=Paper= {{Paper |id=Vol-2917/paper36 |storemode=property |title=Route Selection Method in Military Information and Telecommunication Networks Based on ANFIS |pdfUrl=https://ceur-ws.org/Vol-2917/paper36.pdf |volume=Vol-2917 |authors=Yuriy Zdorenko,Oleksandr Lavrut,Tetiana Lavrut,Vasyl Lytvyn,Yevhen Burov,Victoria Vysotska |dblpUrl=https://dblp.org/rec/conf/momlet/ZdorenkoLLLBV21 }} ==Route Selection Method in Military Information and Telecommunication Networks Based on ANFIS== https://ceur-ws.org/Vol-2917/paper36.pdf
Route Selection Method in Military Information                                                                           and
Telecommunication Networks Based on ANFIS
Yuriy Zdorenko1, Oleksandr Lavrut2, Tetiana Lavrut2, Vasyl Lytvyn3, Yevhen Burov3 and
Victoria Vysotska3
1
  Military Institute of Telecommunications and Informatization, Moskovskaya Street, 45/1, Kyiv, 01011, Ukraine
2
  Hetman Petro Sahaidachnyi National Army Academy, Heroes of Maidan Street, 32, Lviv, 79012, Ukraine
3
  Lviv Polytechnic National University, S. Bandera street, 12, Lviv, 79013, Ukraine


                Abstract
                Military information and telecommunication networks (MITNs) are characterized by increased
                requirements for the reliability of data transmission. Existing routing methods allow the
                transmission of information flows on different routes, balancing the load on network routers.
                Therefore, routing methods should consider reliability indexes when calculating route metrics.
                Route reliability indexes are used in modern dynamic routing protocols. However, their values
                are obtained based on heuristic algorithms for polling the state of the interfaces of neighbouring
                routers. It is proposed to use a priori information about the reliability of the route, which allows
                to make the right decision beforehand when transmitting information flows and avoid
                deterioration of QoS in case of equipment failures. It is proposed to use ANFIS (Adaptive
                Neuro-Fuzzy Inference System) to obtain such information.

                Keywords 1
                Telecommunication network, metric, router, neuro-fuzzy system, dynamic routing protocol,
                reliability index, route metric, routing protocol, mobile ad hoc network, time interval, military
                telecommunication network, membership function, fuzzy logic, priory information

1. Introduction
    In modern military information and telecommunication networks, ensuring the quality of service for
various information flows is one of the high priority tasks. An integral part of this process is the use of
a properly configured dynamic routing protocol. Based on any dynamic routing protocol are route
metrics used to decide on the transmission route of the data stream. The military information and
telecommunication networks are characterized by dynamic topology associated with the specifics of
the operation of such networks. The change in the configuration of such networks can be caused by
many random factors: the change of location of routers due to hostilities, equipment failure due to
destruction by the enemy, loss due to a diagnostic fault. Therefore, the dynamic routing protocol for
such networks should be based on metrics that consider the reliability of intermediate nodes (routers).
Such provisions are currently implemented, for example, in the Enhanced Interior Gateway Routing
Protocol (EIGRP) [12]. However, this protocol does not use a reliability criterion with the default
settings when calculating the route metric. And additional locations to consider the reliability criterion
in the general metric of the route are based on measurements of time parameters of links on the
corresponding interfaces and can lead to the calculation of erroneous values of the reliability criterion
of the node. For instance, it is difficult to determine whether a particular node is active at the current
time, leading to incorrect calculation of metrics and sending information on a non-existent route. As a

