the neural-fuzzy approach as a way of preventing a...

Research ArticleThe Neural-Fuzzy Approach as a Way of Preventing a MaritimeVessel Accident in a Heavy Traffic Zone

Nelly A Sedova1 Viktor A Sedov2 and Ruslan I Bazhenov 3

1Department of Automatic and Information Systems Maritime State University named after GI Nevelskoy Vladivostok Russia2Department of ElectricianTheoretical Bases Maritime State University named after GI Nevelskoy Vladivostok Russia3Department of Information Systems Mathematics and Legal Informatics Sholom-Aleichem Priamursky State UniversityBirobidzhan Russia

Correspondence should be addressed to Ruslan I Bazhenov r-i-bazhenovyandexru

Received 24 May 2018 Accepted 1 August 2018 Published 15 August 2018

Academic Editor Hanbo Zheng

Copyright copy 2018 Nelly A Sedova et alThis 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

The paper dwells on themethodology of neural-fuzzy approach to solving the problem of ship collision prevention in a heavy trafficzone The authors present the technique of using maneuvering board to form the elements of learning sample The authors provethat it is rational to use a neural-fuzzy system where generation is carried out by the latticemethod without clusteringThe authorsinvestigate the effect of optimization on the quality differencesThe researchers define optimal membership functions that are usedto generate the input linguistic variables of a neural-fuzzy system

1 Introduction

Despite all significant positive outcomes the issue of shipcollision avoidance in a heavy traffic zone [1] is still urgentSo in the paper [2] the authors report on the conceptof expected dangerous patterns (areas) projected on theautomatic identification system data The integration of theGeographic Information System the International Regula-tions for Preventing Collisions at Sea (COLREGs) and athorough investigation of various navigation vessel casesgives the system an opportunity to generate a safe shipcollision prevention route andmaritime featuresThe authors[3] suggest a similar task ofmaking up a system for preventingvessel collisions on the ECDIS (electronic chart displayand information system) and AIS (automatic identificationsystem) The authors of the paper [4] introduce a method forautomatic trajectory planning and collision avoidance usingthe APF (artificial potential field) search method and speedvector Another approach providing ship collision avoidanceis Bayesian networks declared in the paper [5] Fuzzy logicis also successfully applied [6] for this kind of problem Inparticular the papers [7 8] are devoted to support systemsof decision making that are undertaken on board vesselsThus the authors specify an approach for decision making

on sea vessels collision avoidance in the research [8] Theauthors are encouraged to use Microsoft Visual Studio tobuild up a list rule according to the International Regulationsfor Preventing Collisions at Sea (COLREGs 1972) That listis able to offer an appropriate collision avoidance algorithmto the boat master after the assessment of maritime trafficaccording to the vessel traffic service (VTS)

In the papers [9 10] authors present a model based onthe fuzzy sets theory to rank a risk of sea vessel collisionin a heavy traffic zone to agree on the navigational decisionsupport because of safe ship control needed In this model amaneuvering boardwas used to draft a fuzzy production rulessystem [11ndash13] In addition a well-known Mamdani Algo-rithm was used as an algorithm for fuzzy logic conclusion

These days neural network technologies are widely usedin navigation issues [14 15] For example the paper [16]focuses on the neural network classification of marine targetson noise images in bad weather conditions and in case ofsea waves In the paper [17] the neural network succeedsin detecting icebergs by typical textural features from theimage of satellite-based Synthetic Aperture Radar Moreoverthe neural network has been used successfully in issues ofimproving an accurate position of a vessel from radar data[18] and designing laser metering systems [19]

HindawiAdvances in Fuzzy SystemsVolume 2018 Article ID 2367096 8 pageshttpsdoiorg10115520182367096

2 Advances in Fuzzy Systems

ANFIS (Sugeno)

Ship-operatorrsquos routeBearing

Ship-purposersquos route

Target shiprsquos speed

Changing ship-operatorrsquos route

Figure 1 Neural-fuzzy ship collision prevention in a heavy traffic zone

Neural networks are also proved to be successful inwarning [20 21] A number of surveys are worth notingin the supplement to navigation practice In particular themethodology of a short-term forecast of the Caspian Sealevel by means of a perceptron-type neural network [22] isdeveloped in the paper [23]The paper [24] deals with onlineforecast of the maneuvering vessel turn a neural networkmodel RBF having amutating nature and the ability to adjustnetwork features by the sliding window method The authorsdesigned a predictive model which was marked by a leanerstructure fast processing and a high degree of measurementaccuracy

As the use of neural nets has clear benefits [22] itis potentially capable of improving the projection of shipcollision risks In addition significant headway had beenmade against it For example the paper [25] comments on themethodology and strategy of ship collision avoidance usingartificial neural networks optimal control theory methods[26 27] and a game theory The paper [28] also mentions anautonomous navigation system for a robotic submarine basedon an adaptive neurocontroller

Several papers [29ndash34] should also be noted in theconnection with developing approaches to prevent shipcollisions

In order to improve the effects of a fuzzy system [35] theauthors carried out hybridization involving the elements ofartificial neural networks theory which resulted in designinga neural-fuzzy network [36 37] In turn a neural-fuzzy shipcollision prevention system is based on it This paper submitsthe results of simulating modelling

2 Materials and Methods

The neural-fuzzy ship collision prevention system in a heavytraffic zone is an adaptive neural-fuzzy inference system(ANFIS) [22 36 37] consisting of 5 layers This kind ofsystem is defined as a multilayer feedforward neural networkwithout any feedback Its features are those of fuzzy logicinference But an algorithm for making a decision of the neu-ral network is a fuzzy logic inference algorithmANFISmodelused for the neural-fuzzy ship collision prevention system ina heavy traffic zone development is based on TakagindashSugenofuzzy inference system which is highly interpretable andefficient in connection with computing

