An Integrated Approach to Occupancy Modeling and Estimation in Commercial Buildings

Transcription

1 An Integrated Approach to Occupancy Modeling and Estimation in Commercial Buildings Chenda Liao and Prabir Barooah Distributed Control System Lab Mechanical and Aerospace Engineering University of Florida, Gainesville, FL American Control Conference July 1 st, 2010 Baltimore, Maryland, USA

2 Introduction 2006 Commercial Energy End-Use Expenditures ($2006 Billion) Cooking 2% Other 13% Adjust to SEDS 9% Lighting 23% Computers 4% Space Heating 13% Refrigeration 5% Ventilation 6% Space Cooling 11% Electronics 7% Water Heating 7% 2009 buildings energy databook

3 Why not use a lot of sensors? Occupancy sensor Passive Infrared Sensor (PIR) Optical tripwires Video camera with peoplecounting software CO2 sensor Problems: Expensive to deploy and maintain for large building. Sensors contain large uncertainty. Image courtesy of Image courtesy of Hutchins et. al Solution: Model+Sensor=Estimation 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

4 Model+Sensor Solution: Model+Sensor=Estimation Covariance graphical model Floor Plan Representation Limited number of sensors Graph Representation Covariance Graphical Model Varying with time

5 o Input: Noisy sensor measurement: Covariance graphical model: Occupancy Estimation o Estimation method: Linear Minimum Variance estimator. o Output: where and The main focus

6 Agent-based Model Flows: Evacuation, traffic, crowd flow, etc. Markets: Stock market, strategic simulation, etc. Organizations: Operational risk, organizational design, etc. Image courtesy of : Page model: J. Page, et al A generalized stochastic model for the simulation of occupant presence, 2007 States: inside and outside ( One occupant in one room) Long absence

7 Model Construction Mixed Agent-based Rules (MARM)

8 Preliminary model validation Preliminary: One occupant in one room Data is provided by Dr. Robinson (Co-author of A generalized stochastic model for the simulation of occupant presence ) First arrival time Last departure time Total duration of daily presence Length of continuous presence Number of daily change Probability of presence

9 Covariance graph model identification Goal: estimate the sparsest possible graph structure that can still explain the first and second order statistics of the data. 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 Model selection Parameter estimation

10 Performance Evaluation Building information: MAE-B third floor, 19 nodes, 54 people work there Obtainment of Informal survey nominal behavior: True value Time series from agent-based model plus random number of people Sensor placement 7 sensors, which can directly measure occupancy Sensor Model

11 Performance Evaluation

12 Summary and Future Work Summary Agent-based model construction and preliminary validation. Covariance graphical models identification. Model+Sensor=Estimation Future work Agent-based model validation for the whole floor. Refine the estimation method and design on-line updating of covariance model. Perform real time estimation.

13 Thank you

14 Backup

15 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. If, based on and, we generate the new random variable. In this fashion, we generate the time series of room occupancy, Page. et. al. 2008

16 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.

17 Algorithm Flow Chart

18 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

19 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. Damping parameter o Access rule Each agent has associated access profile specified which rooms he/she has access to.

20 Multiple rules

21 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 level determined by a design parameter ) at an overall confidence

22 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.

23 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

24 Identification Result