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Наука та прогрес транспорту. Вюник Дншропетровського нацюнального унiверситету залiзничного транспорту, 2019, № 2(80)
ШФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
UDC 004.7.032.26:656.222.3
V. M. PAKHOMOVA1*, T. I. SKABALLANOVICH2*, V. S. BONDAREVA3*
'*Dep. «Electronic Computing Machines», Dnipro National University of Railway Transport named after Academician V. La-zaryan, Lazaryan St., 2, 49010, Dnipro, Ukraine, tel. +38 (056) 373 15 89, e-mail viknikpakh@gmail.com, ORCID 0000-0002-0022-099X
2*Dep. «Electronic Computing Machines», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, 49010, Dnipro, Ukraine, tel. +38 (056) 373 15 89, e-mail sti19447@gmail.com, ORCID 0000-0001-9409-0139
3*Dep. «Electronic Computing Machines», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, 49010, Dnipro, Ukraine, tel. +38 (056) 373 15 89, e-mail bond290848@gmail.com, ORCID 0000-0002-4016-1656
INTELLIGENT ROUTING IN THE NETWORK OF INFORMATION AND TELECOMMUNICATION SYSTEM OF RAILWAY TRANSPORT
Purpose. At the present stage, the strategy of informatization of railway transport of Ukraine envisages the transition to a three-level management structure with the creation of a single information space, therefore one of the key tasks remains the organization of routing in the network of information and telecommunication system (ITS) of railway transport. In this regard, the purpose of the article is to develop a method for determining the routes in the network of information and telecommunication system of railway transport at the trunk level using neural network technology. Methodology. In order to determine the routes in the network of the information and telecommunication system of railway transport, which at present is working based on the technologies of the Ethernet family, one should create a neural model 21-1-45-21, to the input of which an array of delays on routers is supplied; as a result vector - build tags of communication channels to the routes. Findings. The optimal variant is the neural network of configuration 21-1-45-21 with a sigmoid activation function in a hidden layer and a linear activation function in the resulting layer, which is trained according to the Levenberg-Marquardt algorithm. The most quickly the neural network is being trained in the samples of different lengths, it is less susceptible to retraining, reaches the value of the mean square error of 0.2, and in the control sample determines the optimal path with a probability of 0.9, while the length of the training sample of 100 examples is sufficient. Originality. There were constructed the dependencies of mean square error and training time (number of epochs) of the neural network on the number of hidden neurons according to different learning algorithms: Levenberg-Marquardt; Bayesian Regularization; Scaled Conjugate Gradient on samples of different lengths. Practical value. The use of a multilayered neural model, to the entry of which the delay values of routers are supplied, will make it possible to determine the corresponding routes of transmission of control messages (minimum value graph) in the network of information and telecommunication system of railway transport at the trunk level in the real time.
Keywords: information and telecommunication system; ITS; router delay; neural network; NN; sample; activation function; learning algorithm; epoch; error
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЩИНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Introduction
Until recently, the work of the railway transport of Ukraine was the interaction of six railways, on each of which an appropriate information and telecommunication system (ITS) was implemented. The main focus of the development of ITS rail networks is the use of Ethernet (Ethernet, Fast Ethernet, Gigabit Ethernet) family technologies that provide a 10/100/1000 Mbps hierarchy and the use of the TCP/IP protocol stack [9]. The most important part of ITS of railway transport is the data transmission network, which is a three-level hierarchical structure and has the following levels: trunk, road, linear. The node of the data transmission network belongs to the trunk level, if it includes, besides the connections to the nodes of the data transmission network of a particular railway, a connection to the nodes of the data transmission network of other railways. Local enterprise networks belong to the linear level, all other nodes of the data network - to the road level.
To build a unified data transmission network of Ukrzaliznytsia, the network equipment of Cisco [13], which is an integrated software and hardware complex, was selected. One of the key tasks is the organization of routing in the railway transport ITS network. The current routing protocol (OSPF protocol) uses the search for the shortest path on the graph, the real-time implementation of which causes some difficulties, so it is advisable to find solutions to the routing problem using the methods of artificial intelligence [10, 13-20] and study them [1-4, 7]. For example, for the search of the shortest path on the route graph in the railway transport ITS, we analyzed the possibility of using the Hop-field network, ant colony and genetic methods [8], for the integrated network of ITS of railway transport, that in the prospect should work on different technologies, we defined the optimal route by the means of the software model «MLP34-2-410-34», the input of which is an array of bandwidth network channels [17]. In addition to the parameters studied (distance between routers, channel bandwidth) it is appropriate to conduct a study of other parameters, such as: service availability; line losses; router delays.
