AFuzzyRoutingAlgorithmforSolarPoweredWirelessSensorNetworks*

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(School of Electrical Engineering and Automation,Tianjin University,Tianjin 300072,China)

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AFuzzyRoutingAlgorithmforSolarPoweredWirelessSensorNetworks*

LIUChao,LIULiping*,ANXinsheng,CUITingting

(School of Electrical Engineering and Automation,Tianjin University,Tianjin 300072,China)

Resource limitation and unbalanced energy consumption are two main factors to limit the lifetime for Wireless Sensor Networks(WSNs).This paper first introduced a new metric indicating degree of balance,called Theil index,and then proposed a new routing method for solar powered WSNs to extend network lifetime using a fuzzy approach which is to determine an optimal routing path by favoring the node with the highest Node Quality(NQ),largest Transmitting Capacity(TC)and best Degree of Energy Balance(DEB)of Theil index.This paper validated the proposed method with simulations and made comparisons with other two classic routing algorithms and finally compared the performance under three different DEB indexes,which demonstrated that the proposed method has a better effectiveness and balance of energy consumption,prolonging the network lifetime.

wireless sensor networks;solar powered system;routing protocol;fuzzy logic control;theil index

A Wireless Sensor Network(WSN),consisting of a large number of low-cost,low-power,multifunctional sensor nodes to monitor physical conditions,such as temperature,sound,vibration,pressure,motion,etc.usually derives its energy from attached batteries.As shown in Fig.1,a typical sensor node of this network includes:a sensing unit,a transceiver unit,a processing unit,and a power unit composed of solar energy harvesting circuit and NiMH battery.Maximizing the WSN lifetime is a critical issue for applications due to the limited energy resources.Exploiting environmental and renewable energy sources promises to be a breakthrough.

Fig.1 Components of a sensor node

A variety of energy harvesting technologies are available and Table 1[1]shows some of the potential energy generating sources.Among them,solar energy provides the highest power density compared to other sources and sensor nodes work at a power order of mW.In addition,commonly or easy available solar matches the requirement and is considered to be the most effective choice for WSNs system.Although solar powered WSNs can prolong network lifetime by supplying the battery with harvested solar energy,the dynamic energy supply brings big challenge for network design as the current state of technology in energy harvesting is still unable to provide a sustained energy supply to enable WSNs continuously.The system needs a special solar panel recharging circuit and the energy state information for all nodes should be update periodically to prolong the network lifetime by providing the solar energy to sensor nodes.

Many routing algorithms have already been presented to address the problem of effective and balanced energy consumption for solar powered WSNs.Most of these routing algorithms minimize the total energy consumption at the expense of nonuniform energy drainage in the networks,which can significantly reduce network lifetime.This paper first defined two metrics,Node Quality(NQ)and Transmitting Capacity(TC),used to select the next hop,and then introduced another new metric,Theil index,indicating the Degree of Energy Balance(DEB),finally proposed a new algorithm using fuzzy approach to select the optimal routing path from the source to the destination by favoring the node with the highest NQ,largest TC,and best DEB.

Table 1 Performance of energy harvesters

This paper is organized as follows:Section Ⅱ provides a brief overview on related works.Fuzzy logic election of node for routing in WSNs is introduced in detail in section Ⅲ.Section Ⅳ shows simulation results and performance evaluation,section Ⅴ concludes this paper.

1 Related work

In optimal path routing schemes over WSNs,each node selects specific node to relay data according to some criteria in order to satisfy some specific requirements such as minimum energy consumption,shortest time-delay,lowest latency and maximum network lifetime,among which energy issue has been a hot topic and how to balance network energy consumption,extending the network lifetime has become a evaluation criteria for WSN protocols[2].All of these algorithms proposed to prolong the network lifetime should consider both effectiveness and balance of energy dissipation during the process of selecting the next hop.However,there is a conflict between these two aspects.Simple energy efficient routing algorithm has a fixed transmission path,resulting in unbalanced energy consumption.Correspondingly,energy balanced routing algorithm can not guarantee the data flow toward to the Sink quickly and the collected data may temporarily flow along the peripheral nodes with more residual energy,which causes a larger end to end energy overhead.In addition,an ideal routing protocol should perform the minimum transmission energy consumption and the maximum lifetime of every node[3].

