A Low Energy Algorithm of Wireless Sensor Networks Based on Fractal Dimension

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1 Sensors & Transducers 2014 by IFSA Publshng, S. L. A Low Energy Algorthm of Wreless Sensor Networks ased on Fractal Dmenson Tng Dong, Chunxao Fan, Zhgang Wen School of Electronc Engneerng ejng Unversty of Posts and Telecommuncatons ejng, , P. R. Chna, Tel.: E-mal: dongtng@bupt.edu.cn, cxfan@bupt.edu.cn, zwen@bupt.edu.cn Receved: 23 Aprl 2014 /Accepted: 23 May 2014 /Publshed: 31 May 2014 Abstract: For the energy lmtaton of nodes and mbalance energy consumng among nodes, ths paper proposes an optmzaton algorthm --Low Energy Algorthm-- of wreless sensor networks based on fractal dmenson algorthm for the purpose of reducton of the energy consumpton. The nodes n WSN cannot be located evenly, and cannot move wth the montorng envronment changed once be located. Consderng the characterstcs of WSN, the paper desgns an optmzed clusterng method accompany wth dmenson by calculatng the dmenson of each cluster to determne the cluster whch needs to be adjusted dynamcally. If the cluster wth hgh value of dmenson, ncreasng more nodes n ths cluster. If the cluster wth low value of dmenson, reducng more nodes n the cluster. The smulaton results show that the LEA algorthm mproves energy effcency, prolongs the network lfetme, and balances energy consumpton n the sensor network. Copyrght 2014 IFSA Publshng, S. L. Keywords: Wreless sensor networks, Fractal dmenson, ox coverng algorthm, Low energy. 1. Introducton In recent years, wth the rapd development of communcaton and sensor technologes, Wreless Sensor Networks (WSN) are emergng n many ndustral and consumer area. After a large number of sensor nodes are dstrbuted randomly n the montorng area, they have the capablty of self organzaton among all nodes to construct a WSN [1]. The nodes n the network work collaboratvely to processng nformaton. WSN s characterzed as selforganzaton and smple to deploy [2]. WSN s dstrbuted throughout ndustry, agrculture, mltary and transportaton. In recent studes of complexty network, people found that WSN has the same structural features of a tree-lke herarchcal cluster, t can be seen as a complex network mplementaton, and can be studed by usng fractal theory [3]. WSN has had some clusterng algorthms, such as LEACH, PEGASIS and CDCP. LEACH as the bass of many clusterng algorthms s the classc algorthm and wdely used. Classc clusterng algorthms take more consderaton n node energy and base staton energy consumpton, meanwhle the montorng envronment of WSN cannot be predcted and assessed accurately. The deal condtons for WSN are nodes evenly dstrbuted n the open area, and the data quantty of measurement s steady n each area. However n practcal, the nodes are randomly dstrbuted and the montorng data n each area has a great dfferences. For example, to montor one lake water qualty, the 1

2 montorng data of the nodes n polluton area s greater than none polluton area. The data s rcher n aspect of varaton and dfference whch means more complcated. Therefore, the unevenly dstrbuted network and the dynamc envronments wll affect the montorng effcency of WSN and reduce network s lfetme. To ncrease the effcency of WSN and extend the lfetme, the sensor network need to be optmzed by reducng the complexty of the network. How to mprove the montorng effcency by usng the clusterng algorthms s need to be studed. 2. Clusterng Protocol 2.1. LEACH Overvew Low Energy Adaptve Clusterng Herarchy (LEACH) [4] s a classcal algorthm. Ths paper proposes an optmzaton method based on LEACH algorthm. The prncple of LEACH s randomly selectng the nodes as clusters head cyclcally. The cluster head sends the ntegrated data whch receved from each node to the base staton. The randomzed rotaton of cluster head n each cluster can save the energy consumpton of nodes, balance network load, and reduce the network energy consumpton [5, 6]. The typcal WSN LEACH algorthm clusterng structure shown n Fg. 1. number of onlne node n montorng area by judgng the complexty of cluster n order to optmze the deployed self-organzed network. Reducng the number of nodes for cluster of lower level complexty can reduce energy consumpton and extend the network lfetme. Addng the number of nodes for cluster of hgher complexty level can mprove the montorng effcency of cluster and optmze cluster structure. Calculatng the fractal dmenson of network s used to obtan the complexty value. Accordng to the fractal theory, the fractal dmenson of network usually means network complexty value. The optmzaton based on LEACH protocol s proposed n ths paper. 