Building models of technological processes based on neuro-fuzzy technology

The work considers the issues of formalization of the extraction process in the form of a generalized regression neural network model, which are the basis for solving the problem of analysis and synthesis of the extraction process control system for obtaining petroleum products. An adaptive learning algorithm for a neural network model has been developed that is characterized by high speed and accuracy. A comparative analysis of the developed model with existing ones was made, which showed the effectiveness of the proposed algorithm for building the architecture of neural network models and learning the weight coefficients of the model.


Introduction
One of the important aspects of creating control systems for various technological processes is the development of mathematical models that reflect the real characteristics of these processes.As a rule, the creation of a model for a control system is based on the heuristic judgment of the designer and sometimes, if possible, on empirical data consisting of state characteristics; OXQ -values of object characteristics; EL -a set of object elements (for example: communication channel, data transmission line, etc.); OEL is a set of relationships between object elements.The type of relationship between elements is hierarchical [1].
The object element (EL) is the following tuple: where NEL is the element name; ELX and ELXQ are properties of the element and its value.

Method solution
To determine the optimal structure of the technological process model, a set of structures is created that determines the appropriateness of the relationship between any of its elements.A set of structures of technological process models is a function of the Ms vector (with a matrix form of representing sets).
( ) where D is a set of structural components, including state variables ; L is a set describing possible operating situations; L l j  ; " " -character Boolean multiplication operation; A function that determines the variants of model structures formed from the results of the Boolean multiplication of a set of components Q-D and a set of operating states L [2][3].

   
, , , , , This set defines the classification of the technological process according to time parameters T and allows to select the type of model according to the type of equation.The structure of T is determined by the following set of technological process elements: t1 -continuous; t2 -discrete; t3 -continuous discrete; t4 is a discrete continuous.So: In order to understand the dynamics and logic of the technological process one by one, it is necessary to have information about its state.For this purpose, a subset X containing variables carrying information about the state of the technological process (generalized coordinates) is provided as elements:

=
, where f is the smallest number of independent variables describing the state of the technological process at a given moment.
In order for the technological process to be controlled, its model must have elements, changing the values of which it is possible to transfer the technological process from one state to another.This function performs a subset U containing variables that describe the actions of the control: Where  is the number of control variables.The sum of any elements of the structure of the mathematical model of the technological process depends on the state of the activity.In order for the technological process to be controlled, its model must have elements, changing their values, to transfer the technological process from one state to another.This function performs a subset U containing variables that describe the actions of the control should be considered [4][5].
An activity state is a state of a technological process in which the structure of the model does not change.A change in the conditions in which the technological process occurs requires the transition of the model to a different structure.
The dependence of structural changes on the operating situation is important in the formation of the model and therefore should be clearly reflected.It is for this purpose that the set of elements L defines the complete set of possible situations of technological process activity: is a set of elements that determine all possible situations of technological process activity.
Information about the boundary between states is often expressed by concepts that have a vague meaning from a classical mathematical point of view.Therefore, the definition of the state of technological process activity can be considered from the point of view of the theory of fuzzy sets.Based on this theory, the fuzzy-set concept is proposed as a means of mathematical modeling of processes with uncertainties.
The construction of mathematical models of technological processes based on neuro-fuzzy technology consists of several stages, in which the coordinates of the model created based on the results of external influences and physico-chemical characteristics of the technological process under investigation are determined.The main goal of this stage is to determine the coordinate vector of the technological process using existing methods based on the functional and organizational structure of the studied process.
In general, according to the scheme of functional-objective analysis, the technological process is divided into some parts based on the functions it performs.Then, based on the selected symbols, the decomposition operation is performed, that is, a set of coordinates of technological process states is determined as a result of the functional objective analysis corresponding to the sub-parts.
At the next stage, a database of analytical technological research results will be formed.It serves for data processing for each coordination of the technological process.At this stage, a database is created for data processing.In this case, the values of the measured coordinates, the number of discretization steps, and the size of the data are determined.Data arrays corresponding to each coordinate are formed.
The collection of data on technological processes and their preliminary processing consists of several stages, in which the measured parameters and their rate of change are studied, and the most optimal set of parameters is selected.As a result, the statistical values of the data are determined and their reliability is checked.But this method has a number of disadvantages as mentioned above.In this regard, the use of neural network methods for data processing has several advantages.In this case, the interdependence of the variables depends on the selection of the neuron's output function.
The capabilities of the neural network largely depend on the method of activation of the selected relevance function, the number of layers and the complexity and structure of connections between them.Because it can be achieved by simplifying the activation function of the neuron to reduce the complexity caused by the size of the neural network.
Currently, the most universal sigmoidal function of the neuron is widely used in the selection of the neural network.Because it has a continuous character, it differs in the ease of calculation work, that is, in finding the rate of change of variables.
Then, the number of neurons in a layer and the number of layers are changed until a sufficient model is obtained for only connections during the analysis of connections.
One of the main issues is the choice of the structure of the network, which is an important factor affecting the efficiency of the network in the process of studying the characteristics of the process using a model in the form of a neural network and developing a control signal based on them.
The choice of neural network (architecture) is made depending on the characteristics and complexity of the problem.The following is taken into account [6].
Network computing capabilities increase with the growth of the following factors: • the number of neurons in the network; • the number of network layers; • the presence of connections between neurons. 1) the use of feedback leads to the problem of dynamic stability of the network in addition to increasing the computing capacity of the network; 2) if the algorithm of the network is complicated by using several types of activation function, the computational capabilities will also increase.
It is necessary to increase the number of hidden layers and neurons in them in order to ensure the compatibility of the selected neural network with the real process and increase its accuracy.
But this, in turn, leads to an increase in the time of calculating the parameters of the neural network, which means that the speed of the model decreases.Therefore, it is important to choose the number of neurons in the hidden layer to ensure the optimal relationship between the accuracy of the neural network model and the speed of calculating its parameters.
But increasing the number of hidden layers of the neural network and the number of neurons in it, on the one hand, allows to solve the given problem with sufficient accuracy, and at the same time, it should not be too much to ensure the proportionality of the neural network to the object.
The value of the weighting coefficients depends on the amount of data to be measured.In this case, the training set is selected.The smaller the size of the training set, the smaller the necessary weighting coefficients to retain information.The value of the weight coefficients of the network, the number of its input and output elements also indicate the calculation efficiency.After choosing the structure of neural networks, its parameters are determined.We use the following formula to estimate the required number  L of synaptic weights in a multi-layer network with the transfer function "sigma": The number of neurons in the hidden layer L is calculated using the following [7]: Selection of the optimal structure and parameters of the neural network model characterizing the quality indicators of the extraction process was carried out in the object under consideration to find algorithms with high performance indicators.
The researched extraction process management system is multidimensional, the interdependence of variables and the uncertainty of the influence of factors affecting the process cause some difficulties in solving the problem of synthesis.Therefore, choosing the structure of the network function used in the synthesis of the control system based on the fuzzy-set theory, which allows taking these features into account, and finding the optimal values of its weights play an important role.
The construction of a neural network model of the oil product extraction process consists of the following steps: • the first and most important step is to determine the main factors affecting this process, as well as the vector coordinates of the model, taking into account the specific functional and organizational structure of the process, to determine the physico-chemical characteristics of the extraction process; • the efficiency of neural network calculation depends on the shape of the activation function, the number of neurons in the layers and the structural connection between the layers.In this case, the object is rendered as follows: where: A, B -matrices; x -process state; k -value of clocks; y -output value; m -time; C is the output vector.
A neural network (NN) model of an object maps its vector of input variables to a vector of output variables.The characteristics of this reflection are determined by the topological structure of the neural network, that is, the architecture, the number of layers and the number of neurons in each layer, as well as the values of synaptic connections (weight coefficients).
In this case, the issue of adapting the model to the real object is one of the main tasks.In general, building a neural network model of any process consists of several parts.Initially, the architecture of the neural network is selected depending on the nature of the process and the description of the variables.Then the variable fuzzification operation is performed.A fuzzy-logical conclusion is formed based on the knowledge base, and the true value of the process is realized through defuzzification [8].
Neural networks usually consist of several layers, the layers contain neurons and the relationships between them.
The analysis of existing types of neural networks showed that the most important indicator when using them is their accuracy and speed.From this point of view, the use of generalized-regression neural network (GRNN), which is one of the neural network methods, was proposed to solve the problem of controlling the extraction process.The structure of this network consists of one intermediate layer, with the help of which it is possible to model various functions, which in turn eliminates the need to solve the problem of calculating the number of layers and the number of neurons in the neural network structure.Choosing the optimal parameters of the neural network can be done using one of the linear optimization methods (for example, the "gradients" method) [9].
In the generalized-regression neural network, a bell-shaped sigmoidal function was selected as the activation functions for the first and second layers of neurons, and a linear function was selected for the output layer (Figure 1).Expressing the control system of the extraction process using the proposed generalized-regression network allows modeling an arbitrary nonlinear function through only one intermediate layer.Also, by choosing network layers, the number of neurons in them and their interconnections, before building the model of the process, the knowledge base can be formed and the optimal parameters of the adjuster can be calculated.In this work, the activation function of sigmoidal form was chosen to increase the efficiency of the calculation process [10].
Linear programming methods can be used to optimize the linear combination of parameters in the output layer of the network (for example, the method of gradients).The input layer of the generalizedregression neural network consists of radial basis elements, which implements nonlinear dependencies according to the following relationship: where wr is the coefficients of the weights adjusted during training, M is the number of neurons in the first layer, u is the output signal of the neural network, i.e. the control signal of the adjuster.
A one-way network method can be used to train a neural network using the difference backpropagation algorithm.
The essence of training consists in choosing such weights of arcs that minimize the difference between the results of neuro-fuzzy approximation and the actual movement of the object.A system of recurrent relations is used for training [11][12][13] ( ) ( ) ( )  [14][15] The specific derivatives t E included in the relations ( 10) -( 13) describe the sensitivity of the error to changes in the parameters of the fuzzy neural network and are calculated as follows: ( ) As a rule, the fuzzy neural network training algorithm consists of two stages.In the first step, the output model value of object y corresponding to the given network architecture is calculated.In the E is calculated and the weights of interneuron connections are recalculated using formulas ( 12) - (21).
As the activation functions of the first and second layers of the generalized-regression neural network, a sigmoidal function was taken, and as the activation function of its output layer, a linear activation function was selected.This increases the speed of network training.
The use of fuzzy artificial neural network reduces the time spent on building models of objects with different characteristics, that is, linear and fine.
Also, the proposed method of training a fuzzy artificial neural network allows to move to a new method of data processing.In this case, a new kind of fuzzy rule base can be formed.This allows you to present the obtained results in a convenient way and perform the necessary actions on them.
The use of fuzzy neural networks allows to significantly reduce the time spent on solving the problem of nonlinear object detection.
In addition, it should be noted that the training of the proposed fuzzy neural network makes it possible to switch to a new method of processing experimental information: obtaining a fuzzy rule base.The main advantage of this method is the ease of interpretation of the obtained results [16].
Based on these, the procedure for determining the parameters of standard functions was considered.
be a given. the value 1 is deleted, because the boundary points of the carrier and the kernel are taken in some approximation due to the subnormality of the activation functions of neural networks.
Let's look at the function class Obviously, this class is z -shaped sigmoidal membership functions.It is required to calculate the parameters a and b based on the database x.
Based on the properties of sigmoidal functions, we construct a system of transcendental equations:  Based on these relationships, the form and parameters of the relevance function are determined for each layer of the neural network.Then the defuzzification operation is performed, and the output signal of the neural network, that is, the control signal produced by the adjuster, is found as follows: . Algorithms for the synthesis of the control system that fully meet the requirements for the control object were developed on the basis of these relations.
It is related to the problem of finding a functional expression that provides the minimum deviation of the results of the reconstruction of functional dependencies from the results obtained in Using neural networks and fuzzy set theory, a generalized algorithm for restoring the relevance function was developed.The essence of such an algorithm is the step-by-step implementation of methods and procedures, as a result of which data is obtained in a wide format that is convenient for use, storage and processing [17][18][19].
The implementation of the algorithm is carried out according to the following sequence of actions: First, a term-set of linguistic variables of relevance functions is formed in the form of a universal set of fuzzy variables (X,T,U) based on them.Here X is the name of the linguistic variables, T is the set of its terms or values given by the relevance function (each of them are fuzzy variables), U is the universal set.
In the 1st step of the algorithm, a set of classes of functions planned to approximate the fuzzy variables