Fuzzy Logic Control(FLC)system is designed specifically for multi-inputs systems which does not depend on accurate mathematical model and it is a mathematical discipline invented to express human reasoning in rigorous mathematical notation which makes it ideal for wireless sensor network.Aiming to maximize the network lifetime[4],built a fuzzy logic at each node to determine its chance to transfer data based on its residual energy,trust level and distance from the base station.However it directly use the geometric distance from the base station as one selection criteria,which will produce a over impact on selection decisions and the nodes near to the Sink will get drained fast.FML-MP(a fuzzy multi-path maximum lifespan routing scheme),an online multi-path routing scheme that strives to achieve a good distribution of the traffic load was developed in [5],which uses an edge-weight function in the path search process.This scheme is centralized and consumes too much energy.A fully distributed fuzzy logic method based on nodes’ residual energy,hops to the Sink,and traffic loads was proposed in [6].Both the residual energy,and hops to the Sink play over roles on selection decisions as it directly uses the values.In [7] the authors presented Optimal Forwarding by Fuzzy Inference Systems(OFFIS)for flat sensor networks.The OFFIS protocol selects the best node from candidate nodes in the forwarding paths by favoring the minimum number of hops,shortest path and maximum remaining battery power and link usage.Both of these two algorithms are just passive to make up for the emerged unbalanced energy drainage,not proactive in preventing the nonuniform consumption.

In this paper,we proposed a novel fuzzy based routing method for WSNs to extend network lifetime,which is to determine an optimal routing path from the source to the Sink by favoring the node with the highest NQ,largest TC,and best DEB.On the one hand,we made comparisons with other two classic routing algorithms,on the other hand,we compared the algorithm performance under three different DEB indexes,which demonstrates that our proposed method has a better effectiveness and balance of energy consumption,moreover,it can largely prolong the network lifetime.

2 Fuzzy logic election of node forrouting in WSNs

We need to make some definitions before introducing the algorithm.

①WSN can be described with a undirected graphG(V,E),whereVandErepresent the collection of all the sensor nodes and the radio link between different nodes,respectively,as follows.

E={(i,j)}|i∈V,j∈V∪{Sink}}

We should note that,the distance between the sender and the receiver should be shorter than the maximum communication distance(R)of different nodes.

②Neighbor Nodes.

The neighbor nodes ofican be defined as follows:

N(i)={j|j∈V,D(i,j)

WhereD(i,j) is the distance betweeniandj.

③Forward Neighbor Nodes

The forward neighbor nodes ofican be defined as:

FN(i)={j|j∈N(i),H(j)<=H(i)}

WhereH(i) andH(j) represent the hop of nodeiandjwhich can be get with the method mentioned in [8].

Fuzzy logic was first introduced in the mid-1960 s by Lotfi-Zadeh in [9].Since then,its applications have rapidly expanded in adaptive control systems and identification system.It is a mathematical discipline invented to express human reasoning in rigorous mathematical notation and it has the advantages of easy implementation,robustness,and ability to approximate to any nonlinear mapping[8].Moreover,compared to other event classification algorithms based on probability theory,fuzzy logic is much more intuitive and easier to use.

Fig.2 Structure of the fuzzy logic control

Fig.2 shows the typical structure of a FLC system which consists of four components namely:fuzzification,rule base,inference engine and defuzzification.The real inputs are fuzzified into fuzzy variables before being inputted into the inference engine which contains fuzzy rules,and then we get the fuzzy output sets after approximate reasoning,finally we get the real outputs that can be acceptable to control systems,for example here the output is the priority level of selecting a node as the next hop,after a process of defuzzification.The process of making crisp inputs is called fuzzification which involves application of membership functions such as triangular,trapezoidal,Gaussian etc.The inference engine process maps fuzzified inputs to the rule base to produce a fuzzy output.The defuzzification process converts the outputs of fuzzy rule base into crisp outputs by one of defuzzification strategies.

To our best of knowledge,most of the fuzzy based routing algorithms in WSN are focused on the different inputs and outputs of fuzzy system,such as residual energy level,trust level,and distance from the source node to the Sink for inputs and cost value,chance of selecting node as the next hop for outputs.As shown in Fig.3,we proposed a novel mamdani fuzzy based routing algorithm considering three inputs:NQ,TC and DEB of Theil index of all the neighbor nodes and one output:the priority level(PL)for a node to be selected as the next hop.The number in brackets represent fuzzy sets of membership functions.We will introduce the three inputs in details as follows.

