NEUROMODELING OF OPERATIONAL PROCESSES

Context. The problem of synthesis a neural network model of operational processes with the determination of the optimal topology, which is characterized by a high level of logical transparency and acceptable accuracy, is considered. The object of the study is the process of neural network modeling of operational processes using an indicator system to simplify the selection of the topology of neuromodels. Objective of the work is to synthesis a neural network model of operational processes with a high level of logical transparency and acceptable accuracy based on the use of an indicator system


ABBREVIATIONS
ANN is an artificial neural net; CTS is complex technical system; IoT is Internet of Things; MT is maintenance of technical system; OC is organized complexity; OS is organized simplicity; NF is natural frequency.

NOMENCLATURE
J is informative weight of independent attribute; n is a number of input features that characterize sample instances; i N is a multiple neurons at the network input;  p is a number of neurons at the network output; q is a number of connections between neurons in the network; r is number of neurons in the hidden network layer; Sample is a data set; w is a multiple of connections between neurons; q w is a connection between neurons in the network; n x is a independent attribute of the sample instance; X is a set of independent attribute (variables); m y is a value of the dependent variable (attribute) of the sample instance; Y is a set of values of dependent variables.

INTRODUCTION
The quality of modern CTS is largely determined by their reliability.One of the most significant factors of reliability changes is the operating conditions and the adopted operation strategy, which should be understood as a set of organizational and technical measures for maintenance and restoration of serviceability or operability of failed objects.The decrease in the intensity and volume of such measures negatively affects the reliability indicators of the CTS To the greatest extent, this trend is characteristic of systems that operate autonomously, without the possibility of carrying out preventive control and restoration (diagnostics and repair) measures or with the possibility of carrying them out in a reduced volume.Such features are inherent in road transport objects, marine objects and special-purpose systems [1][2][3][4][5].
During the operation of the CTS of this class, periodically, after a while stat t , they leave stationary points (bases, airfields, airports, etc.) to perform tasks for their intended purpose during the time work t .In this case, the object can be in conditions that ensure its immediate use with intensity ).Meanwhile MT, especially in the case of a long stay on the base, the object may also fail with the parameter 0 ω .The resulting failures are eliminated during the next maintenance or during checks before departure for the flight.The duration of these checks PTM t ( ) has a significant impact on the failure rate when performing tasks offline outside of stationary points, i.e.

(
) over, equality is achieved when In the simplest case During modeling, it is convenient to represent the considered process of CTS operation as a random process in a discrete phase space.The phase space of the process includes two states (the first MT and the second MT), as well as indicators of natural oscillations.Taking into account the availability of historical experimental data, an ANN will be used as the basis for the model [1][2][3][4][5].
ANN are statistical computational models applied to a variety of practical tasks, including diagnostics (technical and medical based on multimedia data about an object), assessment, forecasting, etc. [6,7].During process of supervised learning ANN trains on the example of already known data, that is, so it is exist a predefined correct answer for all the initial data.The main idea of training a neural network is to set up a configuration in which the model's responses will be as close as possible to the correct ones.However, at the moment there are many ANN topologies that can be used as a neuromodel.So some can provide a context for each subsequent prediction (recurrent ANN).This helps the ANN to maintain the state in which the decision was made.Therefore, it is so important at the initial stage to correctly assess the complexity of the problem for further selection of the ANN topology and the choice of the training approach for the synthesis of the most optimal model [6,7]..The task of studying the process is to obtain a model that will reflect the behavior inherent in the source data.Such a task can be attributed to the number of template recognition tasks.Regarding the event log as training data, we will be trained to evaluate the results for each event in the ANN log.The ultimate goal will be to synthesize a model based on the ANN representing a neuromodel of the operational process encoded in the event log The object of study is the process of synthesis neuromodels of operational processes with a high level of interpretability and acceptable accuracy of operation.
Using the assessment of the complexity level, it is possible at the initial stage to determine the approach to the synthesis of the model based on the ANN.
The subject of the study is a neural network model of operational processes, characterized by a high level of interpretability and acceptable accuracy.
Using the information about the modeling task and the evaluation of the input data, it is necessary to synthesize a neuromodel.
The purpose of the work is to build and study neuromodels of operational processes with the previous definition of structural features based on the assessment of the level of complexity of the task.

PROBLEM STATEMENT
The operational process can be represented as a modeling problem.Where, at the initial stage, a set of various characteristics (features) of the operation of the object (system) that is being studied is available [8,9].A set of characteristics is represented by a set of conditionally independent features of an object consisting of the n number of such.As a rule, such characteristics are the values of the results of the operation of the object measured using special sensors, sensor systems or devices [6][7][8][9].
In accordance with these independent features, a set of values of the dependent characteristics of the object is compared: consisting of m elements.It is assumed that to some extent each independent feature k x affects the value of the corresponding one l y .The degree of this influence can be represented as the information weight of an independent attribute [6][7][8][9].
Then the neuromodel of the operational process can be represented as an ANN NN consisting of structural elements and a set of parameters ( ) . The structure of such a neuromodel is determined by sets of computational nodes: neurons and connections between them: . In turn, the aggregates of the set of neurons are divided into subsets by layers: the neurons of the input layer , the output layer

= =
and the hidden one . The subset of links consists of the links themselves and their weighting coefficients: Accordingly, the task can be represented as a synthesis of the ANN with optimal structure and accuracy ( ) , based on a sample of initial data about the object under study during operation Y X Sample , = .

