-
SOLUTION WITH I&AB IN
RISKSPECTRUM (A)
Marc Bouissou (EDF R&D)
Pavel Krcal (Lloyd's Register)
-
I&AB aims
Reliability analysis of repairable dynamic systems
Scalability Precision
Precision,
qualitative results
I&AB
Scalability
Scalability
nuclear PSAMarkov analysis
minimal cut sets :
initiator + all barriers
analytical
formulae,
suitable for small
probabilities (unlike
Monte Carlo simulation)
Precision
-
I&AB theory: not the point in
this presentation!
Theory and simple numerical applications in:
- Patent FR3044787 (cf. https://worldwide.espacenet.com/)
- M. Bouissou, O. Hernu: "Boolean approximation for
calculating
the reliability of a very large repairable system with
dependencies
among components",
ESREL 2016, Glasgow
- M. Bouissou: "Extensions of the I&AB method for the
reliability
assessment of the spent fuel pool of EPR",
ESREL 2018, Trondheim.
-
COMPARISON BETWEEN I&AB AND
TRULY DYNAMIC CALCULATIONS
Markov
analysis
Monte Carlo
simulation
I&AB
BDMP modelReal system
required =
'always_true'
Diesel_GenDiesel_Gen
OR
LHA_lostLHA_lost
AND
LHA_and_LHB_lostLHA_and_LHB_lost
!
LHALHA
!
LGDLGD
!
LGALGA
!
SH_CB_LGD2SH_CB_LGD2
AND
TS_not_fedTS_not_fed
!
TSTS
!
InFnHouseInFnHouse
!
SH_CB_GEVSH_CB_GEV
!
TATA
!
GEVGEV
!
SUBSTATIONSUBSTATION
!
TPTP
I !
OnDemHouseOnDemHouse
OR
LHB_lostLHB_lost!
LHBLHB
!
LGFLGF
!
SH_CB_LGBSH_CB_LGB
!
SH_CB_LGF2SH_CB_LGF2
!
LGRLGR
!
GRIDGRID
OR
OR_14OR_14
!
SH_CB_LGASH_CB_LGA
!
SH_CB_LHA1SH_CB_LHA1
!
SH_CB_LGD1SH_CB_LGD1
!
SH_CB_line_LGRSH_CB_line_LGR
!
SH_CB_line_GEVSH_CB_line_GEV
!
SH_CB_LHB1SH_CB_LHB1
!
SH_CB_LGF1SH_CB_LGF1
!
LGBLGB
!
CCF_GEV_LGRCCF_GEV_LGR
Low_voltage_ALow_voltage_A Circuit_breakers_ACircuit_breakers_A
Cirsuit_breakers_BCirsuit_breakers_BLow_voltage_BLow_voltage_B
repair_constraintrepair_constraint
OR
SH_GEV_or_LGRSH_GEV_or_LGR
!
UNITUNIT
UE_1UE_1
AND
LHA_not_fedLHA_not_fed
AND
LHB_not_fedLHB_not_fed
OR
loss_of_supply_by_LGDloss_of_supply_by_LGD
OR
loss_of_supply_by_LGFloss_of_supply_by_LGF
AND
LGF_not_fedLGF_not_fed
AND
LGD_not_fedLGD_not_fed
OR
loss_of_supply_by_TSloss_of_supply_by_TS
OR
loss_of_supply_by_TS1loss_of_supply_by_TS1
OR
loss_of_supply_by_TA1loss_of_supply_by_TA1
OR
TS_lostTS_lost
OR
TA_lostTA_lost
OR
loss_of_supply_by_UNITloss_of_supply_by_UNIT
