Keywords

1 Introduction

With the development of the micro-electro-mechanical system (MEMS) technology, internet of things (IoT) have been widely applied to many applications, such as building structure monitoring and control, data collection and localization, military defense and other fields [1, 2], where a large number of low cost and spatially dispersed position sensors are densely deployed as a general paradigm for information collection, transmission and processing data. Energy efficiency in IoT is one of the most important issues and often needs coverage of broad areas. However, the resources like bandwidth and energy are actually restricted, which has been investigated via the scheduled schemes of sensors to realize the goal of saving energy task while satisfying advanced performance of IoT.

The sensor selection problem has been developed to get the desired information gain or reduction in estimation error in [3,4,5]. Authors in [6] proposed distributed algorithms to select cluster members to gather data and formulated an optimization for data collection to maximize utilization of data quality through a rendezvous-based data collection algorithm which not only integrates above positive factors to track a target but also maintains WSNs’ functions. In [7], the sensor selection problem with and without sensing range is demonstrated by utilizing a fixed area and a circle drawn with the help of communication range to select sensor nodes for two cases, respectively. In order to improve the performance of energy efficiency, the quantization technique has been adopted to decrease the transmission rates for energy saving [8], which would lead to additional errors on the available measurements in terms of quantization effects [9], which may degrade the filtering/estimation performance.

The problem of efficacy and effectiveness for saving and balancing energy consumption via collaborative mobile nodes is studied in [10], where the machine learning algorithm, namely MU-MAB, is employed to solve energy consumption problem, and the stable matching theory based on marginal utility for the allocation of the final one-to-one optimal combinations is used to achieve energy efficiency. Generally, mobility can improve the performance of IoT [11], which characterizes three node sets of the cluster as a theoretical foundation to enhance high performance of WSNs, and propose optimal solutions by introducing rendezvous and Mobile Elements (MEs) to optimize energy consumption for prolonging the lifetime of WSNs. Meanwhile, MEs can be used as mobile edge computing server to collect data from WSNs and process them for data collection due to their capacity of computing, storage, rich energy and so on. Considering offloading this type of deep learning (DL) tasks to a mobile edge computing (MEC) server, Bo Yang [12] proposed an optimization problem to minimize the weighted-sum cost including the tracking delay and energy consumption introduced by communication and computing of the UAVs, while taking into account the quality of data input to the DL model and the inference errors. In [13], the IoT devices can offload the intensive computing tasks to edge computing servers, while saving their own computing resources and reducing energy consumption. In [14], mobile cloud computing as an emerging and prospective computing paradigm, can significantly enhance computation capability and save energy for smart mobile devices (SMDs) by offloading computation-intensive tasks from resource constrained SMDs onto resource-rich cloud.

The main contribution of this paper is that we proposed a Pareto optimality for sensor nodes selection in terms of energy efficiency. Furthermore, we recruit voluntary mobile devices as mobile edge computing servers to collect the data from selected sensor nodes in the cluster. Unlike the most of previous data collection method, it is shown that the proposed algorithm exhibits excellent performances in terms of energy efficiency.

The layout of the paper is as follows: In Sect. 2, problem statements are described, including clustering. Section 3 is Energy statements. Quantization and sensor selection is demonstrated in Sects. 4 and 5. In Sect. 6, collaboration of sensor selection and data quantization scheme is given. Simulation results are discussed. We conclude the paper in Sect. 8.

2 Problem Statements

In order to improve the energy efficiency, we configure the cluster in grid for state estimation of certain data requirement, which is shown in Fig. 1. However, due to random deployment of sensor nodes in WSNs, the node density of the cluster is a random variable that could affect the performance of data collection. In order to balance the energy consumption of local or global WSNs, the sensor node selecting scheme is significant to improve the energy efficiency, which will be illustrated in the follow section.