The first layer of ANFIS is a layer of membership func-tions There is a fuzzification in the first layer ie fuzzy setsare established corresponding to the terms of source (input)and target (output) linguistic variables

The neural-fuzzy ship collision prevention system in aheavy traffic zone observed in the paper (Figure 1) includesfour input linguistic variables

(i) Electronic bearing on the target ship ie on that oneto which the operator vessel needs to prevent collision safely

(ii) The ship-operator course(iii) The target-ship course ie a vessel in a heavy traffic

zone to which if necessary it is required to prevent collision(iv) The target-vessel speed [35] as well as the only

output linguistic variable which is the value of the operator-vessel course change calculated on the maneuvering board inadvance with the output value corresponding to the interval[-60∘ 360∘] where the value of -60∘ corresponds to the termldquomuch to the leftrdquo the value to -30∘ corresponds to the termldquoto the leftrdquo the value 0∘ corresponds to the term ldquokeep itsteadyrdquo (neither the course nor the speed of the operator-vessel changes) 60∘ stands for the term ldquomuch to the rightrdquothe value of 30∘ means the term ldquoto the rightrdquo and the valueof 360∘ implies the maneuver (AmE) or manoeuvre (BrE) ofcirculation (that is the term ldquocirculationrdquo)

The set of values for the inputs ldquobearingrdquo ldquothe ship-operator courserdquo and ldquovessel-target courserdquo is the set [0360]∘ The range of values for the ship-target speed source isdetermined according to the information from the reviewingfeedback of The Russian Maritime Register of Shipping (RS)[0 34] knots

The number of nodes performed in the first layer is equalto the sum of the term powers of the input linguistic variablesetsThe output values focused in the first layer are the valuesof membership functions with specific values of the inputvariables The features of membership functions in the firstlayer compose the first group of features that are to be setduring the learning process

The second layer of ANFIS is a layer of fuzzy productionrulesThe number of nodes is the same as the number of rulesin the second layerMoreover eachnode is connected to thoseones in the first layer that form the premises (antecedents)of the corresponding rule In general the distribution of thelinks between the first and second layers is performed in sucha way that each input variable of the neural-fuzzy network isassociated with each neuron of the rule layer

The output values in the second layer correspond to therelative degrees (weights) of the rules which are calculated asa logical product (intersection) of membership functions ofthe input variables

The third layer of ANFIS is a layer of absolute valuein which the output values of this layer are determinedby adding the outputs of all nodes of the rule layer anddividing each of the output values in the second layer by thistotal value This ensures scaling of the output values so thatincreases the neural-fuzzy network resilience

The fourth layer of ANFIS is the output layer of the linearcombination Each node of the fourth layer is connected to

Advances in Fuzzy Systems 3

one node of the previous layer and as a consequence toall inputs of the neural-fuzzy network In the fourth layerthere is determination of coefficients of linear combinationsas a result for example of an algorithm for backpropagation(backpropa) or hybrid which is a combination of the methodof Ordinary Least Squares (OLS) and a backward propagationof errors (backpropa) Coefficients of linear combinationsconstitute the second group of features to be determined inthe learning process

Finally the fifth layer of ANFIS is the output total layerThefifth layer corresponding to the adder of the legacy neuralnetwork completes defuzzification

Learning a neural-fuzzy network which is a combinationof two stages is an iterative procedure that allows determin-ing the features of membership functions that minimize thediscrepancy between ldquoreal (or valid) and desired behavior ofthe modelrdquo

In the first stage the learning sample goes to the inputsand then the parameters of the fourth layer of the neural-fuzzy network are set up in such a way so as to minimizethe discrepancy between the reference output values and thecalculated output of the neural-fuzzy network

In the second stage residual discrepancy is transferredfrom the network output to the inputs and backpropamodifies the parameters of the nodes in the first layer Besidesthe coefficients of the conclusion of the rules produced in thefirst stage do not change

The iterative setup procedure continues until discrepancyexceeds a preestablished value

Thus the general methodology for constructing theneural-fuzzy network underlying the neural-fuzzy ship col-lision prevention system in a heavy traffic zone includes thefollowing steps

Step 1 Forming a sample for learning which containsimplicit knowledge revealed as a result of learning the neural-fuzzy network

Step 2 Selecting fuzzy inference parameters ie selection ofmembership functions fuzzy intersection and defuzzifica-tion

Step 3 Selecting an algorithm for learning and setting up theparameters of the neural-fuzzy network

Step 4 Direct learning of the neural-fuzzy network to con-figure both groups of parameters

Step 5 Optimizing and verifying learning outcomes of aneural-fuzzy network

The implementation of the neural-fuzzy ship collisionprevention system in a heavy traffic zone was carried out bythe Fuzzy Logic Toolbox of MATLAB system [14 15] Themodel is shown in Figure 1

Furthermore a series of computer experiments wasconducted to define the following

(1)The best type of membership functions used to specifythe terms of input linguistic variables

0

180

270 90

2 nmi 4 nmi8 nmi

60

30330

300

240

210 150

120

Figure 2 Resulting simulation model with ships in a heavy trafficzone

(2) The best type of membership functions used tospecify the terms of the output linguistic variable ie atype of dependence that connects input and output linguisticvariables (constant or linear coefficients)

(3) The best learning algorithm the backpropagationalgorithm (0` backpropa) or the hybrid algorithm Theyare a combination of AOPO and OLS [22]

(4) The optimal number of learning cycles for a neural-fuzzy network

A learning set is designed to carry out simulation mod-elling of the neural-fuzzy collision ship prevention system Atfirst a list of different cases with ships in a heavy traffic zonewas developed by means of a full search having stepped tobroaden the input ranges Then the equation of each certaincase and assessment of a changing value on the operatorship course were made on the maneuvering board It shouldbe noted that the equation on the maneuvering board wasfollowed by the rules of the International Regulations forPreventing Collisions at Sea (COLREGS) commentaries tothem and recommendations on so-called ldquogood seaman-shiprdquo Finally the values of the input vector and the valuecorresponding to that one made with the maneuvering boardfor changing the operator ship course were recorded in alearning sample

