research article multisensor track occupancy detection model based on chaotic...

Research ArticleMultisensor Track Occupancy Detection Model Based onChaotic Neural Networks

Ze-xi Hua and Xiang-dong Chen

School of Electrical Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Xiang-dong Chen xdchenhomeswjtueducn

Received 31 August 2014 Revised 9 November 2014 Accepted 10 November 2014

Academic Editor Huanlai Xing

Copyright copy 2015 Z-x Hua and X-d Chen This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Bad shunting of track circuit is one of the major risks for railway traffic safetyThe occupancy of track will not be correctly detecteddue to bad shunting which could severely degrade the efficiency of the train dispatching command sometimes even causing seriousaccidents such as train collision and derailment To handle the bad shunting problem theThree Points Test Method is commonlyused for detecting track occupancy However this method completely relies on manual confirmation and it thus usually leads tolow detection efficiency and high labor intensity In order to improve the detection efficiency and involve as less human laborsas possible this paper proposes a multisensor track occupancy detection model which is based on chaotic neural networks Thismodel uses the detection results of track occupancy collected bymultiple sensors as the fundamental data and then it calculates theirweights using chaotic neural networks for data fusion and finally themodel determineswhether the track is occupied Experimentalresults and field tests demonstrate that the proposedmodel is able to provide track occupancy detection with high effectiveness andefficiency Moreover the accuracy of detection reaches 999999 which can help to greatly reduce the labor intensity of manualconfirmation

1 Introduction

Nowadays in the Chinese Railway System the number oftrack segments with bad shunting in track circuit is about 36thousand Since the track occupancy cannot be detected inthese segments accidents can be caused easily due to earlyerror unlocking of railway routes and halfway switching ofthe turnout for example turnout extruding train derailmentand side conflict The problem above results in the safetyrisks to rail operating which poses serious threats to theefficiency of rail transportation and has become a majortechnical problem for the railway system [1ndash5] This paperproposes a multisensor technical solution to detect trackoccupancy which employs the data fusion approach tocombine the detection results obtained by the sensors andthen comprehensively analyzes them to determine whetherthe track is occupied

The working conditions of railways are different andcomplex In the process of track occupancy collection theperformance of sensors will be affected by installation cli-mate electromagnetic environment and other factors which

may cause data noise and track occupancy detection errorTherefore to calculate the weights of data from each sensordifferent railway working conditions need to be taken intoaccount when performing track occupancy detecting usingmultisensor information fusion technology Currently thecommonly usedmultisensor information fusion technologiesmainly include the Bayesian estimation Kalman filteringand D-S evidential reasoning [6 7] For railway site thereis the interference of the data transmission to a certainextent a large amount of data to be processed within a shorttime these approaches have several drawbacks in terms ofinformation fusion system modeling They need to buildregression function to solve the large-scale matrix equationand are not able to calculate the weights of the data fromeach sensor accurately for nonlinear system In contrast thispaper uses the neural network and calculates the weightsof data obtained by the sensors according to the historydata which can avoid local optima This paper improves theconventional neural networks by adding a chaos mechanismto increase its convergence rate and recognition rate To dealwith the problem of bad shunting in track circuit (where

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 896340 7 pageshttpdxdoiorg1011552015896340

2 International Journal of Distributed Sensor Networks

uncorrected detections of track occupancy are caused) thispaper proposes a multisensor technical solution to detecttrack occupancy It employs the chaos neural networks tofuse the data obtained from sensorsThe experimental resultsdemonstrate that the proposed detection method is of highaccuracy and applicable to the current Chinese railways [8ndash12]

2 Analysis of Track OccupancyDetection by Sensors

In order to realize track occupancy detection three kindsof sensors are used including infrared shooting sensorproximity switch sensor and ranging sensor to detect trackoccupancyThis section introduces the preliminaries of thesesensors for detecting track occupancy

21 Infrared Shooting Sensor The infrared shooting sensor isused to realize track occupancy via transmitting and receivinginfrared signals Each sensor consists of the transmitter andreceiver If wheels are not busy the receiver can receiveinfrared rays from the transmitter whichmeans that the trackis idle On the contrary if wheels are passing by the receivercannot receive the infrared rays sent which means that thetrack is occupied

