Mining Sequential Patterns for Appliance Usage Prediction

Mathieu Kalksma

, Brian Setz

, Azkario Rizky Pratama

, Ilche Georgievski

and Marco Aiello

Quintor B.V., Ubbo Emmiussingel 112, 9711 BK Groningen, The Netherlands

Distributed Systems, Johann Bernoulli Insititute, University of Groningen,

Nijenborgh 9, 9747 AG, Groningen, The Netherlands

Sustainable Buildings, Nijenborgh 9, 9747 AG, Groningen, The Netherlands

Keywords:

Appliance Usage Prediction, Energy Consumption Prediction, Sequential Pattern Mining.

Abstract:

Reducing the energy consumption in buildings can be achieved by predicting how energy-consuming appli-

ances are used, and by discovering their usage patterns. To mine patterns, a smart-metering architecture needs

to be in place complemented by appropriate data analysis mechanisms. These usage patterns can be employed

to optimize the way energy from renewable installations, home batteries, and even microgrids is managed.

We present an approach and related experiments for mining sequential patterns in appliance usage. We mine

patterns that allow us to perform device usage prediction, energy usage prediction, and device usage predic-

tion with failed sensors. The focus of this work is on the sequential relationships between the state of distinct

devices. We use data sets from three distinct buildings. The data is used to train our modiﬁed Support-Pruned

Markov Models which use a relative support threshold. Our experiments show the viability of the approach,

as we achieve an overall accuracy of 87% in device usage predictions, and up to 99% accuracy for devices that

have the strongest sequential relationships. For these devices, the energy usage predictions have an accuracy

of around 90%. Predicting device usage with failed sensors is feasible, assuming there is a strong sequential

relationship for the devices.

1 INTRODUCTION

Electric appliances are responsible for a signiﬁcant

portion of a household’s energy consumption, hav-

ing a strong impact on a household’s carbon foot-

print. In fact, according to the U.S Energy Infor-

mation Administration (EIA), the energy consump-

tion for household appliances, electronics and light-

ing is responsible for 37% of the total energy con-

sumed by households in 2016 (EIA, 2016). This is an

increase of 10% compared to 1993. Since household

appliances and other electronics are responsible for an

ever-increasing share of a household’s consumption,

it is important to focus on energy usage optimization

efforts in order to meet global greenhouse gases emis-

sion goals.

Smart-metering architectures are essential to gain

insight into the way energy is used and to predict the

future energy consumption. These predictions enable

the optimization of energy production and manage-

ment by smart scheduling of renewable resources and

devices. At the consumer end of the spectrum, this

means measuring and monitoring the way appliances

are utilized and predicting their future usage patterns.

With the emergence of the Internet of Things, we ex-

pect an increasing number of appliances to be con-

nected to the Internet. These appliances shall be able

to provide real-time information on their energy us-

age as a service. Till then, we can use commercially

available electric plug monitoring devices to collect

consumption information. The collected information

can then be exploited to make predictions about future

device utilization and energy consumption. For exam-

ple, in previous work, we investigated device recog-

nition by means of an aggregated power consumption

observed at a single point measurement (Pratama et

al., In Press). This type of information is essential

for home and building energy management systems,

and also has potential for use in smart and micro-grid

applications.

In this work, we focus on mining patterns from

household appliances and propose an approach based

on high-order Markov models to predict: 1) the us-

age of devices, 2) the expected energy footprint, and

3) the usage of a device with a failed sensor. We

focus speciﬁcally on the sequence of device states

over time, and the patterns that exist there. The

model we propose is based on a modiﬁed version of

Kalksma, M., Setz, B., Rizky Pratama, A., Georgievski, I. and Aiello, M.

Mining Sequential Patterns for Appliance Usage Prediction.

DOI: 10.5220/0006669500230033

In Proceedings of the 7th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2018), pages 23-33

ISBN: 978-989-758-292-9

the Support-Pruned Markov Model (Deshpande and

Karypis, 2004) that utilizes a relative support thresh-

old. The results of our experiments demonstrate the

viability of the approach, especially for device usage

predictions. To verify the validity of the model and

the prediction algorithms, we consider three distinct

datasets coming from real-world installations. Two

data sets are from actual households, and one data set

is from an ofﬁce building functioning as a living lab.

We use these data sets to train our model and to eval-

uate the quality of the predictions.

The remainder of the paper is organized as fol-

lows. In Section II, we provide a formal deﬁnition of

the proposed model and describe the algorithms be-

hind our designed solution. Section III describes the

experimentation on three distinct data sets. Section IV

presents related work, while concluding remarks are

presented in Section V.

2 APPROACH AND PROPOSAL

We aim to discover sequential patterns in the state

changes of devices over time, in order to forecast the

future state changes and energy footprint. A Markov

Model (MM) enables the prediction of future states

based on the current state. In MM terms, the current

state refers to the current state of the set of devices.

The future state represents the predicted state changes

for a set of devices, given the current state.