The authors would like to present the way of designingone of the learning pairs They also imagine the situationwhen ships are in a heavy traffic zone as shown in Fig-ure 2 The distance from the ship-operator to the targetship is 2 miles the ship-operator course is 90 degrees andthe operator ship speed is 15 knots The radar navigationdetermined that the target-ship course is 330 degrees anobject bearing is 90 degrees and the target-ship speed is 8knots

In the circumstances described the target ship is rightahead the ship-operator and at risk of colliding since theship-operator and the target ship are too close to each other


As it is prescribed in Rule 16 of the International Regulationsfor Preventing Collisions of Ships at Sea the ship-operatormust give way not to run into the target ship Having simu-lated this case on a maneuvering board and having calculatedit the scholars found out that the new ship-operator coursewas going to be 120 degrees It requires turning a ship at 30degrees to the right and the ship-operatorwill not collide withthe ship-target at a safe distance behind the vessel stern Afterconsidering this situation it was possible to set a learning pairnumber 91 The rest of the 525 training pairs were similarlyset

Simulation modelling of neural-fuzzy ship collision pre-vention system was carried out in two modes First neural-fuzzy networks were generated using the lattice methodwithout clustering and second it was performed by thesubclustering method 192 different neural-fuzzy networkswere trained for the first mode Each of them had fiveterms in each of the four input linguistic variables Althoughthe backpropagation and hybrid algorithms were used [22]backpropagation has been widely applied in solving variousproblems but the algorithm has a number of drawbacksin particular ldquoa long time learningrdquo as well as determininglocal or relative instead of global or absolute minima Theauthors used eight different membership functions (MF) todetermine the input linguistic variables They are trimf (tri-angular MF) trapmf (trapezoidal MF) gbellmf (generalizedbell-shapedMF) gaussmf (GaussrsquosMF) gauss2mf (two-sidedGaussrsquosMF) pimf (P- shapedMF) dsigmf (MF as a differencebetween two sigmoid functions) psigmf (the product oftwo sigmoid MF) and constant or linear coefficients for theoutput variable The learning intervals numbered from 100 to600

3 Results and Discussion

As a result of the simulation modelling of the neural-fuzzyship collision prevention system in the mode of gratinggeneration without clustering it was revealed that the bestwere the hybrid method as a learning algorithm constantfactors as a type of the output linguistic variable the productof two sigmoid MF the difference between two sigmoidfunctions and the U-shaped membership function to deriveinput linguistic variables

The authors chose six out of learned neural-fuzzy net-works with the least learning errors They gave a test for eachone and had quality evaluation

31 Mean Absolute Error MAE is given by the formula [38]

119872119860119864 = 1119873 sdot119873sum119894=1

10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816 (1)

where N is number of model-based testing instances 119862119862119874119878119894

is a standard value of the change in the ship-operatorcourse for the i-model test counted with a maneuveringboard and 119862119862119874119878

119894is the value of changing the ship-operator

course for the i-model test counted using a neural-fuzzynetwork

0000E+001000E-052000E-053000E-054000E-055000E-056000E-057000E-05

psigmf (500)

psigmf (600)

dsigmf (600)

dsigmf (400)

psigmf (400)

pimf (600)

Resulting simulation modeling of the neuro-fuzzy ship collision prevention system in the grating generation without clustering

MAERMSESMAPE

Figure 3 Resulting qualitative evaluation in the neural-fuzzy shipcollision prevention system training in the generation by the latticemethod without clustering

32 Root Mean Square Error RMSE is given by the formula[38]

119877119872119878119864 = radic 1119873 sdot119873sum119894=1

(119862119862119874119878119894minus 119862119862119874119878

119894)2 (2)

33 Symmetric Mean Absolute Percentage Error SMAPE isgiven by the formula [38]

119878119872119860119875119864 = sum119873119894=1 (10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816)sum119873119894=1(10038161003816100381610038161003816119862119862119874119878119894 + 11986211986211987411987811989410038161003816100381610038161003816) (3)

The values of qualitative measures are summarized in Table 1and a resulting diagram is in Figure 3

For the secondmode 288 different neural-fuzzy networkswere trained (144144 by the backpropa and hybrid optimiza-tion method) Parameters of the subclusteringmethod variedas follows the parameter ldquoRange of Influencerdquo is from 02 to05 step size is 01 the parameter lsquoSquash Factorrsquo is from 1 to1375 step size is 0125 the parameter ldquoAccept Ratiordquo is from0 to 04 step size is 02 and the parameter ldquoReject Ratiordquo isfrom 0 to 03 step size is 015 In all 288 neural-fuzzy nets 100learning intervals were being selected

The authors came to the following conclusion aftersimulating the neural-fuzzy ship collision prevention systemin the subclustering generation mode The best method isthe hybrid optimization method for neural-fuzzy networksas a learning algorithm as well as for the grid-free generationmode while ldquoRange of Influencerdquo constantly equals 03 thebest ratio for ldquoSquash Factorrdquo is the parameter that equaled 1and the parameter that equaled 04 is for ldquoAccept Ratiordquo

Six best neural-fuzzy networks were chosen for testingFurthermore the authors made qualitative evaluation foreach of them The resulting Table 2 is presented in Figures4 and 5

Let the authors compare the results presented in thispaper with the results of the neural-fuzzy ship collision


Table 1 Resulting simulation modelling of the neural-fuzzy ship collision prevention system in the grating generation without clustering

