THE USE OF THE EXPERIMENT PLANNING METHOD TO EVALUATE THE ACCURACY OF FLEXIBLE UNITS IDENTIFICATION

Purpose. The identification of rolling stock on the railroads is an integral part of many automation systems as trains in general and cars separately. Various information management systems at sorting yards require the operational information about the object while performing the manufacturing operations. The improvement of the determination accuracy of different parameters characterizing the rolling stock, leads to the immediate quality progress in the traffic volumes management. The aim of the paper is to develop a method to estimate the errors of determination the interaxle distance of the flexible units in the control section using the point path-control transducer for future identification of cars and locomotives. Methodology. To achieve this goal the simulation method and experiment planning were used. The simulation model allowing determining the time intervals between the collisions of wheelset of movable units in point path-control transducer on the control section with variable characteristics of identification devices was developed. The values of the time intervals obtained with using the simulation mode were applied in the method of experiment planning to the final target. Findings. The calculated analytical values of the errors of the interaxle distances do not have the significant differences from values obtained using the simulation model. It makes possible to use the received functional dependence to estimate the possible errors in the identification of rolling stock. The results of this work can be used to identify separate flexible units, and trains in general. Originality. The functional dependence of the error of the interaxle distance error from the fixing point of the wheel path-control transducer, the distance between the sensors and the measured distance was derived using a previously conducted research of the factors influencing the error in determining the interaxle distance of the movable units, and developed simulation model to calculate the interaxle distance. Practical value. This functional dependence allows solving the following tasks: to calculate the maximum possible error of determining the interaxle distance of the movable units at known parameters of control section and calculation of parameters of the control section, when the possible acceptable error of determining the interaxle distance of the flexible units is known.


Introduction
Identification of rolling stock on the railroads, as trains in general and cars separately, is an integral part of many automation systems.Various information and management systems at sorting yards, performing the manufacturing operations, require the operational information about the object [8-11, 16, 17].Improving the determination accuracy of different parameters characterizing the rolling stock, leads to the immediate improvement quality progress of car traffic volumes management.The increase in the accuracy of the information, automatic acquisition and processing of signals increase the capacity of the station due to the time advantage when certain manufacturing operations is amenable to automation.And this in turn the decrease in cost of transportation, increase of cars use rationality, the liberation of human resources, improving the traffic safety on the railways, etc.
To the range of such systems tasks the following definition of the static characteristics of the rolling stock that passed the control section relates: the number of axes, number and number of axes of movable units, movable units type (platform, covered car, etc.), etc.In this case, each of the systems is presented in the form of implemented method to identify the flexible units consisting of reset algorithm, processing and analysis of data, and also the constructive possibilities of the control section and their means of railway automatics [1-3, 7, 14].
This paper considers a method of determining axle base of the movable units; more precisely the analysis of possible faults in determination of this parameter identification is carried out.Determination of interaxle distance of the flexible unit is the most often used to determine its type, which in some systems will allow determining a few figures of its item numbers.One of such systems is described in the paper [7].

Purpose
The aim of this work is to develop a method to estimate the determination errors of the interaxle distances of movable units in the control section using the point path-control transducer for future identification of cars and locomotives.

