Sensor-cloud data acquisition based on fog computation and adaptive block compressed sensing

Abstract

The emergence of sensor-cloud system has completely changed the one-to-one service mode of traditional wireless sensor networks, and it greatly expands the application field of wireless sensor networks. As the high delay of large-scale data processing tasks in sensor-cloud, a sensor-cloud data acquisition scheme based on fog computing and adaptive block compressive sensing is proposed. First, the sensor-cloud framework based on fog computing is constructed, and the fog computing layer includes many wireless mobile nodes, which helps to realize the implementation of information transfer management between lower wireless sensor networks layer and upper cloud computing layer. Second, in order to further reduce network traffic and improve data processing efficiency, an adaptive block compressed sensing data acquisition strategy is proposed in the lower wireless sensor networks layer. By dynamically adjusting the size of the network block and building block measurement matrix, the implementation of sensor compressed sensing data acquisition is achieved; in order to further balance the lower wireless sensor networks’ node energy consumption, reduce the time delay of data processing task in fog computing layer, the mobile node data acquisition path planning strategy and multi-mobile nodes collaborative computing system are proposed. Through the introduction of the fitness value constraint transformation processing technique and parallel discrete elastic collision optimization algorithm, the efficient processing of the fog computing layer data is realized. Finally, the simulation results show that the sensor-cloud data acquisition scheme can effectively achieve large-scale sensor data efficient processing. Moreover, compared with cloud computing, the network traffic is reduced by 20% and network task delay is reduced by 12.8%–20.1%.

Keywords

Sensor-cloud wireless sensor networks fog computing compressive sensing elastic collision optimization algorithm

Introduction

Wireless sensor networks (WSNs) are widely used in the fields of environment detection, forest fire early warning, and military defense for providing various information effectively and monitoring^1–5 the state of the target in real time. However, the limited computing storage capacity, single service mode, and serious waste of resources have become the bottleneck problem of the further development of WSNs.⁶

The concept of “cloud computing” first appeared in the 2006 search engine conference and was clearly defined as three modes of service: platform as a service, software as a service, and infrastructure as a service.⁷ The powerful computing and storage capability of cloud computing platform and the characteristics of openness, flexibility, and sharing provide a new research idea for the development of traditional WSNs.⁸ The integration of cloud computing and WSNs has created a new service mode: sensor is a service,⁶ which completely changed “one to one” service mode of traditional WSNs,⁹ and the concept of sensor-cloud came into being. Studies of Tan¹⁰ and others have found that sensor-cloud, which was a product of organic fusion between WSNs and cloud platform, could provide remote monitoring cloud services, and multiple users could share the same WSNs resources. Yuriyama and Kushida,¹¹ Madria et al.,¹² and others used WSN sensor nodes as virtual nodes of cloud service platform and provided automatic response service to users. In brief, the powerful data processing and storage capabilities of the cloud computing platform provide technical support for WSNs large data analysis, and sensor-cloud can provide users with an unparalleled interaction with the physical world. At present, Xively,¹³ Nimbits,¹⁴ YeeLink,¹⁵ and other sensing cloud systems have appeared successively and showed outstanding advantages in data storage management. However, the cloud service platform is so far away from WSNs that the network communication bandwidth and data transmission delay are large. And, with the expanding scale of WSNs, node data that to be processed present an explosive growth. If these data are directly transmitted to the cloud service platform, it will be a great challenge to WSNs’ communication capability and energy consumption. In order to effectively solve the problem, the concept of fog computing¹⁶ is proposed, in which the operation strategy is on the interactive boundary between the physical world and the cloud service platform, using a device with certain computing storage capacity to preprocess the data to play the role of connecting the real world and the cloud network. It is generally recognized that the fog computing model will bring profound changes to cloud computing. Bonomi et al.¹⁷ analyzed the defining features of fog computing and discussed its application and main problems, but did not give specific implementation strategy of system function. Sarkar and Misra¹⁸ and others analyzed the fog calculation model in theory and researched the application in energy consumption and delay performance, but they focused on the fog computing layer itself, without analyzing the performance index of the whole system. Zhu et al.¹⁹ and others deeply analyzed the fog computing data access and interaction mechanism; Zao et al.²⁰ and Yi²¹ discussed the application of fog computing in smart wearable devices and medical data management, respectively. Most of the researches focus on model analysis, and there is not much attention to the fusion technology of fog computing and sensor-cloud system. In the work of Shojafar and colleagues,^21–23 a number of studies have explored new fast-converge solutions to response delay of query per fog node for the fog-supported WSN. In the long term, sensor-cloud system based on fog computing can better manage sensor nodes, and the performance of network communication bandwidth, delay, and fault tolerance management will be greatly improved.

Data acquisition is one of the most important and the most critical application functions of WSNs.²¹ With the maturity of compressive sensing (CS)²⁴ and mobile agent (MA)²⁵ technology, the efficiency of WSNs data acquisition is improved. How to design more stable and efficient CS and MA strategy is still a research hotspot in WSN data acquisition research.^26,27 Because of the relatively few research achievements on cloud and fog computing technology at home and abroad, especially the research on sensing cloud based on fog computing is still in its infancy. With cloud sensing large-scale data acquisition as the application background, a sensor-cloud data acquisition scheme based on fog computation and adaptive block compressed sensing is proposed in this article, the work and innovation are as follows:

Build a network framework of sensor-cloud system based on fog computing and give the specific definition of each level and the coordinated operation strategy between different levels.

Study the key technologies of adaptive block compression sensing data acquisition strategy, mobile node data acquisition path planning, and multiple mobile node collaboration computer system. The elastic collision optimization (ECO) algorithm is put forward and the specific implementation process of the above key technologies is given.

The sensor-cloud data acquisition scheme based on fog computing is simulated. The total amount of network data communication, system task delay, and network energy consumption are demonstrated, and corresponding conclusions are given.

Sensor-cloud framework based on fog computing

Sensor-cloud module constitute based on fog computing

Building a sensor-cloud framework based on fog computing: the system based on cloud computing provides data mining analysis services for large-scale sensor node data transmitted to the cloud and provides decision-making strategy for different users. The network computing is extended from the cloud center to the network boundary by the fog computing, and the virtual network is formed by the mobile node with certain computing power, which is independent or assisting the cloud to complete the tasks of data processing, storage, management, and so on. Figure 1 shows the sensor-cloud framework diagram based on fog computing.

Figure 1.

The sensor-cloud framework diagram based on fog computing.

Sensor-cloud framework based on fog computing is composed mainly of three layers (module): cloud computing layer, fog computing layer, and WSN layer:

Cloud computing layer: top of the framework, mainly composed of high-performance servers, has powerful computing and storage capability. It can analyze data mining for large data stored in the cloud and provide openness, flexible, and heterogeneous service platform for different users. With the continuous development of cloud computing technology, users only need to obtain the relevant privileges of the sensing cloud platform for rich resources and applications without having to hold WSN devices and not to worry about the docking of equipment interfaces.

WSN layer: it consists of a large number of sensor nodes with low cost, wireless communication, and computing power. These sensor nodes can be isomorphic or heterogeneous, or can be arranged in large scale or in multiple WSN deployments. The sensor nodes can be divided into different virtual clusters²⁸ using virtualization technology to supervise the target area without knowing the actual location of the sensor nodes.

Fog computing layer: it is composed of a certain number of mobile nodes. Nodes can communicate with each other, mainly complete those high tasks including the WSN layer of the bridged lower layer and the upper cloud computing, the coordination of mobile nodes, the processing priority, and the real-time performance. On one hand, the distance between the cloud center and the WSNs is so far that the cloud computing cannot work well for higher delay requirement. While the mobile node in the fog computing layer has the strong computing and storage capability, and the high real-time computing processing task can be placed in the fog computing layer. In particular, the fog computing layer can process high priority data in a very short time for scenarios such as dangerous cargo leakage monitoring. On the other hand, the data that the lower WSNs need to transmit is massive, which requires a lot of bandwidth and energy consumption. The fog computing layer can allocate the data in the mobile node virtual network to improve the total network transmission and reduce the task delay.

