i2SIM-Human

Mathematical Representation of HumanDecisions in an System Solution

José R. Martí

1

© 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.

2

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

3

Physical, Geographical, Management,and Cyber Layers

4

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

5

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

6

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.

7

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

8

QoM with Interdependencies

Resilience of the combinedsystem is less than theresilience of the components

9

QoM Probability Distribution

QoL Distribution Normal Recovery

QoL Distribution with i2SIM

QoM

QoM

10

Human in the Loop

11

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.

12

Manager’s Knowledge of ER Unit’sOperation Represented in Hospital’s HRT

13

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

14

State-Space System Representation

15

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

18

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

20

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

21