Research on Track Condition Monitoring Based on Fiber Bragg Grating Sensing Technology

Abstract

With the increase in the density of the subway network and the shrinking of the train departure interval, the track is prone to geometric irregularities in a long-term high-load state, which threatens the safety of train operations and reduces the comfort experience of passengers. Use fiber grating sensing technology to monitor various parameter information of the track in real time, and realize the prediction of the quality of subway track. Take a line of Beijing Metro as an example, through preprocessing of monitoring data such as box diagram analysis, over-limit analysis and correlation calculation, and using the track quality index to compare the interval prediction model based on the envelope line and the one based on amplitude compression. The prediction effect of the interval prediction model. Experiments have proved that the interval prediction model of the envelope has improved accuracy to varying degrees in the four evaluation indicators of average relative error, root mean square error, coefficient of determination and correlation coefficient, and the prediction results can be more improved. It reflects the state information of the orbital well.

1 Introduction

Structural health monitoring is an important development field in engineering disciplines, especially in the field of railway transportation. The gradual development of advanced sensing technology will undoubtedly accelerate the development of railway health detection technology. Compared with traditional electromechanical sensors, optical fiber sensors have the advantages of small size, light weight, anti-electromagnetic interference, anti-corrosion, and strong burying ability. Therefore, they have been used in the monitoring of various engineering structures worldwide.

In recent years, the monitoring system based on fiber optic sensors has caused great interest among researchers in the field of railway engineering and optical engineering. Zhang et al. [1] used fiber gratings to detect the axial direction of bolts in order to improve the reliability and safety of axle counting sensors. Strain, construct a loose self-checking method for axis counting sensor based on fiber Bragg grating. Xiaomei et al. [2] proposed a train axle counting system that uses fiber grating edge filtering and demodulation technology to achieve high demodulation frequency, which can better monitor the track status. Wheeler et al. [3] used optical fiber sensors to measure the distributed dynamic strain of rail transit during operation. The experiment explained and evaluated the displacement of the rail through displacement measurement, and analyzed the strain of the rail under low and high vibration conditions according to the distributed strain measurement technology. Xiaowei et al. [4] used fiber grating sensors to monitor the strain and temperature of railway steel bridges, and analyzed the changes in the stress of key parts of the bridge under different scenarios through wavelet analysis and genetic algorithms. Cong et al. [5] optical fiber-based quasi-distributed and continuous distributed sensing technology, through real-time data collection, inspection and detection of structural degradation, proved that the checklist is a powerful tool for detailed assessment of the railway system, including train and track behavior. Zhang Zheng [6] used the unique advantages of fiber grating sensing technology to monitor the quality status of high-speed railway tracks. Our country mainly uses the Track Quality Index (TQI) to judge the state of the track. There are single models for track quality prediction, such as the BPNN prediction model [7] and the SVM-based model [8], as well as the current combination method based on gray theory [9]. Existing methods cannot fully guarantee real-time monitoring of orbital status, and prediction methods also have shortcomings which are greatly affected by the amount of sample data, and large prediction deviations when abnormal values appear in the original data. By analyzing the theory of fiber grating and combining the special scenes of the railway track, a distributed monitoring scheme based on fiber grating sensing technology is proposed and use the gray interval prediction method to predict the monitoring data of the typical section to realize the orbit state early warning.

2 Principle and Layout of Monitoring Device

2.1 Principle of Fiber Grating Sensor

The fiber grating sensor is a fiber sensor with different core refractive index. According to Bragg's law, a beam of white light is written into the fiber grating sensor. When the light from the broadband light source passes through the grating at a specific wavelength, the reflected Bragg wavelength is related to the period of the grating and the change of wavelength changes with the change of stress and temperature. When the grating part receives external interference, the period of the grating will change, and the Bragg wavelength will also change accordingly. The change of Bragg wavelength can be calculated with the following formula:

$$ \Delta \lambda_{B} = \lambda_{B} \left\{ {(\alpha + \xi )\Delta T + (1 - } \right.\left. {p_{e} )\Delta \varepsilon } \right\} $$

(1)

Where: $\Delta \varepsilon$ is the stress change, $\Delta T$ is the temperature change, $\alpha$ is the thermal expansion coefficient, $\xi$ is the photothermal coefficient, and $p_{e}$ is the strain-optical coefficient.