Methodology
The simulation method and experiment planning were used to achieve this goal.
Simulation model for determination the interaxle distance of the flexible units.
Definition of interaxle distance of the movable units used in various automated control systems at sorting yards and the adjacent railroad tracks.It is the most relevant to the tasks of determination the type of movable units, car base or cut, the axle counting systems, etc. Various methods of identification are applied, using special control sections, which includes the point path-control transducer, track circuits, photocells and other trackside assets used at the railway transport.In this paper, a method for determining the type of the movable units according to the calculated interaxle distances is considered.This method uses a control section which consists of three control points (point pathcontrol transducer).The error of determining the interaxle distance arising from the use of such methods are associated with the mismatch moment of actuation of the track point detector with the passage of car wheels over the geometric center of the detector.This mismatch in the operation of the detector is taken as a random variable, distributed according to the normal law (Fig. 1).
The values taken in figure 1: δ -error of the detector, L ∆ -the operating range of the detector, S -the interaxle distance of the movable unit, L -the distance between the control points CP1, CP2, CP3 which include one or two coupled track point detectors.
Fig. 1.The section structure of the identification phase of the rolling stock that is implemented in the simulation model To study the effect of various factors affecting the identification process the simulation was chosen.The description of the simulation model is represented in the work [6].It was suggested that the following factors affected the error of identification the most significantly: − the initial speed of the wheel pair run over on the control section − the acceleration of motion at the control section; − the distance between the detectors; − the value of the interaxle distance; − accuracy of the point path-control transducer work (root mean square of the distance of the fixing wheel of movable unit by the normal law of distribution from the detector center, distributed by the normal law of distribution [15]).
The researches have shown that the speed and acceleration of flexible unit movement not have effect on the error of the interaxle distance determination in compared with other factors significantly.
The application of the experiment planning method.The obtained results with using the simulation model provide an opportunity to analyze quantitatively and qualitatively the possible errors of movable units identification, as well as their dependence on a number of factors affecting the identification process.However, this research does not allow calculating an expected error of identification definitely.To complete the task the method of experiment planning was chosen.Using this method, it is necessary to define the formula using of which is possible to determine the expected error for selected control section, means of railway automatics and identifiable rolling stock unambiguously.
All subsequent calculations in this chapter were carried out according to the method of experiment planning which was presented in the works [5,13].
The control section on which was the determination of interaxle distance of the movable units was chosen as the object of research.The factors influencing on this process and described above were selected as the effects on the process, namely: − the initial speed of the wheel pair run over on the control section, namely the first control point CP1 ( i V ); − the acceleration of motion at the control section ( a ); − distance between the detectors ( L ); − the value of the measured interaxle distance ( S ); − precision of point path-control transducer work ( t σ ).
In this case the response is taken as the value of the average quadratic deviation the error of determining the interaxle distance S ∆ σ .
In result the chosen research object is described with five influences and one response, the study of which is our task.The resulting model of the experiment corresponds to a multifactorial experiment with one response.
In the initial experiment was consisted of five factors.The plan FFE 25 (five-factor two-level full factorial experiment) was used.The following values of the factors were taken as levels: − initial speed i V -3 and 15 m/s; − acceleration a -0.1 and 0.5 m/s 2 ; − distance between the detectors L -3 and 6 m; − the value of the measured interaxle distance S -2 and 14 m; − the accuracy of point path-control transducers t σ -0.002 and 0.01 m.
The following results were obtained at processing the conducted experiments: − the above mentioned factor levels of the simulation model did not meet the requirements of uniformity and adequacy; − to achieve uniformity and adequacy of the model is possible only if reduce the intervals of variation of factor levels, which in turn is unacceptable for the description of the identification process; − the values of speed and acceleration were not significant in compared with other factors as it was in the analysis of simulation results, and at processing the results of applying the method of experiment planning.
It was decided to conduct a multi-level threefactor experiment after analyzing the results of the previous experiment.The following independent variables were selected as factors: − distance between the detectors L ; − the value of the measured interaxle distance S ; − precision of point path-control transducer work t σ .
The variation of the factors was made as follows: the distance between the detectors was varied at two levels (range 3-6 m), the levels values -3 and 6; the accuracy of the detector work on three levels (range 0,001-0,008 m), the levels values 0,002, 0,004 and 0.006; interaxle distance at four levels (range 1.5-15 m), the levels values 2, 5, 8 and 11.The levels values of interaxle distance factor were adopted according to the conducted analysis of cars and locomotives of 1 520 mm gauge [4,12].
As it was noted above, the aim of the study is the analytical dependences obtaining the average quadratic deviation of the determination errors of the interaxle distance S ∆ σ as a function of three variables -L , S and i σ .Preliminary analysis showed that this dependence cannot be described neither linear nor quadratic dependence.To determine the required dependence the device of orthogonal polynomials and planning of multi-level experiments was adopted.Control points used to construct the system of orthogonal polynomials, will be varied with a constant step, therefore, the polynomials can be obtained using the recurrence formula [5]: where X -some of the physical independent variable or factor; N -number of experimental points; r -degree of the corresponding polynomial, 1,0,1,..., 1 r N = − − .
In our case, the maximum degree of used polynomials is equal to 3. Therefore, the polynomials will be calculated by the following formulas: ( ) where r λ -the multipliers, which depend on the number of variation levels N and the degree of polynomial r; X -average value of factor; dthe step of varying.
It is necessary to make the transition from the physical to the coded variables by the formulas for the more compact forms of the orthogonal polynomials: when when N -even number.
In result the values of the polynomials for each of the variables will be as follows: − variable L ranges at two levels, it will fit to a single polynomial of the first degree: − variable t σ , ranges at three levels, it will correspond to the polynomials of the first and second degree: − variable S ranges at four levels, it will correspond to the polynomials of the first, second and third degree: In addition to these polynomials the model will include paired and triple products of different variables polynomials.Thus, for ease of notation the polynomials the symbols of the received as follows will be applied: ( ) i P x =Pr i .The experiment plan includes 24 control points, and therefore the same number of coefficients.Numbers of experimental points u , plan and results of the received response are presented in the table.The 5 parallel experiments were conducted for each selection.
The row mean values and dispersion were computed using the formulas: where n -the number of parallel experiments; ui y -the value of i-th response for u-th selection The Cochran criterion was chosen for the checking of row dispersions uniformity.According to this criterion, the coefficient cf G =0,192 (for n=5 and N=24) was obtained from the Cochran distribution for the significance level of α =0,05.The Cochran criterion for conducted experiments was obtained by the formula The value of the p G is equal to 0,165 that is less than the value cf G , and then the uniformity of the row dispersions estimates is evident.The values of b-coefficients were calculated according to the formula ( ) ( ) The obtained values of b-coefficients were included in the resulting table of calculations.In the resulting table the columns of only those model members were taken into account, b-coefficients of which were statistically significant.The statistical significance of the b-coefficients was tested by the formula The coefficient table t = 2.06 was taken from the tables of the Student distribution on significance level α = 0,05 the number of freedom degrees is equal to 24.The next step is to test the adequacy of the model, which was performed by F -criteria.According to this criterion the critical value cr F =1,94, taken from tables of F distribution for significance level α =0,05 and number of degrees of freedom ad f =8 and y f =96, must be less than the calculated calc F calculated by formulasе ( ) where u y -the value of the response at the point; l -the number of significant b-coefficients.
The value of calc F appeared to be equal to 0.49, which is less than cr F , and it shows the adequacy of the model.
As a result of the experiments and processing the data, it became possible to write the adequate equation models 0,00966 0, 00425 It is necessary to move from coded variables to their physical variables to obtain the required analytical dependences.Finally the required equation will be as follows: 2 ( , , ) 0,0593 0,0054

