Intelligent Light Control using Sensor Networks

Vipul Singhvi1,3, Andreas Krause2,

Carlos Guestrin2,3, Jim Garrett1, Scott Matthews1

Carnegie Mellon University

1 Department of Civil and Environmental Engineering2 School of Computer Science

3 Center of Learning and Discovery

Motivation Current built infrastructure

Trillions of dollars investment Cost over the life cycle Research shows potential gains from

reducing operating cost and improving occupant performance $10 - $30 billion/yr from reduced

energy consumption $20 - $160 billion/yr gained from

improvement in comfort leading to better occupant performance

Reduction in energy cost related to reduced comfort & performance: Complex tradeoff optimization

Life cycle building cost

Salary cost overbuilding life cycle

Maintenance andoperation

Construction

Sensor networksSmart monitoring and actuationcan significantly reduce cost and improve occupant performance

10

Motivating Scenario

Lo

uve

rs

All lights0-10 levels

10

5

5

0

05

0

0

0

Operator

Controller

06

AndyBob

Louvers/ Blinds

Feedback

Coordinate lighting to make everybody happy

Strategy to exploit natural lighting

Predictive light control

Challenges

Knowing the current state Light levels and occupants location

Capturing occupant and operator preferences & happiness

Optimization of tradeoff Occupants happier OR save more

energy

Desk

Knowing the current state of the world Indoor Environment

Light levels Pervasive sensor

network Wireless or Wired

Tracking occupants Smart tags RFID tags Camera tracking

Utility Theory: Framework to compare choices based on preferences

Personal preference Attributes: Coolness, Horse Power, Mileage,

COST…. Representation complexity of utility function

Preferences & Happiness

Lamborghini, Second Hand 2003 model, $50,000

Toyota Corolla, New 2006 model,$30,000

Occupant preference:Comfort Light level

Utility Function Task dependent

Light levels Depends on lamp setting Use sensing to learn effect of

lamps on person i – Control lamp settings a to max.

occupant preferences, a=(a1,…,an), aj – level of lamp j

i

Building Operations: Occupants

argmax

1

!n

ii

Try tomakeeverybody happy

aa

iBob

Andy

Building Operations: Operator Operator preference: Cost

Operating cost Maintenance Cost

Decreases monotonically with the energy expended

Utility function

aj , jth lamp

1

( )j j

n

j

a

100 200 300

Operating Cost

0.00

0.20

0.40

0.60

0.80

1.00

No

rma

lize

d u

tili

ty

j

Cheaper the better

Utility Maximization : Tradeoff Maximize system utility: Make occupants and operator

happy!

a = (a1,…….an)

Scalarization technique

is the tradeoff parameter

1 1

( )) (,( )n n

j jj

ii

U F a

a a

OccupantsOperator

1

( ) (* )n

ii

U

a a a

* argmax ( )U

aa a

a6

a5

a4

a4

a2

a1

Utility Maximization: Complexity

Evaluating U(a) for combinations of all lamp setting for just 6 lamps the total number is 106

Evaluating argmax U(a) is also over that big space Exponential in number of lamps!

* argmax ( )Ua

a a 1

( ) (* )n

ii

U

a a a

10 levels

10 levels

10 levels

10 levels

10 levels

10 levels

a6

a5

a4

a4

a2

a1

Reducing Complexity

Exploit problem structure: Zoning

11

*

1

( ),...,g (ar )k jii

m

ji

n

ji

a amax a

a

a

1 2 3 2 3 4

3 4

1 2

3 4

6

4 5

*

15 6

, , , ,

, ,

( ) ( )

( ) ( )argmax *

,(

,)i

i

a a a a a a

a a a a aa

a

a

a

Distributed action selection approach (Guestrin ’03) Exact solution to the coordination problem

Open-loop controller: Coordinated Lighting

Control law using Occupant utility and Coordination Graph

approacha

Test Bed Control Schematics 10 table lamps 12 motes aka occupants Size: 146 * 30 in., 7 zones

146 in.

1234567

Coordinated Lighting: Results

• Comparison to greedy approach

•Each occupant comes and actuates the light

•Caveat: cannot reduce the level of a already ON light

• At = 0.4, reduction in comfort = 7% but reduction in energy cost = 30%

Greedy Heuristic

Energy Cost

Measured utility

30%

0.4

Coordinated Illumination

Coordinated Lighting

Performs significantly better than typical greedy approach

Solves the complex optimization using the structure of the problem (zoning)