A high-order MM considers more historical ac-

tions to predict the future state. In other words, the

-order MM considers the sequence of the previous

k states when predicting the next state. The All-K

Order Markov model (Pitkow and Pirolli, 1999) ad-

dresses the issue of reduced coverage by looking for a

sequence in the k

-order and, if not found, it contin-

ues searching the lower orders. The disadvantage of

All-K

-Order Markov models is that the state space

expands drastically, as all models from 1 to k have to

be trained and stored.

The Support-Pruned Markov Model (SPMM) is

based on the All-K

-Order Markov model (Desh-

pande and Karypis, 2004). It introduces the concept

of pruning in order to reduce the large state space of

All-K

-Order models. The state pruning relies on the

observation that a state with low support often has

a low prediction accuracy associated with it. Prun-

ing these states increases the overall accuracy and

reduces the state-space complexity. States with low

support are identiﬁed by applying an absolute fre-

quency threshold, φ. The frequency threshold is the

minimum absolute number of instances in the train-

ing set required for a state to be included in the model.

If there are less than φ instances, the support for the

state is too low and it is pruned. As higher-order states

often have less support in the training set, these are

more likely to be removed, dramatically decreasing

the state-space complexity.

2.1 Model Deﬁnition

We propose an adapted version of the SPMM in

which, instead of an absolute frequency threshold φ, a

relative support threshold r is applied, inspired by the

method described in (Agrawal et al., 1993). Using

a relative threshold, we ensure that we do not prune

subsequences with a strong relationship. We employ

the following deﬁnitions:

Devices: Let V = {v

,...,v

} be a set of de-

vices. At any given time t, a device has a binary

state s, where s = 1 and s = 0 are equivalent to the

device being turned on or off, respectively. The his-

torical data of a device v

is deﬁned as a set S

{< t

>,...,< t

>}, where s

,...,s

are the

historical states and t

,...,t

are their corresponding

timestamps.

Transaction: A transaction τ is deﬁned as a set of

devices for which s = 1 at a given time t, thus τ(t) =

|∀i : S

(t) = 1}. A set of transactions T is an or-

dered set of transactions such that ∀i, j : i < j,T

< T

;

all transactions in the set T are ordered by time in as-

cending order.

Sequence: Given a set of transactions T , a se-

quence seq is deﬁned as the transitions in time be-

tween the transactions τ ∈ T . The maximum times-

pan between the ﬁrst element in T and the last ele-

ment (T

− T

|T |

) is referred to as m. In this work, m is

always denoted in minutes. To further reduce the state

space, next to the relative support threshold, a maxi-

mum length of a sequence is enforced. Let |seq| ≤ k,

where k is the maximum length of a sequence.

For example, consider the set of devices to be

V = {A,B,C}, τ

= {A}, τ

= {B,C} and τ

= {A},

and τ

transits to B and C via τ

and to A via τ

Thus, according to our deﬁnitions, the transaction

set T = {τ

,τ

} encompasses all of the following

sequences: {ABA},{ACA},{AB}, {AC},{A},{B},

{C}, {AA}, {BA} and {CA}.

Support: The relative support of a sequence seq

is deﬁned as supp(seq

) = w(seq

)/w(seq

), where w

is a function returning the number of times a sequence

occurs in the transaction set T and seq

is the par-

ent sequence of seq

. For example, given a sequence

{A,B,C}, the parent sequence is {A,B}. A sequence

is supported if, and only if, the support for that se-

quence is above r, the minimal support threshold. We

use a relative support threshold instead of an absolute

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

support threshold to prevent the pruning of sequences

that have a low initial support but a strong relationship

with its child sequences.

To illustrate the difference between absolute and

relative thresholds, let there be three sequences:

seq

= {A}, seq

= {AB}, and seq

= {ABC}. We as-

sume the following number of occurrences after 100

measurements: seq

occurs a 100 times, seq

occurs

10 times, and seq

occurs 9 times. We set the thresh-

old to be r = 0.1. The absolute support for seq

is 0.09

(r = 9/100), whereas the relative support supp(seq

)

equals 0.9 (r = 90/100) as seq

follows seq

90%

of the time. If the absolute support were used, seq

would have been pruned (0.09 < 0.1) despite having

a very strong relationship with seq

. Thus, we choose

to use the relative support to prevent the pruning of

strong relationships between (sub)sequences.

2.2 Predictive Algorithms

We utilize algorithms to solve the problems of device

state prediction, energy consumption prediction, and

device state prediction with a failed sensor. We de-

scribe each of the algorithms in the following sub-

sections, while a complete deﬁnition of the pseudo-

code for each individual algorithm can be found

in (Kalksma, 2016).

2.2.1 Device State Prediction

The device state prediction is a prediction of which

devices will be used in the next m time units. To pre-

dict the state of devices in the next m time units, we

take a stream of real-time transactions and store the

last x transactions, such that the time span between

and T

is less than m time units. All possible se-

quences are determined based on the cached transac-

tions. When the model is trained, it predicts which

devices will be in the “on” state for the next m time

units.

