2015, Vol.2 
2. Technical University of Dortmund, Dortmund 44221, Germany;
3. Northeastern University, Shenyang 110819, China
Energy problem in WSN is becoming ever more critical and leads to some phenomena which significantly reduce network lifetime. Tremendous research work has been done to reduce the energy consumption of wireless sensor network(WSN) to extend their lifetime[1, 2, 3, 4]. However,lifetime of battery-powered WSN is limited no matter how the transmission policies or deployment strategies are optimized. To address this issue,energy harvesting device (EHD) has emerged as a promising device to prolong the operating time of WSN. EHD is a device through which sensor node can collect energy from ambient energy sources (including solar,wind, thermal and vibration) and convert it to usable electrical power to feed sensor nodes[5, 6, 7].
Fig. 1 is a simple energy harvesting sensor (EHS) node,where EHD collects energy from environment. The energy is stored in a battery (or super-capacitor). Sensor node controller can adjust sensor node transmitted power and decide when to collect sensing data. Sensing data is forwarded by radio frequency (RF) circuitry[8].
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| Fig. 1 Structure of EHS. | |
As a cost effective approach for oil delivery,oil pipelines have been built in many places since oil pipelines are usually of dozens or even hundreds kilometers length. It is not realistic to real-time monitor pipeline status by human. Sensor nodes are deployed along the pipeline as a linear placement to monitor the security of oil transportation and the free flow of oil through the pipeline. Each node periodic collects sensing data and forwards the data to sink node by multi-hop transmission[9, 10].
We have designed and implemented one node that relies on battery as shown in Fig. 2. The node adopts a low power MCU MSP430 and the TI CC1101 transceiver chip. We can join different sensors to achieve different functions,i.e.,
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| Fig. 2 The real implemented sensor. | |
temperature and humidity. A set of such sensor nodes have been deployed on one pipeline following the uniform distribution in Liaohe oil field in China[11]. However,we need high network maintenance due to the exhaustion of energy of sensor node. Since EHD can collect energy from environment,energy harvesting-wireless sensor network (EH-WSN) has emerged as an efficient way to prolong network lifetime. A high energy harvesting rate EHD can extend network lifetime indefinitely. However,EHD price is proportional to energy harvesting rate. An exorbitant energy harvesting rate will lead to high cost and resource waste. How to guarantee network lifetime with lower network cost is a new issue we need to address.
In this paper,we consider EH-WSN for oil pipeline monitoring and study how to choose EHD to guarantee network has an unlimited life time. We first propose a generalized pipeline monitoring network model. In order to ensure network life-time,we define worst case energy consumption (WCEC) as the maximum energy sensor node could expend in one period. Based on WCEC,we present a worst case-energy balance strategy (WC-EBS) which can guarantee an unlimited network lifetime by reasonable selection of EHD. Theorem 1 has been proposed to obtain the value of WCEC. Since energy harvesting rate in WC-EBS is a pessimistic strategy,two optimization strategies optimization workload-energy balance strategy (OW-EBS) and optimization first node-energy balance strategy (OF-EBS) are presented to reduce network cost based on the unlimited lifetime. Our contribution in this paper is as follows:
1) In many applications,users need to monitor the area-of-interest for a long time with a limitation on cost. In this paper,we study the problem of minimizing network cost whilst ensuring an unlimited network lifetime,which is an important issue in real applications but easy to be neglected in research.
2) We extend critical node to critical area and propose a new definition of WCEC. When energy harvesting rate is equal or greater than WCEC,network can have an unlimited lifetime no matter sensory data transmits in which strategy. By analyzing energy consumption and number of transmission tasks,we can get the upper bound of WCEC.
3) By discussing the relationship among energy harvesting rate, sampling period and network scale,our methods can reduce network cost significantly with an infinite network lifetime.