Coordinated Lighting

Natural Lighting

Predictive light control

Closed-loop controller: Daylight

Harvesting

Control law

aOnline sensing using sensor network

Current Light Level

Sense natural light levels Actuate lamps to compensate for extra light

Variability using the real sunlight data from Pittsburgh

Day Light Harvesting: Sun Simulation Simulated sun using

overhead lamps

Real sun intensitiesMeasured intensities at center

Sun Lamps

Daylight Harvesting: Utility Redefined Represents the sunlight

intensity at time t and point in space x,

New utility definition

Maximization problem

:T X R

1 1, ( ,( , , ) ( , ) ( ))i

n m

ji j

i jit tU x a

xa x a

Sun Lamps

* argmax ( , , )( , )t U ta

ax xa

Running the Simulations

Day Light Harvesting: Evaluation

Gamma values (0.01, 0.4), same setup

Gamma = 0.01, 15% of energy savings Gamma = 0.4, 55% of energy savings Loss in occupant utility due to too much light

Shading, Louvers

Measured Utility

Energy Cost

Measured Utility

Energy Cost

Day light harvesting

Builds on the coordinated lighting approach Saves significant (~50%)energy cost during

sun time Long term sensor

deployment: battery life Sensor scheduling

Save battery life

Coordinated Lighting

Natural Lighting

Predictive light control

Spatial correlation in sunlight distribution Temporal correlation in sunlight intensity Use only a small number of sensor Estimate the light levels at other times and

locations

Active Sensing aka Sensor Scheduling

Desk?

???

When and Where to sense!

Active Sensing: Scheduling Use sunlight observation (samples) to estimate the

current sunlight intensity distribution

1 1 1,1 ,( , ) ,..., ( )|) ( ,,l r l rP

The utility formulation then changes to conditional expected utility

Choose a set of observations that yields best maximum expected utility values

,1 1

( | )( , , | ) ,, ( ) )( ) (i

n m

ji j

jiEU t xPO Ot a

xa x o ao

Sunlight Distribution Conditioned on observation

Active Sensing Calculating a set of observation that maximize

More observation: better accuracy but high battery cost

Constraint the observations to a budget Allocate strategically to max. EU

(1: ) (1: )( ) ( )( max ( , , | ))t t

t T

J O P EU tO O

a

o

a xo o

* argmax ( )O

O J O

Active Sensing: Single Sensor

Optimal solution for single sensor budget allocation in polynomial time (Krause & Guestrin ’05)

Xi where i is the time step, (5 times steps, Budget 2) For just 2 sensors: complexity is NP-hard

* argmax ( )O

O J O

X1 X2 X3 X4 X5X1 X2 X3 X4 X5

X1 X2 X3 X4 X5

Y1 Y2 Y3 Y4 Y5

X1 X2 X3 X4 X5

Y1 Y2 Y3 Y4 Y5

X

1

X

2

X

3

X

4

X

5

Y1 Y2 Y3 Y4 Y5

Heuristic for solving multiple sensor Coordinate ascent scheme (uses optimal solution for

single sensor)

Guaranteed to improve score on each iteration, guaranteed to not perform worse than independent scheduling

Can be used for more than 2 sensors

Active Sensing: Heuristic

X1 X2 X3 X4 X5

Y1 Y2 Y3 Y4 Y5

Optimize sensor 1X1 X2 X3 X4 X5

Y1 Y2 Y3 Y4 Y5

X1 X2 X3 X4 X5

Y1 Y2 Y3 Y4 Y5

Optimize sensor 2

Active Sensing: Results

3 sensors, upto 10 readings per sensor in a day Energy saving are close approximation compared to

sensing continuously Even a small number of readings (3) provides results

as good as continuous

Energy Cost

Measured Utility

No sensing

1 obs./sensor 10 obs./sensor

Active Sensing for Daylight Harvesting Exploit temporal correlation in sunlight

intensity to schedule sensing Significant reduction in sensing requirement

for comparable performance Can be integrated in the coordinated lighting

formulation

Coordinated Lighting

Natural Lighting

Predictive light control

Predictive light control

Probabilistic model on mobility People move independent of each other

Modeled using a random walk Stay in same position Move left, move right

Zone 1Zone 2Zone 2

Integrating mobility

Assuming full observability

Computing expected utility

( 1) 1( . | , )t t ti i iP x x x

1

1,

1

1

( ,( , , , ) ( ( ),( )) ( )ii

n mt t

ji j

ti iix x jx tP xEU t Ex a

a x x a

Probability of motion

Predictive Lighting: Results

20 step random walk Total utility increase of about 25% Low values of trade-off parameter, system prefers

occupants comforts

Occupant Utility

Energy CostTotal Utility

No

rmal

ized

Sca

le

Occupant Utility

Energy Cost

Using prediction

Without prediction

ConclusionCoordinated lighting strategy•Maximizes happiness using utility maximization •Solves complex coordination problem

Day light harvesting•Exploits natural light sources using sensors •50-70% reduction in energy consumption

Active sensing •Sensor scheduling using sunlight distribution• Substantial increase in network life time

Predictive Light control•Captures occupant mobility•Higher total utility for the system