QuantitativeInvulnerabilityAnalysisofArtificialSpider-Web ...downloads.hindawi.com/journals/wcmc/2020/4617239.pdf · Spider webs can be divided into several types, such as the sheet

Research ArticleQuantitative Invulnerability Analysis of Artificial Spider-WebTopology Model Based on End-to-End Delay

Jun Wang 12 Zhuangzhuang Du 1 and Zhitao He1

1College of Agriculture Equipment Engineering Henan University of Science and Technology Luoyang Henan 471003 China2Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province LuoyangHenan 471003 China

Correspondence should be addressed to Zhuangzhuang Du dzzwq123521163com

Received 30 May 2019 Accepted 28 January 2020 Published 18 February 2020

Academic Editor Davide Mattera

Copyright copy 2020 Jun Wang et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-is paper presents an artificial spider-web topology model inspired by the structure and invulnerability of a spider web Ahierarchical clustering routing rule is accordingly established using the vibration transmission features of the natural spider web asa reference Furthermore the end-to-end delay is applied as the quantitative indicator of invulnerability for analyzing thecommunication performance and characteristics of the artificial spider-web topology -e simulation tests of a one-layer and 3-layer artificial spider-web model are implemented to obtain the importance and destructive tolerance of network componentsbased on OPNET with the change of communication conditions and fault types -is paper can provide a practical analysismethod for the invulnerability of the artificial spider-web topology and offer important implications for the construction andmaintenance of wireless sensor networks based on the topology

1 Introduction

Wireless sensor network (WSN) is a multihop ad hocnetwork system that is formed as a result of communicationamong a large number of sensor nodes deployed in a targetarea which is an important technical form of the underlyingnetwork of the Internet of things [1] Adopting the moni-toring method with the application of WSNs is suitable formany fields such as object locations on a battlefield thecollection of physiological data intelligent transportationsystems and ocean exploration [2] However theWSN oftenencounters node failures routing failures and communi-cation interruptions due to energy exhaustion hardwarefailure and so on which cause the segmentation of theconnected network topology the shrinkage of coverage andeven the damage to the whole network [3]-erefore how toenhance the invulnerability of the WSN is an importantresearch field for the realization of its monitoring functions

In recent years topology control technology has becomea hot subject in the study on WSN invulnerability [4] -ecurrent studies mainly focus on scale-free models [5ndash7]

Based on the BarabasindashAlbert (BA) scale-free model Chenet al proposed the B model where an increase in nodes andlinks and link deletion mechanisms conform to the actualnetwork characteristic that the network size changes overtime [8] Although the foregoing research has made someprospective progress the assumption of the network modelis excessively ideal For example the assumptions of accuratelocating even distribution strict synchronization and so onof sensor nodes fail to account for a large number of dif-ficulties found in practical applications [9] -erefore amore practical topology model should be built At presentsome researchers have begun to apply bioinspired networktopology models to improve the network invulnerability[10] Applications of the bionic network topologies exhibitenormous potential value for WSN development Char-alambous et al based on the lateral suppression principleproposed an energy-efficient topology management modelthat is inspired by the signal transmission patterns of bio-logical intercellular communication and they simulated theinduction algorithm on size-limited networks -e resultsshow that the energy efficiency can be improved by building

HindawiWireless Communications and Mobile ComputingVolume 2020 Article ID 4617239 11 pageshttpsdoiorg10115520204617239

compact clusters in the clustering stage of the model [11]Jun studied invulnerability of molecular structures of ade-nylate kinase and its relationship with the rigidity of spatialstructures -e results show that the atomic topologicalstructure preserves the rigid information of the proteinmolecular structure and the invulnerability is strongly as-sociated with the rigidity of spatial structures throughmeasurements of natural connectivity [12] -e above-mentioned network models are too complex and difficult toestablish especially in the case of a large-scale sensor nodedeployment where they cannot secure the quality of com-munication A simple and stable network model with highcommunication quality is more suitable for deployment inreality

A spider web is a special structure that combines ele-gance nature and ultralightness Its simple stable yethighly tough structure is extremely inspirational for researchon WSN invulnerability Spider webs can be divided intoseveral types such as the sheet web dish web irregular weband orb-web Orb-webs have a special status in spider-webevolution and their structure is simple and regular andthus studies on spider webs are mostly concentrated on orb-webs [13] -e network topology of a typical orb-web hasmuch similarity to a WSN model Some researchers havestarted initial research on the topology of artificial spider-web network models From the structure and durability ofspider webs Xiaosheng et al proposed a new PLC networkmodel and discussed the characteristics of the model and theprocess in which a low-voltage power distribution networktransforms from a physical topology to an artificial spider-web logic topology -ey proved that the new networkmodel has advantages in improving the reliability of the PLCnetwork communication [14] Jun et al established amathematical model of artificial spider webs and concludedthat the network structure of an artificial spider web issuperior to that of a traditional network in terms of theimprovement in the reliability and invulnerability of com-munication systems [15] Yuh-Shyan et al establishedmultiple wireless M2M (machine-to-machine) dynamicspider-web network topologies based on the spider-webnetwork topology to extend the networkrsquos lifetime by dy-namically adjusting different sub-spider-web sizes [16] As aconcrete measure of network performance we could makean accurate assessment of the invulnerability of the artificialspider-web topology model Meanwhile we could alsoevaluate the effectiveness by using the topology model toimprove the network invulnerability However currentstudies have merely made related exploration of the in-vulnerability of the topology model through the quantitativeanalysis method and the existing research only makes apreliminary exploration of the invulnerability of the spider-web structure model and does not carry out quantitativeanalysis of the invulnerability of the network topologymodelbased on the in-depth summary of spider-web structurecharacteristics Sergey et al studied the cascading failureproblem of interdependent networks based on the aboveresearch [17] Jingxia and Junjie investigated the dynamicmodel of heterogeneous wireless sensor networks in order tobalance the energy consumption of nodes and prolong the

network life [18] However the model construction andanalysis method driven by scenario adaptability is difficult toanalyze the invulnerability of the proposed artificial spider-web model -erefore in view of the structural character-istics of the spider-web network it is urgently needed to putforward an effective analysis approach

