mm 40 60 80 100 120 Enabling Building Energy Auditing Using Adapted Occupancy Models 40 Ankur U. Kamthe , Varick L. Erickson, Miguel ´ A. Carreira-Perpi˜ n´ an and Alberto E. Cerpa { akamthe,verickson,mcarreira-perpinan,acerpa } @ucmerced.edu 60 BuildSys 2011 80
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary HVAC Systems mm 40 60 80 100 120 Heating, Ventilation and Air-Conditioning (HVAC) systems account for majority ( ≈ 50%) of building energy consumption (2008) ∗ . ◮ Assumption: Condition based on maximum room occupancy 40 ◮ Rooms are often unoccupied or partially occupied ◮ Leads to inefficient environmental conditioning ◮ Optimize energy usage using systems that actuate using occupancy 60 models Alternatively, ensure that buildings adhere to the strictest energy efficiency standards. 80 ∗ Source: Building Energy Data Book (http://buildingsdatabook.eren.doe.gov/docs/htm/1.1.4.htm) 2 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary So where are all the green buildings? mm 40 60 80 100 120 40 60 Figure: South Hall - UC Berkeley (built 1873) ◮ Majority of existing buildings are older than 20 years. ◮ Do not meet current energy efficiency construction standards. 80 ◮ Impact long-term energy consumption. ◮ Energy audits: energy savings through retrofitting. 3 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Building Energy Auditing mm 40 60 80 100 120 ◮ Involves inspection and analysis of the energy consumption from utility bills. 40 ◮ Deploy sensors on-site to measure and verify energy use. ◮ Onsite work takes 1-2 days. ◮ Data is input to DOE-2, EnergyPlus, etc. to evaluate and 60 recommend energy retrofits. Further, maximize energy savings by including occupancy model information within energy audits. 80 4 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Occupancy model caveats mm 40 60 80 100 120 40 ◮ Large training datasets (weeks, months). ◮ Models are specific to the building. ◮ Therefore, for all other buildings, again collect large training dataset. 60 80 5 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Problem Statement mm 40 60 80 100 120 40 How can we maximize energy savings by using occupancy models in building energy audits when collecting only 1-2 days of occupancy traces? 60 80 6 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Occupancy Modeling mm 40 60 80 100 120 ◮ Modern buildings have submetering systems, electronic locking 40 systems, etc. ◮ Use of wireless sensor networks for other buildings: ◮ PIR sensors - binary indicators. ◮ Camera sensors - people counters. 60 ◮ Data collection goal: collect data for 1-2 days. 80 7 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Proposed Approach mm 40 60 80 100 120 40 Use a reference building occupancy model that has been trained with extensive data and adapt it to the new building given a far smaller occupancy data trace than would be necessary to train a new model from scratch. 60 80 8 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Reference Model mm 40 60 80 100 120 ◮ Mixture of multivariate Gaussians ( M ) components in place of a 40 single multivariate Gaussian for every hour. ◮ Parameters: means ( µ ) and covariance matrix (Σ) for each hour. ◮ ( D + 1) M + D 2 − 1 parameters for every hour ( D = # rooms ). ◮ Use Expectation-Maximization (EM) algorithm for parameter 60 estimation ( Retraining ). 