FIND: Faulty Node Detection
for Wireless Sensor Networks
Shuo Guo, Ziguo Zhong and Tian He
University of Minnesota, Twin Cities
Background
 Importance of fault detection in WSNs
• Node failures => performance degradation
 Two types of faults
• Function fault
 Crash of nodes, packet loss, routing failure or
network partition
Shuo Guo@University of Minnesota
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Related Work
 Function faults





Q. Cao, et. al, Declarative Tracepoints in SenSys’08
M. Khan, et. al, DustMiner in SenSys’08
J. Yang, et.al, Clairvoyant in SenSys’07
V. Krunic, et.al, NodeMD in MobiSys’07
N. Ramanathan, et.al, Sympathy in SenSys’05
Shuo Guo@University of Minnesota
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Background
 Importance of fault detection
 Two types of faults
• Function fault
 Crash of nodes, packet loss, routing failure or
network partition
• Data fault
 Behaves normally except for sensing results
Shuo Guo@University of Minnesota
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Related Work
 Function faults





Q. Cao, et. al, Declarative Tracepoints in SenSys’08
M. Khan, et. al, DustMiner in SenSys’08
J. Yang, et.al, Clairvoyant in SenSys’07
V. Krunic, et.al, NodeMD in MobiSys’07
N. Ramanathan, et.al, Sympathy in SenSys’05
 Data faults
 M. Ding, et.al, Localized Fault-Tolerant Event Boundary Detection in
Sensor Networks. In INFOCOM’05
 L. Balzano, et.al, Blind Calibration of Sensor Networks. In IPSN’07
 V. Bychkovskiy, et.al, A Collaborative Approach to In-Place Sensor
Calibration. In IPSN’03
 J. Feng, et.al, Model-Based Calibration for Sensor Networks. In IEEE
Sensors, 2003.
Shuo Guo@University of Minnesota
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Related Work
 Outlier detection
• Identify readings numerically distant from the rest
 After-deployment calibration
• Find a mapping function that maps faulty readings
into correct ones (Y=aX+b)
 Limitations
• Assumptions on data distribution
• Mapping functions may not exist
Shuo Guo@University of Minnesota
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Our Work
 Objective: find a blacklist of possible faulty
nodes, in order of their probability of being faulty
• Node locations are available
• Generally monotonic sensing readings over
distance, can have violations locally, but general
trend holds
• No longer assume any mathematical model for
reading-distance relationship
• No longer assume any function to map faulty
readings into correct ones
• Detect both random and biased faulty readings
Shuo Guo@University of Minnesota
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Node Sequences and Ranks
 Node sequence
RSS: Received Signal Strength
• A complete node list of node IDs sorted by reading
(e.g., RSS), or physical distance from targets
 Rankings
• The rank a node appears in a node sequence
1
physical distance-based sequence:1243
2
RSS-based node sequence: 1243 2413
Node 1’s ranking in 1243 is 1
-50dBm -55dBm
-62dBm
4
-60dBm
3
-65dBm
Node 1’s ranking in 1243 is 1
Node 1’s ranking in 2413 is 3
Shuo Guo@University of Minnesota
Ranking
Difference
8
Main Idea
 Find mismatch between RSS-based and
physical distance-based rankings
1
2
4
3
Events Distance RSS
1243
2314
4123
Ranking Difference
2431
2341
4213
Total:
1 2 3
4
3
1
1
5
1
1
0
2
1
0
1
2
1
0
0
1
1. Unknown target locations?
Estimate distance sequences from RSS-based sequences?
