Spatiotemporal Correlation Based Fault-Tolerant Event Detection in Wireless Sensor Networks

Abstract

Reliable event detection is one of the most important objectives in wireless sensor networks (WSNs), especially in the presence of faulty nodes. Existing fault-tolerant event detection approaches usually take the probability of faulty nodes into account and fusion techniques to weaken the influence of faulty readings are usually developed. Through extensive experiments, we discover a phenomenon that event detection accuracy degrades quickly when the faulty sensors ratio reaches a critical value. This problem has not drawn enough attention and a solution to the problem is our concern. In this paper, a spatiotemporal correlation based fault-tolerant event detection scheme (STFTED) is proposed, which leverages a two-stage decision fusion and spatiotemporal correlation to improve the event detection quality. In the low-level local stage, a location-based weighted voting scheme (LWVS) is developed to make decision fusion locally on each sensor node, which is based on neighboring nodes and the geographical distributions of two decision quorums. In the high-level global stage, a Bayesian fusion algorithm is adopted to reach a consensus among individual detection decisions made by sensor nodes. Simulation results demonstrate that the proposed approach is highly effective and a better quality of event detection can be obtained compared with the optimal threshold decision schemes (OTDS).

1. Introduction

Wireless sensor networks (WSNs) have been of great interest in recent years because of their various applications to environment monitoring [1, 2], battlefield surveillance [3], system health management [4–6], and so forth. One of the critical tasks in designing a WSN is to monitor, detect, and report useful events of interest in the network domain. A sensor node collects data from the environment by utilizing its sensing device [7, 8] and then preliminarily processes the raw data through the network to extract meaningful information before transmitting it to a fusion center, where the final decision is made on whether an event has happened or not. The crucial properties of event detection algorithms are the computational overhead (in terms of processing and memory usage) and scenario-dependent applicability. The overall goals of event detection algorithms are trade-off between minimizing communication overhead [9, 10] (and thus energy expenditure [11]) and maximizing the detection accuracy [12, 13].

In the event detection applications, nodes are responsible for determining whether a particular event of interest occurs in their sensing ranges. Theoretically, all sensor nodes in the event region should report the sensed information to base station or sink node. In fact, the sensor readings may be unreliable due to the noise interference or hardware failures and some erroneous local decisions derived from faulty sensor readings may be made. The sensor can provide a false alarm, which is a decision indicating an event occurred when it did not. The situation of a missed alarm is a decision indicating the absence of event when the event occurs. Both false alarms and missed alarms will reduce the detection quality. One approach to improve the ability of event detection is using fault-tolerant event detection schemes.

Fault-tolerant event detection algorithms are designed in a number of recent works [14–25], which can be divided into two categories. One is the faulty node measurement identification case and the goal is to identify the faulty nodes by comparing measurement from sensor nodes directly and making decisions [14–19]. The other is the case of decision fusion, which determines whether it is a faulty node by distinguishing the opposite conclusion with the majority [20–25]. Extensive experiments have been conducted to compare several classic algorithms. The results indicated that the quality of event detection degrades rapidly when the sensor's fault ratio reaches a critical value.

Many challenges exist to detect event efficiently. Firstly, it is challenging to develop a scheme for reliably detecting the interesting event under the circumstance of faulty nodes due to the fact that the node's reading is unreliable. Secondly, the quality of event detection degrades rapidly, which motivates us to optimize the fault-tolerant event detection scheme. Meanwhile, another challenge issue is to design a model which can characterize the spatial correlation of different scenarios.

To overcome the challenges, we propose a spatiotemporal correlation based fault-tolerant event detection scheme, called STFTED, which leverages a two-stage decision fusion and exploiting spatiotemporal correlation of sensor nodes. The low-level stage is conducted locally inside the sensor nodes with a location-based weighted voting scheme (LWVS). LWVS exploits the spatiotemporal correlation of sensor nodes, which is based on neighboring nodes and the geographical distributions of two decision quorums. The high-level stage aims at optimizing LWVS to solve the problem that the quality of event detection degrades rapidly. The high-level global stage employs a Bayesian fusion algorithm to reach a consensus among individual detection decisions made by sensor nodes.

The contributions of this paper are summarized as follows:

• (i)

We propose a location-based weighted voting scheme, called LWVS, in the low-level local stage, exploiting the spatiotemporal correlation of sensor nodes.

(ii)

We propose a spatiotemporal correlation based fault-tolerant event detection scheme, called STFTED, to optimize LWVS in the high-level global stage, which can detect event efficiently without rapid quality degrading and can be applied to different scenarios.

(iii)

We conduct extensive simulations to evaluate the performance of the proposed algorithms. The results demonstrate the effectiveness of the proposed algorithms.