Collaborative work of sensor-cloud framework module

The different layers of sensor-cloud use their own characteristics to achieve data acquisition, processing analysis, and decision response. The WSN layer is at the bottom of the system, which mainly completes data acquisition. When WSN in the monitoring area completes data acquisition according to the system instruction, then the data are uploaded to the fog computing layer. Data are preprocessed by fog computing layer, according to data size and task priority. Finally, the preprocessed data are transferred to the cloud computing layer for deep data processing analysis.

Taking acidity and alkalinity of soil as an example, the course of sensor-cloud data acquisition based on fog computing is described as follows. Large-scale sensor nodes (Sensor) and a certain number of mobile nodes (Sink) are arranged in a wide range of saline alkali areas. The cloud divides the actual deployment of WSNs into different virtual clusters (Zone), which are responsible for monitoring different target areas. At one moment, the user sends a monitoring request to the specific area and sends the instructions to the cloud through the user side. The cloud computing center sends out the data acquisition instruction to determine the data acquisition Sink node. The fog computing layer uses Sink node to collect and process the sensor node data in the area of the user requested. The preprocessed data are uploaded to the cloud; finally, the results are returned to the user side after data processing analysis. Figure 2 shows the process flow diagram.

Figure 2.

Data acquisition process flow diagram of soil acidity and alkalinity monitoring.

Nowadays, with the continuous development of cloud computing technology, how to effectively reduce the total amount of WSN data acquisition and effectively reduce the delay are the key to determine the performance of the sensor-cloud system. The total amount of communication in the whole system is determined by the WSN data acquisition capacity, and the whole communication delay is determined by the cloud computing layer, the fog computing layer, and the WSN layer. Therefore, in order to reduce the total amount of communication, reduce the requirements of communication broadband, and improve the performance of the system communication delay, this article proposes an adaptive block compressed sensing data acquisition strategy in the WSN layer, which only needs to collect a small amount of node data to monitor. In addition, the mobile node data acquisition path planning strategy and multi-mobile nodes collaborative computer system are also proposed in the fog computing layer. The Sink node collects the sensor data according to the optimal mobile planning path and transfers the collected data to all the mobile Sink (MS) range of the fog layer.

Construction of function module model of sensor-cloud system

Adaptive block compressed sensing

The proposed theory of adaptive block compressed sensing brings new ideas for signal acquisition and processing. The lower WSN layer is directly facing the physical world. It is of great significance to set up a reasonable and scientific data perception acquisition method to reduce the total amount of data communication in the system. Therefore, adaptive block compression sensing technology is introduced in the lower layer of WSN layer. It can realize the accurate perception of high-dimensional signals using a small amount of observation data in low-dimensional space.²⁹ If the N-dimensional signal $x_{N \times 1}$ can be sparse representation $(x_{N \times 1} = Ψ_{N \times N} \times s_{N \times 1})$ with a vector $s_{N \times 1}$ containing $K (K ≪ N)$ non-zero coefficients under a sparse matrix $Ψ_{N \times N}$ , $x_{N \times 1}$ is called K degree sparsity on $Ψ_{N \times N}$ . Select the measurement matrix $Φ_{M \times N}$ to project the signal $x_{N \times 1}$ and get the measurement vector $y_{M \times 1}$

\begin{matrix} y_{M \times 1} = Φ_{M \times N} \times x_{N \times 1} = Φ_{M \times N} \times Ψ_{N \times N} \times s_{N \times 1} \\ \underline{\underline{A_{M \times N} = Φ_{M \times N} \times Ψ_{N \times N}}} = A_{M \times N} s_{N \times 1} \end{matrix}

(1)

In the CS theory, when $A_{M \times N}$ satisfies the RIP condition,²⁴ $s_{N \times 1}$ can be exactly recovered by solving the minimum $l_{0}$ norm, namely

min ‖ s ‖_{l_{0}} \begin{matrix} s . t . \begin{matrix} \begin{matrix}  \end{matrix} y = As = Φ Ψ s \end{matrix} \end{matrix}

(2)

For the WSN $W = {S N_{i}} (i = 1, 2, \dots, Q)$ of a large-scale arrangement of Q sensor nodes in a certain area, the cloud computing layer uses virtual technology to divide $W$ into V virtual cluster $V = {Z_{j}}$ ( $Z_{j}$ as the jth virtual cluster, $j = 1, 2, \dots, V$ ), which can be used to monitor different regions. Users tend to pay more attention to monitoring signals in a specific area. Therefore, the cloud deploys the virtual clusters for perceptual and acquisition in the corresponding area according to the user request. For virtual cluster $Z_{j}$ , according to the energy consumption of sensor nodes, the cloud selects certain nodes to work (the number of working nodes is G) under the condition of meeting the requirements of network coverage.³⁰ In the $Z_{j}$ monitoring area, there are N event sources (taking K as the number of events), set $f_{i}$ to indicate the data collected by the work node ${SN}_{i}^{j} (i = 1, 2, \dots, G)$ within $Z_{j}$ , the sensor data vector $X_{G \times 1} = (f_{1}, f_{2}, \dots, f_{G})^{T}$ ; set $s_{k}$ as the kth $(k = 1, 2, \dots, N)$ event source signal intensity, then the event source vector $s_{N \times 1} = [s_{1}, s_{2}, \dots, s_{N}]^{T}$ , then

X_{G \times 1} = Ψ_{G \times N} s_{N \times 1} = [\begin{matrix} ψ_{11} & \dots & ψ_{1 N} \\ ⋮ & ⋱ & ⋮ \\ ψ_{N 1} & \dots & ψ_{NN} \end{matrix}] (\begin{matrix} s_{1} \\ ⋮ \\ s_{N} \end{matrix})

(3)

where $Ψ_{G \times N}$ is a propagation matrix. According to the compressed sensing theory, obtain $s_{N \times 1}$ by selecting $M (M < G)$ sensor data, so choose $X_{G \times 1}$ from observation matrix $Φ_{M \times G}$ , and to get the measurement vector $y_{M \times 1}$

\begin{matrix} y_{M \times 1} = [\begin{matrix} y_{1} \\ y_{2} \\ ⋮ \\ y_{M} \end{matrix}] = [\begin{matrix} 1 & 0 & \dots & 0 & 0 & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ \\ 0 & 0 & \dots & 1 & \dots & 0 \\ ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ \\ 0 & 0 & \dots & 0 & 0 & 1 \end{matrix}] [\begin{matrix} f_{1} \\ ⋮ \\ f_{j} \\ ⋮ \\ f_{G} \end{matrix}] \\ = Φ_{M \times G} X_{Q \times 1} = Φ_{M \times G} Ψ_{G \times N} s_{N \times 1} \end{matrix}

(4)

In general, at the same time, N events only generate a small number of events $(K ≪ N)$ , that is, $s_{N \times 1}$ is K degree sparse. The related research showed that when the $Ψ_{G \times N}$ and $Φ_{M \times N}$ listed in equations (3) and (4) are used, $Φ_{M \times G} Ψ_{G \times N}$ can satisfy the RIP condition³¹ with the maximum probability. Therefore, the CS technology can be used to realize the monitoring through only a small amount of sensor node data.

