To investigate the resilience of interconnected critical infrastructures (CIs), a framework combining dynamic modeling and resilience analysis is proposed. Resilience is defined in this work as the capacity of a system to absorb the impacts of perturbations and recover quickly from disruptive states. It is seen as a property of the system, which depends on a number of design, operation, and control parameters. Within this framework, we introduce the concept of resilience regions in the parameters space: as long as the parameters values remain inside these regions during operation, the system visits only recoverable states or, in other words, it maintains nominal operation or recovers quickly to it. Based on this concept, we perform a resilience analysis of two interconnected critical infrastructures, a gas network and an electric power system. The analysis is performed by numerical calculation of the resilience conditions in terms of design, operation, and control parameters values for given failure scenarios. To render computationally feasible analysis, we resort to an abstract representation of the system dynamics by a linear model of switching dynamics. Although the high-level modeling adopted may suffer from predictive accuracy, the proposed framework can still provide valuable insights in the analysis of system resilience and its dependence on the design, operation, and control parameters under different failure scenarios, which can be valuable to inform the decision making process of CIs operators and other stakeholders.

References

References
1.
Ellis
,
J.
,
Fisher
,
D.
,
Longstaff
,
T.
,
Pesante
,
L.
, and
Pethia
,
R.
,
1997
, “
Report to the President's Commission on Critical Infrastructure Protection
,” Software Engineering Institute, Carnegie–Mellon University, Pittsburgh, PA,
Report No. CMU/SEI-97-SR-00333
.
2.
Kröger
,
W.
,
2008
, “
Critical Infrastructures at Risk: A Need for a New Conceptual Approach and Extended Analytical Tools
,”
Reliab. Eng. Syst. Saf.
,
93
(
12
), pp.
1781
1787
.
3.
Kröger
,
W.
, and
Zio
,
E.
,
2011
,
Vulnerable Systems
,
Springer Science and Business Media
,
London
.
4.
Zio
,
E.
,
2016
, “
Challenges in the Vulnerability and Risk Analysis of Critical Infrastructures
,”
Reliab. Eng. Syst. Saf.
,
152
, pp.
137
150
.
5.
Zio
,
E.
,
2016
, “
Reliability Analysis of Systems of Systems
,”
IEEE Reliab. Mag.
,
Feb. 2016
(
Spec. Iss.
), pp.
1
6
.
6.
Clinton
,
W.
,
1998
, “
Presidential Decision Directive 63
,” The White House, Washington, DC, accessed Oct. 7, 2015, https://fas.org/irp/offdocs/pdd/pdd-63.htm
7.
Bush
,
G. W.
,
2002
, “
Homeland Security Presidential Directive-3 (HSPD-3)
,” The White House, Washington, DC, accessed Oct. 7, 2015, https://fas.org/irp/offdocs/nspd/hspd-3.htm
8.
Bush
,
G. W.
,
2002
, “
The National Security Strategy of the United States of America
,”
The White House
, Washington, DC.
9.
Bush
,
G. W.
,
2003
, “
Homeland Security Presidential Directive-7 (HSPD-7)
,” U.S. Department of Homeland Security, Washington, DC, accessed Oct. 8, 2015, https://www.dhs.gov/homeland-security-presidential-directive-7
10.
Obama
,
B.
,
2013
, “
Presidential Policy Directive 21: Critical Infrastructure Security and Resilience
,”
The White House
,
Washington, DC
.
11.
EU Commission
,
2005
, “
Green Paper on a European Programme for Critical Infrastructure Protection
,” Brussels, Belgium, COM (2005) 576 Final.
12.
EU Commission
,
2006
, “
European Union Directive Draft
,” Brussels, Belgium, COM (2006) 787.
13.
Lindström
,
M.
, and
Olsson
,
S.
,
2009
, “
The European Programme for Critical Infrastructure Protection
,”
Crisis Management in the European Union
,
Springer
,
Berlin
, pp.
37
59
.
14.
Hämmerli
,
B. M.
, and
Renda
,
A.