In rail transit, when a train passes over the track, a certain displacement or deformation of the track will occur. By monitoring the static stress and strain of the track, the health status of the track can be judged. The main operation of track condition monitoring based on fiber grating sensor is to bury the sensor fixed in the protective device, qualitatively analyze and quantitatively calculate the force of the track line, and then calculate the geometrical individual data of the track, including level, gauge, triangle pit, Seven parameters of left and right orbit, left and right high and low.

2.2 Sensor Placement

The lead wire of the sensor embedded in the track is longer than the structure of the track itself. At the same time, in order to avoid breakage, armored fiber is the best choice for the lead. It has the function of resisting strong pressure and stretching, and can effectively adapt to the harsh outdoor environment and wiring flexible but avoid excessive stirring when pouring the buried point.

Track monitoring parameters are more sensitive to the surrounding environment. Therefore, a temperature sensor is installed at the buried point of each sensor, and it is determined whether to install humidity and wind speed sensors according to the needs of the site. When arranging points, it is necessary to analyze the track structure and the speed of the train, and calculate the stress and geometric deformation of the track under the load operation conditions of trains and passengers. Comprehensive influencing factors, only need to consider rail bending and axial tension and compression normal stress, qualitatively and comprehensively analyze the effects of various forces, evaluate the degree of influence on the track, and quantitatively calculate the ultimate bearing capacity of the track under specific conditions, so as to be more accurate Seven track irregularities parameters of level, gauge, triangle pit, left and right orbit, left and right high and low are monitored [10].

3 Track Condition Monitoring Model

3.1 Interval Prediction Model

3.1.1 Interval Prediction Model Based on Envelope

The orbital monitoring data is not strictly monotonous, but a random oscillation sequence, which is generally within a reasonable range of variation. The oscillating sequence is expanded into upper and lower interval gray sequences by using the envelope, and the range of the oscillating sequence is defined by the interval prediction modeling method [11]. The prediction model is formula (2):

$$ \hat{f}_{i} {\rm{(}}k{\rm{) = }}A_{1} {\rm{(1 - }}B_{1} {\rm{) + ( - 1)}}^{i} A_{2} {\rm{(1 - }}B_{2} {\rm{) + ( - 1)}}^{k} \cdot {\hat{f}_{i}} \rm{(2)} $$

(2)

Among them: $\hat{f}_{{i\left| {i = 1} \right.}} \rm{(}k\rm{)}$ and $\hat{f}_{{i\left| {i = {2}} \right.}} \rm{(}k\rm{)}$ are the prediction formulas for the upper and lower bounds, $k = 2, \cdots ,n$. Take the average of the two as the final predicted value.

$$ A_{1} = \frac{{2\rm{(}1 - e^{{a_{w} }} \rm{)(}w\rm{(}t_{1} \rm{)} - {{u_{w} } \mathord{\left/ {\vphantom {{u_{w} } {a_{w} }}} \right. \kern-\nulldelimiterspace} {a_{w} }}\rm{)(}e^{{ - a_{w} \rm{(}k - 2\rm{)}}} \rm{)}}}{{1 + e^{{a_{w} }} }} $$

(3-1)

$$ A_{2} = \frac{{\rm{(}1 - e^{{a_{s} }} \rm{)(}s\rm{(}t_{1} \rm{)} - {{u_{s} } \mathord{\left/ {\vphantom {{u_{s} } {a_{s} }}} \right. \kern-\nulldelimiterspace} {a_{s} }}\rm{)(}e^{{ - a_{s} \rm{(}k - 2\rm{)}}} \rm{)}}}{{1 + e^{{a_{s} }} }} $$