MoMLeT+DS 2021: 3rd International Workshop on Modern Machine Learning Technologies and Data Science, June 5, 2021, Lviv-Shatsk,
Ukraine
EMAIL: zdorenkoviti@gmail.com (Y. Zdorenko); alexandrlavrut@i.ua (O. Lavrut); Lavrut_t_v@i.ua (T. Lavrut); vasyl.v.lytvyn@lpnu.ua
(V. Lytvyn); Yevhen.V.Burov@lpnu.ua (Y. Burov); Victoria.A.Vysotska@lpnu.ua (V. Vysotska)
ORCID: 0000-000L-5649-771X (Y. Zdorenko); 0000-0002-4909-6723 (O. Lavrut); 0000-0002-1552-9930 (T. Lavrut); 0000-0002-9676-
0180 (V. Lytvyn); 0000-0001-6124-3995 (Y. Burov); 0000-0001-6417-3689 (V. Vysotska)
             ©️ 2021 Copyright for this paper by its authors.
             Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
             CEUR Workshop Proceedings (CEUR-WS.org)
result, this will lead to packet losses, an increase in their average delay, and a deterioration in overall
service quality. Therefore, to provide up-to-date information on the reliability of routes, it is necessary
to have the appropriate tools.
    One of the promising solutions to the problem of obtaining a priori information is the use of systems
for predicting the values of the required parameters [8], [10], [13]. For example, network administrators
have statistics of issues and failures of a particular type of equipment for a certain period of its operation.
Failures are usually random and have various causes. Therefore, such a data set can be used to determine
the failure rate in the future. The capabilities of modern forecasting systems are used to do this. One
way to implement this is to use adaptive fuzzy neural networks [8, 9] - ANFIS.
    Each segment of the military network has its specifics of the operation, which is determined by the
set of equipment used and the conditions of use (network topology, the temperature of equipment, the
nature of hostilities, etc.). The determining specific factors influence the number of possible failures of
the network equipment. Therefore, it is essential to properly train the forecasting system based on the
specifics of the functioning of the military telecommunication network. The obtained value of the
failure rate of the router can be used to calculate the reliability of the node shortly time interval. In
addition, using this indicator to calculate the overall metrics of the route will allow making the right
decision about the routing of data flows in advance.

2. Problem formulation
   Existing dynamic routing protocols use a set of indexes to calculate route metrics [12, 14-16],
including delay, line throughput, probability of loss, reliability, congestion and others. Modern military
networks require the mandatory use of a priori information about the value of the reliability index for
calculating route metrics by the dynamic routing protocol. Therefore, it is proposed to improve the
existing active routing methods by developing and applying forecasting systems to obtain early
information about changes in the network topology and update the route metrics based on it.
   It is assumed that such an approach will significantly improve the quality of service of packages in
the military telecommunication networks.

3. Related works
   The metrics in modern routing protocols are formed based on the obtained values of the
corresponding partial parameters of the metric, which are contained in the header of IP packets. For
example, in the EIGRP protocol, the metric M j for the current j-th time interval can be determined by
the formula [12]:
                                      K * BW               K5                              (1)
                    M j   K1 * BW   2        K 3 * D)  *     * 256 ,
                                        256  L             R  K4 
where Ki for i = {1; 5} - indices, indicating the partial inclusion indicator in the overall metric; they
take the value 0 or 1; BW is the minimum value of bandwidth among all interfaces to the destination
network; D - the total value of all delays to the destination network; R is the reliability of the route,
the values of which are in the range {1; 255}; L is network load rate.
   The routing procedure includes several steps:
       Obtaining information about the components of the metrics that are transmitted in the packet
   header;
       Calculation of the general metric for available routes according to the routing protocol;
       Deciding on the transmission of packets using a determined way.
   However, an approach allows not calculating metrics for predetermined components. Therefore, it
works in uncertain and incomplete information and uses the specifics of a particular network segment.
Furthermore, this approach is based on ANFIS to determine the final metric route. Thus, in [3], the
value obtained by the procedure of fuzzy inference [4-6] is used as a metric. For this purpose, the values
of the components of the metric measured during the operation are fed to the ANFIS input.
Nevertheless, this article does not disclose the learning mechanism of such ANFIS, namely, what data
was used for this and how the correct output values (route metrics) were obtained. Therefore, it is not
always advisable to use such an approach.
   On the other hand, such systems can be used to obtain predictive values of a specific parameter
according to preliminary statistics. The use of ANFIS in such a context is considered in this paper. The
general form of ANFIS is shown in Fig.1 [1, 2, 3, 7]:




Figure 1: Generalized representation of ANFIS

   The mechanisms that underlie ANFIS allow finding the functional dependencies in the form:
                                        yi  f ( x1 , x2 ,..., xi ) .                                (2)
    However, obtaining the correct value using formula (2) depends on the correctness of the data for
training such systems. Thus, one of the most common ways of training is the backpropagation method
[11]. The basis of the training sample is the data obtained during the observation of the input values and
the desired values of the output. The internal structure of ANFIS is determined based on the number of
input values, the number and form of their membership functions and the fuzzy inference algorithm [8]
(Fig. 2).