OR
loss_of_supply_by_LGRloss_of_supply_by_LGR
OR
loss_of_houseload_operationloss_of_houseload_operation
OR
loss_of_supply_by_GEVloss_of_supply_by_GEV
OR
loss_of_supply_by_TAloss_of_supply_by_TA
loss_of_supply_by_DGB
Diesel_Gen
RC_CB_LGF2_
Cirsuit_breakers_B
CB_LGF2_unable
Cirsuit_breakers_B
loss_of_supply_by_DGB
Diesel_Gen
CB_LHB12_unable
Cirsuit_breakers_B
loss_of_supply_by_DGA_and_TAC
Diesel_Gen
loss_of_supply_by_DGA_and_TAC
Diesel_Gen
CB_LHA12_unable
Circuit_breakers_A
CB_LGD2_unable
Circuit_breakers_A
RC_CB_LGD2_
Circuit_breakers_A
UNIT UNIT
GEV
LGR
TSTS
CB_line_GEV CB_line_GEV
TATA
GE
DGA DGA
CB_LHA3 CB_LHA3
CB_GEV CB_GEV
CB_LGA CB_LGA
CB_line_LGR CB_line_LGR
CB_LGF1 CB_LGF1 CB_LGD1 CB_LGD1CB_LGF2 CB_LGF2
CB_LGB CB_LGB
LGD LGD
LGA LGALGB LGB
GE
TAC TAC
CB_LGD2 CB_LGD2
CB_LHA1 CB_LHA1
LGF LGF
CB_LHB1 CB_LHB1 CB_LHB2 CB_LHB2
GE
DGB DGB
LHA LHALHB LHB
CB_LHA2 CB_LHA2
SUBSTATION SUBSTATION
GRID GRID
TPTP
CB_TUA2
CB_power_supply
CB_TUB1
CB_power_supply
CB_LGE1
CB_power_supply
CB_TUB2
CB_power_supply
CB_LGE2
CB_power_supply
Transformer
6.6kV/380V
LGELGE
AC/DC converter
380V/125V
1 hour1 hour
TUA1TUA1
CB_RDA1CB_RDA1
CB_LBA1CB_LBA1
LBALBA
BATTERY_ABATTERY_A
CB_RDA2CB_RDA2
CB_LBA2CB_LBA2
TUA2TUA2
LLALLA LKILKI
LBBLBB
RDB1RDB1RDB2RDB2 CB_LBB3CB_LBB3
CB_LBB2CB_LBB2
BATTERY_BBATTERY_B
CB_RDB1CB_RDB1CB_RDB2CB_RDB2
LLDLLD
TUB2TUB2
CB_TUA2CB_TUA2
TUB1TUB1
CB_TUB2CB_TUB2CB_TUA1CB_TUA1 CB_TUB1CB_TUB1
CB_LGE1CB_LGE1
LKELKE
RDA2RDA2CB_LBA3CB_LBA3
RDA1RDA1
CB_LBB1CB_LBB1
LGD
Page_Principale
LHB
Page_Principale
CB_LGE2CB_LGE2
LGB
Page_Principale
TA
Page_Principale
LHA
Page_Principale
-
Tools used for this experiment
KB3-BDMP
Markov
analysis:
FIGSEQ
Monte Carlo
simulation:
YAMS
FigaroModel (read-
able text)
Faulttree(XML)
I&AB:
RiskSpectrum
-
ResultsBDMP characteristics: 81 basic events, 14 AND gates,
5
PAND (priority AND) gates and 35 OR gates, built in 1 day
(for details on the model, cf. solution with KB3-BDMP)
Calculation type CPUIntel Core [email protected]
Cutoff(proba. at 104h)
Unrel. at 104h « best estimate »
Qualitative results: number of sequences
Asymptotic unavailability
Figseq (exponentialapproximation)
20s1800s
1E-81E-11
3.48E-53.86E-5
106 first3950 first
1.51E-71.58E-7
YAMS (batteries = 1hour)
3600s2E7 sim.