OPNET is a powerful network design and simulationtool that has been widely used in industry and academia[19 20] OPNET offers precise analysis of the performanceand behavior of complex networks and can be used foraccurate descriptions of network invulnerability Further-more there are plenty of available parameters used tocharacterize the network invulnerability numerically atpresent such as degree proximity betweenness shortestpath and minimum spanning tree Nevertheless theseparameters cannot directly reflect the network invulnera-bility which only focus on describing the changes in thenetwork topology structure-e change of data transmissionperformance before and after network destruction is theintuitive reflection of network invulnerability -e param-eter of end-to-end delay can be applied to characterize theimportance and destructive tolerance of the components(eg node and communication link) in the network -emain objective of this study is to perform evaluation analysisof the invulnerability of the artificial spider-web topologymodel through a series of simulation experiments based onOPNET software Specifically we use the software tool tosimulate different communication conditions (channelnoise packet interval and random seed) and different de-grees and types of link or node failures and adopt end-to-enddelay as the indicator to depict the network invulnerability-is study can lay a solid foundation for building an ana-lytical model of invulnerability of the WSN inspired by aspider web with the help of theories and methods such asprobability theory and graph theory

2 Materials and Methods

21 Artificial Spider-Web Topology Modeling -e structureof the orb-web (Figure 1) is composed of dragline threadsand capture threads According to varied functions thedragline thread can be divided into three types frame threadanchor thread and radiating thread -e frame threads arelocated on the periphery of the spider web to build aframework for the whole spider web -e anchor threads arethe net frame for fixing the whole spider web -e radiatingthreads radiate outward from the central area and connectwith the frame threads to maintain and support the stabilityof the whole spider-web structure-e central area is locatedin the center of the orb-web -e capture threads present aspiral structure woven outward rotationally from the centralarea A cell is a grid space surrounded by two adjacentradiating threads and two adjacent capture threads

A typical orb-web structure is a special structure with anorganic combination of star and ring topologies -estructural evolution of a spider web is illustrated in Figure 2where Figure 2(a) is a star structure Figure 2(b) is a ringstructure and Figure 2(c) is an artificial spider-web structureformed after evolution A one-layer artificial spider-web

2 Wireless Communications and Mobile Computing

structure can be obtained by means of a simple combinationof a radial star structure and one-layer ring structure -echaracteristics of the artificial spider-web topology are thusobtained as follows (1) -e artificial spider-web topology isthe integration of a star topology and several ring topologiesChild nodes in the ring topology are also included in all ofthe child nodes in the star topology (2) -ere is definitely acentral area which can be made of one or more nodes andthe center can establish a radial connection with all of theother child nodes (3) In the same layer chordwise con-nections can be established between child nodes and eachchild node can establish up to two chordwise direct con-nection paths with adjacent child nodes

To express the structural characteristics of the artificialspider web and provide a mathematical foundation forfurther research this paper defines the parameters of theartificial spider-web topology (Figure 3) as follows

(1) A center node is defined as the base station (BS) withn being the total number of nodes in one layer

(2) -e spider layers around the BS are represented by L-is parameter reflects the complexity and com-munication coverage of an artificial spider-webtopology

(3) -e total number of nodes in an artificial spider-webtopology is indicated by N which has the followingrelationship with L and n

N L times n (1)

(4) All nodes are numbered in turn along the directionof spiral magnification and Ni refers to a certain

node in an artificial spider-web topology where1le ileN

(5) -e communication link along the radial direction ofan artificial spider-web topology is defined as thefloating chain represented by Fp minus q -e definition ofa floating chain falls into two cases (1) In the case inwhich a node has a direct connection with the BSp BS and 1le qle n in which q represents a certainnode in the first layer that is radially connected to theBS (2) In the case of radial connections between twonodes in adjacent layers p i and q i minus n where pis a node in an artificial spider-web topology exceptnodes in the first layer and q is an adjacent inner-layer node radially connected with it

(6) -e communication link along the chordwise di-rection of an artificial spider-web topology is definedas the string chain represented by Sj minus f -e defi-nition of a string chain can be separated into twocases (1) In the case in which a node on the firstfloating chain has a chordwise connection with anode on the nth floating chain j kn+ 1 andf kn+ n where j and f represent respectively thenumbers of nodes in the same layer on the first andnth floating chains and k denotes a positive integer(2) In the case of chordwise connections between theother adjacent nodes in the same layer except for thenodes on the first floating chain j I and f i minus 1 inwhich 1lt ileNn and ine kn+ 1

(7) θ is the sector angle namely the angle between twoadjacent floating chains

12

3

4

56

7

nc

12

3

4

56

7

nc

12

3

4

56

7

n

(a) (b) (c)

Figure 2 Evolution process of the spider-web structure (the letter c represents the central area and the numbers from 1 to n denote child nodes)

Cell

Central area

Prey surfaceCapture thread

Radiating thread

Frame thread

Anchorthread

Dragline thread

Figure 1 Orb-web structure

Wireless Communications and Mobile Computing 3

θ 360deg

n (2)

22 Artificial Spider-Web Routing Rule Previous studies onthe vibration transmissibility of a spider web have found thatthe vibration signals of the spider web are mainly trans-mitted through radiating threads while the capture threadsonly undertake a small amount of the vibration [21 22]Based on the artificial spider-web topology we use the vi-bration transmission characteristics of the natural spiderweb for reference to establish a hierarchical clusteringrouting rule -e specific routing rule is as follows