Block compressed sensing

Although the use of compressed sensing technology in the WSN layer greatly reduces the amount of data acquisition, it still takes a certain amount of time to data communication using the mobile node of the fog computing layer to carry out the data acquisition of the lower nodes one by one, resulting in the data delay. In addition, cloud computing layer (or fog computing layer) can ensure the uniformity of the distribution of work nodes by reasonably scheduling the working state of the node. The $Z_{j}$ is dynamically divided into C blocks with the same radius $R_{C}$ , and $R_{C} = \sqrt{2} η R$ is derived from the network coverage requirements (R is the node communication radius and $η$ is the maximum number of communication jumps in the block). When the node density of the $Z_{j}$ network is $λ$ , then

C = \frac{G}{λ π R_{C}^{2}} = \frac{G}{2 π λ η^{2} R^{2}}

(5)

Obviously, each block has $O = G / C$ working nodes, and each block can be equivalent to a WSN. For the ith $(1 ⩽ i ⩽ C)$ block in $Z_{j}$ , the node in the center of the block is selected as $C H_{i}$ , which is used to gather the data collected in the block. It uses ${Φ^{i}}_{I \times O}$ to select I nodes in the block for data acquisition $(\sum I = M)$ , then obtains the observed signal ${y^{i}}_{I \times 1} = {Φ^{i}}_{I \times O} {X^{i}}_{O \times 1}$ . After collecting data in all blocks, the fog computing level mobile node collects all block center data of the planning path and obtains the measurement vector $y_{M \times 1} = {{y^{i}}_{I \times 1}} (i = 1, 2, \dots, C)$

\begin{matrix} y = [\begin{matrix} y^{1} \\ y^{2} \\ ⋮ \\ y^{C} \end{matrix}] = [\begin{matrix} Φ^{1} X^{1} \\ Φ^{2} X^{2} \\ ⋮ \\ Φ^{C} X^{C} \end{matrix}] = [\begin{matrix} Φ^{1} \\ Φ^{2} \\ ⋱ \\ Φ^{C} \end{matrix}] [\begin{matrix} f_{1} \\ f_{2} \\ ⋮ \\ f_{G} \end{matrix}] \\ = Φ'_{M \times G} X_{G \times 1} = Φ'_{M \times G} Ψ_{G \times N} s \end{matrix}

(6)

From formula (6), we can see that $O (n \log D)$ is a block matrix. If $O (n)$ , then $T_{max} O (n \log D) + O (n)$ is a block matrix. The data collection amount of nodes is greatly reduced as $T_{max} O (n \log D) + O (n)$ contains a large number of “0” elements. The research shows that for the same sparse signal reconstruction algorithm, the sparse signal recovery rate is faster and the accuracy is higher when the block observation matrix is used.³²

Energy consumption analysis of block compressed sensing

The larger the number of block C, the greater the number of intra-block communication; the smaller the number of block C, the greater the number of inter-block communication. As a result, it is necessary to reasonably determine the number of C to balance intra-block and inter-block communication.

Conclusion 1

When the number of block C adopts the following value, the communication efficiency between blocks can be maximized

\begin{matrix} C = \frac{G}{λ π R_{C}^{2}} = \frac{G}{2 π λ η^{2} R^{2}} \\ η = \sqrt[3]{\frac{3 μ_{1}}{2 π λ μ_{2} R^{2}} + \sqrt{{(\frac{3 μ_{1}}{2 π λ μ_{2} R^{2}})}^{2} + \frac{1}{1728}}} \\ + \sqrt[3]{\frac{3 μ_{1}}{2 π λ μ_{2} R^{2}} - \sqrt{{(\frac{3 μ_{1}}{2 π λ μ_{2} R^{2}})}^{2} + \frac{1}{1728}}} \end{matrix}

(7)

Among them, $μ_{1} \in (0, 1)$ and $μ_{2} \in (0, 1)$ are the control coefficients of intra-block communication and inter-block communication, respectively, and $μ_{1} + μ_{2} = 1$ (the process of proof is attached to Appendices 1 and 2).

From conclusion 1, it is known that the number of block C is closely related to the network node density. When the network node density $λ$ changes, the network partitioning is also dynamic, that is to say, the network block itself is a dynamic adaptive change process. The purpose is to balance intra-block communication and inter-block communication, which is more beneficial to reduce the amount of network data acquisition and reduce network energy consumption.

Block compressed sensing measurement of M lower limit and signal reconstruction

The sufficient but not necessary condition of K-degree sparse signal $s_{N \times 1}$ for satisfying the exact reconstruction is that matrix A has K-order constraint equidistance for any $s_{N \times 1}$ and constant $δ_{K} \in (0, 1)$

(1 - δ_{K}) ‖ s ‖_{2}^{2} ⩽ ‖ As ‖_{2}^{2} ⩽ (1 + δ_{K}) ‖ s ‖_{2}^{2}

(8)

For the (6) block compressed sensing model, the observation matrix $A$ satisfies the upper bound RIP condition with maximum probability, therefore, for $s_{N \times 1}$ , $z_{N \times 1}$ (usually $K ≪ N / 2$ ), there are the following

‖ s - z ‖_{2} ⩾ \sqrt{\frac{K}{2}}; \log | X | ⩾ \frac{K}{2} \log (\frac{N}{K})

(9)

Simultaneous formulas (8) and (9) give

\begin{matrix} ‖ As - Az ‖_{2} ⩾ \sqrt{1 - δ} ‖ s - z ‖_{2} ⩾ \sqrt{K / 4}; \\ ‖ As ‖_{2} ⩽ \sqrt{1 + δ} ‖ z ‖_{2} ⩾ \sqrt{3 K / 2} \end{matrix}

(10)

Therefore, it can be concluded that the observational times M should be satisfied $(Λ \approx 0.28)$

M ⩾ Λ K \log (N / K)

(11)

For the accurate reconstruction of sparse signal $s_{N \times 1}$ , most of the existing reconstruction algorithms need to set the known premise of K, but it is unrealistic. We cannot predict how many event sources will happen; in order to solve the problem of signal restructure under the unknown sparsity, the $min ‖ s ‖_{l_{0}}$ is the objective optimization function. The algorithm is solved by intelligent optimization algorithm (see section “Construction of function module model of sensor-cloud system”).

Multi-mobile-node cooperative computing in fog computing layer

Facing large-scale data collected at low level, multiple mobile nodes collaborative computing technology is introduced into fog computing layer in order to reduce communication delay. As shown in Figure 3(b), the fog computing layer is composed of U MS ${S_{1}, S_{2}, \dots, S_{U}}$ , which can communicate directly with each other. The virtual communication network between Sink is equivalent to $G = (V, E)$ , where $E = {e_{i, j}}$ ( $i, j = 1, 2, \dots, U$ and $i \neq j$ ) is the edge set, $e_{i, j}$ is the communication delay between $S_{i}$ and $S_{j}$ , and $V = {S_{1}, S_{2}, \dots, S_{U}}$ is the vertex set. According to the Sink node physical location and other information, the cloud will update the $e_{i, j}$ before data acquisition:

For $i = 1 : U$ ;

For $j = i : U$ ;

Refresh $e_{i, j}$ according to the location of $S_{i}$ and $S_{j}$ ;

$j = j + 1$ ;

End for;

$i = i + 1$ ;

End for.

Figure 3.

A schematic diagram of cooperative calculation of block communication and fog computing layer: (a) energy consumption analysis of block compression and (b) collaborative calculation of fog computing layer.

When the communication delay between nodes is updated, the collected data will be allocated to other nodes to complete data processing and transmission cooperatively. WSN data acquisition may be taken from any $S_{i}$ , taking data acquisition from $S_{1}$ as an example. The total amount of data processing task is H, the amount of task which assigned to the node $S_{i}$ is $h_{i} (0 ⩽ h_{i} ⩽ H)$ , the task processing speed of node $S_{i}$ is $v_{i}$ , the total time of task processing time is $t_{i}$ , and the total time $t (H)$ of mobile nodes collaborative computing is as follows

t (H) = max {\frac{h_{1}}{v_{1}}, \frac{h_{i}}{v_{i}} + e_{1, i}}, i = 2, 3, \dots, U

(12)

Formula (12) shows that $h = (h_{1}, h_{2}, \dots, h_{U})^{T}$ can make $t (H)$ take the minimum value. At this point, the mobile node cooperative computing problem is transformed into a constrained optimization problem

\begin{matrix} h = \underset{h \in I}{\arg} min t (H) \\ s . t . \begin{matrix} \sum_{k = 1}^{U} h_{k} = H, \end{matrix} 0 ⩽ h_{k} ⩽ H \end{matrix}

(13)

where $I$ is the search space for $h$

I \overset{Δ}{=} Π_{i = 1}^{U} [h_{i, min}, h_{i, max}] = Π_{i = 1}^{U} [0, H]

(14)

The size of data processing task H is closely related to the data collection of low-level WSNs. According to the theory of compressed sensing, only $a (1 ⩽ a ⩽ V)$ virtual clusters collect data in virtual clusters $V = {Z_{j}}$ at a certain time. If the amount of data collected by each virtual cluster is measurement vector ${y^{a}}_{M \times 1}$ , then the total amount of data processing task is $H = \sum {y^{a}}_{M \times 1}$ .

