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Abstract
The distributed acoustic sensing system can obtain the vibration signal caused by the vibration of the train. By analyzing these wheel-rail vibration signals, an abnormal wheel-rail relationship identification scheme is proposed. The variational mode decomposition is employed for signal decomposition, thereby obtaining intrinsic mode functions with prominent abnormal fluctuations. The kurtosis value of each intrinsic mode function is calculated, which is compared with the threshold value for the identification of trains with abnormal wheel-rail relationship. And the extreme point of the abnormal intrinsic mode function is used to locate the bogie with an abnormal wheel-rail relationship. Experimental demonstration verifies that the proposed scheme can identify the train and locate the bogie with an abnormal wheel-rail relationship.
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1. Introduction
Fast and safety transport the passengers to their destination is the prior course of the metro system. Among the factors that affect the safe operation of trains, the wheel-rail relationship is one of the vital aspects. Abnormal wheel-rail relationship may lead to accidents such as derailment and rollover of trains, which will bring serious safety hazards to rail transportation [1]. Periodically machining train wheels is the most important method to maintain the normal wheel-rail relationship, but this method has a long cycle and cannot detect trains with abnormal wheel-rail relationship in time.
In order to ensure the safe and stable operation of trains and timely discover trains with abnormal wheel-rail relationship, researchers have proposed a series of methods. For instance, Wang et al. installed a camera under the train to capture the image of the track, thus realizing the identification of fastener anomalies [2]. However, the cost of deploying cameras on each train is prohibitive, and using images to identify faults can only detect surface defects. Zhou et al. deployed 10 pairs of FBG sensors on the track to detect wheel defects, and analyzed the reasonable layout scheme of the sensors [3]. However, the coverage of ten pairs of sensors is small, and the use of multiple FBG sensors is not conducive to large-scale multiplexing. Yan et al. installed a microphone near the bogie to collect the noise when the train is running, and realized the classification of normal background noise and abnormal impact sound [4]. However, the effect of microphones on sound collection is greatly affected by the environment, and the cost of deploying high-quality microphones on each train is high.
In recent years, significant progress has been made in fiber-optic distributed acoustic sensing (DAS) technology [5–7]. The DAS system can continuously monitor acoustic signals and vibrations within a range of tens of kilometers with high sensitivity and high update rate, thereby realizing all-time and all-domain monitoring [8]. In addition, since the sensing principle of the DAS system is optical fiber sensing, the DAS system has strong anti-electromagnetic interference capability, and the cost is low, which is convenient for large-scale multiplexing. A typical DAS system is the phase-sensitive optical time-domain reflectometer ($\Phi$-OTDR). Compared with the general DAS system, it has higher sensitivity and faster response speed, so it has received extensive attention since it was proposed [9]. Moreover, changing the structure or type of the optical fiber is an important way to further improve the signal-to-noise ratio of the $\Phi$-OTDR, for example, replacing the grating array with an ultra-weak fiber Bragg grating array (UWFBG) [10,11].
We propose an abnormal wheel-rail relationship detection method based on DAS system. The method utilizes variational mode decomposition (VMD) to decompose the vibration signal generated by the DAS system while the subway train passes through the FBG sensors, calculates the kurtosis value of each mode [12], and combines the kurtosis threshold to discriminate the normal wheel-rail relationship signal from the abnormal signal. Finally, this paper proposes a fault localization method based on the position of modal extreme values, which can automatically detect the position of the bogie where the wheel-rail relationship is abnormal.
The rest of this paper is organized as follows. Section 2 introduces the sensing principle of the DAS system and the difference between the normal and abnormal signals detected by the system. Section 3 introduces the principle of the abnormal wheel-rail relationship detection algorithm. In Section 4, the actual wheel-rail vibration signals are used to demonstrate the effectiveness of the proposed algorithm. Finally, conclusions are drawn in Section 5.
2. DAS system and wheel-rail vibration signals
2.1 Principle of distributed acoustic sensing system
Figure 1 shows the basic principle of the employed DAS system. The reflectivity of the UWFBGs of the sensing optical cable in the system is about −50 dB. In addition to improving the signal-to-noise ratio, the use of UWFBGs can also reduce the crosstalk between gratings and greatly improve the multiplexing capacity of the system. In the sensing system, the continuous-wave light emitted by the narrow linewidth laser is modulated into an optical pulse train after passing through an electro-optical modulator. Among them, the central wavelength of the narrow linewidth laser is 1550.12 nm, the linewidth is 3 kHz, the repetition frequency of the optical pulse sequence is 1 kHz, and the pulse width is 20 ns. Then, the optical pulse train is amplified by an erbium-doped fiber amplifier and injects into an UWFBG array. The pulsed light reflected by the UWFBG array enters an unbalanced Michelson interferometer consisting of a $3 \times 3$ coupler, two Faraday mirrors, and a delay fiber whose length matches the distance between the UWFBGs. The output of the coupler is ultimately directed to three photodetectors [13].