Type of MF for input LVs Number of Training intervals Learning error MAE RMSE SMAPEpsigmf 500 54532sdot10minus5 1165sdot10minus5 6063sdot10minus5 62555sdot10minus7psigmf 600 54532sdot10minus5 1165sdot10minus5 6063sdot10minus5 62555sdot10minus7dsigmf 600 54553sdot10minus5 1166sdot10minus5 6063sdot10minus5 6257sdot10minus7dsigmf 400 54556sdot10minus5 1166sdot10minus5 6063sdot10minus5 6257sdot10minus7psigmf 400 5456sdot10minus5 11656sdot10minus5 6063sdot10minus5 6257sdot10minus7pimf 600 55002sdot10minus5 1171sdot10minus5 6064sdot10minus5 62836sdot10minus7Table 2 Resulting simulation modelling of the neural-fuzzy ship collision prevention system through subclustering generation method

Range of influence Squash factor Accept ratio Reject Ratio Optim Methods Learning error RMSE MAE SMAPE03 1 0 0 backpropa 126sdot10minus1 3865sdot10minus1 505sdot10minus2 27sdot10minus303 1125 0 0 backpropa 126sdot10minus1 1365sdot10minus1 354sdot10minus2 19sdot10minus303 1 0 015 backpropa 126sdot10minus1 3865sdot10minus1 505sdot10minus2 27sdot10minus303 1 04 0 hibrid 1363sdot10minus3 136sdot10minus3 55sdot10minus4 294sdot10minus503 1 04 015 hibrid 1363sdot10minus3 136sdot10minus3 55sdot10minus4 294sdot10minus503 1 04 03 hibrid 1363sdot10minus3 136sdot10minus3 55sdot10minus4 294sdot10minus5

000E+00500E-02100E-01150E-01200E-01250E-01300E-01350E-01400E-01

Squash factor 1 Reject Ratio 0

Squash factor 1125 Reject

Ratio 0

Squash factor 1 Reject Ratio

015

Resulting simulation modeling of the neuro-fuzzy ship collision prevention system through the subclustering method

backpropa optimal method

RMSEMAESMAPE

Figure 4 Resulting qualitative evaluation in the neural-fuzzyship collision prevention system training when generating by thesubclusteringmethod through backpropagation error algorithm

prevention system in a heavy traffic zone [35] in which onlythe fuzzy logic apparatus is used

In the paper [35] a fuzzy system is offered The firstlinguistic variable called Peleng included the following fiveterms of the basic term set eastern bearing western bearingnorthern left bearing northern right bearing and southernbearing

The second and third input linguistic variables operator-vessel course and target-vessel course had a basic term setconsisting of the following elements [35] the left course to thenorth the right course to the north easterly course headingsouth and westerly course

The fourth input linguistic variable ship-target speed hadthe following terms of the basic term set [35] fixed target lowspeed average speed high speed and a very high speed

000E+00200E-04400E-04600E-04800E-04100E-03120E-03140E-03



015


Resulting simulation modeling of the neuro-fuzzy ship collision prevention system in the subclustering method

The hybrid optimization method

RMSEMAESMAPE

Figure 5 Resulting qualitative evaluation in the neural-fuzzy shipcollision prevention system training in the generation of the hybridalgorithm through the subclusteringmethod

According to the point from Rule 8 in InternationalRules of Preventing Collision at Sea COLREGS ldquoif thereare enough waters only a course change may be the mosteffective mode of action to prevent collisionsrdquo Boatmastersstate that most of the ways to prevent collision at sea are dueto the coursemaneuvers So the change of the operator-vesselcourse is chosen for the output linguistic variable

In the description of terms for the output linguisticvariable the values of fuzzy set cores corresponding to theterms [35] are given in brackets much to the left (-60∘) tothe left (-30∘) keeping it steady (the course and speed do notchange) (0∘) to the right (30∘) much to the right (60∘) andcirculation (360∘)

In the paper [35] the author presents the results offuzzification of the indicated input and output linguistic


Table 3 Results of imitating simulation of a fuzzy ship collision prevention system in a heavy traffic zone proposed in [35]

Defuzzification Method MAE RMSE SMAPEbentroid 22460sdot10minus1 23120sdot10minus1 119sdot10minus2Bisector 12379sdot100 12568sdot100 712sdot10minus2MOM 12379sdot100 12568sdot100 712sdot10minus2SOM 12379sdot100 12568sdot100 712sdot10minus2variables as well as the characteristics of the fuzzy systemproduct base with a description of the fuzzy logic inferencealgorithm designed byMamdani Algorithm

The author [35] did the testing for fuzzy ship collisionprevention system in a heavy traffic zone It should be notedthat the samemeasures (MAE RMSE and SMAPE)were alsoused to evaluate the quality Four defuzzification methodswere used as a defuzzy centroid bisector and the mean ofmaximums and the smallest of maximums The results aresummarized in Table 3

As a result of testing the fuzzy ship collision preventionsystem in a heavy traffic zone offered in [35] it was foundout that the best defuzzification method is centroid but thediscrepancy quality values are insufficient to decide on seavessels collision prevention in a heavy traffic zone

4 Conclusions

Having verified the results of simulating the neural-fuzzy shipcollision prevention system for both modes (both for grid-generatedwithout clustering and for subclustering generated)the authors draw the following conclusions

First it is advisable to use the neural-fuzzy ship collisionprevention system to avoid ship collision in a heavy trafficzone where generation is held through the lattice methodwithout clustering The comparison of the results of Tables1 and 2 proves much better quality of discrepancies usingthe neural-fuzzy ship collision prevention system in a heavytraffic zone with generation by the lattice method withoutclustering than when generated by subclustering methodwhich produces the best MAE result comparable to 10minus4

Second the hybrid method of optimization gives muchbetter results than the algorithm for backpropagation whenusing both the lattice method without clustering and thesubclustering one In particular 0` produces the bestMAE result equal to 354∙10minus2 while the hybrid algorithmproduces MAE result equal to 55∙10minus4 when generating bysubclustering method

