Joint optimal placement,routing,and energy allocation in wireless sensor networks with a shared energy harvesting module

Abstract

Today, there is significant attention being paid to wireless sensor networks equipped with energy harvesting modules (energy harvesting wireless sensor networks). They have been experimentally applied to some practical scenarios, such as structural health monitoring. However, the constraints (e.g. energy-neutral operation, node placement, and routing protocols) of energy harvesting wireless sensor networks still need further consideration before their actual deployment on structures. In this article, we consider a novel energy harvesting wireless sensor networks system for structural health monitoring in which a common energy harvesting module (including its storage battery) provides shared access to all energy harvesting nodes. The individual nodes do not own the independent energy harvesting modules and can only withdraw energy from the shared battery, which has an optionally changing energy level. Our aim is to find optimal solutions for three problems: (1) the minimum number of nodes needed for deployment, (2) the most efficient path from each node to the sink, and (3) the maximum network utility under energy harvesting constraints. Therefore, a joint optimization algorithm including sensor placement, routing, and energy allocation is introduced and solved; a sensor location optimization scheme is proposed according to the Fisher information matrix; and the condition of the communication channels and the nodes’ energy harvesting status are considered. We then propose an algorithm to jointly minimize the number of nodes and maximize the data sampling quality under energy-neutral working settings. Simulation results show that the proposed algorithm always attains high-efficiency network energy distribution and achieves higher network utility than existing approaches.

Keywords

Wireless sensor network energy harvesting structural health monitoring energy allocation node placement routing protocol joint optimization

Introduction

Wireless sensor networks (WSNs) are ideal for covering or monitoring an operating environment.¹ Generally, sensor nodes sense the environment, help forward data from other nodes, and transmit them wirelessly to several sinks. WSNs are very suitable for structural health monitoring (SHM), especially for some critical infrastructure and protective buildings. Because of the simplicity of installation and low maintenance cost, SHM using WSNs has been given increasing attention and rapid development.^2–7

Numerous challenges for conventional battery-powered WSNs arise when used in SHM. Some typical problems include the large amount of collected data, frequent battery replacement, highly precise requirements for synchronization among nodes, and highly reliable control protocols, especially for large-scale networks. These issues can be significantly resolved by equipping nodes with energy harvesting (EH) functions: EH function blocks could harvest energy from the ambient environment (e.g. solar and wind) and use this energy to drive the workload of sensor nodes. Moreover, if used wisely, the EH-WSN would never break down, except for hardware failure.^8–11 However, it is important to note that because of the stochastic nature of EH procedures, the harvested energy cannot transfer in a steady and uninterrupted fashion. Thus, a method for accurate energy allocation is essential for the EH-WSN system.

In a normal EH-WSN for SHM, sensor nodes are always deployed in strategic locations to capture the building’s dynamic response precisely and sensitively. The process of node deployment is regarded as the selection of the best locations to gather data on the building’s status, while routing is considered to be finding a continuous path with good connectivity from the source node to the sink.^12–14 Since routing is significantly influenced by the node’s location and energy status, a joint optimization of node deployment and its corresponding routing is very necessary for highly efficient and reliable wireless structure monitoring.

In this article, we consider and analyze an EH-WSN system where all sensor nodes share access to a common EH module and storage battery. Here, the common EH module should be installed on the building roof or exterior of the structure and harvest energy from solar, wind, and other sources, whereas indoor nodes do not possess their own EH modules. The EH rate of this single external EH module is X (J/s), and the harvested energy is stored in its storage battery. Then, all distributed nodes send their energy extraction requests to the shared battery, which does not know the future energy arrivals or the data waiting for transmission. After that, the energy of the shared battery will be analyzed and sent to the indoor nodes via wireless radio frequency (RF) energy transference, and each node stores the received energy in its own battery. Each node then starts to sample, process, and transmit data based on these actions. This architecture is particularly helpful in SHM scenarios for its usability and ease of installation. Our focus is on deploying nodes to acquire as much information as possible while ensuring energy-neutral working constraints.