Figure 2: ANFIS layers

    In [8, 10], ANFIS was used to predict various parameters and demonstrated high efficiency in
solving the problem. Therefore, this article proposes to use this type of system to predict the failure rate
of routers in the military telecommunication networks.

4. Updating the route metrics based on predicted reliability values

    The statistics on the reliability of military network units can be grouped into classes of possible
failures, for example, due to equipment failure (software or hardware failures), or failures related to the
intensity and nature of hostilities (destruction of units) and other classes of periodic or random factors.
The number of such classes k = {1, m} is determined by the conditions of operation of the military
network. For each such failure class, it is proposed to implement its ANFIS. The result of its work
should be the predicted value of the number of failures of the corresponding k-th class in the nearest
time interval. Data on the number of failures during previous periods will be used as input. Based on
the forecast of the number of failures, the data obtained are used to calculate the reliability index R j for
the j-th time interval of the military network node. To do this, it is proposed to use the following formula
(3):
                                                  m
                                                                                                        (3)
                                                  y   k
                                            R j  k 1 ,
                                                    yall
where yk is the predicted value of the failure rate of the k-th class; yall is the total number of single
observation intervals, into which the entire observation time is divided.
   The duration of each single time interval is selected based on the recording of one event.
   The diagram of the metric update system based on the approach described above involves
implementing several stages and is shown in Fig. 3.




Figure 3: Block diagram of the metric update system

   The part of the network considered using the proposed approach is shown in Fig. 4.




Figure 4: A segment of network for which the route is build-using ANFIS
    Each intermediate node (router) of the considered network segment contains trained ANFIS of k-th
class, corresponding to the number of defined failure classes m. Each such system predicts the number
of failures of the corresponding k-th class in the next time interval of duration T. Based on these data,
the reliability index of the node is calculated using formula (3), and the route metric is calculated,
according to the algorithm for use in the dynamic routing protocol. Next, the routing tables are updated,
and the route information with the best metrics is transmitted.

5. Route selection method based on the use of ANFIS

    Based on the described process of route metrics updating, a method of route selection using ANFIS
is proposed, which involves the following steps:
    1. Determining the failure classes of routers in the military telecommunication network;
    2. Implementation of the appropriate number of ANFIS on each network node to predict failures
    for a specific class;
    3. Determining the ANFIS architecture according to the method [11], the main stages of which
    include: determining the number and type of input values, the number and form of membership
    functions of each input value, the number of layers of fuzzy neural network;
    4. Training ANFIS based on statistics collected for previous periods for specific failure classes;
    5. Predicting the values of the number of failures of the k-th class in the nearest time interval using
    ANFIS of the corresponding classes;
    6. Calculation of the overall reliability index of the node according to formula (3), and its
    conversion into the reliability index of the corresponding dynamic routing protocol;
    7. Calculate the route metric according to the rules defined by the dynamic routing protocol,
    taking into account the reliability index.
    8. Update routing tables by transmitting partial metric data to neighbouring routers, according to
    the dynamic routing protocol
    Router failure classes are determined based on the analysis of network operating conditions and are
the initial data for further ANFIS synthesis on each network router. Each ANFIS of k-class is designed
to predict a particular k-th failure class and provide the necessary prediction accuracy. To do this, we
need to choose the exemplary architecture of such a system and data for its training. On the one hand,
the choice of architecture is limited by the requirements for forecasting accuracy, and on the other hand,
the ability of routers to perform additional tasks. The most straightforward ANFIS architecture
synthesis with its further training will be carried out in the following part.
    We assume that the failure rates of different classes that are predicted are random and uniform.
Therefore, the total number of failures during the forecast j-th time interval is calculated as the sum of
losses of different classes indicated by other ANFIS classes.
    The basis of any dynamic routing protocol is the calculation of the route metric. We propose to use
such a routing protocol that considers the reliability index when calculating the route metric. In addition,
the proposed method can be used for new dynamic routing protocols. One of the existing protocols that
consider the reliability in the calculation of the overall metric is EIGRP. However, the reliability index
in this protocol is taken into account only if the network topology changed. Let’s calculate the route
metric using this protocol in the router r1 for the network architecture shown in Fig. 4.
    Determine that the router r1 is the entry router and the router r5 is the exit router of the network
segment. So, we have the following values of partial metrics for different parts of the route:
 BW13  100Mb / s , BW35  100Mb / s , BW1 2  100Mb / s , BW2 4  100Mb / s , BW45  100Mb / s ,
 D13  10mks , D35  10mks , D1 2  10mks , D2 4  10mks , D45  10mks , REIGRP  255 , L  255 .
                                                                                i


