integrated probabilistic and deterministic safety ... · • safety and non-safety systems...
TRANSCRIPT
The objectives of (nuclear) safety
THREAT (Release of radioactivity from a Nuclear Power Plant (NPP))
REGULATIONS
Objectives:
▪ ensure that (nuclear) facilities operate normally and without an
excessive risk of operating staff and the environment
▪ prevent incidents and limit the consequences of any incidents that
might occur.
Design
Operation
Decommissioning
Pla
ntlife
time
Safety assessment competence is the key
to making the right decisions in design,
licensing and operation.
Prof. M. El-Shanawany
Department of Nuclear Safety & Security, Head
International Atomic Energy Agency
Deterministic Safety Assessment (DSA)
Probabilistic Safety Assessment (PSA)
Safety Assessment
Prof. George Apostolakis
Commissioner
Safety Assessment
The model of the world:
Deterministic, e.g., a thermal hydraulic code DSA
Probabilistic, e.g., a Monte Carlo simulation PSA
▪ Both deterministic and probabilistic models of the world have assumptions and parameters.
▪ How confident are we about the validity of these assumptions and the numerical values of the parameters?
Towards and integrated DSA and PSA framework
Traditional Deterministic
ApproachesProbabilistic-Based
Approaches
Risk-Informed
Approaches
IDPSA
Combination of
Deterministic
and
Probabilistic
approaches
Complementary methods of safety analysis are used jointly in evaluating the
safety:
1. Deterministic Safety Analysis (DSA)
2. Probabilistic Safety Analysis (PSA)
Application: LBE-XADS
Nuclear island
Conventional island• Accelerator Driven System (ADS)
▪ A means of transmuting nuclear waste
▪ A new type of fission reactor
▪ Both
• How?
▪Some of the “afterheat” of spent
nuclear fuel can be captured in a
power generator, instead of a
mountain– Goal is 95% of Minor Actinides (MA) & Long-
Lived Fission Products (LLFPs) transmuted
– 250 kg/300 days
Accelerator Driven System for Disposing of Spent Nuclear Fuels
The Concept
• Proton accelerator creates neutrons by spallating high-Z
target nuclei (Z=atomic/proton number)
• Spallation neutrons used to maintain fission reaction
where not normally possible
▪ Subcritical piles
▪ In waste actinides
▪ Chain reaction can’t exist w/o accelerator: To stop, just
unplug it
b e a m
s c a n n i n g
L B E f lo w
8 c m s c a n
1 2 c m d u c t w i d th
Lead Bismuth Eutectic Accelerator Driven System (LBE-XADS)
General View inside the Subcritical Assembly
Deterministic Safety Assessment (DSA)Probabilistic Safety Assessment (PSA)
Safety Assessment
The basic principles of DSA
1) Presence of leaktight barriers between the radioactive source and the
public/environment
▪ fuel cladding (1)
▪ primary reactor coolant system (2 and 3)
▪ containment building (4)
The basic principles of DSA
2) Defence-in-depth, which applies to both the design and the operation
of the facility
Accidents may still occur
Systems are to be designed and installed
to combat them and to ensure that their
consequences are limited to a level that is
acceptable for both the public and the
environment
[Commission’s White Paper, February, 1999]
External hazards
Component
failures
Human error
Off-site emergency procedures
Safeguards
Protection
Prevention and surveillance
The defence-in-depth principle
Prevention and surveillance:
▪ Items of equipment are designed with adequate safety margins
Protection:
▪ Provisions are made to detect incidents and to prevent them from
escalating safety systems are designed to restore the plant to a normal
state and maintain it under safe conditions.
Safeguard:
▪ Special safety systems are therefore designed to limit the consequences
of severe accidents to an acceptable level.
Off-site and emergency procedures:
▪ Designed to provide protection against severe conditions under which
defences at the three levels described above prove inadequate.