3. Method to Calculate the Fractal Dmenson 3.1. Fractal Dmenson Overvew It s known that stratfed network s typcal selfsmlar network [9]. Fg. 2 s stratfed network topology. WSN s one of stratfed network, therefore, the fractal dmenson could be used n WSN analyss. Fg. 2. Stratfed network s typcal self-smlar network. Fg. 1. WSN LEACH cluster structure. The LEACH protocol defnes two concepts: the "round" and the "cycle". The operaton n one round can be categorzed nto two phases: named the ntalzaton phase and the steady phase [7, 8] Problems and Dscusson LEACH protocol s able to provde a smple networkng approach of WSN, but t does not take more consderaton for the node unevenly deployed stuaton due to the complexty montorng envronment, t also cannot make any adjustment for t. The optmzaton s based on mprovement of LEACH protocol. It proposes an dea to change the The fractal dmenson can help to understand the topology of the network, and contrbute to the constructon of the reasonable network topology. In one network, a regon wth a hgh value of dmenson means a hgher complexty of the data and the network attrbutes n ths regon, whch represents as the nodes concentrated, hgh energy consumpton and large dfference of measurement value. A regon wth low value of dmenson s known as lower complexty of the data and network topology, whch means the nodes hghly dspersed, low energy consumpton and small dfference of measurement value. The fractal dmenson would contrbute to determne whch cluster needs to be adjusted. As an analytcal tool, fractal dmenson would help to descrbe current network status and provde a bass for network optmzaton. 2

3 3.2. Method for Calculatons The man calculaton methods of fractal dmenson nclude Hausdorff algorthm and box coverng algorthm. ox coverng algorthm s wdely used because t s smple and easy to use. Song and others have researched calculaton of dmenson about complex network [10]. To calculate the geometry dmenson, a box wth sde length L s usng to cover the geometry graphc. The N ( L ) s the mnmum number of boxes needed to completely tle a gven graphc wth boxes of lateral sze L. The box dmenson can be multdmensonal, as a lne descrbes one dmenson, a plane descrbes two dmensons, and a cube descrbes three dmensons. The box dmenson formula s: D ln( N ( L)), ln( L ) Equvalent power-law formula: (1) D N ( L ) L, (2) Fractal dmenson reflects the statstcs of degree of space fllng, and reflects the complexty of space. 4. Optmzaton STEPS ased on Fractal Dmenson In order to calculate actual network dmenson by usng box coverng algorthm whch needs to be refned because fractal dmenson defned n Eucldean Space not exst n actual envronment, and the L of box coverng formula s not the Eucldean dstance between two nodes n actual envronment. In addtonal, the tradtonal box dmenson algorthm selects node equally no matter the node s a cluster head or not. However, n actual calculaton process, the nodes should be dstngushed for selecton because the WSN cluster node nformaton saves n the cluster head. Ths paper proposes the followng optmzaton steps:. Calculate the dmenson of cluster D.. Compare the value of cluster dmenson and threshold. a) When the value of cluster dmenson s hgher than the threshold, t means that the complexty value of cluster s hgher. Such stuaton needs to add more nodes for montorng. In order to obtan more effectve data of the sensng regon, t needs to add adjacent nodes; When the value of cluster dmenson s less than the threshold, t means that the complexty value of cluster