22 Proximity Switch Sensor Proximity switch sensor is asensor whose output can deflect the time when the metalobjects are approaching to the certain range of the inductivehead The sensor used in this paper has a sensing distanceof 2 cm Sensors of this type are fixed inside the rail andthe height from the inner edge of wheels is around 1 cm toachieve the goal of detecting wheels Other metal objects canbe detected within 2 cm which can reduce the misjudgmentcaused by other factors and ensure the system reliability

23 Ranging Sensor Ranging sensor is employed to calculatethe distance of detected objects from sensors according tothe principle of ultrasonic reflection Ranging sensors whichare fixed at the middle of the trail can calculate the distanceamong the sensors and the objects for detectionThe distancefrom the underbody of trains to the ground is shorter than20 cm Therefore if the objects are detected within 20 cm itmeans that the train is passing by indicating idleness of thetrack

With infrared shooting sensor proximity switch sensorand ranging sensor this paper can easily infer whetherthe object passing by these sensors is a train and realizethe detection of track occupancy via the number of trainaxles In the actual scene the detection system can identifyobjects including train inspection trolley person and ani-mal Hence the features of the track-occupying object have tobe extracted so as to provide strong evidence for multisensorobject recognition

Based on the information collected by sensors the veloc-ity acceleration area and frequency of a passing objectwill be calculated Then multisensor information fusiontechnology is applied to realize track occupancy detection

The detection principle is shown in Figure 1 and the devicesinstalled beside the rail are shown in Figure 2

3 Multisensor Information Fusion Model ofChaotic Neural Networks

The weights of the sensor data play the key role in the mul-tisensor information fusion Although the adaptive learningfunction of BP neural networks is the main advantage ofneural networks it is apt to fall into local optima Thereforeusing neural networks separately to achieve multisensorinformation fusion has to a certain extent its limitations [8]

31 Traditional BP Neural Network Model Traditional BPneural network consists of the input layer the hidden layerand the output layer Its weight calculation formula is shownin the following equation

Δ1199081198952 (119899) = minus120578120597119869

1205971199081198952 (119899)

Δ119908119894119895 (119899) = minus120578120597119869

120597119908119894119895 (119899)

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899)

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899)

(1)

As shown in (1) 119869 represents the objective function ofnetwork learning 119899 is number of training samples and 120578is the learning speed 120578 is fixed in traditional BP neuralnetworks where the convergence rate is relatively slow in theflat surface under small 120578 On the contrary when 120578 is set toa large value the shock in canyon area of error surface tendsto become big and the BP neural networks are easily trappedinto local optima

32 Chaotic Neural Network Model The chaos mechanismℎ(119909) is introduced in the phase of weight adjustment here inorder to improve the performance of the BP neural networksby using chaotic characteristics to avoid local optima inthe process of neural network learning This mechanismsimultaneously accelerates the convergence rate by changingthe excitation function of the hidden layers and finallyestablishes the neural network model

321 Improved Weights Correction Algorithm According tothe chaos theory [9]

ℎ (119909) = 11989012(119876

119877)119909119890minus11990921198772

(2)

International Journal of Distributed Sensor Networks 3

Infraredshooting

sensor

Infraredshooting

sensor

Infraredshooting

sensor

Distance is fixed

Distance is fixedDetect time


Speed 1 Speed 2

Acceleration

Ranging sensor

Height is fixedDetect time

Frequency

Calculate the area

Proximityswitch sensor


Figure 1 Detection principle diagram of sensor information

Figure 2 Infrared ray sensor devices installed next to the rail

The correction formula of the weights in neural networksis given as follows

Δ1199081198952 (119899) = minus120578120597119869

1205971199081198952 (119899)+ ℎ (Δ1199081198952 (119899 minus 1))

Δ119908119894119895 (119899) = minus120578120597119869

120597119908119894119895 (119899)+ ℎ (Δ119908119894119895 (119899 minus 1))

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899)

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899)

(3)

where 119909 represents the speed of approaching to the fixedpoint in dynamical systems If 119909 is very big it means thatthe system is far from fixed point In this case ℎ(119909) shoulddecrease quickly so that the improvement of weight could

rapidly get close to the system fixed point with the directiontowards gradient information When 119909 becomes smaller andsmaller the weight dynamical system will gradually move tothe certain neighborhood of some fixed pointThen the self-feedback of ℎ(119909) will generate new driving force to escapefrom the fixed point tuning the weights to the neighborhoodof fixed points from the global point of view In this formula119876 and119877 represent the amplitude and radius of nonlinear self-feedback driven item respectively controlling the activitiesrange of weights 119876 means the shift of power size of localminimum energy in weights dynamical system 119877 is the localability range in the weight dynamical system Accordinglythe dynamics feature of chaos makes the weight dynamicalsystem own complex feature which prevents the networkweights from falling into the local optima during learningconsequently improving the performance of neural networks