221 Selection of Cluster Heads To avoid the communi-cation overhead caused by frequent elections of cluster headsand guarantee the uniform distribution of cluster heads weassign the first-layer nodes N1 minus Nn connected with the BS ascluster heads

222 Determination of a Cluster Member In the initial stageof the network construction the minimum hops to the BS areobtained for each isolated node based on the flood routingalgorithm and the routing table of the minimum hops isestablished All these nodes are arranged hierarchically withthe minimum hops and the nodes with the equal quantity ofhops are classified into the same layer Furthermore the nodesconnected with a cluster head Ni (1le ile n) in different layersby theminimumhops are categorized as themember nodes ofthe cluster head After all nodes are sorted into clusters thenodes in each individual cluster obviously constitute an in-dependent radial link

223 Communications between Cluster Heads and BSAccording to the artificial spider-web topology a clusterhead directly connects with the BS two adjacent cluster

heads and a cluster member node Each cluster head re-ceives the data of all cluster member nodes and forwards tothe BS Once a link failure occurs between a cluster head andthe BS or the radial link flow between the cluster head andthe BS exceeds the threshold Y an adjacent cluster headnode is selected as the relay node in the specified order fordata transmit

224 Data Transmission between Cluster Member Nodes andCluster Head Cluster member nodes convey data to thecorresponding cluster head in the form of multihop inaccordance with the principle of shortest path priority andthen the cluster head transfers the data to the BS If the linktraffic in the shortest path exceeds the threshold Y or thenode or link fails adjacent link nodes in the same layer canbe selected in turn as relay nodes to send data to the adjacentcluster head and further deliver to the BS which is consistentwith the routing rule in case of cluster-head failure

-e steps of the hierarchical clustering routing rule aresummarized in Algorithm 1

23 Invulnerability Analysis Method and Parameter SettingsNumerous studies have shown that the spider web presentsexcellent biological characteristics such as having a simpleand light structure high mechanical strength and strongenergy dissipation [23ndash25] However the related study oninvulnerability analysis of the artificial spider-web topologystill remains in the initial stage End-to-end delay is theduration between the time that a source node produces adata packet and the time that this packet reaches its desti-nation node which is the direct reflection of influence oncommunication caused by network component failure Weuse end-to-end delay as the indicator to evaluate the in-vulnerability of the artificial spider-web topology -econcrete definition of end-to-end delay is as follows the

n 2n

2

n + 1

1

2n + 1

3n + 1

4n + 1

2n + 2

n + 2

3n + 2

4n + 2

33n + 34n + 3 n + 32n + 3

4

n + 4

3n + 4

2n + 4

4n + 4

5

n + 5

2n + 5

3n + 5

4n + 5

3n 4n 5n Nn

Nn ndash 1Nn ndash 2

Nn ndash 3

Nn ndash 4 Nn ndash 5

Floating chain F4n+1ndash3n+1

String chain S4n+1ndash5n

Layer 5

BS

θ

Figure 3 Parameters of the artificial spider-web topology


delay time for any nodeNi to send the data packet to the BS isTi in which 1le ileNn the total end-to-end delay for allnodes is Tn 1113936

Nn

i1 Ti the end-to-end delay Ed is defined asthe ratio between the total delay time in which all nodes sendthe data packet to the BS and Nn which is expressed as

Ed Tn

Nn

(3)

Moreover we choose a one-layer and 3-layer artificialspider web as studying objects in order to analyze the in-vulnerability rule -e parameters of the one-layer artificialspider-web model are the sector angle θ 60deg and 6 nodesFor the 3-layer artificial spider web the parameters are thesector angle θ 60deg and 18 nodes A total of 3 sets of

simulation tests are conducted on the one-layer artificialspider-web model which specifically include (1) the end-to-end delay test of the topology model withwithout noise (2)the end-to-end delay test of the topology model with dif-ferent packet intervals and (3) the end-to-end delay test ofthe topology model with different random seeds -ese testsare for analyzing the influence of different external or in-ternal conditions on the communication performance of theartificial spider-web topology Two sets of simulation testsare conducted on the 3-layer artificial spider-web modelwhich specifically include the following (1) the end-to-enddelay test for damage to a single radial link and single nodelayer by layer and (2) the end-to-end delay test for damage tothe same layer of nodes and links -e two sets of tests are

Input the nodeNi the total number of nodes in one layer n the total number of nodes in the artificial spider-web topologyN andthe threshold YOutput routing path from the node Ni to the BS

(1) lowast Communication between nodes located from the 2nd layer to the outermost layer and BSlowast(2) while nlt ileN do(3) for Ni nlt ileN do(4) if no link failure exists between Ni and Niminus n and link traffic does not exceed the threshold value Y(5) then Ni forwards data to Niminus n(6) end for(7) for i (k+ 1)lowast n 1le kleNn do(8) N(k+1)n transfers data to N(k+1)nminus 1(9) if N(k +1)nminus 1 fails(10) then N(k+1)n transmits data to N(k+1)n+1(11) end for(12) for i kn+ 1 1le kleNn do(13) Nkn+1 delivers data to Nkn+n(14) if Nkn+n undergoes a failure(15) then Nkn+1 passes data to Nkn+2(16) end for(17) for ine (k+ 1)lowast n且ine kn+ 1 1le kleNn do(18) Ni sends data to Niminus 1(19) if Niminus 1 is out of order(20) then Ni conveys data to Ni+1(21) end for(22) end while(23) break(24) lowastCommunication between the first-layer nodes and BSlowast(25) if 1lt ile n(26) then Ni is a cluster head(27) if no link failure exists between Ni and BS and link traffic does not exceed the threshold value Y(28) then Ni forwards data to BS(29) else judge the value of i(30) if i 1(31) thenN1 sends data toNn and forwards them to the BS alongNnrsquos radial link further In case ofNn failureN1 transmits data

to N2 and then passes them to the BS by the radial link through N2(32) else if i n(33) thenNn transmits data toNnminus 1 and forwards them to the BS byNn minus 1rsquos radial link IfNnminus 1 failsNn transfers data toN1 and

then delivers them to the BS along the radial link through N1(34) elseNi conveys data toNiminus 1 and forwards them to the BS viaNiminus 1rsquos radial link IfNiminus 1 malfunctionsNi sends data toNi+1 and

then transfers them to the BS along the radial link through Ni+1(35) end if(36) end if(37) end if