s lower. Such stuaton needs to reduce onlne nodes. In order to be more effectve and reduce energy consumpton, the redundant nodes wll be set sleep. After optmzaton, the number of node deployed n dfferent regon would be adjusted. The effcency of the whole network wll be ncreased, the energy consumpton wll be reduced, and the network lfe tme wll be extended n ths way. 5. Algorthm Descrpton 5.1. Network Model In order to llustrate the practcablty of the algorthm, t needs to create a network model. In ths model, the sensor nodes are randomly dstrbuted n a square regon and assume the followng:. The nodes are randomly dstrbuted and montorng envronment may change at any tme;. Any node has unque dentfer and somorphc;. Sensor nodes would not move after nstallaton; v. ase staton s deployed far away from montorng regon; v. The nodes s not aware of the locaton themselves, but could calculate the dstance accordng to the receved sgnal strength from cluster head or other adjacent nodes; The premse of algorthm s assumng N nodes n the cluster, the count of round calculaton from 1 to untl the network expre Improvement of Dmenson Algorthm The structure of cluster may affect the whole network performance. Good cluster structure not only can reduce the energy consumpton of the network, but also can obtan more accurate montorng data of the network. In the coverng boxes algorthm, the dfferent coverng boxes have dfferent number of nodes. Tradtonal box coverng algorthm does not consder the number of nodes covered by each box. However, t needs to be reflected as a parameter of complexty calculaton, because the box covered more nodes means the network s more complex. Meanwhle, one box wth a lot of nodes means such nodes measurement values may be very smlar to each other. For these reasons, the complex network could be optmzed by reducng the complexty of the network, such as to set some nodes sleep to reduce the complexty whch also helps to reduce the energy consumpton and extend the network lfetme. The box dmenson algorthm s mproved by calculatng the number of nodes covered n each box. Ths method can also be used to calculate the dmenson of measurement dfference of nodes. The changes to box coverng algorthm s as followng:. Numberng each box accordng to the degree of ts fllng (the number of nodes covered by one box). The measurement dfference between the node 3

4 and head node can also be used as an object of box coverng.. Calculatng the probablty P of measurement dfference covered by box: N P =, (3) N. Dervng the measurement dfference from formula below: N I = p log p, (4) = 1 v. Dervng the new dmenson calculaton formula based on formula (3), (4): 5.3. Pseudo Code D = lm r 0 I, l log( ) r (5) Pseudo code of the program to reduce the complexty of cluster s as follow: Pseudo code of calculate D descrbe as follow: Whle ( ) { Float r, D, T n[], T, T, n D, C ; //defne round number, dmenson, dfference of measurement value, head node value, dmenson of round// T [] = C ; n //n round of, n of nodes needed s used to calculate the dfference of the measurement value between head nodes and other nodes saved n array T n[]. Each measurement value saved n array T n[] s dfferent between cluster head node and nonhead nodes.// Whle ( n = 1 ) { Tn[ n] = fabs( Tn TC) //calculate the dfference and save n array T n[] // P [ r] = T [ n]/ T n n c //calculate the probablty Pn under reference value// } I ( r ); // calculate I ( r ), sum the product of the logarthmc;// D ; //Calculate dmenson D, judgng whether there s hgher dmenson value based on D. If ext, then recreated cluster at the next round and added more nodes; f dmenson s small then selected few nodes act as agent and the other nodes enable sleep. // If ( D > D ) // If dmenson s greater than the threshold D, t means that cluster s more complex and the dfference nsde cluster s more complex. The cluster structure needs adjustment at the next round to reduce complexty.// Else f ( D < D /2) // If dmenson s less than the threshold, t means that cluster structure s smple, the dfference nsde cluster s smaller, t could select some nodes to sleep untl next round.