(3-2)

$$ B_{1} = \rm{(} - e^{{a_{w} }} \rm{)}^{k - 2} B_{2} = \rm{(} - e^{{a_{s} }} \rm{)}^{k - 2} $$

(4)

3.1.2 Interval Prediction Model Based on Amplitude Compression

The random oscillation sequence has large volatility and poor smoothness. The smoothing operator can compress the amplitude of the data sequence. The original sequence is converted into a smoother sequence after smoothing operation. The new data sequence is used as the research object to establish DGM (1, 1) The model uses the mathematical geometric sequence formula and the reduction smoothness operation to determine the prediction model of the original stochastic oscillation sequence. The model is a composite function that better simulates the random component and the fluctuation component of the sequence. Its prediction model is:

$$ \hat{x}^{{\rm{(0)}}} \rm{(}t\rm{)} = F\beta_{1}^{t - 3} - \rm{( - 1)}^{k} \rm{(}F\beta_{1}^{ - 1} - C - T\rm{)} - T $$

(5)

Among them: $T$ is the amplitude of the original oscillation sequence, $C$ is the initial value of the prediction model, $y^{{\rm{(0)}}} \rm{(1)}$ and $\beta_{1}$ are the initial value of the smoothing sequence and the model parameters, $t = 3, \cdots ,n$.

$$ F = \frac{{\rm{4(}y^{{\rm{(0)}}} \rm{(1)(}\beta_{1} - \rm{1)} + \beta_{2} \rm{)}}}{{1 + \beta_{1}^{ - 1} }} $$

(6)

3.2 Detection Data Analysis Model

3.2.1 Box Plot Analysis

While the box chart visually expresses outliers, it does not restrict the data and does not require the data to obey a special distribution. Its robustness ensures that the data is true and reliable, and will not be significantly disturbed due to the randomness of abnormal data, and is suitable for the extraction and removal of abnormal points in actual projects. The basic parameters of box chart drawing include the maximum value (max), minimum value (min), lower quartile (Q₁), median (Q₂), upper quartile (Q₃) and passing quartile of the data series. Quantile distance (IQR, the distance between Q₁ and Q₃) is the calculated outlier range.

The data distribution can be visually displayed and analyzed on the box chart. The smaller the IQR, the more concentrated the data, otherwise the more scattered, the upper and lower edges (max, min) are also the same. The relative position of the median can be used to analyze the bias of the data distribution. Relatively speaking, box plots are less affected by outliers, and the discrete distribution of data is relatively accurate and objective, which is helpful to data cleaning and other preprocessing.

3.2.2 Overrun Analysis

Through the over-limit analysis of the individual indicators of track irregularity, the safe operation status of the monitoring indicators can be determined, which can provide targeted guidance to the maintenance department.

$$ \alpha = {{\rm{(}n\beta \rm{ - 1)}} \mathord{\left/ {\vphantom {{\rm{(}n\beta \rm{ - 1)}} {\rm{(2}\gamma \rm{(}n\rm{ - 1))}}}} \right. \kern-\nulldelimiterspace} {\rm{(2}\gamma \rm{(}n\rm{ - 1))}}} $$

(7)

$$ \beta = max\rm{(}x_{i} \rm{) } = {{\mathop {max\left\{ {x_{i} } \right\}}\limits_{{\rm{1} \le i \le n}} } \mathord{\left/ {\vphantom {{\mathop {max\left\{ {x_{i} } \right\}}\limits_{{\rm{1} \le i \le n}} } {\sum\limits_{{i\rm{ = 1}}}^{n} {x_{i} } }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{{i\rm{ = 1}}}^{n} {x_{i} } }} $$

(8)

$$ \gamma = {{\mathop {sec\left\{ {x_{i} } \right\}}\limits_{{\rm{1} \le i \le n}} } \mathord{\left/ {\vphantom {{\mathop {sec\left\{ {x_{i} } \right\}}\limits_{{\rm{1} \le i \le n}} } {\sum\limits_{{i\rm{ = 1}}}^{n} {x_{i} } }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{{i\rm{ = 1}}}^{n} {x_{i} } }} $$

(9)

Among them: $\beta$ is indicates the degree of influence of the largest factor on the entire chain when considering the influence of all factors; $\gamma$ is indicates the degree of influence of any factor on the entire chain when considering the influence of factors.