ALGORITHM 1 Hierarchical clustering routing rule


used to analyze the difference in network communicationperformance before and after the artificial spider-web to-pology damaged

OPNET (Optimized Network Engineering Tool) pro-vides a comprehensive development environment for thespecification simulation and performance analysis ofcommunication networks A large range of communicationsystems from a single WSN to global satellite networks canbe supported In this paper we apply OPNET 145 as thesimulation platform to perform the analysis of the invul-nerability of the artificial spider-web topology model -esimulation process defines three packet formats namelydata packet broadcast packet and noise packet -e datapacket size is defined as 200 bit and that of the broadcastpacket and noise packet is 72 bit the bandwidth of the link isdefined as 9600 bps with a simulation time set to 1000 s andthe default peripheral nodersquos packet interval set to 01 s

3 Results and Discussion

31 One-Layer Artificial Spider-Web Topology -e com-munication conditions of the WSN have a massive influenceon the stability of the network On the one hand the networkchannel is sensitive to channel noise interference causingchannel imbalance and increasing the probability of packetloss On the other hand the packet interval directly affectsthe establishment time of network routing control over-head and transmission delay In addition network com-munication has significant uncertainties and randomness Inorder to assess the communication stability of the artificialspider-web topology model we conducted the followingthree groups of simulation tests

Figure 4(a) shows the waveform variation of the end-to-end delay of the one-layer artificial spider-web topologywithout and with noise Without noise the time delay is

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)

Without noise spiderWith noise spider

(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)

100ms200msIdeal condition

(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)

Seed = 150Seed = 15Ideal condition

(c)

Figure 4 Simulation results of the end-to-end delay time of the one-layer artificial spider-web topology under different conditions(a) Noise (with without) (b) Packet interval (200ms 100ms) (c) Random seed (15 150)


maintained at 0021 s (ideal end-to-end delay before addingnoise) After the addition of random noise between 100msand 500ms the delay fluctuates and the peak value dif-ference in the delay fluctuation is 00003 s which accountsfor 159 of the average time delay and is basically consistentwith that without noise -e waveform variation of the end-to-end delay of the one-layer artificial spider-web topology isdemonstrated in Figure 4(b) where the noise conditions staythe same and the packet intervals are respectively 200msand 100ms Both the end-to-end delay curves fluctuatearound the ideal end-to-end delay When the packet intervalis 200ms the maximum increase of amplitude is 066 andthe minimum decrease of amplitude is 038 When thepacket interval is 100ms the maximum increase of am-plitude is 078 and the minimum decrease of amplitude is057 -e results indicate that the packet interval producesa very small impact on the one-layer artificial spider-webtopology Figure 4(c) shows the waveform variation of theend-to-end delay of the one-layer artificial spider-web to-pology over time where the noise conditions remain un-changed and the random seeds are 15 and 150 respectivelyWhen the random seed is 15 the maximum increase ofamplitude is 080 and the minimum decrease of amplitudeis 039 When the random seed is 150 the maximumincrease of amplitude is 066 and the minimum decrease ofamplitude is 038 -e results show that the delay fluc-tuation against different noise conditions packet intervalsand random seeds all goes below 16 of the ideal end-to-end delay thus noise packet interval and random seed havecomparatively small influence on the network transmissioncapability of the one-layer artificial spider-web topology-etopology presents strong reliability and stability which canmeet the service quality of wireless sensor networks

32 3-Layer Artificial Spider-Web Topology

321 End-To-End Delay Test for Damage to a Single RadialLink and Single Node Layer by Layer Aiming at achievingthe impact of the damage of links in varied layers along thesame radial line on the end-to-end delay of the topologysimulation tests with a complete network and damaged linksFc-2 F8-2 and F14-8 are conducted in turn-e damaged linksare shown in Figure 5 Figure 6 presents the simulationresults By comparison with the complete network it can beseen that in the case of damage to links Fc-2 F8-2 and F14-8the delay in turn increases by 233 116 and 23 re-spectively which shows that the impact of the inner links onthe invulnerability is greater than that of the outer linksFrom the above analysis it can be clarified that when theradial link is damaged the outer node and inner node cannotdirectly transmit data but communicate with the inner nodethrough the relevant relay node according to the hierarchicalclustering routing rule As a result the number of links thatundertake data transmission inevitably increases and thenetwork delay also raises correspondingly Furthermore thecloser the link to the BS on the same radial line is damagedthe longer the end-to-end delay is indicating the higherimportance of the link

Some nodes in the topology are responsible for a largeamount of data send-receive assignment which have moreimportant value than other nodes Whether these nodesoperate normally or not directly affects the performance ofthe network-erefore verifying the importance of nodes inthe network has certain significance for improving thesurvivability of the entire communication network In orderto analyze the importance of the nodes in varied layers alongthe same radial line by the end-to-end delay of the networksimulation tests of the complete network and damage tonodes N2 N8 and N14 are conducted -e damaged nodesare depicted in Figure 7

