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04/19/23 Roberto Filippini AB-BT 1
Topics of the Presentation
• The operational scenario• Re-analyzing the model for the beam losses.• Updating the model.
– Beam loss and normal conclusion.
• The general model.– Some approximations for managing complexity.
• Trading-off safety performance (a case study).• Conclusions.
04/19/23 Roberto Filippini AB-BT 2
System DescriptionOperational Scenario
04/19/23 Roberto Filippini AB-BT 3
The Beam Loss ModelBasic Assumptions
The model.– The system includes the BLM, the BICs, the beam permit loop and the
LBDS. The BEM is included in the LBDS.
– The BIC6 is kept separated from the other BICs, for the function of sending a dump request to the LBDS.
– Failure rates are assumed constant.
Beam Losses– The likelihood of having beam losses at a certain portion is uniformly
distributed along the ring and involves only one BLM at a time.
– Beam losses average rate is assumed 1/48h (200days).
Analysis.– The probability of being available at the time of a beam loss (continuous
operation, no planned dump requests).
04/19/23 Roberto Filippini AB-BT 4
The Beam Loss ModelModeling the Beam Loss Event
Probability of the number of beam loss events respect to time t
tn
BL BLen
tntNP
!
)())((
20 40 60 80 100t
0.005
0.01
0.015
0.02
pBLt
20 40 60 80 100t
0.2
0.4
0.6
0.8
PBLt20
4060
80100
Missions1000
2000
3000
4000
timeh00.020.040.060.08
prob
2040
6080
100
Missions
tBLBL
BLetp )(
tBL
BLetP 1)(
Distribution of a single beam loss
Probability a beam loss occurred in[0,t]
Beam Loss Events
04/19/23 Roberto Filippini AB-BT 5
The Beam Loss ModelMarkov Chain
StatesX0 System available
X1 System available at the time of a beam loss
X2 System no more available for a beam loss
X3 Beam loss and system no available
Parameters
BL Beam loss rate Markov Chain
BLMxyBICxLoopBICLBDS 6
04/19/23 Roberto Filippini AB-BT 6
The Beam Loss ModelResults
Event/Failure Rate
Beam loss 1/48h
BLMxy 10-6/h
BICx 10-6/h
BIC-6 10-6/h
P.Loop 10-6/h
LBDS 10-6/h
P(X3): System not available at a Beam loss
P(X3): Mean System Unreliability after 100 missions of mean duration T = 48h
Model parameters setting
20 40 60 80 100missions
0.0020.0040.0060.0080.01
0.0120.014
1RtT1 T2 Tn
E{T i+1 – Ti }= 48h
E{N(t)} = 100, (t = 4800h)
50 100 150 200mission timeh0.00005
0.0001
0.00015
0.0002
1St1-R(t)
1-R(m)
04/19/23 Roberto Filippini AB-BT 7
The Beam Loss ModelComments
About the model:• The single mission terminates at a beam loss and restarts only if it has
been successfully terminated.• The overall process (one year) is a sequence of dump requests at the
time of the beam loss. It is a Markov renewal process.What is to update:1. The mission has a finite duration T due to the planned dump requests:2. The system configuration at a planned dump requests is in part
different form the configuration needed for a beam loss.
04/19/23 Roberto Filippini AB-BT 8
Updating ModelBeam Loss and Planned Dump Requests
StatesX0 System available
X1 System not available for a beam loss
X2 System not available for a planned dump request (DR)
X3 System no available for a planned DR and a beam loss
X4 System failed at a beam loss
X5 Safe beam dump at a beam loss
Parameters
01 BLMxy OR BICx failed
02 BIC1 failed
23 BLMxy OR BICx failed
13 LBDS OR Permit Loop OR BIC6 OR BIC1
03 LBDS OR Permit Loop OR BIC6
Markov Chain
04/19/23 Roberto Filippini AB-BT 9
Updating ModelResults at the End of a 10h Operation
20 40 60 80 100 120 140Missionaborts
0.010.020.030.040.050.06
Prob
Unavailable at a planned dump
request at any time: P(X2)+P(X3) Unavailable at a beam loss occurred in [0,10] : P(X4)
Mission aborts distribution due to a beam loss (1/48h) over 400 missions
Probability of unsafe dump at time t=10
At time t =10h the unavailability of the system BIC1-Permit Loop-BIC6-LBDS is added
2 4 6 8 10mission timeh1 106
2 106
3 106
4 106
1St1-R(t)
2 4 6 8 10mission timeh5106
0.000010.0000150.00002
0.0000250.00003
1St1-R(t)
2 4 6 8 10 12mission timeh0.00001
0.00002
0.00003
0.000040.00005
1St1-R(t)
04/19/23 Roberto Filippini AB-BT 10
Updating ModelComments
About the model:• More realistic reliability figures are
obtained.• Reliability over 1 year involves a more
complex renewal process.• System is as good as new at the start of a
mission.• Surveillance (BET, etc…) not yet included.The next step: to include surveillance:• Benefits: reduction of the system failure
rate. • Drawbacks: generation of dump requests. Approximations are necessary for
managing complexity.1. For the reliability of a single operation.2. For the reliability over one year.