Figure 2 shows the deployment of the above DAS system in the tunnel of Wuhan Metro Line 7. Specifically, the optical cable of the system is laid beside the subway track between YeZhiHu Station and HuGong Station. The sampling rate of the system is 1 kHz, and the inter-UWFBG distance is 5 meters, which means that every two UWFBGs and 5 meters of fiber between them constitute one sensor [14]. Therefore, the system can detect vibration signals in the tunnel with an accuracy of 5 meters. The DAS system contains a total of 170 UWFBGs between HuGong and BanQiao Stations at a distance of about 1 km, and they constitute 169 vibration sensors, of which the first sensor is near HuGong Station and the 169th sensor is near BanQiao Station. When the train passes each sensor, the remote monitoring center located near the HuGong Station can receive the vibration signal caused by the train running vibration through the sensors of the DAS system.
2.2 Analysis and comparison of wheel-rail vibration signals
Based on the DAS system, as the train passes, we can obtain the wheel-rail vibration signal sensed by each sensor. Figure 3 shows a typical wheel-rail vibration signal. The signal can reflect the structural characteristics of the train, such as the number of carriages [15] and bogies. In the Fig. 3, we mark the positions of the six carriages. And each carriage contains 2 bogies.
Fig. 3. Typical wheel-rail vibration signal obtained by the sensing system. C1: the 1st carriage; C2: the 2nd carriage; C3: the 3rd carriage; C4: the 4th carriage; C5: the 5th carriage; C6: the 6th carriage.
To further illustrate the difference between normal and abnormal signals, we compare a normal and an abnormal wheel-rail vibration signal detected by the sensing system on 10 July 2021. As shown in Fig. 4, the time-domain waveform of the normal signal is smooth and accompanied by regular fluctuations, while the time-domain waveform of the abnormal signal has irregular pulses. Although such anomalous waves can be identified manually, their amplitudes are not prominent in the overall signal. Therefore, in order to automatically identify abnormal signals, we propose a new anomaly identification algorithm.
3. Principle of proposed anomaly detection algorithm
Figure 5 shows the flowchart of the proposed anomaly detection algorithm, which mainly includes signal decomposition by VMD, feature extraction by kurtosis, anomaly identification by kurtosis threshold, and faulty localization by extremum.
3.1 Signal decomposition by VMD
The variational mode decomposition algorithm is a method with a solid mathematical foundation, designed for modal variation and time-frequency analysis of signals [16]. According to the given number of decomposed modes, VMD can adaptively match the optimal center frequency and limited bandwidth of each mode to achieve efficient separation of intrinsic mode functions (IMFs) [17].
VMD assumes that a signal $x(t)$ can be decomposed into a series of IMFs [18], written as:
where $K$ is the preset number of modes and ${u_k}(t)$ is the $k$th mode. IMFs are defined as amplitude-modulated-frequency-modulated (AM-FM) signals [19]: where ${\phi _k}(t)$ is non-decreasing phase function, ${\phi '_k}(t) \ge 0$, ${A_k}(t)$ is non-negative envelope function, ${A_k}(t) \ge 0$. It is important that the instantaneous frequency function ${\omega _k}(t): = {\phi '_k}(t)$ and the envelope function ${A_k}(t)$ vary much slower than the phase function ${\phi _k}(t)$.The specific decomposition process of the VMD algorithm is as follows: First, the unilateral spectrum is obtained by using the Hilbert transform. Second, the spectrum of each mode is transformed to the baseband. Third, the bandwidth of each mode is obtained by using the demodulated signal. Finally, the result of the VMD algorithm can be transformed into a constrained variational problem as:
Then, the updating algorithm of mode $u_k$, center frequency $\omega _k$ and Lagrange multiplier $\lambda$ can be obtained based on the Alternating Direction Method of Multipliers (ADMM):
In addition, the convergence formula of VMD iteration is:
The function of VMD is to adaptively decompose the frequency components of the wheel-rail vibration signal. As described above, the magnitude of the abnormal fluctuations in the abnormal signal is not prominent enough. However, the frequency of abnormal fluctuations is usually above 10Hz, while the main frequency of wheel-rail vibration is within 10Hz. Since VMD calculates the center frequency of each mode by calculating the center of gravity of its power spectrum, we can use VMD to obtain narrow-band IMFs containing extreme anomalous fluctuations.