Figure 8 shows the simulation results of the 3-layerartificial spider-web model in the case of the completenetwork and damage toN2N8 andN14 When nodesN2 andN8 are damaged the network delay is respectively 140and 23 higher than the delay of the complete networkWhen the outermost node N14 is damaged the networkdelay is 23 lower than the delay of the complete networkwhich indicates that while the inner-layer node damageextends the network delay the outermost node damage

0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)

Complete spider webF14ndash8

F8ndash2Fcndash2

Figure 6 Simulation results of the end-to-end delay in the case ofdamage in the radial links in different layers

c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Link damage F14ndash8


Link damage Fcndash2

Figure 5 Layer-by-layer damage of the radial links Fc-2 F8-2 andF14-8


reduces the network delay Consequently the inner nodesare more important Moreover it can be seen from theanalysis that the damage of a node will lead to the failure ofcommunication links connected with it -e outer nodesaccordingly need to establish communication link with theinner nodes through relay nodes which inevitably increasenetwork delay However when the outermost nodes aredamaged due to the fact that they are not responsible forforwarding data the delay is not generated and the end-to-end delay is slightly reduced compared to that of thecomplete network

322 End-To-End Delay Test for Damage to the Same Layerof Nodes and Links -e difference in the end-to-end delaytime of the artificial spider-web topology is evaluated basedon the node and link damage for the quantitative analysis ofthe invulnerability of the topology under the conditions ofdamages in the same layer

Damage of the node or link in each layer can be di-vided into 10 situations Figure 9 illustrates the 10

situations by taking the first-layer nodelink damage asan example as follows damage of any 1 nodelink (A)damage of 2 adjacent nodeslinks (B) damage of 2nonadjacent nodeslinks (C) damage of 3 adjacentnodeslinks (D) damage of 3 nodeslinks with 2 of thembeing adjacent to each other (E) damage of 3 nonadjacentnodeslinks (F) damage of 4 adjacent nodeslinks (G)damage of 4 nodeslinks with 3 of them being adjacentnodeslinks (H) damage of 4 adjacent nodeslinks withany two of them being adjacent nodeslinks (I) anddamage of 5 adjacent nodeslinks (J)

Table 1 shows the simulation results of the end-to-enddelay and delay increment when nodes in the first second andthird layers are damaged Table 1 shows that with an increasein the number of radial nodes damaged delay increments ofthe first and second layers also tend to go up -e end-to-enddelay increment rises from 0006 s to 011 s with the number ofdamaged nodes in the first layer being increased from 1 to 5which is increased by 183 times Meanwhile the end-to-enddelay increment rises from 0001 s to 0026 s with the number ofdamaged nodes in the second layer being increased from 1 to 5which is increased by 26 times When nodes in the inner layerare damaged the smaller their distance to the BS the greaterthe network delay increment and the greater the impact on theartificial spider-web topology For instance one node in thefirst and second layers is damaged and the end-to-end delayincrements are respectively 0006 s and 0001 s

Under the condition of the damage of nodes in the samelayer the greater the number of adjacent nodes the greaterthe degree of impact When the number of damaged nodes is2 where two adjacent nodes and two nonadjacent nodes aredamaged the end-to-end delay increments of first-layernodes are 0019 s and 0014 s respectively and the end-to-end delay increments of nodes in the second layer are re-spectively 0004 s and 0003 s -erefore the damage ofadjacent nodes in the same layer will seriously affect thenormal communication function of the topology networkIn the case of the damage of the outermost nodes (third-layernodes) the network delay decreases with the increase of thenumber of damaged nodesWhen the same number of nodesis destroyed whether the nodes are adjacent or not has noobvious effect on the network delay -e special rule pre-sented by the outermost node is related to its location -eoutermost node only transmits information to the innernode according to the routing rule so if the number ofoutermost node damages increases the network delay will beshorter than that of the complete network indicating thatthe damage of the outermost node has little impact onnetwork communication performance

Table 2 shows the simulation results of the end-to-enddelay and delay increment when radial links in the firstsecond and third layers are damaged Table 2 shows thatwhen the number of damaged links in layers 1 2 and 3increases from 1 to 5 the end-to-end delay increment risesby 16 146 and 19 times indicating that the end-to-enddelay increment shows an upward trend with the increase ofthe number of radial link failures in the same layer When 3radial links in the first second and third layers are damagedit shows that when the same number of links is destroyed at

c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2

Figure 7 Layer-by-layer damage of the radial link nodes N2 N8and N14

0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)

Complete spider webN14

N8N2

Figure 8 Simulation results of the end-to-end delay in the case ofdamage to nodes in different layers


different locations in the same layer the larger the number ofadjacent links the greater the delay increment and the effectof centralized damaged links on the invulnerability is greaterthan that of decentralized damaged links

In the same circumstance with the increase in thenumber of damaged layers the end-to-end delay tends todecrease over time and the increase in the network delayrapidly goes down When 5 links in the first second and

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)

Figure 9 Fault types that may occur when the nodelink is damaged in the first layer (the red solid circle represents the damaged nodes andthe red dotted line denotes the damaged links)

Table 1 Variation in the network delay when the nodes in the first second and third layers are damaged

Number of nodesdamaged

Failuretype

End-to-end delay time (s) Delay increment (s)Damage of the

1st layerDamage of the

2nd layerDamage of the

3rd layerDamage of the



3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003

3D 0082 0052 0039 0039 0009 ndash0004E 0071 0049 0039 0028 0006 ndash0004F 0065 0048 0039 0022 0005 ndash0004

4G 0112 0059 0037 0069 0016 ndash0006H 0093 0054 0037 0050 0011 ndash0006I 0087 0053 0037 0044 0010 ndash0006

5 J 0153 0069 0034 0110 0026 ndash0009

Table 2 Variation in the network delay when links in the first second and third layers are damaged