// // enter steady-state transmsson.// } 5.4. Dscusson Add the mproved dmenson algorthm nto clusterng algorthm could be used to optmze the complexty of the WSN. The optmzaton approach s dvded for two steps below:. Calculatng the cluster dmenson D n the network through formula (1). Calculate the dmenson of each cluster accordng to the measurement dstance between nodes to the cluster head. The dstance between node and cluster can be obtaned through the strength of sgnal from node to cluster head. In formula (1), the sde value of box s L, and the value of L refers to threshold d 0 n energy consumpton model of WSN [11]. 2 le ( elec + ε fsd ), d< d0 ETx(, l d) =, (6) 4 le ( elec + ε mpd ), d d0. Calculatng the cluster dmenson D n the network through formula (5). Analyzng the relatonshp between two dmensons:. If D = D, t means that space dstrbuton s consstent wth measurement value dstrbuton. If the number of nodes n each box s 1, t means the node reached the maxmum utlzaton and all the nodes measured effectvely. If the number of nodes n each box s bgger than 1, then only kept 1 node and the others all go to sleep mode.. If D D, t means that space dstrbuton and measurement value has not unform dstrbuted. Accordng to the fractal dmenson theory, there s always D D. When D > D, t llustrates that the 4

5 measurement value of some cluster nodes s too close to each other. It can be adjusted by changng the number of nodes n the cluster and retan effectve nodes. Or can be adjusted by changng the dstance of nodes or ncrease the adjacent nodes to reduce dmenson value of D. In practcal applcaton, D s changed wth L and D s changed wth threshold of the dfference of measurement value. Therefore, the complexty can be reasonable optmzed by selectng L and threshold based on the practcal requrements Algorthm Analyss The algorthm optmzaton proposed n ths paper s dfferent from the ordnary algorthm optmzaton. The low energy algorthm (LEA) consdered the montorng envronment has changed after a perod of tme when the WSN has been deployed. y usng dmenson calculaton and complexty analyss could help to understand network more objectvely and to provde gudance for the subsequent optmzaton. About complexty of algorthm, tradtonal box coverng algorthm reles on the node ntal sequence as Song proposed [12, 13], but the ntal sequence s randomly allocated, and there are multple possbltes of node covered by box. The node be covered s also randomly allocated. The tradtonal box algorthm can be consdered as an exhaustve attack method. The complexty of algorthm s 2 O( n ), and lots of nodes meet the condtons, the node wll randomly select. The process of box coverng algorthm smlar to greedy colorng algorthm, the complexty of colorng algorthm has been descrbed n detal at the paper of researchers [14]. Unlke random node selecton of Song s box coverng algorthm, the ntal sequence of nodes n the optmzaton algorthm n ths paper s decded by the cluster nformaton stored n the cluster head. The subsequent node wll be covered accordng to the sequence stored n the cluster head durng the box coverng process. Non-cluster nodes no longer execute box coverng mutually. Ths approach avods the random selecton of nodes n ntal phase. The complexty of calculaton of D s O( n ). The complexty of calculaton of D s stll O( n ) because the second calculaton step follows the frst dmenson calculaton completed. Ths wll cause the complexty unchanged. Snce the LEA algorthm appled based on the orgnal clusterng algorthm, t wll affect the complexty and effcency of the algorthm. Comparng wth LEACH algorthm, n the condton of network wth smaller number of nodes and smple structure of clusters, the LEA algorthm wll ncrease the computatonal task. Along wth the development of WSN, there wll be an ncrease n the number of nodes. The LEA algorthm provdes a way of selectng part of the nodes nto sleep whch wll consequentally extend the network overall lfe cycle. The dmenson-based optmzaton should be utlzed n the condton of the cluster structure changes or the measurement envronmental changes. 