,
2010
,
Protecting Critical Infrastructure in the EU
,
Centre for European Policy Studies
,
Brussels, Belgium
.
15.
Luiijf
,
E.
,
Burger
,
H.
,
Klaver
,
M.
, and
Marieke
,
H.
,
2003
, “
Critical Infrastructure Protection in the Netherlands: A Quick-Scan
,”
EICAR Conference Best Paper Proceedings
,
EICAR
,
Copenhagen
,
Denmark
, Vol. 19.
16.
Intelligence C. Information Security Center (CIS Sapienza), 2013, “
2013 Italian Cyber Security Report. Critical Infrastructure and Other Sensitive Sectors Readiness
,” Roma, Italy.
17.
IRGC
,
2006
, “
White Paper on Managing and Reducing Social Vulnerabilities From Coupled Critical Infrastructures
,”
International Risk Governance Council
,
Geneva, Switzerland
.
18.
Chertoff
,
M.
,
2009
, “
National Infrastructure Protection Plan: Partnering to Enhance Protection and Resiliency
,”
Department of Homeland Security (DHS)
,
Washington, DC
.
19.
Yusta
,
J. M.
,
Correa
,
G. J.
, and
Lacal-Arántegui
,
R.
,
2011
, “
Methodologies and Applications for Critical Infrastructure Protection: State-of-the-Art
,”
Energy Policy
,
39
(
10
), pp.
6100
6119
.
20.
Lewis
,
T. G.
,
2014
,
Critical Infrastructure Protection in Homeland Security: Defending a Networked Nation
,
Wiley
,
Hoboken, NJ
.
21.
Brothers
,
R.
,
2015
, “
A Review of Progress by the Department of Homeland Security, Science and Technology Directorate
,” U.S. Department of Homeland Security, Washington, DC, accessed Nov. 23, 2015, https://www.dhs.gov/news/2015/10/27/written-testimony-st-under-secretary-house-committee-science-space-and-technology
22.
Wildavsky
,
A. B.
,
1988
,
Searching for Safety
,
Transaction Publishers
,
Piscataway, NJ
.
23.
Bruneau
,
M.
,
Chang
,
S. E.
,
Eguchi
,
R. T.
,
Lee
,
G. C.
,
O'Rourke
,
T. D.
,
Reinhorn
,
A. M.
,
Shinozuka
,
M.
,
Tierney
,
K.
,
Wallace
,
W. A.
, and
von Winterfeldt
,
D.
,
2003
, “
A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities
,”
Earthquake Spectra
,
19
(
4
), pp.
733
752
.
24.
Haimes
,
Y. Y.
,
Crowther
,
K.
, and
Horowitz
,
B. M.
,
2008
, “
Homeland Security Preparedness: Balancing Protection With Resilience in Emergent Systems
,”
Syst. Eng.
,
11
(
4
), pp.
287
308
.
25.
Hollnagel
,
E.
,
Christopher
,
P. N.
, and
Sidney
,
D.
,
2008
, Resilience Engineering Perspectives, Volume 1: Remaining Sensitive to the Possibility of Failure, Ashgate Publishing, Ltd., Hampshire, UK.
26.
Aven
,
T.
,
2011
, “
On Some Recent Definitions and Analysis Frameworks for Risk, Vulnerability, and Resilience
,”
Risk Anal.
,
31
(
4
), pp.
515
522
.
27.
Society of Risk Analysis
,
2015
, “
Glossary of the Specialty Group on Foundations of Risk Analysis
,” Society for Risk Analysis, McLean, VA, accessed Nov. 2, 2015, http://www.sra.org/news/sra-develops-glossary-risk-related-terms
28.
Zio
,
E.
, and
Sansavini
,
G.
,
2008
, “
Modeling Failure Cascades in Networks Systems Due to Distributed Random Disturbances and Targeted Intentional Attacks
,”
European Safety and Reliability Conference (ESREL 2008)
, pp.
1861
1865
.
29.
Ouyang
,
M.
,
Dueñas-Osorio
,
L.
, and
Min
,
X.
