Model Based Event Detection in Sensor Networks
Jayant Gupchup, Andreas Terzis, Randal Burns, Alex Szalay
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Outline• Motivation
• Data and Model
• Experiments and Results
• Discussion
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Event starts
Detect Event
Increase Sampling Frequency/Trigger
Alarms
Event ends
Return to steady behavior
Data Sampling in WSNs- Most environmental monitoring networks
today sample at fixed frequencies
- The failure of fixed frequency sampling- High Frequency: Generates large volumes
of measurements- Low Frequency: Misses temporal transients
- Solution: Adaptive Sampling based on the ability to detect events of interest- Benefits
- Less but more “interesting” data- Conserve energy- Trigger alarms- Event-based querying in the back-end
database
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Rain Event Non-Event Days
-5
0
5
10
15
20
0 24 48 72 96
hours
Air
Tem
pera
ture
(cel
sius
)Sample Event
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Solution Outline• Model observed phenomena using
Principal Component Analysis (PCA)
• Project original measurements on to a feature space– Benefit: reduces dimensionality
• Look for measurements deviating from average/expected behavior in the feature space
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First Principal Component
Variable #1
Var
iabl
e #2
X : Points in the original spaceO : Projection on PC1
Principal Component Analysis
• PCA : Finds axes of maximum variance in the collected data
• Reduces original dimensionality– Example: 2
variables 1 variable
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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
hoursM
ean
subt
ract
ed A
ir te
mp
(Cel
sius
)
observed Temp. PCA reprojection Temp.residuals (absolute)
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Specific Application• LifeUnderYourFeet:
Environmental Monitoring network for soil moisture
• Deployment details– 10 MICAz Sensors
• Air Temperature (AT)• Soil Temperature (ST)• Soil Moisture• Light intensity
– Deployed for a period of a year
• Goal: Detect significant rain events
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Why not Soil Moisture ?
Reaction to event
Reaction to event
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Air Temp vs. Soil Temp
-6
-4
-2
0
2
4
6
0 5 10 15 20 25
hour
tem
pera
ture
(cel
sius
)
air temperature profile soil temperature (X20 scaleup)
Notice the phase lag for Soil Temperature
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Data Preparation• Build model for Air 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) 144]
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40
50
60
70
80
90
100
110
0 30 60 90 120
Principal Components
% v
aria
nce
cove
red
air temperature soil temperature
Basis1-4 cover 90.95%
Number of PCA basis required
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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
norm
alie
d ai
r te
mpe
ratu
re
eigenvector1 eigenvector2
Eigenvector1 Is the
Diurnal cycle
Soil Temperature eigenvectors (basis vectors)
-0.15-0.1
-0.050
0.050.1
0.150.2
0.25
0 5 10 15 20 25
Hour of day
Norm
aliz
ed s
oil
tem
pera
ture
eigenvector1 eigenvector2
similarity eigenvector1 for ST
&eigenvector2 for AT
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Event Detection 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– Uses the inertia of the soil and seasonal drift
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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
10 sensors
First Basis Vector (PC1)
1 day
• Apply threshold on E1 seriesTag values below the threshold as events
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Method 2 : Highpass Method
• Again, considers only Air Temperature
• Apply highpass filter on E1 series S1 series
• Highpass filter detects sharp changes by focusing on a limited time window removes seasonal drift
• Apply threshold on S1 series– Tag values below the threshold as events
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Method 3 : Delta Method• Considers Air Temperature (AT) and Soil Temperature
(ST)
• Create E1 series for AT and ST
• Apply Highpass filter on E1,AT & E1,ST S1,AT & S1,ST
• Compute Delta = S1,AT -S1,ST for all days
• Set a threshold on the Delta series
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Evaluation• Data Set
– Test Period : 225 days between September, 2005 – July, 2006
– 48 major rain events occurred during this period
• Reported by the BWI weather station
• Evaluation metrics– Precision (true positives)– Recall – Number of false negatives
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ResultsMethod Precision Recall False Negatives
Basic 52.459% 64% 18
Highpass 51.28% 80% 10
Delta 54.79% 85.106% 7
• Method shortcomings- Does not consider seasonal drift (Basic)- Does not use the inertia information of the soil (Basic, Highpass)
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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.
-20-15-10-505
10152025
0 5 10 15 20 25
days
valu
e
Delta Highpass Known events (BWI weather station)
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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
• Detect localized events by forming clusters of motes with similar eigen-coefficients
• Apply technique for faulty sensor detection
• 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
Tem
pera
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
Mea
n su
btra
cted
Air
Tem
pera
ture
Mean Profile Air Temperature
• Remove outliers using a simple median filter to build the training set X
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