The remainder of this paper is organized as follows: Section II provides a brief review of related work. Section III defines the problem model,including WSN model for oil pipeline monitoring and energy consumption model. Section IV proposes WC-EBS to guarantee oil pipeline monitoring network has an unlimited lifetime. Section V proposes two strategies OW-EBS and OF-EBS to reduce network cost based on the unlimited network lifetime. Section VI evaluates the proposed methods by experiments,and conclusions will be given in Section VII.
Ⅱ. RELATED WORKIn many traditional applications of WSN,a large number of sensor nodes are deployed in an area to detect possible events or targets that are interesting to users. How to prolong network lifetime is a critical issue in WSN,and lots of scholars have done research on it,e.g.[2, 4, 11, 12]. However,this kind of research is based on battery powered sensor node and network has a limited lifetime.
As energy harvesting node has a renewable energy budget,some research focuses on optimization using EHD as a new approach to extend network lifetime. Techniques vary in many aspects,such as energy management,node scheduling,or routing protocol. The authors in [13] studied how to achieve close-to-optimal utility performance in energy harvesting networks with only finite capacity energy storage devices. They develop an energy-limited scheduling algorithm (ESA),which jointly manages the energy and makes power allocation decisions for packet transmissions. ESA only has to keep track of the amount of energy left at the network nodes and does not require any knowledge of the harvestable energy process. In [14],the authors addressed the distributed maximum lifetime coverage with energy harvesting (DMLC-EH) problem. They proposed an energy protection algorithm (MEP) that allows sensor nodes to form a minimal set cover using local information whilst minimizing missed recharging opportunities. Yang[15] proposed a myopic policy,the objective is to develop a sensing scheduling policy to ensure the expected long-term average utility generated by the sensors is maximized.
Unfortunately,even though EHD can extend network lifetime,some research focuses on the limitation of EH-WSN cost (Some researchers consider network cost problem in battery-powered sensor network or bidirectional nodes[16, 17, 18],however,these kinds of WSN cannot ensure a long network lifetime). In real applications we must consider network cost as WSN has a large number of nodes and the cost of each EHD node is more than 1.5 dollar. For this purpose,we study the problem of minimizing network cost with an unlimited lifetime in EH-WSN.
Ⅲ. SYSTEM MODELWe have the following fundamental constraints for the sensor network model.
1) There is a large number of sensor nodes. It is impractical to optimize the network on the basis of individual sensor nodes (e.g.,set a different configuration for each individual sensor node).
2) Each sensor node has an EHD while sink node has a continuous energy budget. As oil pipeline is built in a stable open space,we can obtain the minimum value of energy which can be collected from environment in one period. We assume this value is larger than sensor node energy harvesting rate in our system,which means energy harvesting rate of EHD is fixed (Our system is suitable for EH-WSN with stable energy harvesting rate and has some limitations for unstable energy harvesting rate WSN);
3) Each sensor has a maximum transmission range,denoted by $t_{x}$,which is smaller than the distance $L$ between two adjacent sink nodes.
4) Sensor nodes can adjust their transmission range by changing its transmission power level.
Wireless sensor network for oil pipeline monitoring is endowed with one sink node as illustrated in Fig. 3. $n$ EHS nodes are deployed along the pipeline with uniform distribution. The distance between two sensor nodes is $l$. Sink node is deployed at the heat station. The distance between two adjacent sink nodes is $L$. The number of sensor nodes is $n=\frac{L}{l}$. $d$ is sensor node transmission range,the minimum transmission range is $d^{\rm min}=l$,$l\leq t_{x}$. Sensor node valid transmission range can be expressed as $d=s\times l$,where$s$ is the number of transmission crossing nodes. To make sure sensing data could be forwarded to sink node,$s$ satisfies $1\leq s\leq\left\lfloor \frac{t_{x}}{l}\right\rfloor $.