Purpose
To develop a routing methodology in the ITS network of rail transport at the trunk level using the neural network technology.
Methodology
Let us consider a fragment of a hypothetical network of railway transport ITS presented in Fig. 1.
Fig. 1. Graph of routers connections of hypothetical network of information and telecommunication system (ITS) of railway transport
Designations: C1 - Rivne; C2 - Lviv; C3 - Ternopil; C4 - Khmelnytskyi; C5 - Kyiv; C6 - Nizhyn; C7 - Poltava; C8 - Kharkiv; C9 - Sumy; C10 - Luhansk; C11 -Donetsk; C12 - Krasnoarmiisk; C13 - Chaplyne; C14 -Dnipro; C15 - Zaporizhzhia; C16 - Znamianka; C17 -Odesa; C18 - Izmail
The ITS network of rail transport may be represented as a weighted graph G (V, W), where V is the set of vertices of the graph whose number is equal to B (B = 18), with each vertex modeling a node (router) of the network; W is the set of edges of the graph, each edge simulates the relationship between the nodes, the number of graph edges is equal to M (M = 21).
Each edge of the graph is assigned with a certain weight tij. Since the channel transmission time is much smaller, it is expedient to use the router delay time when transmitting data from the i-th to j-th router of the ITS network of railway transport, as a weight, in ps.
It is necessary to determine the minimal spanning tree (MST) of the rail transport ITS network,
that is, to find such a graph G (V, W ), where V eVand W eW, in addition
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального ушверситету з&тзничного транспорту, 2019, N° 2(80)
1НФОРМАЦ1ИНО-КОМУН1КАЦ1ИН1 ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Z t, j ^ m^n. (1)
(i, j )eW'
The construction of MST is useful for distributing messages addressed to all nodes of the ITS network of rail transport at the trunk level, for example, the control messages from the main node (Kyiv), then the weight of the whole spanning tree is the cost of sending a message to all its nodes. It should also be noted that if all the weights of the graph edges are different then there is only one MST of the network.
Neural network as the main mathematical device for solving the problem. To determine the MST in the ITS network of rail transport, we used a two-layer neural network (NN), the input vector of which is a plurality of delays on routers and consists of 21 neurons, the resulting vector is build tags of communication channels to the routes, and also consists of 21 neurons. The corresponding NN structure is shown in Fig. 2.
Input layer Hidden layer Output layer
Fig. 2. Structure of the two-layer neural network (NN)
As an activation function of a hidden layer it is appropriate to use the sigmoidal function, which is presented in Fig. 3, a, in the resulting layer - a lin-
Fig. 3. Activation function graphs:
а - sigmoid; b - linear
Determination of the number of neurons in NN layers is performed using the following formula:
mN .N
—-~<Lw <m( + 1)(n + m +1) + m (2)
1 + log2 N m
where Lw - the number of synaptic weights; n -input signal dimension; m - output signal dimension; N - the number of sample elements.
In this case 210 < Lw < 4020 . Having estimated the required number of synaptic weights Lw, we calculate the required number of neurons in the hidden layer k according to the known formula:
k = . (3)
m + n
If you take Lw = 1900, then the number of neurons in the hidden layer will be 45.
The training of a multi-layered NN involves the use of the reverse error propagation algorithm. The training samples are used for learning. The basis of NM training is the minimization of some target function, which depends on the parameters of the neurons and infinity of training samples. As a minimizing target error function of a multilayer NN, the function of the following type is taken:
1 N H
E(w) =1 ZZGfl (k) " (k))2, (4)
2 k=1 j=1
where Gjl (k) - desired output of the y-th neuron of the /-th output layer for ¿-th sample of the Y-
reference set; -Jv ' - actual output of the j-th neuron of the l-th output layer when supplied to the k-th sample network input from the reference set.
Preparation of the general sample (preparatory stage). The formation of a general sample of NN was carried out for a fragment of a hypothetical network of railway ITS (see Fig. 1). Sample data are obtained on the corresponding simulation model of the ITS network of rail transport, created with assistance of the Master A. Piskun in modelling system OpNet Modeler [6] using Gigabit Ethernet technology under the following conditions: protocol - TCP; type of traffic - FTP; traffic intensity -600 MB/s; package length - 700 bytes; operation time of the network simulation model - 14 min. Learning vectors are formed in the form of tables
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального унiверситету залiзничного транспорту, 2019, N° 2(80)
1НФОРМАЦ1ИНО-КОМУН1КАЦ1ИН1 ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
using the Excel package in two files. In the first file «input.xml», the data submitted to the NN input, are presented in the form of 21 vectors; a fragment of contents of the file «input.xml» is shown in Fig. 4.