The remainder of the paper is organized as follows. Section 2 introduces some prior works in event detection. In Section 3, the system model and problem statement are briefly described. Section 4 presents the spatiotemporal correlation based fault-tolerant event detection scheme. Simulation results are shown in Section 5 and conclusions are made in Section 6.

2. Related Work

Many approaches of event detection in WSNs have been studied and the central concern is to improve the detection accuracy [15, 26–29]. The detection accuracy is limited by the amount of noise associated with the measurement and the reliability of sensor nodes. Sensor nodes are usually low-end inexpensive devices. Sometimes the sensor nodes exhibit unreliable behavior and sensor readings may make erroneous local decisions.

Existing approaches on event detection with faulty data can be divided into two categories, that is, 0/1-event based method and scalar-measurement based method. The first category determines whether a sensor node is faulty by answering a specific question: the event occurs or not. If a node makes an opposite decision with the majority, it is labeled as faulty. Since approaches in this category detect a faulty node by its “ $\mathrm{0}/\mathrm{1}$ ” to the event occurrence, they are called “ $\mathrm{0}/\mathrm{1}$ event-based methods.” Decision fusion is an example of “ $\mathrm{0}/\mathrm{1}$ event-based methods” [20]. When an event occurs, each sensor observes it through a measured signal and makes a local decision which is a binary value. A global decision is made by combining the local decisions in a center by fusion techniques. Then faulty nodes can be determined according to whether the local decision is the same as the global one. To make the above strategy more applicable to WSNs, a distributed version of decision fusion based on Bayesian theorem was proposed in [21]. In the algorithm, each sensor node only communicates with its neighbors and collects their binary decisions. If most neighbor nodes have the same as it, the node's sensor is considered to be correct. The distributed scheme in [21] is further improved in [22] by using part of neighbor nodes in fusion so as to further decrease the energy consumption and communication congestion. Node may become faulty with time and nodes of a heterogeneous sensor network may have different operational capabilities and accuracy performances, Ould-Ahmed-Vall et al. [23] presented a fault-tolerant event detection scheme, which allows nodes to detect erroneous local decisions through leveraging the local decisions reported by their neighbors.

With its simplicity, using “ $\mathrm{0}/\mathrm{1}$ event-based methods” has some limitations when making a decision. Each node needs to compare current sensor readings to give a local answer with a threshold that is difficult to be correctly determined. The local decision is also the preprocessing results of the actual measured data and detection over binary local decision means the second estimation. The second category, that is, scalar measurement-based method, does not rely on detecting over binary local decision but comparing the measurement from some sensor nodes directly. A node is identified as faulty if its measurement is statistically different from others, particularly from the neighborhood, or does not match what it is supposed to be. For this category of event detection, the measurement from each node is a scalar. For example, a distributed method [14] was proposed to detect faulty nodes by determining if the difference between a node's reading and its neighbors' readings is significant, which is based on the premise that data collected from nodes, particularly nodes in the neighborhood, follow the same distribution. Since many sensing readings in sensors networks attenuate over distance that is not to be sneezed at, the assumption in [14] may be untenable. Therefore, a method which works for systems where the measured signal attenuates with distance is proposed by Guo et al. to detect nodes with data faults in [19]. In Guo's method, a node is considered faulty if there is a significant mismatch between the sensor data rank and the distance rank.

In addition, the event detection algorithms have strong scenario-dependence in WSNs. Considering different scenarios, it is necessary to exploit spatiotemporal characteristics of sensors to detect the emergence of event accurately (eliminating faulty readings) and quickly convey this information to the sink node [30] (i.e., the base station). The focus of this paper is not on data gathering or communicating. Here, works based on the spatiotemporal correlation are discussed. Several works have been done to improve fault-tolerant algorithms by exploiting the spatial correlation of sensors. For instance, a weighted model of node decision based on distance for event region fault-tolerant detection was proposed by Li et al. [24]. In [16], confidence levels of sensor nodes were used to adjust the threshold for decision making and a moving average filter to fault tolerance. Besides, the geographical distribution of two decision quorums was taken into account for weighing neighbors' decisions [23]. There are also some cases which detect an event by using the spatiotemporal correlation, such as [29, 31, 32]. The three papers used a dynamic Markov random field model to model the spatiotemporal relationship of the evolving field and proposed a distributed algorithm to track the dynamic event regions.

The above approaches offer efficient methods to detect the event which is interfered by faulty sensor readings. However, they did not involve the problem about the quality of event detection. In monitoring applications, it is necessary to guarantee that nodes in the event region detect an event correctly. In our paper, a detailed analysis for the quality of event detection is carried out, and a solution to improve the quality is also proposed.

3. System Model and Problem Statement

This section provides an overview of our network model which contains some faulty nodes. It also covers the fault-tolerant event detection problem and the relationship between the quality of event detection and the ratio of faulty sensors.