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| Fig. 3 WSN model for oil pipeline monitoring. | |
Sensor nodes send sensory data to sink node by multihop transmission,each task in the $i$-${\rm th}$ node chooses one node closer to sink node as the destination for data delivery. The number of transmission tasks for $i$-${\rm th}$ node is denoted by $k_{i}$. When the transmission range of sensor nodes downstream $i$-${\rm th}$ node satisfies $d_{i+1}=d_{i+2}=\cdots=d_{n-1}=d_{n}$,we can obtain the maximum number of $i$-${th}$ node transmission tasks, which is given by $k_{i}^{\rm max}=n-i+1$.
For each EHS,the energy harvesting rate is $P$,which is a time-invariant value. EHD collects energy all the time,energy is stored in the battery with limited capacity. Network sampling period is $T$,this means sensor node will collect data at every $T$. Then energy collected by one node is $EH=P\,\times\,T$. Since the rest of energy harvested by EHD will be abandoned after a full charge is reached,the optimal battery capacity is $C=EH=P\times T$. In consideration of task forwarding time is very short and much less than $T$,we ignore time slice for data forwarding. The variables are defined in Table Ⅰ.
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Table Ⅰ valuation by $z_m$ for all objectives |
Sensor node energy consumption consists of two parts: the sensing and computation energy consumption,and the communication energy consumption. By [19] and [20],we can see sensing and computation energy is much smaller than communication energy consumption in real world. We can ignore the first part of energy consumption and adopt the communication energy consumption model in [19]
| $\begin{align} E(d)=d^{\alpha}+c, \end{align}$ | (1) |
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Table Ⅱ PATH LOSS INDEX UNDER DIFFERENT ENVIRONMENT |
In this section,we propose a worst case-energy balance strategy (WC-EBS),which guarantees oil pipeline monitoring network has an indefinite lifetime. The key idea is that,we estimate energy consumption of the critical node by transmission range and the number of transmission tasks. Then we select EHD to make sure sensor node worst case energy consumption is equal or less than energy harvested by EHD in one period.
A. Worst Case Energy Consumption We define critical sensor node as the one which has the largest energy consumption in the whole network,and this energy consumption is the worst case energy consumption (WCEC) of this system. Energy consumption of critical node is different in various circumstances,the maximum one among all these circumstances is WCEC in WC-EBS. In order to determine WCEC,we need to know the factors which affect sensor node energy consumption.
Energy consumption depends on both the number of transmission tasks and transmission range,corresponding energy consumption of the $i$-${\rm th}$ sensor node is
| $\begin{align} E_{i}(d_{i})=k_{i}\times(d_{i}^{\alpha}+c). \end{align} $ | (2) |
Since all sensing data is delivered to sink node via sensor nodes one hop away from sink node,energy consumption of these nodes are the bottleneck of the whole network. We call this one hop area as the critical area. By adjusting the range of critical area,we can get WCEC. When the range of critical area is $l$,the first sensor node has the maximum transmission tasks. For $n\geq1$,the maximum energy consumption of the first node is
| $\begin{align} E_{1}^{\rm max}(d_{1})=n\times(l^{\alpha}+c). \end{align}$ | (3) |
Sensor nodes forward sensing data collected by the downstream nodes,the maximum number of transmission tasks for each node satisfies $k_{1}^{\rm max}>k_{2}^{\rm max}>\cdots>k_{n}^{\rm max}$ (the maximum number of tasks denoted by $k_{i}^{\rm max}$,means the maximum number of tasks $i$-${\rm th}$ node needs to forward,e.g., the maximum number of transmission tasks for the first node is $k_{1}^{\rm max}=n$). Increasing the range of critical area to $q\times l$,where $q=\left\lfloor \frac{t_{x}}{l}\right\rfloor $, $q$-${\rm th}$ sensor node is the farthest node one hop away from the sink node. Then the maximum energy consumption of $q$-${\rm th}$ sensor node is
| $\begin{align} E_{q}^{\rm max}(d_{q})=(n-q+1)\times((q\times l)^{\alpha}+c). \end{align}$ | (4) |
| $\begin{align} E_{i}^{\rm max}(d_{i})=(n-i+1)\times(d_{i}^{\alpha}+c). \end{align}$ | (5) |
In this case,WCEC is satisfies $E^{WC}={\rm max}\{E_{i}^{\rm max}\mid1\leq i\leq n\}$. Obviously,when sensor node has the maximum transmission tasks and forward data with transmission range as $(q\times l)$,we could obtain the upper bound of WCEC as
| $ \begin{align} E^{WC}\leq n\times((q\times l)^{\alpha}+c). \end{align}$ | (6) |
Then,we have the following theorem,
Theorem 1. For oil pipeline monitoring WSN,the sum of maximum worst case energy consumption in the critical area,and sensor node energy consumption is not larger than $n\times((q\times l)^{\alpha}+c)$ no matter how the transmission policy is changed.
