OBSERVE: Occupancy-Based System for EfficientReduction of HVAC Energy

Varick L. Erickson, Miguel Á. Carreira-Perpiñán and Alberto E.CerpaElectrical Engineering and Computer Science

University of California - Merced{verickson,mcarreira-perpinan,acerpa}@ucmerced.edu

ABSTRACT

Heating, cooling and ventilation accounts for 35% energyusage in the United States. Currently, most modern build-ings still condition rooms assuming maximum occupancyrather than actual usage. As a result, rooms are often over-conditioned needlessly. Thus, in order to achieve efficientconditioning, we require knowledge of occupancy. This pa-per shows how real time occupancy data from a wireless sen-sor network can be used to create occupancy models whichin turn can be integrated into building conditioning sys-tem for usage based demand control conditioning strategies.Using strategies based on sensor network occupancy modelpredictions, we show that it is possible to achieve 42% an-nual energy savings while still maintaining American Societyof Heating, Refrigerating and Air-Conditioning (ASHRAE)comfort standards.

Categories and Subject Descriptors

I.6.5 [Simulation and Modeling]: Model Development;J.7 [Computers In Other Systems]: Command & control

General Terms

Algorithms, Machine Learning, Measurement

Keywords

Occupancy, HVAC, Ventilation, Energy savings

1. INTRODUCTIONIn 2006, approximately 35% of the energy in the United

States was used for heating, ventilation, and air-conditioning(HVAC) systems[2]. Studies suggest that 15% to 25% ofHVAC energy can be saved by setting ventilation rates basedon maximum occupancy [8]. Currently, the majority ofHVAC systems condition rooms assuming maximum occu-pancy during normal working hours and are turned off atnight. This leads to inefficiency as rooms are often condi-tioned to levels that are not appropriate for the number of

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occupants actually occupying the areas. An HVAC couldwaste energy supplying ventilation enough for 30 peoplewhen only 10 actually occupy a room.

To increase the efficiency of HVAC systems, a system fordetecting occupancy is needed to condition rooms appro-priate to usage. Though there are several methods thatare commonly used for detecting occupancy within mod-ern buildings, these methods present limitations. Passiveinfrared (PIR) sensors, commonly used for controlling light-ing, are a simple way of detecting if a room is occupied ornot, but do not give information regarding how many peo-ple occupy the room. This information is necessary for CO2

ventilation. Using CO2 sensors directly for regulating CO2

is also unsuitable for conditioning strategies. CO2 buildupis slow, and by the time sensors detect high levels of CO2

that trigger ventilation, occupants of the room are likely toalready feel uncomfortable [13]. If not properly calibrated,these sensors can also be inaccurate [13]. Electrical loadshave also been used for occupancy estimation [6]. However,this method assumes each occupant contributes to the loadand requires accurate occupancy data for calibration.

For demand response HVAC control, occupancy detectionneeds to be accurate, reliable, and able to capture occu-pancy changes in real time. The Smart Camera OccupancyPosition Estimation System (SCOPES) [15] is a 16 nodesensor network of cameras that captures occupancy changesamong areas with approximately 80% accuracy in near realtime. With newer more powerful hardware it is likely theaccuracy will be even greater.

Though the ability to adjust an HVAC system based onreal time occupancy is an important step toward greaterefficiency, perhaps just as important is the ability to antic-ipate room usage based on current room usage. This needsto be addressed since conditioning a room is not instanta-neous and requires time for adjustments. For example, ifit is known that a large number of people are in a lobbyarea, we want the HVAC system to know an adjacent con-ference room will be used with high probability and beginconditioning the room beforehand.

The following are the key contributions of our work:

1. Our work on occupancy modeling uses inter-room rela-tionships over time to model occupancy. In addition,our models are developed using accurate real worlddata rather than occupancy walk-through surveys orother similar estimates of occupancy.

2. We demonstrate how models developed from sensornetwork data can be integrated with an HVAC controlstrategy to achieve significant energy savings.

3. We show that we can still satisfy ASHRAE condition-ing standards while saving significant energy. In cer-tain cases, we show that our predictive strategies meetuser demand better than typical baseline strategies.

4. We examine a PIR based WSN solution and show thatbinary measurement of occupancy is not always suffi-cient for HVAC control. Under some circumstances,PIR based HVAC control performs worse than cur-rent strategies; in order to achieve maximum energysavings within a building, accurate real time levels of

occupancy must be incorporated into HVAC strategies.

2. RELATEDWORKFew works on occupancy modeling have been published

that are relevant to demand control systems. Most acknowl-edge that a major obstacle for developing occupancy predic-tion models is lack of data. It is time consuming to gatherground truth occupancy data even for a small set of rooms.The simplest and most commonly used occupancy models

are sets of predefined static coefficients that are multipliedwith a maximum room occupancy. To estimate the occu-pancy of a room at 8am given that the room has a maximumoccupancy of 30, the coefficient for 8am is simply multipliedwith 30. Different sets of coefficients are used dependingif it is a weekday, weekend, or holiday and the purpose ofthe building. ASHRAE Standard 90.1 [5], BLAST [14], andDOE-2 [1] define several occupancy profiles for office build-ings daytypes. These models are commonly used for energysimulation tools such as eQuest [11] or EnergyPlus duringthe design phase of buildings and are also used to determinestatic conditioning strategies for buildings.Several methods of modeling occupancy do so using mul-

tiple sources of sensory input. In [6], the authors shows howoccupancy can be modeled using linear regression models.Data was collected for lighting and equipment loads andoccupancy is estimated using a walkthrough survey of thebuilding. Using the electrical loads as the indicator vari-ables and occupancy estimations as the response variable,linear regression models for weekdays, weekends, and holi-days were created. The main limitation of this model is thereliance on energy usage to determine if someone is present.In general, it will tend to underestimate occupancy levels.For example, occupants attending a large group meeting ina conference room may not be adding any additional loadscausing the model to report the room empty. Occupancyprediction for conditioning is also difficult as it would firstrequire the ability to predict electrical loads.The authors of [7], utilize a deployment of PIR and door

sensors to obtain a binary indication of occupancy. Theyuse a reactive strategy that adjusts the temperature basedon current occupancy and estimate potential savings usingEnergyPlus. This ignores the ramp up time required for aroom to be brought to temperature. The paper also doesnot account for the impact of ventilation on energy savings.In [17], the authors also utilize door and PIR sensors for

binary detection of occupancy for residential buildings andexamine reactive and predictive controls strategies. The pre-dictive strategy is achieved using a Hidden Markov Model.The model estimates the probability of home being in one ofthree states: unoccupied, occupied with an occupant awake,and occupied with all occupants asleep. The authors pro-vide results for real world deployment and EnergyPlus sim-

ulations. However, the results do not take into account ven-tilation, which can have a significant impact on energy ef-ficiency. Also, the modeling approach does not account fordifferent daily schedules. If a person stays out late on Fri-day on a semi-regular basis, the model would not be able topredictively condition for this scenario.

