Research Article Weighed Nonlinear Hybrid Neural …downloads.hindawi.com/archive/2014/864020.pdfResearch Article Weighed Nonlinear Hybrid Neural Networks in Underground Rescue Mission

Research ArticleWeighed Nonlinear Hybrid Neural Networks inUnderground Rescue Mission

Hongxing Yao12 Mary Opokua Ansong13 and Jun Steed Huang4

1 Institute of System Engineering Faculty of Science Jiangsu University 301 Xuefu Zhenjiang 212013 China2 College of Finance and Economics Jiangsu University 301 Xuefu Zhenjiang 212013 China3Department of Computer Science School of Applied Science Kumasi Polytechnic PO Box 854 Kumasi Ghana4Computer Science and Technology School of Computer Science amp Telecommunication Jiangsu University 301 XuefuZhenjiang 212013 China

Correspondence should be addressed to Hongxing Yao hxyaoujseducn

Received 25 September 2013 Accepted 11 November 2013 Published 22 January 2014

Academic Editors O Castillo K W Chau D Chen and P Kokol

Copyright copy 2014 Hongxing Yao et al This 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

In our previous work a novel model called compact radial basis function (CRBF) in a routing topology control has been modelledThe computational burden of Zhang and Gaussian transfer functions was modified by removing the power parameters on themodelsThe results showedoutstanding performance over theZhang andGaussianmodelsThis study researched on several hybridsforms of themodel where cosine (cos) and sine (sin) nonlinear weights were imposed on the two transfer functions such that119884(out) =

logsig(119877) + [exp(minusabs(119877))] lowast (plusmn cos or plusmn sin(119877)) The purpose was to identify the best hybrid that optimized all of its parameterswith a minimum error The results of the nonlinear weighted hybrids were compared with a hybrid of Gaussian model Simulationrevealed that the negative nonlinear weights hybrids optimized all the parameters and it is substantially superior to the previousapproaches presented in the literature with minimized errors of 00098 00121 00135 and 00129 for the negative cosine (HSCR-BFminuscos) positive cosine (HSCR-BF

+cos) negative sine (HSCR-BFminussin) and positive sine (HSCR-BF

+sin) hybrids respectively whilesigmoid andGaussian radial basis functions (HSGR-BF

+cos) were 00117The proposed hybrid could serve as an alternative approachto underground rescue operation

1 Introduction

11 Background In our earlier work we demonstrated how arouting path was generated and how the compact radial basisfunction could be improved by reducing the computationalburden of Gaussian by removing the power parameter fromthemodelWe had discussed the robustness and fault tolerantnature of the compact radial basis function for an emergencyunderground rescue operation and had discussed the perfor-mance of the sigmoid basis function and the compact radialbasis function of which the latter optimised its parametersbetter than that of the former [1] In this paper we look at thehybrid formof this novel algorithm by introducing nonlinearweights of positive and negative cosine and sine

12 Sigmoid Basis Function (SBF) and Radial Basis Func-tion (RBF) Sigmoid basis function (SBF) and radial basis

function (RBF) are the most commonly used algorithmsin neural training The output of the network is a linearcombination of radial basis function of the inputs and neuralparameters Radial basis function networks have many usesincluding function approximation time series prediction [23] classification and system control The structure supportsthe academic school of connectionist and the idea wasfirst formulated in 1988 by Broomhead and Lowe [4] TheSBF a mathematical function having an ldquoSrdquo shape (sigmoidcurve) and is related to brain reasoning and the structurefavors the computational believers The sigmoid functionrefers to the special case of the logistic function Anotherexample is the Gompertz curve which is used in modelingsystems that saturate at large values of input for examplethe ogee curve used in spillway of dams A wide variety ofsigmoid functions have been used as activation functions ofneurons including the logistic and hyperbolic tangent weight

Hindawi Publishing CorporationISRN Artificial IntelligenceVolume 2014 Article ID 864020 13 pageshttpdxdoiorg1011552014864020

2 ISRN Artificial Intelligence

functions Sigmoid curves are also common in statistics suchas integrals and logistic distribution normal distribution andStudentrsquos probability density functions In our opinion SBFoffers nonlinear effects for large input value and RBF providenonlinear effect at small input value A nonlinear hybrid ofcosine and sine will result in more nonlinear blending acrossthe entire region

13 Wireless Sensor Networks (WSN) Wireless sensor net-works (WSN) gather and process data from the environmentand make possible applications in the areas of environmentmonitoring logistics support health care and emergencyresponse systems as well as military operations Transmittingdata wirelessly impacts significant benefits to those inves-tigating buildings allowing them to deploy sensors whichmonitor from a remote location Multihop transmissionin wireless sensor networks conforms to the undergroundtunnel structure and provides more scalability for communi-cation system construction in rescue situations A significantdiscovery in the field of complex networks has shown that alarge number of complex networks including the internet arescale-free and their connectivity distribution is described bythe power-law of the form 120588(119896) sim 119896

minus120601 to allow few nodesof very large degree to exist making it difficult for randomattack A scale-free wireless network topology was thereforeused

This paper proposes a nonlinearHybridNeural Networksusing radial and sigmoid transfer functions in undergroundcommunication based on particle swarm optimisation Analternative to this model is without hybrid either RBF orSBF The SBF is known to be fast while RBF is accurate [5]and therefore blending the two will provide both speed andaccuracy In addition the two models have been examinedin our previous work [1] To this end we model the incidentlocation as a pure random event and calculate the probabilitythat communication chain through particular rock layersto the ground is not broken and allows neural network tomemorize the complicated relationship such that when realaccident happens the neural network resident in the robot isused to predict the probability based on the rock layer it seesinstantly If the result is positive the robot waits to receive therescue signal otherwise it moves deeper to the next layer andrepeats the procedure

Section 2 explains the preliminaries to the study andgenerates the routing path that has the highest survival proba-bility for the neural training Section 3 discusses related workto the study Section 4 discusses the network optimizationmodel based on the nonlinear weight on the compact radialbasis function Section 5 highlights the method used andSection 6 shows the simulation results of the various hybridsand compare with the Gaussian model whiles Section 7 givesa summary of the findings and future work

2 Preliminaries

21 Sensor Deployment Some assumptions such as 20 ofsoftware failure 2 safe exits assumed to be available afteraccidents and additional errors committed after the accidents

and the failure rate of radio frequency identification (RFID)weremade in various sectionsThese assumptions are alreadyincluded in the model and they are there to ensure that thesystem remains reliable

Topological deployment of sensor nodes affects the per-formance of the routing protocol [6 7] The ratio of com-munication range to sensing range as well as the distancebetween sensor nodes can affect the network topology

Let Ω be the sensor sequence for the deployment of totalsensors 119879 = 119909119910119911 = 119871 119877 119862 such that

Ω =

For 119905 = 119905 + 1

node (119905 2) = (

10038171003817100381710038171003817minus (119877 + 1) lowast (1 + (minus1)

tog119869)10038171003817100381710038171003817

2+ 119895)

node (119905 3) = (


tog119870)10038171003817100381710038171003817

2+ 119896)

for 119894 = 1 119871 119895 = 1 119877 119896 = 1 119862 and node (119905 1) = 119894

(1)

tog119869 = ceil(119905119862119877) and tog119870 = ceil(119905119862) check source anddestination node respectively

Ω(119894 119895 119896) = 1 1 1 1 2 1 119894th 119895th 119896th for [level 1row 1 column 1] [level 1 row 2 column 1] [ ] and [119894th level119895th row and 119896th column] respectively Therefore 119879 = 119879 times 119879

matrix in an underground mine with dimensions of 119871 = 3119877 = 2 and 119862 = 1 for depth (level) row (length) and width(column) respectively with ldquopmrdquo a sensor apart implies thata minimum of 6 sensors will have to be deployed

22 Communication The Through-The-Earth (TTE) Com-munication system transmits voice and data through solidearth rock and concrete and is suitable for challengingunderground environments such as mines tunnels and sub-waysThere were stationary sensor nodes monitoring carbonmonoxide temperature and so forth as well as mobilesensors (humans and vehicles) distributed uniformly Bothstationary and mobile sensor nodes were connected to eitherthe Access Point (AP) andor Access Point Heads (APHeads)based on transmission range requirements [6]TheAPHeadsserve as cluster leaders and are located in areas where therock is relatively soft or signal penetration is better to ensurethat nodes are able to transmit the information they receivefrom APs and sensor nodes The APs are connected to otherAPs orThrough-The-Earth (TTE) which is dropped througha drilled hole down 300 meters apart based on the rock typeThe depth and rock type determine the required numberof TTEs needed Next the data-mule is discharged to carryitems such as food water and equipments to the minersunderground and return with underground information torescue team

23 SignalTransmission Reach Major challenges of sen-sor networks include battery constraints energy efficiencynetwork lifetime harsh underground characteristics bettertransmission range and topology design among othersSeveral routing approaches for safety evacuation have been