Third the authors believe that best results to developinput linguistic variables are given by such membershipfunctions as the product of two sigmoid MF as a differencebetween two sigmoid functions and a U-shaped membershipfunction That is proved by the results in Table 1

Fourth it is necessary to refer to constant coefficientsfor the neural-fuzzy ship collision prevention system in themode of grating generation without clustering as a type ofthe output linguistic variable

To sum up 192 different simulating models of neural-fuzzy ship collision prevention systems were generatedthrough the lattice-free clustering method as well as 288

neural-fuzzy ship collision prevention systems where thenetwork was generated through the subclustering methodAfter finishing the simulation the hybrid optimizationmethod turned out to be the best (allows to get MAE valueabout 10minus5) The best neural-fuzzy ship collision preventionsystems testing has proved that they can determine veryaccurately the value of changing the ship-operator courseto avoid ship collision in a heavy traffic zone which isdangerous for the ship-operator The authors compared theresults reflected in this paper for example with those of thefuzzy ship collision prevention system in a heavy traffic zoneproposed in the paper [35] They came to the conclusionthat the defuzzification method Centroid with MAE andRMSE values about 10minus1 and SMAPE about 10minus2 producesthe best result Thus it is correct to say that using neuralnetwork technologies in solving the problem significantlyimproves the quality of safe navigation of sea-going vesselsin a heavy traffic zone The neural-fuzzy collision avoidancesystem investigated in this research is one of the modulesof the intelligent navigation safety system The authors aredefinitely going to keep developing them in the future

Data Availability

Data were obtained by the authors independently The dataused to support the findings of this study are included withinthe supplementary information files

Conflicts of Interest

The authors declare that they have no conflicts of interest

Supplementary Materials

Supplementary 1 Table 1 1xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with500 training intervals using the membership function asa product of two sigmoid membership functions for inputlinguistic variables with the necessary quality assessmentcalculated (MAE RMSE and SMAPE)Supplementary 2 Table 1 2xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with600 training intervals using the membership function asa product of two sigmoid membership functions for inputlinguistic variables with the necessary quality assessmentcalculated (MAE RMSE and SMAPE)


Supplementary 3 Table 1 3xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with 600training intervals using the membership function differenceof functions (as a result of subtraction) between two sigmoidfunctions for input linguistic variables with the necessaryquality assessment calculated (MAE RMSE and SMAPE)Supplementary 4 Table 1 4xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with 400training intervals using the membership function differenceof functions (as a result of subtraction) between two sigmoidfunctions for input linguistic variables with the necessaryquality assessment calculated (MAE RMSE and SMAPE)Supplementary 5 Table 1 5xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with400 training intervals using the membership function as aproduct between two sigmoid functions for input linguisticvariables with the necessary quality assessment calculated(MAE RMSE and SMAPE)

Supplementary 6 Table 1 6xlsx data for testing the neural-fuzzy ship collision prevention system where generation iscarried out by the lattice method without clustering with 600training intervals using the U-shaped membership functionfor input linguistic variables with the necessary qualityassessment calculated (MAE RMSE and SMAPE)

Supplementary 7 Table 2 1xlsx data for testing the neural-fuzzy ship collision prevention system generated by sub-clustering with 100 training intervals using backpropagationwith parameters Range of Influence Squash Factor AcceptRatio and Reject Ratio equal to 03 1 0 and 0 respectivelywith the necessary quality assessment calculated (MAERMSE and SMAPE)

Supplementary 8 Table 2 2xlsx data for testing the neural-fuzzy ship collision prevention system generated by sub-clustering with 100 training intervals using backpropaga-tion with parameters Range of Influence Squash FactorAccept Ratio and Reject Ratio equal to 03 1125 0 and 0respectively with the necessary quality assessment calculated(MAE RMSE and SMAPE)


Supplementary 10 Table 2 4xlsx data for testing the neural-fuzzy ship collision prevention system generated by sub-clustering with 100 training intervals using the hybridoptimization method with parameters Range of InfluenceSquash Factor Accept Ratio and Reject Ratio equal to 03 104 and 0 respectively with the necessary quality assessmentcalculated (MAE RMSE and SMAPE)

Supplementary 11 Table 2 5xlsx data for testing the neu-ral -fuzzy ship collision prevention system generated bysubclustering with 100 training intervals using the hybridoptimization method with parameters Range of InfluenceSquash Factor Accept Ratio and Reject Ratio equal to 031 04 and 015 respectively with the necessary qualityassessment calculated (MAE RMSE and SMAPE)Supplementary 12 Table 2 6xlsx data for testing the neural-fuzzy ship collision prevention system generated by sub-clustering with 100 training intervals using the hybrid opti-mizationmethodwith parameters Range of Influence SquashFactor Accept Ratio and Reject Ratio equal to 03 1 04and 03 respectively with the necessary quality assessmentcalculated (MAE RMSE and SMAPE)

References

[1] A Nyrkov K Goloskokov E Koroleva S Sokolov AZhilenkov and S Chernyi ldquoMathematical models for solvingproblems of reliability maritime systemrdquo Lecture Notes inElectrical Engineering vol 442 pp 387ndash394 2018

[2] M-C Tsou ldquoMulti-target collision avoidance route planningunder an ECDIS frameworkrdquo Ocean Engineering vol 121 pp268ndash278 2016

[3] J He and M Feng ldquoBased on ECDIS and AIS ship collisionavoidance warning system researchrdquo in Proceedings of the 8thInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo15) pp 242ndash245 June 2015

[4] Y Xue B S Lee and D Han ldquoAutomatic collision avoidanceof shipsrdquo Proceedings of the Institution of Mechanical EngineersPart M Journal of Engineering for the Maritime Environmentvol 223 no 1 pp 33ndash46 2015