3.73E-5+-3E-6
143 among the first (99 aftergrouping)
1.66E-7+-2E-8
RiskSpectrum
I&AB(approx expo)
7s
1s
0
1E-10
1.35E-4
1.35E-4
467474 cutsets
2370 first
will come in a future release
RiskSpectrum (PSA method)Pr(Batt failure)=1
8s
-
Sensitivity analysis
Calculation type CPU Cutoff(proba at 104h)
Unrel. at 104h « best estimate »
Qualitative results: number of sequences
Figseq (exponentialapproximation)
8mn 1E-11 3.85E-6 2498 first
YAMS At least 10h…
RiskSpectrum
(I&AB)(approx expo)
1s 1E-11 1.29E-5 2196 first
RiskSpectrum (PSA method)Pr(Batt failure =1)
8s
-
Static PSA method vs I&AB
quantification
• Generally no repairs
• Conservative if mission time large enough
• Fast
• Good for short mission times
Static
● Repairs
● Reduces conservatism
– Significant for long mission times
● Fast: Efficient also for large-scale PSA
● Good ranking of failures importance
● Available in RiskSpectrum
Dynamic: I&AB
-
Conclusion
• BDMP: quick to build, minimizes calculation resources (MC
simulation at least 6 times faster than with all other models),
can
be automatically transformed by KB3 into a RiskSpectrum
model
for I&AB
• I&AB can be used in two kinds of situation
starting from a BDMP: dramatically improves scalability of such
models for the
quantification of rare events (not rare => Monte Carlo can
suffice)
to improve the precision of PSA, at a reasonable computing
cost
• I&AB in RiskSpectrum commercialized soon
=> The tandem KB3 + RiskSpectrum is a perfect tool for
all these applications
-
KB3 & RiskSpectrumEDF and Lloyd's register have signed
a long term collaboration contract
in order to merge KB3 and RS
Top
Unsufficient pumping
Top
Unsufficient pumping
TK_1/FO
Failure in operation of tank
TK_1
422
Obstruction in operation of
MP_1
TP_1/FO
Failure in operation of pump
TP_1
TP_1/FD
Failure on demand of pump
TP_1
CV_3/FO
Failure to open of
check-valve CV_3
564
Obstruction of TP_1
TK_1/FO
Failure in operation of tank
TK_1
539
Obstruction in block
BO_CV_3
TK_1/FO
Failure in operation of tank
TK_1
495
Obstruction in operation of
MP_2
333
Loss of fluid in block
BO_CV_1
531
Loss of fluid in block
BO_CV_3
458
Loss of fluid in block
BO_CV_2
CV_1/RU
Rupture in operation of
check-valve CV_1
CV_3/RU
Rupture in operation of
check-valve CV_3
CV_2/RU
Rupture in operation of
check-valve CV_2
329610
Leakage in leakage group
leakage_group_1
Top
Unsufficient pumping
Top
Unsufficient pumping
TK_1/FO
Failure in operation of tank
TK_1
422
Obstruction in operation of
MP_1
TP_1/FO
Failure in operation of pump
TP_1
TP_1/FD
Failure on demand of pump
TP_1
CV_3/FO
Failure to open of
check-valve CV_3
564
Obstruction of TP_1
TK_1/FO
Failure in operation of tank
TK_1
539
Obstruction in block
BO_CV_3
TK_1/FO
Failure in operation of tank
TK_1
495
Obstruction in operation of
MP_2
333
Loss of fluid in block
BO_CV_1
531
Loss of fluid in block
BO_CV_3
458
Loss of fluid in block
BO_CV_2
CV_1/RU
Rupture in operation of
check-valve CV_1
CV_3/RU
Rupture in operation of
check-valve CV_3
CV_2/RU
Rupture in operation of
check-valve CV_2
329610
Leakage in leakage group
leakage_group_1
KB3
check_valve_1tank_1
380
motor_driven_pump_3
!
test_loss_fluid_1380
motor_driven_pump_2
node_3
check_valve_3
check_valve_2
node_1
380
motor_driven_pump_1
check_valve_2
check_valve_3
test_loss_fluid_1
check_valve_1
motor_driven_pump_2
tank_1
node_3
motor_driven_pump_3
node_1
motor_driven_pump_1
Transformer
6.6kV/380V
LGELGE
AC/DC converter
380V/125V
1 hour1 hour
TUA1TUA1
CB_RDA1CB_RDA1
CB_LBA1CB_LBA1
LBALBA
BATTERY_ABATTERY_A
CB_RDA2CB_RDA2
CB_LBA2CB_LBA2
TUA2TUA2
LLALLA LKILKI
LBBLBB
RDB1RDB1RDB2RDB2 CB_LBB3CB_LBB3
CB_LBB2CB_LBB2
BATTERY_BBATTERY_B
CB_RDB1CB_RDB1CB_RDB2CB_RDB2
LLDLLD
TUB2TUB2
CB_TUA2CB_TUA2
TUB1TUB1
CB_TUB2CB_TUB2CB_TUA1CB_TUA1 CB_TUB1CB_TUB1
CB_LGE1CB_LGE1
LKELKE
RDA2RDA2CB_LBA3CB_LBA3
RDA1RDA1
CB_LBB1CB_LBB1
LGDPage_Principale
LHBPage_Principale
CB_LGE2CB_LGE2
LGBPage_Principale
TAPage_Principale
LHAPage_Principale
RiskSpectrum
Component
importance
Pr(top)
Cutset 1
Cutset 2
…
