Distributed fault tolerant event

International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.3, No. 2, May 2014
DOI :10.5121/ijscai.2014.3203 27
DISTRIBUTED FAULT-TOLERANT EVENT
DETECTION FOR NON-SYMMETRIC ERRORS IN
WIRELESS SENSOR NETWORKS
Nandita Das1, B. Victoria Jancee2 and S. Radha3
1PG Student, Department of ECE, SSN College of Engineering, Chennai, India
2Associate Professor, Department of ECE, St. Joseph‟s College of Engineering, Chennai,
India
3 Professor and Head, Department of ECE, SSN College of Engineering, Chennai, India
Abstract
Wireless sensor network (WSN) are powered by batteries to perform various sensing tasks in a given
environment. The measurements made by the sensors are sometimes unreliable and erroneous due to noise
in the sensor or hardware failure. For a large scale WSN to be economically feasible, it is important to
ensure that the faulty node does not affect the overall behaviour of the system. In this paper a binary fault-
tolerant event detection technique has been proposed for the non-symmetric errors and its performance has
been analysed. Theoretical analysis and simulation show that almost 97 percent of faults can be corrected
even when 10 percent sensor nodes are faulty.
KEYWORDS
Non-Symmetric Errors, Fault Tolerance, Event Detection
1. INTRODUCTION
WSN consists of network of autonomous sensors which are powered by batteries to perform
various sensing tasks in a given environment. These networks are used in various applications
like detection, estimation, monitoring, tracking etc [14],[19],[20].
Lot of effort has been made to develop the hardware and software architectures of sensor devices
as per the requirements of the wireless sensing applications. The various challenges and design
issues of WSN has been addressed in a number of works [14],[17],[18],[20]. In this work the
problem of event detection is addressed. Event detection in the inaccessible environment is one
important application. The measurements made by the sensor are sometimes unreliable and
erroneous due to noise in the sensor or hardware failure. It is therefore mandatory to employ a
fault-tolerance mechanism which can help avoid and correct the failure of any node and also,
which does not affect the overall performance and behavior of the system.

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2. EVENT REGION DETECTION MODEL
Sensor measurements in the operational regions are always spatially correlated while the sensor
faults are likely to be stochastically uncorrelated. Having these two mail assumption we put
forward an algorithm for event detection in a fault tolerant manner. To tackle faults in WSN, the
system should follow two main steps. The first step is event detection. It is to detect that a
specific functionality is faulty, and to predict that it will continue to function properly in the near
future. Fault recovery is the second step to enable the system to recover from faults.
Normally, an event, if it happens, should be detected as “event” by sensors at the location. The
faulty behaviour we consider occurs when the detection decision is converted to “no-event” due
to sensor fault or vice versa.
The first step in event region detection is for the nodes to determine which sensor reading is
interesting. Here interesting reading means the readings of interest. By using a threshold the node
can determine whether their reading corresponds to an event. The threshold can be specified with
a query or otherwise made available to the nodes during deployment.
A more challenging task is to disambiguate events from faults in the sensor readings since an
unusually high reading could probably correspond to both. It is assumed that sensor faults are
uncorrelated while the event measurements are correlated.
One of the key challenges in detecting event in a WSN is how to detect it accurately transmitting
minimum information providing sufficient details about the event. For this reason a fault-tolerant
event detection scheme has to be implemented. A possible solution can be given by providing
high degree of redundancy to compensate for the faulty nodes. However, the cost sensitivity and
energy limitations of sensor networks make such an approach undesirable. So a better and
efficient approach is adopted by collaboration between neighbouring nodes. This increases the
reliability of detection decisions. Here fault-tolerant event detection is addressed in context of
distributed binary detection for non-symmetric errors.
3. FAULT RECOGNITION
Standard Wireless sensor deployment experiences show that the data collected is shown to be
imprecise due to internal or external influences. So an early recognition of faults is necessary for
the effective operation of the network as a whole. In an environment where the event readings are
typically spread out geographically over multiple contiguous sensors, faults can be disambiguated
from the events by examining the correlation in the readings of nearby sensors.
The real situation at the sensor node to be modelled by a binary variable is given as Ti. This
variable Ti=0 if the ground truth is that the node is in normal region and Ti=1 if it is in an event
region. The real output of the sensor is mapped into a binary variable Si. This variable Si=0 if the
sensor measurement indicates normal value and Si=1 if it measures an unusual value. Thus there
can be four possible scenarios which are shown in the table below.

