High-precision distributed detection of rail defects by tracking the acoustic propagation waves

Cunzheng Fan; Hao Li; Baoqiang Yan; Yixiang Sun; Tao He; Tianye Huang; Zhijun Yan; Zhijun Yan; Qizhen Sun; Qizhen Sun; Qizhen Sun

doi:10.1364/OE.468193

1. Introduction

Nowadays, railway transport is moving towards high speed trains and heavy-haul trains, which brings a higher requirement for the track safety. The rail defect is one of the most concerned safety issues, such as rail deformation, poor welds, corrugation and cracks [1]. Owing to the great contact forces between wheels and defects, the track will deteriorate rapidly when a small defect occurs. Therefore, early recognition of small defects is critical for track quality monitoring and reliability assessment, which exhibits a development trend of long-distance, consecutive, high-precision, real-time, and all-weather monitoring.

A large number of works have been reported on monitoring track defects [2,3], including acoustic emission (AE) method [4,5] and ultrasonic method [6]. However, expensive AE sensors cover only a few meters, which is not applicable for long-distance rail monitoring in such a harsh environment. The ultrasound method can be only conducted in railway window period with a low scan speed, leading to the “blind spots” in time domain and high implementation cost. An alternative solution is wheel-rail interaction monitoring [7]. In order to identify and locate the track defects, Axle box acceleration (ABA) sensors and GPSs are both fixed on a train to respectively record vibration signals and locations. The method is faster and more economical than AE detection and ultrasonic detection [8]. However, noisy train environments make it hard to identify the defeats from complex ABA signals [9]. Moreover, the positioning accuracy is also limited. High speed of train and positioning deviation of commercial GPS jointly limit the positioning accuracy over ten meters, which even can confuse the track in a double-track railway. Therefore, it’s necessary to develop a high-precision distributed defeat detection method to ensure rail safety.

Recently, the distributed acoustic sensing(DAS) technology, using the optical fiber as the sensing medium, has presented great potential in distributed acoustic recording [10,11]. Benefiting from the advantages of anti-electromagnetic interference, long-distance passive measurement and corrosion resistance [12–14], fiber optic DAS has been applied in rail transit field, such as intrusions monitoring [15,16], trains position and speed monitoring [17–19] and wheelset anomalies detection [20]. Therefore, it is possible to realize the distributed monitoring by fiber DAS.

In this paper, a high-precision distributed defect detection method based on fiber optic DAS is proposed and demonstrated. When a train goes through a track defect, the wheel-rail interaction will release a elastic wave, which will further travel along forward and backward directions in the rail [21]. To record the propagation trace, the backscattering enhanced optical fiber (BEOF) is mounted on the track as a series of sensors. Further, the acoustic propagation fitting (APF) method and the dual-frequency joint-processing algorithm are introduced to identify and locate the defect with a high precision by solving intersection of two propagation traces. Finally, field test is successfully demonstrated in a 250-meter long railway section with 5 defects, achieving an 100% recognition rate and the maximum location error of 0.493m.

2. Principle

2.1 Wheel-rail interaction characteristics at the defect area

As illustrated in Fig. 1(a), the rail defects can be classified into two types according to the wavelength: long wave defects and short wave defects, which have different wheel-rail interactions but can both stimulate the elastic wave. The long wave defects primarily refer to rail deformation with a wavelength of more than 1m and a wave depth of mm level [22]. The wheel will roll over the deformation due to the minor rail surface fluctuation. As a result, the wheel will lash the rail with the following force, further exciting the elastic wave:

(1)$${F_{lw}}(z )= {{Mg \cdot \cos \theta (z )} / N} + \frac{{M{{[{{v_{train}}\cos \theta (z )} ]}^2}}}{{N \cdot r(z )}}, $$

where z is the position, ${F_{lw}}(z )$ is the force on rail when the wheel is at z, M is the train mass, N is number of wheels, g is gravitational acceleration, $\theta (z )$ is the slope of rail, ${v_{train}}$ and $r(z )$ are the speed and the deformation curvature of train respectively.

Fig. 1. (a) The principle of rail defect detection method. (b) Space-time distribution of acoustic waves.