ISRN Artificial Intelligence 3

Table 1 Common rocks found in typical mines in relation to hardness or softness

Nonlinear mapping Mica Coal Granite Feldspar Quartz MineralSoftness 070 080 083 086 0875 090Hardness 2 3 5 6 7 9Distance 750m 470m 390m 315m 278 78m

proposed [8ndash14]Thesewere developed depending on specificemergency situations and management requirements Trans-mitting data wirelessly impacts significant benefits to thoseinvestigating buildings allowing them to deploy sensors andmonitor froma remote location [15 16] To effectively gain theneeded results researchers have come out with a number oftechniques to address the problem of topology control (TC)These include localization of nodes and time error and pathloss transmission range and total load eachnode experiencesas well as energy conservation which is very crucial inoptimizing efficiency and minimizing cost in wireless sensornetworks [17ndash19] Minimizing transmission range of wirelesssensor networks is vital to the efficient routing of the networkbecause the amount of communication energy that eachsensor consumes is highly related to its transmission range[6]The nodes signal reach119873120575was defined as the integrationof the change of the minimum and maximum signal reachtaking into consideration the number of cases (120591) of the rockstructure120573 120573 is the rock hardness119873120575 is the signal reach for anode and 119873120575min 119873120575max are minimum and maximum signalreach respectively The node signal reach is calculated as

119873120575 = 119873120575min +1003817100381710038171003817119873120575min minus 119873120575max

1003817100381710038171003817lowastrandom (

1015840

1205731015840

rock 1 1)

119873120575min = min (119871min (RowCol))

119873120575max = max (119871max (RowCol)) (2)

andwhere120573 is a geometric figure in the range of 07 to 09 Fora connection to be made the absolute difference between 119894 119895should be less than the node signal reach-119873120575The connectionmatrix was given as

120593119896 (119894 119895) = 1 if 1003817100381710038171003817119894 minus 119895

1003817100381710038171003817 le 119873120575

0 otherwise(3)

The relationship between rock hardness and the signal reachis a complicated nonlinear function which is related to theskin depth of the rock with alternating currents concentratedin the outer region of a conductor (skin depth) by opposinginternal magnetic fields as follows

Skin depth = radic2

(120588 lowast 120596 lowast 120590) (4)

120588 is material conductivity 120596 is frequency and 120590 is magneticpermeability

The signal (119861-field) is attenuated by cube of distance (119889)

119861 = (119896)1198893

Signal reach (distance) is equal to 3lowast skin depth

Table 1 identifies 6 common rocks found inmines in rela-tion to hardness or softness of each rock

A routing path was modeled using a number of 119879times119879 sizematrices namely the connection matrix (120593119896) routing matrix(120593119903) explosion matrix (120593119909) failed matrix (120593119891) hope matrix(120593ℎ) optimized matrix (120593119900) and the exit matrix (120593119890) Thehardware survival rate vector (120593ℎ) the survival rate vector(120593V) of each miner and the final average survival rate vector(119877) were also generated A sensor node is named by its 3Dinteger (119909 119910 119911) coordinates where 1 le 119909 le 119877 1 le 119910 le 1198621 le 119911 le 119871 for 119879 = 119877 lowast 119862 lowast 119871 being total number ofnodes If the node (119886 119887 119888) is connected with node (119889 119890 119891)

then the element on ((119886 minus 1) lowast 119862 lowast 119871 + (119887 minus 1) lowast 119871 + 119888)throw and ((119889 minus 1) lowast 119862 lowast 119871 + (119890 minus 1) lowast 119871 + 119891)th columnis 1 otherwise 0 and routing are limited to total number ofmultiple points connections that can be made In arriving atthe final optimized vector for transmission each matrix wasgenerated 120591 times

The 120593119903 sub 120593119896 119872120588

le 120572 119872120588

is even 119872120588

representing themaximum point-to-multipoint connection and 119872

120588

is evenallowing bidirectional communication with 119894119895 checkingsource and destination nodes respectively

120593119903 =

1 if 1003817100381710038171003817119894 minus 1198951003817100381710038171003817 ge (

119872120588

2)

0 otherwise

for 119894 119895 = 1 119879

(5)

24 Hardware Software and Network Fault Tolerant Con-siderations Network security is a critical issue in wirelesssensor networks as it significantly affects the efficiency ofthe communication andmany keymanagement schemes hadbeen proposed to mitigate this constraint [18 20] In an eventof accidents (120595) occurring the routing pathwould be affectedby (1minus120595) where120595 is any randomvaluewithin120573 whichwouldcause explosion on 119877120593 matrix and result in 120593119909 such that theresulting matrix would be the failed matrix (120593119891)

120593119909 = (1 minus 120595) 120593119903

120593119891 (119894 119895) = 1 if 120593119909 (119894 119895) lt 120582119871

0 if 120593119909 (119894 119895) ge 120582119871

(6)

120593119891(119894 119895) = 0 if 120593119909(119894 119895) ge 120582119867 else 120593119891 = 120593119909(119894 119895)120582119867 for (120582119871or 120582119867) representing the lower and higher accident impactthresholds respectively

A new set of routing paths (120593ℎ) and exit matrices (120593119890) fortransmission was calculated as

120593ℎ = 120593119891 lowast 120593119903

120593119890 = 119873119890 minus 120595

(7)


The mathematical objective here is to find an optimizedrouting matrix (120593119900) that has the maximum survivability Thesurvivability is defined as the entropy of a number of parallelconnections between every node to all the sink(s) The exitmatrix (120593119890) described the success rate from each node to thesink(s) 120593119890 assumes that the number of exits (119873119890) is availablewith an errormargin (120595) Inmost practical applicationsmorethan one sink is used and sink node is either through the fiberorThrough-The-Earth (TTE) link It is important to note thatin real rescue situations the software (relational databasemanagement system (RDBMS)) and hardware includingradio frequency identification (RFID) may fail as a result ofthe effect from the explosion and attack The matrix (120593119904)

was used to describe software survival rate including bugs orattacks

120593119904 = 1 minus ((1

119879 + random) (ldquoGeometricrdquo fail 119879 119879)) (8)

To obtain the final survival vector (120593119877) it was assumed thateach miner will have an RFID a vector 120593119868 was used todescribe its failure rate including risks of running out ofbattery a vector 120593119867 for the hardware failure rate for119879 = totalnumber of nodes

120593119868 = 1 minus ((1

119879 + 119903) lowast (ldquoGeometricrdquo fail 1 119879)) (9)

119903 is a random number generated from the vector 119879 and 119903

0 rarr infin 119879 + random 119879 rarr infin (1(119879 + 119903)) 1119879 rarr 01 minus (1(119879 + 119903)) 1 minus 1119879 rarr 1 is the minimum thereforefor 119879 = 119873 nodes we have 1 minus 1119873 = (119873 minus 1)119873 rarr 1 for(119873 minus 1)119873 rarr node is dead and 1 rarr node is alive

120593119867 = min (1 120593119868 [119883Ψ]) for [119883Ψ]) =120593119890

119872119901

(10)

The survival rate of each miner was (120593V) All these assump-tions happen in real life and must be considered The finalsurvival rate vector (120593119877) was calculated

120593V = 120593119904 lowast 120593119890 (11)

120593119877 = 120593V lowast 120593119904 (12)

119877 = 120593119877 (13)

3 Related Work

31 Artificial Neural Networks (ANN) Having found theoptimum set of routing table that has the highest survivalprobability of communicating with and rescuing miners it isimportant to train the neurons such that the initial error willbe minimized and more importantly have a reliable system[21]The topology of a neural network can be recurrent (withfeedback contained in the network from the output back tothe input) the feedforward (where data flow from the input tothe output units)The data processing can extend over severallayers of units but no feedback connections are presentManyresearchers have come out with neural network predictivemodels in both sigmoid and radial basis functions [22 23]

with applications such as nonlinear transformation [23]extreme learning machine predicting accuracy in gene clas-sification [24] crisp distributed support vectors regression(CDSVR) model was monthly streamflow prediction wasproposed by Valdez et al [25] and other applications includefuzzy inference systems (FIS) which have been successfullyapplied in fields such as automatic control data classificationdecision analysis and expert systems [26] among othersArtificial neural networks (ANN) are learning algorithmusedto minimize the error between the neural network outputand desired output This is important where relationshipsexist between weights within the hidden and output layersand among weights of more hidden layers In addition otherparameters including mean iteration standard variationstandard deviation and convergent time (in sections) wereevaluated The architecture of the learning algorithm andthe activation functions were included in neural networksNeurons are trained to process store recognize and retrievepatterns or database entries to solve combinatorial optimiza-tion problems Assuming that the input layer has 4 neuronsoutput layer 3 neurons and the hidden layer 6 neurons wecan evolve other parameters in the feedforward network toevolve the weight So the particles would be in a group ofweights and there would be 4 lowast 6 + 6 lowast 3 = 42 weightsThis implies that the particle consists of 42 real numbersThe range of weight can be set to [minus100 100] or a fittingrange After encoding the particles the fitness function wasthen determined The goodness of the fit was diagnosedusing mean squared error (MSE) as against mean cubicerror (MCE) and the mean absolute error (MAE) The meancubic error will allow for fast convergence and that willgross over accuracy making the process unstable while themean absolute error is stable but converges slowly A midwaybetween the two is the MSE and is given as