2. Why ranking difference?
3. How many nodes are faulty, given ranking differences?
Shuo Guo@University of Minnesota
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Sequence Estimation
 Estimate physical distance-based sequence ŝ
from RSS-based sequences s
• Map Division: find =
consisting of
all possible distance-based sequences
• Maximum A Posterior (MAP) estimation
N-node
Network
N! Possible Given Topology
Sequences
small subset
O(N4)
ŝ
s
Shuo Guo@University of Minnesota
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Map Division
 Divide map into subareas identified by a unique
node sequence indicating distance information
distance-based sequence
2
2 1
1
distance-based sequence
1 2
Shuo Guo@University of Minnesota
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Map Division
 Divide map into subareas identified by a unique
node sequence indicating distance information
2
1
V  {s1 , s2 ,..., sM }
1243 2134
1423
2314
4123
4
3241
4312
34213
Shuo Guo@University of Minnesota
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Sequence Estimation
 Estimate physical distance-based sequence ŝ
from RSS-based sequences s
• Map Division: find all possible distance-based
sequences =
• Maximum A Posterior (MAP) estimation
N! Possible
Sequences
N-node
Network
subset
s
Shuo Guo@University of Minnesota
ŝ
13
MAP Estimation (1)
 Estimate physical distance-based sequence ŝ
from RSS-based sequences s
V=
Find s V maximizes
i
Pr(s | si ) Pr(s )
i
Ai
Pr(s ) 
i A
Ai : the area of subarea i
A : the total sensing area
Shuo Guo@University of Minnesota
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Main Idea
 Find mismatch between RSS-based and
physical distance-based rankings
1
2
4
3
Events RSS
2431
2341
4213
Ranking Difference
Distance
1243
2314
4123
Total:
1 2 3
4
3
1
1
5
1
1
0
2
1
0
1
2
1
0
0
1
1. Unknown target locations?
DONE!
Estimate distance sequences from RSS-based sequences?
2. Why ranking difference?
3. How many nodes are faulty, given ranking differences?
Shuo Guo@University of Minnesota
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Why ranking difference?
 Average ranking difference is a provable
indicator of possible data faults
 Theorem 1: A node is faulty if its average
ranking difference is above a bound B given by
• N: Total number of nodes
• Ne: Total number of faulty nodes
• μe: Average ranking difference of faulty nodes
Shuo Guo@University of Minnesota
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Why ranking difference?
 Theorem 2: Nodes with larger average ranking
difference have higher probability of being faulty
Sorting by ranking differences
gives correct order in likelihood of
being faulty nodes
Theorem 1
Theorem 2
Ranking Difference
1
2
3
4
3
1
1
Total: 5
1
0
1
2
1
0
0
1
1
1
0
2
High
Sort in descending order of
ranking differences:
4
1
2
3
probability of being faulty
Shuo Guo@University of Minnesota
Low
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Why ranking difference?
 Theorem 2: Nodes with larger average ranking
difference have higher probability of being faulty
Theorem 1
Theorem 2
 : defective rate
α=25%
1
α=75%
1 2 4
α unknown??
Sorting by ranking differences
gives correct order in likelihood of
being faulty nodes
High
Sort in descending order of
ranking differences:
4
2
1
3
probability of being faulty
Shuo Guo@University of Minnesota
Low
18
Main Idea
 Find mismatch between RSS-based and
physical distance-based rankings
1
2
4
3
Events RSS
2431
2341
4213
Ranking Difference
Distance
1243
2314
4123
Total:
1 2 3
4
3
1
1
5
1
1
0
2
1
0
1
2
1
0
0
1
1. Unknown target locations? DONE!
Estimate distance sequences from RSS-based sequences?
2. Why ranking difference? DONE!
3. How many nodes are faulty, given ranking differences?
Shuo Guo@University of Minnesota
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Detection Algorithm
K
1
High
Theorem 1
Blacklist
2
3
4
5
6
7
8
9
ranking difference
probability of being faulty nodes
Low
D(nk )  B
Update
Check
D(nk )  B
Yes!
Add next node
Shuo Guo@University of Minnesota
Stop
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Practical Issues
 Detection in noisy environments
Distance-Based
1
2
3
4
5
6
7
8
9
RSS, Noise Free
1
2
3
4
5
6
7
8
9
RSS, with Noise
1
2
3
4
5
6
7
8
9
• Increases ranking differences of normal nodes
Remove nodes from blacklist if their ranking
difference is close to that of normal nodes
Shuo Guo@University of Minnesota
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Practical Issues
 Simultaneous events elimination
1
2
4
3
Radio signal : sum of RSS
• Detected sequence no longer matches with any
distance sequence
Remove sequences with short Longest Common
Subsequence (LCS)
Shuo Guo@University of Minnesota
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Practical Issues
 Subsequence estimation
1
-50dBm
4
-60dBm
2
-55dBm
3
???
• Complete RSS-based node sequences unavailable
Use also truncated distance-based subsequence in
mapping process
Shuo Guo@University of Minnesota
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Evaluation
 Two test-bed experiments
• Radio signal: 25 nodes recording RSS, 35m×35m
map, R=25m
29,39 and 49 events
Shuo Guo@University of Minnesota
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Evaluation
 Two test-bed experiments
• Radio signal: 25 nodes recording RSS, 35m×35m
map, R=25m
29,39 and 49 events
49 events
19 events
Avg.