Findings
In the result of research and calculations the analytically valid values computation of the errors of the inteaxle distances of the movable units depending on the parameters of the control section, means of railway automatics and object identification became possible.

Originality and practical value
In the work the estimation mechanism of the possible errors of determination the center distance of the movable units was improved.That can improve the accuracy of identifying methods work, using the control section with defined point pathcontrol transducer.Using the previously conducted studies of factors influencing on the errors of determining the interaxle distances of the movable units and developed simulation model to calculate the interaxle distance, the functional dependence of the error of the inteaxle distances from the error of the fixing point with the wheel point path-control transducer, the distances between the detectors and the measured distance was derived.
This functional dependence allows solving the following tasks: to calculate the maximum possible errors of determining the interaxle distance of the movable units at known parameters of control section and the parameters computations of the control section, at the possible acceptable errors of determining the inteaxle distance of movable units.

Conclusions
Results processing of the simulation process of determining the interaxle distance of the movable units on the control section allow drawing the following conclusions: − values of speed and acceleration motion of the movable units are not essential for the identification process in comparison with other factors; − the errors increase of the detector work leads to the error increasing in determining the interaxle distance; − the increase of the measured interaxle distance increases the value of the identification error; − increasing of the control section length leads to a reduction of the identification error.
Applying the method of experiment planning the analytical dependence of the interaxle distance error determination was obtained as a function of the following quantities: − distance between the detectors L ; − the value of the measured interaxle distances S ; − precision of the point path-control transducer t σ .
These recommendations are relevant for building the various information systems which are used as the input data of the movable units characteristics, received using the measuring on the control sections with applying the point path-control transduce.