MSE =1

119899119904

119899

sum

119895=1

119904

sum

119894=1

(119884119895119894

minus 119910119895119894

)2

(14)

where 119899 is number of samples 119904 is the number of neurons atoutput layer 119884

119894119895

is the ideal value of 119894th sample at 119895th outputand 119884

119894119895

is the actual value of 119894th sample at 119895th output

32 The Gaussian and Zhang Models The standard or directapproach to interpolation at locations 119909

1

119909119873

sub 119877119889

without the first term using Gaussian kernel is given as

120601 (119903) = 119890minus(120576119903)

2

(15)

Zhang has [27] tried tomodify theGaussianmodel as followsa function 120595 [0infin) rarr R such that 119896(119909 1199091015840) = 120593(119909 minus 119909

1015840

)where 119909 1199091015840 isin 120594 and 119909 sdot 119909

1015840 denotes the Euclidean norm with119896(119909 119909

1015840

) = exp(minus119909 minus 1199091015840

2

1205752

) as an example of the RBFkernels The global support for RBF radials or kernels hasresulted in dense Grammatrices that can affect large datasetsand therefore construct the following two equations119896119862V(119909 119909

1015840

) = 120601119862V(119909 minus 119909

1015840

)119896(119909 1199091015840

) and 120601119862V(119909 minus 119909

1015840

) =

[(1 minus 119909 minus 1199091015840

119862)(sdot)+

]V where119862 gt 0 V ge (119889+1)2 and (sdot)

+

isthe positive part The function 120601C(sdot) is a sparsifying operator


which thresholds all the entries satisfying (119909 minus 1199091015840

) ge 119862

to zeros in the Gram matrix The new kernel resulting fromthis construction preserves positive definiteness This meansthat given any pair of inputs 119909 and 119909

1015840 where 119909 = 1199091015840 the

shrinkage (the smaller 119862) is imposed on the function value119896(119909 119909

1015840

) the result is that the Gram matrices 119870 and 119870119862V can

be either very similar or quite different depending on thechoice of 119862 However Zhang also ended up with an extrapower parameter

4 The Proposed Hybrid

The previous work looked at the Gaussian model and par-alyzed the computational power parameter The result wascompact radial basis function (CRBF) This was used to runboth SBF and RBF and the results compared The scalabilityand processing efficiency were also analyzed

The novelty of this algorithm the weighed nonlinearhybrid was to find several hybrids and the best for rescueoperationsThe cosine and sine functionswere used to reducehigh level nonlinear and increase small level nonlinearBoth the previous and the current algorithm used the samepreliminary considerations but the results is slightly differentbecause data are random

The sigmoid basis function was given as

log sig (119877) 119877 = 119882 sdot 119875 + 119861

log sig (119882 sdot 119875 + 119861) =1

1 + 119890minus(119882sdot119875+119861)

(16)

Neuron function 119878 (sigmoid) is log sig 119882 is weight matrix119875 is input vector and 119861 is threshold We therefore proposeda compact radial basis function based on the Gaussian radialbasis function and Helensrsquo [28] definition expressed as

[exp (minus 119877)] 119877 = 119882 sdot 119875 + 119861

(exp (minusabs ((119882 sdot 119875 + 119861)))

120601 (out) = [exp (minus 119877)]

(17)

119882 is weight matrix 119875 is input vector and 119861 is threshold Thefocus was to improve on the radial basis function for themineapplication

An optimized vector 119877 was generated as the optimumset of transmission routing table that has the highest survivalprobability for data transmission (13)

119875119873 =

119873

sum

119894=1

119877119894

119878119894

+

2

sum

119894=1

119878119894

+

2

sum

119894=1

119878119894

119878119894

+ 1

for 1 le 119894 le 119878 1 le 119896 le 119877

(18)

119877 1198781

1198782

are number of neurons at input hidden and outputlayers respectively

119875119873 is the position of the 119899th particle

119882119894

= 119878119894

1198771198822

= 119878119894

119877 119882119898

= 119878119898

119877

119875119894

= [119877 (119894 minus 119895) + 119870] = 119882119894

(119894 119896)

(19)

There are two thresholds (1198781

rArr 1198611

)Hidden 119861

1

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr S1

Output 1198612

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr 1198782

From (16) (17) and (18) the nonlinear weight of [plusmn cos(119877)] or[plusmn sin(119877)] was imposed on the CRBF before being combinedwith the SBF as (HSCR-BF

minus cos HSCR-BF+ cos HSCR-BF

minus sinHSCR-BF

+ sin)The cosine weight was used to keep high levelnonlinear for small input value and reduce the nonlinear forlarge input values while sine weight was used to keep highlevel nonlinear for large input value and reduce the nonlinearfor small input values

HSCR-BFminus cos

119884 (out) = log sig (119877) + [exp (minus 119877)] sdotlowast

[minus cos (119877)]

HSCR-BF+ cos


[+ cos (119877)]

HSCR-BFminus sin


[minus sin (119877)]

HSCR-BF+ sin


[+ sin (119877)]

(20)

Thenonlinear weight of [+ cos(119877)]was imposed on theGRBFbefore being combined with the SBF

HSGR-YBF+ cos

119884 (out) = log sig (119877) + [exp (minus1198772

)] sdotlowast

[+ cos (119877)]

(21)

5 Particle Swarm Optimization

Particle swarm optimization (PSO) an evolutionary algo-rithm is a population based stochastic optimization tech-nique The idea was conceived by an American researcherand social psychologist James Kennedy in the 1950s Thetheory is inspired by social behavior of bird flocking or fishschooling The method falls within the category of swarmintelligence methods for solving global optimization prob-lems Literature has shown that the PSO is an effectivealternative to established evolutionary algorithms (GA) It isalso established that PSO is easily applicable to real worldcomplex problems with discrete continuous and nonlineardesign parameters and retains the conceptual simplicity ofGA [29 30] Each particle within the swarm is given an initialrandom position and an initial speed of propagation Theposition of the particle represents a solution to the problemas described in a matrix 120591 where 119872 and 119873 represent thenumber of particles in the simulation and the number ofdimensions of the problem respectively [31 32] A randomposition representing a possible solution to the problem withan initial associated velocity representing a function of thedistance from the particlersquos current position to the previous


position of good fitness value was given A velocity matrix119881el with the same dimensions as matrix 120591

119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)

The best feasible alternative is the genetic algorithmHoweverthis is generally slow as compared to the PSO and thereforecomputationally expensive hence the PSO

While moving in the search space particles commit tomemorize the position of the best solution they have foundAt each iteration of the algorithm each particle moves witha speed that is a weighed sum of three components the oldspeed a speed component that drives the particles towardsthe location in the search space where it previously foundthe best solution so far and a speed component that drivesthe particle towards the location in the search space wherethe neighbor particles found the best solution so far [7] Thepersonal best position can be represented by an119873times119873matrix120588best and the global best position is an 119873-dimensional vector119866best

120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)

All particles move towards the personal and the globalbest with 120591 120588best 119881el and 119892best containing all the requiredinformation by the particle swarm algorithmThese matricesare updated on each successive iterations

119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882

are constants set to 13 and 2 respectively and1205781199031

1205781199032

are random numbers

51 AdaptiveMutation according toThreshold Particle swarmoptimization has been effective in training neural networkssuch as a Parallel Particle Swarm optimization (PPSO)methodwith dynamic parameter adaptation used to optimizecomplex mathematical functions and improved evolutionarymethod in fuzzy logic [30 31 33] To prevent particlesfrom not converging or converging at local minimum an

Input nodes64748

64748

64748

Hidden nodesOutput nodes

S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09

Figure 1 The structure AMPSO for CRBF GRBF and SBF transferfunctions

1 2 3 4 5 6 7 8 9 100

02040608

11214

The impact of the accident

Link

avai

labi

lity

The curve of transmission link after accident

The higher the impact the lower the link availability

Region 3Links are completely dead

Region 1Links are not

Region 2Indicate probability of link being able to transmit data

affected

Figure 2 Impact of explosionaccident on transmission link

adaptivemutation according to thresholdwas introduced Analternative to this is the use of the nonadaptive mutation andthis could converge to the local minimum or fail to convergeat all The advantage of the nonadaptation is simple and fastbut may not provide the needed results

Particles positions were updated with new value onlywhen the new value is greater than the previous value 20 ofparticles of those obtaining lower values weremade tomutatefor faster convergence and the structure of adaptive mutationPSO (AMPSO) with threshold can be found in [1] The inputlayer takes the final survival vector (13) with a number ofhidden layers and an output layer The feedforward neuralnetwork was used The structure of Adaptive Mutation PSO(AMPSO) with threshold Neural Network was used Figure 1[32]

6 Results and Discussion

61 Generating the Routing Path Elements 0 1 and 2 in 120593119909

imply that the link(s) were not affected and elements 3 45 and 6 represent a probability for the links being able totransmit data while figures from 7 means the link is totallydead Region 1 that indicates that links are not affected region