Constraint processing

Intelligent optimization technology is an effective method to solve the problem of objective optimization. However, the particle objective function value cannot be simply equivalent to the particle fitness value; as a result, it is necessary to be constrained to process the particle target function value. Formula (12) contains U inequality constraint $0 ⩽ h_{k} ⩽ H$ and one equality constraint $g_{U + 1} = \sum_{k = 1}^{U} h_{k} - H = 0$ . The degree of constraint violation of the kth constraint condition is

G_{k} (y) = {\begin{matrix} max {0, - h_{k}}, 1 ⩽ k ⩽ U \\ max {0, | \sum_{k = 1}^{U} h_{k} - H | - δ}, k = U + 1 \end{matrix}

(15)

where $δ$ is the tolerance degree of constraint violation. So, the degree of constraint violation for all constraints is

G (y) = \sum_{k = 1}^{U + 1} G_{k} (y)

(16)

For particle $x$ , population particles are divided into feasible solution subpopulation $P_{1}$ and non-feasible solution subpopulation $P_{2}$ according to whether it is in the feasible domain. The fitness value of $x$ is defined as $f (x)$

f (x) = h' (x) + G' (x)

(17)

The objective function value $h' (x)$ and the degree of constraint violation $G' (x)$ are calculated as follows

h' (x) = {\begin{matrix} h (x), x \in P_{1} \\ max {ω \times h (x_{b}) - (1 - ω) \times h (x_{w}), h (x)}, x \in P_{2} \end{matrix}

(18)

G' (x) = {\begin{matrix} 0, & x \in P_{1} \\ G (x), & x \in P_{2} \end{matrix}

(19)

\begin{matrix} G (x) = \sum_{k = 1}^{U + 1} G_{k} (x), G_{k} (x) = \\ {\begin{matrix} max {0, - h_{k}}, 1 ⩽ k ⩽ U \\ max {0, | \sum_{k = 1}^{U} h_{k} - H | - δ}, k = U + 1 \end{matrix} \end{matrix}

(20)

Among them, $x_{b}$ and $x_{w}$ are the best solution fitness value and the worst fitness solution of $P_{1}$ , respectively, and $ω \in (0, 1)$ is the weight coefficient.

After constrained processing of population particles, the individuals with good fitness are selected to continue to evolve when the constraints conditions are satisfied. It improves the efficiency and accuracy of algorithm for solving constrained optimization problems.³³

Mobile node data acquisition path planning strategy

The traditional WSN transfers the node data to the Sink node in wireless multi-hop mode, but the biggest problem of this communication mode is that it can easily lead to the energy hole phenomenon, and the network communication delay is large. In the sensor-cloud system based on fog computing system, the fog computing layer composed of a certain number of MS can collect WSNs conveniently and quickly, and multiple MSs can collect the $C H_{i}$ data of all the central blocks in the lower WSN layer according to the predetermined path, which improves the communication quality, reduces the network delay and node energy consumption. Therefore, the mobile node data acquisition path planning strategy is introduced in fog computing layer and WSN layer.

Data acquisition time length

The fog computing layer sends B MS to collect data. For the mth $M S_{m} (1 ⩽ m ⩽ B)$ , its mobile path can be described as: $Star t_{m} \to {CH}_{1}^{m} \to \dots \to {CH}_{j}^{m} \to \dots {CH}_{‖ m ‖}^{m} \to Star t_{m}$ (among them, $Star t_{m}$ is the starting point of $M S_{m}$ , ${CH}_{j}^{m}$ is the jth block center of $M S_{m}$ , $‖ m ‖$ is the total number of nodes in $M S_{m}$ path, obviously there is $\sum_{m = 1}^{B} ‖ m ‖ = C$ ). Suppose the amount of ${CH}_{j}^{m}$ data acquisition is ${Da}_{j}^{m}$ and the data transmission rate is S, the time $r_{j}^{m}$ for $M S_{m}$ to collect ${CH}_{j}^{m}$ data is

r_{j}^{m} = {Da}_{j}^{m} / S

(21)

The total time consumed by $M S_{m}$ in ${CH}_{j}^{m}$ is

t_{j}^{m} = \frac{\sum_{i = 2}^{j} d_{{CH}_{i - 1}^{m}, {CH}_{i}^{m}} + d_{Star t_{m}, {CH}_{i}^{m}}}{v_{m}} + \sum_{i = 1}^{j} r_{i}^{m}

(22)

Among them, $v_{m}$ represents the mobile speed of $M S_{m}$ and $d_{{CH}_{i - 1}^{m}, {CH}_{i}^{m}}$ represents $M S_{m}$ moving distance between adjacent nodes. Obviously, when $M S_{m}$ completes data acquisition, the data acquisition time is

\begin{matrix} T (M S_{m}) = \frac{\sum_{i = 2}^{‖ m ‖} d_{{CH}_{i - 1}^{m}, {CH}_{i}^{m}} + d_{Star t_{m}, {CH}_{i}^{m}}}{v_{m}} \\ + \frac{d_{{CH}_{‖ m ‖}^{m}, Star t_{m}}}{v_{m}} + \sum_{i = 1}^{‖ m ‖} \frac{{Da}_{i}^{m}}{S} \end{matrix}

(23)

When B $M S_{m}$ completes the data acquisition, the longest time-consuming $M S_{m}$ is the total data acquisition time

\begin{matrix} DT = max_{m = 1, 2, \dots, B} T (M S_{m}) \\ \begin{matrix} = max_{m = 1, 2, \dots, B} \end{matrix} (\frac{\sum_{i = 2}^{‖ m ‖} d_{{CH}_{i - 1}^{m}, {CH}_{i}^{m}} + d_{Star t_{m}, {CH}_{i}^{m}}}{v_{m}} + \frac{d_{{CH}_{‖ m ‖}^{m}, Star t_{m}}}{v_{m}} + \sum_{i = 1}^{‖ m ‖} \frac{{Da}_{i}^{m}}{S}) \end{matrix}

(24)

Energy consumption equilibrium degree of data acquisition

The network energy consumption is an important evaluation index of the lower WSNs. In the process of data acquisition, MS should balance the energy of the block center in the path to achieve the maximum extension of the network life. When ${CH}_{j}^{m}$ node energy consumption is set to $E_{j}^{m}$ , the energy consumption equilibrium degree of data acquisition is defined as $B_{load}$

B_{load} = \frac{\sum_{m = 1}^{B} | max {E_{1}^{m}, E_{2}^{m}, \dots, E_{‖ m ‖}^{m}} - \sum_{j = 1}^{‖ m ‖} E_{j}^{m} |}{\sum_{m = 1}^{B} \sum_{j = 1}^{‖ m ‖} E_{j}^{m}}

(25)

It can be concluded from formula (25) that the smaller the $B_{load}$ value, the more balanced the network energy consumption. From formulas (24) and (25), it can be seen that data acquisition time length and energy consumption equilibrium degree of data acquisition are closely related to the $M S_{m}$ path. Therefore, the data acquisition of mobile nodes can be transformed into solving the cooperative path planning problem of multi-mobile nodes. The objective function $f (G)$ of multi-MS_m collaborative path planning is defined as

f (G) {\begin{matrix} f_{1} = min (DT) \\ f_{2} = min (B_{load}) \end{matrix}

(26)

It can be seen from formula (26) that the evaluation function is used to optimize the time length and energy consumption equilibrium degree of the network, and to reduce data acquisition time length as much as possible to ensure that the energy consumption of each node is more balanced. In addition, the essence of the $f (G)$ solving process is the multi-traveling salesman problem (TSP),³⁴ which can be solved by intelligent optimization algorithm.