= =
, for each fuzzy variable W, expert information is collected about the values of the boundary points of the kernel and carriers, that is, the left boundary of the carrier, the left boundary of the kernel, the right boundary of the kernel, and the right boundary of the carrier.The values of these points must belong to the universal set.
Qualitative analysis of W data is performed by non-parametric classification methods using the Euclidean metric as a measure of proximity between objects.In this case, the optimal number of nearest Based on the conditions of the problem being solved, the threshold value of stability of object classes Repeat steps 4-7.
The N transformation procedure is applied to the data represented by the set W1, that is, W1 is implemented as a training sample in a neural network with a training algorithm that uses error backpropagation.the error value N  is set based on the conditions of the modeling process and the set is extracted, in this case , 4 Using the C metric, the proximity measure of the functions calculated in 12 steps with the values of the relevance functions obtained as a result of the neural network is evaluated, that is, it is calculated:  As a result, we will be able to automatically determine the type of relevance function and calculate the values of its parameters based on expert conclusions about the values of the carrier and kernels of fuzzy sets [20][21][22][23][24][25].

Conclusion
It was proposed using a generalized-regression neural network, which allows to reflect the characteristics of the considered process, to formulate the issue of controlling the oil products extraction process.An algorithm for synthesizing the parameters of the relevance function, which has different forms and is distinguished by ease of implementation, has been developed.

Figure 1 .
Figure 1.Structure of generalized-regression neural network in Simulink system the value of the output signals in the r-layer of the neural network; x -is the values of the input signals to the neural network; , r  cr -neural network parameters that can be adjusted during training.( )   -is Gaussian function.The process of collecting signals in the output layer of the neural network is carried out in the intermediate layer and looks like this: have the following system of equations: sigmoidal z-shaped function looks like this:

,
are formed, which negatively affect the stability of object classes.

2 P 2 ,
points of the fuzzy variables carriers obtained at the output of the neural network.The value of the first parameter is not used, because the parameter l W P is information about the type of the relevance function.In the analytic view l W the values are available as parameters in an undisclosed form.The error value is set based on the conditions of the process being modeled.
the result of the algorithm execution is received.
is the size of the input signal; m is the size of the output signal; N is the number of elements in the training set.