   The values of coefficients are Ki  1 for i={1;5}. Then, according to formula (1), for route 1: r1 - r3
- r5 , the metric will have a value M=202, and for route 2: r1 - r2 - r4 - r5 M= 203. If a priori information
about the reliability index of the router r3 is available, for example, R3 j  0,5 the metric will be
recalculated.
   The appropriate steps of the proposed method were executed to obtain the value R n j . For the EIGRP
protocol, the value of the reliability index is in the range {1; 255}. Therefore, it is necessary to establish
the correspondence of the obtained values of the reliability index R j , which is in the range {0,1}, with
the range of the EIGRP protocol. The paper proposes a gradation of the correspondence values, shown
in Table 1 to do this.

Table 1
The correspondence of the values of the predicted reliability index with the EIGRP protocol index
                #     EIGRP reliability index, REIGRP Predicted reliability index, R j
                     1.                         1                                        0,0039
                     2.                         2                                        0,0078
                     3.                         3                                         0,011
                     …                          …                                           …
                    128.                       128                                       0,5019
                    129.                       129                                       0,5058
                     …                          …                                           …
                    255.                       255                                          1

   Thus, for the values of the reliability index defined for the router r3 - R 3 j , we have the corresponding
value of the reliability index according to the EIGRP protocol - REIGRP  127 .             1


