SCAIS_TSD_2

Calle Tarrragona 30, Madrid
Indizen Technologies
SCAIS-TSD
System of Codes for an
Integrated Safety Assessment.
Theory of Stimulated Dynamics
Iván Fernández
Indizen Technologies S.L.
Javier Hortal
Consejo de Seguridad Nuclear Justo Dorado 11, Madrid
Consejo de Seguridad Nuclear

2Indizen Technologies ®
Index.
1. ISA Methodology
1.History
2.Features
2. SCAIS
1.Overview
2.Path Analysis
3.Risk Assessment
3. TSD (Javier Hortal Presentation)
4. Conclusions

ISA. History.
The Spanish Nuclear Safety Council (CSN) started in 1974 a painful work of
fast assimilation of transient and accident analysis methodologies for Nuclear
Power Plants.
✔ Methods used by the nuclear industry to ensure safety of the Spanish
nuclear plants that were under licensing at that time.
✔ Understand the overall approach through the available information.
✔ New frame that summarised CSN experience in licensing of transient
analysis, Start-up Testing, Nuclear Operations as well as licensing of the
operating crews.
✔ Methodologies were generated and software packages implementing
the conceptual framework and provided great help to CSN licensing
work.

✔ Specific approach for PSA implementation.
✔ Adapted to present engineering practices.
✔ Consistent theoretical inclusion of FT to APS.
✔ Study of probabilities at transient level.
ISA. Features

ISA. PSA comparative.
✔ Header Branches and Probability:
➔ In PSA event trees, header actuation is decided on the basis of generic
analyses and experts criteria.
➔ In ISA methodology, simulations result to Dynamic Event Trees (DET).
Headers contain a system configuration probability that could depend on
process variables.

ISA. PSA comparative.
✔ Stochastic Actions:
➔ In PSA an action is failed if it is not performed within a pre-specified time
interval (available time). ie. Human actions
➔ In ISA methodology, delayed actions are allowed (uncertain times).
✔ End State:
➔ PSA end state has two possible values: success or fail.
➔ ISA end state sequence, is a random variable where each final state (damage
or success) has an associated probability.

ISA. Scheme.
A U T O M A T I C
G E N E R A T I O N
O F P A T H S / S E Q U E N C E S
R IS K
A S S E S S M E N T :
E X C E E D A N C E
F R E Q U E N C Y
A N D IT S F A C T O R S
IN P U T D A T A R E S U L T S
F T / E T / A P E T :
S D T P D IN F O
C L A S S IC A L
F R E Q U E N C Y
E S T IM A T E
P A T H A N A L Y S I S :
S U C C E S S C R IT E R I A
T E C S P E C S
S O J O U R N T IM E A N A L Y S IS
P L A N T D A M A G E S T A T E S
E X C E E D A N C E
F R E Q U E N C Y
E T /F T
F R E Q U E N C Y /
D E M A N D
D E M A N D
P R O B A B I L I T Y
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
S T O C H A S T I C
D A T A
P S A F T / E T
D A T A
I N IT I A T O R
D A T A
P L A N T
D Y N A M I C M O D E L
S I M U L A T O R D A T A
P L A N T
P R O C E D U R E S
A U T O M A T I C
G E N E R A T I O N
R IS K
E X C E E D A N C E
F R E Q U E N C Y
F T / E T / A P E T :
S D T P D IN F O
C L A S S IC A L
F R E Q U E N C Y
E S T IM A T E
T E C S P E C S
E X C E E D A N C E
F R E Q U E N C Y
E X C E E D A N C E
F R E Q U E N C Y
E T /F T
F R E Q U E N C Y /
D E M A N D
E T /F T
F R E Q U E N C Y /
D E M A N D
D E M A N D
D E M A N D
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
S T O C H A S T I C
D A T A
P S A F T / E T
D A T A
I N IT I A T O R
D A T A
P L A N T
P L A N T
P R O C E D U R E S