DSA before PSA (prior to 1975)
Design Basis Accidents (DBA) [ NUREG/CR-6042, USNRC, 1994]
▪ postulated accidents that a NPP must be designed and built to
withstand, without loss of the system structures and components
necessary to assure public health and safety
▪ include at least one significant failure of a component: failures
beyond those consistent with the single-failure criterion are not
required (unlike in PSAs)
• Very unlikely events (possible inconsistencies in requirements and decisions, unbalancing safety measures and introducing excessive burden)
• Small in number (Need to consider a broader set of safety threats, raking them, identifying and assessing uncertainties. Need to consider many operational situations (start up, shutdown, refuelling, maintenance, etc.), concurrent failures and human performance)
• Conservative initial conditions (to compensate for uncertainties)
CONCERNS ABOUT UNCERTAINTY MANAGEMENT
“Conservatism” of DSA
Assumed
threats profile
Assumed conservative
case
Protection
against
assumed
conservative
threat
Importance of the principles of DSA
Application: LBE-XADS
SAFETY BY DESIGN
Subcritical reactor
MULTI-BARRIERS:
Pellet
Safety vessel
Containment
Secondary coolant
- The accident, caused by a sudden surge of power, destroyed the reactor and
released massive amounts of radioactive material into the environment
- Lack of containment
Chernobyl experience should remain a valuable part of the information to be taken into
account when dealing with reactor safety issues in the future
importance of the principles of DSA
The accident in 1986 at Chernobyl (I)
- The accident, caused by a sudden surge of power, destroyed the reactor and
released massive amounts of radioactive material into the environment
- Lack of containment
Chernobyl experience should remain a valuable part of the information to be taken into
account when dealing with reactor safety issues in the future
importance of the principles of DSA
The accident in 1986 at Chernobyl (I)
Deterministic Safety Assessment (DSA)
Probabilistic Safety Assessment (PSA)
Safety Assessment
Farmer’s Paper (1967)
Credible (DBAs) VS incredible accidents
not logicalALL is based on assumptions in expert judgment about the credible cases
Example: consider a loss-of-coolant accident (LOCA),
various outcomes: - safe cooldown/shutdown
- partial failures
- accidental cooldown/shutdown
- severe accident
Classification of events according to the probability of its occurrence and potential consequences
• Design-basis accident (DBA):
• Beyond design-basis accidents (BDBA):
Accident sequences that are possible but were not fully considered in the
design process because they were judged to be too unlikely.
The concept of risk
Risk and Safety are considered as two opposed terms, that can be used to assess a same thing
Remember PRA = PSA
• What can go wrong? (accident sequences or scenarios)
• How likely are these scenarios?
• What are their consequences?
Definition of Risk
{ , , }i i i
R s c
is
ic
i
Three different aspects of risk:Risk assessmentRisk perceptionRisk communication
Decision makers can be influenced by all of these
The concept of risk
"Farmer curve”
Techniques for PSA
Hazard identification: FMEA (Failure Modes and Effects Analysis) & HAZOP (HAZard and OPerabilitystudy)
Accident Scenarios Identification: ETA, FTA
System Failure Probabilty Assessment: ETA, FTA, Monte Carlo simulation
ETA: comments
1. One ET for each accident initiator
2. Time and logic of Sk interventions important for the tree structure (simplifications possible)
3. Sk states conditional on accident initiator and previous Sj’s
4. Conditional probabilities of Sk states (FTA)
ETA+FTA
PSA Reactor Safety Study (WASH-1400; 1975)
Prior Beliefs
• Protect against Large LOCA
• Core Damage Frequency (CDF) is low
(about once every 100 million years, 10-8 per reactor year)
• Consequences of accidents would be disastrous
Major Findings
• Dominant contributors: Small LOCAs and Transients
• CDF higher than earlier believed(best estimate: 5x10-5, once every 20,000 years; upper bound: 3x10-4 per reactor year, once
every 3,333 years)
• Consequences significantly smaller
• Support systems and operator actions very important
“Conservatism” of DSA PSA
The accident in 1979 at the Three Mile Island (TMI-2)
- Combination of equipment malfunctions, design-related problems and worker errors
led to TMI-2's partial meltdown and very small off-site releases of radioactivity
- Small radioactive releases
- No detectable health effects on plant workers or the public
Reveals potential consequences of failure to manage
NPP safety only based on DSA
Pilot operating relief valve
(PORV) fails stuck-open
PSA Policy Statement (1995)
The use of PSA should be increased to the extent supported by the
state of the art and data and in a manner that complements the
defense-in-depth philosophy.