Realization of functional module of sensor-cloud system based on ECO

ECO algorithm

Scholars have proposed a series of intelligent optimization algorithms which have been widely used in all fields of production and life by simulating the evolution of species survival.³⁵ But premature convergence and low convergence efficiency are still the key problems to be solved in the current intelligent optimization algorithm. A large number of studies have shown that effectively maintaining the diversity of population samples is the key factor to improve the global optimization ability of intelligent optimization algorithm. In this article, a new intelligent optimization algorithm, ECO algorithm, is proposed by simulating three kinds of complete elastic collision (CE), complete inelastic collision (CI) and non-complete elastic collision (NCE).

Collision update

The two different particles $X_{i}$ and $X_{j}$ are moving oppositely at speeds $f (X_{i})$ and $f (X_{j})$ , respectively. The collision occurred at $Δ t$ and then $X_{i}$ arrived at the new position $X_{i, new}$ after $Δ t$ moment. For CE, according to the conservation of momentum and the law of conservation of energy, it is concluded that

\begin{matrix} {\begin{matrix} mf (X_{i}) + mf (X_{j}) = mf (X_{i, new}) + mf (X_{j, new}) \\ \frac{1}{2} m {[f (X_{i})]}^{2} + \frac{1}{2} m {[f (X_{j})]}^{2} = \frac{1}{2} m {[f (X_{i, new})]}^{2} + \frac{1}{2} m {[f (X_{j, new})]}^{2} \end{matrix} \\ \Rightarrow X_{i, new} = X_{i} \frac{2 f (X_{j})}{f (X_{j}) + f (X_{i})} + X' \frac{f (X_{i}) - f (X_{j})}{f (X_{j}) + f (X_{i})} \\ \Rightarrow X_{i, new} = CE (X_{i}, X_{j}) \end{matrix}

(27)

In the same way, for CI, there is

\begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \begin{matrix}  \end{matrix} mf (X_{i}) + mf (X_{j}) = 2 mf (X_{i, new}) \\ \Rightarrow X_{i, new} = X_{i} \frac{3 f (X_{j}) - f (X_{i})}{2 (f (X_{j}) + f (X_{i}))} + X' \frac{3 f (X_{i}) - f (X_{j})}{2 (f (X_{j}) + f (X_{i}))} \\ \Rightarrow X_{i, new} = CI (X_{i}, X_{j}) \end{matrix}

(28)

For NCE, there is

\begin{matrix} X_{i, new} = β \times CE (X_{i}, X_{j}), β \in (0, 1) \\ \Rightarrow X_{i, new} = NCE (X_{i}, X_{j}) \end{matrix}

(29)

It can be seen from the collision updating formula that $CE (X_{i}, X_{j})$ , $CI (X_{i}, X_{j})$ , and $NCE (X_{i}, X_{j})$ provide a variety of different learning evolutionary strategies, which can maximize the diversity of the population. The ECO implementation process can be described as

Step 1. Initialization: for n-dimensional optimization, the initial population $Θ (0) = {X_{1} (0), X_{2} (0), \dots, X_{P} (0)}$ composed of P unit mass particles is generated randomly in the solution space $R^{n}$ . $X_{i} (0) = [x_{i 1} (0), x_{i 2} (0), \dots, x_{in} (0)]$ is a possible solution to the optimization problem.

Step 2. Particle evolution update: the update mechanism for particle $X_{i} (t)$ at t is defined as

\begin{matrix} X_{i} (t + 1) = {\begin{matrix} X_{i, new} (t) + σ_{i} (t) N (0, 1), r_{1} ⩾ ε \\ X_{i} (t) \end{matrix} \\ X_{i, new} (t) = {\begin{matrix} CE (X_{i} (t), G_{i} (t)), r_{2} ⩽ 0.5 \\ CI (X_{i} (t), B (t)), 0.5 < r_{2} ⩽ 0.5 + ξ \\ α [NCE (X_{i} (t), X_{j} (t)) + NCE (X_{i} (t), X_{k} (t))], else \end{matrix} \end{matrix}

(30)

Among them, $σ_{i} (t)$ is the variance of population particle position; $ε \in (0, 1)$ ; $ξ \in (0, 0.5)$ are particle update coefficients; $G_{i} (t)$ and $B (t)$ are the historical optimal solution and population optimal solution of $X_{i} (t)$ , respectively; $r_{1} \in (0, 1)$ , $r_{2} \in (0, 1)$ , and $α \in (0, 0.5)$ are random numbers. If the fitness value of the updated $X_{i} (t)$ becomes worse, the original individual remains unchanged:

Step 3. Termination condition determination: if the algorithm satisfies the termination condition, the optimal solution is output, otherwise it will go to “Step 2.”

ECO computational complexity

The computation complexity of ECO algorithm is $O (n \log D)$ , and the complexity of initialization is $O (n)$ , so the complexity of ECO computation is $T_{max} O (n \log D) + O (n)$ .

Markov chain theory and other related theories can prove that ECO can converge to the global optimal solution with probability “1,” so it has global convergence. The ECO algorithm only involves three parameters of $ε$ , $ξ$ , and $β$ . The algorithm is easy to implement, and there are three different ways of “extreme collision” in the process of particle update. Meanwhile, the study of history and population optimal solution and the introduction of Gauss disturbance make the algorithm still maintain the diversity of the population in the later operation and effectively improve the convergence performance. The ECO population sample diversity index is defined as

O (t) = \frac{1}{Pn} \sum_{i = 1}^{P} \sum_{j = 1}^{n} {[x_{ij} (t) - \frac{1}{P} \sum_{i = 1}^{P} x_{ij} (t)]}^{2}

(31)

Conclusion 2

ECO can effectively maintain group diversity.

Proof: $\bar{x_{j} (t)} = [\sum_{i = 1}^{N} x_{ij} (t)] / N$ , then

\begin{matrix} E [O (t)] = \frac{1}{Pn} \sum_{i = 1}^{P} \sum_{j = 1}^{n} E {[x_{ij} (t) - \bar{x_{j} (t)}]}^{2} \\ = \frac{1}{Nn} \sum_{i = 1}^{N} \sum_{j = 1}^{n} {E {[x_{ij} (t) - E x_{ij} (t)]}^{2} \\ - 2 E ([x_{ij} (t) - E x_{ij} (t)] [E x_{ij} (t) - \bar{x_{j} (t)}]) \\ + E {[E x_{ij} (t) - \bar{x_{j} (t)}]}^{2}} \end{matrix}

(32)

Set $σ_{ij}^{2} (t) = E [x_{ij} (t) - E x_{ij} (t)]^{2}$ , then

E ([x_{ij} (t) - E x_{ij} (t)] [E x_{ij} (t) - \bar{x_{j} (t)}]) = σ_{ij}^{2} (t) / P

(33)

\begin{matrix} E {[\bar{x_{j} (t)} - E x_{ij} (t)]}^{2} = \frac{1}{P} \sum_{k = 1}^{P} σ_{kj}^{2} (t) \\ + {[E x_{kj} (t) - \frac{1}{P} \sum_{k = 1}^{P} E x_{kj} (t)]}^{2} \end{matrix}

(34)

Coupling equations (32)–(34) gives

E [O (t)] = \frac{P - 1}{P^{2} n} \sum_{i = 1}^{P} \sum_{j = 1}^{n} σ_{ij}^{2} (t) + O (E x_{ij} (t))

(35)

Among them, $O (E x_{ij} (t))$ is the ECO population sample diversity index of $E x_{ij} (t)$ . It can be seen from “Conclusion 2” that the ECO population diversity expectation value is closely related to $σ_{ij}^{2} (t)$ , and the ECO update strategy ensures the diversity of population particles; therefore, ECO can effectively maintain the diversity of the population.