Recently, the joint optimization of sensor placement and routing for WSN has been widely studied in previous studies.^15–21 ZA Eu et al.¹⁵ have optimized network performance by finding the optimal routing algorithm and relay node placement scheme for EH-WSN. They researched metrics including network throughput, goodput, source sending rate, efficiency, data delivery ratio, and hop count. J Skulic et al.¹⁶ proposed a methodology for calculating the optimal placement of sensor nodes in linear network topologies (along the length of a bridge). Both simple packet relay and network coding are considered for the routing of the collected data packets toward two sink nodes positioned at both ends of the bridge. S Halder and D Sipra¹⁷ find node density as the parameter that has a significant influence on network lifetime and derive desired parameter values for balanced energy consumption. Their simulation results show that their proposed node deployment algorithm performs better on coverage connectivity, energy balance, and network lifetime. C Yang and K-W Chin¹⁸ aim to determine the locations to place the minimum number of nodes required for sensing and relaying that covers all targets and have an optimal path to the sink under energy-neutral operations. They propose two heuristics to accomplish this task, but the EH rate remains the same for all sensor nodes, making it an unrealistic approach for actual applications. M Dong et al.¹⁹ propose a novel protocol which jointly optimizes the energy and delay efficiency under reliable constraint in a cluster-based WSN, result shows that it can increase the network lifetime by more than 8% and reduce network delay by more than 25%. F Mansourkiaie et al.²⁰ present an optimal solution to maximize the lifetime of WSN for SHM by joint use of optimal power and route selection. Especially, Elsersy et al.²¹ introduce a joint formulation that optimizes placement, routing, and flow assignment in a normal WSN for SHM. A genetic algorithm (GA)-based solution is designed and some parameters such as information quality, total energy consumption, and their normalized ratio are analyzed and optimized.

Our work intends to both maximize the information quality and minimize the power consumption under EH constraints. We design an efficient and reliable energy distribution method along with a corresponding node placement algorithm and a routing protocol. To the best of our knowledge, this article is the first to consider the network utility of EH-WSN in SHM. The main results and innovations are as follows:

A novel formulation that can jointly optimize node placement, network routing, and energy allocation has been introduced. The optimized result can meet both civil engineering demands and networking requirements.

We propose an optimization algorithm using the effective independence model based on the Fisher information matrix (FIM). The novel algorithm achieves a high-accuracy near-optimal solution.

We evaluate the performance of our algorithm. Results show that the algorithm efficiently allocates the harvested energy to each individual node, significantly reduces the outage probability of the deployed network, and notably improves the information quality.

The remainder of this article is as follows: Section “System model” presents the system model of our EH-WSN for SHM. Section “The problem” introduces the new formulation of the node deployment, routing, and energy allocation optimization problem. Section “Solution” shows a greedy search-based approach for finding a near-optimal solution. Section “Numerical results” analyzes and compares the experimental results of the proposed algorithm. Finally, section “Conclusion” summarizes the article and looks to the future.

System model

In this section, we discuss the system model and the assumptions made to mathematically represent its parameters. Specifically, the following subsections present the framework with respect to energy dynamics, packet transmission, node placement, and information quality.

Energy dynamics and packet transfer

The designed monitoring system under study is shown in Figure 1, where N single-antenna nodes are mounted in a classical historic building to inspect the structural health status. All nodes (except the sink) share access to a common EH module, which is wired with an associated shared storage battery, and its EH rate is X (J/s). The storage battery periodically reallocates any harvested energy to the N nodes based on a mechanism G during every T seconds, and this operating mode is called an epoch. The EH rate X can be modeled in general as a non-negative continuous random variable, similar to Mukherjee.²² It is supposed that X follows a uniform distribution law: $X ~ U [a, b]$ .

Figure 1.

System architecture of our EH-WSN for SHM.