Figure 1: Illustration of a transactions time line.

Figure 1 provides an example of a time line with

m = 3 time units. The transactions that occurred at

t − 0, t − 1 and t − 2 have been cached. At t − 0 de-

vice A is in the on state (s

= 1), at t −1 device C is on,

and at t − 2 both device A and B are on. In this case,

the possible sequences based on the cached trans-

actions are {ACA}, {AC}, {A},{BCA},{BC},{B},

{AA},{BA},{CA} and {C}.

For each device a certainty P is determined,

which is the probability for a device to be in use given

a certain supported sequence. The certainty P can be

deﬁned in two ways: average certainty and weighted

average certainty. The average certainty, P

avg

, is the

sum of all probabilities of the supported sequences,

divided by the total number of supported sequences.

The weighted average certainty, P

wavg

, is the sum of

all probabilities of the supported sequences times a

weight w, divided by the number of supported se-

quences. The methods used to calculate P

avg

and

wavg

are referred to as avg and wavg, respectively.

If P is greater than 0.5, the device is considered to be

used (s = 1) in the next m time units.

2.2.2 Energy Consumption Prediction

Next, we predict the energy consumption, also re-

ferred to as the energy footprint, of a set of devices.

The prediction of energy consumption is based on an

extension of the state prediction algorithm. The out-

put of the state prediction is used as input for the en-

ergy consumption prediction. When a device is pre-

dicted to be in use for a given time interval, we pre-

dict the energy consumption for this interval. In or-

der to perform these predictions, a second Support-

Pruned Markov Model is trained. The model predicts

the transitions between the energy consumption lev-

els of a device. The energy consumption levels for

each device are deﬁned in bands. For example, an

energy consumption band could be {0W , 5W , 10W ,

30W }, where 0, 5, 10, and 30 are the levels we iden-

tiﬁed for this speciﬁc device. The actual consumption

measurements are rounded to the nearest band. From

these measurements, a Markov chain is created based

on the energy consumption measurements of the last

m = 3 time units.

To predict the future energy consumption of a

device, we follow a similar approach to training as

we did for the energy consumption model. First,

the observed energy consumption measurements are

rounded to the nearest band and a sequence is cre-

ated from the last three measurements. When the state

prediction indicates that a device will be used, the en-

ergy consumption model is used to retrieve the pre-

dicted energy consumption for the given device. Us-

ing the current consumption sequence as input, the

model predicts the future energy consumption by se-

lecting the most probable sequence. When the input

sequence is not available in the model, the algorithm

will select the last known consumption as the pre-

dicted energy consumption. If the state prediction al-

Mining Sequential Patterns for Appliance Usage Prediction

Table 1: Properties of the data sets used in the evaluation.

Properties Data sets

Name RUG ECO1 ECO2

Number of devices 5 4 7

Measurement Period 195 days 237 days 245 days

Coverage (

records

minutes

) 77.84% 99.64% 98.58%

Training set (N

records

) 131,386 211,619 175,679

Validation set (N

records

) 86,066 120,960 169,860

gorithm concludes that the device will not be used, the

lowest consumption band is selected as the predicted

energy consumption.

For example, given a device with bands deﬁned

as {0W , 5W , 10W , 30W }, and an actual consumption

history of {1.2W , 4.3W , 12W , 19W }. The histori-

cal consumption will be rounded to the nearest band,

resulting in the following measurements: {0W , 5W ,

10W , 10W }. The ﬁrst three measurements (m = 3)

of the consumptions for this device are 0W , 5W and

10W . Thus, the state sequence 0 − 5 − 10 is trained

with a future state of 10W . Once the model is trained

on a data set, it enables the prediction of the most

likely energy consumption for the next time interval

for each sequence per device.

2.2.3 Device State Prediction with Failed Sensor

Finally, we predict the state of devices while one of

the sensors has failed. The algorithm for this pre-

diction is also based on the algorithm used for state

prediction. To verify if the model is still capable of

predicting device states when a device is removed or

a sensor has failed, the sequences that contain the se-

lected device are ignored when retrieving supported

sequences. This simulates the same behaviour of a

sensor (or device) failing.

3 EVALUATION

We evaluate our approach on real-world data sets by

performing experiments for each type of predictive

model: device state, energy consumption, and device

state with failed sensors.

3.1 Data Sets

Table 1 shows the properties of the three different

data sets from real-world buildings considered in this

work: RUG, ECO1, and ECO2. All data sets are ad-

justed by reducing the original data sets to one mea-

surement per minute. The data sets are further split

into a training set and a validation set.

The RUG data set is composed of data collected in

our own ofﬁce building at the University of Gronin-

gen, originally set up for the research presented

in (Georgievski et al., 2012). It contains power con-

sumption data from ﬁve devices, namely a boiler, cof-

fee maker, printer, microwave and TV-screen. The

original data set has six power consumption measure-

ments per minute for each device.