   The metrics of both routes from router r1 to router r5 were calculated using the obtained reliability
index. Thus, the metric of route 1: r1 - r3 - r5 , obtained taking into account the reliability index will
be M = 404, and for route 2: r1 - r2 - r4 - r5 , M = 203. Therefore, the data streams will be directed along
the route with a smaller value of the metric. The obtained a priori information about the reliability of
the nodes based on the proposed method allowed updating the metrics and taking into account possible
failures on the packet transmission route. As a result, the route will be selected, which in the j-th time
interval will be more reliable, namely route 2: r1 - r2 - r4 - r5 .
    Possible failures of network nodes during the operation of the telecommunication network can lead
to a deterioration in QoS: increased network delays, increased packet loss, packets sent on a non-
existent route. Therefore, it is mandatory to consider the reliability index in the general metric of the
network route. Subsequently, ANFIS was synthesized and trained to predict k-th class failures.
    For the synthesis of ANFIS, the method defined in [8] was used. Thus, as input values, we use the
value of the number of failures of the k-th class during the last four periods of time, namely: y( i 1) ,
y( i  2) , y( i 3) , y( i  4) . Thus, the initial value is yk - the number of failures of the k-th class during the
following time interval. It is proposed to use the Sugeno algorithm of the 1st type to obtain an accurate
prediction. For each input value, two triangular membership functions were defined. Then the
synthesized ANFIS will have the following structure on Fig. 5.
    The complete knowledge base will contain sixteen rules, which have the following form (4) - (19):
           If (y(i 1)  O1 ) and (y(i  2)  P1 ) and (y( i 3)  R1 ) and (y( i  4)  S1 ), then (yk  Z1 ) ,   (4)
           If (y(i 1)  O1 ) and (y(i  2)  P1 ) and (y( i 3)  R1 ) and (y ( i  4)  S2 ), then (yk  Z 2 ) , (5)
           If (y(i 1)  O1 ) and (y(i  2)  P1 ) and (y( i 3)  R2 ) and (y( i  4)  S1 ), then (yk  Z3 ) ,   (6)
            If (y(i 1)  O1 ) and (y(i  2)  P1 ) and (y( i 3)  R2 ) and (y( i  4)  S2 ), then (yk  Z 4 ) ,    (7)
            If (y(i 1)  O1 ) and (y(i  2)  P2 ) and (y( i 3)  R1 ) and (y( i  4)  S1 ), then (yk  Z5 ) ,     (8)
            If (y(i 1)  O1 ) and (y(i  2)  P2 ) and (y( i 3)  R1 ) and (y( i  4)  S2 ), then (yk  Z 6 ) ,    (9)
            If (y(i 1)  O1 ) and (y(i  2)  P2 ) and (y( i 3)  R2 ) and (y( i  4)  S1 ), then (yk  Z 7 ) ,   (10)
           If (y(i 1)  O1 ) and (y(i  2)  P2 ) and (y( i 3)  R2 ) and (y( i  4)  S2 ), then (yk  Z8 ) ,     (11)
            If (y(i 1)  O2 ) and (y(i  2)  P1 ) and (y( i 3)  R1 ) and (y( i  4)  S1 ), then (yk  Z9 ) ,    (12)
            If (y(i 1)  O2 ) and (y(i  2)  P1 ) and (y( i 3)  R1 ) and (y( i  4)  S2 ), then (yk  Z10 ) ,   (13)
            If (y(i 1)  O2 ) and (y(i  2)  P1 ) and (y( i 3)  R2 ) and (y( i  4)  S1 ), then (yk  Z11 ) ,   (14)
           If (y(i 1)  O2 ) and (y(i  2)  P2 ) and (y( i 3)  R2 ) and (y( i  4)  S1 ), then (yk  Z12 ) ,    (15)
            If (y(i 1)  O2 ) and (y(i  2)  P2 ) and (y( i 3)  R1 ) and (y( i  4)  S1 ), then (yk  Z13 ) ,   (16)
           If (y(i 1)  O2 ) and (y(i  2)  P2 ) and (y( i 3)  R1 ) and (y( i  4)  S2 ), then (yk  Z14 ) ,    (17)
           If (y(i 1)  O2 ) and (y(i  2)  P2 ) and (y( i 3)  R2 ) and (y( i  4)  S1 ), then (yk  Z15 ) ,   (18)
             If (y(i 1)  O2 ) and (y(i  2)  P2 ) and (y( i 3)  R2 ) and (y( i  4)  S2 ), then (yk  Z16 ) . (19)
where O1 is the first term of the input value y(i 1) ; O2 is the second term of the input value y(i 1) ; P1 is
the first term of the input value y( i  2) ; P2 is the second term of the input value y( i  2) ; R1 is the first term
of the input value y(i 3) ; R2 is the second term of the input value y(i 3) ; S1 is the first term of the input
value y( i  4) ; S 2 is the second term of the input value y( i  4) ; Z1 , Z 2 , Z3 …, Yk are the values of the
individual conclusions of the fuzzy rules number k ( 1  k  16 ).




Figure 5: The synthesized ANFIS structure

    The training of such ANFIS, expressions for membership functions of input values was obtained as
a result of:
                                                  1,                          y(i 1)  15;                         (20)
                                                  27  y
                                                             ( i 1)
                              1 ( y(i 1) )                           , 15  y( i 1)  27;
                                                        27  15
                                                  0,                         y(i 1)  27;
                                                       0,                     y(i 1)  18;                         (21)
                                                      y      18
                                                      
                              2 ( y(i 1) )   (i 1)                  , 18  y( i 1)  42;
                                                       42  18
                                                       1,                    y(i 1)  42;