PSA should be used to reduce unnecessary conservatisms
associated with current regulatory requirements.
PSA Model Overview
PLANT MODEL (PHYSICS, FUEL AND THERMAL
HYDRAULIC MODELS)
CONTAINMENT
MODEL
SITE/CONSEQUENCE
MODEL
(ATMOSPHERIC,
DISPERSION
MODELS)
Level I Level II Level III
Results
Accident sequences
leading to plant
damage states
(CDF frequencies)
Results
Containment
failure/release
sequences
Results
Public health
effects
PLANT MODE
At-power Operation
Shutdown / Transition
Evolutions
SCOPE
Internal Events
External Events
Uncertainties
Event Sequence Analysis
Event Tree Analysis
Fault Tree Analysis
Containment Event Tree
Application: LBE-XADS
The model of the LBE-XADS has been embedded within an MC-driven fault
injection engine to sample component failures.
Maxim
um
dia
therm
ic o
il t
em
pera
ture
Upper threshold
Lower threshold
“High-temperature failure mode”
“Low-temperature failure mode”
“safe”
4 control/actuator faults
64 accident scenarios
E. Zio, F. Di Maio, “Fuzzy Clustering Classification of Dynamic Scenarios of Digital Instrumentation and Control in Nuclear Power
Plants”, Proceedings of the American Nuclear Society (ANS) NPIC HMIT 2009 Topical Meeting - Nuclear Plant Instrumentation,
Controls, and Human Machine Interface Technology, 5-9 April 2009, Knoxville, Tennessee, American Nuclear Society.
E. Zio, F. Di Maio, “Processing Dynamic Scenarios from a Reliability Analysis of a Nuclear Power Plant Digital Instrumentation and
Control System”, Annals of Nuclear Energy, doi:10.1016/j.anucene.2009.06.012, 2009.
SIMULINK model of the LBE-XADS
Level I PSA: an example
PLANT MODEL (PHYSICS, FUEL AND THERMAL
HYDRAULIC MODELS)
Level I
Results
Accident sequences
leading to plant
damage states
(CDF frequencies)
Fault Tree Analysis
PSA contain uncertainties arising from three main sources:
• lack of comprehensive data: It is impossible to demonstrate the
exhaustiveness of a PSA, even when the scope of the analysis
has been extended to as large a number of situations as possible
• reliability of data: frequency of initiating events (e.g., rare initiating
events such as the combination of a steam piping break and a
steam-generator tube break) common-mode failures and failures
resulting from human actions.
• modelling assumptions that cannot easily be quantified (e.g.,
resistance of certain components under accident conditions, poorly
understood physical phenomena or human actions).
Limitations of PSA (I)
The accident in 2011 at the Daichi NPP
- Following a major earthquake, a 15-metre tsunami disabled the power supply and
cooling of three Fukushima Daiichi reactors, causing a nuclear accident on 11 March
2011.
- All three cores largely melted in the first three days.
