Development of a multi-channel classifier of rail line states

. The article deals with the construction of a three-channel invariant classifier that has the properties of classifying the states of rail lines into a set of classes that are invariant to changes in the longitudinal resistance of the rail line and the transverse conductivity of the insulation of the ballast material. Invariance is achieved taking into account the change in the transverse conductivity of the insulation and the longitudinal resistance of the rail line while compiling systems of equations of state for rail lines, which are the decisive functions of the classifier. The article shows that the three-channel method allows for the correct recognition of all three classes of rail line states by three decision functions with arguments - voltages and currents at the input and output of the rail line. The block diagram of the operation algorithm of the three-channel classifier of the states of the rail lines allows to form the recognition process and the majority classification depending on the states of the channels. The feasibility of the algorithm is confirmed by simulation studies on a mathematical model and graphical results.


Introduction
At the current stage of development of railways, an intensive increase in the flow of highspeed and heavy trains is characteristic, which leads to a significant increase in the requirements for the safety of train traffic, an increase in the reliability of technical means for regulating train traffic, and the problem of improving safety can be solved by the widespread use of microprocessor systems that allow software-algorithmically expanding the functionality systems of interval traffic control depending on the change in the control algorithm of the rail lines state control (RLSC).
RLSC, built on the relay of the first class of reliability, provide high reliability and operability, but their classifying functionality is limited to only two stable states of the relay.First is switched on state, which is classified as a free and serviceable state of the rail line, and second is switched off classified as a busy by train or a faulty state of the rail line [1].The switched off state of the relay implies a ban on the movement of trains, but, according to the rules of technical operation, in some cases it is allowed to pass a prohibiting traffic light with a minimum speed and readiness to stop if an obstacle is detected.At the same time, the classifier, implemented on the basis of an electromagnetic relay, classifies the faulty state of the rail line (a broken rail and a block section occupied by a train) as a class of train traffic prohibition.In this case, when the driver passes a prohibiting traffic light with a faulty rail line, the rolling stock may derail, so the movement of the train must be unconditionally prohibited.A change in the longitudinal resistance of a rail line due to fluctuations in the resistance of current-carrying joints, as well as the transverse conductivity of the insulation of rail lines, leads to the fact that the class boundaries become blurred, and the correct recognition of the states of the rail lines and the reliability of the classification become inaccurate and the electromagnetic relay cannot provide this kind of invariance influences.

Problem statement
To avoid such situations, it is necessary to develop a classifier with many classes of states with a separate classification of the control mode, which has high reliability and safety not lower than the level provided by the relay of the first reliability class, and also has invariance to the effects of disturbing factors in the form of fluctuations in the primary parameters of the rail line quadripoles.
Technological processes of complex systems, which include systems for monitoring the state of rail lines, are featured by many classes of states and a relatively small number of control commands.Regarding classifiers of rail line states, the set of classes implies the division of the state space of rail lines into subspaces of Vijk class: normal mode, when the rail lines are serviceable and free, shunt mode, when the rail lines are serviceable, but occupied by the train, and control mode, when the rail lines are free from rolling stock, but faulty (the rail breakage) [2].At the same time, the classifier also contains many components that provide control of the states of rail lines, namely: a device for matching the supply end of a rail line with a power source containing various elements in the form of transformers, capacitors, resistors, as well as a device for matching a rail line with a classifier that also contains a large number of passive elements.It follows from this that the reliability of the classification of rail line states depends on the reliability of a large number of classifier components.To diagnose and predict the states of the classifier circuit components, it is necessary to carry out continuous diagnosis of the states of the classifier circuit elements by splitting the classifier state into a set of subclasses vi, i=1,2,…,n [3].The complexity of classification of states of rail lines is also due to the fact that the class boundaries are blurred and depend on changes in the primary parameters of rail lines, namely: the longitudinal resistance of the rail line and the transverse conductivity of the insulation, which are complex variables, the nature of the impact is similar to information impacts [4][5][16][17].For example, a change in the conductivity of the insulation of rail lines is similar in nature to the presence of a train shunt, and at high conductivity, the boundaries of the classes of normal and shunt modes have common areas.The states of a rail line located on the boundaries of intersecting classes can belong to both the shunt mode and the normal mode classes with equal probability.Therefore, while synthesizing classifiers of states, it is necessary to ensure the invariance of the classifier to disturbing influences in the form of fluctuations in the conductivity of the insulation and the longitudinal resistance of the rail line.

Research questions
Thus, in the classifiers of the states of rail lines, which ensure the safety of train traffic, the occurrence of errors of the first or second kind is unacceptable.
Problems of this kind are most effectively solved by using the theory of identification with an adjustable model or the theory of recognition of multidimensional images [6,[18][19][20].Both methods have a high degree of formalization and self-tuning of the algorithm for complicating the recognition procedure under conditions of significant perturbations, by choosing the optimal number of primary informative features, the type and complexity of the decision function as well as decision rule, which allow to carry out reliable classification of states of rail lines under conditions of disturbing influences [7][8].
Thus, the problem of classifying the states of rail lines and diagnosing the classifier components can be solved by selecting the most informative features that describe the classes of states [9][10][11] (when the class is identically described within the specific class but there are differences between classes) as well as by construction of adequate decision functions of the rail line state classifier.