Table 2 Optimum set of routing table redundancy with the highest survival probability (6 cases)

Vectors for each case Rock hardness cases1198771 05409 04281 08834 0585 08134 05163 071198772 04526 05841 04547 08997 08436 02696 081198773 02931 05899 05903 08309 06971 02898 0831198774 04851 06085 06913 04002 05026 0 0861198775 04917 05857 07805 06037 05182 06472 08751198776 02902 07253 0458 05762 01397 0 09

2 gives the probability of link available and the last regionindicates the link is completely down (Figure 2)

Thematrices120593119894 120593119896 120593119903 120593119909 120593ℎ for 120591 = 119899 with dimensionsof 119871 = 3 119877 = 2 and119862 = 1 for depth (level) row (length) andwidth (column) respectively were generated as follows

119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = transmission path

120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)

1 or fractional figures are transmission path

(26)

Element ldquo0rdquo on 120593119891 depicts a connection lost while ldquo1rdquo meansthat the connection will never go down and represent theconnection to the fixed sink node(s) along the edge or theemergency connection to the mobile data mule(s)

120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)

The survival rate of RFID hardware and each minervectors was displayed as

120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)

Optimization was done numerically usingMatlab simulationtool to find the optimum set of routing tables throughparticle swarm search for rescue operation as discussed inthe preliminaries From (13) the final survival vector fordimensions of 119871 = 3 119877 = 2 and 119862 = 1 will be an average ofthe 6 vectors as in Table 2 Total cases 119877119899 = 120591 = 119879times119879 (which


Table 3 Scalability of model to survival probability range robot location and rock type

Location Mica Coal Granite Feldspar Quartz MineralCompact radial basis function with negative nonlinear weight (HSCR-BF

minus cos)(10 6 5) 08769ndash10000 09070ndash09927 08402ndash09943 08023ndash09778 07386ndash09376 07345ndash08740(10 5 4) 09024ndash09696 09032ndash09505 08836ndash09430 08633ndash09527 07944ndash09465 07263ndash08720(6 5 4) 08906ndash09877 08827ndash09845 08384ndash09675 08627ndash09820 07911ndash09142 06392ndash07840(3 1 10) 07302ndash08481 06588ndash07816 06341ndash07473 06503ndash07249 05930ndash07156 04445ndash05621

Gaussian radial basis function with positive nonlinear weight (HSGR-BF+ cos)

(10 6 5) 08732ndash09963 08526ndash09987 08492ndash09950 07867ndash09568 07404ndash09025 06606ndash08315(10 5 4) 08843ndash09593 08843ndash09853 08444ndash09753 07746ndash09828 07304ndash09595 06678ndash08817(6 5 4) 08785ndash09983 08902ndash09996 08200ndash09997 07927ndash09446 07065ndash08565 06572ndash08063(3 1 10) 07608ndash08552 06600ndash08325 06090ndash07371 05482ndash06249 05026ndash06056 04856ndash05453

10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904

Number of iterations

Fitn

ess v

alue

PSO optimized error for hybrid SBF-CRBF with negative nonlinear weight

15 2 25 3 35 4 45 5 55 604

06

08

1 Output

Rock hardness case (07ndash09)

Surv

ival

pro

babi

lity

(HSCRminuscos )

(a) HSCR-BFminus cos

50 100 150 200 2500

01

02

03

X 249Y 001151

PSO optimized error with nonlinear weight [minussine(R)]


Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity

(b) HSCR-BFminus sin

Figure 3 Hybrid of SBF and CRBF (HSCR-BF) with (a) HSCR-BFminus cos and (b) HSCR-BF

minus sin nonlinear weight

represent the total nodes deployed) for this scenario Rocksoftness or hardness takes the values of 120573 and each matrix isgenerated 120591 timecases and the final routing vector will be anaverage of the 119899 vectors 120593119877 = Average (1198771 1198776) [Table 2]which becomes the input for the PSO training

The final survival rate is 119877 = (05409 04281 08834

0585 08130 05163) from (13)

62 The Final Survival Vector The 119877 = (05409 04281

08834 0585 08130 05163) from (13) is the maximumsurvival probability for a total of 6 nodes deployed Itdescribes the success rate from each node to the sink(s) Inmost practical applications more than one sink is used andsink node is either through the fiber or TTE connection Thesize of the vector depends on the dimensions of the fieldThe elements 119877 = (05409 04281 08834 0585 08130

05163) represent the probability of 54 43 88 5981 and 52 success of each node transmitting data to andfrom its source or destination It assists decision makers as towhether to send data through one ormore nodes or send each

message twice The total nodes used for the simulation were300 with undergroundmine dimensions of 119871 = 10119877 = 6 and119862 = 5 for depth (level) row (length) and width (column)respectively with ldquopmrdquo a sensor apart pm = 100119872

120588

= 4 and119873119890 = 2 The PSO training used swarm size of 20 maximumposition was set to 100 max velocity = 1 and maximumnumber of iteration = 250 The thresholds 120582119871 and 120582119867 were3 and 6 respectively 120591 = 6 cases (each case representa rock hardness case and also represent the total neuronsused) thus each matrix and vectors were run 6 times beforeneural training The survival probability (bottom) indicatesthat the model survived between 90 and 100 where rockcases were relatively soft (ge07) The survival probabilitydeclines as the rock becomes harder and approaches 08 Atthe hardest rock of 09 the survival probability fell between72 and 84 for the entire hybrids In view of this the APheads had to be deployed at a location where the rock isrelatively soft for maximum signal strength Each computersimulation incorporated all the 6 different cases of rockhardnesssoftness to produce the matrices Detailed locationanalysis or the scalability of the model in relation to survival


Table 4 Hybrid of SBF and CRBF with negative nonlinear weight on CRBF (HSCR-BFminus cos)

Runs Mean iteration Std variation Std deviation Convergent time Final errorTotal 231020 343498 0382 91650 00985AVG 23102 34350 0038 9165 00098MinMax 29540 45314 0024 80000 00043

Table 5 Hybrid of SBF and CRBF with nonlinear weight on CRBF (HSCR-BFminus sin)


probability range robot location and different rock types isrecorded in Table 3 Figures 4ndash6 represent different scenariosof SBF and CRBF hybrids with the [plusmn cos(119877)] and [plusmn sin(119877)]

nonlinear weights while Figure 7 represents the SBF andGaussian hybrids for [+ cos(119877)] nonlinear weight The tophalf of each figure indicates the optimized error or the finalerror after the neural training and the bottom half revealsmodel survival probability

Figure 3 discusses the SBF and CRBF hybrids (HSCR-BF) with nonlinear weight Training in negative nonlinearweights (HSCR-BF

minus cos HSCR-BFminus sin) responded well The

HSCR-BFminus cos had a steady and compact routing path which

was consistent through all rock layers with initial survivalprobability between 877 and 100 in soft layers decliningto 735ndash874 at harder rock layers The HSCR-BF

minus sinperformed quite well but was more dispersed (879 to 985at the soft rock and 665 to 818 at the hard rock)

In addition the various parameters mean iterationstandard variance standard deviation and the convergenttime of HSCR-BF

minus cos were optimised This is demonstratedby finding the relationship between the maximum and theminimum values of the parameters and comparing with theaverage figures and the closer the difference is to the averagethe more consistent the data are in the dataset (Table 4) thusHSCR-BF

minus cos provided the best results among the proposedhybrids The HSCR-BF

minus sin on the RBF yielded strength inmean iteration and standard variance with error of 0013(Table 5)

In Figure 4 training with nonlinear weight of positivecosine and sine of HSCR-BF (HSCR-BF

+ cos and HSCR-BF+ sin) had some similarities The two models streamed

well at the initial stages from 896 to 992 and 908to 990 at soft layers of the rock respectively Howeverat the last stages the probability of transmitting effectivelybecame marginal from 795 to 852 and 821 to 854respectively Much as this hybrid could perform well in areaswhere routing conditions aremuch better in less dense rescuesituations this could hamper rescue mission in both casesdue to battery drain or collision from traffic conjunctionThedata formean iteration and convergent time forHSCR-BF

+ cos(Table 6) and mean Iteration standard variance the final

error HSCR-BF+ sin (Table 7) were consistent with the nega-

tive sine having better results than the positive cosineThe survival probability of the positive nonlinear weight

Gaussian hybrids (HSGR-BF+ cos) in Figure 5 is more com-

pact both at the initial (ie 873ndash996) and later (661ndash832) stages declining to harder rock layers with an errorof 001173 (Table 8)

At the initial stage particles are sensitive to inputs asthey moved quickly in the search space towards the targetand while particles peaked closer to the target it became lesssensitive to the input and began to align (Figure 6) At thelater stage more RBF are used to keep the error at minimumfor accuracy It was also noticed that instead of acceler-ating higher and becoming more sensitive to the inputswhile particles were far from the target the hybrids withlowast

