Railway monitoring system using optical fiber grating accelerometers

From a general point of view, fiber optic accelerometers based on FBG technology not only benefit from all the advantages of fiber optic sensors but offer also an important instrumentation capability that is not possible using conventional accelerometers: compatibility with FBG-based strain and temperature sensors, thereby enabling the operation of fiber-based sensing networks. In our work, we benefit from this feature by taking the measurements using both FBG strain sensors and FBG-based accelerometers interrogated by the same equipment from a remote location.

As sketched in figure 1(a), a typical FBG accelerometer includes a flexible cantilever with an FBG mounted on it at one end, and a mass at the other end. When a vertical acceleration is applied on the cantilever beam, a varying axial strain is created on the grating (due to the alteration of flexion and compression), which is proportional to the distance from the neutral axis. The induced strain is demodulated by measuring the corresponding Bragg wavelength shift (alternating between positive and negative extremes).

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In our implementation, a commercial accelerometer (OS7100, MicronOptics) with one axis configuration was attached on the sleeper and connected to the sensors network, as shown in figure 1(b). The frequency range of this particular accelerometer was sufficient for both axle counting and speed calculations.

Fibers connected to the accelerometers, as well as fibers containing the FBG strain sensors were positioned on the Mons-Liège rail tracks (Belgium), nearby the railway station of La Louvière Sud (GPS position of 50.465 643, 4.188 260) in a $\ll 100\,{\rm{zone}}\gg ,$ i.e. a zone for which the speed of the trains does not exceed 100 km h⁻¹. In general, the train speed at the measurement point is about 30–90 km h⁻¹.

The layout of the whole monitoring system used in our measurements is shown in figure 2. It comprises one FBG accelerometer mounted on the sleeper, various FBG strain sensors placed on the rails, couplers, junction boxes, and the protected feeder cable providing the connection between the sensor network and the interrogator. For a given measurement, the outputs of the FBG strain sensors and the FBG accelerometer are acquired simultaneously on input channels of the interrogator that is located in a remote equipment room. Commercial spectrometer-based interrogators with acquisition rates between 1 and 3 kHz, an absolute wavelength measurement accuracyae of 40 pm and a precision of 1 pm were used in the measurements.

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The relationship between the main geometry of the train (i.e. wheel set spacing, bogie spacing and carriage length) and the spectral content of rail vibration has already been demonstrated and successfully validated in a previous work [5]. The periodicity of the axle (L_a), the bogie (L_b), and the cars (L_c) lead to three different amplitude modulations of the spectrum having corresponding frequency components, f_a, f_b, and f_c. These frequency contents can be calculated as [15, 16]:

$$\begin{eqnarray*}&&{f}_{a}=\displaystyle \frac{v}{{L}_{a}}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{f}_{b}=\displaystyle \frac{v}{{L}_{b}}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{f}_{c}=\displaystyle \frac{v}{{L}_{c}}\end{eqnarray*}$$

in which the vehicle speed is assumed to be constant. In addition to these dominant frequency components, in phase (50–300 Hz) and out of phase (200–600 Hz) vertical vibrations between the rail and the sleepers, together with the pinned-pinned resonances (800–1000 Hz) affect the vertical track dynamics [13]. Moreover, there are residual vibrations recorded by the accelerometer when the wheels are approaching to (and leaving from) the sensor location. These unwanted frequency components have been eliminated by using low-pass filters (LPF) in the proposed trace analysis. Instead of applying a single LPF on the whole trace however, we first divided into segments the raw signal at the accelerometer output. Indeed, the vibration signature (hence the frequency response) corresponding to different parts of the train differ from each other, depending on the train geometry (i.e. the total length, number of cars, and the wheel set positions), the train load and the wheel set conditions. In our analysis, based on the analysis of several raw traces corresponding to different train configurations, this behavior has been validated.