3.2.3 TQI Correlation Calculation

The calculation of gray correlation degree is universal, suitable for data samples of any size, and the calculation process is not complicated. The main idea is to judge the degree of correlation between the two sets of data series through the similarity of the curve distribution shapes of the two sets of data. In order to connect the discrete data points into the polyline of the segments, a gray correlation degree calculation model is further established according to the characteristics of the polyline [11]. The closer the geometric shapes are, the greater the correlation between the corresponding sequences, and vice versa.

Deng’s gray correlation degree is used to calculate and analyze, and the system behavior sequence is set as:

$$ {\varvec{X}}_{i} = (x_{i} {(1),} \cdots ,x_{i} (k), \cdots ,x_{i} (n)) $$

(10)

Among them: $i = 1, \cdots ,m$, $k = 1, \cdots ,n$.

$$ \gamma_{i} {\rm{(}}k{\rm{)}} = \frac{Min + \xi Max}{{f_{i} \rm{(}k\rm{)} + \xi Max}} $$

(11)

$$ \gamma \rm{(}{\varvec{X}}_{0} ,{\varvec{X}}_{i} \rm{)} = \frac{\rm{1}}{n}\sum\limits_{{k = \rm{1}}}^{n} {\gamma_{i} \rm{(}k\rm{)}} $$

(12)

Among them: $f_{i} \rm{(}k\rm{)} = \left| {x_{0} \rm{(}k\rm{)} - x_{i} \rm{(}k\rm{)}} \right|$, $Min = \mathop {min}\limits_{i} \mathop {min}\limits_{k} f_{i} (k)$, $Max = \mathop {max}\limits_{i} \mathop {max}\limits_{k} f_{i} (k)$, the resolution coefficient $\xi \in \rm{(0,1)}$, ${\varvec{X}}_{0}$ and ${\varvec{X}}_{i}$ the gray correlation degree with $\gamma \rm{(}{\varvec{X}}_{0} \rm{,}{\varvec{X}}_{i} \rm{)}$ is abbreviated as $\gamma_{oi}$, $\gamma_{oi} \rm{(}k\rm{)}$ is the $k$-point correlation coefficient.

4 Monitoring Data Application Examples

4.1 Data Collection

The fiber grating sensor is applied to the track structure monitoring of Beijing subway line. The monitoring parameters include seven parameters such as level, gauge, triangle pit, left and right orbit, left and right high and low, etc., and the monitored data is consistent with the track status detected by the track inspection vehicle. The data in the report has good consistency. Taking the track monitoring data of Beijing subway line from March 2017 to June 2018 as the research object, taking the 200m track section as the recording unit, a total of 110 sets of data.

4.2 Monitoring Data Analysis

4.2.1 Box Plot Analysis

Use the Origin data processing tool to read the monitoring data and draw the TQI curve diagram and the box diagram of each individual indicator. Figure 1 shows the distribution of seven single-item box diagrams, and Fig. 2 is a TQI line diagram. Although the TQI curves are within the normal standard value range, the box diagram shows that there are more offset points in the gauge and left and right tracks.

Fig. 1.

7 single-item box diagrams.

Fig. 2.

TQI line diagram.

4.2.2 Overrun Analysis

Because there are many abnormal track gauge data, and the overrun is more serious, this indicator is selected as the research object of overrun analysis, of which 8 overrun data, and the rest are data within the range of normal standard values. The weight distribution is obtained by calculation. The over-gauge weight distribution is shown in Fig. 3, and the normal-gauge weight distribution is shown in Fig. 4. The analysis found that whether for normal data or over-limit data, the larger the value, The smaller the weight, that is, the farther away from the management standard value, the healthier the orbital state or the more serious the overrun. For overrun data, the larger the value, the more serious the overrun, the smaller the weight; for normal data, the smaller the value, The healthier the monitoring indicators.

