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

Abstract

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.

Keywords

Resilience / Electric distribution / Statistical distance / Resourcefulness / Nonparametric statistics

Data availability statement

Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. These include the MATLAB® and R codes for modeling, data processing, and part of simulation data for analysis in this effort.

Relevance to resilience

This work proposes a general framework for quantifying the effects of physical and socioeconomic parameters on system resilience by specifically considering that random values of system resilience follow nonparametric distributions. A set of statistical tools is developed, centering on the notion of resilience mitigation. The methodology is applied to electric distribution systems commonly found in urban, suburban, and rural regions around the world, which are critical links in the system-level resilience of power grids, the resilience of connected civil infrastructure systems, and community resilience as a whole. The proposed methodology can be adapted, subject to modification, and applied to evaluate the resilience mitigation of other civil structures and infrastructure systems, not limited to cities and rural regions.

CRediT authorship contribution statement

ZhiQiang Chen: Formal analysis, Methodology, Software, Validation, Writing - original draft. Prativa Sharma: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This material is partially based upon work supported by the National Science Foundation (NSF) under Award Number IIA-1355406. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF. We would like to thank the anonymous reviewers for their insightful comments.

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