In [10], the authors propose using a belief network for oc-cupancy detection within buildings. The authors use mul-tiple sensory input to probabilistically infer occupancy. Byevaluating multiple sensory inputs, they determine the prob-ability that a particular area is occupied. In each office PIRand telephone on/off hook sensors were used to determine ifrooms are in occupied states. The authors model the occu-pied state of individual rooms with a Markov Chain, wherethe transition matrix probabilities are calculated by exam-ining the exponential distribution of the sojourn times ofthe observed states. While these strategies are more suit-able for predictive demand control strategies, there are lim-itations that diminish their usefulness. The strategies areaimed for modeling occupancy for individual offices and can-not be applied to spaces with larger occupancies. Thoughthe multiple telephone sensors could potentially be used tohelp determine a lower bound of occupancy, it is difficult todetermine when someone leaves since the presence of mul-tiple people essentially nullifies the usefulness of the PIRsensor. The approach does not consider room interdepen-dences and only focuses on occupancy detection.

In [12], an agent based model (ABM) and a multivariateGaussian model (MVGM) are examined. We will discussthese models in Section 4.

3. SENSING AND DATA COLLECTIONIn our work, we use the SCOPES system developed by

Kamthe et al. [15]. SCOPES is a system comprising 16 sen-sor nodes on the ceiling of the corridors a University build-ing. Nodes were deployed at transition boundaries withinthe hallways of the building. Each transition boundary iscomprised of a group of three nodes. Each node is a Cy-clops camera interfaced with a Moteiv Tmote Sky modulevia an intermediate adapter board. Both pieces of hard-ware run TinyOs as the operating system. The Cyclops isa low power camera with an on-board 4MHz ATmega128Lmicro-controller (MCU) and 512KB of external SRAM. Theexternal SRAM is divided into eight, 64KB memory banks toovercome the limitations of the addressable memory. Eachbank is capable of storing 80 64x64 pixel grayscale images.At every transition boundary location, three nodes sense thesame area where the nodes take turns capturing the sensedarea. Whenever a person crosses any one of these transitionpoints, the cameras capture and process the image data anddetermine the if a transition occurred and the direction.

Since the computational resources of the nodes are lim-ited, only lightweight image processing algorithms are used.Object detection is achieved by background subtraction, andthe background is updated continuously. When an object isdetected, the pixels of the image are classified as an ob-ject, shadow, or background depending on a pre-determinedthreshold. All pixels classified as objects are grouped us-ing a connected component algorithm creating a blob. Thecentroid and pixel count of the blob is determined and thedirection is inferred by consecutive images. Once a motehas processed all images in its bank, object information istransfered to a base station using multi-hop communication.

Office 1

Lab 2 Lab 3Lab 1

Office 3Hall 1 Hall 2 Hall 3

Office 2 Conference

Room

Office 1 Office 2

Office 3

Lab 1

Hall 1 Hall 2

Lab 2

Hall 3

Lab 3

Conf.

Rm

Figure 1: The left shows the ten areas data was col-lected for and the 18 boundaries (gray lines) definingthe areas. The right shows a graph representation.

We found SCOPES was able to detect 80% of all recordedtransitions within a 24 hour period of time.

3.1 Data CollectionFive days (Mon-Fri) of ground truth occupancy data were

gathered for ten areas using seven cameras covering 18 tran-sition boundaries. Figure 1 shows the building areas usedfor data collection. The cameras recorded images at 1.5 fps.Simple background subtraction methods were used to firsthelp identify images containing people and then processedby hand to verify direction and the boundaries being crossed.The hall occupancies are generally 0. When the hallway

is occupied, the occupancy is usually low and the occupantstypically exit within 4 to 8 seconds. There are a few in-stances that the hall occupancy deviate from this typicalpattern. When the data was collected, there was construc-tion work being done near Lab 1. On Monday and Thurs-day, about 7 people conducted building inspections in thehallway. There are also some instances where people heldlengthy conversations in the hallway sections.Figure 2 shows the occupancy data for ten areas. The

Office 1, Office 3, Lab 1, and Lab 3 show occupancy pattensmore typical of work routines though with some slight vari-ations. Office 1 is used by school administration. Workerscome in consistently at 8am, leave for lunch, come back fromlunch, and then leave at 5pm. Office 3, Lab 1, and Lab 3are used by professors and graduate students. Though thesame general daily pattern can be seen, we can also see someoccupants stay later (all night in some cases) and arrive andleave at odd hours. Office 2 and the Conference Room aresimilar since they both are mainly used for meetings. Office2 is a small office that is used for student counseling meet-ings and certain administrative work. Lab 2 is currently notbeing used by any department and serves as storage space.

4. PREVIOUS MODELSIn our previous work [12], we developed an agent based

model (ABM) and a multivariate Gaussian model (MVGM).The ABM simulates occupancy by modeling the behaviorof the individual. Agents are given paths, walking speed,and itineraries based on the occupancy changes seen in thetraining data. Occupancy is simulated by creating multipleagents that follow probabilistically generated instructions.Based on their simulated movement, room occupancies overthe course of the day can be estimated. While this is usefulfor estimating daily occupancy changes that are possible, itis difficult to use this model to predict future room usage.The second model evaluated is a multivariate Gaussian

fit of room occupancies. Hourly defined pdfs allow the cal-culation of the probability for a particular occupancy stateoccurring within a given hour. Let Oh = (r1 . . . rm) denote

all occupancies that occur per second during hour h where1 ≤ h ≤ 24 and ri is a vector of occupancies for room iwhere i = 1 . . .m. Let µi denote the average occupancy forroom ri. The means will change based on h.

We calculate a vector of means µh = (µ1, . . . , µm) andcovariance matrix Σh from Oh. Using µh and Σh, we definea probability density function (PDF) f :

f(Oh;µh,Σh) =1

(2π)n

2 |Σh|1

2

exp

{

1

2(Oh − µh)

′Σ−1

h(Oh − µh)

}

The PDF f can give a probability of an occupancy occur-ring for a specific hour dataset Oh. Using this function, wecan randomly draw occupancy vectors from the distribution.Given a starting occupancy, all the possible occupancies thatcan occur in the next timestep are examined. For each pos-sible occupancy the probability of the occupancy occurringusing the current PDF is calculated. Using these probabil-ities, the occupancy for the next timestep is chosen. Thedrawback of this method is that it causes a great deal ofpacing behavior. For example, if a person leaves the officeto enter a hallway at one timestep, there is a high prob-ability that the person will re-enter the office in the nexttimestep. This occurs since the distribution does not takeinto account the behavior observed in the previous timestep.This can cause predictions to favor parts of the distributionthat have high probabilities. This is particularly pronouncedfor rooms rarely occupied. In these cases the model rarelyallows room entry and vacates the room too quickly.