3.1. Network Model

In the network model, each node has a sensor to detect the presence of an event by comparing the node's sensor readings with a fixed threshold. Considering that the presence of an event corresponds to a high sensor reading, a low reading indicates the absence of the event. The mean value of sensor reading in the presence of an event is $m_e$ , while in the absence of event it is $m_n$ . A fixed threshold value is given by $\varphi =(m_e+m_n)/\mathrm{2}$ . And a fault occurs when node decision is false alarm or missed alarm.

Define the following three binary variables which are similar to those in [21].

• (i)

$T_n(t)$ indicates the actual state of node n at t.

(ii)

$S_n(t)$ indicates the sensor decision of node n at t. It could be incorrect in the case of sensor failure.

(iii)

$R_n(t)$ indicates the estimate of the real value through the event detection algorithm of node n at t.

Thus, there are four possibilities for the node detective scenarios.

• (i)

The sensor correctly reports a normal reading: $S_n(t)=\mathrm{0}$ , $T_n(t)=\mathrm{0}$ .

(ii)

The sensor faultily reports a normal reading (missed alarm): $S_n(t)=\mathrm{0}$ , $T_n(t)=\mathrm{1}$ .

(iii)

The sensor correctly reports an unusual/event reading: $S_n(t)=\mathrm{1}$ , $T_n(t)=\mathrm{1}$ .

(iv)

The sensor faultily reports an unusual reading (false alarm): $S_n(t)=\mathrm{1}$ , $T_n(t)=\mathrm{0}$ .

In this paper, we assume that the sensor fault probability $p=P(S_n(t)\ne T_n(t))$ is uncorrelated and symmetric. The probability of detection error $p_n$ at node n is given by $p_n=P(S_n(t)=j\hspace{0.17em}|\hspace{0.17em}{T}_n(t)\ne j)$ and the probability of estimator detection error $p_e$ at node n is given by $p_e=P(R_n(t)=j\hspace{0.17em}|\hspace{0.17em}{T}_n(t)\ne j)$ . Here, j represents two situations in event detection, and $j=\mathrm{0}$ or $\mathrm{1}$ .

A sample scenario of the network model is shown as Figure 1. There is an event region with the interesting event occurrence. The above four possibilities of node detective scenarios are all included in this figure.

Figure 1

A typical sample scenario with uniformly distributed nodes shows some single-modality event occurred in an interesting region (enclosed inside the square with the bold line). “∗” denotes reporting an event, while “∘” denotes reporting no event, “□” denotes the missed alarm sensor, and “⊳” denotes the false alarm sensor.

3.2. The Fault-Tolerant Event Detection Problem

The problem is how to estimate $R_n(t)$ that minimizes the detection error probability, especially for the nodes in event region. Due to the high density in the network topology, spatial proximal sensor observations are highly correlated with the degree of correlation increasing with decreasing internode separation. The local decision of neighboring nodes, which are nodes within a fixed range r of n, the so called fault-tolerant neighbourhood, is used to estimate $R_n(t)$ .

Define the fault-tolerant neighborhood, ${\text{FTN}}_n$ , as the set of nodes that a node n takes into account in its fault-tolerant decision. For a fault-tolerant range of r, the neighborhood is given by ${\text{FTN}}_n=k\in \left\{d\left(n,k\right)<r\right\}$ , where $d(n,k)$ is the Euclidean distance between the nodes n and k. ${\text{FTN}}_n$ does not contain the node n itself which is at the center of ${\text{FTN}}_n$ .

Using the Abbreviations which are defined in the Summary of Notations for Analysis of Fault-Recognition, the problem is to find an estimation function that takes the values of the sensor states $S_n(t)$ as an input and $R_n(t)$ as an output that minimizes the probability of error $p_e$ . The optimal estimation function will be discussed in Section 4.

With the increase of faulty sensors, the percentage of nodes in the event region which detect the event is decreasing. Theoretically, the detection percentage can be enhanced via fault-tolerant algorithms. Through extensive experiments, we discover that reality does not match the theory. Although the number of faulty nodes is significantly reduced via fault-tolerant schemes, the number of faulty nodes in event region does not change obviously. It means that event detection performance is not improved dramatically. Taking the optimal threshold decision scheme (OTDS) proposed in [21] as an example, Figure 2 shows a snapshot of the result of a sample simulation run when $p=\mathrm{0.2}$ . Figure 3 presents the result after using OTDS. In contrast to Figure 2, the number of faulty nodes in the event region in Figure 3 does not decrease rapidly.

Figure 2

A snapshot of the result of a sample simulation run when $p=\mathrm{0.2}$ .

Figure 3

A snapshot of the result after OTDS.