Fig.3 Schematic diagram of the proposed algorithm

2.1 Node Quality

Simple energy efficient routing algorithm has a fixed transmission path,resulting in unbalanced energy consumption.Correspondingly,energy balanced routing algorithm can not guarantee that the data flow toward to the Sink quickly and the collected data may temporarily flow along the peripheral nodes with more residual charge,which causes a larger end to end energy consumption.We proposed a novel metric called node quality which considers both effectiveness and balance of energy dissipation.We defined node quality of thekthforward neighbor node of nodeias follows:

(1)

In whichk∈FN(i),j∈FN(i),Qand Hop are the residual energy and hop count to the Sink,respectively,andα,βare weighting exponent for residual energy and hop.We can intuitively see from Eq.(1)that a node with more residual energy and smaller hop count to the Sink has a higher quality to be selected as the next hop.Moreover,we can set differentαandβfor different kinds of data to meet different requirements,for example we can set a higherαand lowerβfor data which is insensitive to time delay to get a balance energy consumption and set a higherβand lowerαfor delay-sensitive data,conversely.Most importantly,this proposed metric is fully distributed that can be performed with local information,which largely reduces the overhead of control and communication and realizes the combination of both effectiveness and local balance.

2.2 Transmitting Capacity

The TC is defined as the ratio of the number of forward neighbor nodes and the traffic load(or intensity)which represents the pending amount of traffic in a node’s queue.On the one hand,the high traffic load causes a data queue overflow in the sensor nodes,resulting in loss of important information.In addition,since the battery energy of the sensor nodes is quickly exhausted,the entire lifetime of wireless sensor networks would be shortened[10].Therefore,the traffic load in nodes will affect the lifetime of the networks.On the other hand,a node with more forward neighbor nodes has more hubs to assign its traffic load,achieving a predictable balance of traffic load to prolong the network lifetime.

Different sensor nodes have large different traffic loads and number of forward neighbor nodes,which will cause too much impact on the selecting decision if we directly input the transmitting capacity to the fuzzy system.Meanwhile,as the distributed routing algorithms make routing decision based on local information,such as the forward neighbors’ information,we fixed the node transmitting capacity as Eq.(2).

Wherek∈FN(i),j∈FN(i),Forward and TL are the number of forward neighbor nodes and traffic load mentioned above,respectively.From Eq.(2)we can see that a node with more forward neighbor nodes and less traffic load has a larger transmitting capacity representing a higher priority level being selected to be the next hop.

(2)

2.3 Degree of Energy Balance

Most of the existing routing algorithms in WSNs will commonly make a selection decision considering residual energy of nodes,giving more chance to these nodes with more energy and less chance to those with less energy.It is a passive routing adjustment method to make selection decision based on residual energy as the energy has been uneven before the adjustment.We adopted a proactive routing adjustment strategy before data transmission,making a selection decision for every forward neighbor node based on the degree of energy balance of all their own neighbor nodes.There are two different metrics often used in terms of degree of balance,standard deviation and Atkinson(ATK)index which are often used to represent the imbalance of economic development in socioeconomics[11].Here we proposed another economic concept,the Theil index,which is also used to indicate the degree of balance of income or development of different regions[12].We will introduce definitions of these three variables as follows.

The traditional metric in terms of degree of balance is standard deviation whose definition is as follows.

(3)

(4)

In which,λis the uneven aversion parameter reflecting the degree of social aversion to inequality(or equal preference).ATK is in accordance with Lorenz in terms of consistency,and on this basis,it has a good quality of decomposability.

Inspired by the excellence performance of ATK,we introduced another concept in socioeconomics,the Theil index(TI),which is also used to indicate the degree of balance of income or development of different regions as shown in Eq.(5).

(5)

TI is one kind of generalized entropy index in socioeconomics and as ATK,it has a good quality of consistency,but TI out-performs ATK in the aspect of internal and external decomposability of different groups.

All these three inputs mentioned above rang from zero to one,however,we find that all of them tend to be concentrated in a certain interval of [0,1],and the same values for different forward neighbor nodes of different nodes are quite different,making it tough to determine the appropriate membership functions.As we make a selection decision among all of the forward neighbor nodes,we can change the unprocessed domain to a standard domain of [0,1] with a linear transformation as Eq.(6)

(6)

Wherevunprocessedis the unprocessed input,vminandvmaxare the maximum and minimum of these inputs of all the forward neighbor nodes.