In order to create a prediction model suitable for HVACcontrol, we need a model that captures the temporal natureof the occupancy changes along with the inter-room correla-tions and occupant usage of the areas. The ABM does nottake into account inter-room correlations and would requirean additional modeling framework to be used for predictionsbased on time. The MVGM considers both the temporal andinter-room correlations. However, the distributions do nottake into account previous behavior and do not accuratelycapture the usage of seldom used rooms.

5. MARKOV CHAIN MODELWe model the temporal dynamics of the occupancy in a

building with a Markov Chain (MC). The state of the chainconsists of the occupancy at each room and transitions toa new state occurs with a probability that depends only onthe current state and the time. This allows us to predictthe occupancy distribution at t + ∆t given the occupancydistribution at time t by multiplying the ∆t times of thetransition matrix. This allows us to predict when roomswill be likely occupied and begin conditioning beforehand.

The MC state at each time is represented by a vectorwhere each component represents occupancy in a specific

Rm1

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{8,1, 4, 3}

{8,0, 4, 3}

{9,0, 4, 3}

{8,2, 3, 3}

...

...

...

...

Current

State

Room Occupancy Reachable States

Figure 3: The occupancy state representation.

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Figure 2: 5 days of ground truth occupancy data for eight areas.

room (Figure 3). Let R represent the set of n rooms to bemodeled. For each room in R, there is a maximum occu-pancy. We define S = {s0, ..., sm} to be the set of all roomoccupancy combinations that are possible given the maxi-mum room occupancies of R where m is the total number ofstates. Thus, S represents all observable occupancy statesthat can be represented by a given set of rooms R.One issue that needs to be addressed is the potentially

large state space. Assume we have n = 4 rooms, each witha maximum occupancy of 20 people. In this case, the MCwill contain m = 204 = 160, 000 states. As the numberof states increases, more data is required to calculate theprobabilities of the observable states. The transition ma-trix is sparse because many transitions are impossible dueto physical constraints of the building. However, the factstill remains that as more rooms are added, the numberof states to manage increases exponentially. To reduce thecomponent cost, we define the MC only on the states thatwere actually observed during training. Although we willnot be able to generate transitions to all observable states,practically our model will be realistic if using a large enoughtraining set. As the WSN gathers data over time, more ofthe state space will be represented. Additional strategies ofreducing the state space are addressed in Section 5.3.With the observable states of the MC defined, we next

define the transition probability matrix. Let pij representthe probability of moving from state j to i where Xt rep-resents an occupancy state at time t. For each state in Swe calculate pij = P (Xt+1 = i|Xt = j). Since the train-ing data collected is at the resolution of seconds, each timestep of the MC represents 1 second. The transition prob-abilities are estimated from the data normalized counts:pij = nij/

∑m

k=1nik where nij is the number of times a

transition from state i to state j in the set, and m is thetotal number of states.Since certain occupancy changes occur with greater prob-

ability depending on the time of day, the time of day mustbe incorporated into the model. Consider a person standing

in a hallway at 8:00 am. Since it is early in the day, it islikely that the person has arrived for work and will moveinto either a lab or office. However, if we consider the samescenario at 8:00 pm, it is more likely that the person will exitthe hallway in order to leave the building. To incorporatetime into the model, we define multiple transition matricesthat govern the state changes within different slots of time,thus defining an inhomogeneous MC.

While considering only observed (as opposed to observ-able) states and multiple transition matrices does allow usto model occupancy dynamics efficiently, a problem arises.Since we only consider states observed in the training data,partitioning the data in temporal sets will create discontinu-ities at the slot boundaries. Suppose we partition the datato create hourly transition matrices and are predicting oc-cupancy for hours h and h+1. After 3600 steps (one hour),we are in some state X, the hour changes from h to h + 1,and the model switches to the hourly transition matrix forh+1. It is possible the transition matrix for hour h+1 hasno probability for occupancy state X. This occurs if stateX never occurs in the training data for hour h + 1. Eventhough in reality the state X can occur in hour h + 1, ifX does not occur in hour h + 1 of the training data, thenwe cannot calculate the transition probabilities for X. Thiscannot be solved by introducing a small epsilon probabilityvalue of transitioning into another state because the nextstate chosen may also not be represented in the transitionmatrix. The MC becomes a random walk until it enters astate that was captured by the training data.

Similarly sink states can also occur if an occupancy stateonly occurs once in the training set. Suppose we have aset of occupancy states O that we use to train a transitionmatrix. Let X be the last occupancy state of the training setof O. If X is a unique state in O, then X never transitionsto any other state. If the occupancy state transitions to X,it will remain in that state until the model changes to atransition matrix that does contain a transition probability.We propose two different methods of solving the boundary

Rm1

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0

2 x-ings 1 x-ing Distance = 5

2 x-ings

State = {1,8, 4, 3} State = {0, 7, 4, 4}

Figure 4: Example of the closest distance metricwith state (Hall, Rm1, Rm2, Rm3) and distance 5.

discontinuities and avoiding sink states.

5.1 Closest Distance Markov ChainThe closest distance Markov Chain (CDMC) attempts to

solve the discontinuities the time slot boundaries. Supposewe finish simulating hour h and are currently in state X.Before switching to the transition matrix for h+ 1, we firstcheck to see if it contains a probability for X. If the proba-bility does not exist, then we examine all the states of tran-sition matrix h+ 1 that does have a probability and choosethe state closest to X.We define the distance between two states to be the num-

ber of transition to or from the outside world in order toaccount for the difference between the states. Let Mi repre-sent the minimum number of area transitions that is neededfor a single person to enter or exit out of a building fromroom i. Let X = (x0, ..., xn) and Y = (y0, ..., yn) representtwo occupancy states where xi and yi are the occupanciesof room i. We define distance dX,Y between X and Y to bedX,Y =

∑n

i=0Mi|xi − yi|. Figure 4 shows an example of this

distance metric. For this four room example, the distancebetween the states is 5. One transition boundary is crossedto leave Hall. Two transitions crossings are needed for theperson to leave Rm1. Two transition crossings are neededfor the person to enter Rm3. Rm1 and Rm2 require twotransitions each since a person must first enter the hallwayand then from the hallway exit to the outside world.Although this method eliminates sink states at the hourly

breaks, it does not guarantee that the sequence of statesis valid. It is possible for people to “teleport” in or out ofareas. Consider the floor plan in Figure 4. Suppose wehave the state (0, 0, 0, 0) (all the rooms are empty) and theclosest state is (0, 0, 2, 0) (two people are in the office). Thetransition from (0, 0, 0, 0) to (0, 0, 2, 0) is impossible sincethe two people must first pass through the hallway to enterthe office. Also, it is still possible to enter sink state inthe middle of a prediction. Applying the closest distancemetric again does little to help since it will likely choose theprevious state and then immediately re-enter the sink state.