With different fault-tolerant algorithms, a large number of simulation experiments are conducted to evaluate the relationship between the quality of event detection and the ratio of faulty sensors. A phenomenon is discovered that the quality of event detection degrades rapidly when the sensor's fault probability reaches a critical value. OTDS is taken as an example to recount this phenomenon. The result was obtained by averaging over 1,000 runs under the different sensor fault probability p, which is presented in Figure 4. It can be seen that the event detection percentage only reduces less than $\mathrm{5}\%$ when p changes from $\mathrm{5}\%$ to $\mathrm{20}\%$ and the event detection percentage was falling rapidly when p reached $\mathrm{20}\%$ . Nevertheless, the problem in the proposed approaches is much less serious. The proposed model addresses these problems in event region by employing a spatiotemporal correlation based fault-tolerant event detection scheme (STFTED) in Section 4.

Figure 4

The relationship between the quality of event detection and the ratio of faulty sensors.

4. Spatiotemporal Correlation Based Fault-Tolerant Event Detection (STFTED)

A spatiotemporal correlation based fault-tolerant event detection scheme (STFTED) is proposed in this section, which is constituted by two-stage decision fusion that addresses the above problems. The first-stage decision fusion is conducted locally inside the sensor nodes with a location-based weighted voting scheme (LWVS). LWVS is established based on neighbor nodes and the geographical distributions of two decision quorums. The second stage is carried out in a high level and incorporates a Bayesian fusion algorithm to make a decision among individual detection decisions made by sensor nodes. The basic idea of the approach is shown in Figure 5.

Figure 5

The general concept of the approach in a form of block-diagram: the first-stage fusion of event region detection is conducted locally inside the sensor nodes, while the second stage is carried out in a high level (e.g., in a cluster head or a gateway).

4.1. Location-Based Weighted Voting Scheme (LWVS)

Spatiotemporal correlation is one of the significant characteristics of WSNs. Supposing that the samples from nodes are temporally independent, there should be a heavily dense deployment of sensor nodes in order to achieve satisfactory coverage. As a result, multiple sensors record information about a single event in the sensor field. Due to the high density in the network topology, spatial proximal sensor observations are highly correlated with the degree of correlation increasing with decreasing internode separation. In [33], several key elements are investigated to capture and exploit the correlation for the realization of advanced efficient communication protocols. Taking a node n which is estimated as the decision source, the distortion increases as the increasing of the distance between the node n and the neighborhood node k. Assuming both nodes a and b are in ${\text{FTN}}_n$ , as the distance between these nodes increases, the distortion for the decision source n decreases. For example, a typical scenario can be shown in Figure 6 that node 1 be placed in the center of sensing field and the dotted line represents FTN₁. The value of $d(\mathrm{1,5})$ is minimum which means the spatial correlation between nodes $\mathrm{1}$ and $\mathrm{5}$ is higher than that with other nodes in FTN₁. A decision reported by nodes $\mathrm{4}$ and $\mathrm{7}$ is more reliable than the ones by nodes $\mathrm{2}$ and $\mathrm{3}$ . The reason is that if all nodes that report a decision of “ $\mathrm{1}$ ” are on one side of node $\mathrm{1}$ , it is conceivable that these nodes are at the border of the event region. In this case, node $\mathrm{1}$ may be outside of the event region and no event should be detected. On the other hand, if nodes from different sides of n report a decision of “ $\mathrm{1}$ ”, it is very likely that an event is also present at node $\mathrm{1}$ . This is especially true in the case of an event region.

Figure 6

The spatial correlation between nodes $\mathrm{1}$ and $\mathrm{5}$ is higher than that of other nodes in $\mathrm{F}\mathrm{T}{\mathrm{N}}_{\mathrm{1}}$ . A decision reported by nodes $\mathrm{4}$ and $\mathrm{7}$ is more reliable than a decision reported by nodes $\mathrm{2}$ and $\mathrm{3}$ .

Considering the correlation between nodes, a weighted model based on group node locations is defined. This model is a function of the geographical distribution of the decision group to which they belong. There are two decision groups $G_{\mathrm{0}}(n)=\{i\in {\text{FTN}}_n,n:S_i(t)=\mathrm{0}\}$ and $G_{\mathrm{1}}(n)=\{i\in {\text{FTN}}_n,n:S_i(t)=\mathrm{1}\}$ . $g_j$ is set as a weighted factor for the decision group $G_j(n)$ with $j\in \{\mathrm{0,1}\}$ . The weighted factor is defined as

$$\begin{array}{cc}& g_j\left(i\right)=\mathrm{1}-\frac{d\left(n,i_j\right)}{r}\hspace{1em}\left(i_j\in {\text{FTN}}_n\right),\end{array}$$

(1)

where n is the geographical centroid of nodes in $G_j(n)$ .