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Table 1. Possible scenarios of sensors
By implementing the fault recognition algorithm an estimate Ri can be determined of the true
readings Ti after obtaining information about the sensor readings of the neighbouring sensors.
4. DECISION SCHEMES FOR FAULT RECOGNITION
There are various decision schemes for fault recognition. Here three schemes are examined [1].
They are mentioned below.
1. Randomised decision scheme
2. Threshold decision scheme
3. Optimal threshold decision scheme
The detailed descriptions of these schemes are explained in the following sections.
Here the sensor fault probability p is assumed to be uncorrelated and non-symmetric.
P(Si=0|Ti=1)≠P(Si=1|Ti=0) (1)
If P(Si=0|Ti=1)=p1 and P(Si=1|Ti=0)=p2 then p is such that p=(p1+p2). Thus the probability
that there is no fault in the sensor is (1-p).
The binary model is obtained by applying threshold on the real-valued readings of the sensor. If
mn is the mean of normal reading and mf is the mean of event reading, then a reasonable
threshold for distinguishing between the two probabilities can be given as
Θ= 0.5(mn+mf) (2)
The errors due to sensor faults and environmental fluctuations are modelled as Gaussian
distribution with mean 0 and a standard deviation σ. The fault probability can thus be given as
p=Q((mf-mn)/2σ) (3)
Q function decreases monotonically, hence it can be said that the fault probability is low when
mean normal and the event readings are not sufficiently distinguishable or when the standard
deviation σ of the sensor measurement error is high. The assumption that the sensor failures are

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uncorrelated is a standard and reasonable assumption because these failures are primarily due to
imperfections in manufacturing and not a function of nodes spatial deployment.
4.1. Randomised decision scheme
Let each node i have N neighbours and evidence Ei(a,k) is that k of the neighbouring sensors
report the same binary readings „a’ as node i, while N-k of them report the reading ‘-a‟, then
P(Ri=a|Ei(a,k))= k/N (4)
The task of each sensor is to determine a value for Ri given information about its own sensor
reading Si and the evidence Ei(a,k) reading the readings of the neighbour.
Assuming when, the error is symmetric. Paak shows the statistics with which the sensor node
makes the decisions about whether or not to disregard its own sensor reading Si in face of the
evidence from its neighbour.
Paak = P(Ri=a|Si=b,Ei(a,k)) (5)
The above expression can also be written as
Thus the above expression can be simplified as follows
Each node could incorporate randomization and announce if its sensor readings is correct with
probability Paak.
Then a random number u is generated such that u belongs to (0,1) . If u<Paak , then Ri is set to Si
else Ri is set to -Si.
4.2. Threshold decision scheme
This scheme makes use of a threshold value θ which ranges from 0 to 1 i.e. 0<θ<1. If Paak > θ ,
then Ri is set to a and the sensor believes that the sensor reading is correct. If the metric is less
than threshold then the node decides that the sensor reading is faulty and sets Ri to -a.

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4.3. Optimal threshold decision scheme
The optimal decision threshold scheme also uses a threshold value. Here picking the threshold
value θ is equivalent to picking an integer kmin such that the node decodes to a value Ri=Si=a if
and only if at least kmin of its N neighbours report the same sensor measurements a.
5. ANALYSIS OF FAULT RECOGNITION ALGORITHM
The analysis of each of the Fault-Recognition scheme is given as follows.
5.1 Analysis of the Randomized Decision Scheme
Here an assumption is made that, if node i is in the event region, then all its neighbours are also in
event region. And, if i is not in an event region, neither are any of its neighbours in event region.
This assumption is valid everywhere except at nodes which lie on the boundary of an event
region.
When the error is symmetric, gk is the probability that exactly k of node i’s N neighbours are not
faulty gk is given as
Here j1 and j2 is integer. With the binary values possible for the three variables corresponding to
the ground truth Ti, the sensor measurement Si, and the decoded message Ri, there are eight
possible combinations. The conditional probabilities corresponding to these combinations are
useful metrics in analysing the performance of these fault recognition algorithms.
α gives the average number of errors after decoding.
The reduction in average number of errors is thus given as β gives the average number of sensor
faults corrected by the Bayesian fault recognition algorithm.
A related metric is γ, which gives the average number of faults uncorrected.

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The Bayesian fault recognition algorithm has one drawback, though it can help us correct sensor
faults, it may introduce new errors if the evidence from the neighbouring sensors is faulty. This
effect can be captured by the metric δ, the average number of new errors introduced by the
algorithm.
5.2 Analysis of the Optimal Threshold Decision Scheme
In the optimal threshold decision scheme with a threshold value θ is equivalent to picking an
integer kmin such that node i decodes to a value Ri=Si=a if and only if at least kmin of its N
neighbours report the same sensor measurement a.
The optimal threshold value which minimizes α , the average number of errors after decoding , is
θ =(1-p). this threshold value corresponds to kmin = 0.5N.
The performance metrics for the Optimal threshold decision scheme are listed below.
α : the average number of errors after decoding.
β : the average number of sensor faults corrected by the Bayesian fault recognition algorithm
γ : gives the average number of faults uncorrected.
δ : the average number of new errors introduced by the algorithm.