5.2 Blended Markov ChainSink states only occur when the next transition matrix

does not contain a probability for the current state. In or-der to avoid sink states, we wish to ensure that a transitionprobability for the current state is always available. Ratherthan only consider states within the hourly transition ma-trix, we instead blend each matrix into a single state spacecontaining each state of each transition matrix.If the day is partitioned inK parts, then we haveK transi-

tion matrices T1 . . . TK each with m states. We now linearlycombine these K transition matrices to obtain K blendedtransition matrices T 1, . . . , TK , as follows. The blendedtransition matrix for slot t is

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1

1.5

2

TK

T1

T2

T3

T4

T5

T6

T7

T8

T47

T48

Slot Blending Coefficient Value

Hour

Ble

nd

ed

Co

eff

icie

nt

Va

lue

Figure 5: Relationship of blending coefficient,hourly time slot, and transition matrices.

T t =

K∑

s=1

βtsTs (1)

where the coefficients βt1, . . . , βtK are positive and sum toone (so that T t is a valid transition matrix). We want thesecoefficients to be approximately 1 for close slots and quicklydecrease to 0 for farther slots. We can achieve this by defin-ing the coefficients as

βts =α(ct − cs)

∑Ks′=1

α(ct − cs′ )(2)

where ct, cs are the centers of slots t, s, and with a “slot”function

α(x) = σ

(

2a

d

(

x+d

2

))

− σ

(

2a

d

(

x−d

2

))

x ∈ R (3)

where σ(x) = 1/(1 + e−x) is the sigmoid function, a > 0 isthe slope at the slot boundaries and d > 0 is the slot width.Since the sigmoid is monotonically increasing and satisfiesσ(−x) = 1− σ(x), it follows that α(x) is positive and sym-metric around its center. Figure 5 shows the slot functionsfor several slots. This way, each entry in the blended transi-tion matrix T s incorporates information from all slots, butheavily weighting slot s.

For our model, we choose K = 48, partitioning the datainto half hour transition matrices with slot widths of d = 3.We set a slope of a = 10 at the boundaries. We choosethe ck to be center of the current hour. Figure 5 showsthe blending coefficient for these particular parameters. Bydefining the parameters in such a manner, we create overlap-ping slot boundaries. This increases the number of preferredstates available to transition into, and decreases the chanceof choosing states completely outside the slot boundaries.The coefficient heavily favors transitions to states within agiven hour time slot and somewhat considers states in theadjacent half-hour slots. States outside this time frame arestill considered, but with greatly reduced probability. Theseparameters were chosen through trial and error. The cri-teria of the parameter selection was to maximize slot sizewhile minimizing the transitions into states completely out-side the preferred slot boundaries. While larger values of Kcould be used, smaller values of K are preferred since a largeK reduces the slot size and the number of observed statesfor each transition matrix. We also prefer to only draw fromstates that are close with respect to time.

5.3 Large Building ScalabilityThe number of observable states increases exponentially

with the number of rooms, but as described earlier we limitthe complexity of our model by using only states observedin the data sample. If this has length s over a given time pe-riod, then the number of observed states N satisfies N ≤ s,

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Figure 6: Comparison of training data with the models for several areas.

and practically N ≪ s because of repeated states. Besides,the N × N transition matrix T is typically sparse, becausephysical constrains make many transitions impossible andbecause not every possible transition is observed in the sam-ple anyway. Indeed, the number of nonzeros in T must besmaller than s, and again is practically much smaller than sbecause of repeated transitions. For our 5-day training set,we observed s = 432K samples resulting in N = 3809 and19 578 nonzero transitions (= 0.14% of all N2 transitions).It is conceivable that, with a very large number of rooms

and a very long sample, N or the number of nonzeros ofT are prohibitively large. Several simple strategies can beused to achieve a manageable model. Firstly, s should notbe larger than necessary to achieve a sufficiently accuratemodel. Another strategy for managing the number of statesis to utilize multiple MCmodels. Suppose we have a buildingwith 40 rooms that is divided into two wings each contain-ing 20 rooms. Rather than have a state representation thatincludes all 40 rooms, we can train one MC per wing. Thetrade off is that more MC models would be required to de-scribe all possible relationships of all the rooms. Lastly, it isoften possible to aggregate multiple rooms together thus re-ducing the number of states. This is because HVAC systemstypically condition groups of rooms called zones. We can ag-gregate room occupancies within a zone, and then create anMC model using zones rather than individual rooms.

6. MARKOV CHAIN PERFORMANCEIn this section we will examine how well BMC and CDMC

capture room occupancy. For each model, 100 simulationsof 24 hours were created. Five days (Mon-Fri) of groundtruth occupancy data was used to train the models. Anadditional three days (Mon, Wed, Fri) of ground truth datais used for testing. Figure 6 shows two days of trainingdata along with model simulated room occupancy schedules.Even without formal tests, the models seem be capturingthe dynamics of the ground truth room occupancies. Asexpected, the CDMC enters sink states and remains in thestate until the end of the hour. Qualitatively, BMC seemsto model occupancy variability better than CDMC.

6.1 Comparison MetricsWe use three metrics to evaluate the quantitative per-

formance of the models. We first examine how long roomoccupancies remain static to measure occupancy variability.We expect our occupancy models to remain at the differentlevels of occupancy for similar durations as compared withthe ground truth data. The next metric utilizes Jensen-Shannon divergence (JSD). This is a method that appliesKullback-Leibler divergence (KLD) to compare the similar-

ity of two distributions. The advantage of JSD over KLDis that JSD will always return a finite value and is symmet-rical. We compare the room occupancy distributions of themodels and testing data for different windows of time dur-ing the day. The last metric considered is the rate peopleenter and exit a room. By examining the durations betweenentrances and exits of a room, we can measure the flow ofoccupants in and out of a room. Specifically, for a window oftime w, we calculate λin,w and λout,w for each room wherethe variables represent the rate of flow in and the rate offlow out of a room respectively. Time is taken into accountsince the rate of flow changes depending on the time of day.

6.2 EvaluationFigure 7 compares the average static durations of the var-

ious occupancy levels with those seen in the testing set. Du-ration differences closer to 0 indicate a closer fit to testingdata. For high traffic areas and rooms with low occupancy,BMC and CDMC show similar differences. CDMC typicallyshows larger differences of durations since the CDMC stilltends to get stuck in states near the ends of the hourly par-titions. This causes the occupancy level to remain static forperiods of time longer than normal. Areas with larger occu-pancies are prone to containing sink states as more data isrequired to cover the possible state space. This can be seenin Figure 7 for Office 1 where CDMC remains at several oc-cupancy levels for long durations. Similar results were foundfor the other areas with higher levels of occupancy such asOffice 1, Office 3, Lab 1, and Lab 3.