In each epoch, node i transmits data to its own intended receiver node j at power $P_{i}^{t}$ , while the distance between them is $d_{ij}$ , and the total transmission time to a node is assumed to be $T_{i}$ , where $T_{i} \leq T$ . The data transmitting varies in size, and consequently, $T_{i}$ is a time-changing parameter across epochs. We think each node should exhaust all their available energy in a best-effort transmission mode and thus empty their local batteries after each epoch.

At the start of an epoch, every node sends out its individual energy request to the shared battery, with node i requesting energy ${\bar{E}}_{i}^{th}$ . Then, the shared battery proceeds with the energy allocation mechanism based on its available total energy $E \overset{Δ}{=} XT$ and global request vector $e = [{\bar{E}}_{1}^{th}, {\bar{E}}_{2}^{th}, \dots, {\bar{E}}_{N}^{th}]$ . Here, let $E_{i}$ denote the energy ultimately allocated to node i. The net energy actually received by node i is assumed to be $η_{i} E_{i}$ , where $0 \leq η_{i} \leq 1$ is a deterministic parameter that accounts for conversion losses during the energy transfer from the shared to the local battery.

In the proposed monitoring system, the sensor nodes communicate with their receivers over N orthogonal channels. For this indoor network, multipath scattering is expected to be limited and the signal propagation will be dominated by shadow fading, in addition to penetration and path losses. Thus, the received power at the receiver of node i (i.e. node j) is approximated as²³

P_{j}^{r} = \frac{K_{i} P_{i}^{t}}{Ψ_{i} d_{ij}^{α}}, i = 1, 2, \dots, N

(1)

where $K_{i} \leq 1$ is a constant path penetration loss factor, $Ψ_{i}$ is a log-normal shadow fading variable with $10 \log_{10} Ψ_{i} ~ N (0, σ_{dB, i}^{2})$ , and $α > 2$ is the path loss exponent. The linear mean of $Ψ_{i}$ is given by $E {Ψ_{i}} = \exp (σ_{dB, i}^{2} / 2 ε^{2})$ , where $ε = 10 / \ln 10$ . To achieve a minimum power target of $P_{j}^{min}$ at node j, the instantaneous transmitting energy requirement for node i is

E_{i}^{th} = \frac{Ψ_{i} d_{ij}^{α} T_{i} P_{j}^{min}}{K_{i}}, i = 1, 2, \dots, N

(2)

Correspondingly, the receiving energy requirement for node j is approximately $P_{j}^{min} T_{i}$ . So, briefly speaking, node i could calculate its average energy requirement

{\bar{E}}_{i}^{th} \overset{Δ}{=} E {E_{i}^{th}} = E {Ψ_{i}} d_{ij}^{α} T_{i} P_{j}^{min} K_{i}^{- 1}

(3)

While node j’s average energy requirement should be

{\bar{E}}_{j}^{th} \overset{Δ}{=} E {E_{j}^{th}} = E {Ψ_{j}} d_{jz}^{α} T_{j} P_{z}^{min} K_{j}^{- 1} + P_{j}^{min} T_{i}

(4)

here, z is the next hop of node j. The above formulae should be periodically computed at each epoch. Notice that ${\bar{E}}_{i}^{th}$ is different in each epoch since $T_{i}$ is time-changing.

Node placement and information quality

In the proposed EH-WSN for SHM, nodes are deployed in select locations to collect data reflecting the structure status. To ensure the effectiveness of this EH-WSN, the sensor node deployment must be energy-efficient and possess high information quality. The sensor node deployment method using the effective independence model is a deployment algorithm that arranges sensor locations subject to the FIM results:²⁴ The core idea is a local search among all possible locations. It takes the following input parameters: the structure vibration pattern (known as the “modal shape”); the set of candidate locations (M) given by the civil engineering placement criteria; the number of sensor nodes to be placed (N); and the constraint assumptions related to the routing, power, topology, and other factors. In summary, the sensor node deployment problem is just the process of selecting N locations out of the total M potential locations given by the civil engineering model.