Realization of functional module of sensor-cloud system based on ECO

The sensor-cloud data acquisition based on fog computing mainly involves three functional modules, namely, adaptive block compressed sensing, fog computing layer multi-mobile-node collaborative computing, and mobile node data acquisition path planning. Fog computing layer multi-mobile-node collaborative computing is a continuous optimization problem. And, ECO can be used to solve the fitness value function; thus, the optimal multi-mobile node data cooperative processing scheme is obtained. For the other two discrete optimization problems, we need to discretize the ECO. In addition, sparse data compression reconfiguration, multi-mobile node collaborative computing, and mobile node data acquisition path planning are implemented by the upper sensor-cloud system which provides the possibility of parallel computing, thus greatly improving the computational efficiency of the intelligent optimization algorithm.

Discrete elastic collision optimization algorithm implementation

A discrete elastic collision optimization algorithm (DECO) is proposed for discrete optimization problems. Each particle $X_{i} = [x_{i 1}, x_{i 2}, \dots, x_{in}]$ in DECO represents a solution. For sparse signal reconstruction, $X_{i}$ is equivalent to the reconfigurable signal $s_{N \times 1}$ , the value of each dimension is 1 or 0, and the number of dimensions of 1 is exactly equal to the signal sparsity K. For $M S_{m}$ mobile path planning, $X_{i}$ dimension is the network block number C, and the value of each dimension corresponds to the block center ${{CH}_{i}^{m}}_{i = 1 : C}$ , namely, $X_{i} - {1, 2, \dots, C} = \emptyset$ . Whether it is a sparse signal reconfiguration or a mobile path planning, two different particles can be reciprocal transformed through a series of coded bits, and the DECO update strategy is given.

Define particle coded switching operation $a \leftrightarrow^{X_{i}} b$ is defined as the operation of select a and b dimension coding in $X_{i} = [x_{i 1}, \dots, x_{in}]$ to switch. The transformation operation $X_{i} \leftrightarrow X_{j}$ of two different particles $X_{i}$ and $X_{j}$ is defined as a series of coding and switching operations, as follows

X_{j} = X_{i} + X_{i} \leftrightarrow X_{j}, X_{i} \leftrightarrow X_{j} = {a \leftrightarrow^{X_{i}} b}_{V_{i, j}}

(36)

where $V_{i . j}$ indicates that the number of $X_{i} \leftrightarrow X_{j}$ contains coded swap operations. Figure 4 shows a schematic of $a \leftrightarrow^{X_{i}} b$ and $X_{i} \leftrightarrow X_{j}$ .

Figure 4.

Schematic diagram of coded switching operation and particle transformation operation.

After defining the particle transformation operation, the DECO update strategy is given as follows

\begin{matrix} X_{i} (t + 1) = {\begin{matrix} X_{i, new} (t), r_{1} ⩾ ε \\ X_{i} (t) \end{matrix}, r = ⌊ r_{min} \times {(\frac{r_{max}}{r_{min}})}^{\frac{1}{1 + χ \times t / T_{max}}} ⌋ \\ X_{i, new} (t) = {\begin{matrix} X_{i} (t) + r ⊙ (X_{i} (t) \leftrightarrow G_{i} (t)), r_{2} ⩽ 0.5 \\ X_{i} (t) + r ⊙ (X_{i} (t) \leftrightarrow B (t)), 0.5 < r_{2} ⩽ 0.5 + ξ \\ X_{i} (t) + ⌊ r α ⌋ ⊙ [X_{i} (t) \leftrightarrow X_{j} (t) + X_{i} (t) \leftrightarrow X_{k} (t)], else \end{matrix} \end{matrix}

(37)

where $r ⊙ (X_{i} \leftrightarrow X_{j})$ indicates that, there are r coded interchange operations in the random selection $X_{i} \leftrightarrow X_{j}$ transformation operation, obviously $r ⩽ V_{i . j}$ . It is concluded from formula (43) that DECO keeps three learning strategies. With the increasing number of evolution, coded switching operation is adaptively adjusted; thus, the convergence accuracy and convergence speed of the algorithm are effectively balanced.

Reconstruction implementation of adaptive block compressed sensing sparse signal

First, the particle is coded according to $s_{N \times 1}$ dimension information of the reconstructed signal, and $min ‖ X ‖_{l_{0}}$ is selected as the target optimization function. Second, the function is solved by DECO, and the non-zero element position of the sparse signal is obtained. Third, the non-zero element amplitude value can be obtained by the least square method. Finally, the reconstruction of the sparse signal is realized. In order to improve the accuracy and efficiency of reconstruction, the parallel computing technology in the upper sensor-cloud is used and run $K_{max}$ DECO objective function optimization process simultaneously. Each optimization process sets different sparsity value K. K that makes the target function value minimum is chosen as the sparsity of the reconstructed signal, and the corresponding optimal solution is the reconstructed signal. Figure 5(a) is a sparse signal reconstruction flowchart of adaptive block compressed sensing.

Figure 5.

Flowchart of sensor-cloud system function module: (a) adaptive block compression sensing sparse signal reconstruction, (b) multi-mobile node collaborative computing implementation, and (c) mobile node data acquisition path planning.

Implementation of multi-mobile nodes collaborative computing system

It is assumed that there are z mobile nodes in a fog computing layer that need to transfer data to the upper sensor-cloud, and the ECO algorithm is used to solve the problem. The optimization target is selected as the fitness value function shown in formula (17), that is

f (X) = h' (X) + G' (X)

(38)

The particle $X$ coding is defined as the $z \times U$ matrix $Φ_{z \times U}$

X = Φ_{z \times U} = [\begin{matrix} h_{1}^{1} & h_{2}^{1} & \dots & h_{U}^{1} \\ h_{1}^{2} & h_{2}^{2} & \dots & h_{U}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ h_{1}^{z} & h_{2}^{z} & \dots & h_{U}^{z} \end{matrix}]

(39)

where the ith row data $(h_{1}^{i}, h_{2}^{i}, \dots, h_{U}^{i})$ in $Φ_{z \times U}$ represents data distribution of the ith mobile node. In the process of particle updating, $X_{i}$ updates the data line by line according to the ECO evolutionary update strategy. After z row data are updated, the particle fitness value and population optimal solution are updated. Figure 5(b) is a flowchart of multi-mobile nodes collaborative computing.

Implementation of the mobile node data acquisition path planning strategy

The essence of the mobile node data acquisition path planning strategy is the multiple TSP. DECO is used to solve the problem. According to formula (26), the objective function is set as follows

f (G) = τ_{1} min (DT) + τ_{2} min (B_{load})

(40)

Among them, $τ_{1}$ and $τ_{2}$ are weight coefficients. For particle $X$ coding block processing, the number of blocks M is exactly equal to the number of mobile nodes used for lower WSN data acquisition

X = [\overset{M S_{1}}{\overset{︷}{\begin{matrix} x_{1} & x_{2} & x_{3} \end{matrix}}} \overset{M S_{2}}{\overset{︷}{\begin{matrix} x_{4} & x_{5} & x_{6} \end{matrix}}} \begin{matrix} \dots \end{matrix} \overset{M S_{M}}{\overset{︷}{\begin{matrix} x_{C - 3} & x_{C - 2} & x_{C - 1} & x_{C} \end{matrix}}}]

(41)

From formula (41), we can conclude that the particle coding can make the $M S_{m}$ paths of M mobile nodes correspond to particle coding. In order to improve the efficiency of path planning, C block centers are randomly divided into M groups at initialization. In order to improve the efficiency of path planning solution, the C block center is randomly divided into M groups at initialization. Each group contains at least one block center. The process repeats J times, and a series of grouping methods ${({MS}_{1}^{i}, {MS}_{2}^{i}, \dots, {MS}_{M}^{i})}_{i = 1 : J}$ are obtained. Then, according to the grouping results of the J initial block center. The parallel computing technology is used to optimize the DECO path planning process. Finally, the solution of the minimum target function value is selected as the final path planning result. Figure 5(c) is a flowchart for mobile node data acquisition path planning.

