Determination of rail deformations using fiber optic technologies

. This paper discusses the application of the fiber-optic technologies in measuring the parameters of the stress-strain state of a seamless track rail. Measuring modules are attached directly to the side surface of the rail and contain fiber-optic sensors with a special structure for changing the refractive index along the length of the base part. The values of deformations are determined during full-scale measurements when analyzing changes in the parameters of the light pulses passing through an optical channel with Bragg gratings. The implemented approaches in measurements and simulation are relevant for the sections of the railway track that are most susceptible to deformations with a large gradient of values, for example, at turnouts, in the places of subgrade heaving, etc.


Introduction
The increase in vehicle speeds, passenger and cargo transportation, connectivity of settlements and territories within a single agglomeration forces the development of transport highways, including not only the construction and reconstruction of transport infrastructure facilities, but also the improvement of the operational characteristics of the existing transport network [1], including rail transport. From the point of view of deformation of the upper structure of the path [1,2], the most vulnerable are the areas with different rigidity, for example, structures of a ballast-free path (due to possible problems with water drainage and frost heaving) (Fig. 1a), the paths in deep recesses and tunnels (due to the peculiarities of groundwater occurrence) (Fig. 1b).
In this paper, approaches are developed that allow modeling and implementing a system for diagnosing rail strings based on fiber-optic measurement and data transmission systems [3]. Optical fiber in a protective sheath is proposed to be glued to the stripped side surface of the neck of the rail whip [4][5][6] and, according to the changes in the parameters of the transmitted light pulses, it can help to evaluate the deformation of the rail in real time. When a signal is transmitted over an optical fiber, it is attenuated, dispersed, nonlinear effects (self-modulation, cross-modulation, four-wave mixing, etc.) [7,8]. Analyzing the changes in the characteristics of the pulse at the entrance and exit of the fiber-optic system [7][8][9], it is possible to obtain information about the factors that caused these changes, including the deformation of the rail fragments. After processing, the information obtained can be interpreted in the form of standard defects, the types and parameters of which are regulated by current industry standards [10,11]. The structure of the proposed monitoring system is implemented as a software and computing complex. With the help of simulation, the possibilities of using optical pulses with shapes of six types are studied. The stages of setting up the measuring system precede the actual installation of sensors at the railway landfill and make it possible to reduce both the cost of the life cycle of the monitoring system and the number of errors during its operation.

The problem statement
Fiber-optic sensors measuring sample deformations use a change in the spectrum of a direct or reflected optical pulse as primary information about the state of the detected element. In this case, it is required to fully know the characteristics of the optical waveguide, and, along the length of the measuring base, it is proposed to use a fiber with a Bragg grating alternating layers with different values of the refractive index [12,13]. Bragg elements make it possible to install a significant number of sensors on one waveguide and, due to spectral and wave multiplexing, receive, process and interpret data from each of them. A significant advantage of this approach is the passivity of the devices used, i.e. they do not require additional energy transmitted through conductive wires, and such sensors are not susceptible to external electromagnetic interference and aggressive environment at different times of the year. The principle of operation of Bragg elements is to transmit radiation through a fiber from a source (or a system of radiation sources) with a significant wavelength range, which sequentially passes through a system of sensors, each of which has its own unique central resonance wavelength. Radiation with its own wavelength range is reflected from each Bragg element, which is then processed by a spectroanalyzer. Based on the determination of the shift of the central resonant wavelengths, the temperature and absolute strain of the Bragg gratings can be calculated according to the following expression [4,7]: where eff n is an effective refractive index of the grating, Λ is the lattice period, l is the absolute deformation at the base length of the measuring element, T is the actual temperature change, which can act as a detectable value or a verification parameter for the third-party measurement of the temperature of the rail lash. The first and the second terms of the expression (1) determine the shift of the central wavelength of the sub-band depending on the absolute elongation of the sample at the base length and on the temperature, respectively. The central wavelength of the reflected radiation sub-band depends on the relative deformation according to the formula [10,11]: where z is the deformation of the sample at the base length of the sensor, is the effective elasto-optic coefficient considered constant for each specific type of the waveguide. In (3), 11 p and 12 p are Pockels' coefficients in the elastic-optical tensor, is Poisson's ratio for the fused silica. For a standard SF type optical fiber, these values take the following values: The change in the wavelength of radiation due to mechanical deformations is determined by the lengthening /shortening of the rail at the base length of the sensor, and the change in wavelength due to temperature changes is determined geometrically (the sensor itself is lengthened and the period of the Bragg element changes) and the optical increase in the sensor array. Therefore, the dependence of the central wavelength of the reflected radiation subrange on temperature is determined by the following expression [7,8]: where is the coefficient of thermal expansion of the material, n is the thermo-optical coefficient. For the germanium doped optical waveguide used, these magnitudes take the following values: When using the radiation of the third window of transparency ( nm) in the informationmeasuring system, the sensitivity of the sensor in determining the relative deformation at a fixed temperature is 12.5 nm/%, and the sensitivity of determining the temperature is 13.5 pm/ C.