Fig. 1.
figure 1

Clustering for IoT

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3 Energy Statements

The cost is expressed as energy consumption, and energy model in [11] is shown as follows. For the sake of convenience, we consider energy consumption at the cost of a \( b \)-bit message and a distance \( d \) between sensor \( s_{i} \) as a transmitter and sensor \( s_{j} \) as a receiver. The energy consumed in transmitting by the sensor \( s_{i} \) is

$$ E_{Tx} (s_{i} ,s_{j} ) = b \cdot E_{Telec} + b \cdot \varepsilon_{amp} \cdot d_{i,j}^{\alpha } $$
(1)

and to receive this message, the radio expends:

$$ E_{Rx} (s_{j} ) = b \cdot E_{Relec} $$
(2)

In addition, the receiver \( s_{j} \) also spends energy in sensing or processing. The radio expends:

$$ E_{Sx} (s_{j} ) = b \cdot E_{Selec} $$
(3)

where \( E_{Telec} \) and \( \varepsilon_{amp} \) are determined by transmitter \( s_{i} \), \( d_{i,j} \) indicates the distance between sensor \( s_{i} \) and sensor \( s_{j} \). \( E_{Relec} \) and \( E_{Selec} \) are decided by receiver \( s_{j} \). \( \alpha \) depends on the channel characteristics and is known as \( \alpha = 2 \).

Therefore, the total energy consumption between senor \( s_{i} \) and sensor \( s_{j} \) is demonstrated by

$$ \begin{aligned} E(s_{i} ,s_{j} ) = & \, E_{Tx} (s_{i} ,s_{j} ) + E_{Rx} (s_{j} ) + E_{Sx} (s_{j} )r \\ \, = & b \cdot E_{Relec} \;{ + }\;b \cdot E_{Selec} { + }b \cdot E_{Telec} \; + \;b \cdot \varepsilon_{amp} \cdot d_{i,j}^{2} \\ { = } & E_{0} \;{ + }\;e_{0} d_{i,j}^{2} \\ \end{aligned} $$
(4)

4 Quantization

Considering the sensor node density, we deal with a more complicated scenario which includes redundant sensors. Although we introduce the wake-up mechanism, redundant information maybe produce which also consume more energy of IoT. As a result, we adopt quantization technology for further energy saving, and the quantization for sensor node \( i \) is shown as follows

$$ m_{i} = \left\{ {\begin{array}{*{20}l} {0,{ - }\infty {\text{ < z}}_{i} { < }\gamma_{1} } \hfill \\ {1, \, \gamma_{1} {\text{ < z}}_{i} { < }\gamma_{2} } \hfill \\ { \vdots \, \vdots \, } \hfill \\ {L - 1, \, \gamma_{(L - 1)} {\text{ < z}}_{i} { < }\infty } \hfill \\ \end{array} } \right. $$
(5)

where \( \gamma_{i} \) in Eq. (5) indicates the quantization thresholds and \( L = 2^{m} \) is the number of quantization levels.

5 Collaboration of Sensor Node Selection and Data Quantization

In this section, we consider the optimality of sensor selection for energy efficiency in the process of data collection.

5.1 Pareto Optimality

We utilize Pareto optimality to select sensor nodes for data collection in terms of a given certain accuracy. In the grid cluster including a sensor set \( S = \left\{ {s_{1} ,s_{2} ,\cdots ,s_{n} } \right\} \), we supposed that there exist a set \( S' = \left\{ {s'_{1} ,s'_{2} ,\cdots ,s'_{r} } \right\} \) to accomplish the tracking task, where \( S' \subseteq S \) holds. However, this is a permutation and combination problem and it is hard to solve this problem when the sensors are densely deployed in the area. Naturally, the permutation and combination problem of sensor selection for data collection can be evolved into the constraint optimization problem as follows.

$$ \begin{aligned} & \hbox{min} \sum\limits_{i = 1}^{r} {(E_{{s_{i}^{'} }} - \bar{E})^{2} } \\ & s.t.\Phi_{S'} \le \Phi_{0} \\ \end{aligned} $$
(6)

where \( E_{{s_{i}^{'} }} \) is the residual energy of sensor \( s_{i}^{'} \) in set \( S' \), \( \bar{E} \) denotes the average energy of the cluster, \( \Phi_{S'} \) is the actual data accuracy obtained by the sensor combination of set \( S' \), and \( \Phi_{0} \) denotes the given data accuracy. According to expression (16), we design a Pareto optimality mechanism to get the approximate sensor combination set.