The wheel-rail vibration signal is preliminarily decomposed into 4 IMFs by VMD, and the quadratic penalty parameter $\alpha$ is set to 1000 by default. Figure 6 and Fig. 7 show the normal wheel-rail vibration signal and the abnormal wheel-rail vibration signal in Fig. 4 and their VMD decomposition results.
As mentioned in the previous section, in Fig. 6, there are no abnormal fluctuations in the signal and no outliers in the IMFs. However, in Fig. 7, there are abnormal fluctuations in the signal, and the abnormal fluctuations are mainly decomposed into IMF3. The difference between the IMFs obtained by decomposing the two signals is obvious. Therefore, it is effective to perform VMD decomposition on wheel-rail vibration signals.
3.2 Feature extraction by kurtosis
Achieving low-loss dimensionality reduction of signals is a key issue in feature extraction, which will greatly affect the judgment of the algorithm. More importantly, the result of feature extraction must be able to distinguish the features of the original signal [12].
We first use VMD to decompose the wheel-rail vibration signal. Since the decomposed IMFs contain extreme abnormal fluctuations, we choose to calculate the kurtosis coefficient value of each IMF component.
Kurtosis is a statistical measure used to describe the time-domain distribution of time series [20], which can indicate the peak and impulsiveness of time series. Compared with Gaussian distribution, it can measure the shape characteristics of time series. Specifically, when there are extreme values in the time series, the corresponding kurtosis will increase significantly. Therefore, kurtosis can effectively describe the time domain distribution of the signal and the peaks in the signal. Based on the characteristics of VMD and kurtosis, we perform further feature extraction on the wheel-rail vibration signal, which is mainly divided into two steps:
(1) Calculate the kurtosis values of modes obtained by VMD decomposition:
(2) The feature vector of signal is constructed based on the kurtosis values of all modes:
Figure 8 shows the VMD-based kurtosis eigenvectors of the above two signals. It is clear from Fig. 8 that the eigenvector component of the normal wheel-rail vibration signal is around 4, while the abnormal wheel-rail vibration signal has a component much larger than 4. Therefore, two kinds of wheel-rail vibration signals can be easily distinguished by the VMD-based kurtosis feature vectors.
Although the signal features extracted using VMD and kurtosis can effectively distinguish the two signals, further research is needed on effective quantifiers of the abnormal level of the abnormal wheel-rail relationship.
3.3 Anomaly recognition and faulty localization
As mentioned in section 3.2, IMFs derived from anomalous signal decomposition contain anomalous fluctuations, while time series that contain extreme values have greater kurtosis calculated. Therefore, the components of the eigenvectors calculated by the abnormal signal will be significantly larger than the components of the eigenvectors of the normal signal. We preliminarily set a kurtosis threshold to 10 in order to discriminate these signals. If a kurtosis value greater than the threshold is detected, the corresponding IMF is considered to be an abnormal IMF, and the corresponding original signal is considered to be an abnormal wheel-rail vibration signal.
In addition, in the wheel-rail vibration signal, the abnormal fluctuation of the signal indicates the abnormal position of the wheel-rail relationship. When the abnormal fluctuations are separated into IMFs, the position of the extreme value of the abnormal IMF is consistent with the position of the abnormality of the wheel-rail relationship. Therefore, combined with the position of the extreme value of the abnormal IMF, we can locate the bogie with abnormal wheel-rail relationship.
The correspondence between the above abnormal IMF and the abnormal signal is shown in Fig. 9. In Fig. 9, the abnormal fluctuations in IMF3 are the abnormal fluctuations separated from the original signal, and the position of the extreme value of IMF3 is consistent with the position of the abnormal fluctuations in the original signal. Therefore, the first bogie with abnormal wheel-rail relationship in the corresponding train is located by the position of the extreme value of IMF3. It is worth noting that the train corresponding to the abnormal wheel-rail vibration signal is found to have wheel tread wear on the first bogie in the subsequent maintenance.