,
2012
, “
A Three-Stage Resilience Analysis Framework for Urban Infrastructure Systems
,”
Struct. Saf.
,
36–37
, pp.
23
31
.
30.
Fang
,
Y. P.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2014
, “
Comparing Network-Centric and Power Flow Models for the Optimal Allocation of Link Capacities in a Cascade–Resilient Power Transmission Network
,”
IEEE Syst. J.
,
PP
(
99
), pp.
1
12
.
31.
Cavallaro
,
M.
,
Asprone
,
D.
,
Latora
,
V.
, and
Manfredi
,
G.
,
2014
, “
Assessment of Urban Ecosystem Resilience Through Hybrid Social-Physical Complex Networks
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
29
(
8
), pp.
608
625
.
32.
Dessavre
,
D. G.
,
Ramirez-Marquez
,
J. E.
, and
Barker
,
K.
,
2016
, “
Multidimensional Approach to Complex System Resilience Analysis
,”
Reliab. Eng. Syst. Saf.
,
149
, pp.
34
43
.
33.
Francis
,
R.
, and
Bekera
,
B.
,
2014
, “
A Metric and Frameworks for Resilience Analysis of Engineered and Infrastructure Systems
,”
Reliab. Eng. Syst. Saf.
,
121
, pp.
90
103
.
34.
Cimellaro
,
G. P.
,
Villa
,
O.
, and
Bruneau
,
M.
,
2014
, “
Resilience-Based Design of Natural Gas Distribution Networks
,”
J. Infrastruct. Syst.
,
21
(
1
), p.
05014005
.
35.
Bensi
,
M.
,
Kiureghian
,
A. D.
, and
Straub
,
D.
,
2014
, “
Framework for Post-Earthquake Risk Assessment and Decision Making for Infrastructure Systems
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A
,
1
(
1
), p.
040140
.
36.
Hosseini
,
S.
, and
Barker
,
K.
,
2016
, “
Modeling Infrastructure Resilience Using Bayesian Networks: A Case Study of Inland Waterway Ports
,”
Comput. Ind. Eng.
,
93
, pp.
252
266
.
37.
Lee
,
E. E.
,
Mitchell
,
J. E.
, and
Wallace
,
W. A.
,
2007
, “
Restoration of Services in Interdependent Infrastructure Systems: A Network Flows Approach
,”
IEEE Trans. Syst., Man Cybern., Part C
,
37
(
6
), pp.
1303
1317
.
38.
González
,
A. D.
,
Duenas-Osorio
,
L.
,
Sánchez-Silva
,
M.
, and
Medaglia
,
A. L.
,
2015
, “
The Interdependent Network Design Problem for Optimal Infrastructure System Restoration
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
31
(
5
), pp.
334
350
.
39.
Cavdaroglu
,
B.
,
Hammel
,
E.
,
Mitchell
,
J. E.
, and
Sharkey
,
T. C.
,
2013
, “
Integrating Restoration and Scheduling Decisions for Disrupted Interdependent Infrastructure Systems
,”
Ann. Oper. Res.
,
203
(
1
), pp.
279
294
.
40.
Dudenhoeffer
,
D.
,
Permann
,
M.
,
Wolsey
,
S.
, and
Timpany
,
R.
,
2007
, “
Interdependency Modeling and Emergency Response
,”
2007 Summer Computer Simulation Conference, Society for Computer Simulation International
, San Diego, CA, July 16–19, pp.
1230
1237
.
41.
Sharkey
,
T.
,
Nurre
,
S.
,
Nguyen
,
H.
,
Chow
,
J.
,
Mitchell
,
J.
, and
Wallace
,
W.
,
2016
, “
Identification and Classification of Restoration Interdependencies in the Wake of Hurricane Sandy
,”
J. Infrastruct. Syst.
,
22
(
1
), p.
04015007
.
42.
Hassel
,
H.
, and
Johansson
,
J.
,
2013
, “
Mapping Societal Functions, Flows and Dependencies to Strengthen Community Resilience–Results From an Initial Study
,”
Society for Risk Analysis Annual Meeting
(
SRA 2013
), Paper No. W2-K.1.