Number of radiallinks damaged

Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019


third layers are damaged the network delay increments arerespectively 37 17 and 044 times that of the completenetwork which demonstrates that the impact of the innerlinks on the network delay is much greater than that of theouter links on the network delay

Moreover we can conclude that the importance dis-tribution rule of nodes and links in the artificial spider-webtopology model is as follows (1) -e nodes and links in theinner layers are much more important than the nodes andlinks in the outer layers (2) Damage of adjacent links andnodes in the same layer is more likely to paralyze the to-pology network (3) Damage of the outermost nodes re-duces the coverage area of the model but it has no impacton the proper communication of the inner layers -roughthis analysis it can be testified that the importance dis-tribution rule of nodes is basically consistent with that ofthe links so we should focus on maintenance of the nodesand links in inner layers in the network construction orenhance the networkrsquos invulnerability by increasing thedeployment density of nodes at important places Mean-while it is obviously an effective method to improve thefault tolerance ability of the artificial spider-web topologyby reducing the possibility of simultaneous failures ofadjacent nodes or links

4 Conclusions

-e spider-web structure is simple and lightweighttherefore spiders can quickly capture the information onvarious objects slammed into the web after sustaining theimpact of large loads the web can still maintain a powerfuland effective connection Local damage of a spider webdoes not affect the capture of prey and the transmission ofvibration information -e structure of the spider web issomewhat similar to a WSN topology and thus the arti-ficial spider-web topology is very inspirational for study oninvulnerability Inspired by specific advantages of thespider web this paper establishes an artificial spider-webtopology model which defines the related structural pa-rameters and takes the end-to-end delay as the indicator fordescribing the invulnerability performance of the topologyA series of simulation tests are conducted on a one-layerand 3-layer artificial spider-web model based on OPNETfor the quantitative analysis Analysis of simulation resultsshows the following (1) -e simulation results of thesingle-layer artificial spider web under different conditionsshow excellent network transmission stability and reli-ability (2) -rough the destruction of a single node asingle link nodes and links at the same time and thedestruction of different density under the same quantity itis found that the importance of the location of the node andlink is inversely proportional to the distance of the basestation and the denser the damage the more serious theinfluence (3) -e invulnerability performance of the ar-tificial spider-web topology under different communica-tion conditions and different degrees and types of link ornode failures is obtained which provides a meaningfulreference for extensive application of the spider webrsquosadvantageous characteristics for WSNs

Data Availability

-e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research activity described in this paper was jointlysupported in part by the National Natural Science Foun-dation of China (Grant no 61771184) Key Research Projectof Education Bureau of Henan Province China (Grant no17A416002) Key Scientific and Technological Project ofHenan Province China (Grant no 172102210040) andProgram for Science amp Technology Innovation Talents inUniversities of Henan Province (Grant no 20HASTIT029)Finally the authors would like to thank Dr Jiajia Wang forher valuable suggestions on the research methods of thisarticle

References

[1] R Krishnan and D Starobinski ldquoEfficient clustering algo-rithms for self-organizing wireless sensor networksrdquo Ad HocNetworks vol 4 no 1 pp 36ndash59 2006

[2] G Song D Xinwu and Y Jumei ldquoStudy on measurementerror of iron ore pipeline transportation flow based on weightfunction theory of electromagnetic flow sensorrdquo 8e Journalof Supercomputing vol 75 no 5 pp 2289ndash2303 2018

[3] S M Zin N B Anuar M L M Kiah et al ldquoRouting protocoldesign for secure WSN review and open research issuesrdquoJournal of Network and Computer Applications vol 41pp 517ndash530 2014

[4] T M Chiwewe and G P Hancke ldquoA distributed topologycontrol technique for low interference and energy efficiency inwireless sensor networksrdquo IEEE Transactions on IndustrialInformatics vol 8 no 1 pp 11ndash19 2012

[5] Z Gengzhong and L Qiumei ldquoScale-free topology evolutionfor wireless sensor networksrdquo Computers amp Electrical Engi-neering vol 39 no 6 pp 1779ndash1788 2013

[6] Z Gengzhong L Sanyang and Q Xiaogang ldquoScale-freetopology evolution for wireless sensor networks with re-construction mechanismrdquo Computers and Electrical Engi-neering vol 38 no 3 pp 643ndash651 2012

[7] N Sarshar and V Roychowdhury ldquoScale-free and stablestructures in complex ad hoc networksrdquo Physical Review EStatistical Nonlinear and Soft Matter Physic vol 69 no 2Article ID 026101 2004

[8] C Qinghua and S Dinghua ldquo-e modeling of scale-freenetworksrdquo Physica A Statistical Mechanics and its Applica-tions vol 335 no 1-2 pp 240ndash248 2004

[9] L Shudong L Lixiang and Y Yixian ldquoA local-world het-erogeneous model of wireless sensor networks with node andlink diversityrdquo Physica A Statistical Mechanics and its Ap-plications vol 390 no 16 pp 1182ndash1191 2011

[10] W Jiajia Q Zhihui and R Luquan ldquoBiomechanical com-parison of optimal shapes for the cervical intervertebral fusioncage for C5-C6 cervical fusion using the anterior cervical plateand cage (ACPC) fixation system a finite element analysisrdquoMedical Science Monitor vol 7 no 25 pp 8379ndash8388 2019


[11] C Charalambous and S Cui ldquoA biologically inspired net-working model for wireless sensor networksrdquo IEEE Networkvol 24 no 3 pp 6ndash13 2010

[12] W Jun T Yuejin D Hongzhong et al ldquoHeterogeneity ofscale-free networkrdquo System Engineering 8eory and Practicevol 27 no 5 pp 101ndash105 2007

[13] B J Kaston ldquo-e evolution of spider websrdquo AmericanZoologist vol 4 no 2 pp 191ndash207 1964