Such a segmentation procedure is demonstrated in figure 4, for a 3-coaches train circulating at about 84 km h⁻¹ (23.33 m s⁻¹). In this example, the raw trace is segmented into 4 parts corresponding to first and last axles, as well as axle pairs of contiguous train coaches. As it can be seen from the figure, the frequency response is different for each segment. Still, for all the segments, the noise components are observed to be significantly stronger in the same frequency range of about 700–800 Hz.

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By taking the frequency value at the center of this dominant noise band (700–800 Hz in this particular example) and applying a multiplication constant, the cut-off frequencies of the individual filters are determined. In this way, for each segment, high frequency vibrations above cut-off frequency are eliminated from the useful low frequency components such as f_a (axle periodicity that is related to wheel set spacing, f_a = 10 Hz in this example case).

The dominant noise frequencies observed on the raw traces by the on-side measurements (tens of measurements over more than three months on 7 different train types) varied between 150 and 800 Hz. These frequency components are absolutely beyond the frequency range of f_a, f_b, and f_c (e.g. f_a would have been equal to 25 Hz even if the train speed had been increased to 200 km h⁻¹. It should also be noted that f_a > f_b > f_c).

Once the segments of the raw trace are low-pass filtered, the envelope detection algorithm is applied on them to determine the axle positions (peaks of the envelope trace). The envelope detection process consists in: first, converting the measured real-valued signal to the corresponding analytic signal (using Hilbert transform), and then, taking the magnitude of this analytic signal. In this process, we implemented the option that applies the spline interpolation over two successive local maxima of the envelope over a given number of samples (i.e. envelope width).

These steps are represented in figure 5 for segment 3 of our example case. The accelerometer output for segment 3 (figure 5(a)) is first low-pass filtered (using F_c−1 = 225 Hz). The vibration signature becomes fine at the output of the filter (figure 5(b)). Envelope of the filtered signal is then found as represented in figure 5(c) (blue line). The width of the envelope detection algorithm is taken as about 1 m, providing the required spatial resolution to resolve wheel positions (distance between axes varies from 2.30 to 2.55 m). Peak search algorithm applied to the envelope trace determines the axle points. In this example segment, the time difference between peaks 2 and 1 is found to be 0.10 s. Using this value and the distance between axles (L_a = 2.3 m), the instantaneous speed of the train is calculated as 23.00 m s⁻¹ (82.8 km h⁻¹), which is in good agreement with the average speed of the train measured on the reference video. Similar result has been obtained considering the peaks 3 and 4.

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In the final stage of the signal processing algorithm, the analyzed segments are merged to re-obtain the global processed signal. Axle positions now being indicated on this signal, the time difference between the last axle and the first axle positions is determined. Knowing the total length of the train, the average speed is then calculated. The flowchart of the signal processing steps applied on the raw trace is summarized in figure 6.

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Figure 7 represents two traces before and after the proposed data processing steps for our example case (3-car Desiro AM08 train at 84 km h⁻¹). As can be seen in the figure, the axle positions in the raw trace are blurred with the vibration noise components but are clearly resolved after the suppression of this effect with the provided signal processing steps explained above (see figure 6).

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Thanks to our long-term outdoor installation, numerous field tests were carried out (with intervals of few months) to validate both the hardware of the monitoring system and the related signal demodulation algorithm. Results demonstrate the capability of the proposed system in both counting the number of axles of a given track section (without any miscount), as well as the average train speed estimation. Table 1 summarizes some examples of axle counting and speed measurement results for different train types. Main properties of the tested trains are given in Table 2. Speed values obtained by the proposed system are compared with that coming from FBG strain sensors deployed on the field trial as well as reference videos.

The results provided by the three approaches (video, FBG strain, FBG accelerometer) are presented in figure 8 for the ten different train configurations (train number 6 and 9 are excluded from this figure as one of the reference speed information is missing for these two cases). The error on the reference speed values is determined by the camera resolution (which is 1/30 s). Based on the resolution value and time intervals measured for all the trains, the maximum absolute error was calculated as 1 km h⁻¹.

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