The ECO1 and ECO2 data sets are collected from

two Swiss households, which are part of the Electron-

ics Consumption Occupancy (ECO) data set (Beckel

et al., 2014). ECO1 is the data set of the ﬁrst house-

hold and contains power consumption measurements

of four devices: a fridge, washing machine, dryer, and

freezer. ECO2 is the data set of the second house-

hold and contains power consumption measurements

of seven devices: a dishwasher, air exhaust, fridge,

freezer, dimmable lamp, TV, and stereo. ECO2 is

created from the original household data set by select-

ing records of seven out of twelve available devices to

maintain a trainable density of our data set.

Both RUG and ECO datasets are collected using

commercially available Plugwise

measurement de-

vices which have a measurement error of about 5%.

The missing data in the ECO dataset is handled by re-

placing a missing value with the last known measure-

ment if there are less than a 100 missing data points

(Beckel et al., 2014). In the RUG data set, the miss-

ing data is replaced with the value of -1. The RUG

dataset uses a sample rate of 10 seconds for each of

the sensors. On the other hand, the ECO data sets are

both sampled at 1 second intervals. For our experi-

ments, we downsample the RUG, ECO1 and ECO2

data sets to 1 minute intervals in order to provide a

fair comparison.

3.2 Experiments & Parameters

In order to optimize our models we have to employ

the correct parameters. This section provides a de-

scription of the experiments and parameters used for

evaluating each of the three different types of predic-

tive models. If the parameters for a certain model type

https://www.plugwise.nl/

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

Table 2: Bands deﬁned for each device per data set.

Device Bands

RUG data set

Screen {0,100,200}

Microwave {0,100,200,...,1100,1200}

Printer {0,100,200,...,1300,1400}

ECO1 data set

Fridge {0,5,10,30,40,60,100,200,400,600,800,1000}

Dryer {0,5,50,300,350,400,...,900,950}

Washing machine {0,100,200,...,2100,2200}

Freezer {0,5,10,...,75,80}

ECO2 data set

Dishwasher {0,100,200,...,1500,1600}

Air exhaust {0,5,10,30,40,60,100,200,400,600,800,1000}

Fridge {0,5,10,30,40,60,100,200,400,600,800,1000}

Freezer {0,5,10,30,40,60,100,200,400,600,800,1000}

Lamp {0,10,20,...,190,200}

TV {0,2,5,140,150,160,170}

Stereo {0,10,20,...,190,200}

are not explicitly given, the parameters from the pre-

viously discussed model are reused.

3.2.1 Device State Prediction

We derive a near-optimal conﬁguration by tuning the

following parameters: the relative support threshold

(r), time-unit length (m), and sequence length (k). We

test the impact of each of these parameters in isola-

tion by changing one parameter while keeping the rest

constant. The ﬁne-tuning of the parameters was per-

formed on the RUG data set.

The number of supported sequences per thresh-

old value r inﬂuences the model complexity; the more

supported sequences, the higher the complexity. With

only a small threshold (r < 0.3), the number of sup-

ported sequences drops signiﬁcantly (to about 355). If

trained sequences also include devices that are turned

off, the number of supported sequences grows dras-

tically (to about 15,290). The drop in the number

of supported sequences has a minimal effect on the

accuracy of predictions for all r < 0.4, which means

the most important sequences are not dropped. When

tuning the time-unit length m, we note that the accu-

racy is best when using either a small value (m = 5),

or a large value (m ≥ 20). We test the impact of the

maximum sequence length k on the accuracy by using

avg with m = 10 and r = 0.3. The test results indicate

acceptable accuracy when 2 ≤ k ≤ 10 within which

range the accuracy stabilizes at k ≥ 5 with a value of

45%.

To summarize, our conﬁgurations consist of m = 5

and k = 5, and either r = 0.2 or r = 0.4 depending on

the data set. Since there is hardly any difference in

the accuracy of predictions between the avg and wavg

methods, we choose to use wavg.

3.2.2 Energy Consumption Prediction

We deﬁne bands for all of the devices in each

data set in order to discretize the measurements.

For example, for the screen device in the RUG

data set, we specify {0,100,200}, for the freezer

in ECO1 and the dishwasher in ECO2, we

use {0,5, 10, 30, 40, 60, 100, 200, 400, 600, 800, 1000}

and {0, 100, 200, . . . , 1500, 1600}, respectively. Only

the boiler and coffee maker (RUG data set) are not

conﬁgured because they are never predicted to be on,

thus having empty (

0) bands. Table 2 shows the bands

for the rest of the devices in all three datasets.

To compare the predicted energy consumption

with the actual one, we look for patterns in small frag-

ments of energy consumption data. We use the fol-

lowing standard Mean Absolute Error (MAE) mea-

surement to see how close predictions are to the actual

observed value.

MAE =

∑

i=1

| f

− y

| (1)

where f

is the prediction at point i and y

is the actual

observation at that moment.