The solution method
The presented ratios (1)-(4) allow one to simultaneously determine the temperature and deformation changes in the state of the detected element, if an information-measuring system is used with the sensors that have different periods and experience the same effects, i.e. it is possible to separate the influence of the used spectrum of mechanical deformation and temperature influence on the displacement. The disadvantage of using Bragg sensors is the low polling speed, which some measurement and monitoring systems try to increase by using Fabry-Perot interferometers, but this, in turn, leads to an increase in the error of the measured values due to an increased interference. To solve this problem, it is necessary to take into account the resolution of the interferometer, which affects the dynamic range of the measured values and the accuracy of detecting useful signals against noise [11]. The graph presented in Fig. 2 shows how the resolution of the Fabry-Perot interferometer affects the dynamic range of the received signals. While carrying out the simulation, it was taken into account that the measurement error of the resonant wavelength should not exceed 10 pm.
where own -own losses ( abs -signal power loss for absorption in the core and primary fiber shell material, sc -scattering losses); add -additional losses ( cab -cable losses; op -operating losses). Further, the results of simulation of the proposed system using a mathematical computing complex are carried out, since full-scale experiments in laboratory conditions are possible on only short fragments of rails, and the installation of the system equipment at a test site or on an actually operating section of the railway requires many approvals and is possible exlusively within the technological windows for major repairs taking place once every 5-10 years. Figure 3 shows graphical dependences for the power of the light pulses at the output of the fiber-optic path of the information and measurement system, obtained by the joint resolution of expressions, for six different types of input optical pulses. On the abscissa axis, the duration of the optical pulse in seconds is represented, and on the ordinate axisthe reduced signal power.
From the analysis of the graphs in Fig. 3, it can be seen that the pulses with the numbers 1, 2, 3, 5 are more distorted due to attenuation than the pulses with shapes 4 and 6. For the application in an information-measuring system, it is proposed to choose a Gaussian pulse with a chirp (lower right graph in Fig. 3), as it has spectral characteristics that change less due to chromatic dispersion than the type 4 pulse. Simulation has demonstrated that the pulse duration of this form will monotonically increase under the condition 0 2 C , and when the inequality 0 2 C holds, the duration will decrease to a minimum value ( 2 0 min 1 C T T ),and then it will begin to increase. The pulse duration (the Gaussian form with chirp) at the output of the fiber-optic path of the monitoring system can be represented in the following form:

Conclusion
The presence of the chip makes it possible to exert a controlling effect on the output duration of the signal at a given geometric length of the optical channel and the maximum broadening of the pulse. The chip also allows transmitting additional information that is needed for optimal tuning of the receiving optoelectronic module and improving the accuracy of measuring the absolute deformations of rail lashes along the length of the Bragg grid. The proposed approach to the procedure for estimating and measuring the condition of rail lashes/lashings allows using simulation to select the parameters of sensors and monitoring systems before their direct installation into the railway track, thus saving time and finances during a subsequent verification. The proposed approach makes it possible to measure the parameters of the stress-strain state of the rail lashes with high accuracy, noise immunity, speed and resistance to external factors. The analysis of the influence of various factors for the developed monitoring and diagnostics system has proven that the proposed approach for creating, configuring and operating an information and measurement system based on fiber-optic measurement modules can be used in the field of monitoring the condition of track facilities and transport infrastructure in general.