ISA. Scheme.
A U T O M A T I C
G E N E R A T I O N
R IS K
E X C E E D A N C E
F R E Q U E N C Y
F T / E T / A P E T :
S D T P D IN F O
C L A S S IC A L
F R E Q U E N C Y
E S T IM A T E
T E C S P E C S
E X C E E D A N C E
F R E Q U E N C Y
E T /F T
F R E Q U E N C Y /
D E M A N D
D E M A N D
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
S T O C H A S T I C
D A T A
P S A F T / E T
D A T A
I N IT I A T O R
D A T A
P L A N T
P L A N T
P R O C E D U R E S
A U T O M A T I C
G E N E R A T I O N
R IS K
E X C E E D A N C E
F R E Q U E N C Y
F T / E T / A P E T :
S D T P D IN F O
C L A S S IC A L
F R E Q U E N C Y
E S T IM A T E
T E C S P E C S
E X C E E D A N C E
F R E Q U E N C Y
E X C E E D A N C E
F R E Q U E N C Y
E T /F T
F R E Q U E N C Y /
D E M A N D
E T /F T
F R E Q U E N C Y /
D E M A N D
D E M A N D
D E M A N D
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
F R E Q U E N C Y
W E I G H T E D
F R A C T I O N O F
D A M A G E
P A T H S
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
A C T IV A T IO N
F R E Q U E N C Y
S T IM U L I
S T O C H A S T I C
D A T A
P S A F T / E T
D A T A
I N IT I A T O R
D A T A
P L A N T
P L A N T
P R O C E D U R E S

SCAIS
TRACE
MAAP
RELAP5
Dendros
PVM
Babieca
SIMPROC
Path Analysis and
Risk Assessment
SCAIS. Overview.

SCAIS. The Platform

SCAIS. Babieca Motivation.
Probabilistic Safety Assessment (PSA) is a widespread technique used during
design and operating stages of a Nuclear Plant.
✔ Acquiring an in-depth understanding of the facility and collecting a large
volume of related information.
✔ Identifying initiating events and states of plant damage.
✔ Modeling the main plant systems using event and fault trees.
✔ Relationships between events and human actions.
✔ Specific plant systems and components DB.
The results of these analysis can therefore identify not only the weaknesses
but also the strengths regarding to the plant safety.

Event scheduler (DENDROS), drives the dynamic simulation of the different
sequences in the generation of the Dynamic Event Tree.
✔ Stimulus.
A stimulus is generated when the simulation of a sequence crosses a
defined condition (activation event). It has to be previously defined in
the Event Tree as a header, and it is the cause of the creation of
branching points.
✔ Branch Opening.
When a dynamic simulation finds events, it generates nodes with
associated restarts that stand as points in the sequence that may lead
to the opening of a new branch. The nodes have associated two
probabilistic parameters that are the probability for branch opening
and the temporal delays.
SCAIS. Dendros

Any code allowing time step concept can be adapted to SCAIS general
calculus flow.
SCAIS. Code Coupling

Stochastic Stimulus are managed almost naturally during the dynamic
simulation by SCAIS.
Current developments are focused in;
✔ Distinct techniques to minimize the number of simulations finding
the damage domain.
✔ System configurations without success criteria.
SCAIS. Path Analysis and Sequence Generation

✔ Uncertain Parameters. A new SCAIS module is currently under
development using DAKOTA tool as an input generator.
✔ Sensitivity Studies. DAKOTA is also being studied to perform the output
studies, but also in house developments will be carried out.
SCAIS. Path Analysis and Sequence Generation

✔ The Risk Assessment module calculates frequency density of each path
following the Theory of Stimulated Dynamics (TSD).
✔ Future developments will integrate every damage path of a sequence to
find the damage exceedance frequency of a sequence.
SCAIS. Risk Assessment

`pk TSD Background
• Last year, an overview of TSD was presented at the 1st. IDPSA
workshop in Espoo.
• TSD can be seen as a path and sequence solution of
non-homogeneous, continuous time Markov systems.
• A sequence is an ordered set of discrete states j. A path
(also called transient) is an instance of a sequence where
transitions between states j occur at specified times.
• Discrete states j are composed by system states (connected or
not) and phenomenon states (occuring or not).
• Each discrete state j is bi-univocally associated to a dynamic
state (i.e., a set of dynamic equations) that determines the
evolution of process variables.
• Transitions j → k between discrete states are produced by
dynamic events. In general, they are stochastic and
characterized by occurrence rates pj→k(x) which are
functions of the process variables.
IDPSA Workshop. Stockholm, Sweeden 19-20 November 2012 1

`pk TSD Background
• The stimulus of a dynamic event is a condition that makes
the occurrence rate of that event different from zero.
• In a sequence, the event occurrence times can be seen as a
space where each point is a path of the sequence. The
sequence frequency gets distributed over this space.
• Each path of the sequence has a frequency density that can
be calculated with the TSD equations.
• The sequence sub-space composed by paths ending in a
damage condition is the Damage Domain of the sequence.
• The contribution of a sequence to the damage frequency
results from integrating the frequency density over the
damage domain.