In addition, we also employ the following stan-

dard Mean Absolute Percentage Error (MAPE) mea-

surement to observe the accuracy of prediction in per-

centage.

MAPE =

MAE

∑

i=1

∗ 100% (2)

Mining Sequential Patterns for Appliance Usage Prediction

where y

is again the observed value at point i.

For each device in the data sets, a table is provided

which shows the MAE, the average energy consump-

tion, and the MAPE. Lower MAE and MAPE values

indicate better results.

3.2.3 Device State Prediction with Failed Sensor

Sensor failures can severely impact the accuracy of

certain state prediction methods. Since our approach

uses the states of all devices to predict the state of

a given device, we expect to be able to handle sen-

sor failures in some cases. Thus, to verify this we

dedicate experiments to device state predictions with

failed sensors. To simulate a sensor or device failure,

we retrieve all supported sequences except those that

contain the device being predicted for. Since we know

the actual state of the device, we can validate the pre-

dictions that were made when excluding this device

from the supported sequences. Except for ﬁltering

supported sequences, this experiment is performed in

the same way as the experiment on device state pre-

dictions, allowing us to directly compare the results

of both experiments.

3.3 Results

In this section, the results for each of the predictive

models are given. First, the results for device state

predictions are presented, followed by the energy con-

sumption prediction results. Finally, the results for

device state prediction with a failed sensor are given.

In several occasions, we use the following statistic pa-

rameters:

• Correct: the algorithm predicts a correct state.

• Correct off: the device is off and the algorithm

predicts it as off, sometimes abbreviated as Corr.

off.

• Correct on: the device is on and the algorithm pre-

dicts it as on, sometimes abbreviated as Corr. on.

• Wrong: the algorithm predicts a wrong state.

• Device off: time that a device is in the off state,

sometimes abbreviated as Dev. off.

• Device on: time that a device is in the on state,

sometimes abbreviated as Dev. on.

• On coverage: the algorithm predicts the device as

on and it is on, sometimes abbreviated as On cov.

• Off coverage: the algorithm predicts the device as

off and it is off, sometimes abbreviated as Off cov.

3.3.1 Device State Prediction

Table 3 shows comparable results for state prediction

on each data set with an overall accuracy of almost

90%. The accuracy for predicting that a device will

not be turned on (> 90%) is better than the accuracy

for predicting that a device will be turned on (between

65% and 77%). This difference in accuracy can be ex-

plained by the amount of time devices are turned on –

the longer devices are turned on, the higher the accu-

racy of predicting devices ‘correctly on’. In general,

devices in our data sets spend more time in the ‘off’

state.

Table 3: Overall comparison of the state predictions results.

Statistic RUG ECO1 ECO2

Correct 0.8978 0.8892 0.8786

Correct off 0.91 0.9458 0.9628

Correct on 0.6492 0.7707 0.7179

Wrong 0.1023 0.1109 0.1215

Device off 0.8838 0.7145 0.7289

Device on 0.1163 0.2856 0.2712

On coverage 0.2617 0.8713 0.9098

Off coverage 0.9815 0.8964 0.8671

Table 4 shows the state prediction results speciﬁc

to each device in each data set. At ﬁrst glance, we no-

tice a high accuracy for the RUG data set, especially

for the screen, microwave and boiler. However, when

looking exclusively at the ‘on coverage’, the results

are not as high. The microwave is the only device

whose ‘on coverage’ is greater than 50%, while for

the boiler and coffee maker the coverage is 0%.

The results for ECO1 are signiﬁcantly better. The

device with the lowest accuracy, the freezer, has an

accuracy of almost 72%. The dryer and the washing

machine have an accuracy of 99% and 97%, respec-

tively, which is achieved by the ‘off coverage’ being

nearly 100% for both devices, and a decent ‘on cov-

erage’ of 82% and 74%, respectively.

Except for the fridge and freezer, the results for

ECO2 also report high accuracy. The issue with the

fridge and freezer is their ‘off coverage’ (only 52%

for the fridge and even 30% for the freezer), which

negatively affects the detection that they will not be

used. On the other hand, the air exhaust has a low ’on

coverage’, possible caused by the fact that the device

is turned on for only 1.2% of the time. Interestingly,

the dishwasher is turned on 1.6% of the time, but does

have a high ‘on coverage’ of 60%.

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

Table 4: State predictions results per device for all data sets.

Device Correct Corr. off Corr. on Wrong Dev. off Dev. on On cov. Off cov.