                                                 1,                           y(i  2)  10;                        (22)
                                                 37  y
                                                             ( i  2)
                              1 ( y(i  2) )                          , 10  y(i  2)  37;
                                                 37  10
                                                 0,                          y(i  2)  37;
                                                    0,                        y(i  2)  16;                        (23)
                                                   y        
                                                                 16
                              2 ( y(i  2) )   (i  2)                , 16  y(i  2)  45;
                                                    45  16
                                                    1,                       y(i  2)  45;

                                                   1,                         y(i 3)  12;                         (24)
                                                   22  y
                                                             ( i  3)
                              1 ( y(i 3) )                           , 12  y(i 3)  22;
                                                        22  12
                                                   0,                        y(i 3)  22;
                                                     0,                       y(i 3)  16;                         (25)
                                                    y        16
                                                    
                              2 ( y(i 3) )   (i 3)                  , 16  y(i 3)  37;
                                                     37  16
                                                     1,                      y(i 3)  37;

                                                       1,                      y(i  4)  9;                        (26)
                                                       20  y
                                                               ( i  4)
                              1 ( y(i  4) )                           , 9  y(i  4)  20;
                                                       20  9
                                                       0,                    y(i  4)  20;
                                                      0,                      y(i  4)  15;                        (27)
                                                     y       
                                                                  15
                              2 ( y(i  4) )   (i  4)                , 15  y( i  4)  35;
                                                      35  15
                                                      1,                     y(i  4)  35;
and the obtained values of the coefficients of individual conclusions of fuzzy rules, which are the result
of training neurons of the fourth layer (Table 2):

Table 2
The results of forth neuron layer training
     Rule                                                 The value of the coefficient
   number,             zk             zk                                  z3 k                      z4 k      z5 k
                       1                       2
       k
       1           0,09625             0,005382                        0,7238                      0,2093   -0,5021
       2          0,0004083             -0,1041                       0,04222                     0,03792   0,07806
       3           0,12625             0,025382                        0,8238                      0,6083   -0,4061
       4           0,000605             -0,4107                         0,082                     0,05592    0,088
       5           0,01625             0,00732                          0,658                      0,4093   -0,6024
       6           0,04086              -0,5643                       0,05642                     0,03891   0,04386
      7            0,00725               0,00765                       0,00234                          0,0054     -0,341
      8            0,00055               -0,00125                       0,0675                          0,0743     0,0125
      9             0,0356               0,00567                        0,0004                         0,02437    -0,0556
      10           0,00044                -0,1055                       0,0542                         0,06492    0,00406
      11           0,15525               0,03532                        0,4438                          0,0554    -0,0065
      12           0,00705               -0,06607                        0,002                         0,02392     0,0508
      13            0,0955               0,07582                        0,0039                         0,20043   -0,00561
      14            0,0081                -0,1001                      0,00242                         0,03002    0,07006
      15           0,10025                 0,0202                        0,808                          0,6003   -0,40061
      16           0,00545               -0,40007                       0,0052                          0,0502     0,0803

