of the system for its resilience at different stages during a disruptive event. Given the methodological nature of the work, a simplified infrastructure model describing an interconnected gas network and electric power grid is taken as case study: this allows us to show that the approach is straightforward to understand and implement, and the results obtained show the usefulness of the approach in providing meaningful insights that can be used by stakeholders and decision makers to inform strategies for the improvement of system resilience. By the application of the simplified ICIs model to the case study, it is shown that the approach can be straightforwardly implemented to identify the most relevant variables on system resilience and obtain the most important subsystems. The key factors which affect system resilience in multiple initial failures scenarios are found; this allows us to identify the key resilience improvement measurements, and their priorities.