[5] M Hanninen ldquoBayesian networks for maritime traffic accidentprevention benefits and challengesrdquo Accident Analysis amp Pre-vention vol 73 pp 305ndash312 2014

[6] A A Yefremov ldquoNew operations on fuzzy numbers and inter-valsrdquo in Proceedings of the International Conference on Mechan-ical Engineering Automation and Control Systems (MEACS rsquo14)pp 1ndash4 Tomsk Russia October 2014

[7] Z Pietrzykowski J Magaj P Wołejsza and J Chomski ldquoFuzzylogic in the navigational decision support process onboard asea-going vesselrdquo Artificial Intelligence and Soft Computing vol6113 no 1 pp 185ndash193 2010

[8] C-M Su K-Y Chang and -Y Cheng ldquoFuzzy decision onoptimal collision avoidance measures for ships in vessel trafficservicerdquo Journal of Marine Science and Technology vol 20 no1 pp 38ndash48 2012

[9] N A Sedova V A Sedov and R I Bazhenov ldquoAnalysis ofemergency level at sea using fuzzy logic approachesrdquo Advancesin Artificial Systems for Medicine and Education AIMEE 2017Advances in Intelligent Systems andComputing vol 658 pp 314ndash322 2018

[10] V A Sedov N A Sedova and S V Glushkov ldquoThe fuzzy modelof ships collision risk rating in a heavy traffic zonerdquo in Proceed-ings of the 22nd International Conference on Vibroengineeringvol 8 pp 453ndash458 October 2016

[11] E E Luneva P I Banokin and A A Yefremov ldquoEvaluationof social network user sentiments based on fuzzy setsrdquo inProceedings of the IOP Conference Series Materials Science andEngineering 21st International Conference for Students andYoungScientists pp 012ndash054 2015


[12] I V Chernova S A Sumin M V Bobyr and S P SereginldquoForecasting and diagnosing cardiovascular disease based oninverse fuzzy modelsrdquo Biomedical Engineering Online vol 49no 5 pp 263ndash267 2016

[13] M V Bobyr V S Titov and A A Nasser ldquoAutomation ofthe cutting-speed control process based on soft fuzzy logiccomputingrdquo Journal of Machinery Manufacture and Reliabilityvol 44 no 7 pp 633ndash641 2015

[14] A V Kryukov S K Kargapolrsquocev Y N Bulatov O N Skrypnikand B F Kuznetsov ldquoIntelligent control of the regulatorsadjustment of the distributed generation installationrdquo Far EastJournal of Electronics and Communications vol 17 no 5 pp1127ndash1140 2017

[15] M L Sokolova and V G Chernov ldquoThe logistics managementa transportation system rsquopoint of departure point of destinationrsquoin real time regimerdquo The Progressive Researches Science ampGenesis vol 1 pp 147ndash149 2014

[16] A Khayati and S Mirghasemi ldquoA new neural network forsea target detectionrdquo in Proceedings of the 24th CanadianConference on Electrical andComputer Engineering (CCECE rsquo11)pp 33ndash37 May 2011

[17] R Ressel A Frost and S Lehner ldquoNavigation assistance forice-infested waters through automatic iceberg detection andice classification based on TerraSAR-X imageryrdquo in Proceedingsof the 36th International Symposium on Remote Sensing ofEnvironment International Archives of the PhotogrammetryRemote Sensing and Spatial Information Sciences vol 47 no 7pp 1049ndash1056 May 2015

[18] K Czaplewski and M Waz ldquoImprovement in accuracy ofdetermining a vesselrsquos position with the use of neural networksana robustM-estimationrdquo Polish Maritime Research vol 24 no1 pp 22ndash31 2017

[19] L P Perera and C G Soares ldquoLaser Measurement Systembased maneuvering Target tracking formulated by AdaptiveCompetitive Neural Networksrdquo in Proceedings of the SecondInternational Conference on Adaptive and Self-Adaptive Systemsand Applications pp 84ndash90 2010

[20] S Chernyi and A Zhilenkov ldquoModeling of complex structuresfor the shiprsquos power complex using xilinx systemrdquoTransport andTelecommunication Journal vol 16 no 1 pp 73ndash82 2015

[21] N Anatoliy S Chernyi A Zhilenkov and S Sokolov ldquoTheuse of fuzzy neural structures to increase the reliability ofdrilling platformsrdquo in Proceedings of the 26th DAAAM Interna-tional Symposium on Intelligent Manufacturing and Automation(DAAAM rsquo15) pp 672ndash677 October 2015

[22] N V Andrievskaya I I Bezukladnikov and N RMubarakzyanov ldquoIdentification of parametres of nonlinearmodel of a hydro-mechanical systemrdquo in Proceedings of the 19thInternational Conference on Soft Computing and Measurements(SCM rsquo16) pp 145ndash147 May 2016

[23] M Imani R-J You and C-Y Kuo ldquoCaspian Sea level pre-diction using satellite altimetry by artificial neural networksrdquoInternational Journal of Environmental Science and Technologyvol 11 no 4 pp 1035ndash1042 2014

[24] J-C Yin Z-J Zou and F Xu ldquoOn-line prediction of shiproll motion during maneuvering using sequential learning RBFneuralnetworksrdquo Ocean Engineering vol 61 pp 139ndash147 2013

[25] J Lisowski ldquoComputational intelligence methods of a safe shipcontrolrdquo in Proceedings of the Knowledge-Based and IntelligentInformation amp Engineering Systems 18th Annual Conference(KES rsquo14) pp 634ndash643 Procedia Computer Science 2014

[26] A F Antipin ldquoImproving response time of real time control sys-tems based on multidimensional interval-logical controllersrdquoAutomation and Remote Control vol 76 no 3 pp 480ndash4862015