We next examine the JSD for the different models. Wepartition the day into 2 hour slots and examine the JSD foreach window of time. Examining the ground truth data inFigure 2, we can expect a fair amount of variation amongdifferent days. To establish a baseline of how much diver-gence is typical from day to day, we compare the occupancydistributions of each testing set day to the remaining testingset days for each window of time and establish the maximumdivergence for each time slot. Rooms that are mostly emptysuch as Lab2 and the conference room have JSD of nearly0 for each window of time. Figure 8 shows the JSD for therooms that are consistently occupied. When we comparethe testing set for each model, we see that the JSD for eachwindow is consistent. We find that both models have JSD’sthat are below the maximum observed JSD.

Lastly we examine the flow of occupants for each rooms.We consider the hours 7am - 10am to be morning, 11pm -2pm to be afternoon, and 3pm - 6pm to be evening. Basedon these windows of time, we calculate the flow into and outof rooms. Figure 9 shows the flows into Hall 1 and Office 1for the different simulations. As with JSD, we will use the

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

50

100

Office 1: Difference of Avg. Static Occupancy Duration

Occupancy

Seco

nd

s

CD

MC

= 8

29

BM

C =

458

BMC CDMC

0 1 2 30

200

400

Office 2: Difference of Avg. Static Occupancy Duration

Occupancy

Se

co

nd

s

0 1 2 3 4 5 6 7−5

0

5

10

15

Hall 1: Difference of Avg. Static Occupancy Duration

Occupancy

Se

co

nd

s

Figure 7: The difference of the average static occupancy duration from 7am - 10pm.

0

0.1

0.2

0.3

0−2 3−5 6−8 9−11 12−14 15−17 18−20 21−23

Hour Slots

Office 1: JSD(Mon Occupancy||CDMC Occupancy)

JS

Div

erg

en

ce

Max Obs JSD

0

0.1

0.2

0.3

0−2 3−5 6−8 9−11 12−14 15−17 18−20 21−23

Hour Slots

Office 1: JSD(Wed Occupancy||CDMC Occupancy)

JS

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ce

0

0.1

0.2

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0−2 3−5 6−8 9−11 12−14 15−17 18−20 21−23

Hour Slots

Office 1: JSD(Fri Occupancy||CDMC Occupancy)

JS

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ce

0

0.1

0.2

0.3

0−2 3−5 6−8 9−11 12−14 15−17 18−20 21−23

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Office 1: JSD(Mon Occupancy||BMC Occupancy)

JS

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ce

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Office 1: JSD(Wed Occupancy||BMC Occupancy)

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0

0.2

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0−2 3−5 6−8 9−11 12−14 15−17 18−20 21−23

Hour Slots

Lab 3: JSD(Mon Occupancy||CDMC Occupancy)

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Lab 3: JSD(Wed Occupancy||CDMC Occupancy)

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Lab 3: JSD(Fri Occupancy||CDMC Occupancy)J

S D

ive

rge

nc

e

0

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Lab 3: JSD(Mon Occupancy||BMC Occupancy)

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Lab 3: JSD(Wed Occupancy||BMC Occupancy)

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0

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Hour Slots

Lab 3: JSD(Fri Occupancy||BMC Occupancy)

JS

Div

erg

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ce

Figure 8: Each boxplot is for the JSDs observed within the time slot where the + is an outlier.

0

200

400

7−10 11−14 15−18

Hour Slots

Se

co

nd

s

Hall 1 BMC: Lambda Flow In

Max Obs λ

Min Obs λ

0

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2000

7−10 11−14 15−18

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Office 1 BMC: Lambda Flow In

Seco

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x 104

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Hall 1 CDMC: Lambda Flow In

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x 104

7−10 11−14 15−18

Hour Slots

Office 2 CDMC: Lambda Flow In

Se

co

nd

s

Figure 9: Flows for Hall 1, Office 1, and Office 2 and the min and max flows observed in the testing set.

ground truth test data to establish upper and lower limitsfor the λ values. Again, both BMC and CDMC simulationsfall mostly within the limits. However, CDMC tends to havemore outliers, which again is caused by sink states.Overall, both models perform well, but in general, BMC

performs better since it does not encounter discontinuitiesat the boundaries. The sequence predicted by BMC is alsoalways valid, which may not be the case for the CDMC.

7. HVAC CONDITIONING STRATEGIESUsing the BMC, we define a predictive control algorithm

for temperature. We start by defining the thermal and ven-tilation criteria that our HVAC strategies must meet to havean ASHRAE compliant building. We then define the occu-pancy based temperature control strategy OBSERVE.

7.1 Conditioning Criteria

7.1.1 Temperature

Thermal comfort is a complex measurement that dependson many aspects such as temperature, humidity, air velocity,occupants clothing and activity [16, 19]. The most commoncomfort measurement is Fanger’s Predicted Mean Vote PMVas standardized in ISO 7730 [18]. Fanger’s model is not anundisputed thermal comfort measurement [18, 19, 20], butprovides good generalized results in many cases. Fangercomputes the thermal comfort PMV value between -3.5 and3.5. Rounding the PMV results in the comfort classes hot(PMV > 2.5), warm (1.5 ≤ PMV < 2.5), slightly warm (0.5≤ PMV < 1.5), neutral (−0.5 ≤ PMV < 0.5), slightly cool(−1.5 ≤ PMV < -0.5), cool (−2.5 ≤ PMV < −1.5), andcold (PMV < −2.5). Fanger’s PMV depends on air tem-perature [18], radiant temperature, humidity, air velocity,occupants clothing and activity. The model is non-linearand based on large scale studies in climate chambers.Measuring the PMV based on this model is very com-

plex due to the many influences. The activity and clothinglevel of occupants is simplified by assuming defaults suchas office work and clothing level is correlated to the outsidetemperature [4]. However, this still requires an air tempera-ture, radiant temperature, humidity and air velocity sensorin each room. Air temperature and simple humidity sensorscould be added to our wireless sensor node, but radiant tem-perature and air velocity sensors are complex and expensive,such that large scale installations are not affordable. Giventhese complexities, our work focuses on optimally controllingtemperature rather than attempting to control PMV. Froma control perspective, our goal is to meet a target tempera-ture defined by a comfort metric, which may not necessarilybe Fanger PMV. Different comfort metrics will establish dif-ferent temperature set-points. It is thus more important tomeet specific target temperatures than to meet a specificcomfort metric. As metrics are developed and better envi-ronment sensing is available, we want our system meet thetemperature goals dictated by the new comfort criteria.

7.1.2 Ventilation

ASHRAE Standard 62.1 [4] uses the following to calculateoutdoor air ventilation rates:

Vbz = RpPz +RaAz (4)

where z denotes the zone, Vbz is the ventilation rate, Rp isthe minimum CFM/person, Pz is the number of people, Ra

is the minimum CFM/ft2, and Az is the floor area. The Pz

Algorithm 1 OBSERVE temperature control algorithm.