The likelihood test ratio is employed to develop this optimal estimation function that selects $R_n\left(t\right)=j$ , $j=\{\mathrm{0,1}\}$ . In the experiments, the presence or absence of an event is equal. Functions $G_{\mathrm{0}}(n)$ and $G_{\mathrm{1}}(n)$ are defined as follows:

$$\begin{array}{cc}& G_j\left(n\right)={\displaystyle \sum }{g}_j\left(i\right)\ln \left(\frac{\mathrm{1}-p_i}{p_i}\right)\hspace{1em}\left(\forall i_j\in {\text{FTN}}_n\right).\end{array}$$

(2)

Using this weight in the node location-based weighted voting scheme (LWVS), this scheme will provide the corresponding estimator of $R_n(t)$ by contrasting with the majority and m-out-of-n schemes used in [21].

Note that the estimator for LVWS is given by the following:

• (i)

Choose $R_n(t)=\mathrm{0}$ , if $G_{\mathrm{0}}(n)\ge G_{\mathrm{1}}(n)$ .

(ii)

Otherwise, choose $R_n(t)=\mathrm{1}$ , where $i\in {\mathrm{F}\mathrm{T}\mathrm{N}}_n$ .

Proof.

The likelihood ratio is given by

$$\begin{array}{cc}& \gamma =\frac{{\prod }_{S_i\left(t\right)=\mathrm{0}}{\left(\left(\mathrm{1}-p_i\right)/p_i\right)}^{g_{\mathrm{0}}\left(i\right)}}{{\prod }_{S_i\left(t\right)=\mathrm{1}}{\left(\left(\mathrm{1}-p_i\right)/p_i\right)}^{g_{\mathrm{1}}\left(i\right)}}={\displaystyle \prod }_i{\left(\frac{\mathrm{1}-p_i}{p_i}\right)}^{\left(\mathrm{1}-S_i\left(t\right)\right)g_{\mathrm{0}}\left(i\right)}{\left(\frac{p_i}{\mathrm{1}-p_i}\right)}^{S_i\left(t\right)g_{\mathrm{1}}\left(i\right)}.\end{array}$$

(3)

Since ${\left(\left(\mathrm{1}-p_i\right)/p_i\right)}^{g_j(i)}=e^{G_j(i)}$ , γ can be written in the following form:

$$\begin{array}{cc}& \gamma ={\displaystyle \prod }_i{\left(\frac{\mathrm{1}}{e^{G_j\left(i\right)}}\right)}^{S_i\left(t\right)}\left(e^{G_j\left(i\right)}\right)={\displaystyle \prod }_i{\left(e^{G_j\left(i\right)}\right)}^{\mathrm{1}-\mathrm{2}{S}_i\left(t\right)}=e^{{\sum }_i{G}_j\left(i\right)\left(\mathrm{1}-\mathrm{2}{S}_i\left(t\right)\right)}.\end{array}$$

(4)

When $\gamma >\mathrm{1}$ , which is equal to the weight sum of these node votes in ${\mathrm{F}\mathrm{T}\mathrm{N}}_n$ , the sum can be written as ${\sum }_i{G}_j\left(i\right)\left(\mathrm{1}-\mathrm{2}{S}_i\left(t\right)\right)={\sum }_{i\hspace{0.17em}|\hspace{0.17em}{S}_i(t)=\mathrm{0}}‍G_{\mathrm{0}}(i)-{\sum }_{i\hspace{0.17em}|\hspace{0.17em}{S}_i(t)=\mathrm{1}}‍G_{\mathrm{1}}(i)$ .

This corresponds to a weighted vote in favor of the hypothesis of $T_n(t)=\mathrm{0}$ .

4.2. Bayesian Based Fault-Tolerant Event Detection

In the low-level local stage, an estimator $R_n(t)$ of node n is given by LWVS which may not be equal to the real value $T_n(t)$ . This means the estimator of LWVS could be unreliable. A method in high-level global stage should be found to determine a value for $R_n(t)$ given information about the evidence from $\mathrm{F}\mathrm{T}{\mathrm{N}}_n$ . Two elements of $R_n(t)$ which are $\mathrm{0}$ and $\mathrm{1}$ to node n estimate the absence or presence of an event, while all nodes' real values are unknown and the prior probability of detection error p is known. Here the Bayesian theorem is used to found the probability of each instance belonging to a specific class. In Bayesian statistic, a probability can be assigned to a hypothesis between $\mathrm{0}$ and $\mathrm{1}$ under uncertainty circumstances. Then a hypothesis of $T_n(t)$ is given by the Bayesian formula. A threshold is given by the idea of voting. For instance, nodes' distribution is shown as in Figure 6. The values of $R_n(t)$ are shown as in Figure 7.

Figure 7

The estimator of nodes given by LWVS, $R_n(t)=\mathrm{1}$ , is depicted by dark-colored nodes.