322 Improvement of the Excitation Function in the HiddenLayers Generally the excitation function of BP neural net-works in the hidden layers always adopts 119878 type function asshown below

119891 (119909) =1

1 + 119890minus119909 (4)

Its derivative is obtained by the following

1198911015840(119909) = 119891 (119909) [1 minus 119891 (119909)] (5)

The work in literature [13] shows that the adjustmentamount of weights between the input layer and the hiddenlayer has different contribution to network training comparedwith that of the adjustment amount of weights between thehidden layer and the output layer in the BP algorithm If theadjustment amount of weights between the input layer andthe hidden layer is appropriate and that between the hiddenlayer and the output layer is too big the networks are apt tohave a big shock On the contrary if the adjustment amountof weights between the output layer and the hidden layer isappropriate and that between the input layer and the hiddenlayer is too small the convergence rate of the network maybe slowTherefore to adjust the contributions on the networktrainingwith regard to theweights in each layer the excitationfunction is improved as below

1198911 (119909) =1

1 + 119890minus120582119909 (6)

Its derivative is shown in the following

11989110158401 (119909) = 1205821198911 (119909) [1 minus 1198911 (119909)] (7)

Clearly parameter 120582 will affect the form of the 119878 typefunction When 120582 gt 1 the curve of the 119878 type functionbecomes steep accelerating the convergence rate of networkswhen 120582 lt 1 the curve becomes flat which makes theconvergence rate of networks slow and the output morestable Generally 120582 ge 1 is to balance the difference among theadjustment amount of weights between the input layer andthe hidden layer as well as that between the hidden layer andthe output layer which guarantees a decent convergence rateand keeps the network stable

33 Multisensor Information Fusion Model Based on ChaoticNeural Networks This section presents how to identifywhether the passing objects are trains or not according tothe characteristics of the detected targets The characteristicsof the detected targets include the detected targetsrsquo speedacceleration sequence of passing infrared ray tube movingdirection area and state of track occupancy which arethe input of the neural network The recognition result iscategorized into train and not train which is the output ofthe neural network

According to the characteristics of detected targets theinput of neural networks is expressed as the followingmatrix

119909 =

[[[[

[

1199091 (1) 1199092 (1) sdot sdot sdot 1199096 (1)

1199091 (2) 1199092 (2) sdot sdot sdot 1199096 (2)

d

1199091 (119899) 1199092 (119899) sdot sdot sdot 1199096 (119899)

]]]]

]

(8)

The output of the neural network is as below

119910 = [119910 (1) 119910 (2) 119910 (119899)] (9)

The network model is shown in Figure 3According to the chaotic network the learning objective

function is shown as

119869 =1

2[119910 (119899) minus 119910 (119899)]

2 (10)

where 119910(119899) is the real output of the neural networkAccording to the chaotic neural network model we build

the mathematical model with three layers(1) input layer

1198741119895 (119899) =

1199091 (119899)

1199092 (119899)

1199096 (119899)

(11)

(2) hidden layer

1198832119894 (119899) =

119898

sum

119895=1

1199081198941198951198741119895

1198742119894 (119899) = 119891 (1198832119894 (119899))

(12)

(3) output layer

1198833 (119899) =

119898

sum

119895=1

11990811989521198742119894

119910 (119899 + 1) = 1198833 (119899)

(13)

where 119898 is the number of nodes in the hidden layer 119908119894119895 and1199081198952 are the weights between the input layer and the hiddenlayer and those between the hidden layer and the output layerrespectively and 120578 is the learning speedThe calculation of thelearning procedure is given below

119890 (119899) = 119910 (119896) minus 119910 (119896)

Δ1199081198952 (119899 + 1) = 120578119890 (119896)1198742119894 (119899)

+ 11989012119876

119877Δ1199081198952 (119899) 119890

minus(Δ1199081198952(119899))21198772

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899 + 1)

Δ119908119894119895 (119899 + 1) = 120578119890 (119896) 119891 [1199092119894 (119899)] 119890 (119896) 11990811989521198741119895