Beam Loss Model: Unreliability over 400 missions (10h each)
Beam Loss and Planned dump requests Model: Unreliability over 400 missions (10h each)
100 200 300 400missionsh0.002
0.0040.0060.0080.01
0.0120.014
1Rm
100 200 300 400missions
0.00250.005
0.00750.01
0.01250.015
0.01751Rm
04/19/23 Roberto Filippini AB-BT 11
The Model Including SurveillanceAssumptions
Assumptions during a single mission• A1: The probabilities are evaluated at time t = T.• A2: All the cases leading to a dump requests are modeled and analyzed
separately.• A3: The system reliability R(T) is calculated with respect to the system
configuration at the time of a dump request.Assumptions over one year• A4: The system is as good as new after the check (no aging and wearing).• A5: We assume 400 LHC operation cycles per year (average).
The approximations 1,2,3 lead to a lower bound for the system reliability over one mission. The assumptions 4 can be relaxed.
04/19/23 Roberto Filippini AB-BT 12
The General ModelPutting All Together
)()()(
...)(
)()()(1)()()(
400
400...1400
onscontributiOther
52
5...21
request dumpPlanned
11
TRTRTR
TP
TRTPTPTRTPTR
nnn
kk
kkk
04/19/23 Roberto Filippini AB-BT 13
MKDA Case Study (EPAC Paper)
• Analysis of safety and average number of false dumps of the MKD (LBDS) over one year.
04/19/23 Roberto Filippini AB-BT 14
The MKD ModelRedundancy, Surveillance, Post mortem
Not-Homogeneous Markov Chain
StatesX0 System available
X1 BET failed, no more surveillance
X2 Dump request, safe mission aborts
X3 System failed unsafe
Parameters BET failure (failed silent)
Powering failure, surveillance fail safe modes (channels)
Power triggers, switches, magnets failure (above redundancy)
Every failure in the system
04/19/23 Roberto Filippini AB-BT 15
MKD AnalysisAssumptions
Modeling assumptions1. BEM, triggering and re-
triggering systems have not been included.
2. The data acquisition channels going to the BET are identical and fail always safe (dump request).
3. Constant failure rates.4. The length of an LHC
operation (the mission) is 10h.5. After the post mortem the
system is as good as new.
Components Failure rates/h
Capacitors 1x10-6 (1) 1x10-5(2)
Power triggers, switches 1x10-5
Power supplies 1x10-5
Magnets 1x10-6
Channels 1x10-6
BET 1x10-8
04/19/23 Roberto Filippini AB-BT 16
MKD AnalysisResults Over One Year (400 Missions)
2 4 6 8 10 12 14Mission aborts
0.05
0.1
0.15
0.2
0.25
Prob 12
Probability of MKD system failure
(a) Default case 4.2x10-6
(b) No post mortem 2.7x10-3
(c) No generator redundancy 3.4x10-3
(d) No surveillance 5.4x10-3
Distribution of mission aborts
(1) Capacitors failure rate 1x10-6 2 average
(2) Capacitors failure rate1x10-5 6 average
04/19/23 Roberto Filippini AB-BT 17
Conclusions
• The beam loss model was updated considering the conclusion due to a planned dump request
• The model is very compact although complex in the transition rates.
• To manage things at higher level needs approximations.
• The next steps:– To analyze the contribution of surveillance in terms of safety gain
and false dumps per year as shown for the MKD system.
– Sensitivity analysis and trade-off studies (safety against false dumps) of the most critical systems.