The estimator of nodes $\mathrm{2}$ , $\mathrm{3}$ , $\mathrm{7}$ , and $\mathrm{5}$ is “ $\mathrm{1}$ ”, which is depicted by dark-colored nodes, and this group is expressed as $E(\mathrm{1,4})$ . Set the actual state $T_n(t)$ of node $\mathrm{1}$ to be “ $\mathrm{1}$ ”, and the prior probability of detection error of node $\mathrm{1}$ is p. The formula of total probability for node $\mathrm{1}$ is given by $P(R_{\mathrm{1}}(t)=\mathrm{1})=(\mathrm{1}-p)\times \mathrm{4}+p\times \mathrm{2}$ . Then, the probability of the hypothesis that the value of $R_{\mathrm{1}}(t)$ equals “ $\mathrm{1}$ ” is

$$\begin{array}{cc}& P\left(R_{\mathrm{1}}\left(t\right)=\mathrm{1}\hspace{0.17em}|\hspace{0.17em}E\left(\mathrm{1,4}\right)\right)=\frac{\left(\mathrm{1}-p\right)\times \mathrm{4}}{P\left(R_{\mathrm{1}}\left(t\right)=\mathrm{1}\right)}.\end{array}$$

(5)

Assume there are $k_n$ nodes whose $R_n(t)$ is “ $\mathrm{1}$ ”. Set the (symmetric) probability of detection error p as the prior probability. According to the law of total probability, when node n indicates the presence of an event, the formula of total probability of node n is given by

$$\begin{array}{cc}& \left(\mathrm{1}-p\right)k_n+p\left(N_n-k_n\right).\end{array}$$

(6)

Then the Bayesian formula of node $R_n(t)=\mathrm{1}$ can be obtained as

$$\begin{array}{cc}& P_{\mathrm{11}k}=P\left(R_n\left(t\right)=\mathrm{1}\hspace{0.17em}|\hspace{0.17em}E\left(\mathrm{1},k_n\right)\right)=\frac{\left(\mathrm{1}-p\right)k_n}{\left(\mathrm{1}-p\right)k_n+p\left(N_n-k_n\right)},\end{array}$$

(7)

in which $E(\mathrm{1},k_n)$ indicates the number of nodes whose value of $R_n(t)$ after LWVS is $\mathrm{1}$ . Following the main idea of voting, when $k_n\ge \mathrm{0.5}(N_n-\mathrm{1})$ the threshold θ minimizes the average number of errors after decoding [34]. Thus, the threshold is written as

$$\begin{array}{cc}& {\theta }_n=\frac{\left(\mathrm{1}-p\right)\left(N_n-\mathrm{1}\right)}{\mathrm{2}p+\left(N_n-\mathrm{1}\right)}.\end{array}$$

(8)

Note that the estimator for the stable event detection scheme is given by the following:

• (i)

Choose $R_n(t)=\mathrm{1}$ , if $P_{\mathrm{11}k}\ge \theta$ .

(ii)

Otherwise, choose $R_n(t)=\mathrm{0}$ , where $i\in {\mathrm{F}\mathrm{T}\mathrm{N}}_n$ .

According to the above analysis on fault-tolerant event detection, we propose a spatiotemporal correlation based fault-tolerant event detection scheme to improve the event detection accuracy. The algorithm is formally presented in Algorithm 1.

Algorithm 1: The spatiotemporal correlation based fault-tolerant event detection scheme (STFTED).

Input: $S_k(t)$ , $k\in {\mathrm{F}\mathrm{T}\mathrm{N}}_n$

Output: $R_n(t)$

(1)    group $S_k(t)$ into two teams

(2)    calculate $g_j(i)$ of all the neighbors of node n

(3)    calculate $G_j(n)$ of the two teams.

(4)    if   $G_{\mathrm{0}}(n)>G_{\mathrm{1}}(n)$   then

(5)     set $R_n(t)=\mathrm{0}$

(6)    else

(7)     set $R_n(t)=\mathrm{1}$

(8)     obtain $R_n(t)$ of all nodes in ${\mathrm{F}\mathrm{T}\mathrm{N}}_n$

(9)    end if

(10) count $k_n$ , the number of nodes whose value of $R_n(t)$ is $\mathrm{1}$ in ${\mathrm{F}\mathrm{T}\mathrm{N}}_n$

(11) calculate $p_{\mathrm{11}k}$ and of node n

(12) if   $p_{\mathrm{11}k}\ge \theta$   then

(13)  set $R_n(t)=\mathrm{1}$

(14) else

(15)  set $R_n(t)=\mathrm{0}$

(16) end if

5. Simulation

In this section, a set of simulation results are presented to analyze the features of the proposed fault-tolerant approach and evaluations are compared with the OTDS proposed in [21]. The scenario consists of $n=\mathrm{900}$ nodes uniformly deployed in a $\mathrm{70}\times \mathrm{70}$ square field. The communication range r determines which neighbors each node can communicate with. Every node only communicates with nodes in its fault-tolerant range. Suppose that the fault-tolerant range is in the communication range, which is set to $\mathrm{4}$ . All sensors have binary values: they report a “ $\mathrm{0}$ ” to indicate no event and a “ $\mathrm{1}$ ” to indicate an event. The faults are modeled by the uncorrelated, symmetric, Bernoulli random variable. Each node has an independent probability $p_n$ of detection error. Faulty nodes are randomly chosen based on p in the scenario. One sensed event is placed at the bottom left corner of the interesting region, and the sensing range is set to be a $\mathrm{10}\times \mathrm{10}$ square field. All simulation results are obtained by the average of 1,000 independent runs.