+ 11989012119876

119877Δ119908119894119895 (119899) 119890

minus(Δ119908119894119895(119899))21198772

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899 + 1)

(14)

4 Simulation and Analysis

To evaluate the validity of the proposed model 1000 his-toric samples are obtained from real-site measurement dataincluding 800 random samples for training neural networksand 200 samples for test


Speed

Acceleration

Sequence byinfrared

Trackoccupation

x1

x2

x3

x6

y(n)

Figure 3 Structure of target recognition based on chaotic neural network

0 500 1000 1500 20000

002

004

006

008

01

012

014

Number of training

Mea

n sq

uare

erro

r con

verg

ence

curv

e

BP neural networkChaotic neural network

Figure 4 Convergence curve of root mean squared error in neuralnetwork training

41 Performance Comparison of the BP and Chaotic NeuralNetworks in Training The structures of the neural networksare all 6-50-1 That is there are 6 neurons in the input layerrepresenting the detected targetrsquos speed acceleration movingdirection sequence of passing infrared ray tube area andstate of occupied track respectively while 1 neuron as thestate of track occupancy is in output layer Initially theweights are identical and selected from the range (minus1 1) andthe other parameters are set as 120578 = 001 120582 = 2 119877 = 1 and119876 = 02 All neural networks for comparison are trained 2000times respectively based on 800 groups of sample data Thesimulation results are shown in Figure 4

Simulation results show that the convergence rate of thechaotic neural network is faster than that of the BP neuralnetwork Besides the chaotic neural network outputs smallernetwork training error

42 Performance Comparison of the BP and Chaotic NeuralNetworks in Testing Here 200 groups of sample data are

0 50 100 150 2000

0002

0004

0006

0008

001

0012

0014

0016

0018

Test samples


Mea

n sq

uare

erro

r con

verg

ence

curv

e

Figure 5 Convergence curve of root mean squared error in neuralnetwork test

used to test the neural network which is completely trainedin (1) and compare the performance between the BP neuralnetwork and the chaotic neural network The simulationresults are shown in Figures 5 6 and 7

The output of track occupancy model has only twocases the occupation (output is 1) and the idleness (outputis 0) Hence the output of neural networks is binarizedand specified as 1 if it is greater than 05 and 0 otherwiseThe simulation results of neural networks are illustrated inFigures 8 and 9 and Table 1

The results show that (1) after training both BP neuralnetwork and the chaotic neural network obtain promisingresults very close to the desired output where high test preci-sion and detection accuracy rate are achieved (2) comparedwith the BP neural network the chaotic neural network hasfaster error convergence rate higher test precision and detec-tion accuracy rate and better network performance Besidesthe proposed one is able to detect the track occupancystatus with 100 accuracy and meet the requirements of the


Table 1 Performance comparison results

MSE Correct number Correct rate of occupancy detection Test time (s)BP neural network 00063 198 99 00312Chaotic neural network 00025 200 100 00287

0 20 40 60 80 100 120 140 160 180 200Test samples

The desired outputNetwork output

The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12

Figure 6 Test result of BP neural network

0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12

Figure 7 Test result of chaotic neural network

0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut

The desired outputNetwork output (after processing)

Figure 8 Test result of binarized BP neural network

0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp

utFigure 9 Test result of the binarized chaotic neural network

track occupancy detection model (3) test speed of neuralnetwork is fast enough to meet the real-time requirementof the railway system Chaotic neural network combinesthe advantages of randomness and deterministic algorithmsIts optimization process consists of global searching stageand gradient searching stage which can effectively avoidlocal optima Randomness guarantees the global searchingcapability and overcomes the limitations of BP algorithmwith uniform distribution as its searchingmechanism In thissense chaotic neural network retains optimization duringsearching process The improved excitation function canenhance speedwhilemaintaining network stabilityThereforechaotic neural network can achieve better simulation resultsthan BP neural network This paper applies chaotic neuralnetwork to the detection of track occupancy Simulation andexperimental results demonstrate that the proposed chaoticneural network can meet the requirement of applications inChinese railways

The track occupancy detection solution based on multi-sensor information fusion technology is tested and validatedin the field It has been evaluated at some railway stationsin Hebei province for more than one year The test resultsshow that it can handle strong distractions caused by harshenvironments with response time smaller than 20ms andaccuracy of 999999 The proposed solution complies withthe standard of security for SIL-4 The infrared ray tubeembedded circuit board and the device installation are shownin Figure 10