Combination of external events (earthquake and tsunami)
Multi-unit severe accident
Deterministic Safety Assessment (DSA)
Probabilistic Safety Assessment (PSA)
Safety Assessment
Integrated Deterministic
Probabilistic Safety Assessment
IDPSA = DSA+PSA
State-of-the-art PSA / DSA are challenged by increasing complexity of
the existing plants safety systems
▪ Passive safety systems in new plants and retrofits in existing plants
▪ Digital Instrumentation & Control (I&C) and Human reliability
▪ Severe accident management implemented in design
WHY? very low CDF by reducing the number of equipment that can
breakdown
Difficult heuristic “a priori” judgment about conservatism in selected DSA
and PSA scenarios
The need of integration
IDPSA
• Unquantified Probabilities
• Design-Basis Accidents
• Defense in Depth
• Can impose heavy regulatory
burden
• Incomplete
•Quantified Probabilities
• Scenario Based
• Realistic
• Rationalist Defense in
Depth
• Incomplete
Complementary methods of safety analysis are used jointly in evaluating the
safety of an NPP:
1. Deterministic Safety Analysis (DSA)
2. Probabilistic Safety Analysis (PSA)
Traditional Deterministic
ApproachesProbabilistic-Based
Approaches
Risk-Informed
Approaches
IDPSA
Combination of
Deterministic
and
Probabilistic
approaches
IDPSA definition
Integrated Deterministic-Probabilistic Safety Analysis
(IDPSA) is a collective name for the variety of different
tools which use tightly coupled probabilistic and
deterministic approaches to address in a consistent
manner:
– stochastic aspects of scenario
– modelling uncertainties
Benefits of integration
IDPSA can provide additional help to PSA and DSA practitioners in:
1) Resolving time dependent interactions between
• physical phenomena,
• equipment failures,
• safety and non-safety systems interactions,
• control logic and operator actions.
2) Identification of a-priori unknown vulnerable scenarios, or “sleeping
threats”
3) Reduction of reliance on expert judgment and simplifying assumptions
about complex interdependencies
• PSA and DSA can calculate what we know as an issue
• PSA and DSA are not capable of revealing what, and to what extent, we do
not know
“Conservatism” of DSA
Assumed
threats profile
Assumed
conservative case
Protection against
assumed
conservative threat
Deterministic and probabilistic safety assessment
(DSA&PSA)
DSA
Design Basis Accidents (DBAs)
PSA
Minimal Cut Sets
(MCS)(Precautionary
principle)
The problem:
Unknown plant
vulnerabilities are
left unknown in
traditional DSA
and PSA
(Safety margins,
multiple barriers)
T
1
2 3 4
5 6
MCS
{1}
{2,4}, {2,5}, {2,6}
{3,4}, {3,5}, {3,6}
PSA: Construction of threat profiles by MCS
Each minimal cut set is an AND gate of a
set of basic events necessary and
sufficient to cause the top event
T
………
T
1
2 3 4
5 6
PSA APPROXIMATION of threat profiles: MCS-order cut-off
CONSIDER:
Small order mcs
T
………
T
1
2 3 4
5 6
T
………
CONSIDER:
Probability of occurrence larger
than a given threshold
PSA APPROXIMATION of threat profiles: MCS-order cut-off
WORRY!!!! Wrong:
Probabilities of top events
Frequencies of sequences
Safety margins
Importance factors
Sensitivity indexes
APPROXIMATED
threat profiles
DSA
Design Basis Accidents (DBAs)
PSA
Minimal Cut Sets
(MCS)(Precautionary
principle)
Deterministic and probabilistic safety assessment
(DSA&PSA)
Integrated Deterministic and Probabilistic Safety
Assessment (IDPSA=DSA + PSA)
IDPSA
IDENTIFIED SCENARIO!!!
-Timing of events
-Sequences of failures
PRIME IMPLICANTS
«CORRECT» THREAT
PROFILE
DSA
Design Basis Accidents (DBAs)
PSA
Minimal Cut Sets
(MCS)(Precautionary
principle)
Application: LBE-XADS
The model of the LBE-XADS has been embedded within an MC-driven fault
injection engine to sample component failures.
Maxim
um
dia
therm
ic o
il t
em
pera
ture
Upper threshold
Lower threshold
“High-temperature failure mode”
“Low-temperature failure mode”
“safe”
4 control/actuator faults
64 accident scenarios
E. Zio, F. Di Maio, “Fuzzy Clustering Classification of Dynamic Scenarios of Digital Instrumentation and Control in Nuclear Power
Plants”, Proceedings of the American Nuclear Society (ANS) NPIC HMIT 2009 Topical Meeting - Nuclear Plant Instrumentation,
Controls, and Human Machine Interface Technology, 5-9 April 2009, Knoxville, Tennessee, American Nuclear Society.