As shown in Fig. 2, there are 169 sensors between Hugong Station and Banqiao Station on Wuhan Metro Line 7, the fusion detection results of all these sensors can improve the abnormal wheel-track relationship detection performance. Since the effect of using kurtosis to extract signal features is greatly affected by signal quality, we select 70 good signals with smooth and clear waveforms to perform sensor fusion. In addition, the quality of the signal can be measured by spectral entropy, which measures the uncertainty of the energy of the signal under the division of the power spectrum. The calculation formula of spectral entropy is:
where $f_s$ is the sampling rate, and ${P(f)}$ is the normalized power spectral density of the signal. In fact, the quality of the signal is better when its spectral entropy value is less than or equal to 0.3.For each passing train, we can collect the detection results from selected 70 sensors using a simple voting scheme. If a sensor thinks that a passing train may have an abnormal wheel-track relationship, it votes for that train. The trains with a relative majority of votes have a high probability of having an abnormal wheel-track relationship. On 10 July 2021, there are 156 passing trains in Wuhan Metro Line 7, and we calculate the voting map of the signals generated by these trains in the selected 70 sensors, as shown in Fig. 10.
In the Fig. 10, the voting results of the 8th, 31st, 54th, 77th, 100th, 123rd, and 144th passing trains have relative majority votes. These passing trains are the same metro compartment that passes through the Hugong-Banqiao section seven times a day. The interval of these passing trains is basically 23, which is the running number of metro trains on Wuhan Metro Line 7 on that day. The periodic pattern of abnormal wheel-rail relationship in the voting map verifies the effectiveness of the proposed algorithm in determining whether the train has an abnormal wheel-rail relationship. We can tentatively conclude that the trains with a relative majority of votes are the trains most likely to have abnormal wheel-rail relationships and require further maintenance by mechanical specialists, while the remaining trains with a relatively small number of votes are the trains that may have abnormal wheel-rail relationships and require attention.
4. Experimental results and analysis
In order to verify the effectiveness of the proposed anomaly detection algorithm, field experiments are conducted on Wuhan Metro Line 7. The vibration signal caused by the train running vibration is obtained by the sensing system shown in Fig. 1 and the experimental platform shown in Fig. 2.
Before performing anomaly detection, we first set the appropriate VMD decomposition parameters. Considering the kurtosis distribution of the two signals, we need to ensure that the difference between the maximum modal kurtosis obtained from the abnormal signal and the maximum modal kurtosis obtained from the normal signal is the largest. Based on this idea, we performed three-mode, four-mode, five-mode, and six-mode decompositions on the signal on 18 July 2021 in the experiment, and found that the difference in kurtosis is the largest when performing four-mode decomposition. Furthermore, it takes an average of 0.5 seconds for the test computer to decompose each signal into 4 modes. When processing a large number of signals sensed by the DAS system, the multi-threaded execution of the algorithm can have high efficiency. Therefore, in this paper, the number of decomposition modes is finally set to 4. In addition, after analyzing abnormal signals and normal signals detected by the DAS system on 18 July 2021, we set the kurtosis threshold to 10.
On 18 July 2021, there were 157 passing trains between Hugong Station and Banqiao Station, the temperature change throughout the day in the subway tunnel has no obvious effect on the signal sensed by the DAS system. And we calculate the voting map of the signals generated by these trains in the selected 70 sensors, as shown in Fig. 11.
In Fig. 11 the 11th, 34th, 57th, 80th, 103rd, 126th and 146th trains have a majority of votes. The periodic pattern of the abnormal wheel-rail relationship in the voting map is observed again. According to the position of the extreme point in the abnormal IMF corresponding to the 11th passing subway, we locate the bogie with abnormal wheel-rail relationship as the 1st bogie. The corresponding abnormal signal and abnormal IMF are shown in Fig. 12.
5. Conclusion
In this paper, an abnormal wheel-rail relationship identification scheme based on DAS system is proposed. First, sensors with good signal quality are selected. Then, the wheel-rail vibration signals are decomposed into a series of IMFs by VMD, so as to obtain modes with obvious abnormal fluctuations. After that, the kurtosis value of each mode is calculated and compared with a threshold value to identify abnormal wheel-rail vibration signals. Finally, the bogie with abnormal wheel-rail relationship is located by the extreme point of the abnormal mode. The experimental results show that the scheme can identify the train and locate the bogie with abnormal wheel-rail relationship. It is worth noting that the further work of this paper may involve working with the mechanical expert to quantify the level of anomaly of the abnormal wheel-rail relationship.
Funding
National Natural Science Foundation of China (61735013, 62075171, 62275205); Natural Science Foundation of Hubei Province of China (2022CFA034).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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