Empirical data and regression analysis for estimation of infrastructure resilience, with application to electric power outages

Recent natural disasters have highlighted the need for increased planning for disruptive events. Forecasting damage and time that a system will be inoperable is important for disruption planning. The resilience of critical infrastructure systems, or their ability to recover quickly from a disruption, can mitigate adverse consequences of the disruption. This paper quantifies the resilience of a critical infrastructure sector through the dynamic inoperability input-output model (DIIM). The DIIM, which describes how inoperability propagates through a set of interdependent industry and infrastructure sectors following a disruptive event, includes a resilience parameter that has not yet been adequately assessed. This paper provides a data-driven approach to derive the resilience parameter through regression models. Data may contain different disruption scenarios, and regression models can incorporate these scenarios through the use of categorical or dummy variables. A mixed-effects model offers an alternate approach of accounting for these scenarios, and these models estimate parameters based on the combination of all scenarios (fixed effects) and an individual scenario (random effects). These regression models are illustrated with electric power outage data and a regional disruption that uses the DIIM to model production losses in Oklahoma following an electric power outage.

[1]  Yacov Y. Haimes,et al.  A Risk-based Input–Output Methodology for Measuring the Effects of the August 2003 Northeast Blackout , 2007 .

[2]  Kash Barker,et al.  A Risk‐Based Approach for Identifying Key Economic and Infrastructure Systems , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[3]  Ali A. Ghorbani,et al.  The state of the art in critical infrastructure protection: a framework for convergence , 2008, Int. J. Crit. Infrastructures.

[4]  Christopher W. Zobel,et al.  Representing perceived tradeoffs in defining disaster resilience , 2011, Decis. Support Syst..

[5]  Joost R. Santos,et al.  A Framework for Linking Cybersecurity Metrics to the Modeling of Macroeconomic Interdependencies , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[6]  Joost R. Santos,et al.  Estimating Workforce-Related Economic Impact of a Pandemic on the Commonwealth of Virginia , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  Seth D Guikema,et al.  Prestorm Estimation of Hurricane Damage to Electric Power Distribution Systems , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[8]  A. Rose.  Economic resilience to natural and man-made disasters: Multidisciplinary origins and contextual dimensions , 2007 .

[9]  Barry J. Goodno,et al.  Interdependent Response of Networked Systems , 2007 .

[10]  Joost R. Santos,et al.  INOPERABILITY INPUT-OUTPUT MODEL 2 . 1 . Background : Leontief Input-Output Model , 2005 .

[11]  Haibin Liu,et al.  Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms , 2008, Reliab. Eng. Syst. Saf..

[12]  Kenny Q. Ye.  Statistical Tests for Mixed Linear Models , 2000, Technometrics.

[13]  Thomas L. Landers,et al.  Interdependent Impacts of Inoperability at Multi-Modal Transportation Container Terminals , 2011 .

[14]  E. Demidenko,et al.  Mixed Models: Theory and Applications (Wiley Series in Probability and Statistics) , 2004 .

[15]  Seth D Guikema,et al.  Improving the Predictive Accuracy of Hurricane Power Outage Forecasts Using Generalized Additive Models , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  Yacov Y. Haimes,et al.  Application of systems engineering and information models to optimize operation of gas export systems , 2008 .

[17]  Albert Jones,et al.  Toward modeling and simulation of critical national infrastructure interdependencies , 2005 .

[18]  Yacov Y. Haimes,et al.  Uncertainty Analysis of Interdependencies in Dynamic Infrastructure Recovery: Applications in Risk-Based Decision Making , 2009 .

[19]  Jose Emmanuel Ramirez-Marquez,et al.  Resiliency as a component importance measure in network reliability , 2009, Reliab. Eng. Syst. Saf..

[20]  Cihan H. Dagli,et al.  Postearthquake Recovery of a Water Distribution System: Discrete Event Simulation Using Colored Petri Nets , 2011 .

[21]  James H. Lambert,et al.  Inoperability Input-Output Model for Interdependent Infrastructure Sectors. II: Case Studies , 2005 .

[22]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[23]  Joost R. Santos,et al.  Modeling the Demand Reduction Input‐Output (I‐O) Inoperability Due to Terrorism of Interconnected Infrastructures * , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[24]  R. Cook.  Detection of influential observation in linear regression , 2000 .

[25]  Yacov Y. Haimes,et al.  Managing the risk of terrorism to interdependent infrastructure systems through the dynamic inoperability input–output model , 2006, Syst. Eng..

[26]  Peter D. Blair,et al.  Input-Output Analysis , 2021 .

[27]  Leonardo Dueñas-Osorio,et al.  Cascading failures in complex infrastructure systems , 2009 .

[28]  Julian J. Faraway,et al.  Extending the Linear Model with R , 2004 .

[29]  Jery R. Stedinger,et al.  Negative Binomial Regression of Electric Power Outages in Hurricanes , 2005 .

[30]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[31]  W. Leontief.  Quantitative Input and Output Relations in the Economic Systems of the United States , 1936 .

[32]  J. Faraway.  Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models , 2005 .

[33]  E. Bagheri,et al.  Conceptualizing Critical Infrastructures as Service Oriented Complex Interdependent Systems , .

[34]  R. Dennis Cook,et al.  Detection of Influential Observation in Linear Regression , 2000, Technometrics.

[35]  K. C. Kapur,et al.  Methodology for Assessing the Resilience of Networked Infrastructure , 2009, IEEE Systems Journal.

[36]  Michel Bruneau,et al.  A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities , 2003 .

[37]  James H. Lambert,et al.  Extreme Event Scenarios for Planning of Infrastructure Projects , 2002 .

[38]  A. Rose.  DEFINING AND MEASURING ECONOMIC RESILIENCE TO DISASTERS , 2004 .

[39]  Kash Barker,et al.  Measuring the efficacy of inventory with a dynamic input-output model , 2010 .

[40]  Thijs ten Raa.  The Economics of Input-Output Analysis: The dynamic inverse , 2006 .

[41]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[42]  Ligang He,et al.  Supply-driven dynamic inoperability input-output price model for interdependent infrastructure systems , 2011 .

[43]  W. Hays.  Applied Regression Analysis. 2nd ed. , 1981 .

[44]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[45]  Stephanie E. Chang,et al.  Fostering resilience to extreme events within infrastructure systems: Characterizing decision contexts for mitigation and adaptation , 2008 .

[46]  L. Dueñas-Osorio,et al.  Probabilistic Response of Interdependent Infrastructure Networks , 2004 .

[47]  André I. Khuri,et al.  Statistical Texts for Mixed Linear Models: Khuri/Statistical , 1998 .

[48]  Kash Barker,et al.  Evaluating the Consequences of an Inland Waterway Port Closure With a Dynamic Multiregional Interdependence Model , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.