5 Conclusion

To realize track occupancy detection this paper applies thechaos mechanism in the weight adjustment and excitationfunction to create chaotic neural networkmodel based on BP


(a) Infrared ray tube embedded circuit board (b) Device installation

Figure 10 Infrared ray tube embedded circuit board and the device installation

neural networks A multisensor track occupancy detectionmodel is designed to deal with the problem of bad shuntingfor track circuitsThismodel can recognize detected target byanalyzing sensor information through BP and chaotic neuralnetworks so as to detect status of the track occupancy Byexperiments and onsite verification the multisensor infor-mation fusion for target recognition using chaotic neuralnetwork can reach 100 accuracy Compared with BP neuralnetwork the proposed chaotic neural network has faster con-vergence and consumes less training time meeting all systemrequirements The multisensor track occupancy detectionsolution proposed in this paper can solve the bad shuntingof track circuit and fulfill the task of the track occupancydetection which to a certain extent has relatively importanttheoretical and practical values for multisensor informationfusion research

Conflict of Interests

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

References

[1] J Wu and YWang ldquoPreservationmeasures against track circuitdefective shunting in train control center of dedicated passengerlinerdquo Journal of Beijing Jiaotong University vol 32 no 3 pp 21ndash24 2008

[2] Y Xiao-Jun ldquoResearch on bad shunting of track circuitrdquoRailway Signalling amp Communication vol 43 no 4 pp 11ndash142007

[3] Y Hu ldquoResearch on remediation program of bad shunting oftrack circuitrdquo Railway Signalling amp Communication vol 44 no5 pp 24ndash26 2008

[4] W-Q Guo and P Guo ldquoCause and countermeasure to badshunting of track circuitrdquo Railway Transport and Economy vol27 no 2 pp 61ndash62 2005

[5] H Gui-Yang and H Ze-Xi ldquoSolution analysis for defectiveshunting of track circuitrdquo Railway Computer Application vol21 no 1 pp 46ndash48 2012

[6] WYao-nan andL Shu-tao ldquoSummary ofmulti-sensor informa-tion fusion and applicationrdquo Control and Decision vol 16 no 5pp 518ndash522 2001

[7] Y He X Guan and G-H Wang ldquoSurvey on the progressand prospect of multisensor information Fusionrdquo Journal ofAstronautics vol 26 no 4 pp 524ndash530 2005

[8] M Cang-zhen Y Ding-bo X Jia P Shi-bao and W Xiao-junldquoA new target-correlation algorithm for heterogeneous sensorsbased on neural network classificationrdquo Journal of Radars vol11 no 4 pp 399ndash405 2012

[9] Y-N Wang Q-M Yu and X-F Yuan ldquoProgress of chaoticneural networks and their applicationsrdquo Control and Decisionvol 21 no 2 pp 121ndash128 2006

[10] L Wang S Li F Tian and X Fu ldquoA noisy chaotic neu-ral network for solving combinatorial optimization problemsstochastic chaotic simulated annealingrdquo IEEE Transactions onSystems Man and Cybernetics Part B Cybernetics vol 34 no5 pp 2119ndash2125 2004

[11] T Wen Y Wang and H Dan ldquoTracking control for uncertainchaotic system using dynamic neural networksrdquo Control andDecision vol 19 no 4 pp 455ndash458 2004

[12] Q Zhang C Wang and J Xu ldquoA multicast routing algorithmbased on transient chaotic neural networksrdquo Journal of Com-puter Research and Development vol 40 no 2 pp 177ndash1792003

[13] L Feng ldquoResearch on license plate location based on improvedBP neural networksrdquo Journal of SoochowUniversity EngineeringScience vol 24 no 6 pp 5ndash8 2004

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


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Propagation




Navigation and Observation



DistributedSensor Networks



uncorrected detections of track occupancy are caused) thispaper proposes a multisensor technical solution to detecttrack occupancy It employs the chaos neural networks tofuse the data obtained from sensorsThe experimental resultsdemonstrate that the proposed detection method is of highaccuracy and applicable to the current Chinese railways [8ndash12]