[27] A F Antipin ldquoA computer-aided system for designing multidi-mensional logic controllers with variables representing a set ofbinary logic argumentsrdquo Automation and Remote Control vol74 no 9 pp 1573ndash1581 2013

[28] F Garcıa-Cordova and A Guerrero-Gonzalez ldquoIntelligent nav-igation for a solar powered unmanned underwater vehiclerdquoInternational Journal of Advanced Robotic Systems vol 10 no4 pp 185ndash198 2013

[29] Th Koester N Hyll and J Stage ldquoDistributed Cognition inShip Navigation and Prevention of Collisionrdquo in Proceedingsof the European Conference on Cognitive Ergonomics DesigningBeyond the Product - Understanding Activity and User Experi-ence in Ubiquitous Environments (VTT Symposia rsquo09) vol 258p 202 2009

[30] P T Pedersen ldquoReview and application of ship collision andgrounding analysis proceduresrdquo Marine Structures vol 23 no3 pp 241ndash262 2010

[31] H Karahalios ldquoThe contribution of risk management in shipmanagement the case of ship collisionrdquo Safety Science vol 63pp 104ndash114 2014

[32] C Huang S Hu F Kong and Y Xi ldquoPre-warning system anal-ysis on dynamic risk of ship collision with bridge at restrictedwatersrdquo in Proceedings of the 4th International Conference onTransportation Information and Safety (ICTIS rsquo17) pp 698ndash703August 2017

[33] E Akyuz ldquoA marine accident analysing model to evaluatepotential operational causes in cargo shipsrdquo Safety Science vol92 pp 17ndash25 2017

[34] A A Lentarev and N G Levchenko ldquoPerspectives of usingintelligent control systems for managing north searouterdquoMarine Intellectual Technologies vol 1 no 3 pp 339ndash343 2016

[35] N A Sedova ldquoA logical-linguistic model of ship collisionavoidance in a heavy traffic zonerdquo in Proceedings of the 21st SaintPetersburg International Conference on Integrated NavigationSystems (ICINS rsquo14) pp 166ndash170 May 2014

[36] V P Kolosov N S Bezrukov D Y Naumov Y M Perel-man and A G Prikhodko ldquoPrediction of osmotic airwayhyperresponsiveness in patients with bronchial asthma usingadaptive neuro-fuzzy networkrdquo in Proceedings of the Interna-tional Conference on Biomedical Engineering andComputationalTechnologies (SIBIRCON rsquo15) pp 130ndash133 October 2015

[37] E Lavrov N Pasko A Krivodub and A Tolbatov ldquoMathe-matical models for the distribution of functions between theoperators of the computer-integrated flexible manufacturingsystemsrdquo in Proceedings of the 13th International Conferenceon Modern Problems of Radio Engineering Telecommunicationsand Computer Science (TCSET rsquo16) pp 72ndash75 February 2016

[38] K Ramesh A P Kesarkar J Bhate M Venkat Ratnam and AJayaraman ldquoAdaptive neuro fuzzy inference system for profilingof the atmosphererdquo Atmospheric Measurement Techniques Dis-cussions vol 7 no 3 pp 2715ndash2736 2014

Computer Games Technology

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Hindawiwwwhindawicom Volume 2018

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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom


ANFIS (Sugeno)

Ship-operatorrsquos routeBearing

Ship-purposersquos route

Target shiprsquos speed

Changing ship-operatorrsquos route

Figure 1 Neural-fuzzy ship collision prevention in a heavy traffic zone

Neural networks are also proved to be successful inwarning [20 21] A number of surveys are worth notingin the supplement to navigation practice In particular themethodology of a short-term forecast of the Caspian Sealevel by means of a perceptron-type neural network [22] isdeveloped in the paper [23]The paper [24] deals with onlineforecast of the maneuvering vessel turn a neural networkmodel RBF having amutating nature and the ability to adjustnetwork features by the sliding window method The authorsdesigned a predictive model which was marked by a leanerstructure fast processing and a high degree of measurementaccuracy

As the use of neural nets has clear benefits [22] itis potentially capable of improving the projection of shipcollision risks In addition significant headway had beenmade against it For example the paper [25] comments on themethodology and strategy of ship collision avoidance usingartificial neural networks optimal control theory methods[26 27] and a game theory The paper [28] also mentions anautonomous navigation system for a robotic submarine basedon an adaptive neurocontroller

Several papers [29ndash34] should also be noted in theconnection with developing approaches to prevent shipcollisions

In order to improve the effects of a fuzzy system [35] theauthors carried out hybridization involving the elements ofartificial neural networks theory which resulted in designinga neural-fuzzy network [36 37] In turn a neural-fuzzy shipcollision prevention system is based on it This paper submitsthe results of simulating modelling

2 Materials and Methods

The neural-fuzzy ship collision prevention system in a heavytraffic zone is an adaptive neural-fuzzy inference system(ANFIS) [22 36 37] consisting of 5 layers This kind ofsystem is defined as a multilayer feedforward neural networkwithout any feedback Its features are those of fuzzy logicinference But an algorithm for making a decision of the neu-ral network is a fuzzy logic inference algorithmANFISmodelused for the neural-fuzzy ship collision prevention system ina heavy traffic zone development is based on TakagindashSugenofuzzy inference system which is highly interpretable andefficient in connection with computing

The first layer of ANFIS is a layer of membership func-tions There is a fuzzification in the first layer ie fuzzy setsare established corresponding to the terms of source (input)and target (output) linguistic variables

The neural-fuzzy ship collision prevention system in aheavy traffic zone observed in the paper (Figure 1) includesfour input linguistic variables

(i) Electronic bearing on the target ship ie on that oneto which the operator vessel needs to prevent collision safely