Fig. 3.

Distribution of weights of over-gauge.

Fig. 4.

Distribution of normal gauge weights.

4.2.3 TQI Correlation Calculation

Use the track monitoring data of this line in Beijing to conduct statistical analysis and data mining on the TQI of the section and the standard deviation data of its seven sub-items. Calculate the gray correlation degree between the standard deviation of each individual index and TQI through Matlab programming, reduce the dimensions of the seven parameters of level, gauge, triangle pit, left and right orbit, left and right high and low, and arrange track maintenance more pertinently maintenance work.

Figure 5 shows the correlation between the track left and right orbit, left and right height, level, gauge, triangle pit and TQI. It can be seen from the figure that the correlation coefficients of the four sub-items of gauge, left and right orbit, and level are low, indicating that the track quality index is mainly affected by the gauge, left and right orbit, and level. The left and right height and the standard deviation of the triangle pit have little effect on the TQI. The change trend of indicators with lower correlation coefficients can reflect the change trend of TQI to a certain extent. The seven indicators are reduced to four relatively important indicators. The public works maintenance department needs to focus on the inspection and maintenance of these four indicators.

4.3 Predictive Warning of Data

The 25 sets of TQI monitoring data from a 200 m track section of this line in Beijing are used for early warning analysis. The data can be regarded as a set of oscillation sequences, so the interval prediction model based on envelope curve and the interval prediction model based on amplitude compression are used for the analysis. For short-term data early warning, the comparison of the prediction results of the two prediction models is shown in Fig. 6. To verify the reliability of the model, Mean Relative Error (MRE), Root Mean Square Error (RMSE), coefficient of determination (R2) and correlation coefficient (r) are used to evaluate the early warning effect of the model. The evaluation index results of the two models are shown in Table 1.

Fig. 5.

Distribution of gray correlation degree.

Fig. 6.

Comparison of model prediction results.

Table 1. Comparison of evaluation indicators of interval prediction models.

It can be seen from Fig. 6 that the predicted values of methods 1 and 2 are both near the true value, but the development trend of the prediction result curve of method 1 (based on the envelope-based interval prediction model) is more consistent with the development trend of the true value, and method 2 (based on The prediction trend of the amplitude compression interval prediction model) is relatively poor.

The results show that the interval prediction model based on the envelope is better. MRE is 1.585%, RMSE is 0.163, R² is 0.233, and r is 0.739. Compared with the interval prediction model based on amplitude compression, MRE, RMSE, R2 are respectively Decreased by 2.004%, 0.116, 4.291, and r increased by 0.582, indicating that the envelope-based interval prediction model is more suitable for track monitoring and early warning. Related departments can refer to the prediction results of the model to arrange work tasks reasonably and efficiently, which saves manpower and material resources. At the same time, it can ensure the safe and reliable train operation.

5 Conclusion

• (1) The use of fiber grating sensing technology to monitor the track has good consistency with the method of track inspection vehicle detection, the data is accurate and the health status of the track can be monitored in real time.

• (2) The track monitoring data is many and complex. The box chart can visually analyze the overall trend of the data, analyze the weight of normal data and over-limit data, determine the health of the monitoring data, and then analyze the TQI correlation degree to reduce the data. Maintenance treatment has been reduced from seven dimensions to four dimensions, and the public works maintenance department needs to focus on the inspection and maintenance of these four indicators.

• (3) Using the actual collected data to compare the results of the two interval prediction models, the interval prediction model based on the envelope curve has higher prediction accuracy, smaller errors, and the data distribution is closer to the distribution of real data, which is more suitable for orbital status. Monitoring and early warning.