E. Zio, F. Di Maio, “Processing Dynamic Scenarios from a Reliability Analysis of a Nuclear Power Plant Digital Instrumentation and
Control System”, Annals of Nuclear Energy, doi:10.1016/j.anucene.2009.06.012, 2009.
A. Cammi, L. Luzzi, A. Porta, M. E.
Ricotti, Modelling and control strategy of
the Italian LBE-XADS. Progress in
Nuclear Energy 48 (2006) pp. 578-589.
Level I PSA: traditional approaches
PLANT MODEL (PHYSICS, FUEL AND THERMAL
HYDRAULIC MODELS)
Level I
Results
Accident sequences
leading to plant
damage states
(CDF frequencies)
Fault Tree Analysis
ON OFF
Failure
As Good As New Failed
• Static: PSA is “Yes/No”, “black-and-white”
t
X(t)
100%
0%
System unavailability U(t) = Pr[X (t) <100%]
U(t) = Pr[X (t) =0%]
Conventional modelling to PSA
Continuous “Grey” zone can integrally contain not less risk than “black-and-
white” skeleton of PSA tree
What can be worse than failure?
• Wrong timing of successful operation
• Partial success
• …
Conventional modelling to PSA
• Dynamic: Timing makes even discrete (0/1) parameters
continuous
LBE-XADS: dynamic effects
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64
Fre
qu
en
cy o
f th
e e
nd
sta
te
occu
rren
ce
Failure sequence
Low-temperature failure mode Safe mode High-temperature failure mode
LBE-XADS: effect of the ORDER of failure events
Dependence of the accident sequence end state from the ordering of the
components faults in the sequence
0 500 1000 1500 2000 2500 3000
240
260
280
300
320
340
360
380
400
Time [s]
Oil
tem
pera
ture
[C
]
Scenario: Air coolers fail at t=1500 [s], PID fails at t=2000 [s]
Air coolers @ 300[kg/s], PID output @ 500 [kg/s]
Air coolers @ 500[kg/s], PID output @ 220 [kg/s]
Air coolers @ 450[kg/s], PID output @ 100 [kg/s]
Air coolers @ 797[kg/s], PID output @ 0 [kg/s]
0 500 1000 1500 2000 2500 3000260
280
300
320
340
360
380
400
Time [s]
Oil
tem
pera
ture
[C
]
Scenario: PID fails at t=1500 [s], air coolers fail at t=2000 [s]
PID output @ 500 [kg/s], air coolers @ 300[kg/s]
PID output @ 220 [kg/s], air coolers @ 500[kg/s]
PID output @ 100 [kg/s], air coolers @ 500[kg/s]
PID output @ 0 [kg/s], air coolers @ 300[kg/s]
LBE-XADS: digitalization effects
Dependence of the accident sequence end state on the exact timing of the
components failures
0 500 1000 1500 2000 2500 3000250
300
350
400
450
500
550
Time [s]
Oil
tem
pera
ture
[C
]
PID controller fails at time t=2239
PID controller fails at time t=2240
LBE-XADS: magnitude effects
Dependence of the accident sequence end state with respect to the
components faults magnitudes
0 500 1000 1500 2000 2500 3000260
280
300
320
340
360
380
Time [s]
Oil
tem
pera
ture
[C
]
Scenario: PID fails at t=1500 [s]
PID controller fails at time t=1500, output @ 500 [kg/s]
PID controller fails at time t=1500, output @ 220 [kg/s]
PID controller fails at time t=1500, output @ 100 [kg/s]
PID controller fails at time t=1500, output @ 0 [kg/s]
0 500 1000 1500 2000 2500 3000260
280
300
320
340
360
380
400
Time [s]
Oil
tem
pera
ture
[C
]
Scenario: PID fails at t=1500 [s], air coolers fail at t=2000 [s]
PID output @ 500 [kg/s], air coolers @ 300[kg/s]
PID output @ 220 [kg/s], air coolers @ 500[kg/s]
PID output @ 100 [kg/s], air coolers @ 500[kg/s]
PID output @ 0 [kg/s], air coolers @ 300[kg/s]
Methods for IDPSA
Conventional approaches to PSA
Fault-tree/event-tree (FT/ET) at best can account for the order