Experimental simulation

Build a sensor-cloud architecture based on fog computing. The lower layer WSN is simulated on the NS2 platform, and $Q = 2000$ sensor nodes with known location information and performance parameters are arranged in the $10 km \times 10 km$ region. The upper cloud computing layer is simulated on the CloudSim test platform. And, the cloud computing layer divides the monitoring area into four regions: I, II, III, and IV. The $Q = 2000$ sensor nodes are divided into $V = 4$ virtual clusters by virtual technology to monitor the four regions. Set the user to monitor the signal in the “I” area, and set up the $N = 50$ event source in the area. The collaborative calculation of multi-mobile nodes in fog computing layer and the path planning process of the mobile node data acquisition are simulated on the MATLAB simulation platform. There are $U = 20$ mobile nodes in the fog computing layer. Each mobile node has the same physical parameters and known initial location information. The mobile node data processing speed is $v_{i} = 1.5$ GHz, and $e_{i, j}$ is generated randomly in the range of 0.08–0.12 s. The parameters of ECO algorithm are set by experiment: $P = 300$ , $ε = 0.35$ , $ξ = 0.15$ , $β = 0.35$ , and $T_{max} = 500$ . $r_{min}$ , $r_{max}$ is set by the specific optimization problem.

Experimental simulation of adaptive block compression sensing

In the face of a user’s monitoring request, the upper sensor-cloud system selects certain nodes in the working state according to the energy consumption and network coverage requirements of the lower WSN nodes and then obtains the network working node density $λ$ .The best network partition number $C = 16$ is obtained from “Conclusion 1.”

Contrast experiment of compressed sensing reconstruction algorithm based on DECO

In order to further analyze the performance of compressed sensing reconfiguration algorithm based on DECO, the signal values of $K = 6$ , $K = 8$ , $K = 10$ , and $K = 20$ events are measured, respectively, as the original signal $s_{N \times 1}$ . The classical StOMP reconstruction algorithm²⁹ and BSMP reconstruction algorithm³¹ are selected for comparative experiments. Experiments are repeated 30 times independently under each K value. The premise is that the size of the sparsity K is not known, and the number of sensor nodes M measured by the three algorithms is the same in the experiment. The average reconstruction error RE and the reconstruction success rate DSR are selected as the comparison index

\begin{matrix} RE = \frac{1}{Z} (\sum_{i}^{Z} \frac{{‖ s - \hat{s_{i}} ‖}_{2}}{{‖ s ‖}_{2}}); \\ DSR = \frac{\sum_{i}^{Z} z_{i}}{Z}, {\begin{matrix} z_{i} = 1, [\sum_{j = 1}^{N} (s_{j} - {\hat{s}}_{j})] / N ⩽ λ_{min} \\ z_{i} = 0, [\sum_{j = 1}^{N} (s_{j} - {\hat{s}}_{j})] / N > λ_{min} \end{matrix} \end{matrix}

(42)

Among them, ${\hat{s}}_{j}$ is the jth time reconstruction result, Z is the number of experiments, and $λ_{min}$ is the control threshold of reconstructing success rate. Figure 6 shows the comparison results of sparse signal reconstruction in three reconstruction algorithms (x axis represents sparse signal sequence, $y = 1$ indicates corresponding sequence number event source produces events). Figure 7 shows the RE comparison results of three refactoring algorithms under different K and M. Table 1 gives the comparison results of different evaluation indicators.

Figure 6.

Comparison of three reconstruction algorithms for sparse signal reconstruction.

Figure 7.

Comparison of three reconfiguration algorithms RE under different K and M.

Table 1.

Comparison results of different evaluation indicators $(M = 100)$ .

Algorithm	Index	$k = 6$	$k = 8$	$k = 10$	$k = 20$
DECO	RE	0.013	0.017	0.021	0.035
	$D S R (%)$	100	100	100	100
	$t (s)$	13.64	12.57	14.35	16.08
BSMP	RE	0.024	0.031	0.046	0.052
	$D S R (%)$	99.6	99.4	98.7	98.3
	$t (s)$	16.28	20.14	21.37	22.06
StOMP	RE	0.67	1.02	1.43	1.86
	$D S R (%)$	33.2	10.7	8.8	6.4
	$t (s)$	9.74	10.25	11.83	12.47

DECO: discrete elastic collision optimization algorithm.

As can be seen from Figure 6, for sparse signal reconstruction under $K = 6$ conditions (three algorithms do not know sparsity K in advance), DECO and BSMP can accurately find non-zero element positions of sparse signals (3, 14, 27, 28, 41, 45), and StOMP algorithm cannot achieve accurate reconstruction, and the result of the reconstruction is far from the original signal. This indicates that StOMP is not ideal for sparse signal reconstruction. As can be seen from Figure 7, for different K and M, DECO is better than the other two algorithms in terms of reconstruction error and reconstruction success rate. As can be seen from Table 1, a large number of experimental data show that reconstruction success rate of DECO is 100%, the maximum reconfiguration error is only 0.035, and the two indexes are better than the BSMP reconstruction. In the operation time of the algorithm, although K takes different values to determine the best sparsity strategy, the introduction of parallel computing technology greatly shortens the running time of the algorithm, and the operation time is better than the other two algorithms. DECO reconstruction parallel computing technology not only improves the accuracy of sparse signal reconstruction but also effectively improves the algorithm efficiency.

Contrast experiment of adaptive block compressed sensing data acquisition

In order to further analyze the performance of the lower layer WSNs adaptive block compressed sensing data acquisition, the DGSP data acquisition algorithm proposed by Tian³⁶ and the classical CDG data acquisition algorithm are compared. In the process of the experiment, three schemes are set to use the fixed Sink node to collect data, in which the DGSP algorithm is also based on the compression perception theory, but the data tree is used to carry out data transmission. Figure 8 shows the comparison between M and network energy consumption under different reconstruction error requirements.

Figure 8.

The comparison between M and network energy consumption under different reconstruction error requirements.

This shows that, on the premise of satisfying the reconstruction accuracy, the proposed scheme only needs to collect a small amount of work node data to achieve accurate monitoring, thus effectively reducing the network data communication. Compared with the other two schemes, the data acquisition amount is reduced by about 20%. CDG needs to improve the reconstruction precision by repeated acquisition of data. With the continuous reduction of the system’s demand for reconfiguration error, the energy consumption of the network also decreases, but it is still far higher than this and DGSP. Especially, although in the same system reconstruction error, and in the same number of nodes M, the energy consumption requirement of this method is less than DGSP. This can be proved by the fact is the introduction of adaptive block strategy makes more node data only need to be transferred within the block, resulting in more balanced network nodes. For the DGSP algorithm, every node needs data transmission in the form of data tree, which increases the energy consumption of the local nodes and increases the energy consumption of the network. The experimental result shows that the adaptive block compressed sensing data acquisition mechanism can effectively reduce the amount of data acquisition, and the energy consumption of network nodes is more balanced and the lifetime of the network is longer.

Simulation experiment of multiple mobile nodes cooperative computing in fog computing layer

It is assumed that only one mobile node data in fog computing layer need load balancing allocation, and ECO is compared with Greedy-LB (greedy load balancing algorithm), WRR (weighted rotation method), and CPSO-LB algorithm proposed by the literature,³⁷ respectively. The evaluation index is set to the data coordination computation delay, that is, the load balancing time of the data in the fog computing layer. Figure 9 shows the comparison results of three load balancing algorithms. Figure 10 shows the comparison result between ECO algorithm and genetic algorithm (GA),²¹ quantum particle swarm optimization algorithm (QPSO)³⁵ objective function convergence curve. Figure 11 shows the effect of the number of mobile nodes on data co-computing delay.

Figure 9.

Comparison of data processing time delay between three load balancing algorithms.

Figure 10.

The convergence curve of three algorithm target functions.

Figure 11.

Influence of mobile node number on data co-computing delay.