2 Analysis of Track OccupancyDetection by Sensors

In order to realize track occupancy detection three kindsof sensors are used including infrared shooting sensorproximity switch sensor and ranging sensor to detect trackoccupancyThis section introduces the preliminaries of thesesensors for detecting track occupancy

21 Infrared Shooting Sensor The infrared shooting sensor isused to realize track occupancy via transmitting and receivinginfrared signals Each sensor consists of the transmitter andreceiver If wheels are not busy the receiver can receiveinfrared rays from the transmitter whichmeans that the trackis idle On the contrary if wheels are passing by the receivercannot receive the infrared rays sent which means that thetrack is occupied

22 Proximity Switch Sensor Proximity switch sensor is asensor whose output can deflect the time when the metalobjects are approaching to the certain range of the inductivehead The sensor used in this paper has a sensing distanceof 2 cm Sensors of this type are fixed inside the rail andthe height from the inner edge of wheels is around 1 cm toachieve the goal of detecting wheels Other metal objects canbe detected within 2 cm which can reduce the misjudgmentcaused by other factors and ensure the system reliability

23 Ranging Sensor Ranging sensor is employed to calculatethe distance of detected objects from sensors according tothe principle of ultrasonic reflection Ranging sensors whichare fixed at the middle of the trail can calculate the distanceamong the sensors and the objects for detectionThe distancefrom the underbody of trains to the ground is shorter than20 cm Therefore if the objects are detected within 20 cm itmeans that the train is passing by indicating idleness of thetrack

With infrared shooting sensor proximity switch sensorand ranging sensor this paper can easily infer whetherthe object passing by these sensors is a train and realizethe detection of track occupancy via the number of trainaxles In the actual scene the detection system can identifyobjects including train inspection trolley person and ani-mal Hence the features of the track-occupying object have tobe extracted so as to provide strong evidence for multisensorobject recognition

Based on the information collected by sensors the veloc-ity acceleration area and frequency of a passing objectwill be calculated Then multisensor information fusiontechnology is applied to realize track occupancy detection

The detection principle is shown in Figure 1 and the devicesinstalled beside the rail are shown in Figure 2

3 Multisensor Information Fusion Model ofChaotic Neural Networks

The weights of the sensor data play the key role in the mul-tisensor information fusion Although the adaptive learningfunction of BP neural networks is the main advantage ofneural networks it is apt to fall into local optima Thereforeusing neural networks separately to achieve multisensorinformation fusion has to a certain extent its limitations [8]

31 Traditional BP Neural Network Model Traditional BPneural network consists of the input layer the hidden layerand the output layer Its weight calculation formula is shownin the following equation

Δ1199081198952 (119899) = minus120578120597119869

1205971199081198952 (119899)

Δ119908119894119895 (119899) = minus120578120597119869

120597119908119894119895 (119899)

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899)

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899)

(1)

As shown in (1) 119869 represents the objective function ofnetwork learning 119899 is number of training samples and 120578is the learning speed 120578 is fixed in traditional BP neuralnetworks where the convergence rate is relatively slow in theflat surface under small 120578 On the contrary when 120578 is set toa large value the shock in canyon area of error surface tendsto become big and the BP neural networks are easily trappedinto local optima

32 Chaotic Neural Network Model The chaos mechanismℎ(119909) is introduced in the phase of weight adjustment here inorder to improve the performance of the BP neural networksby using chaotic characteristics to avoid local optima inthe process of neural network learning This mechanismsimultaneously accelerates the convergence rate by changingthe excitation function of the hidden layers and finallyestablishes the neural network model

321 Improved Weights Correction Algorithm According tothe chaos theory [9]

ℎ (119909) = 11989012(119876

119877)119909119890minus11990921198772

(2)


Infraredshooting

sensor

Infraredshooting

sensor

Infraredshooting

sensor

Distance is fixed



Speed 1 Speed 2

Acceleration

Ranging sensor


Frequency

Calculate the area






Δ1199081198952 (119899) = minus120578120597119869

1205971199081198952 (119899)+ ℎ (Δ1199081198952 (119899 minus 1))

Δ119908119894119895 (119899) = minus120578120597119869

120597119908119894119895 (119899)+ ℎ (Δ119908119894119895 (119899 minus 1))

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899)

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899)

(3)





119891 (119909) =1

1 + 119890minus119909 (4)


1198911015840(119909) = 119891 (119909) [1 minus 119891 (119909)] (5)