We fuzzified these three processed inputs mentioned above with membership functions as shown in Fig.4,from which we can see there are three linguistic variables in every input crisp set,{good,middle,bad},and nine linguistic variables {PL1-PL9}in output crisp set.

Current node performs decision making by using the mamdani If-Then rule-based technique about the priority level of selecting the next hop from all of the forward neighbor nodes.Some of the 27 rules is shown by Table 2.

Table 2 Some of the If-Then rules

(7)

We performed the defuzzification process with the most used method:Center of Area(COA)[13]which is shown in Eq.(7).WhereμA(x) is the membership function of fuzzy set A.

Fig.4 Membership function inputs and output

3 Simulation results and performanceevaluation

3.1 First Order Radio Model

Radio model is an important issue to calculate the energy consumption and different assumptions about the radio characteristics,including energy dissipation in the transmit and receive modes,will change the advantages of different protocols.We choose the first order radio model proposed in [14] as the consumption model in which the overhead for sending and receiving a packet ofkbits are formulated as follows.

ETx(k,d)=Eelec·k+εamp·k·d2
ERx(k,d)=Eelec·k

(8)

Wheredis the distance between source and destination nodes,Eelecandεampare per bit energy dissipation in transmitting or receiving circuitry and energy that amplifier circuit takes from the node respectively.

3.2 Simulation results

To demonstrate the excellence of the proposed method in terms of effectiveness and balance of energy consumption,we compared our FLC approach with the Maximum Residual Energy Based Routing(MREBR)algorithm and Minimum Energy Cost Routing(MECR)[15]algorithm.We also compared the FLC performance under three different inputs of DEB indexes,standard deviation,Atkinson index and Theil index.

We made the following reasonable assumptions in order to simplify the model of the system:

①All of the 100 homogeneous sensor nodes are randomly distributed in the monitoring area of a square of 200 m×200 m and the Sink node at the middle of the area.

②Sensor nodes and the Sink node will no longer move once deployed randomly.Each node knows its location coordinate and has a table that records its neighbors’ information,such as their locations,hops or activeness.

③As the output voltage of solar panel fluctuates within a small range,we used the same constant voltage MPPT based solar energy harvesting control circuit which was proposed in [16]and the output voltage of the solar panelV0=1.78 V.

④We chose 500 simulation periods in one day and every periodTpt=2.88 min.The sensing activity has always being executed during every period,while the transmission occurs at the end of every period.

⑤As shown in Fig.5,we used the recharge model proposed in [17] as a function of time in one day.As we used only one small capacity battery to storage the harvested solar energy,the area of the panel we chose is a quarter of that in [17],as a result,the output current of solar panelIois correspondingly a quarter on the condition of a constant output voltage.

Fig.5 Recharge current Io for different time points in one day

⑥The efficiency of the MPPT control circuitEmppt-cc,proposed in [17],is approximately 87% and the battery efficiency,Eff-batis about 66%[18].So the total power that the battery can output during a period is given by:

Eout=0.25·Io·Vo·Tpt·Emppt-cc·Eff-bat

(9)

Other parameters relevant are shown in Table 3.Part of these parameter settings were adopted from [14].As toαandβ,we chose fixed optimal values in our simulation and the case where they vary with will be our future work.

Table 3 Simulation parameters relevant

As shown in Fig.6,Stage of Charge(SoC)of all the 100 nodes under FLC algorithm maintains a fairly high level and has a relative balanced consumption after working all night,from which we can infer WSN coupled with harvested solar energy can work theoretically for infinite time,SoC under MECR gets to two extremes,nodes far away from the Sink keeps a very high energy level and those near to the Sink consume almost all the relative available energy,from which we can infer that the WSN will soon get paralyzed after some rounds later because of the death of nodes near to the Sink,while that under MREBR keeps a best balance but worst effectiveness.

Fig.6 SoC of all the nodes at 6:00 on the third day

Fig.7 Average hops to the Sink under three different algorithms in five days

Fig.7 and Fig.8 show the contradistinctions of average hops to the Sink of FLC,MECR,MREBR and three different fuzzy based algorithms after working a few cycles,respectively.As every node has a determined path to the Sink under MECR,the average hops will not change with time.The curve for MREBR maintains maximum as the collected data transfer only between those nodes with higher residual energy.The average hop to the Sink for FLC fluctuates between those of MECR and MREBR as it considers both effectiveness and balance of energy consumption.Fig.8 shows that Theil index based FLC algorithm outperforms those of both Atkinson index and standard deviation in terms of effectiveness.