of occurrence of events in system evolution
Dynamic methodologies are defined as those that explicitly
• account for the time element in probabilistic system
evolution
• are needed when the system has
hardware/process/software/human interactions
Dynamic methodologies for IDPSA
Continuous: CET (Continuos Event Tree)
CCCMT (Continuous Cell-to-Cell Mapping Technique)
Discrete: CCMT (Cell-to-Cell Mapping Technique)
MCDET/DYLAM/DETAM/ISA (Dynamic Event Tree
Generation)
Graphical: PETRI NETS
DYNAMIC FLOWGRAPHS
GO-FLOW
Dynamic methodologies for IDPSA
Continuous: CET (Continuos Event Tree)
CCCMT (Continuous Cell-to-Cell Mapping Technique)
Continuous Event Trees (CET)
Describes the system behavior in terms of the probability pn(x,t) of finding the
system in the state-space (x-space) with configuration n at a given time t.
Input:
• Configuration transition rates h(n|m, x, t)
• Probability Fn(x,t) that the system leaves configuration n before time t
• Initial condition p0(x,0)
Output:
pn(x,t)
Solution Method:
Monte Carlo simulation
x1
x2 h(n|m, x, t)
m
p0(x,0)
n
Fn(x,t)Fm(x,t)h(m|0, x, 0)
Continuous Cell-to-Cell Mapping (CCCMT)
Describes the system behavior in terms of the probability πi(j,t) of finding the
system in the cell j of the state-space (x-space) with configuration i at a given
time t.
• Derivable from CET
Input:
• Cell-to-cell transition probabilities g(j|j’,i’,t) in the state space
• Configuration transition rates Fi(j’,t) that the system leaves configuration i
before time t
• Initial condition π0(j0,0)
Output:
πi(j,t)
Solution Method:
Monte Carlo simulation
ODE solvers
x1
x2 g(j|j’,i’,t)
j'
π0(j0,0)
j
Fi(j,t)Fi’(j’,t)g(j’|j0,i’,t)
j0
Dynamic methodologies for IDPSA
Discrete: CCMT (Cell-to-Cell Mapping Technique)
MCDET/DYLAM/DETAM/ADS/ISA (Dynamic Event
Tree Generation)
Cell-to-Cell Mapping (CCMT)
Describes the system behavior in terms of the probability πi(j,k) of finding the
system in the cell j of the state-space (x-space) with configuration i at a given
time k (k=0,1,…).
• Derivable from CET
Input:
• Cell-to-cell transition probabilities g(j|j’,i’,k) in the state space
• Configuration transition rates Fi(j’,k) that the system leaves configuration
i before time step k
• Initial condition π0 (j0,0)
Output:
πi(j,k)
Solution Method:
Monte Carlo simulation
Matrix solvers
x1
x2 g(j|j’,i’, k)
j'
π0(j0,0)
j
Fi(j, k)Fi’(j’, k)g(j’|j0, i’,k)
j0
Comparison
Dynamic Event Tree Methodologies
MCDET/DYLAM/DETAM/ISA
• All methods generate event trees based on possible trajectory branching during system
evolution
• Methods differ in terms of branching and pruning rules, human reliability models and operator
representation
Branching occurs when particular
conditions have been reached:
•Value of specific variables
•Specific time instants
•Plant status
Traditional PRA tools (ET/FT) not suitable because:
• ORDER of failure events neglected
• TIMING of failure events neglected
IDPSA Methods proposed as suitable but:
• Modelling and computationally demanding
• Number of scenarios to be analyzed much larger than in the classic
FT/ET approach
A posteriori information retrieval
Key Points of IDPSA
A posteriori information retrieval
The number of the scenarios that are simulated is much larger than
that of the classical ET/FT approaches
Aim: Identify and group the scenarios of a dynamic safety assessment by