The sensor deployment scheme in SHM can be described as discovering a location indicator set $S = {s_{1}, s_{2}, \dots, s_{M}}$ , where $s_{i}$ is a binary indicator. If location i is selected, then $s_{i}$ equals one and vice versa. Additionally, $s_{0}$ represents the sink that is the destination of all data flows. We assume that the information quality is a function of the collected modal shapes, where different modal shapes are generally associated with different vibration frequencies. The modal shape matrix $Φ$ is shown as

Φ = [\begin{matrix} δ_{11} & δ_{12} & \dots & δ_{1 k} & \dots & δ_{1 L} \\ \dots & \dots & \dots & \dots & \dots & \dots \\ δ_{M 1} & δ_{M 2} & \dots & δ_{Mk} & \dots & δ_{ML} \end{matrix}]

(5)

here, $Φ$ synthesizes the individual contributions of all sensor nodes; $δ_{Mk}$ is the measured vibration gathered by the Mth sensor for the kth modal shape, and L is the total number of structure modal shapes. Thus, the FIM determinant $| Q (S) |$ can be given as²⁴

| Q (S) | = det [(Φ)^{T} R^{- 1} Φ]

(6)

here, R is the covariance matrix account for the noise in the modal shape measurements. Let $O$ represent the normalized sensor information quality and be defined as

O = \frac{| Q (S) |}{| Q_{max} (S) |}

(7)

here, $| Q (S) |$ is the FIM determinant for a set of selected sensor nodes and $| Q_{max} (S) |$ is the FIM determinant when all sensor nodes have been chosen. $| Q (S) | = | Q_{max} (S) |$ when S equals all but one vector.

The problem

We are now ready to define the minimize the number of nodes and maximize the data sampling quality under energy-neutral (MNMQN) problem. Its aim is to minimize the number of sensor nodes and their corresponding locations such that the target structure can be continuously monitored as much as possible, maximize the sensor information quality, and ensure that it is energy neutral. Let $E_{total} (S)$ represent the total energy consumption of all nodes, and it is shown as follows

E_{total} (S) = \sum_{i = 1}^{M} η_{i} E_{i}

(8)

Then, we have the joint MNMQN optimization problem

Maximize

| Q (S) | / E_{total} (S)

(9)

Subject to

\sum_{i = 1}^{M} s_{i} = N

(10)

\sum_{i = 1}^{N} E_{i} = E

(11)

\sum_{i = 1}^{N} {\bar{E}}_{i}^{th} \leq \sum_{i = 1}^{N} η_{i} E_{i}

(12)

d_{ij} \leq R_{max}, \forall i, j, i \neq j

(13)

d_{i} > d_{j}, \forall i, j, i \neq j

(14)

The formula has the following constraints, as defined in the indicated equations: equation (10) enforces that the number of chosen nodes must be same as N, equation (11) imposes that the allocated energy is equal to the energy harvested during the last time epoch (as for the shared battery), equation (12) ensures that the sum of energy requested by each node does not exceed the sum of energy harvested and stored in each node, equation (13) guarantees the nodes’ connectivity by ensuring that the distance $d_{ij}$ between any two sequential connected nodes does not exceed the maximum transmission range $R_{max}$ , and equation (14) enforces that node i’s distance to the sink node (d_i) must be greater than the next hop node j’s distance (d_j).

We can see that the MNMQN aims to choose the suitable nodes, determine their routing sequence (which also determines the energy cost of the sensor nodes), and compute the minimum number of sensor nodes to sustain optimal monitoring performance, which is the ultimate aim. Moreover, the total energy consumed by nodes is no greater than the energy harvested. In this respect, the MNMQN will deploy sufficient sensor nodes to satisfy constraints under a given X.

Solution

Since node deployment is represented by a binary variable, it is convenient to execute and operate in an optimization algorithm. We can use an efficient non-exhaustive search method to find the optimal solution. In this article, such methods are adopted to deploy nodes and discover routes to maximize information quality and maintain the total energy consumption less than but most close to the energy harvested by the common EH module.