43.
Eusgeld
,
I.
,
Nan
,
C.
, and
Dietz
,
S.
,
2011
, “
System-of-Systems Approach for Interdependent Critical Infrastructures
,”
Reliab. Eng. Syst. Saf.
,
96
(
6
), pp.
679
686
.
44.
Galbusera
,
L.
,
Ntalampiras
,
S.
,
Azzini
,
I.
, and
Giannopoulos
,
G.
,
2013
, “
Resilience Assessment and Optimization Methodology for Critical Infrastructure
,” JRC Technical Reports, Report No. JRC85475.
45.
Ferrario
,
E.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2015
, “
Analysis of the Robustness and Recovery of Critical Infrastructures Within a Multi-State System-of-Systems Framework, in Presence of Epistemic Uncertainty
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
1
(
3
), p.
031001
.
46.
Zio
,
E.
,
2009
, “
Reliability Engineering: Old Problems and New Challenges
,”
Reliab. Eng. Syst. Saf.
,
94
(
2
), pp.
125
141
.
47.
Buldyrev
,
S. V.
,
Parshani
,
R.
,
Paul
,
G.
,
Stanley
,
H. E.
, and
Havlin
,
S.
,
2010
, “
Catastrophic Cascade of Failures in Interdependent Networks
,”
Nature
,
464
(
7291
), pp.
1025
1028
.
48.
Ouyang
,
M.
,
2014
, “
Review on Modeling and Simulation of Interdependent Critical Infrastructure Systems
,”
Reliab. Eng. Syst. Saf.
,
121
, pp.
43
60
.
49.
Valencia
,
V. V.
,
Thal
,
A. E.
,
Colombi
,
J. M.
, and
Sitzabee
,
W. E.
,
2015
, “
Infrastructure Decay Modeling With the Input–Output Inoperability Model
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
1
(
1
), p.
011006
.
50.
Zio
,
E.
, and
Sansavini
,
G.
,
2013
, “
Vulnerability of Smart Grids With Variable Generation and Consumption: A System of Systems Perspective
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
43
(
3
), pp.
477
487
.
51.
Setola
,
R.
,
De Porcellinis
,
S.
, and
Sforna
,
M.
,
2009
, “
Critical Infrastructure Dependency Assessment Using the Input–Output Inoperability Model
,”
Int. J. Crit. Infrastruct. Prot.
,
2
(
4
), pp.
170
178
.
52.
Jonkeren
,
O.
, and
Giannopoulos
,
G.
,
2014
, “
Analysing Critical Infrastructure Failure With a Resilience Inoperability Input–Output Model
,”
Econ. Syst. Res.
,
26
(
1
), pp.
39
59
.
53.
Mayne
,
D. Q.
,
Rawlings
,
J. B.
,
Rao
,
C. V.
, and
Scokaert
,
P. O.
,
2000
, “
Constrained Model Predictive Control: Stability and Optimality
,”
Automatica
,
36
(
6
), pp.
789
814
.
54.
Kouvaritakis
,
B.
, and
Cannon
,
M.
,
2015
, “
Developments in Robust and Stochastic Predictive Control in the Presence of Uncertainty
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
1
(
2
), p.
021003
.
55.
Liu
,
X.
,
Prodan
,
I.
, and
Zio
,
E.
,
2014
, “
On the Resilience Analysis of Interconnected Systems by a Set-Theoretic Approach
,”
Safety and Reliability: Methodology and Applications
,
CRC Press
,
Leiden, The Netherlands
, pp.
197
205
.
56.
Saltelli
,
A.
,
2002
, “
Sensitivity Analysis for Importance Assessment
,”
Risk Anal.
,
22
(
3
), pp.
579
590
.
57.
Fang
,
Y. P.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2016
, “
Resilience-Based Component Importance Measures for Critical Infrastructure Network Systems
,”
IEEE Trans. Reliab.
,
65
(
2
), pp.
502
512
.
58.
Turati
,
P.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2016
, “
An Adaptive Simulation Framework for the Exploration of Extreme and Unexpected Events in Dynamic Engineered Systems
,”
Risk Anal.