1198911 (119909) =1

1 + 119890minus120582119909 (6)


11989110158401 (119909) = 1205821198911 (119909) [1 minus 1198911 (119909)] (7)




119909 =

[[[[

[

1199091 (1) 1199092 (1) sdot sdot sdot 1199096 (1)

1199091 (2) 1199092 (2) sdot sdot sdot 1199096 (2)

d

1199091 (119899) 1199092 (119899) sdot sdot sdot 1199096 (119899)

]]]]

]

(8)


119910 = [119910 (1) 119910 (2) 119910 (119899)] (9)



119869 =1

2[119910 (119899) minus 119910 (119899)]

2 (10)



1198741119895 (119899) =

1199091 (119899)

1199092 (119899)

1199096 (119899)

(11)

(2) hidden layer

1198832119894 (119899) =

119898

sum

119895=1

1199081198941198951198741119895

1198742119894 (119899) = 119891 (1198832119894 (119899))

(12)

(3) output layer

1198833 (119899) =

119898

sum

119895=1

11990811989521198742119894

119910 (119899 + 1) = 1198833 (119899)

(13)


119890 (119899) = 119910 (119896) minus 119910 (119896)

Δ1199081198952 (119899 + 1) = 120578119890 (119896)1198742119894 (119899)

+ 11989012119876

119877Δ1199081198952 (119899) 119890

minus(Δ1199081198952(119899))21198772

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899 + 1)

Δ119908119894119895 (119899 + 1) = 120578119890 (119896) 119891 [1199092119894 (119899)] 119890 (119896) 11990811989521198741119895

+ 11989012119876

119877Δ119908119894119895 (119899) 119890

minus(Δ119908119894119895(119899))21198772

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899 + 1)

(14)




Speed

Acceleration

Sequence byinfrared

Trackoccupation

x1

x2

x3

x6

y(n)


0 500 1000 1500 20000

002

004

006

008

01

012

014

Number of training

Mea

n sq

uare

erro

r con

verg

ence

curv

e






0 50 100 150 2000

0002

0004

0006

0008

001

0012

0014

0016

0018

Test samples


Mea

n sq

uare

erro

r con

verg

ence

curv

e








0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut



0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp




5 Conclusion








References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Infraredshooting

sensor

Infraredshooting

sensor

Infraredshooting

sensor

Distance is fixed



Speed 1 Speed 2

Acceleration

Ranging sensor


Frequency

Calculate the area






Δ1199081198952 (119899) = minus120578120597119869

1205971199081198952 (119899)+ ℎ (Δ1199081198952 (119899 minus 1))

Δ119908119894119895 (119899) = minus120578120597119869

120597119908119894119895 (119899)+ ℎ (Δ119908119894119895 (119899 minus 1))

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899)

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899)

(3)





119891 (119909) =1

1 + 119890minus119909 (4)


1198911015840(119909) = 119891 (119909) [1 minus 119891 (119909)] (5)


1198911 (119909) =1

1 + 119890minus120582119909 (6)


11989110158401 (119909) = 1205821198911 (119909) [1 minus 1198911 (119909)] (7)




119909 =

[[[[

[

1199091 (1) 1199092 (1) sdot sdot sdot 1199096 (1)

1199091 (2) 1199092 (2) sdot sdot sdot 1199096 (2)

d

1199091 (119899) 1199092 (119899) sdot sdot sdot 1199096 (119899)

]]]]

]

(8)


119910 = [119910 (1) 119910 (2) 119910 (119899)] (9)



119869 =1

2[119910 (119899) minus 119910 (119899)]

2 (10)



1198741119895 (119899) =

1199091 (119899)

1199092 (119899)

1199096 (119899)

(11)

(2) hidden layer

1198832119894 (119899) =

119898

sum

119895=1

1199081198941198951198741119895

1198742119894 (119899) = 119891 (1198832119894 (119899))

(12)

(3) output layer

1198833 (119899) =

119898

sum

119895=1

11990811989521198742119894

119910 (119899 + 1) = 1198833 (119899)

(13)


119890 (119899) = 119910 (119896) minus 119910 (119896)

Δ1199081198952 (119899 + 1) = 120578119890 (119896)1198742119894 (119899)

+ 11989012119876

119877Δ1199081198952 (119899) 119890

minus(Δ1199081198952(119899))21198772

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899 + 1)