As can be seen from Figure 9, as the amount of task processing is increasing, the time delay of the four algorithms is increasing, but ECO is better than the other three algorithms, especially when the data processing quantity is larger (20 GB), the time delay advantage of ECO data cooperative computing is more obvious, about 50.1% ∼ 77.6%. As can be seen from Figure 10, the ECO algorithm has faster convergence speed and higher accuracy. It only needs iteration 204 times to find the global optimal solution, which is faster than QPSO and GA algorithm. As can be seen from Figure 11, when the amount of data processing is small, the number of mobile nodes in the fog computing layer has little effect on the time delay of data co-computing, but if the amount of data processing increases gradually, the more number of mobile nodes, the smaller time delay of data cooperative computing. The above experiments show that, for large data processing task, ECO can give a better load balancing scheme and increasing the number of mobile nodes can effectively reduce the time delay of data collaborative computing.

In the fog computing layer, the mobile node can respond to the data acquisition results quickly because of its ability of data processing.³⁸ In order to further analyze the data processing capability of fog computing layer, the sensor-cloud system contained only one mobile node and no fog computing layer and cloud network proposed by Li and Wang³⁷ are compared and analyzed. The evaluation index is data processing time delay, and the comparison results are given in Figure 12.

Figure 12.

Time delay comparison of data processing in different systems.

As can be seen from Figure 12, when the amount of data is very small, the data delay of a single mobile node system is smaller than the other three systems. Because there is no data co allocation time, and only a small amount of data is processed in the fog computing layer, there is no need to pass it to the cloud. With the increasing amount of data processing tasks, and CPSO-LB algorithm proposed in Li and Wang³⁷ system data processing delay is better than the other two systems. Because the cloud system without fog computing layer is far from the lower WSNs, resulting in a large delay in data communication. Under the same amount of task, the data processing delay of the system is better than that of CPSO-LB algorithm, which reduces by about 12.8%, compared with the simple cloud system, which reduces about 20.1%. However, when the task processing volume reaches a certain scale, the data processing time delay of this article and CPSO-LB algorithm is higher than the pure cloud system. Because the large amount of data has exceeded the fog computing layer processing capacity and takes more time to deal with the data. The cloud is able to complete the large-scale data processing in a short time with the powerful computing power. The experimental results show that when the data processing task is within a reasonable range, the fog computing layer can effectively lower the data processing delay.

Mobile node data acquisition path planning

In order to analyze the effectiveness of DECO to solve the path planning problem of mobile node data acquisition, the discrete particle swarm optimization (DPSO)²⁷ and the GA proposed in the literature²¹ are compared. The experimental content selects the classic TSP single traveler path optimization centralized eil151, ch150 and the number of mobile nodes 2 and the data acquisition path planning of multiple mobile nodes in $C = 16$ , $C = 25$ . Each algorithm runs 30 times independently and selects the average distance $\bar{S}$ , the mean operation time $\bar{T}$ , and the path planning error Err as the evaluation index. Table 2 shows the comparison results of three kinds of algorithms.

Table 2.

Comparison of evaluation indexes of three algorithms.

Algorithm	Index	eil151	ch150	$C = 16$	$C = 25$
DECO	$\bar{S}$	430.8	6530.4	7034.5 m	7782.4 m
	$\bar{T}$	8.15	14.07	6.45	7.24
	$E r r (%)$	0.61	0.73	–	–
DPSO	$\bar{S}$	507.2	7113.8	7563.8 m	8016.7 m
	$\bar{T}$	11.54	28.17	10.88	25.16
	$E r r (%)$	12.3	15.7	–	–
GA	$\bar{S}$	455.6	6678.3	7215.8 m	7954.7 m
	$\bar{T}$	9.57	19.82	13.34	17.32
	$E r r (%)$	9.4	11.2	–	–

DECO: discrete elastic collision optimization algorithm; DPSO: discrete particle swarm optimization; GA: genetic algorithm.

It can be seen from Table 2 that DECO is better than the other two algorithms in solving the accuracy, and the path planning distance is shorter and the algorithm efficiency is better. After introducing parallel computing technology, multiple populations will perform DECO evolution operation at the same time, so that the efficiency is higher and the accuracy is better. This also shows that DECO can solve the traveling salesman path planning problem well.

When the divided block number of lower WSNs is c = 16, the fog computing layer sends 1 and 2 mobile nodes to collect the underlying WSN network data, respectively. Figure 13 shows the path planning results of mobile nodes with different node moving speed. Figure 14 shows the time delay comparison results of mobile nodes with different node moving speeds.

Figure 13.

The mobile nodes path planning results with different node moving speeds.

Figure 14.

The time delay comparison results of mobile nodes with different node moving speeds.

As can be seen from Figure 13, for different node moving speed, path planning results are different, which indicate that the speed of mobile nodes has an important impact on the delay. As can be seen from Figure 14, with the increasing speed of mobile nodes, the delay of data acquisition decreases gradually, whether it is a single mobile node or a dual mobile node. However, mobile nodes data acquisition is not suitable for places with high real-time requirements.

In order to further analyze the influence of mobile node data acquisition on the energy consumption of the system, respectively set up a system that does not include mobile nodes (using adaptive block compressed sensing for data acquisition), a system containing only one mobile node, a system containing two mobile nodes (using adaptive block compressed perception for data acquisition), and the general data acquisition system (without mobile node and adaptive block compressed sensing strategy) are compared. The comparison results are given in Figure 15.

Figure 15.

Comparison of energy consumption of different data collection.

From Figure 15, it can be seen that the introduction of mobile nodes and adaptive block compressed perception can greatly reduce the energy consumption of the network, and the energy consumption of the general data acquisition system is far greater than the other three systems. Because mobile nodes are used for data acquisition, there is no data communication between the nodes of the block center, and the path planning uses the energy consumption balance degree of the network node as the optimization objective, thereby effectively reducing the energy consumption of the network. The experimental results show that the use of mobile nodes for data acquisition can reduce the network energy consumption and prolong the network survival time when the time delay is low.

Analysis of simulation results of sensor-cloud data acquisition based on fog computing

Combined fog computing and adaptive block compressed sensing sensor-cloud can effectively achieve data acquisition. The introduction of adaptive block compressed sensing enables the effective monitoring of the target area with only a small amount of observation node data, which greatly reduces the network traffic. The load balancing allocation strategy of mobile nodes is processed by collaborative computing among mobile nodes, which significantly improves the time delay characteristics of the system. The simulation results show that compared with the simple sensing cloud system, the network traffic is reduced by about 20% and the network task delay is reduced by 12.8%–20.1%.

The application of fog computing layer has strong performance advantages. In the range of reasonable data tasks, the fog computing layer has strong data processing capability, the data delay is small, and it can respond to unexpected situations quickly. The data acquisition path planning of multiple mobile nodes is more suitable for the application of periodic data acquisition and analysis. The simulation experiment also proves that it is of great significance to the energy consumption of the equilibrium network and the prolongation of the network lifetime.

Sensor-cloud system based on fog computing can provide better services. The system combines many key technologies and has powerful service functions. It can provide different technical support for different user requests. For example, the response time and response accuracy are more concerned with the sudden response, and the adaptive block compressed perception and fog computing layer mobile node load balancing allocation strategy can be used to provide more rapid and accurate decision information.

Conclusion

In this article, the problem of data acquisition in WSNs was studied. A sensor-cloud data acquisition scheme based on fog computing and adaptive block compression was proposed, which solved the problems of large data processing network, high task delay, and unbalance of energy consumption. On the basis of building fog computing sensor-cloud system architecture, adaptive block compressed perception, fog computing layer mobile node load balancing allocation, multi-mobile node data acquisition path planning, and ECO algorithm were designed, and the concrete implementation process was given. Finally, the simulation experiment also verified the effectiveness and outstanding advantages of the proposed scheme. Next, we will study the direction of sensor-cloud security and privacy, quality of service, and so on.

Footnotes

Appendix 1

Appendix 2

Handling Editor: Francesco Longo

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported, in part, by the National Natural Science Foundation of China under grant 61871313; the Natural Science Basic Research Plan in Shaanxi Province, China, under grant 2017JM6096; China Postdoctoral Science Foundation funded project, China, under grant 2018M633573; the Xi’an Science and Technology Project, China, under grant 2017076CG/RC039(XAHK001).

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