(Online).
59.
Aven
,
T.
, and
Zio
,
E.
,
2011
, “
Some Considerations on the Treatment of Uncertainties in Risk Assessment for Practical Decision Making
,”
Reliab. Eng. Syst. Saf.
,
96
(
1
), pp.
64
74
.
60.
Hadjipaschalis
,
I.
,
Poullikkas
,
A.
, and
Efthimiou
,
V.
,
2009
, “
Overview of Current and Future Energy Storage Technologies for Electric Power Applications
,”
Renew. Sustainable Energy Rev.
,
13
(
6
), pp.
1513
1522
.
61.
Luo
,
X.
,
Wang
,
J.
,
Dooner
,
M.
, and
Clarke
,
J.
,
2015
, “
Overview of Current Development in Electrical Energy Storage Technologies and the Application Potential in Power System Operation
,”
Appl. Energy
,
137
, pp.
511
536
.
62.
Friedland
,
B.
,
2005
,
Control System Design: An Introduction to State-Space Methods
,
Dover Publications
,
Mineola, NY
.
63.
Sun
,
K.
, and
Han
,
Z.-X.
,
2005
, “
Analysis and Comparison on Several Kinds of Models of Cascading Failure in Power System
,” 2005
IEEE/PES
Transmission & Distribution Conference & Exposition: Asia and Pacific
, Aug. 18.
64.
Yi
,
X. J.
,
Shi
,
J.
,
Dong
,
H. P.
, and
Lai
,
Y. H.
,
2015
, “
Reliability Analysis of Repairable System With Multiple Fault Modes Based on Goal-Oriented Methodology
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B
,
2
(
1
), p.
011003
.
65.
Fang
,
Y. P.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2015
, “
Optimization of Cascade-Resilient Electrical Infrastructures and Its Validation by Power Flow Modeling
,”
Risk Anal.
,
35
(
4
), pp.
594
607
.
66.
Cimellaro
,
G. P.
,
Reinhorn
,
A. M.
, and
Bruneau
,
M.
,
2010
, “
Framework for Analytical Quant1ification of Disaster Resilience
,”
Eng. Struct.
,
32
(
11
), pp.
3639
3649
.
67.
Ayyub
,
B. M.
,
2015
, “
Practical Resilience Metrics for Planning, Design, and Decision Making
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A
,
1
(
3
), p.
04015008
.
68.
Kalman
,
R. E.
,
1963
, “
Mathematical Description of Linear Dynamical Systems
,”
J. Soc. Ind. Appl. Math., Ser. A
,
1
(
2
), pp.
152
192
.
69.
Li
,
Y. F.
,
Pedroni
,
N.
, and
Zio
,
E.
,
2013
, “
A Memetic Evolutionary Multi-Objective Optimization Method for Environmental Power Unit Commitment
,”
IEEE Trans. Power Syst.
,
28
(
3
), pp.
2660
2669
.
70.
Nozick
,
L. K.
,
Turnquist
,
M. A.
,
Jones
,
D. A.
, and
Davis
,
J. R.
,
2005
, “
Assessing the Performance of Interdependent Infrastructures and Optimising Investments
,”
Int. J. Crit. Infrastruct.
,
1
(
2/3
), pp.
144
154
.
71.
Grigg
,
C.
,
Wong
,
P.
,
Albrecht
,
P.
,
Allan
,
R.
,
Bhavaraju
,
M.
,
Billinton
,
R.
,
Chen
,
Q.
,
Fong
,
C.
,
Haddad
,
S.
,
Kuruganty
,
S.
, and
Li
,
W.
,
1999
, “
The IEEE Reliability Test System-1996. A Report Prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee
,”
IEEE Trans. Power Syst.
,
14
(
3
), pp.
1010
1020
.
72.
Lofberg
,
J.
,
2004
, “
Yalmip: A Toolbox for Modeling and Optimization in MATLAB
,”
CACSD Conference
, Taipei, Taiwan, pp.
284
289
.
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