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A Non-parametric Cumulative Sum Approach for Online Diagnostics of Cyber Attacks to Nuclear Power Plants

  • Wei Wang
  • Francesco Di MaioEmail author
  • Enrico Zio
Chapter
Part of the Advanced Sciences and Technologies for Security Applications book series (ASTSA)

Abstract

Both stochastic failures and cyber attacks can compromise the correct functionality of Cyber-Physical Systems (CPSs). Cyber attacks manifest themselves in the physical system and, can be misclassified as component failures, leading to wrong control actions and maintenance strategies. In this chapter, we illustrate the use of a nonparametric cumulative sum (NP-CUSUM) approach for online diagnostics of cyber attacks to CPSs. This allows for (i) promptly recognizing cyber attacks by distinguishing them from component failures, and (ii) guiding decisions for the CPSs recovery from anomalous conditions. We apply the approach to the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED) and its digital Instrumentation and Control (I&C) system. For this, an object-oriented model previously developed is embedded within a Monte Carlo (MC) engine that allows injecting into the I&C system both components (stochastic) failures (such as sensor bias, drift, wider noise and freezing) and cyber attacks (such as Denial of Service (DoS) attacks mimicking component failures).

Keywords

Cyber-physical system Cyber attacks Stochastic failures Diagnostics Nonparametric cumulative sum (NP-CUSUM) Nuclear power plant The authors would like to capitalize each word as Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED) 

Abbreviations

CPS

Cyber-Physical System

NP-CUSUM

Non-Parametric CUmulative SUM

ALFRED

Advanced Lead-cooled Fast Reactor European Demonstrator

I&C

Instrumentation and Control

MC

Monte Carlo

NPP

Nuclear Power Plant

PI

Proportional-Integral

DoS

Denial of Service

PID

Proportional-Integral-Derivative

FDI

False Data Injection

SG

Steam Generator

FA

Fuel Assembly

CR

Control Rod

SISO

Single Input Single Output

DAC

Digital-to-Analog Converter

LSB

Least Significant Bit

Nomenclature

PTh

Thermal power

hCR

Height of control rods

TL,hot

Coolant core outlet temperature

TL,cold

Coolant SG outlet temperature

Г

Coolant mass flow rate

Tfeed

Feedwater SG inlet temperature

Tsteam

Steam SG outlet temperature

pSG

SG pressure

Gwater

Feedwater mass flow rate

Gatt

Attemperator mass flow rate

kv

Turbine admission valve coefficient

PMech

Mechanical power

Kp,j

Proportional gain value of j-th PI

Ki,j

Integral gain value of j-th PI

t

Time

tR

Accident time

tM

Mission time

Δt

Sensor measuring time interval

y

Variable (safety parameter)

yref

Reference value of controller set point value of y

yreal(t)

Real value of y

ysensor(t)

Sensor measurement

yfeed(t)

Measurement received by the computing (feeding) subsystem

ymonitor(t)

Measurement received by the monitoring subsystem

Y(t)

Redundant channel measure, Y = yfeed and ymonitor

δy(t)

Sensor measuring error

qy(t)

Converter quantization error

a

Accidental scenario

b

Bias factor

c

Drift factor

SY(t)

Score function-based statistic of the collected Y(t), SY(t) = \( {S}_y^{feed}(t) \) and \( {S}_y^{monitor}(t) \)

hy

Positive threshold

τY

Time to alarm, τY = \( {\tau}_y^{feed} \) and \( {\tau}_y^{monitor} \)

Δτy

Delay difference between \( {\tau}_y^{feed} \) and \( {\tau}_y^{monitor} \)

\( {\Gamma}_y^{ref} \)

Reference delay difference

cy

NP-CUSUM parameter

εy

NP-CUSUM parameter

ωy

NP-CUSUM positive weight

gY

Score function

ΔgY

Score function difference value

μY

Pre-change mean value of Y

θY

Post-change mean value of Y

\( {\widehat{\theta}}_Y(t) \)

On-line estimate of θY

\( {\mu}_{\Delta {g}_Y} \)

Known pre-change mean value of ΔgY

\( {\theta}_{\Delta {g}_Y} \)

Unknown post-change mean value of ΔgY

\( {\alpha}_y^h \)

False alarm rate

\( {\beta}_y^h \)

Missed alarm rate

\( \gamma \left({\Gamma}_{T_{L, cold}}^{ref}\right) \)

Misclassification rate with respect to \( {\Gamma}_y^{ref} \)

Notes

Acknowledgement

The authors are thankful to Prof. Antonio Cammi and Dr. Stefano Lorenzi of the Energy Department, Politecnico di Milano, for providing guidance and training on code simulating the ALFRED reactor.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Energy DepartmentPolitecnico di MilanoMilanoItaly
  2. 2.Chair on System Science and the Energy Challenge, Fondation Electricite’ de France (EDF), CentraleSupélecUniversité Paris SaclayGif-sur-YvetteFrance

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