B. Balance of EnergyIn this subsection,we study how to prolong network lifetime based on network WCEC. When the energy harvested by EHD in one period is equal to or greater than than WCEC,network can obtain an indefinite lifetime. By applying (6),$EH\geq E^{WC}$ can be written as
| $\begin{align} P\times T\geq n\times((q\times l)^{\alpha}+c). \end{align}$ | (7) |
To reduce network cost,we can obtain $P$ as
| $\begin{align} P=\frac{n\times((q\times l)^{\alpha}+c)}{T}. \end{align}$ | (8) |
When the energy harvesting rate and the maximum transmission range is fixed,we can adjust sampling period $T$ and network size to maximize EHD utilization; Similarly,we can reduce network cost by choosing the right EHD based on a given sampling period $T$ and network size.
Ⅴ. OPTIMIZATION OF ENERGY BALANCE STRATEGIESIn last section we have presented a general strategy WC-EBS to prolong network lifetime based on the worst case energy consumption. WC-EBS can apply to all situations when $P\geq\frac{n\times((q\times l)^{\alpha}+c)}{T}$. However,WC-EBS is a pessimistic strategy which generates energy waste (when energy storage is charged up to its capacity,excess harvesting energy will be wasted). The excessive energy harvesting rate will result in a high cost of network .
In this section,we propose two optimization energy balance strategy (OEBS) to reduce network cost by rationally selecting EHD. The main idea of OEBS is to minimize WCEC by optimizing critical node transmission range and transmission workload. OW-EBS and OF-EBS are presented respectively in the following.
A. OW-EBSNetwork worst case energy consumption is expressed as (5),by enhancing sensor nodes transmission range outside the critical area,we can minimize critical node transmission workload. As $t_{x}$ is the maximum value of sensor transmission range,we can get $k_{q}^{\rm min}$ as
| $\begin{align} k_{q}^{\rm min}=\left\lceil \frac{L}{t_{x}}\right\rceil. \end{align}$ | (9) |
To calculate $E_{q}(d_{q})=EH$,the minimum energy harvesting rate is
| $\begin{align} P=\frac{((q\times l)^{\alpha}+c)\left\lceil \frac{L}{t_{x}}\right\rceil }{T}. \end{align}$ | (10) |
With the optimal transmission workload,OW-EBS can reduce WCEC significantly.
B. OF-EBSSince sensor node transmission range has a great influence on sensor energy consumption,we propose OF-EBS to guarantee the first node as the critical node by adjusting each node transmission range,means $EH=E_{1}(d_{1})={\rm max}\{E_{i}\mid i=1,2,\ldots,n\}$. Then energy harvesting rate is
| $\begin{align} P=\frac{n\times(l^{\alpha}+c)}{T}. \end{align}$ | (11) |
As the node at the end of the pipeline,i.e.,$n$-${\rm th}$ sensor node,only forwards sensing data collected by itself,means $k_{n}=1$,then we have
| $\begin{align} E_{n}(d_{n})=(s_{n}\times l)^{\alpha}+c=n(l^{\alpha}+c)=E_{1}(d_{1}). \end{align}$ | (12) |
By (12),we can obtain $s_{n}$ as
| $\begin{align} s_{n}=\left\lfloor \frac{(nl^{\alpha}+(n-1)c)^{\frac{1}{\alpha}}}{l}\right\rfloor. \end{align}$ | (13) |
Since sensor nodes from $(n-s_{n}+1)$ to $n$ will not receive sensing data collected by other nodes,they have the same number of transmission tasks $k_{(n-s_{s}+1)}=k_{(n-s_{s}+2)}=\cdots =k_{n}=1$,and the same transmission range $s_{(n-s_{s}+1)}=s_{(n-s_{s}+2)}=\cdots=s_{n}= \left\lfloor \frac{(nl^{\alpha}+(n-1)c)^{\frac{1}{\alpha}}}{l}\right\rfloor $. If $s_{i}>q$,$1\leq i\leq n$,we set $s_{i}=q$.
