Nonparametric statistical analysis of system resilience migration and application for electric distribution structures

This paper proposes a set of nonparametric statistical tools for analyzing the system resilience of civil structures and infrastructure and its migration upon changes in critical system parameters. The work is founded on the classic theoretic framework that system resilience is defined in multiple dimensions for a constructed system. Consequentially, system resilience can lose its parametric form as a random variable, falling into the realm of nonparametric statistics. With this nonparametric shift, traditional distribution-based statistics are ineffective in characterizing the migration of system resilience due to the variation of system parameters. Three statistical tools are proposed under the nonparametric statistical resilience analysis (npSRA) framework, including nonparametric copula-based sensitivity analysis, two-sample resilience test analysis, and a novel tool for resilience attenuation analysis. To demonstrate the use of this framework, we focus on electric distribution systems, commonly found in many urban, suburban, and rural areas and vulnerable to tropical storms. A novel procedure for considering resourcefulness parameters in the socioeconomic space is proposed. Numerical results reveal the complex statistical relations between the distributions of system resilience, physical aging, and socioeconomic parameters for the power distribution system. The proposed resilience distance computing and resilience attenuation analysis further suggests two proper nonparametric distance metrics, the Earth Moving Distance (EMD) metric and the Cramévon Mises (CVM) metric, for characterizing the migration of system resilience for electric distribution systems.