Figure 8 shows snapshots of the results of a sample simulation run with different p. The sensor nodes are depicted by “∘”, and the nodes detect an event “ $\mathrm{1}$ ”, which are indicated with “∗”. “⊲” represents a false alarm node and “□” means a missed alarm node (before the fault-tolerant scheme), while “·” indicates a node whose estimator (after the fault-tolerant scheme) is “ $\mathrm{0}$ ”. Thus, before the fault-tolerant scheme, nodes with both “⊲” and “∗” are nodes with false alarms, while nodes with both “□” and “∘” are nodes with missed alarms. In a snapshot of the results after the fault-tolerant scheme, nodes with both “·” and “⊲” are correctly detection nodes with no event “ $\mathrm{0}$ ”, and nodes with both “∗” and “□” are correctly detection nodes with no event “ $\mathrm{1}$ ”. Nodes of false alarms with “·” and nodes of missed alarms with “∗” are nodes whose errors are corrected. Some new errors are introduced by the fault-tolerant algorithm. The correctly detection nodes in the event region have no “∗” while the nodes out of the event be with “·”. It can be seen that most of the faulty nodes in the event region are corrected by this algorithm, but the number of uncorrected faulty nodes outside the region increased when p changed from $\mathrm{5}\%$ to $\mathrm{20}\%$ and further to $\mathrm{35}\%$ , while there are also some remaining errors and new introduced errors in this figure.

Figure 8

A snapshot of the result of a sample simulation run after the STFTED with different p.

Metrics defined in [21] are used to evaluate the proposed method by comparison with the OTDS proposed in [21] and the LWVS in the low-level stage, as mentioned in Section 4.

• (i)

Number of Errors Corrected. Number of original sensor errors corrected by using the algorithm.

(ii)

Number of Errors Uncorrected. Number of original sensor errors uncorrected by using the algorithm.

(iii)

Number of Errors Introduced by the Solution. Number of new errors introduced by the algorithm.

(iv)

Number of Errors after Decoding. Overall number of errors after using the algorithm.

Since there is a linear correlation between the average number of errors uncorrected and that of those corrected, we only discuss the average number of errors corrected. Currently, the event detective and event region ensuring are the most concerned among all environment monitoring issues. Here, we provide a new metric, the average number of event detection in event region, to show the ability of the event detection. Nodes in the event region and the proportion of correctly detected nodes are particularly discussed as the following equations:

$$\begin{array}{cc}& N_d=n\in \left\{S_n\left(t\right)=T_n\left(t\right)=\mathrm{1}\right\},\\ N_e=n\in \left\{S_n\left(t\right)\ne T_n\left(t\right)\right\},\\ N_c=n\in \left\{R_n\left(t\right)=T_n\left(t\right)\ne S_n\left(t\right)\right\},\\ N_i=n\in \left\{S_n\left(t\right)=T_n\left(t\right)\ne R_n\left(t\right)\right\}.\end{array}$$

(9)

Note that these different metrics are normalized by the network size. We set α, β, γ, and δ as parameters to evaluate the algorithm, which are defined as follows.

α: the normalized number of nodes correctly event detected:

$$\begin{array}{cc}& \alpha =\frac{N_d}{n\in \left\{T_n\left(t\right)=\mathrm{1}\right\}}.\end{array}$$

(10)

β: the normalized reduction in average number of errors:

$$\begin{array}{cc}& \beta =\frac{n\in \left\{R_n\left(t\right)\ne T_n\left(t\right)\right\}-N_e}{n\in \left\{R_n\left(t\right)\ne T_n\left(t\right)\right\}}.\end{array}$$

(11)

γ: the normalized number of nodes detecting errors corrected:

$$\begin{array}{cc}& \gamma =\frac{N_c}{n\in \left\{S_n\left(t\right)\ne T_n\left(t\right)\right\}}.\end{array}$$

(12)

δ: the normalized number of nodes detecting new errors introduced:

$$\begin{array}{cc}& \delta =\frac{N_i}{n}.\end{array}$$

(13)

The effect of one parameter, the nominal local detection error probability level, on these metrics is studied. In Figures 9(a) and 10(a), the normalized number of original errors detected and correctly event detected using the fault-tolerant algorithm is plotted as a function of the normalized error probability. These graphs show the quality of event detection optimized by the fault-tolerant event detection scheme. The simulation results shows STFTED be with a high effective performance. More concretely, α of STFTED keeps above $\mathrm{90}\%$ when the normalized error probability is less than $\mathrm{50}\%$ , while the percentage of correct event detection nodes degrades quickly for both OTDS and LWVS when the variation goes from $\mathrm{5}\%$ to $\mathrm{45}\%$ . Figure 9(a) presents that α of LWVS decreases $\mathrm{5}\%$ with p changing from $\mathrm{5}\%$ to $\mathrm{20}\%$ , and α of OTDS, shown in Figure 10(a), only reduces less than 3% when p changes from 5% to 20%. The event detection percentage becomes falling rapidly when p reaches $\mathrm{20}\%$ .