For $(n-s_{n})$-${\rm th}$ sensor node,this node needs to forward sensing data collected by itself and $n$-${\rm th}$ node,then the number of transmission tasks is $k_{(n-s_{n})}=k_{n}+1=2$.
It is not hard to find that the transmission range and the number of network hops have a stepwise relationship,the length of each step is $[1,s_{n}-1]$. As Fig. 4 shown,in OF-EBS,a cluster of nodes have same transmission range,the number of steps is the number of hops,number of transmission tasks of each node is equal to the step number,,and $n$-${\rm th}$ node is the first step.
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| Fig. 4 Relationship between transmission range and number of hops. | |
By determining the endpoints of the step,all sensor nodes transmission range and task workload can be obtained. Network can have an unlimited lifetime with $P=\frac{n\times(l^{\alpha}+c)}{T}$.
Ⅵ. COMPARISON AND ANALYSIS OF DIFFERENT STRATEGIESIn this section we compare the performance among different sensor node strategies. The comparison considers energy harvesting rate variation trend in different strategies with changing pipeline length,sampling period and the maximum transmission range,respectively.
As introduced in Section Ⅲ,sensor nodes are placed along the pipeline with uniform distribution linearly. The parameter settings are as shown in Table Ⅲ.
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Table Ⅲ PARAMETER SETTING |
Fig. 5(a) illustrates that,for the same $\alpha$,$l$ and $T$, when $L$ is changed from $200\,{\rm m}$ to $500\,{\rm m}$,the energy harvesting rate increases with $L$ gradually for all the strategies. WC-EBS needs the biggest energy harvesting rate to guarantee energy harvested by EHD in a round is equal to the WCEC. Equation (5) shows that WCEC is decided by the number of sensor nodes $n$ as other parameters are fixed,$n=\frac{L}{l}$. Therefore,energy harvesting rate $P$ changes with $L$ linearly; since $k_{q}^{\rm max}\leq(n-q+1)$,energy harvesting rate in OW-EBS is always less than WC-EBS. Energy harvesting rate in OW-EBS changes with $L$ as a ladder relationship,that is because $k_{q}^{\rm min}$ increases once when the additional part of $L$ reaches $t_{x}$; energy harvesting rate in OF-EBS is much lower than the other two strategies and $P$ increases slowly with $L$. The reason is critical node transmission range in OF-EBS is $l$, which is less than $t_{x}$. Sensor node energy consumption increases with transmission range exponentially. Energy harvesting rate in OF-EBS is less than the one in OW-EBS,although number of transmission tasks in OF-EBS is more than in OW-EBS.
As Fig. 5(b) shown,energy harvesting rate is inversely proportional to sampling period. When sampling period $T$ increases from $0.1\,{\rm h}$ to $1\,{\rm h}$ with unit of $0.1\,{\rm h}$,EHD has longer time to harvest energy from environment,then energy harvesting rate reduces for all strategies. Based on the same situation,energy harvesting rate satisfies $P^{\rm WC{\mbox -}EBS}>P^{\rm Ow{\mbox -}EBS}>P^{\rm Of{\mbox -}EBS}$. That is because WCEC in the three strategies is different and satisfies $WCEC^{\rm WC{\mbox -}EBS}>WCEC^{\rm OW{\mbox -}EBS}>WCEC^{\rm OF{\mbox -}EBS}$.
