Research Papers

Resilience Quantification for Probabilistic Design of Cyber-Physical System Networks

[+] Author and Article Information
Yan Wang

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yan.wang@me.gatech.edu

Manuscript received March 12, 2016; final manuscript received January 21, 2018; published online March 2, 2018. Assoc. Editor: Nii Attoh-Okine.

ASME J. Risk Uncertainty Part B 4(3), 031006 (Mar 02, 2018) (12 pages) Paper No: RISK-16-1072; doi: 10.1115/1.4039148 History: Received March 12, 2016; Revised January 21, 2018

Cyber-physical systems (CPS) are the physical systems of which individual components have functional identities in both physical and cyber spaces. Given the vastly diversified CPS components in dynamically evolving networks, designing an open and resilient architecture with flexibility and adaptability thus is important. To enable a resilience engineering approach for systems design, quantitative measures of resilience have been proposed by researchers. Yet, domain-dependent system performance metrics are required to quantify resilience. In this paper, generic system performance metrics for CPS are proposed, which are entropy, conditional entropy, and mutual information associated with the probabilities of successful prediction and communication. A new probabilistic design framework for CPS network architecture is also proposed for resilience engineering, where several information fusion rules can be applied for data processing at the nodes. Sensitivities of metrics with respect to the probabilistic measurements are studied. Fine-grained discrete-event simulation models of communication networks are used to demonstrate the applicability of the proposed metrics.

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Fig. 1

System performance curve used by Francis and Bekera [4]

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Fig. 2

Performance measure in Eq. (12) for a simulated CPS network with 10 nodes: (a) the maximum number of disconnected edges is 39 and (b) the maximum number of disconnected edges is 76

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Fig. 3

The entropies and prediction probabilities of the simulated system in Fig. 2(b), where the maximum number of disconnected edges is 76: (a) the average conditional entropy calculated from Eq. (10) and the average entropy calculated from prediction probability in Eq. (8) and (b) the minimum and maximum values of prediction probabilities among ten nodes

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Fig. 4

Performance measure of a simulated CPS network with 30 nodes: (a) the maximum number of disconnected edges is 49 and (b) the maximum number of disconnected edges is 834

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Fig. 5

The entropies and prediction probabilities of the simulated system in Fig. 4(b), where the maximum number of disconnected edges is 834: (a) the average conditional entropy and the average entropy and (b) the minimum and maximum values of prediction probabilities among 30 nodes

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Fig. 6

Simulation results based on the Bayesian fusion rule for a system of 30 nodes with a maximum of 826 disrupted connections: (a) average mutual information performance measure and (b) average conditional entropy and entropy

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Fig. 7

Sensitivity of conditional entropy with respect to prediction probability

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Fig. 8

Sensitivity analysis based on the best-case fusion rule by increasing all reliance probabilities by 25% (+25%), reducing all by 25% (−25%), increasing only those large probabilities that are greater than 0.5 by 25% (Large + 25%), reducing only these large probabilities (Large −25%), increasing only those small probabilities that are less than 0.5 by 25% (Small + 25%), and reducing only those small probabilities (Small −25%): (a) average conditional entropies and entropies and (b) average mutual information

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Fig. 9

Sensitivity of a simulated system based on the Bayesian rule

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Fig. 10

Two ring models simulated in ns-2 for demonstration

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Fig. 11

Comparison of metrics for the two simulated ring models




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