Fig. 4. Fragment of contents of the file «input.xml»
In the second file «target.xml», the data submitted to the NN output are also represented as 21 vectors; a fragment of contents of the «tar-get.xml» file is shown in Fig. 5.
A в :■ D E F ■г H 1 . К L M N О p Q R
tl.2 1 L L 1 1 L 1 1 L 1 1 L L 1 L L 1
1 О L 1 1 L 1 1 L О О О L О L L 1
V2JS 1 L L 1 1 L 1 1 L 1 1 L L 1 L L 1
t3.4 О L О О ii L О il О 1 1 L О 1 О О О
U.5 1 L L 1 1 О 1 1 L 1 1 L L 1 L L 1
Ofi 1 L L 1 О L 1 1 L 1 1 О L 1 L L О
ti.B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
tS.ll. 1 L L 1 1 L 1 1 L 1 1 L L 1 L L 1
Î5-.14 1 L L 1 1 L 1 1 L 1 1 L L 1 L L 1
t5-.1T 1 L L 1 1 L 1 1 L 1 1 L L 1 L L 1
Щ.7 о О О О 1 О О il 1 о о 1 О О О О 1
ал 1 L L 1 1 L 1 1 О 1 1 L L 1 L L 1
i\ Neural Fitting (nftool)
Validation arid Test Data
Set aside some samples for validation and testing.
Select Percentages
Randomly divide up the 72 samples:
9 Training: 70%
9 Validation: 15% -
® Testing: 15% -
50 samples 11 samples 11 samples
Fig. 6. Data validation and testing window
Fig. 7. Setting the hidden neurons
Fig. 5. Fragment of contents of the file «target.xml»
Creating a neural network. Neural Network Toolbox for the MatLab environment was chosen as a neural package to solve the problem of routing the rail transport ITS network. Using Import Data on the Matlab toolbar, the data were imported from the created Excel-table. Training, testing and analysis of NN work are carried out on appropriate samples (Training, Testing and Validation), whose percentage from the general sample is shown in Fig. 6.
The «Network Architecture» window provides the required number of hidden neurons (Figure 7).
Fig. 8 shows the structure of the created neural network.
Fig. 8. Structure of the created NN
Teaching and testing of neural network. In the Train Network window, one of the three proposed learning algorithms for the NN (LevenbergMarquardt, Bayesian Regularization, and Scaled Conjugate Gradient) is selected. For example, learning of the 21-1-45-21 configuration NN by the Levenberg-Marquardt algorithm took place during 11 epochs, the time spent was 26 s (Fig. 9).
I_I
Algorithms
Data Division: Random (dividerand)
Training: Levenberg-Marquardt (trainlm)
Performance: Mean Squared Error nse
Calculations: MEX
Progress
Epoch: 0 II 11 iterations ]] 1000
Time; 1 0:00:26
Performance: 133 m 0.775 ]] 0,00
Gradient: 0381 1 0,102 ]] 1,00 e-07
Mu: 0.00100 1 10.0 ]] l,00e-bl0
Validation Checks: 0 1_ 6 J] 6
Fig. 9. Characteristics of the NN training
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Mean Squared Error (MSE) is the mean square deviation between output and target; the lower the value, the better; zero means no error. The value of regression R means the correlation between output and target. If R = 1, this means close correlation, zero is a random relationship. The MSE values of training, validation and testing of the neural network made 0.204, 0.186 and 0.183, respectively; R has a value of 0.38, 0.43 and 0.44, respectively (Fig. 10).
Results
j Training: 9 Validation: Testing:
"¡r Samples El MSE g)R
50 2,04886e-l 3.89591e-l
11 1,86199e-1 439712e-l
11 Ш325е-1 4,40943e-l
Fig. 10 Results of the NN 21-1-45-21
Regression diagrams and error histograms of the 21-1-45-21 configuration NN by the Levenberg-Marquardt algorithm are presented in Fig. 11.
Edit View Insert Tools Desktop Windm
Training: R=0.38959
Validation: R=0.43971
' Neural Network training Error Histogram Iploterrfrist), Epoch 4, 'Mairimum ML t.,. L
File Edit View Insert Tools Desktop Window Help
Error Histogram with 2D Bins
800 700 600
I
j 500 ] 400 300 200 100
...ll
|Training I Validation I Test Zero Error
lil.l.
a ........
