Chenda Liao and Prabir Barooah

An Integrated Approach to Occupancy Modeling and Estimation in Commercial Buildings

Distributed Control System Lab

Mechanical and Aerospace Engineering

University of Florida, Gainesville, FL

American Control Conference July 1st, 2010

Baltimore, Maryland, USA

Introduction

Lighting23%

Space Heating13%

Space Cooling11%

Water Heating7%

Electronics7%

Ventilation6%

Refrigeration5%

Computers4%

Cooking2%

Other13%

Adjust to SEDS9%

2006 Commercial Energy End-Use Expenditures ($2006 Billion)

2009 buildings energy databook

Why not use a lot of sensors?

• Occupancy sensor

Passive Infrared Sensor (PIR)

Optical tripwires

Video camera with people-counting software

CO2 sensor

•Problems:

Expensive to deploy and maintain for large building.

Sensors contain large uncertainty.Image courtesy of Hutchins et. al. 2007

Solution: Model+Sensor=Estimation

Image courtesy of www.trafsys.com

Sean Meyn, et al, A Sensor-Utility-Network Method for Estimation of Occupancy Distribution in Buildings, CDC, 2009: MAP Estimator Utility function(prior information) + measurement from multiple sensors

Model+Sensor

Floor Plan Representation Graph Representation

Varying with time

Covariance Graphical Model

Solution: Model+Sensor=Estimation

Covariance graphical model Limited number of sensors

Occupancy Estimation

o Input:

Noisy sensor measurement:

Covariance graphical model:

o Estimation method: Linear Minimum Variance estimator .

o Output:

where and

The main focus

Agent-based Model

•Flows:

Evacuation, traffic, crowd flow, etc.

•Markets:

Stock market, strategic simulation, etc.

•Organizations:

Operational risk, organizational design, etc.Image courtesy of : www.tunnels.mottmac.com/

• Page model:J. Page, et al A generalized stochastic model for the simulation of occupant presence, 2007

( One occupant in one room)

States: inside and outside

Long absence

Model Construction

•Mixed Agent-based Rules (MARM)

Preliminary model validation

Preliminary: One occupant in one roomData is provided by Dr. Robinson (Co-author of A generalized stochastic model for the simulation of occupant presence )

First arrival timeLast departure timeTotal duration of daily presenceLength of continuous presenceNumber of daily changeProbability of presence

Covariance graph model identification

•Goal: estimate the sparsest possible graph structure that can still explain the first and second order statistics of the data.

Model selection

Parameter estimation

Individual level Room level

•Estimation of covariance matrix Drton et.al, Model selection for Gaussian concentration graphs, Biometrika, 2004 Chaudhuri et.al, Estimation of a covariance matrix with zeros, Biometrika, 2007

Performance Evaluation

Building information: MAE-B third floor, 19 nodes , 54 people work there

Obtainment of nominal behavior:

Informal survey

“True value” Time series from agent-based model plus random number of people

Sensor placement 7 sensors, which can directly measure occupancy

Sensor Model

Performance Evaluation

Summary and Future Work

•SummaryAgent-based model construction and preliminary validation.

Covariance graphical models identification.

Model+Sensor=Estimation

•Future workAgent-based model validation for the whole floor.

Refine the estimation method and design on-line updating of covariance model.

Perform real time estimation.

Thank you

Backup

If , based on and ,we generate the new random variable .In this fashion, we generate the time series of room occupancy ,

Page model

Page model:

o Focus on individual occupancy behavior by developing a generalized stochastic model for the simulation of occupant presence with derived probability distributions based on inhomogeneous Markov chains.

Page. et. al. 2008

Page model

•Benefit of Markov chain: mimic the real life ( sensor data) and smooth the series of room occupancy (generated data).

•The algorithm for the generation of time series of transition probability is just designed for single-occupied offices case.(1 person and 1 room).

• It will be cumbersome to implement such algorithm for one person and multiple rooms case, to say nothing of multiple persons and multiple rooms case. (too many states).

• Intuitively,

Goal:Make a model with ability to deal with the case of multiple persons and rooms, but keep the similar good property in Markov chain.

Algorithm Flow Chart

Behavior specification

•Behavior specification for each agent:

o Nominal occupancy profile:

Where

• Two transition probability parameters:

o Damping rule parameter

o Acceleration rule parameter

• Long absence profile:

o Probability of initiating a long absence

o Distribution of duration of long absence

Multiple rules

•Multiple rules for each agents:

o Damping and acceleration rules

To redesign the state chosen from nominal occupancy profiles in order to mimic Markov property.

o Access rule

Each agent has associated access profile specified which rooms he/she has access to.

Damping parameter

Multiple rules

Model Selection

•Model selection

o Choose the structure of the graph G. (or equivalently, the sparsity pattern of )

①Conduct N Monte-Carlo experiments using agent-based model, for every time k, we compute:

Sample mean:

Sample covariance:

②Hypotheses on all edges (all entries of ) at an overall confidence level determined by a design parameter

Parameter estimation

•Parameter estimation

o Choose the values of those entries of that have been decided to be non-zero in the model selection step.

----An iterative conditional fitting algorithm based on maximum likelihood estimation is used for estimating the values of the non-zero entries of .

Occupancy Estimation

•Linear Minimum Variance estimator:

Consider two jointly distributed random vectors X and Y whose means

and covariance are assumed known, we want to find the linear estimator

of X in terms of Y that is best in the sense that

minimizes:

Solution:

Where and

Identification Result