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| Fig. 5 Energy harvesting rate plotted against various parameters. | |
The relationship of energy harvesting rate and the maximum transmission range is shown in Fig. 5(c). Energy harvesting rate in WC-EBS shows exponential growth with the maximum transmission range. The reason is we decide energy harvesting rate in WC-EBS by computing $P\times T=n\times((q\times l)^{\alpha}+c)$, where $q=\left\lfloor \frac{t_{x}}{l}\right\rfloor $; $P^{\rm OW{\mbox -}EBS}$ changes slower than $P^{\rm WC{\mbox -}EBS}$. That is because number of transmission tasks is inversely proportional to the maximum transmission range,$P^{\rm OW{\mbox -}EBS}$ has a $(\alpha-1)$ exponent relation to $t_{x}$; since the critical node energy consumption is just concerned with $n$,$l$ and $T$,energy harvesting rate in OF-EBS remain unchanged with the increase of $t_{x}$.
Fig. 5(d) shows the results of energy harvesting rate changes with the distance between adjacent nodes. The length of pipeline is $L=500\,{\rm m}$,when $l$ is changed from $10\,{\rm m}$ to $60\,{\rm m}$,number of sensor nodes is changed from $50$ to $9$. Energy harvesting rate in OW-EBS is a fixed value and does not change when $l$; in WC-EBS,energy harvesting rate reduces with $l$ increases,$P^{\rm WC{\mbox -}EBS}$ is equal to $P^{\rm OW{\mbox -}EBS}$ when $l=t_{x}$. The reason is transmission energy consumption in both WC-EBS and OW-EBS is $(t_{x}^{\alpha}+c)$, number of transmission tasks in WC-EBS reduces with $l$ increases. When $l$ reaches its maximum value,$k^{\rm WC{\mbox -}EBS}$=$\left\lceil \frac{L}{t_{x}}\right\rceil =k^{\rm OW{\mbox -}EBS}$. Then WC-EBS translates into OW-EBS; transmission range in OF-EBS is equal to $l$,critical node energy consumption in OF-EBS grows up with the increasing of $l$. When $l=t_{x}$,we have $P^{\rm OF{\mbox -}EBS}=P^{\rm OW-EBS}=P^{\rm WC-EBS}$. The reason is when $l=t_{x}$,the number of transmission tasks in OW-EBS is equal to the number of tasks in the other two strategies,$k^{\rm OF{\mbox -}EBS}=k^{\rm OW{\mbox -}EBS}=k^{\rm WC{\mbox -}EBS}=\left\lceil \frac{L}{t_{x}}\right\rceil =n$. By equation (8),(10) and (11) we can get $P^{\rm OF{\mbox -}EBS}=P^{\rm OW{\mbox -}EBS}=P^{\rm WC{\mbox -}EBS}=\frac{n\times((q\times l)^{\alpha}+c)}{T}$.
Ⅶ. CONCLUSIONSIn this paper,{we study the problem of minimizing cost of oil pipelines monitoring through reasonable selection of EHD to infinitely extend lifetime of WSN. We first propose a general strategy WC-EBS,which defines WCEC as the maximum energy expenditure which the oil pipeline monitoring sensor node can consume in one period. As an EHD choice criterion,network can have an unlimited lifetime when energy collected by EHD in one period is equal to or greater than WCEC no matter sensor nodes forward data in which strategy. Energy harvesting rate in WC-EBS can be obtained as $P=\frac{n\times((q\times l)^{\alpha}+c)}{T}$. Then we present OW-EBS and OF-EBS,which reduce network WCEC by setting sensor node transmission range and optimizing number of transmission tasks. The evaluation results show that OF-EBS can indefinitely extend network lifetime with lower energy harvesting rate than WC-EBS and OW-EBS,means network can obtain an unlimited lifetime with low cost in OF-EBS.
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