80 9 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Reference and Adaptation Model Datasets mm 40 60 80 100 120 1 Hallway 40 1 2 1 Student Lab 60 Office Conference Room 80 (a) (b) Reference Adaptation 10 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Reference and Adaptation Model Datasets mm 40 60 80 100 120 Hall 1 Hall 2 Office 1 Lab 1 Num. of Occupants 3 4 10 3 10 2 2 5 1 5 1 0 0 0 0 0 6 40 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 Hour of Day Hour of Day Hour of Day Hour of Day (a) Reference Dataset Room Occupancy Hall Conference Office Lab Num. of Occupants 3 4 10 3 10 2 2 5 5 1 1 0 0 0 0 60 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 Hour of Day Hour of Day Hour of Day Hour of Day (b) Adaptation Dataset Room Occupancy Figure: Room occupancy averaged over the length of dataset (5-days) for every hour for the reference model (a) and adaptation (and retrained) model (b), 80 respectively. 11 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Adapted Model mm 40 60 80 100 120 40 ◮ Assumptions: Well-trained reference model and occupancy data for target (audited) building. ◮ Adaptation Approach: Tie the means of the reference model using a non-linear transformation . 60 80 12 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Adaptation Illustration with 2 Rooms mm 40 60 80 100 120 5 60 4 40 3 2 20 40 1 0 0 8 10 12 4 6 8 10 12 Ref Data Histogram Adapt Data Histogram 60 9 10 11 Comp 1 µ 1 = 10 80 4 5 6 Comp 2 µ 2 = 5 13 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Adaptation Illustration with 2 Rooms mm 40 60 80 100 120 60 5 Om µ d = � 4 1+ e − ( a µ d / Om + b ) 40 3 a = −3.1183 b = 3.6972 2 20 11 40 1 12 0 9 0 4 6 8 10 12 8 10 12 12 Adapt. Parms. Ref Data Histogram Adapt Data Histogram 60 9 10 11 8 9 10 Comp 1 µ 1 = 10 Comp 1 � µ 1 = 9 5 10 12 12 Ref. Parms. 80 Sigmoid Transformation 4 5 6 10 11 12 O m = 12 Comp 2 µ 2 = 5 Comp 2 � µ 2 = 11 14 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Adapted vs Retrained Model mm 40 60 80 100 120 ◮ The objective function is the log-likelihood of the adaptation data given the constrained MVGM with 3 M − 1 free parameters: � � = � N n =1 log � M π m , a m , b m } M L { � m =1 � π m p ( x n ; a m , b m ) 40 m =1 ◮ Adaptation: 3 M − 1 adaptation parameters. ◮ Retraining objective function 60 � � = � N n =1 log � M π m , µ hm , Σ h } M L { � m =1 � π m p ( x n ; µ hm , Σ h ) m =1 80 ◮ Retraining: ( D + 1) M + D 2 − 1 parameters for every hour. 15 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Modeling Performance mm 40 60 80 100 120 8 x 10 Loglikelihood (on test set) 0 −1 40 −2 Adaptation −3 60 Retraining −4 Optimal 1 2 3 4 Adaptation Dataset (in days) 80 Figure: Log-likelihood of the different models as a function of the days in the adaptation dataset. 16 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Estimated occupancy models mm 40 60 80 100 120 Office Num. of Occupants 40 4DayRetrain 1DayRetrain 10 1DayAdapt 60 5 0 0 6 12 18 24 80 Hour of Day 17 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Estimated occupancy models mm 40 60 80 100 120 Conference Room 5 40 4DayRetrain 4 1DayRetrain 1DayAdapt 3 2 60 1 0 0 6 12 18 24 80 Hour of Day 18 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Building Energy Simulation Results mm 40 60 80 100 120 ◮ Construct occupancy schedule using models 4DayRetrain (MVGM-R4), 1DayRetrain (MVGM-R1) and 1DayAdapt (MVGM-A1). 40 ◮ EnergyPlus model of the building floorplan (total 32,000 sq.ft.) from which we have adaptation data for a Hall, Office, Lab and Conference room (approx. 12,000 sq.ft.) ◮ Compare to: 60 ◮ Baseline: maximum room occupancy between 7a.m.-10p.m. and is off at other times. ◮ OBSERVE: Markov chain approach to model the temporal changes in occupancy of a building. Close to optimal conditioning. 80 19 / 23
Introduction Related Work Adapting Occupancy Models Performance Evaluation Discussion Summary Energy Savings mm 40 60 80 100 120 0.25 OBSERVE 4DayRetrain 1DayAdapt 1DayRetrain Energy Savings (%) 0.2 40 0.15 0.1 0.05 60 0 Apr Aug Dec Month of Year 1DayAdapt (10.9%) < OBSERVE (11.2%) < 1DayAdapt (11.4%) < 1DayRetrain (12.9%) 80 20 / 23
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