Figure 9

Metrics versus nominal error probability for LWVS and STFTED.

Figure 10

Metrics versus nominal error probability for OTDS and STFTED.

Other metrics as functions of the nominal probability are shown in Figures 9 and 10. To optimize the low-level local stage decision fusion for the fault-tolerant event detection, we propose the high-level global stage fusion. In Figure 9, it can be observed that STFTED makes δ obviously optimized, and β has been optimized when $p_k<\mathrm{0.35}$ . With increasing nominal error probability, the value of γ of STFTED declines faster than LWVS's. Generally, LWVS has been optimized when $p_k<\mathrm{0.35}$ . However, compared with OTDS shown in Figure 10, the decline of β and γ in STFTED is less than 10% and that of δ is less than 4%.

Finally, through many simulations with the collecting nodes data, the adaptability of STFTED in various environments is simulated. In environment monitoring, any change of the environment or network is responded by the sensor readings. Assume the mean value of the sensor reading for the presence of an event is $m_e$ , while for the absence of an event the mean value is $m_n$ . A fixed threshold value is given by $\varphi =(m_e+m_n)/\mathrm{2}$ . When the node reading is higher than ϕ, the node ensures the presence of an event; on the contrary, if it is lower than ϕ, the node informs the absence of an event. To simulate heterogeneous network, a Gaussian error term which has a mean $\mathrm{0}$ and a varied standard deviation σ can be assumed. If σ is varied, the error probability p of the network is changed. If $m_e$ is set as $\mathrm{32}$ and $m_n$ is set as $\mathrm{0}$ , then the value of ϕ is obtained which is $\mathrm{16}$ . When $\sigma =\mathrm{10}$ , a snapshot of the result of a sample simulation run is shown in Figure 11(b). σ is set as changing from $\mathrm{0}$ to $\mathrm{30}$ . Through statistics and analysis, the relationship between σ and p can be obtained, which is shown as in Figure 11(a). With the above idea, many different scenarios can be simulated. A snapshot of the result after OTDS and STFTED when $\sigma =\mathrm{10}$ is shown in Figures 11(c) and 11(d). As Figure 11 shows, there are more nodes which detect an event correctly by using STFTED.

Figure 11

A snapshot of the result of a sample simulation run when $\sigma =\mathrm{10}$ .

In Figure 12, supposing that σ is ranged from $\mathrm{6}$ to $\mathrm{25}$ and corresponding statistics of p is from $\mathrm{0}$ to $\mathrm{0.5}$ , each σ generates 1,000 data groups, and then the results are obtained by the average of 1,000 iterative simulations by separately using STFTED and OTDS. In each simulation, p can be evaluated by the known σ and is used to estimate $R_n(t)$ by OTDS and STFTED. As Figure 12 shows, the results are similar to that in Figure 10. Compared with OTDS, there are a little declines in the parameters of β, γ, and δ of STFTED, while α has a better performance when p is high. Summarizing the experience, the false alarms are more prone to be tolerated than the missed alarms in practical applications. Therefore, STFTED may be more useful than the OTDS in event region detection.

Figure 12

Metrics responded to heterogeneous networks for OTDS and STFTED.

6. Conclusions

In this paper, a spatiotemporal correlation based fault-tolerant event detection scheme (STFTED) is proposed for the binary event detection in WSNs. Our approach aims at improving the quality of event detection and reducing the scenario-dependence and offering a solution for the problem that the ability of event detection degrades rapidly when the sensor fault probability reaches a critical value.

The simulations indicate that STFTED has good performances in event detection under various scenarios. Extensive simulation results demonstrate the effectiveness of STFTED and show that STFTED achieves better performance of event detection than OTDS. It has been found that the normalized number of nodes detecting event is above $\mathrm{90}\%$ , and the normalized percentage of new errors introduced is less than $\mathrm{20}\%$ , when the sensor fault ratio is lower than $\mathrm{50}\%$ .

Although this scheme can effectively detect a single event, the ability of tolerant false alarm needs to be further studied. When multiple events occur in a region, the performance of the proposed approach needs to be penetratingly investigated. Future works will be focused on optimizing the proposed method to meet multi-modality event detection in WSNs.