We call a solution of the optimization problem a chromosome. It is assembled by a list of variables called genes. It contains two main parts: in the first node placement part, there are M genes arranged in order from the left. If the gene value is 1, then the corresponding sensor node is placed, and if it is 0, then no sensor node is placed. In the second routing part, there are N genes arranged in order from the left. The first gene indicates the placed sensor node that is farthest from the sink, and its corresponding value indicates its next hop sensor node. The last gene in the second part is the sink $S_{0}$ and we set its next hop to be just itself. The size of a chromosome should be equivalent to the sum of the total number of possible locations plus the total number of possible routings, as shown in Figure 2.

Figure 2.

Solution representations with placement and routing.

For example, if we want to select 4 locations out of 10 potential locations, the first random placement part could be shown as follows, in which locations $S_{2}$ , $S_{7}$ , $S_{8}$ , and $S_{9}$ have been chosen. Second, given the condition ( $d_{9} > d_{8} > d_{7} > d_{2}$ ), the routing part could be designed as Figure 3(b): $S_{9}$ transmits to $S_{8}$ , $S_{8}$ transmits to $S_{2}$ , the next hop of $S_{7}$ is also $S_{2}$ , and $S_{2}$ directly links to $S_{0}$ .

Figure 3.

Example of solution representation: (a) placement and (b) routing.

We randomly produce a certain number of solutions to develop an initial population, and then, the solutions that fit equations (10)–(14) survive and move on to the next step. Based on these generated solutions, energy request $e = [{\bar{E}}_{1}^{th}, {\bar{E}}_{2}^{th}, \dots, {\bar{E}}_{N}^{th}]$ should be formed and calculated with equations (3) and (4). After that, each solution’s $E_{total} (S)$ and $| Q (S) |$ can also be computed with equations (6) and (8), so we obtain every feasible solution’s result of $| Q (S) | / \sum_{i = 1}^{N} η_{i} {\bar{E_{i}}}^{th}$ , and the one with the highest value becomes the optimal answer of the MNMQN problem. The detailed diagram of this joint optimization algorithm is shown in the following.

Numerical results

In this part, we evaluate the performance of the proposed joint MNMQN mechanism with a common experimental mechanism. This mechanism is characterized by a random node placement scheme, a shortest path routing model (Dijkstra’s algorithm)²⁵ and a uniform energy allocation strategy where $E_{i} = E / N, \forall i$ . The performance metrics include the total energy consumption $E_{total} (S)$ , the normalized information quality $O$ , and the ratio $ζ$ of the information quality to the total energy consumption. Some detailed parameters are shown in Table 1.

Algorithm 1. Joint node placement, routing, and energy allocation optimization algorithm.
1: InputsM is the number of candidate locations.
X is the energy harvesting rate.
2: Initialize $T, η_{i}, T_{i}, K_{i}, P_{i}^{min}, E {Ψ_{i}}, d_{i}, d_{ij} \forall i, j$
3: Generate random solutions $ℝ$ .
4: Compare and select feasible solutions $ℝ^{†}$
according to equations (13) and (14).
5: Calculate energy request $e = [{\bar{E}}_{1}^{th}, {\bar{E}}_{2}^{th}, \dots, {\bar{E}}_{N}^{th}]$
for every solution in $ℝ^{†}$ .
6: Compare and select feasible solutions $ℝ^{† †}$
according to equations (10)–(12).
7: Calculate FIM determinant $\| Q (S) \|$
for every solution in $ℝ^{† †}$ .
8: Compute value $ζ = \| Q (S) \| / \sum_{i = 1}^{N} η_{i} {\bar{E_{i}}}^{th}$
for every solution in $ℝ^{† †}$ .
9: Set the solution with highest $ζ$ to be the optimum value.
10: Outputs optimal sensor location indicators S, routing sequence L and allocated energy E.

Table 1.

Simulation parameters.

Parameter	Value	Parameter	Value
Path penetration loss factor $K_{i}$	−11.57 dB	Transmission time Ti	$T_{i} ~ U [0, 2] s$
Minimum power target $P_{i}^{min}$	−55 dB m	Energy transfer loss η_i	$η_{i} ~ U [0.5, 0.7]$
Path loss exponent $α$	2.7	EH rate X	$X ~ U [2.5, 5] mJ / s$
$σ_{dB, i}^{2}$	3 dB	R _max	30 m

EH: energy harvesting.