(ii) The ship-operator course(iii) The target-ship course ie a vessel in a heavy traffic

zone to which if necessary it is required to prevent collision(iv) The target-vessel speed [35] as well as the only

output linguistic variable which is the value of the operator-vessel course change calculated on the maneuvering board inadvance with the output value corresponding to the interval[-60∘ 360∘] where the value of -60∘ corresponds to the termldquomuch to the leftrdquo the value to -30∘ corresponds to the termldquoto the leftrdquo the value 0∘ corresponds to the term ldquokeep itsteadyrdquo (neither the course nor the speed of the operator-vessel changes) 60∘ stands for the term ldquomuch to the rightrdquothe value of 30∘ means the term ldquoto the rightrdquo and the valueof 360∘ implies the maneuver (AmE) or manoeuvre (BrE) ofcirculation (that is the term ldquocirculationrdquo)

The set of values for the inputs ldquobearingrdquo ldquothe ship-operator courserdquo and ldquovessel-target courserdquo is the set [0360]∘ The range of values for the ship-target speed source isdetermined according to the information from the reviewingfeedback of The Russian Maritime Register of Shipping (RS)[0 34] knots

The number of nodes performed in the first layer is equalto the sum of the term powers of the input linguistic variablesetsThe output values focused in the first layer are the valuesof membership functions with specific values of the inputvariables The features of membership functions in the firstlayer compose the first group of features that are to be setduring the learning process

The second layer of ANFIS is a layer of fuzzy productionrulesThe number of nodes is the same as the number of rulesin the second layerMoreover eachnode is connected to thoseones in the first layer that form the premises (antecedents)of the corresponding rule In general the distribution of thelinks between the first and second layers is performed in sucha way that each input variable of the neural-fuzzy network isassociated with each neuron of the rule layer

The output values in the second layer correspond to therelative degrees (weights) of the rules which are calculated asa logical product (intersection) of membership functions ofthe input variables

The third layer of ANFIS is a layer of absolute valuein which the output values of this layer are determinedby adding the outputs of all nodes of the rule layer anddividing each of the output values in the second layer by thistotal value This ensures scaling of the output values so thatincreases the neural-fuzzy network resilience

The fourth layer of ANFIS is the output layer of the linearcombination Each node of the fourth layer is connected to

















0

180

270 90

2 nmi 4 nmi8 nmi

60

30330

300

240

210 150

120















119872119860119864 = 1119873 sdot119873sum119894=1

10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816 (1)





0000E+001000E-052000E-053000E-054000E-055000E-056000E-057000E-05

psigmf (500)

psigmf (600)

dsigmf (600)

dsigmf (400)

psigmf (400)

pimf (600)


MAERMSESMAPE



119877119872119878119864 = radic 1119873 sdot119873sum119894=1

(119862119862119874119878119894minus 119862119862119874119878

119894)2 (2)


119878119872119860119875119864 = sum119873119894=1 (10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816)sum119873119894=1(10038161003816100381610038161003816119862119862119874119878119894 + 11986211986211987411987811989410038161003816100381610038161003816) (3)










000E+00500E-02100E-01150E-01200E-01250E-01300E-01350E-01400E-01



Ratio 0


015



RMSEMAESMAPE






000E+00200E-04400E-04600E-04800E-04100E-03120E-03140E-03



015




RMSEMAESMAPE










4 Conclusions








Data Availability














References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




















0

180

270 90

2 nmi 4 nmi8 nmi

60

30330

300

240

210 150

120















119872119860119864 = 1119873 sdot119873sum119894=1

10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816 (1)





0000E+001000E-052000E-053000E-054000E-055000E-056000E-057000E-05

psigmf (500)

psigmf (600)

dsigmf (600)

dsigmf (400)

psigmf (400)

pimf (600)


MAERMSESMAPE



119877119872119878119864 = radic 1119873 sdot119873sum119894=1

(119862119862119874119878119894minus 119862119862119874119878

119894)2 (2)


119878119872119860119875119864 = sum119873119894=1 (10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816)sum119873119894=1(10038161003816100381610038161003816119862119862119874119878119894 + 11986211986211987411987811989410038161003816100381610038161003816) (3)










000E+00500E-02100E-01150E-01200E-01250E-01300E-01350E-01400E-01



Ratio 0


015



RMSEMAESMAPE






000E+00200E-04400E-04600E-04800E-04100E-03120E-03140E-03



015




RMSEMAESMAPE










4 Conclusions








Data Availability














References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in











119872119860119864 = 1119873 sdot119873sum119894=1

10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816 (1)





0000E+001000E-052000E-053000E-054000E-055000E-056000E-057000E-05

psigmf (500)

psigmf (600)

dsigmf (600)

dsigmf (400)

psigmf (400)

pimf (600)


MAERMSESMAPE



119877119872119878119864 = radic 1119873 sdot119873sum119894=1

(119862119862119874119878119894minus 119862119862119874119878

119894)2 (2)


119878119872119860119875119864 = sum119873119894=1 (10038161003816100381610038161003816119862119862119874119878119894 minus 11986211986211987411987811989410038161003816100381610038161003816)sum119873119894=1(10038161003816100381610038161003816119862119862119874119878119894 + 11986211986211987411987811989410038161003816100381610038161003816) (3)










000E+00500E-02100E-01150E-01200E-01250E-01300E-01350E-01400E-01



Ratio 0


015



RMSEMAESMAPE






000E+00200E-04400E-04600E-04800E-04100E-03120E-03140E-03



015




RMSEMAESMAPE










4 Conclusions








Data Availability














References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








000E+00500E-02100E-01150E-01200E-01250E-01300E-01350E-01400E-01



Ratio 0


015



RMSEMAESMAPE






000E+00200E-04400E-04600E-04800E-04100E-03120E-03140E-03



015




RMSEMAESMAPE










4 Conclusions








Data Availability














References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









4 Conclusions








Data Availability














References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in












References













































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




the neural-fuzzy approach as a way of preventing a...

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