[minus sin(119877)] and lowast[ + sin(119877)] were less sensitive to the inputsas lowast[minus sin(119877)] descended from [119909 = minus1 119910 = 05785] to[119909 = 1 119910 = 04215] while lowast[+ sin(119877)] descended from [119909 =

minus3 119910 = 00404] to [119909 = minus1 119910 = minus004062] before becomingconscious of the inputs In addition the hybrids with thelowast

[+ cos(119877)] lagged slightly between [119909 = minus4 119910 = 0006014]

and [119909 = minus2 119910 = 006288] before becoming sensitive toinputs However they all lined up for accuracy in terms of theminimised error

The nonlinearity of the hybrids is presented (Figure 7)the negative cosinesine weight is used to reduce nonlinearfor small input values and this lies between minus1 lt 119909 lt +1 andthe positive cosinesine weight is used to keep high nonlinearfor large inputs for the remaining region

63 CPU Time Efficiency The relationship between varioushybrids with respect to the central processing time (CPU)was profiled for different runs (Table 9) and expressed in asixth-order polynomial given as 119884

119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831

is time (seconds) and 120573

is the coefficient of the polynomial (Figure 8) The proposedhybrid has better usage of CPU time with 119877

2

= 09160followed byHSCR-BF

minus sin andHSCR-BF+ cos with119877

2 of 07551and 07244 respectively (Table 10) Applying the proposedalgorithm into Gaussian the CPU usage had 119877

2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103

PSO optimized error for hybrid SBF-CRBF with positive nonlinear weight


Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247

PSO optimized error with nonlinear weight [+sine(R)]


Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin

Figure 4 Hybrid of SBF and CRBF (HSCR-BF) with (a) HSCR-BF+ cos and (b) HSCR-BF

+ sin nonlinear weight

Table 6 Hybrid of SBF and CRBF with nonlinear weight on CRBF (HSCR-BF+ cos)

Runs Mean iteration Std variation Std deviation Convergent time Final errorTotal 350780 522257 0311 115650 0121AVG 35078 52226 0031 11565 0012MaxMin 54840 63413 0009 93500 0006

and indeedmarginally outperformedHSCR-BF+ cos Detailed

work on SBF CRBF and GRBF with regard to scalabilitymemory usage and the central processing time has beencarried by the authors [1]

7 Conclusion

In summary we made the following contributions First weused the mix of SBF and CRBF to present several hybridswith different nonlinear weights of cosine and sine func-tions on compact radial basis function Next we showedthe performance of the proposed nonlinear weight hybridsHSCR-BF


minus sin and HSCR-BF+ sin optimised all the parameters with minimised error

of 00098 0012 0013 and 0013 respectively compared to00117 for Gaussian HSCR-BF

+ cos The analyzed CPU usagewith corresponding 119877

2 values of 09160 075 072440 06731and 07345 for HSCR-BF


minus sinHSCR-BF

+ sin and HSCR-BF+ cos respectively demonstrated

that the algorithm is scalable There exist some evacuationmodels that is Goh and Mandic [11] which offered a choicefor travelers and several schemes for the decisionmakersmaynot be applicable in emergency undergroundmine situationsThe proposed nonlinear hybrid algorithm with particle swarmoptimisation has better capability of approximation to underly-ing functions with a fast learning speed and high robustness and

is competitive and more computationally efficient to Gaussianwith the same nonlinear weight The algorithm is new andthat makes it difficult to identify limitations and we intend toinvestigate other hybrids and comparewith genetic algorithm(GA) in the future

Nomenclature

119873120575min 119873120575max Minimum and maximum signalreach

HSCR-BFHSGR-BF Hybrid of SBF with CRBFHybrid ofSBF with GRBF

HSCR-BFminus cos Hybrid of SBF and CRBF minuscos

nonlinear weightHSCR-BF

+ cos Hybrid of SBF and CRBF +cosnonlinear weight

HSCR-BFminus sin Hybrid of SBF and CRBF minussine


+ sin Hybrid of SBF and CRBF +sinenonlinear weight

HSGR-BF+ cos Hybrid of SBF and GRBF +cos

nonlinear weight

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Table 7 Hybrid of SBF and CRBF with nonlinear weight on CRBF (HSCR-BF+ sin)


Table 8 Hybrid of SBF and GRBF with nonlinear weight on GRBF (HSGR-BF+ cos)


0 50 100 1500

005

01

015

02

X 144Y 0009595

GRBF-PSO optimized error with nonlinear weight [+cos(R)]


Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

Figure 5 Hybrid of SBF and GRBF with nonlinear weight on GRBF(HSCR-BF

+ cos)

0 2 4 6 8 10

002040608

1121416

Weighed position of particles

Min

imise

d er

ror

Optimised error in nonlinear weighed SBF-CRBF hybridsParticles

Less sensitive to inputsmuch closer to target

more accurate

Less sensitive to inputsmuch closer more accurate

Neurons are more sensitive to inputsfast and far from target

minus02minus2minus4minus6minus8minus10

[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]

Hybrid+cosHybrid+sin

HybridminuscosHybridminussin

Figure 6 Particles weighed position

Acknowledgments

The authors would like to appreciate the immense contribu-tion of the mining companies where the study was under-taken The authors are grateful to these individuals for

0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror

Nonlinear weight hybrids

Keep large inputvalues more

nonlinear

Keep small inputvalues lessnonlinear

Large input values

Small input values

Using positive cosine and sine

Using negative cosine and sineminus05

minus5 minus4 minus3 minus2 minus1

HSCR-BF+cosHSGR-BF+cos

HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin

HSCR-BF+cos HSCR-BF+sin HSCR-BFminussinand HSGR-BF+cos

Figure 7 Nonlinear weighed curves for optimized error withoutGaussian negative cosine curve

HSGR-BF+cos

HSGR-BF+cos

HSCR-BF+sinHSCR-BFminuscosHSCR-BFminussin

00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids

Figure 8 The trend of hybrids CPU time curves using sixth-OrderPolynomial

their immeasurable contributions to this work Fred Atta-kuma Patrick Addai Isaac Owusu Kwankye Thomas KwawAnnan Willet Agongo Nathaniel Quansah Francis OwusuMensah Clement Owusu-Asamoah Joseph Adu-MensahShadrack Aidoo Martin Anokye F T Oduro Ernest Ekow


Table 9 CPU time usage efficiency for the hybrids

Runs HSCR-BFminus cos HSCR-BF

minus sin HSCR-BF+ cos HSCR-BF

+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813

Table 10 Analysis of CPU time on the various hybrids

1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772

HSCR-BFminus cos 00159119909 minus02575119909 minus0759119909 33494119909 minus19901119909 40345119909 25322 09160

HSCR-BF+ cos 00903119909 minus23158119909 19932119909 minus58027119909 minus31337119909 32808119909 14747 07244

HSCR-BFminus sin minus0033119909 11354119909 minus15811119909 11368119909 minus4337119909 78008119909 minus20794 07551

HSCR-BF+ sin 02571119909 minus14263119909 17173119909 minus10069119909 2993119909 minus42374119909 27879 06731

HSGR-BF+ cos minus00437119909 10911119909 minus82923119909 66218119909 15934119909 minus53939119909 8191 07345

Abano E Omari-Siaw and Qiang Jia This work was sup-ported by the National Natural Science Foundation of China(no 71271103) and by the Six Talents Peak Foundation ofJiangsu Province

References

[1] M O Ansong H X Yao and J S Huang ldquoRadial and sigmoidbasis functions neural networks in wireless sensor routingtopology control in underground mine rescue operation basedon particle swarm optimizationrdquo International Journal of Dis-tributed Sensor Networks-Hindawi vol 2013 Article ID 37693114 pages 2013

[2] R Neruda and P Kudova ldquoLearning methods for radial basisfunction networksrdquo Future Generation Computer Systems vol21 no 7 pp 1131ndash1142 2005

[3] C T Cheng J Y Lin and Y G C Sun ldquoLong-term predictionof discharges in Manwan hydropower using adaptive-network-based fuzzy inference systems modelsrdquo in Advances in NaturalComputation vol 3498 of Lecture Notes in Computer Sciencepp 1152ndash1161 2005

[4] D Broomhead and D Lowe ldquoMultivariate functional interpo-lation and adaptive networksrdquo Complex System vol 2 pp 321ndash355 1988

[5] Y Chen C Chuah and Q Zhao ldquoNetwork configuration foroptimal utilization efficiency of wireless sensor networksrdquo AdHoc Networks vol 6 no 1 pp 92ndash107 2008

[6] P S Rajpal K S Shishodia and G S Sekhon ldquoAn artificialneural network for modeling reliability availability and main-tainability of a repairable systemrdquo Reliability Engineering andSystem Safety vol 91 no 7 pp 809ndash819 2006

[7] W Jang W M Healy and S J Mirosław ldquoWireless sensornetworks as part of a web-based building environmental mon-itoring systemrdquo Automation in Construction vol 17 no 6 pp729ndash736 2008

[8] M S Pan C H Tsai and Y C Tseng ldquoEmergengy guiding andmonitoring application in indoor 3D environment by WirelessSensor Networkrdquo Internation Journal Os Sensor Netwourk vol1 pp 2ndash10 2006