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5.2 Analysis of the Optimal Threshold Decision Scheme with Non-Symmetric Error
When the error is non- symmetric, gk is the probability that exactly k of node i’s N neighbours are
not faulty gk is given as
6. SIMULATIONS AND RESULTS
Some experiments to analyse the performance of the fault recognition algorithms. The simulation
results of the randomized decision scheme and the optimal threshold decision scheme are
analysed in detail.
The scenario consists of n=1024 nodes placed in a 32X32 square grid of unit area. The
communication radius is set to so that each node can communicate with its immediate
neighbour in each cardinal direction. All sensors are binary: they report a “0” to indicate no event
and a “1” to indicate there is an event. Thus each sensor has an independent probability of
reporting a “0” or “1” or vice versa.
In figure 1, it is seen that, for p<0.1 (10 percent of the nodes being faulty on average), over 75
percentage of the fault can be corrected. However, this algorithm has a setback that, though it can
correct sensor faults, it may introduce new errors if the evidence from the neighbour is faulty.
Hence the number of new errors introduced δ is seen to increase steadily with the fault rate and
starts to affect the overall reduction in error significantly after about p=0.1. From the figure 2, we
can conclude that when the number of neighbourhood size is increased, then, for p<0.1, more
than 75 percentage of fault can be corrected and the number of errors introduced can be reduced
relatively.
6.1. Randomised Decision Scheme for Symmetric Error
The performance metrics for the randomized decision scheme with two different neighbourhood
sizes and symmetric error has been analysed with respect to the sensor fault probability.The
figures below shows the various metrics with respect to the sensor fault probability.

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Figure 1. Metrics of randomized decision scheme for symmetric error (N=4)
Figure 2. Metrics of randomized decision scheme for symmetric error (N=8)

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6.2 Optimal threshold decision scheme for symmetric error
In the optimal threshold decision scheme with a threshold value θ is equivalent to picking an
integer kmin such that node i decodes to a value Ri=Si=a if and only if at least kmin of its N
neighbours report the same sensor measurement a.
The optimal threshold value which minimizes α, the average number of errors after decoding, is θ
=(1-p). This threshold value corresponds to kmin = 0.5N. The optimal threshold value which
minimizes α, the average number of errors after decoding, is θ=(1-p). This threshold value
corresponds to kmin = 0.5N.
Here, if k>kmin of its neighbour and also read the same value, the node decides on Ri=a, thus the
Paak term from (9) – (12) can be replaced by a step function.
Figure 3. Metric of optimal threshold decision scheme for symmetric error (N=4)
The most significant way in which the simulations differ from theoretical analysis is that, the
theoretical analysis ignores edge and boundary effects. At the edge of the deployed network, the
number of neighbours per node is less than that in the interior and, also, the nodes at the edge of
an event region are more likely to show erroneous reading if their neighbours provide wrong
information. Such boundary nodes are likely to be sites of new error introduced by the fault
recognition algorithm.

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From the figure 3, it can be inferred that the number of new errors introduced in the optimal
threshold decision algorithm is less than that of the randomized decision scheme. Thus it can be
concluded that the best policy for each node is to accept its own sensor reading if and only if at
least half of its neighbours have the same reading. This eases out the sensors work as it can help
the sensor perform the optimal decision even without having to calculate the sensor error
probability.
6.3. Optimal threshold decision scheme for non-symmetric errors
It is seen that the optimal threshold decision scheme is better than the randomized decision
scheme. So implementing this scheme for the binary event detection with non-symmetric errors
shows notable changes.
In the figure 4, it is seen that, for p<0.1 (10 percent of the nodes being faulty on average), more
than 97 percentage of the fault can be corrected. However, this algorithm has a setback that,
though it can correct sensor faults, it may introduce new errors if the evidence from the neighbour
is faulty. Hence the number of new errors introduced δ is seen to increase steadily with the fault
rate and starts to affect the overall reduction in error significantly after about p=0.1.
Figure 4. Metrics of optimal threshold decision scheme for non-symmetric error (N=4)

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7. CONCLUSIONS
The randomised decision scheme and the optimal threshold decision scheme are thoroughly
analysed. And the analysis showed that the optimal threshold decision scheme has a better
performance in terms of minimising the error, and also, it introduced very lesser number of new
errors (due to faulty evidence from the neighbouring sensors). It has also been observed that, in
the optimal threshold decision scheme, the probability of detection error reduces if the number of
neighbourhood nodes taken under consideration for the decision making process is increased. In
the event detection technique for the non-symmetric error, more than 97 percent of faults can be
corrected even when 10 percent sensor nodes are faulty. The limitation here is that the number of
new error introduced is seen to increase steadily. In some practical applications like that of the
real life environment monitoring, the chances of errors to be symmetric is very rare
because errors are always random in nature. In such scenarios, the technique of the fault-tolerant
event detection for the non-symmetric errors can be applied.
ACKNOWLEDGEMENTS
The author would like to thank the co-authors for their constant support and innovative ideas and
also their willingness to share the knowledge.
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