Step 1: arbitrarily select a sensor with a certain probability, and get \( \left\{ {s'_{1} } \right\} \);

Step 2: select another sensor in the set \( S\backslash \{ s'_{1} \} \) and get \( \{ s'_{1} ,s'_{2} \} \). According to the concept of Pareto optimality, increasing sensor \( s'_{2} \) is not reduce the revenues of \( s'_{1} \);

Step 3: continue to select a set \( S' = \left\{ {s'_{1} ,s'_{2} ,\cdots ,s'_{r} } \right\} \) until expression (16) is satisfied.

5.2 Collaboration of Sensor Selection and Data Quantization

Considering the energy consumption of data transmission, we collaborate the sensor selection and data quantization for energy efficiency in the data collection process. In this scenario, we deal with data collection of sensors being randomly deploy in the interest area. Actually, due to the approximate solution in terms of Sect. 5.1, we demonstrate four cases for collaboration of sensor selection and data quantization according to the density of the cluster, which are shown in Table 1.

Table 1. Collaboration of sensor selection and data quantization
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Case 1: for energy efficiency, we not only select sensors but also quantize the data, that is (1,1) in Table 1. In this scenario, the density of the cluster is higher.

Case 2: (1,0) in Table 1, that is, we plan to select sensors while not quantize the data;

Case 3: (0,1) denotes we are about to quantize the data of sensing data while not select sensors for data collection.

Case 4: (0,0) stands for neither selection nor quantization. In this scenario, the density of the cluster is lower.

6 MEC Server Placement

In the process of data collection, MEC server play roles of collecting data, processing data and transmitting data.

For further reducing the energy consumption of the cluster, we set the optimal position of MEC server according to Eq. (1). After selecting the sensing nodes, the position of each node is confirmed. Therefore, we can find a point to place the MEC server to minimize the expression (6). So we can get the following theorem.

Theorem 1. After selecting sensors, there exist a point in cluster for MEC server to make the energy consumption least.

Proof according to Eq. (1), it is easy to get the conclusion, so we omit it here.

7 Simulation Results

To illustrate advantages of the new method, some simulation results are discussed and some assumptions for simulations here. To illustrate advantages of the new method, some simulation results are discussed and some assumptions for simulations here. In these simulations, the number of sensors N = 400, sensor radius \( R = 60\;{\text{m}} \).They are randomly deployed in a square field 100 * 100 m2. Simulation parameters about energy consumption model are listed in Table 2.

Table 2. Simulation parameters
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In Fig. 2, collaboration of sensor selection and data quantization as shown in Table 1 are considered with the number of sensors N = 400. Seen from Fig. 2, energy consumption changes with different scenarios. Especially, the scenario of (1,1) gets the best performance of IoT due to dense sensor for rich selection and data quantization. The scenario of (0,0) gets the worse performance of IoT when no selection and quantization. Apparently, this scenario consumes many times energy than the scenario of (1,1). Nevertheless, although different collaboration of sensor selection and data quantization plays the role of reducing different energy consumption, they can keep the performance of energy balance for IoT.

Fig. 2.
figure 2

Energy consumption with 50 rounds and N = 400

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8 Conclusions

In this paper, dynamic clustering methods is adopted to improve energy efficiency while guaranteeing energy consumption balance. We deign the sensor selection scheme for carrying out the data collection tasks according to energy distribution of sensor nodes. Concretely, by considering the reality of random deployment and introducing the definition of node density for IoT, we develop a Pareto optimality for sensor nodes selection in terms of energy efficiency. Furthermore, we recruit voluntary mobile devices as mobile edge computing servers to collect the data from selected sensor nodes in the cluster, offloading and processing them to achieve energy efficiency.