»tr'Ji-^KßrJ^'iOr^lftNO 1 1 >6 ddd'-iddddd
in m m л in л
Errors = Targets ■ Outputs
Fig. 11. Graphical presentation of results of NN 21-1-45-21: a - regression diagrams; 6 - error histogram
b
a
Findings
Analysis of the neural network operation. Based on the results obtained on the 21-1-45-21 configuration NN, the MST of the ITS network of railway transport was built and presented in Fig. 12 (the bold line shows the route for sending control messages from Kyiv).
According to the Kruskal algorithm [5] (without using NN), the MST of the ITS network of railway transport was built, as shown in Fig. 13.
As can be seen from Fig. 12-13, the results coincided, that is, the NN of configuration 21-1-4521 works correctly. Ten launches were conducted
on this NN, the data obtained are summarized in Table 1.
From the table it is clear that the probability of building the MST of the ITS network of rail transport is 0.9 (experiments No. 1-2, 4-10), herewith in experiment No. 7 another MST was obtained (different edges had the same value of weight), but the solution is correct (Fig. 14), but in experiment No. 3, the solution provided by the NN is, unfortunately, incorrect (gap in the route: separation of C1-C2-C3 fragment from C5, which is the source of sending control messages), Fig. 15.
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУНЖАЩЙШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Fig. 13. MST the ITS network, built by the Kruskal algorithm Designations: edge weights - delays on ITS network routers, ps
Наука та прогрес транспорту. Вюник Дншропетровського нащонального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЩИШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Table 1
Analysis of operation of 21-1-45-21configuration NN
Edge weigh Organization of experiments on NN
1 2 3 4 5 6 7 8 9 10
t x y x y x y x y x y x y x y x y x y x y
'1,2 1 828 1 1 859 1 1 895 1 2 549 1 2 549 1 1 686 1 2 674 1 2 674 1 2 674 1 2 070 1
'2,3 1 776 1 2 502 1 1 810 1 1 603 1 1 630 1 2 716 1 1 660 1 1 678 1 1 768 1 1 809 1
'2,5 2 125 1 2 162 1 2 549 1 1 568 1 2 822 1 1 621 1 1 596 1 1 613 1 1 700 1 1 740 1
'3,4 2 460 1 806 2 598 2 197 2 234 2 309 2 273 0 2 298 2 422 2 479
'4,5 1 527 1 1 553 1 1 582 1 2 437 1 2 478 1 2 561 1 2 521 1 2 548 1 2 685 1 2 748 1
'5,6 1 493 1 1 518 1 1 547 1 2 148 1 2 184 1 2 257 1 2 222 1 2 246 1 2 366 1 2 422 1
'5,8 2 092 1 2 127 1 2 168 1 2 321 1 2 360 1 2 440 1 2 402 1 2 428 1 2 558 1 2 618 1
'5,11 2 320 1 2 359 1 2 405 1 2 775 1 1 595 1 2 918 1 2 872 1 2 904 1 1 861 1 3 059 1
'5,14 2 045 1 2 080 1 2 119 1 1 688 1 1 717 1 1 775 1 1 747 1 1 766 1 3 059 1 1 905 1
'5,17 2 210 1 2 247 1 2 290 1 1 793 1 1 823 1 1 885 1 1 855 1 1 875 1 1 976 1 2 022 1
'6,7 2 642 2 687 2 738 2 108 2 145 2 217 2 183 0 2 207 2 325 2 379
'7,8 1 607 1 1 635 1 1 666 1 2 029 1 2 063 1 2 132 1 2 099 1 2 856 1 2 237 1 2 289 1
'8,9 1 707 1 1 736 1 1 769 1 1 723 1 1 752 1 2 870 1 2 825 1 2 122 1 3 010 1 3 080 1
'10,11 2 007 1 2 041 1 2 080 1 2 731 1 2 777 1 1 811 1 1 783 1 1 802 1 1 899 1 1 943 1
'11,12 1 932 1 1 965 1 2 002 1 1 667 1 1 695 1 1 752 1 2 749 1 1 744 1 1 837 1 1 880 1
'12,13 2 600 2 645 2 695 2 656 2 701 2 792 1 725 0 2 779 2 929 2 255
'13,14 1 640 1 1 668 1 1 700 1 2 000 1 2 034 1 2 102 1 2 069 1 2 091 1 2 204 1 2 997 1
'14,15 1 586 1 1 613 1 1 645 1 1 910 1 1 942 1 2 007 1 1 976 0 1 997 1 2 104 1 2 154 1
'15,16 2 528 2 571 1 974 1 2 549 2 549 1 686 2 692 1 2 564 2 642 2 070
'16,17 1 905 1 1 937 1 2 620 0 1 628 1 1 647 1 2 756 1 1 658 1 1 678 1 1 771 1 1 816 1
'17,18 1 818 1 1 849 1 1 885 1 1 583 1 2 872 1 1 692 1 1 596 1 1 627 1 1 707 1 1 756 1
MAS I + Correct solut ncorrect solut + on ion + + + + + + + +
Note: Delay values on routers in the ITS network of rail transport are given in ^s
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
eis
Fig. 14. MST of the ITS network built on the basis of NN (experiment No. 7) Designations: edge weights - delays on ITS network routers, ^s
CIS
Fig. 15. Incorrect solution obtained on NN (experiment No. 3) Designations: edge weights - delays on ITS network routers, ^s
Originality and practical value
Study of the error and time of NN training on the number of hidden neurons by different learning algorithms. Experiments were performed on the NN of 21-1-X-21 configuration with a sigmoidal activation function in the hidden layer and a linear
activation function in the output layer at 10, 45 and 90 hidden neurons using the following algorithms: Levenberg-Marquardt; Bayesian Regularization; Scaled Conjugate Gradient. The results obtained are summarized in Table 2.
ЩФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Error and time of NN training on the number of hidden neurons
Number of hidden neurons
Levenberg-Marquardt
MSE
Number of epochs
Bayesian Regularization
MSE
Number of epochs
Scaled Conjuga
MSE
10 45 90
The depenc
0.775 0.204 0.991
2 11
29
0.392 0.870 1.270
0.00770 0.00015 0.00004
ence of error and time of NN train- learning algorithms is presented in Fig
ing on the number of hidden neurons by different
Fig. 16. MSE and NN training time versus the number of hidden neurons
Designations:
■ Levenber^-Marquandt ■ Bayesian Regularization ■ 5 cal e c Co rj Lg ate G ra c i e rt
From Fig.16 it can be seen that with the increased number of neurons in the hidden layer, the time of training for the 21-1-X-21 configuration NN increases, with 45 neurons in the hidden layer being optimal by the Levenberg-Marquardt algorithm.
Study of the error and time of training NN on the length of the training sample by the LevenbergMarquardt algorithm. Experiments were performed on the 21-1-45-21 configuration NN with a sigmoid activation function in the hidden layer and a linear activation function in the output layer, while the length of the training sample was 50, 100 and 152 examples. Dependence of the error and time of training of the NN on the length of the
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Table 2
ate Gradient
Number of epochs
125
154
302
. 16
90
training sample is presented in Fig. 17. The Figure shows that the increased length of the training sample results in decrease in the root mean square error, while the training time of NN increases rapidly, but the use of the sample with 100 examples for the NN training is sufficient.
The use of a multilayered neural model, to the entry of which the delay values of routers are supplied, will make it possible to determine the corresponding routes of transmission of control messages from Kyiv (minimum value graph) in the ITS network of railway transport at the trunk level in the real time.
Наука та прогрес транспорту. Вюник Дншропетровського нащонального ушверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЩИШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
Fig. 17. MSE and NN training time versus the training sample length
Conclusions
1. To determine routes for sending the control messages in the ITS network (at the trunk level) of railway transport using the Neural Network Toolbox of the Matlab environment the neural network of configuration 21-1-45-21 is created, to the input of which an array of delays on the routers is supplied; as a result vector - build tags of communication channels to the routes.
2. The neural network of configuration 21-1-45-21 with a sigmoidal activation function in the hidden layer and a linear function in the resulting layer under the learning algorithm of Levenberg-Marquardt for 11 epochs gives the MSE value of 0.204, 0.186 and 0.183 in the training, validation and testing samples, respectively. The result given by the neural network coincides with the graph obtained by the Kruskal algorithm. In addition, 10 experiments on the neural network were
conducted: the correct result is achieved with a probability of 0.9.
3. On the 21-1-X-21 neural network, a study was made of the mean square error and time of training on the number of hidden neurons (10, 45 and 90) under different learning algorithms: Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient. It is determined that the optimal variant is the configuration 21-1-45-21 by the Levenberg-Marquardt algorithm.
4. On the 21-1-45-21configuration neural network, there was conducted the study of the mean square error and the time of training depending on the length of the training sample: 50, 100 and 152 examples using the Levenberg-Marquardt algorithm. It is determined that the increased length of the training sample results in decrease in the root mean square error, while the training time of the neural network increases rapidly, but the use of the sample with 100 examples for its training is sufficient.