[14] L Xiaosheng Z Liang Z Yan et al ldquoPerformance analysis ofpower line communication network model based on spiderwebrdquo in Proceedings of the IEEE International Conference onPower Electronics and ECCE Asia Jeju South Korea June2011

[15] W Jun G Song H Zhitao et al ldquoResearch on artificial spiderweb model for farmland wireless sensor networkrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6393049 11 pages 2018

[16] Y-S Chen and W-L Chiang ldquoA spiderweb-based massiveaccess management protocol for M2M wireless networksrdquoIEEE Sensors Journal vol 15 no 10 pp 5765ndash5776 2015

[17] S V Buldyrev R Parshani G Paul H E Stanley andS Havlin ldquoCatastrophic cascade of failures in interdependentnetworksrdquo Nature vol 463 no 7291 pp 1025ndash1028 2010

[18] J Zhang and J Chen ldquoAn adaptive clustering algorithm fordynamic heterogeneous wireless sensor networksrdquo WirelessNetworks vol 25 no 1 pp 455ndash470 2017

[19] E Biegeleisen M Eason C Michelson et al Network in theLoop Using HLA Distributed OPNET Simulations and 3DVisualizations Military Communications Conference At-lantic City NJ USA 2005

[20] M S Hasan H Yu A Griffiths et al ldquoSimulation of dis-tributed wireless networked control systems over MANETusing OPNETrdquo in Proceedings of the IEEE InternationalConference on Networking London UK April 2007

[21] R Das A Kumar A Patel S Vijay S Saurabh andN Kumar ldquoBiomechanical characterization of spider websrdquoJournal of the Mechanical Behavior of Biomedical Materialsvol 67 pp 101ndash109 2017

[22] H Yu J Yang and Y Sun ldquoEnergy absorption of spider orbwebs during prey capture a mechanical analysisrdquo Journal ofBionic Engineering vol 12 no 3 pp 453ndash463 2015

[23] V Tietsch J Alencastre H Witte and F G Torres ldquoEx-ploring the shock response of spider websrdquo Journal of theMechanical Behavior of Biomedical Materials vol 56 pp 1ndash52016

[24] Z Qin B G Compton J A Lewis et al ldquoStructural opti-mization of 3D-printed synthetic spider webs for highstrengthrdquo Nature Communications vol 6 Article ID 70382015

[25] B D Opell and J E Bond ldquoCapture thread extensibility oforb-weaving spiders testing punctuated and associative ex-planations of character evolutionrdquo Biological Journal of theLinnean Society vol 70 no 1 pp 107ndash120 2000


compact clusters in the clustering stage of the model [11]Jun studied invulnerability of molecular structures of ade-nylate kinase and its relationship with the rigidity of spatialstructures -e results show that the atomic topologicalstructure preserves the rigid information of the proteinmolecular structure and the invulnerability is strongly as-sociated with the rigidity of spatial structures throughmeasurements of natural connectivity [12] -e above-mentioned network models are too complex and difficult toestablish especially in the case of a large-scale sensor nodedeployment where they cannot secure the quality of com-munication A simple and stable network model with highcommunication quality is more suitable for deployment inreality

A spider web is a special structure that combines ele-gance nature and ultralightness Its simple stable yethighly tough structure is extremely inspirational for researchon WSN invulnerability Spider webs can be divided intoseveral types such as the sheet web dish web irregular weband orb-web Orb-webs have a special status in spider-webevolution and their structure is simple and regular andthus studies on spider webs are mostly concentrated on orb-webs [13] -e network topology of a typical orb-web hasmuch similarity to a WSN model Some researchers havestarted initial research on the topology of artificial spider-web network models From the structure and durability ofspider webs Xiaosheng et al proposed a new PLC networkmodel and discussed the characteristics of the model and theprocess in which a low-voltage power distribution networktransforms from a physical topology to an artificial spider-web logic topology -ey proved that the new networkmodel has advantages in improving the reliability of the PLCnetwork communication [14] Jun et al established amathematical model of artificial spider webs and concludedthat the network structure of an artificial spider web issuperior to that of a traditional network in terms of theimprovement in the reliability and invulnerability of com-munication systems [15] Yuh-Shyan et al establishedmultiple wireless M2M (machine-to-machine) dynamicspider-web network topologies based on the spider-webnetwork topology to extend the networkrsquos lifetime by dy-namically adjusting different sub-spider-web sizes [16] As aconcrete measure of network performance we could makean accurate assessment of the invulnerability of the artificialspider-web topology model Meanwhile we could alsoevaluate the effectiveness by using the topology model toimprove the network invulnerability However currentstudies have merely made related exploration of the in-vulnerability of the topology model through the quantitativeanalysis method and the existing research only makes apreliminary exploration of the invulnerability of the spider-web structure model and does not carry out quantitativeanalysis of the invulnerability of the network topologymodelbased on the in-depth summary of spider-web structurecharacteristics Sergey et al studied the cascading failureproblem of interdependent networks based on the aboveresearch [17] Jingxia and Junjie investigated the dynamicmodel of heterogeneous wireless sensor networks in order tobalance the energy consumption of nodes and prolong the

network life [18] However the model construction andanalysis method driven by scenario adaptability is difficult toanalyze the invulnerability of the proposed artificial spider-web model -erefore in view of the structural character-istics of the spider-web network it is urgently needed to putforward an effective analysis approach