Fig.8 Average hops to the Sink under three different metrics of degree of balance in five days

Fig.9 compares the performance in the aspect of balance of residual energy.Once again,the curve for our proposed algorithm varies within the range between those of MECR and MREBR.Moreover,every day from 0:00 to 6:00 and 18:00 to 24:00,nodes near to the Sink consume almost all the relative available energy,while remote nodes keeps a very high energy levels,which leads to a increase in standard deviation.During the daytime,the SoC of all the nodes comes to increase because of the increasing charging current,which leads to a decrease in standard deviation.

Fig.9 Standard deviation of SoC in five days

The residual energy under these three algorithm are shown in Fig.10.As MECR chooses a shortest path from the source to the Sink,it keeps the maximum residual energy,on the contrary,MREBR maintains the lowest as it performs the largest end to end energy dissipation,while the proposed algorithm waves in the middle.

Fig.11 and Fig.12 compares the degree of balance of these three different fuzzy based algorithms.For more comparative,we chose standard deviation as the balance index when the DEB input is Theil index or Atkinson index,and the Atkinson index when the DEB input is Theil index or standard deviation,from which we can deduce that the Theil index based fuzzy algorithm outperforms that of standard deviation all the time and Atkinson for most of the time in one day in terms of balance of residual energy.

Fig.10 Average residual energy in five days

Fig.11 Degree of balance using standard deviation

Fig.12 Degree of balance using Atkinson Index

4 Conclusion

In this paperwe introduced three metricsnodes qualitytransmitting capacity and Theil indexindicating the degree of balance of residual energyto select the next hop.A new fuzzy based routing methodwhich is to determine an optimal routing path from the source to the sink by favoring the node with the highest NQlargest TCand best DEBis proposed for solar driven WSNs to solve the problems of energy shortage and the uneven energy consumptionultimately to extend network lifetime.We finally validated the proposed algorithm with simulations and in addition to the comparisons with MECR and MREBRwe also compared the algorithm performance under three different DEB indexesstandard deviationAtkinson index and Theil indexwhich demonstrates that our proposed method has a better effectiveness and balance of energy consumptionand it can largely prolong the network lifetime.

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劉超(1989-),男,山東省濟(jì)寧市人,漢族,碩士研究生,主要研究方向?yàn)闊o線傳感器網(wǎng)絡(luò)路由協(xié)議;

劉麗萍(1979-),女,河北省保定市人,漢族,副教授,研究方向?yàn)闊o線傳感器網(wǎng)絡(luò)、網(wǎng)絡(luò)優(yōu)化、智能信息獲取等。

2014-04-10修改日期:2014-08-05

基于模糊控制的太陽能驅(qū)動(dòng)無線傳感器網(wǎng)絡(luò)路由算法*

劉 超,劉麗萍*,安新升,崔婷婷

(天津大學(xué)電氣與自動(dòng)化工程學(xué)院,天津 300072)

能量受限和能耗的不均衡性是限制無線傳感器網(wǎng)絡(luò)(WSNs)生命周期的兩大主要因素。首先引入了一個(gè)新均衡性指數(shù)—泰勒指數(shù),其次為太陽能驅(qū)動(dòng)的無線傳感器網(wǎng)絡(luò)提出了一個(gè)新的基于模糊邏輯控制的路由算法。該算法綜合考慮最優(yōu)節(jié)點(diǎn)質(zhì)量,傳輸能力以及剩余能量的泰勒均衡性最終確定最優(yōu)路由路徑。實(shí)驗(yàn)將該算法與另外兩種經(jīng)典路由算法做對(duì)比,并且比較了不同均衡性參數(shù)下該算法的性能,最后仿真結(jié)果表明:本文提出的路由算法改善了能耗有效性和均衡性,延長了網(wǎng)絡(luò)生命周期。

無線傳感器網(wǎng)絡(luò);太陽能驅(qū)動(dòng)系統(tǒng);路由協(xié)議;模糊邏輯控制;泰勒指數(shù)

TP393

:A

:1004-1699(2014)09-1238-09

項(xiàng)目來源:國家自然科學(xué)基金項(xiàng)目(61104208);天津市自然科學(xué)基金項(xiàng)目(13JCQNJC00800);國際科技合作專項(xiàng)項(xiàng)目(2013DFA11040)

10.3969/j.issn.1004-1699.2014.09.016