RUG data set

Screen 0.9998 0.9998 0.9334 0.0003 0.9996 0.0005 0.3889 1

Microwave 0.967 0.9734 0.9084 0.0331 0.8861 0.114 0.7895 0.9898

Boiler 0.9691 0.9691 0 0.031 0.9691 0.031 0 1

Coffee maker 0.8077 0.8077 0 0.1924 0.8077 0.1924 0

Printer 0.7564 0.79 0.4588 0.2548 0.7564 0.2437 0.2544 0.9034

ECO1 data set

Fridge 0.8764 0.9082 0.8303 0.1237 0.6063 0.3938 0.8621 0.8856

Dryer 0.9922 0.9928 0.9738 0.0079 0.9606 0.0395 0.8238 0.9991

Washing machine 0.971 0.9749 0.9209 0.0291 0.9104 0.0897 0.7397 0.9938

Freezer 0.7173 0.7198 0.7167 0.2828 0.3806 0.6195 0.8993 0.4213

ECO2 data set

Dishwasher 0.9929 0.9935 0.9364 0.0072 0.9842 0.0159 0.5908 0.9994

Air exhaust 0.9898 0.9903 0.7716 0.0103 0.9886 0.0115 0.1475 0.9995

Fridge 0.6662 0.7733 0.6053 0.3339 0.532 0.4681 0.8244 0.527

Freezer 0.6586 0.6948 0.651 0.3415 0.409 0.5911 0.9106 0.2943

Lamp 0.9852 0.9854 0.9846 0.0149 0.8247 0.1754 0.9303 0.9969

TV 0.8851 0.9962 0.7024 0.115 0.732 0.2681 0.991 0.8463

Stereo 0.9728 0.9914 0.943 0.0273 0.6321 0.368 0.9855 0.9653

3.3.2 Energy Consumption Prediction

Table 5 shows the results of the accuracy of predict-

ing energy consumption. For the RUG data set, the

MAPE is 90% of the total average consumption. This

is due to the dependency of energy consumption pre-

dictions on the state predictions, meaning that the

state prediction errors impact the accuracy of energy

consumption predictions. Since the state prediction

always fails for the coffee machine and boiler, the en-

ergy consumption prediction for these is always close

to zero. When in use, the coffee machine and boiler

use over 2500W and 2000W , respectively. Only these

two devices already cause an error of 4500W in the

predictions when both turned on at the same time.

Thus, both, the coffee maker and the boiler, have an

MAE which is almost the same as their average con-

sumption values. For ECO1, each device has a MAPE

less than 50% of the average consumption with an

overall MAPE of 29% of the total average consump-

tion. For ECO2, the air exhaust has a MAE of 3W ,

which is an error of 278%. In this case, the MAE of

3W should serve as an indication rather than the per-

centage error because of the low average consump-

tion, which makes even a small MAE to causes a big

MAPE. The most interesting results are for the lamp,

TV and the stereo with a MAE of only a few Watt

and a MAPE of around 10% (notice that these devices

have an ‘on coverage’ in the order of 90%). This in-

dicates that only a few errors are passed on from the

state prediction to the energy consumption prediction.

3.3.3 Device State Prediction with Failed Sensor

First, we evaluate how many times the state prediction

with a failed sensor is the same as the state prediction.

These two types of predictions are in fact the same for

about 95% (RUG), 80% (ECO1) and 90% (ECO2) of

the time. Next, we evaluate the device state predic-

tion with a failed sensor for each device separately,

as shown in Table 6. The results show that predicting

device states when a sensor has failed is impossible

with the RUG data set; for all devices, our approach

is unable to predict the ‘on’ state correctly. This is due

to the very weak sequential relationship between de-

vices in this data set. The results with ECO1 are bet-

ter. Our approach is capable of predicting the fridge

and freezer to be used while the measurement of their

power consumption is disabled (simulating a failed

sensor). Although the accuracy of their state predic-

tions with a failed sensor is lower than the original

state predictions (87% versus 60% for the fridge, and

71% versus 49% for the freezer), the results show that

our approach is capable of predicting device states

correctly as long as a strong sequential relationships

between devices exist. As for ECO2, there are vary-

ing results for different devices of which the TV and

stereo have the most interesting outcomes. The TV

has the same accuracy with a failed sensor, as it has

with the original state prediction for 99.98% of the

time with an overall accuracy of 88.5%. The stereo

has even more accurate results, with an overall accu-

racy of 89%, and 92% of the predictions simulating a

failed sensor are the same as the original state predic-

Mining Sequential Patterns for Appliance Usage Prediction

Table 5: Errors in predicting energy consumption.

Device MAE (W) Average Consumption (W) MAPE

RUG data set

Screen 0.92 2.1 43.81%

Microwave 28.75 27.67 103.90%

Boiler 35.75 37.22 96.05%

Coffee maker 149.08 152.08 98.03%

Printer 20.58 32.15 64.01%

Overall 227.62 251.23 90.60%

ECO1 data set

Fridge 9.88 25.74 38.38%

Dryer 3.67 29.59 12.40%

Washing machine 19.89 40 49.73%

Freezer 5.23 18.86 27.73%

Overall 33.48 114.15 29.33%

ECO2 data set

Dishwasher 11.16 18.01 61.97%

Air exhaust 3.26 1.17 278.63%

Fridge 33.99 48.04 70.75%

Freezer 33.56 49.74 67.47%

Lamp 3.55 27.09 13.10%

TV 2.55 42.22 6.04%

Stereo 1.91 19.48 9.80%

Overall 79.32 205.71 38.56%

tions. There is a strong sequential relationship be-

tween the TV and the stereo.