6. Smulaton Results Usng MATLA, we smulate a WSN n an area dmensons m. All 100 and 500 nodes are randomly dstrbuted over the feld. Fg. 3 and Fg. 4 show graphs of WSN alve nodes result between LEACH, LEACH-C and optmzaton algorthm. We notce that the optmzaton algorthm extend longer node lfe than LEACH and LEACH-C. The frst node des and the last node des extended about 30 %. Ths means that optmzaton algorthm s more effcent than LEACH for that hghly beneft from reducng complexty. Lve nodes Lve nodes Round LEA LEACH LEACH-C Fg. 3. The number of lve nodes (100 nodes) LEACH-C LEACH Round Fg. 4. The number of lve nodes (500 nodes). 6. Conclusons In ths paper, the use of dmenson algorthm s proposed as an optmzaton dea and method for WSN. Takng the WSN as a knd of complex network, the paper proposed to utlze fractal dmenson algorthm to calculate the dfferent measure dmenson of cluster, and analyzed LEA algorthm. Smulaton results show that LEA LEA 5

6 prolongs the network lfetme compared to LEACH and LEACH-C, so the total energy s effcently consumed. There may stll have been trends apparent wthn the results. These could be a valuable gudance for future study. Acknowledgements The work presented n ths paper was supported by the Natonal Natural Scence Foundaton of Chna (Grants No. NSFC ), Fund for the Doctoral Program of Hgher Educaton of Chna (Grants No ), Natonal Great Scence Specfc Project (Grants No. 2012ZX , 2012ZX ) and ejng Muncpal Commsson of Educaton uld Together Project. References [1]. R. Gupta, K. Sultana, P. Sngh, Securty for wreless sensor networks n mltary operatons, n Proceedngs of the 4 th Internatonal Conference on Computng, Communcatons and Networkng Technologes (ICCCNT), 2013, pp [2]... Mandelbrot, Fractals: Form, chance and dmenson, Freeman, San Francsco, [3]. M. Nswar, A. A. Ilham, E. Palante, Performance evaluaton of Zgee-based wreless sensor network for montorng patents' pulse status, n Proceedngs of the Internatonal Conference on Informaton Technology and Electrcal Engneerng (ICITEE), 2013, pp [4]. R. H. Wend, C. Anantha,. Har, Communcaton protocols for wreless sensor networks, n Proceedngs of the IEEE Hawa Internatonal Conference on System Scences, 2000, Vol. 8, pp [5]. Ioanns Ch. Paschalds, R. M. Wu, Robust maxmum lfetme routng and energy allocaton n wreless sensor networks, Internatonal Journal of Dstrbuted Sensor Networks, [6]. Anfeng Luyz, Z. M. Zheng, C. Zhang, Z. G. Chen, X. M. Shen, Secure. energy-effcent dsjont multpath routng for WSNs, IEEE Transactons on Vehcular Technology, Vol. 61, Issue 7, 2012, pp [7]. Habn Yu, Peng Zeng, Intellgent wreless sensor network system, Scence Press, ejng, [8]. H. Wend, C. Anatha,. Har, An applcatonspecfc protocol archtecture for wreless mcrosensor networks, IEEE Transactons on Wreless Communcaton, Vol. 1, Issue 4, 2002, pp [9]. K. Tadak, The Hausdorff dmenson of the haltng self-smlar sets of T-unversal prefx-free machnes, n Proceedngs of the Internatonal Conference on Informaton Theory Proceedngs (ISIT), 2010, pp [10]. Chaomng Song, Lazaros K. Gallos, Shlomo Havln, Herńan A. Makse, How to calculate the fractal dmenson of a complex network: the box coverng algorthm, Journal of Statstcal Mechancs, 2007, P [11]. V. V. Deshpande, A. R. hagat Patl, Energy effcent clusterng n wreless sensor network usng cluster of cluster heads, n Proceedngs of the Internatonal Conference on Wreless and Optcal Communcatons Networks (WOCN), 2013, pp [12]. Song Chao-mng, S. Havln, H. A. Makse, Selfsmlarty of complex networks, Nature, Vol. 433, 2005, pp [13]. Song Chao-Mng, L. K. Gallos, S. Havln, et al, How to calculate the fractal dmenson of a complex network, The box coverng algorthm, Journal of Statstcal Mechancs, 2007, P [14]. Yao Shang-Ln, Qn Sheng-Gao, Wang Guo-Hu, Mult-fractal fractal characterstcs of the heterogeneous pore dstrbuton of cores, n Proceedngs of the Internatonal Conference on Computer Dstrbuted Control and Intellgent Envronmental Montorng (CDCIEM), 2012, pp Copyrght, Internatonal Frequency Sensor Assocaton (IFSA) Publshng, S. L. All rghts reserved. ( 6