CondTempi,j ← Condition temperature from time i to jCurrHour ← Current hourTTG ← Temperature such that PMV = 0TASH ← Temperature such that −0.5 < PMV < 0.5pThresh← Probability threshold of occupancy

for Every n minutes do

CurrOcc← Current occupancy stateoccPred← BMC(CurrOcc, predLen)

for Each room r and point of time t in occPred do

occupied← All periods occPredt→t+60 > pThresh

if occupied > 5 minutes of next 15 minutes then

CondTempt−60,t+15 = TTG

else if occupied > 20 minutes of next 60 minutes then

CondTempt−60,t+60 = TTG

else if 5 ≤ CurrHour ≤ 24 then

CondTempi,i = TASH

end if

end for

end for

00:00 4:00 8:00 12:00 16:00 20:000

5

10

15

Time

Occu

pan

cy

Simulated Occupancy: SCOPES vs Actual

SCOPESActual

Figure 10: Simulated SCOPES data.

by determining Az. The other constants are determined byASHRAE Standard 62.1.

7.2 OBSERVETemperature Control StrategyThis section defines the Occupancy-Based System for Effi-

cient Reduction of hVac Energy (OBSERVE) predictive con-trol algorithm, which uses a BMC to predictively conditionroom temperature. The function BMC(OccState, predLen)return a predicted schedule of occupancy occPred, whereoccPredt is a probability a space being occupied at timet = 1 . . . predLen and OccState is the occupancy state attime t = 0. This conditioning strategy is also applicable forbinary occupancy data. The BMC can be easily adapted tobinary data by representing the MC state at each time as avector where each component is a binary indication of oc-cupancy (instead of actual occupancy). Algorithm 1 definesthe OBSERVE temperature control strategy.

This strategy conditions for two different types of occu-pancy. It first checks short windows of time for occupancyto ensures that rooms, such as copy rooms, that are not fre-quented often but have occupied durations of several min-utes are conditioned. The second longer window ensuresrooms that are frequented constantly but may have shortstay durations are still conditioned. Hallways are an exam-ple of such an area. Since no standards currently define whatconstitutes a significant duration of occupancy, we chose val-ues that seem reasonable.

8. EVALUATED STRATEGIESFour different strategies are considered. The first is coef-

ficient based baseline strategy that employs a typical HVACcontrol strategy assuming maximum occupancy for ventila-

EnergyPlus Building Parameters

HVAC Single Duct AHU, VAV with terminal reheatGas heating and cooling9 zones

Temperature Heating: Ttg = 75oF, TASH = 70oFSetbacks Cooling: Ttg = 78oF, TASH = 82oF

Areas Total: 30,130 ft2

Materials Concrete exterior wallsMetal interior walls30% double glazed windows

Table 1: Main building parameters used.

tion and conditions all rooms from 7:00 - 22:00. The secondstrategy is a binary based reactive control of temperatureand ventilation. Rooms are conditioned to a target tem-perature when occupied and are not predictively precondi-tioned. Rooms that are unoccupied are still conditionedto the max/min temperatures allowed by ASHRAE. Sinceprecise room occupancies are unknown, rooms are venti-lated according to the estimated maximum occupancy whenoccupied. The maximum occupancy is determined usingASHRAE Standard 62.1 based on area and room purpose.The third strategy uses the OBSERVE algorithm describedin Section 7.2. Ventilation is based on the observed room oc-cupancy using equation 4 during warm months (Apr - Oct).During the colder months ventilation rates are increased.This increased ventilation is an optimization for terminalreheat HVAC system and is discussed in Section 9.2.1. Thelast strategy uses the OBSERVE algorithm but uses binarydata to train the BMC model. This strategy makes binarypredictions of occupancy and ventilates with the same maxi-mum occupancy assumption of the reactive control strategy.

9. PERFORMANCE RESULTS

9.1 Building Energy SimulatorEnergyPlus is one of the premiere tools for modeling the

energy of buildings. It takes into account factors such asweather, HVAC design, and construction materials. In thissection we define the main parameters used for an Energy-Plus model to test our HVAC strategies.

9.1.1 Building Parameters

EnergyPlus simulations are run for three different loca-tions; Fresno CA, Miami FL, and Chicago IL. The Energy-Plus model replicates the geometry shown in Figure 1 andis constructed to ASHRAE standards. Table 1 summarizesthe main model parameters. The HVAC is a terminal re-heat system that uses a single air handler unit (AHU) withvariable air volume vents (VAV). The sizing of the AHU isdone according to ASHRAE Standard 62.1 [4]. This type ofHVAC system cools air at the AHU level and heats primar-ily at the VAV level. This is common for many office build-ings [9]. This type of system is often used since it is able toheat and cool areas while still sharing the same AHU. Wesave the evaluation of other types of HVAC systems for fu-ture work. The set-points correspond the temperatures thatpredict −0.5 ≤PMV≤ 0.5 assuming 40% humidity, 1 m/sairflow, and clothing coefficients of 1.0 and 0.5 for winterand summer respectively. Fresno, Miami, and Chicago have40%, 52%, and 32% average humidities respectively. TheHVAC system controls humidity to be between 35% and45% using a cool-reheat heating coil.

9.1.2 Simulated Occupancy Schedules

EnergyPlus models typically use static occupancy sched-ules specified in sources such as ASHRAE 90.1 and DOE-2 [1] and are often based on survey data. For our model,however, we will use the BMC to generate occupancy sched-ules. A BMC trained with 5 days of ground truth data isused to generate 23 days of simulated “ground truth” occu-pancy data for the building model. These simulations willserve as our occupancy schedules for the weekdays of themonth. The building is assumed to be empty on weekends.Static occupancy schedules are used for the restrooms sincewe have no data for privacy reasons.

Our control strategy assumes a system similar to SCOPESfor occupancy monitoring. For 20% of the time, the systeminverts the direction or detects a false positive or negativetransition. We simulate SCOPES system error by artificiallyintroducing errors into the simulated ground truth data. Be-cause directional errors occur with roughly the same fre-quency, even with 80% accuracy, the observed system datais close to ground truth. Since errors may produce statesthat do not exist in the BMC, the closest distance metricdefined earlier is used to find the closest state for the OB-SERVE algorithm. Figure 10 compares the simulated scopeswith the simulated ground truth.

9.2 Energy SavingsWe evaluate the energy savings possible using the defined

HVAC strategies for each location. These results take intoaccount the fan, pump, heating (gas), and cooling (gas)energy consumption of the building. Figure 11 shows themonthly breakdown of the energy consumption for each lo-cation. Significant energy savings are achievable over a stan-dard commonly used baseline; we see up to 112% improve-ment in some cases. We see that heating and cooling accountfor most of the energy usage and that heating requires moreenergy than cooling. OBSERVE Occupancy out-performsbinary strategies. The strategies have the most substantialsavings during the colder months. This is primarily becauseheating costs are greater than cooling costs.

