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Model Based Event Detection in Sensor Networks

Jayant Gupchup, Andreas Terzis, Randal Burns, Alex Szalay

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Outline

• Motivation

• Data & Model

• Experiments and Results

• Discussion

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Motivation

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Importance of detecting events

- Fixed Sampling:

High Freq => too much data

Low Freq => miss temporal transients

- Detect Events: Adaptive Sampling

(increase % of usable data)

- Conserve Energy

- Alarm Triggers

- Correlate events and observed

phenomena in large databases

“Event starts”

Detect Event

Increase Sampling Frequency/Trigger

Alarms

“Event ends”

Return to steady behavior

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Sample Event

Rain Event Non-Event Days

-5

0

5

10

15

20

0 24 48 72 96

hours

Air

Tem

per

atu

re (

cels

ius)

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Solution: Rough Sketch

- Model observed quantities using Principal Component Analysis (PCA).

- Project original data on a “feature space” (reduce dimensionality)

- Look for observations “deviating” from Average/Expected behavior in the feature space

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Principal Component Analysis (PCA)

PCA :- Finds axes of maximum

variance

- Reduces original dimensionality

(In e.g. from 2 variables => 1 variable)

First Principal Component

Variable #1

Var

iabl

e #2

X : Points original spaceO : Projection on PC1

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Motivation for Using PCATypical day: “Fits model well”

-4

-3

-2

-1

0

1

2

3

4

5

0 5 10 15 20 25

hours

Mea

n su

btra

cted

Air

tem

p (C

elsi

us)

observed Temp, PCA reprojection Temp.

residuals (absolute)

Event day: “Large residuals”

-8

-6

-4

-2

0

2

4

6

0 5 10 15 20 25

hours

Me

an

su

btr

act

ed

Air

te

mp

(C

els

ius)

observed Temp. PCA reprojection Temp.

residuals (absolute)

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Why Not Soil Moisture ?

Reaction to event

Reaction to event

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LifeUnderYourFeet Data

&

Model Preparation

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LifeUnderYourFeet data

• 10 MICAz Sensors– Air Temperature (AT)– Soil Temperature (ST)– Soil Moisture– Photo Sensor

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Air Temp vs. Soil Temp

-6

-4

-2

0

2

4

6

0 5 10 15 20 25

hour

tem

per

atu

re (

cels

ius)

air temperature profile soil temperature (X20 scaleup)

Notice the phase lag for Soil Temperature

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Data Preparation• Model built on Air temperature and Soil Temperature.

AT1_1 AT1_2 …. … …. AT1_144

AT2_1 AT2_2 …. … …. AT2_144

. . …. … …. .

. . …. … …. .

AT10_1 AT10_2 …. … …. AT10_144

. . …. … …. .

. . …. … …. .

. . …. … …. .

t=10 t=20 … t=1440

1 day,

10 sensors

Size of matrix : [(# of days x 10) X 144]

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40

50

60

70

80

90

100

110

0 30 60 90 120

Principal Components

% v

ari

an

ce

co

ve

red

air temperature soil temperature

Basis1-4 cover 90.95%

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PCA Bases (AT & ST)Air Temperature Eigenvectors (Basis vectors)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25

Hour of day

no

rmal

ied

air

te

mp

erat

ure

eigenvector1 eigenvector2

Eigenvector1 Is the

Diurnal cycle

Soil Temperature eigenvectors (basis vectors)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20 25

Hour of day

No

rmal

ized

so

il

tem

per

atu

re

eigenvector1 eigenvector2

similarity eigenvector1 for ST

&eigenvector2 for AT

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Methods and Results

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MethodsThree methods

1) Basic Method – Projections on the first principal component for AT

2) Highpass Method– Removes seasonal drift by looking at sharp changes

in the local neighborhood.

3) Delta method– Makes use of the inertia of the soil and seasonal drift

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Test Data

• Test Period : 225 days between September, 2005 – July, 2006

• 48 major events were known to occur (taken from the BWI weather station,

http://www.wunderground.com/US/MD/Bwi_Airport.html)

• Offline Analysis

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Method 1 : Basic Method• Considers only Air Temperature.

• First Basis Vector covers 55% of variation in the data

AT1_1 AT1_2 …. … …. AT1_144

AT2_1 AT2_2 …. … …. AT2_144

. . …. … …. .

AT10_1 AT10_2 …. … …. AT10_144

V1_1

V1_2

.

V1_144

e1_1

e2_1

.

e10_1

X =

Average

E1 E2 … ….. …………….. En-1 En

Day 1 Day 2 Day n

1 day

First Basis Vector (PC1)

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Method 1: Basic Method (cont.)

Results :

Drawback:- Does not consider seasonal drift- Does not make use of the inertia information

of the soil.

Method Precision Recall False Negatives

Basic 52.459% 64% 18

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Method 2 : Highpass Method

• Again, Considers only Air Temperature

• Highpass filter on ‘E1’ series. Call this series ‘S1’

• Highpass filters detects sharp changes by considering the local neighborhood only => Removing seasonal drift

• Threshold on ‘S1’, values below the threshold are tagged as events.

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Method 2: Highpass Method (cont.)

Results :

Drawback:- Does not make use of the inertia information

of the soil.

Method Precision Recall False Negatives

Basic 52.459% 64% 18

Highpass 51.28% 80% 10

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Method 3 : Delta Method• Considers Air Temperature and Soil Temperature

• Create E1 series for AT and E1 series for ST separately as discussed before

• Highpass filter on AT_E1 & ST_E1

=> AT_S1 & ST_S1

• Delta = AT_S1 – ST_S1 for all days.

• Set a threshold on the Delta series.

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Method 3: Delta Method (cont.)

Results :

Method Precision Recall False Negatives

Basic 52.459% 64% 18

Highpass 51.28% 80% 10

Delta 54.79% 85.106% 7

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Event detection for 12/13/2005 – 01/02/2006

Due to the inertia of the soil, ‘Delta method’ shows sharper negative peaks for event days.

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20 25

days

valu

e

Delta Highpass Known events (BWI weather station)

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Discussion

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Future work

• Implement “Online event detection”– Compute Basis vectors from historic data.– Load the ‘basis vectors’ and ‘threshold’ values on the motes.

• Apply technique for faulty sensor detection

• Detect localized events by forming clusters of motes with similar eigencoefficients.

• Consider variants of PCA (Gappy-PCA, online-PCA).

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Acknowledgements• Ching-Wa Yip 1

- PCA C# library and Discussions.

• Katalin Szlavecz 2 & Razvan Musaloui-E 3

– Domain expertise and data collection.

• Jim Gray 4 & Stuart Ozer 4

– Online database

1 : JHU, Dept of Physics & Astronomy2 : JHU, Dept of Earth and Planetary science3 : JHU, Dept of Computer Science.4 : Microsoft Research

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Future work

• Online event detection on the motes

• Apply this method for faulty sensor detection

• Detect localized events by forming clusters of motes with similar eigencoefficients.

• Consider incomplete days using Gappy-PCA.

• Explore incremental & robust PCA techniques.

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Training Set (Air Temp) • Seasons exhibit “Diurnal

Cycles” around their daily mean (DC component)

• Construct Zero-Mean Vectors for each Sensori for each day (remove DC Component)

0

5

10

15

20

25

30

0 6 12 18 24

Hour of the day

Air

Te

mp

era

ture

Winter Air Temp profile Summer Air Temp profile

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 6 12 18 24

Hour of the day

Mean

sub

tract

ed A

ir

Tem

pera

ture

Mean Profile Air Temperature

• Remove outliers using a

simple median filter to

build the training set X