[9] S Zarifzadeh A Nayyeri and N Yazdani ldquoEfficient construc-tion of network topology to conserve energy in wireless ad hocnetworksrdquo Computer Communications vol 31 no 1 pp 160ndash173 2008

[10] R Riaz A Naureen A Akram A H Akbar K Kim and HFarooq Ahmed ldquoA unified security framework with three keymanagement schemes for wireless sensor networksrdquo ComputerCommunications vol 31 no 18 pp 4269ndash4280 2008

[11] S L Goh and D P Mandic ldquoAn augmented CRTRL forcomplex-valued recurrent neural networksrdquo Neural Networksvol 20 no 10 pp 1061ndash1066 2007

[12] L A B Munoz and J J V Ramosy ldquoSimilarity-based heteroge-neous neural networksrdquo Engineering Letters vol 14 no 2 pp103ndash116 2007

[13] R Taormina K Chau and R Sethi ldquoArtificial neural networksimulation of hourly groundwater levels in a coastal aquifer sys-tem of the Venice lagoonrdquo Engineering Applications of ArtificialIntelligence vol 25 no 8 pp 1670ndash1676 2012

[14] K Leblebicioglu and U Halici ldquoInfinite dimensional radialbasis function neural networks for nonlinear transformationson function spacesrdquo Nonlinear Analysis Theory Methods andApplications vol 30 no 3 pp 1649ndash1654 1997

[15] F Fernandez-Navarro C Hervas-Martınez J Sanchez-Monedero and P A Gutierrez ldquoMELM-GRBF a modifiedversion of the extreme learning machine for generalized radialbasis function neural networksrdquo Neurocomputing vol 74 no16 pp 2502ndash2510 2011

[16] C L Wu KW Chau and Y S Li ldquoPredicting monthly stream-flow using data-drivenmodels coupledwith data-preprocessingtechniquesrdquoWater Resources Research vol 45 no 8 Article IDW08432 2009

[17] C EACheng ldquoLong-termprediction of discharges inManwanReservoir using artificial neural network modelsrdquo in Advancesin Neural NetworksmdashISNN 2005 vol 3498 of Lecture Notes inComputer Science pp 1040ndash1045 2005

[18] H H Zhang M Genton and P Liu ldquoCompactly supportedradial basis function kernelsrdquo 2004

[19] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1945 December 1995

[20] J Eberhart R Eberhart and Y Shi ldquoParticle swarm optimiza-tion developments applications and resourcesrdquo IEEE vol 1 pp81ndash86 2001

[21] R Malhotra and A Negi ldquoReliability modeling using ParticleSwarm optimisationrdquo International Journal of System AssuranceEngineering and Management vol 4 no 3 pp 275ndash283 2013

[22] D Gies and Y Rahmat-Samii ldquoParticle swarm optimization forreconfigurable phase-differentiated array designrdquo Microwaveand Optical Technology Letters vol 38 no 3 pp 168ndash175 2003


[23] F Valdez P Melin and C Oscar ldquoAn improved evolution-ary method with fuzzy logic for combining Particle Swarmoptimization and genetic algorithmsrdquo Applied Soft ComputingJournal vol 11 no 2 pp 2625ndash2632 2011

[24] J Zhang and K Chau ldquoMultilayer ensemble pruning vianovel multi-sub-swarm particle swarm optimizationrdquo Journalof Universal Computer Science vol 15 no 4 pp 840ndash858 2009

[25] F Valdez P Melin and O Castillo ldquoParallel Particle Swarmoptimization with parameters adaptation using fuzzy logicrdquoin Proceedings of the 11th Mexican International Conference onArtificial Intelligence (MICAI rsquo12) vol 2 pp 374ndash385 San LuisPotosi Mexico October 2012

[26] J Peng and C P Y Pan ldquoParticle swarm optimization RBFfor gas emission predictionrdquo Journal of Safety Science andTechnology vol 7 pp 77ndash85 2011

[27] G Ren Z Huang Y Cheng X Zhao and Y Zhang ldquoAnintegrated model for evacuation routing and traffic signaloptimization with background demand uncertaintyrdquo Journal ofAdvanced Transportation vol 47 pp 4ndash27 2013

[28] X Feng Z Xiao and X Cui ldquoImproved RSSI algorithm forwireless sensor networks in 3Drdquo Journal of ComputationalInformation Systems vol 7 no 16 pp 5866ndash5873 2011

[29] F Valdez and P Melin ldquoNeural network optimization witha hybrid evolutionary method that combines particle swarmand genetic algorithms with fuzzy rulesrdquo in Proceedings ofthe Annual Meeting of the North American Fuzzy InformationProcessing Society (NAFIPS rsquo08) NewYork NYUSAMay 2008

[30] F Fernandez-Navarro C Hervas-Martınez P A Gutierrez JM Pena-Barragan and F Lopez-Granados ldquoParameter estima-tion of q-Gaussian Radial Basis Functions Neural Networkswith a Hybrid Algorithm for binary classificationrdquo Neurocom-puting vol 75 pp 123ndash134 2012

[31] H Soh S Lim T Zhang et al ldquoWeighted complex networkanalysis of travel routes on the Singapore public transportationsystemrdquo Physica A vol 389 no 24 pp 5852ndash5863 2010

[32] C K S Kumar R Sukumar and M Nageswari ldquoSensorslifetime enhancement techniques in wireless sensor networksmdasha critical reviewrdquo International Journal of Computer Science andInformation Technology amp Security vol 3 pp 159ndash164 2013

[33] S Li and F Qin ldquoA dynamic neural network approach forsolving nonlinear inequalities defined on a graph and itsapplication to distributed routing-free range-free localizationof WSNsrdquo Neurocomputing vol 117 pp 72ndash80 2013

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks


Advances in

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ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



functions Sigmoid curves are also common in statistics suchas integrals and logistic distribution normal distribution andStudentrsquos probability density functions In our opinion SBFoffers nonlinear effects for large input value and RBF providenonlinear effect at small input value A nonlinear hybrid ofcosine and sine will result in more nonlinear blending acrossthe entire region

13 Wireless Sensor Networks (WSN) Wireless sensor net-works (WSN) gather and process data from the environmentand make possible applications in the areas of environmentmonitoring logistics support health care and emergencyresponse systems as well as military operations Transmittingdata wirelessly impacts significant benefits to those inves-tigating buildings allowing them to deploy sensors whichmonitor from a remote location Multihop transmissionin wireless sensor networks conforms to the undergroundtunnel structure and provides more scalability for communi-cation system construction in rescue situations A significantdiscovery in the field of complex networks has shown that alarge number of complex networks including the internet arescale-free and their connectivity distribution is described bythe power-law of the form 120588(119896) sim 119896

minus120601 to allow few nodesof very large degree to exist making it difficult for randomattack A scale-free wireless network topology was thereforeused

This paper proposes a nonlinearHybridNeural Networksusing radial and sigmoid transfer functions in undergroundcommunication based on particle swarm optimisation Analternative to this model is without hybrid either RBF orSBF The SBF is known to be fast while RBF is accurate [5]and therefore blending the two will provide both speed andaccuracy In addition the two models have been examinedin our previous work [1] To this end we model the incidentlocation as a pure random event and calculate the probabilitythat communication chain through particular rock layersto the ground is not broken and allows neural network tomemorize the complicated relationship such that when realaccident happens the neural network resident in the robot isused to predict the probability based on the rock layer it seesinstantly If the result is positive the robot waits to receive therescue signal otherwise it moves deeper to the next layer andrepeats the procedure

Section 2 explains the preliminaries to the study andgenerates the routing path that has the highest survival proba-bility for the neural training Section 3 discusses related workto the study Section 4 discusses the network optimizationmodel based on the nonlinear weight on the compact radialbasis function Section 5 highlights the method used andSection 6 shows the simulation results of the various hybridsand compare with the Gaussian model whiles Section 7 givesa summary of the findings and future work

2 Preliminaries

21 Sensor Deployment Some assumptions such as 20 ofsoftware failure 2 safe exits assumed to be available afteraccidents and additional errors committed after the accidents

and the failure rate of radio frequency identification (RFID)weremade in various sectionsThese assumptions are alreadyincluded in the model and they are there to ensure that thesystem remains reliable

Topological deployment of sensor nodes affects the per-formance of the routing protocol [6 7] The ratio of com-munication range to sensing range as well as the distancebetween sensor nodes can affect the network topology

Let Ω be the sensor sequence for the deployment of totalsensors 119879 = 119909119910119911 = 119871 119877 119862 such that

Ω =

For 119905 = 119905 + 1

node (119905 2) = (


tog119869)10038171003817100381710038171003817

2+ 119895)

node (119905 3) = (


tog119870)10038171003817100381710038171003817

2+ 119896)

for 119894 = 1 119871 119895 = 1 119877 119896 = 1 119862 and node (119905 1) = 119894

(1)

tog119869 = ceil(119905119862119877) and tog119870 = ceil(119905119862) check source anddestination node respectively