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doi: 10.15802/stp2019/166092 © V. M. Pakhomova, T. I. Skaballanovich, V. S. Bondareva, 2019
Наука та прогрес транспорту. Вюник Дншропетровського нащонального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЩЙШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
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6. Никитченко, В. В. Утилиты моделирующей системы Opnet Modeler / В. В. Никитченко. - Одесса : Одес. нац. акад. связи им. А. С. Попова, 2010. - 128 с.
7. Павленко, М. А. Анализ возможностей искусственных нейронных сетей для решения задач однопуте-вой маршрутизации в ТКС [Electronic resource] / М. А. Павленко // Проблеми телекомушкацш. - 2011.
- № 2 (4). - Available at: http://pt.journal.kh.ua/index/0-139 - Title from the screen. - Accepted : 20.11.2018.
8. Пахомова, В. М. Аналiз методiв з природними мехашзмами визначення оптимального маршруту в комп'ютернш мереж Придшпровсько! залiзницi / В. М. Пахомова, Р. О. Лепеха // Iнформ.-керуючi системи на залiзн. трансп. - 2014. - № 4. - С. 82-91.
9. Пахомова, В. М. Дослщження шформацшно-телекомушкацшно! системи залiзничного транспорту з використанням штучного штелекту : монографiя / В. М. Пахомова. - Дшпро : Стандарт-Сервю, 2018.
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10. Погорiлий, С. Д. Генетичний алгоритм розв'язання задачi маршрутизаци в мережах / С. Д. Погорiлий, Р. В. Бшоус // Проблеми програмування. - 2010. - № 2-3. - С. 171-178.
11. Реалiзацiя задачi вибору оптимального авiамаршруту нейронною мережею Хопфвда / А. М. Бриндас, П. I. Рожак, Н. О. Семенишин, Р. Р. Курка // Наук. вюн. НЛТУ Украши : зб. наук.-техн. пр. - Львiв, 2016. - Вип. 26.1. - С. 357-363.
12. CiscoTips [Electronic resource] : [веб-сайт]. - Електрон. текст. дат. - Available at: http://ciscotips.ru/ospf -Title from the screen. - Accepted : 20.05.2018.
13. Dorigo, M. Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem / M. Dorigo, L. M. Gambardella // IEEE Trans. on Evolutionary Compytation. - 1997. - Vol. 1. - Iss. 1. -Р. 53-66. doi: 10.1109/4235.585892
14. Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities / J. J. Hopfield // Proceedings of National Academy of Sciences. - 1982. - Vol. 79. - Iss. 8. - P. 2554-2558. doi: 10.1073/pnas.79.8.2554
15. Neural Network Based Near-Optimal Routing Algorihm / Chang Wook Ahn, R. S. Ramakrishna, In Chan Choi, Chung Gu Kang // Neural Information Processing - IC0NIP'02 : Proc. of the 9th Intern. Conf. (18-22 Nov. 2002). - Singapore, 2002. - P. 1771-1776.
16. New algorithm for packet routing in mobile ad-hoc networks / N. S. Kojic, M. B. ZajeganoviC-Ivancic, I. S. Reljin, B. D. Reljin // Journal of Automatic Control. - 2010. - Vol. 20. - Iss. 1. - P. 9-16. doi: 10.2298/JAC1001009K
17. Pakhomova, V. M. Optimal route definition in the network based on the multilayer neural model /
V. M. Pakhomova, I. D. Tsykalo // Наука та прогрес транспорту. - 2018. - № 6 (78). - P. 126-142. doi: 10.15802/stp2018/154443
18. Schuler, W. H. A novel hybrid training method for hopfield neural networks applied to routing in communications networks / W. H. Schuler, C. J. A. Bastos-Filho, A. L. I. Oliveira // International Journal of Hybrid Intelligent Systems. - 2009. - Vol. 6. - Iss. 1. - P. 27-39. doi: 10.3233/his-2009-0074
19. Towards QoS-aware routing for DASH utilizing MPTCP over SDN / K. Herguner, R. S. Kalan, C. Cetinkaya, M. Sayit // IEEE Conference on Network Function Virtualization and Software Defined Networks (NFV-SDN) (6-8 Nov. 2017). - Berlin, Germany, 2017. - P. 1-6. doi: 10.1109/nfv-sdn.2017.8169844