`pk TSD ongoing developments
Multiple outcome events. System events
• Very often, a dynamic event may produce different outcomes,
i.e., it may result in different transitions.
• In this case, transition rates are given by the event
occurrence rate times the outcome probability.
• An important case is that of plant systems that may work in
different modes (e.g., different number of working trains in a
multi-train system).
• Each working mode results from a different system
configuration.
• The start-up of a stand-by multi-mode system is a dynamic
event whose dynamic impact on the plant depends on the
working mode, i.e., on the system configuration.
• In this case, the outcome probability is the conditional
probability of the system configuration.

`pk TSD ongoing developments
Configuration probability
• There are multiple dependences among system configurations.
Calculation of configuration probabilities is a complex task.
• When considering multiple outcome events, discrete states j
should be extended to include system configurations.
• The plant configuration is composed by all the system
configurations.
• The TSD equations are also extended to include the plant
configuration probability. Consistency with current PSA
technology must be carefully taken into account.
• Due to the complexity of system dependences, the use of fault
tree models and PSA quantification tools is highly
recommendable.
• Configuration fault trees are embedded in existing PSA fault
trees but in most cases they cannot be easily extracted.

`pk Algorithms and Strategies for TSD
Implementation
Integration algorithm for sequences of protective
actions
• A frequent case in a PSA-1 context is that dynamic events
consist of protective actions stimulated by deterministic
conditions.
• Deterministic stimuli means:
Event occurrence rates are a direct result of the simulation.
They are non-null only while the corresponding stimulus is
activated.
• Protective actions means:
The more delay in the event occurrence, the closer the
situation to a damage condition.

Implementation
Parents and children sequences/transients
• A sequence is an ordered set of dynamic events. A transient is
an instance of a sequence where the event occurrence times
are specified. (Let us consider single outcome events for the shake of
simplicity)
• If a new event is added at the end of a previous sequence, the
resulting sequence is a child of the previous one.
• A transient of the child sequence is a child of a transient of
the parent sequence if the common events occur at the
same times.
• Damage domains of parent/child sequences are related. For
protective action events:
A non-damage transient cannot have damage children.
Among the children of a damage transient there is always
a non-empty set of damage transients.

Implementation
Integration of the TSD equations
• Let us think of an accident scenario with two possible protective
actions, A and B whose occurrence times are τA and τB.
• Taking apart the initiating event, the possible dynamic
sequences are (), (A), (B), (A,B) and (B,A).
• Note that both (A) and (B) are children of (), (A,B) is a child
of (A) and (B,A) is a child of (B).
• The conditional damage probability (given the initiating event)
should be calculated as:
pdam = p() +
D(A)
fA(τA)dτA +
D(B)
fB(τB)dτB + (1)
+
D(A,B)
fA,B(τA, τB)dτAdτB +
D(B,A)
fB,A(τB, τA)dτBdτA

Implementation
Application of parental relationships
• Due to parental relationships, integration limits of different
integrals become related.
• For the occurrence time of an event, integration limits are:
The upper limit is the damage time in the parent
transient.
The lower limit is the maximum of:
∗ Activation of the event stimulus.
∗ The occurrence time of the previous event.
∗ The border of the damage domain.
• All this information but the border of the damage domain can
be taken from the corresponding parent transient.
• When a transient has been calculated, the set of its children
can be integrated.
• The border of the damage domain can be found during the
integration process.

Implementation
Recursive integration algorithm
With these considerations, equation (1) can be rewritten as:
pdam = p() +
+
T D
()
τmin
A
fA(τA) +
T D
(A)(τA)
τmin
B
(τA)
fA,B(τA, τB)dτB dτA + (2)
+
T D
()
τmin
B
fB(τB) +
T D
(B)(τB)
τmin
A
(τB)
fB.A(τB, τA)dτA dτB
Note that:
• Equation (2) represents a recursive algorithm that can be
extended to any number of dimensions.
• All the integrals in (2) are one-dimensional and can be
optimized in an independent way.
• The adequate discretization strategy for calculating (2) is to
take occurence times in decreasing order.

`pk CONCLUSIONS
• ISA is a mature Methodology to implement an IDPSA analysis.
• SCAIS Platform developed to perform ISA Methodology, but the
platform is broad enough to implement other IDPSA
Methodologies, including non-nuclear industries using PSA.
• Some SCAIS developments and applications are needed to
achieve an advanced platform able to perform full IDPSA
studies.
• Consistent incorporation of configuration fault trees is needed.
Extensions of the theoretical framework are being developed to
this aim.
• Computational algorithms should be optimized to reduce the
amount of required resources. To this aim, an efficient
recursive algorithm has been developed for sequences of
protective actions.

SCAIS_TSD_2

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