   The values of the individual conclusions of the rules by the Sugeno algorithm of type 1 are
determined according to expression (28):
                          Zk  z1k y(i 1)  z2k y(i 2)  z3k y(i 3)  z4k y(i 4)  z5k . (28)
   Synthesized ANFIS consists of five layers. The first layer is designed to fuzzily the input values
according to formulas (21) - (27) to find membership functions.
   The second layer of ANFIS performs aggregation based on expressions (29) - (44):
                        G1  1 ( y(i 1) )  1 ( y( i  2) )  1 ( y( i 3) )  1 ( y( i  4) ) , (29)
                        G2  1 ( y(i 1) )  1 ( y( i  2) )  1 ( y( i 3) )  2 ( y( i  4) ) , (30)
                        G3  1 ( y(i 1) )  1 ( y(i  2) )  2 ( y(i 3) )  1 ( y(i  4) ) ,    (31)
                        G4  1 ( y(i 1) )  1 ( y(i  2) )  2 ( y(i 3) )  2 ( y(i  4) ) ,    (32)
                        G5  1 ( y(i 1) )  2 ( y(i  2) )  1 ( y( i 3) )  1 ( y( i  4) ) ,  (33)
                        G6  1 ( y(i 1) )  2 ( y(i  2) )  1 ( y(i 3) )  2 ( y(i  4) ) ,    (34)
                        G7  1 ( y(i 1) )  2 ( y(i  2) )  2 ( y(i 3) )  1 ( y(i  4) ) ,    (35)
                        G8  1 ( y(i 1) )  2 ( y(i  2) )  2 ( y(i 3) )  2 ( y(i  4) ) ,    (36)
                        G9  2 ( y(i 1) )  1 ( y(i  2) )  1 ( y(i 3) )  1 ( y(i  4) ) ,    (37)
                         G10  2 ( y( i 1) )  1 ( y( i  2) )  1 ( y( i 3) )  2 ( y( i  4) ) ,                (38)
                         G11  2 ( y(i 1) )  1 ( y(i  2) )  2 ( y(i 3) )  1 ( y(i  4) ) ,                    (39)
                         G12  2 ( y(i 1) )  1 ( y(i  2) )  2 ( y(i 3) )  2 ( y(i  4) ) ,                    (40)
                         G13  2 ( y(i 1) )  2 ( y( i  2) )  1 ( y( i 3) )  1 ( y( i  4) ) ,                 (41)
                         G14  2 ( y(i 1) )  2 ( y(i  2) )  1 ( y(i 3) )  2 ( y(i  4) ) ,                    (42)
                         G15  2 ( y(i 1) )  2 ( y(i  2) )  2 ( y(i 3) )  1 ( y(i  4) )                      (43)
                         G16  2 ( y(i 1) )  2 ( y(i  2) )  2 ( y(i 3) )  2 ( y(i  4) ) .                    (44)
   In the third layer of neurons, normalization of the result of aggregation is carried out:
                                                   G                                                                    (45)
                                             Gk  16 k ; 1  k  16 .
                                                   Gkk 1

   In the fourth layer of ANFIS activation is carried out, and the product of the results of activation and
normalization is calculated using the formula:
                                      J k  Gk Zk , 1  k  16 .                                      (46)
   The fifth layer performs the procedure of defuzzification:
                                                               16
                                                                                                                        (47)
                                                       yk   J k .
                                                               k 1

   The result of defuzzification is a crisp value of the predicted number of failures of the k-th class.
   To teach ANFIS to predict the number of failures of the k-th class, test data were obtained by
generating random numbers with a uniform distribution. The test sample was divided into two parts.
The first part was used for ANFIS training. The method of inverse error propagation was used in the
learning algorithm.
    The second part of the test data was used to verify the learning outcomes of ANFIS. The data used
for training were organized in matrix form:
                                    y1   y2    y3    y4 y5                                    (48)
                                     y          y6        y7       y8       y9 
                                     5
                                    .          .        .         .        . 
                                                                                ,
                                     yi  4     yi 3    yi  2    yi 1    yk 
                                    .          .        .         .        . 
                                                                                
                                     yI  4   yI 3    yI  2    yI 1     yI 
where yk is the predicted number of failures of the k-th class in the time interval i, 1  і  І . The training
was based on data for І  5000 cycles and was conducted in the Matlab environment [11]. The result of
the training was finding the correct values of the corresponding parameters of the membership functions
of formula (20) - (27) and coefficients (Table 2).
    After training, data from the second test part were submitted to the ANFIS input, and the initial value
was compared with the expected result. As a result of numerical simulation simulations, it was found
that the accuracy of predicting the value yk is 94-96%.



6. Conclusion
    The paper proposes an approach for updating route metrics using a priori data on the reliability of
military network routers based on ANFIS. ANFIS allows getting the reliability index value, which
provides an early decision on using backup routes in the next time interval and helps to ensure better
QoS parameters. The ANFIS synthesis was performed to predict the number of k-th class failures. This
system was trained on test data, and its effectiveness was investigated. Further research aims to
determine the dependences of QoS indicators using the proposed approach in implementing the military
telecommunication network.


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