3.4 Discussion

Looking at the results, the approach performs best

on devices with regular patterns. For state predic-

tions, devices with regular usage patterns are more

suitable. For energy consumption predictions, devices

with regular patterns of consumption, such as a TV,

have higher accuracies. For devices that are rarely

used, it is hard to predict their future states or their

energy consumption, as a strong sequential relation-

ship is usually not developed. For devices, such as

a fridge, that have cyclic patterns – run on an auto-

matic schedule instead of being triggered by a user –

it is difﬁcult to predict their state with an approach

based on Markov chains, thus a different approach is

required. Devices with peak patterns (e.g., fridge),

which do not heavily depend on previous consump-

tion records, have less accurate energy consumption

predictions in our models.

For certain devices, it is more accurate to predict

when a device will not be used than when it will be

used. The reason for this is that such devices are not

used most of the time (i.e. not used around 70% of

the time), thus it is more likely to guess right. The

accuracy of energy consumption predictions depends

on the accuracy of the state predictions. This means

that errors from state predictions are taken over by

energy consumption predictions, which we observed

for the coffee machine and boiler in the RUG data

set). While we could have ﬁltered the input of the en-

ergy consumption prediction model by removing in-

correctly predicted states, we decided not to do so in

order to create the most realistic scenario.

As the number of devices considered by the model

increases, the complexity also increases dramatically.

Furthermore, the density of data sets also inﬂuences

the complexity of the model. To optimize the model

for training, we prune infrequent sequences from the

model. A consequence of pruning the model is that

the devices used less often will be removed, making

their prediction harder. To overcome the complexity

of considering a large number of devices, we can par-

tition the devices. By separating devices that have no

relationship whatsoever in separate partitions which

have their own models, we can drastically reduce the

overall complexity.

4 RELATED WORK

There are numerous studies that consider state and

energy consumption prediction for devices. Basu et.

al. (Basu et al., 2013) utilize a decision tree, a de-

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

(a) RUG data set.

(b) ECO1 data set.

Figure 2: Energy consumption prediction for all data sets.

cision table, and a Bayesian Network to predict the

device usage for 1 hour and 24 hour intervals. While

they report the overall accuracy over 90% for the RE-

MODECE dataset (De Almeida et al., 2006), there is

no algorithm that generalizes well for all appliances;

the state prediction of lighting devices and oven appli-

ances perform better with the decision table approach,

while the state prediction for a washing machine is

most accurate when using the decision tree approach.

In (Zhang et al., 2016), Zhang et. al. proposed

a method using a weighted Support Vector Machine

with a differential evolution algorithm. Their goal is

to predict both the short-term and mid-term energy

consumption. The results of their experiments show a

MAPE of 5.843% for daily predictions and a MAPE

of 3.767% for half-hourly predictions. The authors

of (Jung et al., 2015) proposed an approach using

a Least Squared Support Vector Machine technique

for forecasting the daily energy usage of buildings.

To optimize the parameters of the model, DSOR-

CGA is applied, a hybrid of direct search optimiza-

tion and real-coded genetic algorithm. They report

an average Root Mean Square Error (RMSE) between

7.5994 and 11.1319, depending on the data set used.

In (Wang and Ding, 2015), the authors describe an an-

nual occupancy-based energy consumption prediction

method for ofﬁces, combining a Markov chain and the

Monte Carlo method. Their reported error rates vary

from 0.99% to 3.95%, depending on the ofﬁce. The

authors of (Li et al., 2015) apply an Artiﬁcial Neural

Mining Sequential Patterns for Appliance Usage Prediction

Table 6: Results for state prediction with failed sensor per device for all data sets.