Δ119908119894119895 (119899 + 1) = 120578119890 (119896) 119891 [1199092119894 (119899)] 119890 (119896) 11990811989521198741119895

+ 11989012119876

119877Δ119908119894119895 (119899) 119890

minus(Δ119908119894119895(119899))21198772

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899 + 1)

(14)




Speed

Acceleration

Sequence byinfrared

Trackoccupation

x1

x2

x3

x6

y(n)


0 500 1000 1500 20000

002

004

006

008

01

012

014

Number of training

Mea

n sq

uare

erro

r con

verg

ence

curv

e






0 50 100 150 2000

0002

0004

0006

0008

001

0012

0014

0016

0018

Test samples


Mea

n sq

uare

erro

r con

verg

ence

curv

e








0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut



0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp




5 Conclusion








References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119891 (119909) =1

1 + 119890minus119909 (4)


1198911015840(119909) = 119891 (119909) [1 minus 119891 (119909)] (5)


1198911 (119909) =1

1 + 119890minus120582119909 (6)


11989110158401 (119909) = 1205821198911 (119909) [1 minus 1198911 (119909)] (7)




119909 =

[[[[

[

1199091 (1) 1199092 (1) sdot sdot sdot 1199096 (1)

1199091 (2) 1199092 (2) sdot sdot sdot 1199096 (2)

d

1199091 (119899) 1199092 (119899) sdot sdot sdot 1199096 (119899)

]]]]

]

(8)


119910 = [119910 (1) 119910 (2) 119910 (119899)] (9)



119869 =1

2[119910 (119899) minus 119910 (119899)]

2 (10)



1198741119895 (119899) =

1199091 (119899)

1199092 (119899)

1199096 (119899)

(11)

(2) hidden layer

1198832119894 (119899) =

119898

sum

119895=1

1199081198941198951198741119895

1198742119894 (119899) = 119891 (1198832119894 (119899))

(12)

(3) output layer

1198833 (119899) =

119898

sum

119895=1

11990811989521198742119894

119910 (119899 + 1) = 1198833 (119899)

(13)


119890 (119899) = 119910 (119896) minus 119910 (119896)

Δ1199081198952 (119899 + 1) = 120578119890 (119896)1198742119894 (119899)

+ 11989012119876

119877Δ1199081198952 (119899) 119890

minus(Δ1199081198952(119899))21198772

1199081198952 (119899 + 1) = 1199081198952 (119899) + Δ1199081198952 (119899 + 1)

Δ119908119894119895 (119899 + 1) = 120578119890 (119896) 119891 [1199092119894 (119899)] 119890 (119896) 11990811989521198741119895

+ 11989012119876

119877Δ119908119894119895 (119899) 119890

minus(Δ119908119894119895(119899))21198772

119908119894119895 (119899 + 1) = 119908119894119895 (119899) + Δ119908119894119895 (119899 + 1)

(14)




Speed

Acceleration

Sequence byinfrared

Trackoccupation

x1

x2

x3

x6

y(n)


0 500 1000 1500 20000

002

004

006

008

01

012

014

Number of training

Mea

n sq

uare

erro

r con

verg

ence

curv

e






0 50 100 150 2000

0002

0004

0006

0008

001

0012

0014

0016

0018

Test samples


Mea

n sq

uare

erro

r con

verg

ence

curv

e








0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut



0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp




5 Conclusion








References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Speed

Acceleration

Sequence byinfrared

Trackoccupation

x1

x2

x3

x6

y(n)


0 500 1000 1500 20000

002

004

006

008

01

012

014

Number of training

Mea

n sq

uare

erro

r con

verg

ence

curv

e






0 50 100 150 2000

0002

0004

0006

0008

001

0012

0014

0016

0018

Test samples


Mea

n sq

uare

erro

r con

verg

ence

curv

e








0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut



0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp




5 Conclusion








References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 200Test samples


The d

esire

d ou

tput

and

netw

ork

outp

ut

minus02

0

02

04

06

08

1

12


0 20 40 60 80 100 120 140 160 180 2000

02

04

06

08

1

Test samples

The d

esire

d ou

tput

and

netw

ork

outp

ut



0 20 40 60 80 100 120 140 160 180 200Test samples

0

02

04

06

08

1


The d

esire

d ou

tput

and

netw

ork

outp




5 Conclusion








References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article multisensor track occupancy detection model based on chaotic...

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