An image classification approach for hole detection in wireless sensor networks

Abstract

Hole detection is a crucial task for monitoring the status of wireless sensor networks (WSN) which often consist of low-capability sensors. Holes can form in WSNs due to the problems during placement of the sensors or power/hardware failure. In these situations, sensing or transmitting data could be affected and can interrupt the normal operation of the WSNs. It may also decrease the lifetime of the network and sensing coverage of the sensors. The problem of hole detection is especially challenging in WSNs since the exact location of the sensors is often unknown. In this paper, we propose a novel hole detection approach called FD-CNN which is based on Force-directed (FD) Algorithm and Convolutional Neural Network (CNN). In contrast to existing approaches, FD-CNN is a centralized approach and is able to detect holes from WSNs without relying on the information related to the location of the sensors. The proposed approach also alleviates the problem of high computational complexity in distributed approaches. The proposed approach accepts the network topology of a WSN as an input and generates the identity of the nodes surrounding each detected hole in the network as the final output. In the proposed approach, an FD algorithm is used to generate the layout of the wireless sensor networks followed by the identification of the holes in the layouts using a trained CNN model. In order to prepare labeled datasets for training the CNN model, an unsupervised pre-processing method is also proposed in this paper. After the holes are detected by the CNN model, two algorithms are proposed to identify the regions of the holes and corresponding nodes surrounding the regions. Extensive experiments are conducted to evaluate the proposed approach based on different datasets. Experimental results show that FD-CNN can achieve 80% sensitivity and 93% specificity in less than 2 minutes.

Appendices

Appendix A - Force-directed algorithms

Davidson-Harel algorithm The energy value E used in the simulated annealing defined in the DH algorithm is the sum of attractive force ($f_a$) and repulsive force ($f_r$), which can be calculated as follows:

$$\begin{aligned} E=\sum \limits _{i=1}^{n-1}{\sum \limits _{j=i+1}^{n}{f_a(\left\| u_i-u_j\right\| )+f_r(\left\| u_i-u_j\right\| ))}} \end{aligned}$$

(1)

During initialization, a node u is randomly selected from the network. Next, the DH algorithm creates a temporary node v. The DH algorithm then assigns the location to the node v based on the location of the node u. The position of the node v and other nodes in the network can be used to calculate the new energy value $E^{'}$, which is defined as follows:

$$\begin{aligned} E^{'} = \sum \limits _{u\in V, v\notin V}^{n}{ f_a(\left\| u-v\right\| )+f_r(\left\| u-v\right\| ) } \end{aligned}$$

(2)

In addition, when the liquid cools slowly, the DH algorithm obeys the Boltzmann distribution rule [14]. If $E^{'} - E \le 0$, then use $E^{\prime }$ as the energy of the next iteration, because $E^{\prime }$ has a lower energy value. If $E^{'} - E > 0$, the probability equation is used to determine whether to use the new energy $E^{\prime }$ in the next iteration. The probability equation is defined as follows:

$$\begin{aligned} p=e^{-\frac{E^{'}-E}{k\times T}} \end{aligned}$$

(3)

where T is the temperature variable and k is the Boltzmann constant. If the probability p is less than the threshold $\varepsilon$, the new energy $E^{\prime }$ is accepted; otherwise, the old energy E will be used in the next iteration. The time complexity of DH algorithm is $O(V^2 \times E)$, where V is the number of nodes in the network topology, E is the number of edges in the network topology.

ForceAtlas2 algorithm Jacomy et al. [20] proposed a revised attractiveness based on the LinLog model, which is defined as follows:

$$\begin{aligned} F_a\left( u,v\right) =log\left( 1+d(u,v)\right) \end{aligned}$$

(4)

where d is the distance between nodes u and v. In addition, a degree-dependent repulsion model is proposed in the FA2 algorithm to reduce the repulsive force. This repulsion model increases the chance that nodes with lower than average degrees are connected to nodes with higher than average degrees. The repulsion model of FA2 algorithm is defined as follows:

$$\begin{aligned} F_r\left( u,v\right) = k \times \frac{\left( deg(u)+1\right) \times \left( deg(v) + 1\right) }{d(u,v)} \end{aligned}$$

(5)

where k is the ideal pairwise distance constant, as used in FR algorithm. d is the distance between nodes u and v, and deg(n) is the number of associated edges Node n, including the edge of in-out degree. The time complexity of FA2 algorithm is $O(V^2+E)$ where V is the number of nodes in the network topology, E is the number of edges in the network topology.

KK-MS-DS algorithm The goal of the KK-MS-DS algorithm [8] is to push the nodes in the outer boundary away from the inner nodes. Nodes tag with a decaying stiffness (m). The higher the decaying stiffness value of the node (m), the farther the distance of the node can be moved. The value of m of the node decreases with the execution time, which is defined as follows:

$$\begin{aligned} m^{'} =m-zp^{t} \end{aligned}$$

(6)

where t is the number of times that the selected node is updated. p is the decay rate, and z is the remaining energy possessed by the node. The KK-MS-DS algorithm terminates, when the stable state (r) remains unchanged until a predefined iteration or r is less than the threshold $\varepsilon$. The stable state (r) means that a coarse visualization of the graph has been constructed, but the final stage of the entire graph has not yet been reached. The ratio of the stable state r is defined as follows:

$$\begin{aligned} r=\frac{\frac{1}{d}\sum \nolimits _{i=1}^{d}{\left| L^{'}_{i}-L_i \right| }}{\sqrt{\sum \nolimits _{i=1}^{d}\left( L^{'}_{i}-\frac{1}{d}\sum \nolimits _{i=1}^{d}{L^{'}_{i}-L_i}\right) } } \end{aligned}$$

(7)

where d is the total number of edges in the graph, $L^{'}_{i}$ is the edge length from the graph generated by the KK-MS-DS algorithm, and $L_i$ is the edge length of the input graph. The time complexity of KK-MS-DS algorithm is $O(n \times (V + v^2))$, where n is the number of iteration, V is the number of nodes in the given graph, and v is the number of nodes in the ordered queue.

Appendix B - Pseudocode of force-directed algorithms

The pseudocode for DH algorithm, FA2 algorithm and KK-MS-DS algorithm are given in Algorithm 4, Algorithm 5 and Algorithm 6 respectively.