Materials and methods
While forming a vector of images, a system of variables based on ijk -x values of the complex amplitudes of voltages and currents at the input and output of the rail line quadripole 1 2 1 2 , , , U U I I and other variables, which can be used as four complex gear ratios and the input resistance of the rail quadripole are used: Where 1 H is the voltage transfer function; H2 is the transfer resistance; H3 is the current transfer function; H4 is the transfer conductivity, Zвх is the input resistance.
The vector of images of complex amplitudes of voltages and currents at the input and output of the rail line quadripole has the following form: It features the state of the rail line at each moment of time through a change in the amplitudes and phases of currents and voltages.
The vector of images of transfer functions and input resistance has the following form: , , , , It represents the generalized features of the classification.Decisive function A common decisive function is built for all classes and subclasses of states.The decision functions are scalar single-valued functions of the parameters of the states of the rail lines.They have the property of taking certain values (indicators) in the space of Vijk classes orijk subclasses through the images of the states [12][13].It is most convenient to use orthogonal polynomials as the decisive function of rail line state classifiers, since the complication of their form is carried out by sequentially adding new terms, which is extremely convenient while self-tuning the complexity of the decision function [14].
The classification decision rule is formed based on the results of the "training" of the classifier as follows: Where Vi -is normal mode class; Vjis shunt mode class; Vk -is control mode class.While constructing a classifier based on a microprocessor element base, the problem of ensuring the hardware reliability of state classification arises.This task can be solved by means of self-diagnostics method), as well as hardware redundancy (application of the multichannel principle and majority comparison of classification results).

Results
The principle of spatial multichanneling using frequency division of channels using the example of a three-channel rail line state classifier for railway sections with heavy train traffic and a significant fluctuation of the primary parameters of the rail line shall be considered.
A priori, on the mathematical model, the fluctuation of the primary parameters of the rail line ξ (disturbing factors) is simulated and the corresponding sets of complex amplitudes of voltages and currents are formed at the input and output of the rail quadripole (images of states) at the fundamental frequency and two additional frequencies in each of the classes of states, in the form of a system (6): Where Vijk,vijk are classes of normal, shunt and control modes and subclasses of diagnostics; ξ -perturbing factors that affect the signals of the rail line.
Based on the obtained data, systems of decisive functions are formed at the main frequency and two additional frequencies.Using (for example) the Gauss method, the resulting systems of decision functions form a working decision functions [15].It allows to classify the states of the rail lines using the current values of the complex amplitudes of voltages and currents measured at the input and output of the rail line as arguments of the working decision functions:

Findings
Figure 1 shows a block diagram of the algorithm for the formation of decisive functions and the operation of a three-channel classifier of rail line states .Invariance to disturbing influences is provided at the stage of formation of working decisive functions, when a disturbing action is assigned to each equation of decisive functions, and when solving the system of equations of decisive functions, these disturbances are compensated.Block 1 (simulation modeling) generates a set of images of the states of the rail line at three different frequencies using a four-pole equivalent circuit of the rail line and simulation mathematical modeling (system of equations ( 6)).

Classification
Blocks 2-4 form working decision functions (7) by solving systems of equations of decision functions.
Blocks 5-7 carry out a three-channel classification of the states of the rail lines, using the obtained working decision functions (7), using the measured real current values of the complex amplitudes of voltages and currents at the input and output of the rail line, used as arguments of the working decision functions.
Block 8 allows to get the measured current values of the complex amplitudes of voltages and currents at the input and output of the rail line to classify the states of the rail lines in blocks 5-7.
Blocks 9-13 implement the principle of classification according to the majority logic "2 out of 3", i.e. the system classifies the states of the rail lines correctly if at least two of the three channels are operational and the information on the outputs of these two channels is adequate.

Conclusion
It follows from the analysis of the graphs that the state space of rail lines can be classified into several classes, and this possibility is demonstrated by the example of division into three classes.The pre-trained decision functions are invariant to perturbations, and the classes are compact and well placed in the state space.It is known that the class separation coefficient, taking into account the hardware coefficient, must be at least K=1.2.Analysis of the research results shows that the decision functions satisfactorily recognize the classes of states, namely: the separation coefficients of the shunt mode class from the normal mode class are K1=1.45;K2=1.42 and K3=1.54 at the corresponding frequencies of the signal for polling the rail lines ( f1=25 Hz for the first channel, f1=50 Hz for the second channel and f1=75 Hz for the third channel).Invariant capabilities are demonstrated by a small range of change class boundaries from the minimum to the maximum values presented in the graphs in Figure 2 (a-c).

List of abbreviations
RLSCrail line condition monitoring system.

9 Fig. 1 .
Fig. 1.Block diagram of the algorithm for the formation of decisive functions and the operation of a three-channel classifier of rail line states.

Figure 2
Figure 2 shows a graphical illustration of the classification of class of normal, shunt and control modes when used as a decision function of a polynomial of the second degree of complexity and with a length of the control section of 2.5 km.While "training" the classifier and forming the decision rule (5), the following scalar values of the classes were taken as class indicators (class centers): 5.0 is normal mode class; 3.0 is shunt mode class, and 1.5 is control mode class.

Fig. 2 .
Fig. 2. Graphical illustration of the classification of rail line states: inf N , sup N are the upper and lower bounds of the normal mode class; inf S , sup S are the upper and lower limits of the shunt mode class; inf K , sup K are the upper and lower boundaries of the control mode class; ξ -disturbing factor (change in insulation conductivity, longitudinal rail line resistance); d ( X )values of the decision function; frequency of polling current of rail lines: a ) f = 25 Hz; b ) f = 50 Hz; c ) f = 75 Hz.