Ω(119894 119895 119896) = 1 1 1 1 2 1 119894th 119895th 119896th for [level 1row 1 column 1] [level 1 row 2 column 1] [ ] and [119894th level119895th row and 119896th column] respectively Therefore 119879 = 119879 times 119879

matrix in an underground mine with dimensions of 119871 = 3119877 = 2 and 119862 = 1 for depth (level) row (length) and width(column) respectively with ldquopmrdquo a sensor apart implies thata minimum of 6 sensors will have to be deployed

22 Communication The Through-The-Earth (TTE) Com-munication system transmits voice and data through solidearth rock and concrete and is suitable for challengingunderground environments such as mines tunnels and sub-waysThere were stationary sensor nodes monitoring carbonmonoxide temperature and so forth as well as mobilesensors (humans and vehicles) distributed uniformly Bothstationary and mobile sensor nodes were connected to eitherthe Access Point (AP) andor Access Point Heads (APHeads)based on transmission range requirements [6]TheAPHeadsserve as cluster leaders and are located in areas where therock is relatively soft or signal penetration is better to ensurethat nodes are able to transmit the information they receivefrom APs and sensor nodes The APs are connected to otherAPs orThrough-The-Earth (TTE) which is dropped througha drilled hole down 300 meters apart based on the rock typeThe depth and rock type determine the required numberof TTEs needed Next the data-mule is discharged to carryitems such as food water and equipments to the minersunderground and return with underground information torescue team

23 SignalTransmission Reach Major challenges of sen-sor networks include battery constraints energy efficiencynetwork lifetime harsh underground characteristics bettertransmission range and topology design among othersSeveral routing approaches for safety evacuation have been





119873120575 = 119873120575min +1003817100381710038171003817119873120575min minus 119873120575max

1003817100381710038171003817lowastrandom (

1015840

1205731015840

rock 1 1)




120593119896 (119894 119895) = 1 if 1003817100381710038171003817119894 minus 119895

1003817100381710038171003817 le 119873120575

0 otherwise(3)


Skin depth = radic2

(120588 lowast 120596 lowast 120590) (4)



119861 = (119896)1198893





The 120593119903 sub 120593119896 119872120588

le 120572 119872120588

is even 119872120588


120588


120593119903 =

1 if 1003817100381710038171003817119894 minus 1198951003817100381710038171003817 ge (

119872120588

2)

0 otherwise

for 119894 119895 = 1 119879

(5)


120593119909 = (1 minus 120595) 120593119903

120593119891 (119894 119895) = 1 if 120593119909 (119894 119895) lt 120582119871

0 if 120593119909 (119894 119895) ge 120582119871

(6)



120593ℎ = 120593119891 lowast 120593119903

120593119890 = 119873119890 minus 120595

(7)




120593119904 = 1 minus ((1



120593119868 = 1 minus ((1




120593119867 = min (1 120593119868 [119883Ψ]) for [119883Ψ]) =120593119890

119872119901

(10)


120593V = 120593119904 lowast 120593119890 (11)

120593119877 = 120593V lowast 120593119904 (12)

119877 = 120593119877 (13)

3 Related Work



MSE =1

119899119904

119899

sum

119895=1

119904

sum

119894=1

(119884119895119894

minus 119910119895119894

)2

(14)


119894119895


119894119895



1

119909119873

sub 119877119889


120601 (119903) = 119890minus(120576119903)

2

(15)


1015840



1015840

) = exp(minus119909 minus 1199091015840

2

1205752


1015840

) = 120601119862V(119909 minus 119909

1015840

)119896(119909 1199091015840

) and 120601119862V(119909 minus 119909

1015840

) =

[(1 minus 119909 minus 1199091015840

119862)(sdot)+


+




) ge 119862


1015840 where 119909 = 1199091015840 the


1015840







log sig (119877) 119877 = 119882 sdot 119875 + 119861

log sig (119882 sdot 119875 + 119861) =1

1 + 119890minus(119882sdot119875+119861)

(16)


[exp (minus 119877)] 119877 = 119882 sdot 119875 + 119861


120601 (out) = [exp (minus 119877)]

(17)



119875119873 =

119873

sum

119894=1

119877119894

119878119894

+

2

sum

119894=1

119878119894

+

2

sum

119894=1

119878119894

119878119894

+ 1

for 1 le 119894 le 119878 1 le 119896 le 119877

(18)

119877 1198781

1198782



119882119894

= 119878119894

1198771198822

= 119878119894

119877 119882119898

= 119878119898

119877

119875119894

= [119877 (119894 minus 119895) + 119870] = 119882119894

(119894 119896)

(19)


rArr 1198611

)Hidden 119861

1

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr S1

Output 1198612

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr 1198782



minus sinHSCR-BF


HSCR-BFminus cos



HSCR-BF+ cos


[+ cos (119877)]

HSCR-BFminus sin



HSCR-BF+ sin


[+ sin (119877)]

(20)


HSGR-YBF+ cos


)] sdotlowast

[+ cos (119877)]

(21)





119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)



120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)


119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882


1205781199032

are random numbers


Input nodes64748

64748

64748


S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09


1 2 3 4 5 6 7 8 9 100

02040608

11214


Link

avai

labi

lity






affected












119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







119873120575 = 119873120575min +1003817100381710038171003817119873120575min minus 119873120575max

1003817100381710038171003817lowastrandom (

1015840

1205731015840

rock 1 1)




120593119896 (119894 119895) = 1 if 1003817100381710038171003817119894 minus 119895

1003817100381710038171003817 le 119873120575

0 otherwise(3)


Skin depth = radic2

(120588 lowast 120596 lowast 120590) (4)



119861 = (119896)1198893





The 120593119903 sub 120593119896 119872120588

le 120572 119872120588

is even 119872120588


120588


120593119903 =

1 if 1003817100381710038171003817119894 minus 1198951003817100381710038171003817 ge (

119872120588

2)

0 otherwise

for 119894 119895 = 1 119879

(5)


120593119909 = (1 minus 120595) 120593119903

120593119891 (119894 119895) = 1 if 120593119909 (119894 119895) lt 120582119871

0 if 120593119909 (119894 119895) ge 120582119871

(6)



120593ℎ = 120593119891 lowast 120593119903

120593119890 = 119873119890 minus 120595

(7)




120593119904 = 1 minus ((1



120593119868 = 1 minus ((1




120593119867 = min (1 120593119868 [119883Ψ]) for [119883Ψ]) =120593119890

119872119901

(10)


120593V = 120593119904 lowast 120593119890 (11)

120593119877 = 120593V lowast 120593119904 (12)

119877 = 120593119877 (13)

3 Related Work



MSE =1

119899119904

119899

sum

119895=1

119904

sum

119894=1

(119884119895119894

minus 119910119895119894

)2

(14)


119894119895


119894119895



1

119909119873

sub 119877119889


120601 (119903) = 119890minus(120576119903)

2

(15)


1015840



1015840

) = exp(minus119909 minus 1199091015840

2

1205752


1015840

) = 120601119862V(119909 minus 119909

1015840

)119896(119909 1199091015840

) and 120601119862V(119909 minus 119909

1015840

) =

[(1 minus 119909 minus 1199091015840

119862)(sdot)+


+




) ge 119862


1015840 where 119909 = 1199091015840 the


1015840







log sig (119877) 119877 = 119882 sdot 119875 + 119861

log sig (119882 sdot 119875 + 119861) =1

1 + 119890minus(119882sdot119875+119861)

(16)


[exp (minus 119877)] 119877 = 119882 sdot 119875 + 119861


120601 (out) = [exp (minus 119877)]

(17)



119875119873 =

119873

sum

119894=1

119877119894

119878119894

+

2

sum

119894=1

119878119894

+

2

sum

119894=1

119878119894

119878119894

+ 1

for 1 le 119894 le 119878 1 le 119896 le 119877

(18)

119877 1198781

1198782



119882119894

= 119878119894

1198771198822

= 119878119894

119877 119882119898

= 119878119898

119877

119875119894

= [119877 (119894 minus 119895) + 119870] = 119882119894

(119894 119896)

(19)


rArr 1198611

)Hidden 119861

1

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr S1

Output 1198612

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr 1198782



minus sinHSCR-BF


HSCR-BFminus cos



HSCR-BF+ cos


[+ cos (119877)]

HSCR-BFminus sin



HSCR-BF+ sin


[+ sin (119877)]

(20)


HSGR-YBF+ cos


)] sdotlowast

[+ cos (119877)]

(21)





119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)



120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)


119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882


1205781199032

are random numbers


Input nodes64748

64748

64748


S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09


1 2 3 4 5 6 7 8 9 100

02040608

11214


Link

avai

labi

lity






affected












119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






120593119904 = 1 minus ((1



120593119868 = 1 minus ((1




120593119867 = min (1 120593119868 [119883Ψ]) for [119883Ψ]) =120593119890

119872119901

(10)


120593V = 120593119904 lowast 120593119890 (11)

120593119877 = 120593V lowast 120593119904 (12)

119877 = 120593119877 (13)

3 Related Work



MSE =1

119899119904

119899

sum

119895=1

119904

sum

119894=1

(119884119895119894

minus 119910119895119894

)2

(14)