We simulate and evaluate the performance of our algorithm in a supposed 10-floor tower. The building’s height is considered to be 30 m and the floor height is 3 m. A two-dimensional plane graph is shown in Figure 4, where the sink node’s position is assumed to be (0, 0) and the potential candidate EH nodes with a total number $M = 28$ can be placed on each floor according to the SHM requirements. Therefore, we calculate the distances from every potential monitoring site to the sink (d_i) and the mutual distances among these sites themselves (d_ij). After this, we check the normalized information quality $O$ with different N, and the results are shown in Figure 5.

Figure 4.

The 10-floor tower of L = 30 m. (The blue dot represents the sink and green dots represent the candidate EH nodes.)

Figure 5.

The normalized information quality versus number of nodes.

It is apparent that the index $O$ remains almost the same for our joint optimization mechanism under the given EH rate. The proposed MNMQN algorithm computes the optimal locations and makes the sensors energy neutral. Obviously, it is highly unlikely that full deployment can be achieved due to the energy constraints. While in the random placement step, we can see an increase in the information quality along with the deployed sensors (omitting the EH constraint). This is a normal response, as more sensors have been set down.

Next, to investigate the total energy consumption $E_{total} (S)$ , we compare the MNMQN algorithm with the random deployment strategy that has a shortest path routing protocol. Figure 6 shows the exact comparison between the two schedules.

Figure 6.

The energy consumption request versus the number of nodes.

Similar to the former measurement, MNMQN automatically calculates the optimal number of sensor nodes and the corresponding individual energy requests, while the random strategy computes average energy consumption requests after the number value has been set. Only successful routing results can advance to the following statistical analysis stage (average operation). Its energy consumption increases when the number of nodes increases because there is more traffic flowing through the network. From Figure 6 it is clear that the MNMQN algorithm consumes a relatively small amount of energy than the harvested power during one time slot.

Then, the ratio $ζ$ of the information quality to the total energy consumption must be studied. Figure 7 plots the ratios for the MNMQN algorithm and an integrated random placement strategy. Here, the integrated random strategy contains the shortest routing component and a uniform energy allocation mechanism wherein $E_{i} = E / N, \forall i$ . Once we set the number of nodes, they will be randomly placed. Therefore, the routing sequence can be created and the working energy $E_{i}$ will be transferred simultaneously. Note that accidents may occur when the energy consumption request exceeds the gathered energy, which may cause network outages.

Figure 7.

$| Q (S) | / E_{total}$ versus the number of nodes.

Finally, we research the MNMQN’s performance when the EH rate changes. If the EH rate increases, then the energy harvested increases. Therefore the number of nodes that can be supported also increases, which improves the information quality. Figure 8 captures the changes of $O$ and $E_{total} (S)$ during the evolution process as shown in the following.

Figure 8.

Changes of metrics as the EH rate varies.

In conclusion, these simulations indicate that the proposed joint optimization MNMQN mechanism offers the best combination of system monitoring information and individual node energy utilization and has also been analytically shown to be applicable and truthful.

Conclusion

This work proposes a novel formulation that jointly optimizes the placement, routing, and energy allocation for an EH-WSN used in SHM. Its aim is to determine the minimum number of sensor nodes and their corresponding locations such that the target structure can be continuously monitored as much as possible and maximize the sensor information quality while ensuring that the system is energy neutral. Numerical simulations are evaluated for a 10-floor tower to analyze the performance of the proposed algorithm. Parameters such as information quality, total energy consumption, and their normalized ratio have been analyzed and reviewed. The results show the effectiveness and efficiency of the proposed algorithm. Future work will focus on the proposal of a Medium Access Control (MAC) protocol for EH-WSN and consider cluster-based topology structures.

Footnotes

Academic Editor: Roberto Casas

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 by the Natural Science Foundation of Jiangsu Province, China (No. BK20150880). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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