During the coldest months in Fresno, the strategies are45%-47% more efficient than baseline; in particular OB-SERVE Occupancy shows 88% to 112% improvement overbaseline. For Fresno, OBSERVE Occupancy, OBSERVE Bi-nary, and Reactive Binary show annual savings of 42.3%,38.3%, and 37.9% respectively. Similar results are foundfor the Chicago location. The difference among strategiesincreases during the warmer summer months. For summermonths in Fresno, OBSERVE Occupancy shows 9%-11% im-provement over Reactive Binary and 7%-10% improvementover OBSERVE binary. For summer months in Chicago,OBSERVE Occupancy shows 10%-12% improvement overReactive Binary, and 6%-7% improvement over OBSERVEBinary. This suggests OBSERVE Occupancy is more effi-cient for warm weather areas. When we examine the resultsfrom the warmer Miami location, OBSERVE Occupancyshows 11%- 18% improvement over both binary strategiesthroughout the year. OBSERVE Occupancy again showssignificant improvement over baseline (33%-69%). We seethat OBSERVE Occupancy is 26%-41% more efficient thanbaseline whereas Reactive Binary is 17%-30% more efficient.OBSERVE Occupancy, OBSERVE Binary, and Reactive Bi-nary have annual savings of 30.4%, 23.7%, and 21.4% respec-tively for Miami.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

20

40

60

80

100

120

OBSERVE OccupancyPerformance Improvement: Fresno

Month

Imp

rov

em

en

t%

ASHRAE Baseline

Reactive Binary

OBSERVE Binary

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

10000

20000

30000

40000

50000

60000 A → ASHRAE Baseline

R → Reactive Binary

B → OBSERVE Binary

O → OBSERVE Occupancy

46%45

%

47%

ARBO

45%45

%

48%

ARBO

48%47

%

52%

ARBO

43%41

%

48%

ARBO

29%28

%

33%

ARBO

19%

20%

26%

ARBO

17%

18%

22%

ARBO

21%

23%

29%

ARBO

29%27

%

34%

ARBO

40%38

%

43%

ARBO

45%

48%

52%

ARBO

46%45

%

47%

ARBO

Monthly HVAC Consumption: Fresno

Month

kW

h

Pump

Fan

Heating (Gas)

Cooling (Gas)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

20

40

60

80

100

120

OBSERVE OccupancyPerformance Improvement: Miami

Month

Imp

rov

em

en

t%

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

10000

20000

30000

40000

50000

60000

30%

36%

41%

A R B O

27%

32%

37%

A R B O

26%

30%

36%

A R B O

20%

24%

31%

A R B O

17%

19%

26%

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17%

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17%

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A R B O

17%

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25%

A R B O

17%

18%

25%

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19%

19%

27%

A R B O

23%

24%

32%

A R B O

31%

34%

40%

A R B O

Monthly HVAC Consumption: Miami

Month

kW

h

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

20

40

60

80

100

120

OBSERVE OccupancyPerformance Improvement: Chicago

Month

Imp

rov

em

en

t%

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

42%43

%

45%

A R B O

41%41

%43

%

A R B O

45%45

%48

%

A R B O

37%37

%41

%

A R B O

30%32

%34

%

A R B O

29%

31%36

%

A R B O

19%

22%

27%

A R B O

25%

28%

33%

A R B O

35%

37%40

%

A R B O

38%38

%38

%

A R B O

41%41

%44

%

A R B O

42%42

%

44%

A R B O

Monthly HVAC Consumption: Chicago

Month

kW

h

Figure 11: The breakdown of the energy consumption for each month and strategy for three different locations.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1

2

3

4

5Office 1: RMSE Temperature (North)

Month

RM

SE

(F

o)

BaselineBinary ReactiveOBSERVE BinaryOBSERVE Occupancy

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1

2

3

4

5Conference Room: RMSE Temperature (North)

Month

RM

SE

(F

o)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1

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5Office 2: RMSE Temperature (North)

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RM

SE

(F

o)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

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5Office 3: RMSE Temperature (North)

Month

RM

SE

(F

o)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1

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4

5Conference Room: RMSE Temperature (South)

Month

RM

SE

(F

o)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1

2

3

4

5Office 2: RMSE Temperature (South)

Month

RM

SE

(F

o)

Figure 12: Monthly RMSE temperature for each strategy for Fresno.

9.2.1 Discussion

We see that all three strategies are significantly more effi-cient than baseline and that there are noticeable differencesamong the strategies. The main source of these differencesis related to ventilation and the terminal reheat system usedfor the building. OBSERVE Occupancy is able to adjust theventilation rate according to estimated occupancy whereasOBSERVE Binary and Binary Reactive use the maximumventilation rate during periods of occupancy. Typically, in-creasing the ventilation rate introduces additional outsideair into the air handler loop and increases the energy con-sumption since the outside air needs to be conditioned; re-circulating air is more efficient since it takes less energy tomaintain pre-conditioned air. However, there are other ven-tilation efficiency factors that need to be considered with aterminal reheat system. A terminal reheat system partiallypreheats outside air before entering the AHU then reheatsair at the room VAV. Under certain conditions, it is more ef-ficient to increase ventilation. Increasing ventilation meanslosing some energy since more outside air needs to be condi-tioned. However, increased ventilation distributes the heat-ing load across all the VAV’s and increases the amount ofVAV pre-heated air into the loop. Based on EnergyPlus sim-ulations, we found increased ventilation during cold monthsincreases efficiency. The same is not true for cooling. Sincecooling is done completely at the AHU level, the VAV’scan no longer be recruited to help distribute the load andany additional ventilation decreases efficiency. The signifi-cant improvement of OBSERVE Occupancy over the binarystrategies in Miami confirms this. Thus, an HVAC systemthat does all the conditioning in the AHU will benefit themost from optimal venting. This could be achieved in manyterminal reheat systems by increasing the AHU preheating.

9.3 Conditioning EffectivenessWhile substantial energy savings are possible, we must

verify the building is ASHRAE compliant. For this analysiswe focus on the Fresno EnergyPlus simulations.