20. Zhukovyts'kyy, I. Research of Token Ring network options in automation system of marshalling yard / I. Zhukovyts'kyy, V. Pakhomova // Transport Problems. - 2018. - Vol. 13. - Iss. 2. - P. 145-154. doi: 10.20858/tp.2018.13.2.14
Наука та прогрес транспорту. Вюник Дншропетровського нащонального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУНЖАЩЙШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
В. М. ПАХОМОВА1*, Т. I. СКАБАЛЛАНОВИЧ2*, В. С. БОНДАРЕВА3*
'*Каф. «Електронн! обчислювальш машини», Дншровський нацюнальний унiверситет залiзничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна, 2, Дншро, Украша, 49010, тел. +38 (056) 373 15 89, ел. пошта viknikpakh@gmail.com, ORCID 0000-0002-0022-099X
2*Каф. «Електронн! обчислювальш машини», Дншровський нацiональний уншерситет залiзничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна, 2, Дншро, Украша, 49010, тел. +38 (056) 373 15 89, ел. пошта sti19447@gmail.com, ORCID 0000-0001-9409-0139
3*Каф. «Електронн! обчислювальш машини», Дншровський нацiональний уншерситет залiзничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна, 2, Дшпро, Украша, 49010, тел. +38 (056) 373 15 89, ел. пошта bond290848@gmail.com, ORCID 0000-0002-4016-1656
1НТЕЛЕКТУАЛЬНИЙ П1ДХ1Д ДО ВИЗНАЧЕННЯ МАРШРУТ1В У МЕРЕЖ1 ШФОРМАЦШНО-ТЕЛЕКОМУШКАЦШНО! СИСТЕМИ ЗАЛ1ЗНИЧНОГО ТРАНСПОРТУ
Мета. На сучасному етапi стратегiя iнформатизацii' залiзничного транспорту Укра!ни передбачае перех1д на трирiвневу структуру керування зi створенням единого шформацшного простору, тому одшею iз ключо-вих задач залишаеться оргашзашя маршрутизацй' в мережi шформацшно-телекомушкацшно! системи (1ТС). У зв'язку з цим метою статп е розроблення методики визначення маршрутiв у мережi шформацшно-телекомушкацшно! системи залiзничного транспорту на мапстральному рiвнi з використанням нейромере-жноi' технологи. Методика. Для визначення маршрупв у мереж! шформацшно-телекомушкацшно! системи залiзничного транспорту, що на сучасному етат працюе за технологиями родини Ethernet, створено нейронну модель 21-1-45-21, на вхвд яко! подають масив затримок на маршрутизаторах. За результуючий вектор взят! ознаки входження канал!в зв'язку до маршрупв. Результати. Оптимальним вар!антом е нейронна мережа (НМ) конфпурацп 21-1-45-21 !з сигмо!дальною функщею активацп у прихованому шар! й лшшною функшею активацп у результуючому шар!, що навчаеться за алгоритмом Levenberg-Marquardt. Нейронна мережа на-вчаеться найб!льш швидко на виб!рках р!зно! довжини, менше за шш! шддаеться перенавчанню, досягае значения середньоквадратично! помилки в 0,2 i на контрольнш виб!рш визначае оптимальний шлях з !мовь ршстю 0,9, при цьому достатньо довжини навчально! виб!рки з! 100 приклад!в. Наукова новизна. Побудо-ван! залежносп середньоквадратично! похибки й часу навчання нейронно! мереж! (кшъкосп епох) в!д к!ль-косл прихованих нейрон!в за алгоритмами навчання Levenberg-Marquardt, Bayesian Regularization, Scaled Conjugate Gradient на виб!рках р!зно! довжини. Практична значимкть. Використання багатошарово! нейронно! модел!, на вх!д яко! подають значення затримок на маршрутизаторах, дозволить у масштаб! реального часу визначити ввдповщш маршрути передач! кер!вних пов!домлень (граф м!н!мально! вартосп) в мереж! !нформац!йно-телекомун!кац!йно! системи зал!зничного транспорту на маг!стральному р!вн!