119894119895


119894119895



1

119909119873

sub 119877119889


120601 (119903) = 119890minus(120576119903)

2

(15)


1015840



1015840

) = exp(minus119909 minus 1199091015840

2

1205752


1015840

) = 120601119862V(119909 minus 119909

1015840

)119896(119909 1199091015840

) and 120601119862V(119909 minus 119909

1015840

) =

[(1 minus 119909 minus 1199091015840

119862)(sdot)+


+




) ge 119862


1015840 where 119909 = 1199091015840 the


1015840







log sig (119877) 119877 = 119882 sdot 119875 + 119861

log sig (119882 sdot 119875 + 119861) =1

1 + 119890minus(119882sdot119875+119861)

(16)


[exp (minus 119877)] 119877 = 119882 sdot 119875 + 119861


120601 (out) = [exp (minus 119877)]

(17)



119875119873 =

119873

sum

119894=1

119877119894

119878119894

+

2

sum

119894=1

119878119894

+

2

sum

119894=1

119878119894

119878119894

+ 1

for 1 le 119894 le 119878 1 le 119896 le 119877

(18)

119877 1198781

1198782



119882119894

= 119878119894

1198771198822

= 119878119894

119877 119882119898

= 119878119898

119877

119875119894

= [119877 (119894 minus 119895) + 119870] = 119882119894

(119894 119896)

(19)


rArr 1198611

)Hidden 119861

1

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr S1

Output 1198612

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr 1198782



minus sinHSCR-BF


HSCR-BFminus cos



HSCR-BF+ cos


[+ cos (119877)]

HSCR-BFminus sin



HSCR-BF+ sin


[+ sin (119877)]

(20)


HSGR-YBF+ cos


)] sdotlowast

[+ cos (119877)]

(21)





119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)



120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)


119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882


1205781199032

are random numbers


Input nodes64748

64748

64748


S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09


1 2 3 4 5 6 7 8 9 100

02040608

11214


Link

avai

labi

lity






affected












119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





) ge 119862


1015840 where 119909 = 1199091015840 the


1015840







log sig (119877) 119877 = 119882 sdot 119875 + 119861

log sig (119882 sdot 119875 + 119861) =1

1 + 119890minus(119882sdot119875+119861)

(16)


[exp (minus 119877)] 119877 = 119882 sdot 119875 + 119861


120601 (out) = [exp (minus 119877)]

(17)



119875119873 =

119873

sum

119894=1

119877119894

119878119894

+

2

sum

119894=1

119878119894

+

2

sum

119894=1

119878119894

119878119894

+ 1

for 1 le 119894 le 119878 1 le 119896 le 119877

(18)

119877 1198781

1198782



119882119894

= 119878119894

1198771198822

= 119878119894

119877 119882119898

= 119878119898

119877

119875119894

= [119877 (119894 minus 119895) + 119870] = 119882119894

(119894 119896)

(19)


rArr 1198611

)Hidden 119861

1

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr S1

Output 1198612

(119894 119895) = 119875(1198771198781

+ 1198781

1198782

) rArr 1198782



minus sinHSCR-BF


HSCR-BFminus cos



HSCR-BF+ cos


[+ cos (119877)]

HSCR-BFminus sin



HSCR-BF+ sin


[+ sin (119877)]

(20)


HSGR-YBF+ cos


)] sdotlowast

[+ cos (119877)]

(21)





119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)



120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)


119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882


1205781199032

are random numbers


Input nodes64748

64748

64748


S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09


1 2 3 4 5 6 7 8 9 100

02040608

11214


Link

avai

labi

lity






affected












119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119909

described this

120591119909

= (

12059111

12059112

1205911119873

12059121

12059122

1205912119873

1205911198981

1205911198982

120591119872119873

)

119881el = (

V11 V12 V1119873

V21 V22 V2119873

V1198981 V1198982 V119872119873

)

(22)



120588best = (

12058811

12058812

1205881119873

12058821

12058822

1205882119873

1205881198981

1205881198982

120588119872119873

)

119866best = (119892best1

119892best12

119892best119873

)

(23)


119881119898119899

= 119881119898119899

+ 1205741198881

1205781199031

(119901best119898119899

minus 119883119898119898

)

+ 1205741198882

1205781199032

(119892best119899

minus 119883119898119899

)

119883119898119899

= 119881119898119899

(24)

1205741198881

and 1205741198882


1205781199032

are random numbers


Input nodes64748

64748

64748


S11R

S12R

SR

120573 ge 07

S1mR

120573 ge 07 le 09

120573 ge 07 le 09


1 2 3 4 5 6 7 8 9 100

02040608

11214


Link

avai

labi

lity






affected












119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








119878eq = (

(

1 1 1

1 2 1

2 2 1

2 1 1

3 1 1

3 2 1

)

)

119894120593 =

[[[[[[[

[

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

]]]]]]]

]

120593119896 = (

(

1 1 1 1 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)

1 = signal points

120593119903 = (

(

1 1 1 0 0 0

1 1 1 0 0 0

0 1 1 1 0 0

0 0 1 1 1 0

0 0 0 1 1 1

0 0 0 1 1 1

)

)


120593119909 = (

(

0 1 2 2 0 0

1 5 1 2 0 0

0 8 1 5 9 1

1 1 5 1 1 17

1 1 4 11 0 2

4 4 19 5 3 0

)

)

explosion sizes

120593119891 = (

(

1 1 1 1 1 1

1 6 1 1 1 1

1 0 1 6 0 1

1 1 6 1 1 0

1 1 75 0 1 1

75 75 0 6 1 1

)

)

(25)

120593ℎ = (

(

1 1 1 0 0 0

1 6 1 0 0 0

0 0 1 6 0 0

0 0 6 1 1 0

0 0 0 0 1 1

0 0 0 6 1 1

)

)

120593119900 = (

(

8 8 8 0 0 0

8 48 8 0 0 0

0 0 8 48 0 0

0 0 48 8 8 0

0 0 0 0 8 8

0 0 0 48 8 8

)

)

120593119890 = (

(

144 144 144 0 0 0

144 864 144 0 0 0

0 0 144 864 0 0

0 0 864 144 144 0

0 0 0 0 144 144

0 0 0 864 144 144

)

)


(26)


120593s = (

(

8333 8889 9091 8333 8571 8333

8889 8333 8750 8571 8750 8333

8571 9167 8750 9091 8889 8333

8750 8571 8571 8571 8571 8333

8333 8333 8571 8333 8889 9000

9167 8333 9091 8333 8889 8571

)

)

(27)


120593119868 = 8571 8750 8571 8889 8571 8333

120593119867 = 6236 4976 1 6851 9286 6086

120593V = 5409 4281 8834 5850 8134 5163

(28)








10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









10 20 30 40 50 60 70 80 90 1000

02

04

06

X 94Y 0009904


Fitn

ess v

alue


15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity

(HSCRminuscos )


50 100 150 200 2500

01

02

03

X 249Y 001151



Fitn

ess v

alue

1 2 3 4 5 6

07

08

09

1 Output


Surv

ival

pro

babi

lity






0585 08130 05163) from (13)





120588

































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in


































119903

= 1205737

1198836

1

+ 1205736

1198835

1

+ 1205735

1198834

1

+

1205734

1198833

1

+ 1205733

1198832

1

+ 1205732

1198831

+ 1205730

where 1198831



2




2 of 07345


0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 50 100 150 200

002

004

006

008

X 249Y 001103



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 607

08

09

1

11 Output


Surv

ival

pro

babi

lity

(HSCR+cos )

(a) HSCR-BF+ cos

0 50 100 150 200

005

01

015

02

X 249Y 001247



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 6

070809

111 Output


Surv

ival

pro

babi

lity

(b) HSCR-BF+ sin







7 Conclusion








minus sinHSCR-BF




Nomenclature










nonlinear weight








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








0 50 100 1500

005

01

015

02

X 144Y 0009595



Fitn

ess v

alue

1 15 2 25 3 35 4 45 5 55 604

06

08

1 Output


Surv

ival

pro

babi

lity


+ cos)

0 2 4 6 8 10

002040608

1121416


Min

imise

d er

ror



more accurate




[x = minus1 y = 05785]

[x = 1 y = 04215]

[minus1 004062]

[x = minus2 y = 006288]

[x = minus4 y = 0006014]

[minus3 00404]




Acknowledgments


0 1 2 3 4 5

0

05

1

15

2

X 37Y 0989

Particles position

Opt

imise

d er

ror



nonlinear


Large input values

Small input values





HSCR-BF+sin

HSCR-BFminuscos

HSCR-BFminuscos

HSCR-BFminussin



HSGR-BF+cos

HSGR-BF+cos


00020000400006000080000

100000120000

0 2 4 6 8 10 12

CPU

tim

e

Time (s)

Nonlinear hybrids







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







+ sin HSGR-BF+ cos

Total 255889 254350 422344 643962 438133Average 25589 25435 42234 64396 43813


1205736

1205735

1205734

1205733

1205732

1205731

1205730

1198772







References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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