OPNET is a powerful network design and simulationtool that has been widely used in industry and academia[19 20] OPNET offers precise analysis of the performanceand behavior of complex networks and can be used foraccurate descriptions of network invulnerability Further-more there are plenty of available parameters used tocharacterize the network invulnerability numerically atpresent such as degree proximity betweenness shortestpath and minimum spanning tree Nevertheless theseparameters cannot directly reflect the network invulnera-bility which only focus on describing the changes in thenetwork topology structure-e change of data transmissionperformance before and after network destruction is theintuitive reflection of network invulnerability -e param-eter of end-to-end delay can be applied to characterize theimportance and destructive tolerance of the components(eg node and communication link) in the network -emain objective of this study is to perform evaluation analysisof the invulnerability of the artificial spider-web topologymodel through a series of simulation experiments based onOPNET software Specifically we use the software tool tosimulate different communication conditions (channelnoise packet interval and random seed) and different de-grees and types of link or node failures and adopt end-to-enddelay as the indicator to depict the network invulnerability-is study can lay a solid foundation for building an ana-lytical model of invulnerability of the WSN inspired by aspider web with the help of theories and methods such asprobability theory and graph theory

2 Materials and Methods

21 Artificial Spider-Web Topology Modeling -e structureof the orb-web (Figure 1) is composed of dragline threadsand capture threads According to varied functions thedragline thread can be divided into three types frame threadanchor thread and radiating thread -e frame threads arelocated on the periphery of the spider web to build aframework for the whole spider web -e anchor threads arethe net frame for fixing the whole spider web -e radiatingthreads radiate outward from the central area and connectwith the frame threads to maintain and support the stabilityof the whole spider-web structure-e central area is locatedin the center of the orb-web -e capture threads present aspiral structure woven outward rotationally from the centralarea A cell is a grid space surrounded by two adjacentradiating threads and two adjacent capture threads

A typical orb-web structure is a special structure with anorganic combination of star and ring topologies -estructural evolution of a spider web is illustrated in Figure 2where Figure 2(a) is a star structure Figure 2(b) is a ringstructure and Figure 2(c) is an artificial spider-web structureformed after evolution A one-layer artificial spider-web







N L times n (1)






12

3

4

56

7

nc

12

3

4

56

7

nc

12

3

4

56

7

n

(a) (b) (c)


Cell

Central area


Radiating thread

Frame thread

Anchorthread

Dragline thread



θ 360deg

n (2)









n 2n

2

n + 1

1

2n + 1

3n + 1

4n + 1

2n + 2

n + 2

3n + 2

4n + 2

33n + 34n + 3 n + 32n + 3

4

n + 4

3n + 4

2n + 4

4n + 4

5

n + 5

2n + 5

3n + 5

4n + 5

3n 4n 5n Nn


Nn ndash 3




Layer 5

BS

θ




Nn


Ed Tn

Nn

(3)















00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)


(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(c)








0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References

































N L times n (1)






12

3

4

56

7

nc

12

3

4

56

7

nc

12

3

4

56

7

n

(a) (b) (c)


Cell

Central area


Radiating thread

Frame thread

Anchorthread

Dragline thread



θ 360deg

n (2)









n 2n

2

n + 1

1

2n + 1

3n + 1

4n + 1

2n + 2

n + 2

3n + 2

4n + 2

33n + 34n + 3 n + 32n + 3

4

n + 4

3n + 4

2n + 4

4n + 4

5

n + 5

2n + 5

3n + 5

4n + 5

3n 4n 5n Nn


Nn ndash 3




Layer 5

BS

θ




Nn


Ed Tn

Nn

(3)















00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)


(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(c)








0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References




























θ 360deg

n (2)









n 2n

2

n + 1

1

2n + 1

3n + 1

4n + 1

2n + 2

n + 2

3n + 2

4n + 2

33n + 34n + 3 n + 32n + 3

4

n + 4

3n + 4

2n + 4

4n + 4

5

n + 5

2n + 5

3n + 5

4n + 5

3n 4n 5n Nn


Nn ndash 3




Layer 5

BS

θ




Nn


Ed Tn

Nn

(3)















00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)


(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(c)








0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References





























Nn


Ed Tn

Nn

(3)















00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)


(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(c)








0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References

































00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

0 200 400 600 800 1000Time (s)


(a)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(b)

0 200 400 600 800 1000

00206

00208

00210

00212

00214

End-

to-e

nd d

elay

(s)

Time (s)


(c)








0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References

































0 200 400 600 800 10000042

0044

0046

0048

0050

0052

0054

End-

to-e

nd d

elay

(s)

Time (s)


F8ndash2Fcndash2


c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18













c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References



































c

5

12

3 6

4

10 11

129

8 7

1314

15

16 17

18

Node damage N14

Node damage N8

Node damage N2


0 200 400 600 800 10000041

0042

0043

0044

0045

0046

0047

0048

0049

0050

End-

to-e

nd d

elay

(s)

Time (s)


N8N2





c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References






























c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

c

5

12

3 6

4

(A) (B) (C) (D) (E)

(F) (G) (H) (I) (J)




Failuretype







3rd layer1 A 0049 0044 0042 0006 0001 ndash0001

2 B 0062 0047 0040 0019 0004 ndash0003C 0057 0046 0040 0014 0003 ndash0003



5 J 0153 0069 0034 0110 0026 ndash0009



Failuretype







3rd layer1 A 0053 0048 0044 0010 0005 0001

2 B 0075 0058 0047 0032 0015 0004C 0064 0053 0045 0021 0010 0002

3D 0107 0072 0050 0064 0029 0007E 0085 0062 0048 0042 0019 0005F 0074 0057 0047 0031 0014 0004

4G 0149 0092 0055 0106 0049 0012H 0117 0077 0052 0074 0034 0009I 0106 0072 0050 0063 0029 0007

5 J 0203 0116 0062 0160 0073 0019




4 Conclusions


Data Availability




Acknowledgments


References






























4 Conclusions


Data Availability




Acknowledgments


References












































Documents

QuantitativeInvulnerabilityAnalysisofArtificialSpider-Web ...downloads.hindawi.com/journals/wcmc/2020/4617239.pdf · Spider webs can be divided into several types, such as the sheet