Shuo Guo@University of Minnesota
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Evaluation
 Two test-bed experiments
• Radio signal: 25 nodes recording RSS, 35m×35m
map, R=25m
29,39 and 49 events
19 events
Shuo Guo@University of Minnesota
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Evaluation
 Two test-bed experiments
• Radio signal: 25 nodes recording RSS, 35m×35m
map, R=25m
• Acoustic signal: 20 nodes recording timestamp,
5m×6m map, 18 events
Shuo Guo@University of Minnesota
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Evaluation
 Simulations
• 100 nodes, 250m×250m map, 50 events, R=25m
•
where
With Noise
Noise Free
Shuo Guo@University of Minnesota
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Summary
 FIND detects faulty nodes by assuming only
monotonic sensing readings over distance
 Ranking difference is a provable indicator of
possible faulty nodes
 Detection algorithm finalizes blacklist given
node list ordered by ranking difference
 5% false positive rate and false negative
rate can be achieved in most noisy
environments
Shuo Guo@University of Minnesota
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Preliminary Experiments
EVENT 1
RSS vs. Distance
49 sensor nodes, 49 events
Shuo Guo@University of Minnesota
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Preliminary Experiments
EVENT 1
EVENT 2
RSS vs. Distance
49 sensor nodes, 49 events
Shuo Guo@University of Minnesota
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Preliminary Experiments
EVENT 1
Average of 49 Events
Y = f(x)??
Large Variance!
EVENT 2
RSS vs. Distance
The monotonicity assumption is more accommodating to real
world environments than the assumption based on a more
specific model.
Shuo Guo@University of Minnesota
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Evaluation
 Simulations
• 100 nodes, 250m×250m map, 50 events, R=25m
•
where
α sensitivity: α is changed from 25% to 400% of true value
4α
0.25α,0.5α, α, 2α
Shuo Guo@University of Minnesota
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Detection Algorithm
 Given a node list {n1 , n2 ,...nN } in descending order
of ranking differences, find k such that {n1 , n2 ,...nk }
are best estimation (blacklist) for faulty nodes.
Theorem 1
D(nk )  B
Theorem 2
Pr(ni is f aul t y） Pr（ni 1 is f aul t y）
 Starting from n1 , add nodes into blacklist one by one
 Update Ne , e , B , after adding a new node
 Stop if D(nk )  B no longer holds
Uniqueness proved!
Shuo Guo@University of Minnesota
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MAP Estimation (2)
How to calculate
si
s
Pr(s | s )
i
1
2
3
4
5
1
K
2 6
3
5
( 6)Pr(
s ' | s' )
faulty
i
N
s'
i
s'
6
L
4
+
1
2
3
4
5
7
8
9
1
2
3
5
4
7
8
9
…
5 faulty
4 faulty
 : defective rate
?
7
7
8
9
distance-based
9 RSS-based
(1 6)( normal
)(LK ) Pr(s '' | s'')
i
3 4N 5 faulty
8
s''
i
s ''
1 2 7 8 9
1 2 7 8 9
Subsequence Matched, Stop!
Shuo Guo@University of Minnesota
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MAP Estimation (1)
 Estimate physical distance-based sequence ŝ
from RSS-based sequences s
V=
Find s V maximizes
i
Pr(s | si ) Pr(s )
i
Ai
Pr(s ) 
i A
Ai : the area of subarea i
A : the total sensing area
Shuo Guo@University of Minnesota
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Map Division
 Divide map into subareas identified by a unique
node sequence indicating distance information
2
1
1243 2134
1423
2314
4123
4
V  {s1 , s2 ,..., sM }
Size of V = 8 << 4! = 24
3241
4312
34213
s
Shuo Guo@University of Minnesota
ŝ
37
MAP Estimation (2)
How to calculate
si
s
Pr(s | s )
i
1
2
3
4
5
1
K
2 6
3
5
( )Pr(s ' | s' )
i
N
+
6 faulty
s'
i
s'
6
L
4
7
8
9
distance-based
7
8
9
RSS-based
(1 )(  )(LK ) Pr(s '' | s'')
i
N
6 normal
1
2
3
4
5
7
8
9
1
2
3
5
4
7
8
9
…
5 faulty
 : defective rate
?
4 faulty
s''
i
s ''
1 2 7 8 9
1 2 7 8 9
Subsequence Matched, Stop!
Shuo Guo@University of Minnesota
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