1

Estimation of Occupancy

Distribution in Buildings

ME236: Control & Optimization of Distributed Systems

Professor: Alexandre Bayen

University of California, Berkeley

Spring 2009

Mehdi Maasoumy

Estimation of Occupancy Distribution in Buildings ME 236 2

Why Energy (consumption) Matters?!

7 gigatons of carbon emission per year (While the sink is only 3 gigatons per year!)

Uncertainty in energy supplies

Environmental concerns

Total US energy consumption

Estimation of Occupancy Distribution in Buildings ME 236 3

Global Energy & Carbon Balance

Estimation of Occupancy Distribution in Buildings ME 236 4

Why buildings matter?

•40% of global energy use

•21% of greenhouse gas emissions

•One billion metric tons of greenhouse gasses In USA /yr

Source: Buildings Energy Data Book 2007

Estimation of Occupancy Distribution in Buildings ME 236 5

DOE and State of California’s Goal

Reduction of 90% of energy used by

commercial buildings in 20 years from now…

Cool… But how…?

Estimation of Occupancy Distribution in Buildings ME 236 6

Possible ways…

Building more efficient construction

components (lighting, windows, isolation…)

Sounds good! but not enough…

Estimation of Occupancy Distribution in Buildings ME 236 7

Possible ways…

Integration of systems for better operations

Sounds Great!

But, could you give me an example?

Estimation of Occupancy Distribution in Buildings ME 236 8

For Example…

Statistically, 1/3 of buildings are constantly

unoccupied, but fresh air supplies are provided

almost permanently to most buildings, and air

conditioning systems do not take this into account…

How many people occupy a building and where they are located

Key component of building

energy management

Estimation of Occupancy Distribution in Buildings ME 236 9

Dynamic Occupancy

Devising Optimal control schemes for using

the knowledge of “Dynamic Occupancy”

The fundamental challenge in assessing

dynamic occupancy of buildings: To estimate it with an infrastructure at a reasonable cost.

Estimation of Occupancy Distribution in Buildings ME 236 10

How to monitor?

Network of cameras (not practical in most buildings)

iPods / Cellular phones

Badges with RFID tags

Laptops

Internet tablets

Estimation of Occupancy Distribution in Buildings ME 236 11

Two Approaches

Sensor-Utility-Network (SUN)

Bayesian Modeling

Estimation of Occupancy Distribution in Buildings ME 236 12

Sensor-Utility-Network (SUN)

A method for estimating occupancy

distribution in buildings

Based on: Inputs from a variety of sensor

measurements

Estimates through the solution of a receding horizon optimization problem

Estimation of Occupancy Distribution in Buildings ME 236 13

Sensor-Utility-Network (SUN)

Objectives and Contributions of SUN:

Introduce a framework and algorithms to analyze

Sources of information:

Sensor data

Peoples preferences and patterns of behavior

Historical data (from same or similar buildings)

Applications:

Demand-driven ventilation

Lighting controls leading to energy savings

Improve security monitoring

Accelerate safe evacuation

Estimation of Occupancy Distribution in Buildings ME 236 14

Technical Challenges

Variety of data:

Temperature sensors

sensors

Smoke detectors

CCTV video cameras

Water flow sensors

RFID sensors

Phone usage

Calendar or scheduling info.

2CO

Estimation of Occupancy Distribution in Buildings ME 236 15

Technical Challenges

Goal of the estimation procedure

Cost-benefit trade-offs (involved in the selection of

sensors and their placement)

Complement sensor measurements

Adapt models and algorithms to a changing

environment

Use all these potential information sources and address the following issues:

Estimation of Occupancy Distribution in Buildings ME 236 16

Estimator architecture

)(

)()(

tr

txt

Vector of occupancy

in each zone

l

jl

j

jiii rtrtxtx )()()1(

•Mass-balance constraints on the states:

Vector of number of people moving from one zone to another

The state process is not observable

(based on observations of the flow (r) alone.)

Indeed, observability requires measurement of each

)(txi

Estimation of Occupancy Distribution in Buildings ME 236 17

Estimator architecture

In Bayesian settings:

Y: sequence of observations

We need to obtain an estimation of an unobserved

quantity on the basis of empirical data.

)1())(()1( tWtft t

)1())(()( tVthtY t

MAP estimator

Estimation of Occupancy Distribution in Buildings ME 236 18

MAP (Maximum A Posteriori) estimation

If…

The noise and the initial condition are jointly Gaussian and mutually independent and the noise is i.i.d.:

Where:

are the covariance matrices for

is the covariance of the initial condition, and is its mean

)))(()1())(()((

)),...,|,...,(log(

21

0

22

00

00

111

0 dtyt

tftthtyK

yyp

t

T

t

t

TT

dtyt,

tt VW ,

0 0

QP!

Estimation of Occupancy Distribution in Buildings ME 236 19

are linear

No hard constraints on

tt fh ,

)(t

Map Estimator Kalman Filter

In this special

case

Estimation of Occupancy Distribution in Buildings ME 236 20

Utility and Penalty Functions

Penalty function based on

sensor information

Penalty function based on

temporal dynamics

))()(())(),(( tCtyPtytP yy

))()1(())(),1(( tArtrPttP rd

)( irU

0

ir0

ix

)( ixU

Utility function for a room with reservation for people 0

ix Utility function for occupancy flow

Estimation of Occupancy Distribution in Buildings ME 236 21

Experimental Results

Zone level occupancy estimates

obtained from conventional people

count estimator

Zone level occupancy estimates

obtained from SUN and the zonal

occupancy bounds used during SUN

estimation

Estimation of Occupancy Distribution in Buildings ME 236 22

Conclusion

SUN method approach reduced the

average occupancy estimation errors

from 70% obtained using conventional

estimator to 11%

Estimation of Occupancy Distribution in Buildings ME 236 23

Bayesian Modeling

Each sensor responds in its

own way to the presence or

absence of occupants

)(

),()|(

BP

BAPBAP

A C D

EDCBAPEBP ),,,,(),(

Estimation of Occupancy Distribution in Buildings ME 236 24

Belief Network

Combining the effect of occupancy on observable variables

Estimation of Occupancy Distribution in Buildings ME 236 25

Experiment

Network of multiple independent and redundant sensors:

3 PIR occupancy detectors

Handset sensor (off-hook detector)

handset

N: number of people

PIR1

PIR2 PIR3

N

Independent measure of occupancy from each of these detectors

Estimation of Occupancy Distribution in Buildings ME 236 26

Results

Detail of room 203D occupancy profile from morning of February 3rd 2005.

Estimation of Occupancy Distribution in Buildings ME 236 27

Future works

Evaluation of performance of SUN estimation for predictive use, adaptive techniques, associated utility function, sensitivity of the impact of sensor placement and sensor types on occupancy estimation performance.

Investigation of other available approaches to occupancy data analysis (regression function, logical rules for computing inferences,…).

To make SUN estimator scalable, decentralized algorithms should be developed.

Estimation of Occupancy Distribution in Buildings ME 236 28

ATTENTION!

This project is open ended by nature!

It is only a preliminary approach to a project which will

grow up next months (year).

Collaboration between LBL and UC Berkeley

Notice

before evaluating

Estimation of Occupancy Distribution in Buildings ME 236 29

Thanks for your attention