Device Correct Corr. off Corr. on Wrong Dev. off Off cov. Same prediction

RUG data set

Screen 0.9996 0.9996 0 0.0005 0.9996 1 0.9998

Microwave 0.8861 0.08861 0 0.114 0.8861 1 0.8932

Boiler 0.9691 0.9691 0 0.031 0.9691 1 1

Coffee maker 0.8077 0.8077 0 0.1924 0.8077 1 1

Printer 0.7564 0.7564 0 0.2437 0.7564 1 0.8649

ECO1 data set

Fridge 0.598 0.607 0.4071 0.4021 0.6063 0.9563 0.636

Dryer 0.9606 0.9606 0 0.0395 0.9606 1 0.9623

Washing machine 0.9104 0.9104 0 0.0897 0.9104 1 0.9215

Freezer 0.4919 0.3835 0.623 0.5082 0.3806 0.5516 0.6754

ECO2 data set

Dishwasher 0.9842 0.9842 0 0.0159 0.9842 1 0.9901

Air exhaust 0.9886 0.9886 0 0.0115 0.9886 1 0.9979

Fridge 0.544 0.5619 0.5156 0.4561 0.532 0.6489 0.7482

Freezer 0.5518 0.4458 0.612 0.4483 0.409 0.3952 0.8107

Lamp 0.8247 0.8427 0 0.1754 0.8247 1 0.8344

TV 0.885 0.9959 0.7025 0.1151 0.732 0.8464 0.9998

Stereo 0.8932 0.8763 0.932 0.1069 0.6321 0.9675 0.9177

Network (ANN) to perform hourly predictions of a

building’s electricity consumption. They apply an im-

proved Particle Swarm Operation to adjust the ANN’s

structure, weights, and thresholds, ultimately result-

ing in a MAPE of 0.0162%. They also experiment

with a Genetic Algorithm-ANN and report a MAPE

of 0.00185%. These results improve the energy con-

sumption prediction using a normal ANN that deliv-

ers a MAPE of 0.0211%.

The work of Barbato et. al. (Barbato et al., 2011)

is closely related to our presented work. The authors

take a probabilistic approach to device state predic-

tions. Devices that were considered in their research

include: an oven, TV, boiler, and computer. For these

devices, they obtain a state prediction accuracy of

76%, 82%, 94%, and 88%, respectively. To compare

our approach to Barbato’s approach, we implement

their approach and evaluate it on an ECO data set.

We choose the ECO2 dataset, as it has the highest re-

liability: only 3% of the values are missing for the

fridge, freezer, dishwasher, TV, and stereo (Cicchetti,

2014). The evaluation of the approach on the ECO2

data set is shown in Table 7. When compared to our

approach (Table 4), we can see that in some cases the

performance is similar, while in general our approach

performs better. Barbato’s approach fails to identify

when the dishwasher and air exhaust are turned on.

For the fridge and freezer the results are closer to-

gether, though our approach performs approximately

10% to 15% better. The accuracy of the predictions

for the lamp come closest to ours, but once more their

approach struggles with the accuracy of ‘on’ predic-

tions. We observe a similar trend for the TV and

stereo.

In Tang et. al. (Tang et al., 2014), the authors also

consider the device states and estimate energy usage.

Based on the predicted device states, the authors esti-

mate power consumption using the rated power given

by hardware vendors. Their main concern is to break

the aggregated energy consumption to individual ap-

pliance for every timestamp, without learning the se-

quence of the device activation. Our work differs in

the way how energy consumption is predicted, as we

focus on individual devices instead of the aggregated

consumption.

5 CONCLUDING REMARKS

We proposed an approach based on a modiﬁed ver-

sion of Support-Pruned Markov Models to mine pat-

terns of device usage. We designed experiments in-

volving three data sets that represent real-world envi-

ronments. We achieved 87% accuracy in device usage

predictions over three different data sets. Moreover,

the approach is very reliable for devices that exhibit

a strong sequential pattern over time, achieving up to

99% accuracy in state predictions. For these selected

devices, the expected energy footprint is predicted

correctly with only a few Watts of error, resulting in

an accuracy of around 90%. We also demonstrated

that our approach can handle, to some degree, the us-

SMARTGREENS 2018 - 7th International Conference on Smart Cities and Green ICT Systems

Table 7: State predictions results for Barbato et.al. approach (Barbato et al., 2011) on ECO2.

Device Correct Corr. Off Corr. on Wrong Dev. off Dev. on On cov. Off cov.

Dishwasher 0.9854 0.9854 0 0.0147 0.9854 0.0147 0 1

Air exhaust 0.962 0.9923 0.0155 0.0381 0.992 0.0081 0.0598 0.9693

Fridge 0.5004 0.6292 0.378 0.4997 0.6256 0.3745 0.5175 0.4902

Freezer 0.5146 0.4954 0.5281 0.4855 0.4817 0.5184 0.597 0.4259

Lamp 0.8987 0.9213 0.4768 0.1014 0.901 0.0991 0.2446 0.9706

TV 0.7156 0.835 0.4159 0.2845 0.7635 0.2366 0.501 0.7821

Stereo 0.6213 0.751 0.448 0.3788 0.6659 0.3342 0.5737 0.6452

age predictions of devices for which the sensor havew

failed. This is accurate for devices that have strong

sequential relationships amongst each other, that is,

these devices are often used together, or one after the

other. Cyclic and peak patterns, on the other hand, are

harder to predict with the proposed approach. This is

especially true when there is not a large quantity of

data available, therefore cyclic and peak patterns will

require a different set of techniques.

ACKNOWLEDGEMENT

Mathieu Kalksma thanks the Distributed Systems

Group at the University of Groningen for the opportu-

nity of and support while performing the presented re-

search. The work is partially supported by the Dutch

National Research Council Beijing Groningen Smart

Energy Cities Project, contract no. 467-14-037.

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Mining Sequential Patterns for Appliance Usage Prediction