REVIEW OF THE LITERATURE
The idea of ANN is to model (repeat) the behavior of various processes based on historical (experimental) information.The ANN itself is a set of special mathematical functions with many parameters that are configured in the process of learning from previous data.Then the trained ANN processes the initial real data and gives its forecast of the future behavior of the studied system.The essence of ANN is the desire to imitate the processes taking place.In its structure, the neural network is similar to the human brain and is also capable of learning [6][7][8].
The main difference between models based on ANNs and growth curves or regression methods is that if these methods adjust a real process or phenomenon to a standard mathematical function, then ANNs select the parameters of a system of equations, bringing it to real life [7].
Schematically, an artificial neural network consists of a layer of input signals, an output layer and several internal layers (Fig. 1).
The processes of building and training a network in a software package that supports the creation of neural net-works are as follows: the values of input variables are fed to the input, the type of connection and weight coefficients are selected randomly, then the values of the output variable are calculated.The obtained values are compared with the real ones, after that, the weights and the type of network are adjusted, aimed at reducing the error.The general scheme is shown in Fig. 2  An important issue is also the organization of the transmission of the same historical (experimental) data.Thus, with the correct organization of data transmission and storage processes, it is possible to organize a complex system within the IoT technology, which will be aimed at online diagnostics and MT the operability of the technical system [10][11].Such an organization involves the installation of deployed sensor networks on technical elements and nodes.Sensor networks provide automated recording of operational indicators with a specified time lag, which can reach miles and microseconds.All recorded data is transferred to the cloud, where a data bank is formed.Wireless network data transmission technologies are used for transmission.An external computing server or several such servers have access to the accumulated data bank.These installations can perform real-time analysis of constantly updated data.Among the possible types of analysis, the following can be distinguished [10][11]: -data verification: checking the truth and correctness of the received data (for example, filling in empty data or tracking unexpected run-ups in indicators); -statistical data analysis: identifying and visualizing the simplest patterns and relationships between data.Data normalization and standardization can also be included here; -data reduction: reducing the dimension of data is sometimes necessary to optimize resource consumption in data analysis.Thus, the selection of informative features, preliminary data mining and other operations help to speed up the process of further processing (for example, the synthesis of models based on data), and sometimes also improve accuracy (by removing noisy data).
Also, an important task of the server in such systems of the synthesis, updating (additional training) or modernization of new or pre-built models [10][11].
Such models, based on constantly updated data, can more accurately diagnose, monitor, or make a forecast.All the results generated by the models are redirected to the workstation (this can be done via the cloud or directly), since in some systems the results obtained either have to pass moderation, or may require the involvement of the operator.
Thus, for the most part, such an organization of IoT systems is aimed at maintaining the operability of technical systems: diagnostics, non-destructive control or forecasting of operability.The general principle is shown in Fig. 3.
However, the organization of an IoT system or simpler solutions is associated with an assessment of the complexity of the simulated problem for choosing a model synthesis strategy based on the ANN and choosing the appropriate topology.

MATERIALS AND METHODS
As it was given in the previous section, the modeling task can be unified for a specific task after a certain comprehensive assessment of its complexity.Given that the structure of ANN ( ( ) ) allows to most subtly encode the relationships between the input data ( ), it is necessary to accurately select the synthesis option for such a non-network model.to synthesize the most acceptable structure [12].
In the case when a problem with input data that is questionable can be modeled (there is a question about the accuracy of the data, their excess or a high degree of interconnectedness), it is necessary to resort to input data preprocessing.Thus, the selection of informative features will allow to exclude unin- , which will subsequently increase the level of logical transparency of the neuromodel.By spending more time on data preprocessing, it is possible to significantly reduce the time resources at the stage of model synthesis based on the ANN [12].
Stepwise regression methods can be used to feature selection.Stepwise regression is a method that iteratively checks the statistical significance of each independent variable in a linear regression model [8,9].This is done through iteration, that is, the process of obtaining results or solutions by repeating rounds or cycles of analysis.
Automatic testing with the help of statistical software packages allows you to save time and reduce the number of errors.A bidirectional exception is a combination of forward and reverse exclusion methods that check which variables should be included or excluded [8,9].
Firstly, it must be sorted ( ) . After that it must be update6 . Finally, internal iteration calculation must be update.
Such manipulation on the first step guarantees that it will be removed a feature, − x from our feature subset n X .Moreover, − x is the feature that maximizes our cri- terion function upon removal, that is, the feature that is associated with the best classifier performance if it is removed from n X .Secondly, pull must be update based on the rule ( ) , where with special condition: so in this case have: . And again internal iteration calculation must be update.
Second manipulation search for features that improve the classifier performance if they are added back to the feature subset.If such features exist, we add the feature + x for which the performance improvement is maximized.If internal iteration calculation came to the 2 or an improvement cannot be made (i.e., such feature + x cannot be found), go back to exclusion manipulation; else, repeat the adding.
However, after the selection of features, the problem can be considered already in the category of OS, when a simple direct propagation ANN is sufficient for modeling, and the number of neurons in the hidden layer is calculated based on the statistical characteristics of the data sample [12]:

EXPERIMENTS
The blades of the single stage compressor engine TV3-117, made of alloy BT8 and having operational damage to the feather of the engine blades, were selected as the object of research.The studies were carried out on two engines operated under the same conditions, but having different operating hours and, accordingly, different degrees of damage to the blades.Engine D1 have 1971 h and D2: 990 h.Operational damage to the pen creates not only a stress concentration, but also leads to a change in the geometry of the blades.For research, 20 blades with no gross mechanical damage were selected from two engines [13][14][15][16].
The study of the geometry of the blades consisted in measuring the chord, C 1 and C 2 in sections from A2-A2 to A8-A8.The measurement results indicate that the greatest change in the geometry of the blade parameters occurs in the peripheral zone (sections A7-A7 and A8-A8) [13][14][15][16].
The table shows that x 1 , x 4 , x 7 , x 10 , x 13 , x 16 , x 19 : B, the value of the chord, in Table 1 in different sections; x 2 , x 5 , x 8 , x 11 , x 14 , x 17 , x 20 : C 1 , the thickness of the input edge; x 3 , x 6 , x 9 , x 12 , x 15 , x 18 , x 21 : C 2 , the thickness of the output edge; x 22 : HB, the hardness of the initial blade, HRC.
x 23 : Ϭ 0,2 , yield strength of the starting material, MPa; x 24 : Ϭ в tensile strength, MPa; y 1 : Т 1 total operating time; y 2 : Т2 operating time up to first repair, h; y 3 is the frequency of natural vibrations of the blades, Hz.

RESULTS
The table 1 shows the part of the sample that was used for the experiments.
Table 2 presents regression models for different engines and their aggregates.The models are based on a reduced number of input features.
Table 3 presents ANN-based models in matrix form.6 DISCUSSION At first, the task for modeling was assigned to the OC category.However, after preprocessing the input data, information-important features were selected.Accordingly, after data reduction, the task was transferred to the OS group.In the end, the input sample was not excessive, and the risks of human influence were excluded.The only significant complicating factor is poorly conditioned correlation matrices.
Further calculations showed that the use of 6-8 neurons in the hidden layer is sufficient to build a neural model with acceptable accuracy.
Analyzing the initial results, we should note a fairly large run-up in the model training time: from 4 seconds (the largest indicator among the ANN-based models) to 34.37 for linear regression models.
The results obtained on the data after the reduction showed that the accuracy increased when constructing a neural model with a certain structure based on a system of indicators, and the time was significantly reduced.
In addition, it should be noted the high level of logical transparency of the obtained models based on the ANN.

CONCLUSIONS
The urgent scientific and applied problem of determining the optimal and logically transparent structure of a neuromodel for modeling the operational processes is solved.
The scientific novelty lies in the fact that using the feature selection methods for pre-processing of input data allows to re-define the level of task complexity and use more resource-efficient methods for synthesis model based on ANN.Such models have the optimal, logically transparent topology and hight level of accurancy.
The practical significance lies in the fact that such approches that were used allow speed up the process of synthesis 8.6 times.Moreover, such models based on ANN demonstrate better accuracy average by 6%.
Prospects for further research are using additional information as input data set for trackeng implicit factors on operational processes.In this case using more complex topologies of ANN with modern methods for training can demonstrate good results.

ACKNOWLEDGEMENTS
The carried out with the support of the state budget research projects of the state budget of the National University "Zaporozhzhia Polytechnic" "Intelligent methods and software for diagnostics and non-destructive quality control of military and civilian applications" (state registration number 0119U100360) and "Development of methods and tools for analysis and prediction of dynamic behavior of nonlinear objects".Цель работы заключается в построении нейросетевой модели эксплуатационных процессов с высоким уровнем логической прозрачности и приемлемой точностью на основе использования индикаторной системы.

N
is a neuron at the network input; o N is a multiple neurons at the network output; p o N is a neuron at the network output; h N is a multiple neurons of the hidden network layer; r h N is a hidden network layer neuron;

Table 1 -
General information about data set Figure 1 -General scheme of simple topology of ANNFigure 3 -General scheme of interaction in IoT systems for operational process

Table 3 -
Neural networks models for engines in matrix format