9.3.1 Temperature Effectiveness

We examine the temperature of the rooms during all timesof occupancy. In particular, we are interested in areas suchas the Conference Room, which are not occupied the ma-jority of the day. In order to be ASHRAE [3] compli-ant, we must maintain the set-point temperatures to ensure−0.5 ≤ PMV ≤ 0.5. As mentioned before, we examine tem-perature directly rather than PMV; our goal is to meet thetemperature set by any metric of thermal comfort. For thisanalysis, we examine the root mean square error (RMSE) ofthe room temperatures. We also examine building orienta-tion to observe the influence of solar gain.All four strategies perform similarly for Office 1. Reactive

Binary has the highest RMSE (1.3o) for Nov-Mar. Both OB-SERVE strategies have similar results throughout the year.Baseline performed best during the coldest months.OBSERVE Occupancy performs the best out of the four

strategies for Office 3 with a RMSE of 0.1-0.3 Fo. OBSERVEBinary has a slightly higher RMSE of 0.1-0.5 Fo. The Reac-tive Binary strategy is highest with a RMSE of 0.9-2.8 Fo.For Dec-Jan Reactive Binary has a RMSE of 2.5 Fo as com-pared with the RMSE of 0.1 Fo and 1.0 Fo for OBSERVEOccupancy and baseline respectively.Two different building orientations are considered for Con-

ference Room and Office 2 to show the effect of solar gain.North is defined in Figure 1. South refers to the build-ing turned 180o. Reactive Binary has higher RMSE forthe south orientation (0.4-3.6 Fo) than the north orientation(0.2-2.4 Fo). Both OBSERVE strategies have lower RMSEthan Reactive Binary for both orientations. Generally, bothOBSERVE strategies have slightly lower RMSE than base-line for the north orientation. Both OBSERVE strategiesshow higher RMSE for the south orientation than the northorientation; this is caused by solar gain.

For the Conference Room, Reactive Binary has higherRMSE during the colder months (4.0-4.2 Fo) for both ori-entations. During the summer, Reactive Binary has higherRMSE for the south orientation. For the north orientation,the baseline does better than OBSERVE strategies for win-ter and spring. During the summer, however, both OB-SERVE strategies have lower RMSE than baseline. Com-paring OBSERVE strategies, OBSERVE Binary has lowerRMSE than OBSERVE Occupancy for the summer southorientation (0.3-1.1 Fo vs 0.8-1.2 Fo).

9.3.2 Discussion

Reactive Binary tends to have higher RMSE than theother strategies because of the slow ramp up to target tem-perature. Once an occupant enters a room, it takes timeto reach the target temperature. For areas occupied mostof the time such as Office 1, Reactive Binary performanceimproves but does not match quality of service of predictivestrategies since there is still a temperature reaction delay atthe beginning of the day when the first occupant enters. Thisdelay becomes more critical for areas sporadically occupiedsuch as Office 2 and the Conference Room. A room occu-pied once or twice a day, such as the Conference Room hasinsufficient time to reach the target temperature and is onlyat the correct temperature if the outside conditions happensto match the target temperature (spring, fall). RMSE in-creases if the room receives afternoon sun as is shown forthe southern orientation of the Conference Room and Office2. Rooms such as Office 2 that are constantly visited haveslightly lower RMSE since the thermal momentum createsan additive effect that helps maintain temperature. Theseresults show that reactive strategies based on a PIR WSN do

not work in practice and cannot reach the target temperature

required by the users for all the different scenarios tested.In some cases, OBSERVE strategies perform better than

the baseline since the baseline uses a static HVAC schedule.This is seen for Office 3, which is occupied by professorsand graduate students working at odd hours. The staticbaseline schedule stops conditioning during normal work-ing hours whereas OBSERVE anticipates after hours usage.Even Reactive Binary out-performs the baseline during mildmonths (spring and fall) when rooms are occupied off-hoursand the outside and target temperatures are close.

Both OBSERVE strategies perform similarly. However,there are instances in warm weather where OBSERVE Bi-nary performs slightly better. This is related to over venti-lation. Assuming maximum occupancy forces the VAV ventto open fully when conditioning a room and less time is re-quired to cool the room. The same is not true for heatingsince air from the loop is only partially preheated.

9.3.3 Ventilation Effectiveness

The minimum ventilation rate is established by Equa-tion 4. Since the occupancy detection system can under-

0:00 4:00 8:00 12:00 16:00 20:00 24:001800

2000

2200

2400

2600

Hour

CF

MTotal Building Ventilation Rate (Warm Weather)

Baseline ASHRAE

Reactive/OBSERVE Binary

OBSERVE Occupancy

Required

Figure 13: Total building ventilation rates for eachstrategy for one particular summer day.

count occupants, we add an additional 10% to occupancyestimates. Figure 13 shows the ventilation rate for a sum-mer day. The baseline strategy assumes a maximum ventila-tion rate. The binary strategies use a maximum ventilationrate only when an area is occupied. OBSERVE Occupancyuses a modified schedule. It uses maximum ventilation dur-ing cold months (Oct-Apr for Fresno/Chicago) and optimalventilation during the warm months (year-round for Miami).From the summer day ventilation, we can see that the base-line greatly over-ventilates the building. While binary basedstrategies are an improvement, we can see that binary ven-tilation rate far exceeds the required ventilation rate. It hasa RMSE of 335.0 CFM (Normalized RMSE of 146%). OB-SERVE however, remains close to the required ventilationrate and has a RMSE of 9.5 CFM (NRMSE of 4.1%). OB-SERVE is usually above the required ventilation because ofthe 10% safety margin for under-counting. OBSERVE fellbelow the required ventilation rate only 0.0004% of the time.From Oct-Apr, both binary and OBSERVE share the sameventilation rates and have a NRMSE of 146%.

10. CONCLUSIONS AND FUTUREWORKWe propose a statistical model of the temporal occupancy

of a building based on an inhomogeneous Markov chain esti-mated from occupancy data collected from a sensor network.We control the complexity of the state space by using onlystates observed during training, and prevent discontinuitiesin the chain by a closest distance Markov chain (CDMC) ap-proach, or by continuously blending the transition matricesover time (BMC). Comparing samples generated from themodel with ground-truth data using various metrics showsthat the model captures the occupancy dynamics accurately.We have also shown how the model can be integrated with aWSN for demand control based conditioning strategies. Wepropose the OBSERVE predictive demand control strategyand test the energy savings and conditioning performance.We learned several lessons from our results. First, in orderto achieve energy savings, real time occupancy data is crit-

ical. This can be seen by the average 42% annual energysavings compared to the current state of the art baselinestrategy. Second, predictive strategies show better energysavings performance and even significantly better qualityof service conditioning than reactive strategies. Finally, inorder to achieve maximum energy savings, actual level of

occupancy is required in order to optimize ventilation levels.For future work, we plan to deploy a new occupancy estima-tion system on two floors and train the model in real timeover longer period of time. Once deployed we can integrateOBSERVE into the HVAC system and refine the OBSERVEalgorithm to optimally determine precondition times.

11. ACKNOWLEDGMENTSSpecial thanks to Ankur Kamthe for valuable discussions

of the MC models and OBSERVE, J. Lindblom, P. Felkai, D.Burch, A. Magnana and M. Torio for processing the groundtruth data, the reviewers for their feedback, and Qing Caofor shepherding this paper. This material is based upon workpartially supported by the National Science Foundation un-der grant #0923586, the California Institute for Energy andEnvironment under grant #MUC-09-03, and the Center forInformation Technology Research in the Interest of Societyunder grant #442130-19900.

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