i2sim-human...large complex systems a complex system is a network of heterogeneous agents with...
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i2SIM-Human
Mathematical Representation of HumanDecisions in an System Solution
José R. Martí
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© José R. Martí, UBC, 15 March 2019
Large Complex Systems
§ A complex system is a network of heterogeneous agentswith nonlinear behaviour and multiple time scales.
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ElectricalSystem
PowerPlant
Substation
Transmission
DistributionCenter
ProductionCenter
Local Store
PurificationPlantPump
Station
Pipe
Refinery
Oil FieldCompressor
Station
PhoneInternet
Mobile
LocalRoad
BridgeRegionalHighway
Firefighter
ParamedicHospital911 E-Comm
CriticalEvent
LocalRoad
FoodDistribution
System
Oil & GasDistribution
System
EmergencyResponse
SystemWater
System
TransportationSystem
Information andCommunication
Technologies
Critical Interdependent (CI) Systems
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Physical, Geographical, Management,and Cyber Layers
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PhysicalProduction
Layer
Geographical &Damage Layer
(GIS)
Management &Organizational
Layer
CyberSystemLayer
People’sWell-Being
Layer
Electrical substationWater pumpHospitalHomes
DecisionsOrganizational structurePublic Private PartnershipsPolicies & ProceduresTraining
Mountains, lakesWeatherDamage caused byearthquake, floodHardening of equipment
TelecommunicationsSystemSCADACybersecuritySocial networks
WealthEmploymentPersonal satisfactionCommunities
Other Layers:Financial System,
EconomicDevelopment,Environment,
Others
i2SIM Multisystem/Multilayer Simulator
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CoordinatedIntegration
i2SIM
Quality of Mission (QoM) versusQuality of Individual Services (QoS)
§ QoS (Quality of Service) (reliability)
Failures of Equipment and Design
§ QoM (Quality of Mission) (resilience)
Impact of Failures on the Mission
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Quality of Mission (QoM) Index
( )
( )
R
o
t
tindex
N R o
y t dtQoM
y t t=
-
ò
A disruptive event occurs at to. Restoration to an acceptable level achieved at tR.
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Electrical System (HRT)y (elec)(MW)
S1(elec)(MW)
x1 (ICT)(units)
m1 (idam)(%)
600 600 33 100
300 300 22 50
0 0 0 0
Public Service (HRT)y (service) (%) X1 (elec) (MW) x2 (water) (ML/
day)x3 (ICT) (units)
100 180 150 3375 135 80 3050 90 50 25
25 45 20 150 0 0 0
Well-Being Table Residences (HRT)y (WBL)
(%)x1
(elec)(MW)
x2 (water)(ML/day)
x3(services)
(%)
x4 (ICT)(units)
100 200 150 150 3375 120 130 130 3050 70 100 90 2525 30 40 40 150 0 0 0 0
Water System (HRT)
y (ML/day) S2(ML/day) x1 (MW)
300 300 30
200 200 20
100 100 10
0 0 0
ICT System (HRT)
y (units) x1(elec)(MW)
m2 (idam)(%)
100 20 100
50 10 50
0 0 0
S1
m1
S2
X
X
X Xm2
HRT: Table torelate inputs and
outputs
The Quality of Life (QoL) in Smart Cities depends onthe recovery actions of multiple interdependent CIs
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QoM with Interdependencies
Resilience of the combinedsystem is less than theresilience of the components
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QoM Probability Distribution
QoL Distribution Normal Recovery
QoL Distribution with i2SIM
QoM
QoM
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Human in the Loop
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Modelling Human Experience
1. i2SIM uses the concept of the Human Readable Table tocapture human and physical relationships.
2. For example, the number of patients treated in the ERunit of a hospital depends on the availability of physicalquantities: electricity, water, doctors, nurses, etc.
3. How these quantities determine the number of patientstreated is known from experience. The manager of theunit knows these relationships.
4. The more experienced the manager, the better he/shewill know the relationships.
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Manager’s Knowledge of ER Unit’sOperation Represented in Hospital’s HRT
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y(t) x1(t) x2(t) m1(t) m2(t) m3(t) m4(t)
Patientsper hour
Electricity(kW)
Water(L/h)
Doctors Nurses PhysicalIntegrity
DoctorsShift
Factor
20 100 2,000 4 8 100% 100%
16 80 1,000 3 6 80% 75%
10 60 600 2 5 50% 50%
7 40 400 2 3 20% 25%
0 0 0 0 0 0% 0%
• Table relates inputs to output in a nonlinear manner.• The Operating Level is determined by the least available
resource.
EngineeringLayer
EngineeringLayer
EngineeringLayer
ManagementLayer
ManagementLayer
ManagementLayer
ManagementLayer
OperatingLevel
HRT Tables are Parameterized by AnalyticalFunctions
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State-Space System Representation
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1L
1S
2S
1( )h
4 ( )h3 ( )h
2 ( )h1d 2d
3d
1 1k y1x
11x
10x
9 3k y
8 3k y
7x
6 2k y5 2k y
4 2k y
3 1k y
2 1k y1y
4y3y
2y4x
7 3k y
9x
2x
5x6x
3x g
hi = min fi{xi}{ }di = g{xi,ki}
ìíï
îï
UBC Campus
16JIIRP Public Safety Canada Project
Vancouver 2010 Winter Olympics
17DRDC Project
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Transportation
Hospital System Residential System Electrical System Water System
Guadeloupe Island Earthquake 1974
402,000 inhabitants covering 1632 km².Earthquake of magnitude 7.5 in 1974
MATRIX fp7 EU Project 18
Japan Sendai Earthquake 2011
19CANARIE Project
City of Rome Electrical System
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PS 1
PS 2SS9SS1 SS2SS9
SS9SS1 SS2SS9
SS9SS1
PS 3
PS 4
Line 1,1
Line 1,2
Line 1,19
Line 2,1
Line 3,1
Line 4,1
HV
HV
HV
HV
SS2
SS2
SS2
SS1
SS1
PS 73 PS 74 HVHV
SS2SS9 SS1
1.6 million customers, 74 HV substations, 13,500secondary substations
CIPRNet fp7 EU Project
Thanks
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