characterizing the principal patterns of system evolution towards failure with
an evolutionary Fuzzy C-Means (FCM) clustering algorithm
E. Zio, F. Di Maio, “Processing Dynamic
Scenarios from a Reliability Analysis of a
Nuclear Power Plant Digital
Instrumentation and Control System”,
Annals of Nuclear Energy, Vol. 36(9),
2009
Application: LBE-XADS
Maxim
um
dia
therm
ic o
il t
em
pera
ture
Upper threshold
Lower threshold
“High-temperature failure mode”
“Low-temperature failure mode”
“safe”
Feedforward control stuck @ t=0 AND failed
coomunication between air coolers and actuators
PID output stuck @ t=0
Nominal
Application: LBE-XADS
Maxim
um
dia
therm
ic o
il t
em
pera
ture
Upper threshold
Lower threshold
“High-temperature failure mode”
“Low-temperature failure mode”
“safe”
Feedforward control stuck @ t=0
Failed communication between air
coolers actuators and PID @ t=0
Air coolers stuck @ t=0
Application: LBE-XADS
Maxim
um
dia
therm
ic o
il t
em
pera
ture
Upper threshold
Lower threshold
“High-temperature failure mode”
“Low-temperature failure mode”
“safe”
Failed communication
between air coolers actuators
and PID @ t=0 AND Air
coolers stuck
Air coolers stuck @ t=0
PID output stuck @ t=0
The method
Fuzzy C-MEANS classifier
Matlab® fcm(…)
The FCM algorithms
Target: identify similarity in data
partitioning the data set to minimize:
•Constraints
•Iterative scheme
c
i
N
k
ikr
ik vxdVJ m
1 1
2 ),()(),(
Degree of membership of to cluster Γikx
Center of the cluster Γi
ikiv ,
Nk
c
i
ik ,...,2,11
1
Nkciik , 2, 1, , , 2, 1,10
Nkxk ,...,1,
Clustering results
System state variables Process variable
Fault 1
time
Fault 1
magnitude
Fault 2
time
Fault 2
magnitude
Fault 3
time
Fault 3
magnitude
Fault 4
time
Temperature of the primary
coolant at time t=3000 [s]
1- Feature Selection:
• Engineering judgement
RESULTS:
• Functional Principal Components analysis
2- RESULTS:
Fuzzy C-Means
Temperature 1st, 2nd, 3rd PC’s 5.25%
Test Set Misclassification Rate
Fuzzy C-Means
System state variables and Process Variable 7.65%
Test Set Misclassification Rate
ARTIFICIAL INTELLIGENCE AND ADVANCED SIMULATION FOR THE
SAFETY, RELIABILITY AND MAINTENANCE OF ENERGY SYSTEMS
(10 ECTS – 5+5) – 1st semester AA 2018/2019
• INTEGRATED DETERMINISTIC AND PROBABILISTIC SAFETY ANALYSIS
OF NUCLEAR POWER PLANTS (5 ECTS)
The objective of the course is to provide students with an understanding of the
Deterministic (D) and Probabilistic (P) Safety Analysis (SA) methods, and their
integration (IDPSA), which requires Artificial Intelligence (AI) and advanced
simulation methods. These will be presented with respect to practical cases of
nuclear systems.
• COMPUTATIONAL METHODS FOR RELIABILITY, AVAILABILITY AND
MAINTENANCE (5 ECTS)
The goal of this course is to provide students with the knowledge on Artificial
Intelligence (AI) and advanced simulation methods used for the reliability
and availability analysis, and maintenance engineering of industrial
equipment and energy systems.
SAFETY PERFORMANCE ASSESSMENT OF RADIOACTIVE WASTE
REPOSITORIES (5 ECTS)
• The primary goal of this course is to provide the students with the adequate
competence on methods and techniques for the assessment of the
safety performance of a radioactive waste repository, which requires the
systematic analysis of the performance of the engineered and natural barriers
of protection against radionuclide release and dispersion.