Ключовi слова: !нформац!йно-телекомун!кац!йна система; 1ТС; затримка на маршрутизатор!; нейронна мережа; НМ; виб!рка; функц!я активацп; алгоритм навчання; епоха; похибка
В. Н. ПАХОМОВА1*, Т. И. СКАБАЛЛАНОВИЧ2*, В. С. БОНДАРЕВА3*
'*Каф. «Электронные вычислительные машины», Днипровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днипро, Украина, 49010, тел. +38 (056) 373 15 89, эл. почта viknikpakh@gmail.com, ORCID 0000-0002-0022-099Х
2*Каф. «Электронные вычислительные машины», Днипровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днипро, Украина, 49010, тел. +38 (056) 373 15 89, эл. почта sti19447@gmail.com, ORCID 0000-0001-9409-0139
3*Каф. «Электронные вычислительные машины», Днипровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днипро, Украина, 49010, тел. +38 (056) 373 15 89, эл. почта bond290848@gmail.com, ORCID 0000-0002-4016-1656
Наука та прогрес транспорту. Вюник Дншропетровського нацюнального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
ИНТЕЛЛЕКТУАЛЬНЫЙ ПОДХОД К ОПРЕДЕЛЕНИЮ МАРШРУТОВ В СЕТИ ИНФОРМАЦИОННО-ТЕЛЕКОММУНИКАЦИОННОЙ СИСТЕМЫ ЖЕЛЕЗНОДОРОЖНОГО ТРАНСПОРТА
Цель. На современном этапе стратегия информатизации железнодорожного транспорта Украины предусматривает переход на трехуровневую структуру управления с созданием единого информационного пространства, поэтому одной из ключевых задач остается организация маршрутизации в сети информационно-телекоммуникационной системы (ИТС). В связи с этим целью статьи является разработка методики определения маршрутов в сети информационно-телекоммуникационной системы железнодорожного транспорта на магистральном уровне с использованием нейросетевой технологии. Методика. Для определения маршрутов в сети информационно-телекоммуникационной системы железнодорожного транспорта, которая на данном этапе работает по технологиям семейства Ethernet, создано нейронную модель 21-1-45-21, на вход которой подают массив задержек на маршрутизаторах сети. В качестве результирующего вектора приняты признаки включения каналов связи до маршрутов. Результаты. Оптимальным вариантом является нейронная сеть (НС) конфигурации 21-1-45-21 с сигмоидальной функцией активации в скрытом слое и линейной функцией активации в результирующем слое, обучаемая по алгоритму Levenberg-Marquardt. Нейронная сеть обучается наиболее быстро на выборках любой длины, менее других подвержена переобучению, достигает значения среднеквадратичной ошибки в 0,2 и на контрольной выборке определяет оптимальный путь с вероятностью
0.9. при этом достаточно длины обучающей выборки со 100 примеров. Научная новизна. Построены зависимости среднеквадратичной погрешности и времени обучения нейронной сети (количества эпох) от количества скрытых нейронов по алгоритмам обучения Levenberg-Marquardt, Bayesian Regularization, Scaled Conjugate Gradient на выборках различной длины. Практическая значимость. Использование многослойной нейронной модели, на вход которой подают значения задержек на маршрутизаторах, позволит в масштабе реального времени определить соответствующие маршруты передачи управляющих сообщений (граф минимальной стоимости) в сети информационно-телекоммуникационной системы железнодорожного транспорта на магистральном уровне.
Ключевые слова: информационно-телекоммуникационная система; ИТС; задержка на маршрутизаторе; нейронная сеть; НС; выборка; функция активации; алгоритм обучения; эпоха; погрешность
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Creative Commons Attribution 4.0 International
doi: 10.15802/stp2019/166092 © V. M. Pakhomova, T. I. Skaballanovich, V. S. Bondareva, 2019
Наука та прогрес транспорту. Вюник Дншропетровського нащонального унiверситету залiзничного транспорту, 2019, № 2(80)
ЩФОРМАЦШНО-КОМУШКАЦШШ ТЕХНОЛОГИ ТА МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ
11. Bryndas, A. M., Rozhak, P. I., Semenyshyn, N. O., & Kurka, R. R. (2016). Realizatsiia zadachi vyboru optymalnoho aviamarshrutu neironnoiu merezheiu Khopfilda. The Scientific Bulletin of UNFU, 26.1, 357-363. (in Ukrainian)
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17. Pakhomova, V. M., & Tsykalo, I. D. (2018). Optimal route definition in the network based on the multilayer neural model. Science and Transport Progress, 6(78), 126-142. doi: 10.15802/stp2018/154443 (in Ukrainian)
18. Schuler, W. H., Bastos-Filho, C. J. A., & Oliveira, A. L. I. (2009). A novel hybrid training method for hopfield neural networks applied to routing in communications networks. International Journal of Hybrid Intelligent Systems, 6(1), 27-39. doi: 10.3233/his-2009-0074 (in English)
19. Herguner, K., Kalan, R. S., Cetinkaya, C., & Sayit, M. (2017). Towards QoS-aware routing for DASH utilizing MPTCP over SDN, 2017 IEEE Conference on Network Function Virtualization and Software Defined Networks (NFV-SDN). Berlin, Germany. doi: 10.1109/nfv-sdn.2017.8169844 (in English)
20. Zhukovyts'kyy, I., & Pakhomova, V. (2018). Research of Token Ring network options in automation system of marshalling yard. Transport Problems, 13(2), 145-154. doi: 10.20858/tp.2018.13.2.14 (in English)
Received: Nov. 05, 2018 Accepted: March 14, 2019