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Besides, when the train encounters a short wave defect, the wheel-rail will disengage. Further, the wheel will fall back onto the rail, producing an impact force at the impact site ${z_0}$, which can be expressed as

(2)$${F_{sw}}({{z_0},t} )= E \cdot \zeta (t ), $$

where E and $\zeta $ are Young's modulus and crash deformation of rail respectively, which can be calculated through the following differential equations:

(3)$$\left\{ \begin{array}{l} \zeta^{\prime}(t )= v(t )\cdot t\\ v^{\prime}(t )={-} \frac{{E \cdot \zeta (t )}}{M} \cdot t\\ \zeta ({{t_0}} )= 0\\ v({{t_0}} )= {v_{train}} \end{array} \right.. $$

where t represents time, ${t_0}$ is the start time of impact, $v(t )$ is the normal velocity of wheel at the impact site ${z_0}$, and $\zeta ^{\prime}$ and $v\mathrm{^{\prime}}$ mean the first derivatives of $\zeta $ and v. Therefore, whether the train goes through the long wave defect or the short wave defect, an instantaneous elastic wave will be excited by the wheel-rail interaction.

2.2 Rail defect recognition based on elastic wave propagation

The principle of rail defect recognition method is depicted in Fig. 1. The backscattering enhanced optical fiber (BEOF) is installed on the waist rail, which serves as a series of continuous acoustic sensing channels. One end of BEOF is attached to the interrogator, which demodulates the acoustic signals and records the propagation trace of the elastic wave. Owing that the rail is a strip acoustic waveguide, the elastic wave will propagate forward and backward at a steady speed in the rail, which are presented in Fig. 1(b). Considering that defects are acoustic sources of elastic waves, it can be recognized from acoustic signal data through the propagation characteristics and then located at the intersection of two propagation paths.

2.3 Rail defect location based on APF algorithm

The forward $({{\mathrm{{\cal L}}_f}} )$ and backward (${\mathrm{{\cal L}}_b}$) propagation paths can be described as:

(4)$$\left\{ {\begin{array}{c} {{\mathrm{{\cal L}}_f}:L(t )= {v_f} \times t + {L_{f0}}}\\ {{\mathrm{{\cal L}}_b}:L(t )= {v_b} \times t + {L_{b0}}} \end{array}} \right., $$

where t is the time, $L(t )$ is the location of sound waves at the time of t, ${v_f}$ and ${v_b}$ are velocities of acoustic wave in forward and backward directions respectively, and ${L_{f0}}$ and ${L_{b0}}$ are intercepts of ${\mathrm{{\cal L}}_f}$ and ${\mathrm{{\cal L}}_b}$ respectively. As a result, the location of defect ${L_c}$ is the intersection of ${\mathrm{{\cal L}}_f}$ and ${\mathrm{{\cal L}}_b}$, which can be described as:

(5)$${L_c} = \frac{{{v_b}{L_{f0}} - {v_f}{L_{b0}}}}{{{v_b} - {v_f}}}. $$

Therefore, defects can be located successfully by fitting the waves of the two propagation paths. Here, the time of acoustic wave front reaching a certain sensing channel is defined as ToA. For ease of analysis, Fig. 1(b) is replotted as Fig. 2(a), in which the acoustic signal waveform is removed while the ToA-location distribution is retained. Moreover, the ${i^{th}}$ sensing channel at forward and backward propagation paths are named as ${f_i}$ and ${b_i}$ respectively. Correspondingly, the location of sensing channels is ${L_{fi}}$ or ${L_{bi}}$, and the ToA in different sensing channels is $To{A_{fi}}$ or $To{A_{bi}}$. Therefore, the velocities and intercepts of propagation lines can be calculated through linear fitting based on least square method:

(6)$$\left\{ \begin{array}{c} {v_f} = \frac{{\sum\nolimits_{i = 1}^N {{L_{fi}}} ({To{A_{fi}} - \overline {To{A_f}} } )}}{{\sum\nolimits_{i = 1}^N {{{({To{A_{fi}} - \overline {To{A_f}} } )}^2}} }}\\ {v_b} = \frac{{\sum\nolimits_{i = 1}^N {{L_{bi}}} ({To{A_{bi}} - \overline {To{A_b}} } )}}{{\sum\nolimits_{i = 1}^N {{{({To{A_{bi}} - \overline {To{A_b}} } )}^2}} }}\\ {L_{f0}} = \overline {{L_f}} - {v_f} \times \overline {To{A_f}} \\ {L_{b0}} = \overline {{L_b}} - {v_b} \times \overline {To{A_b}} \end{array} \right., $$

where N is the number of sensing channels in each propagation line and $\bar{x} = \mathop \sum \limits_{i = 1}^N {x_i}/N$. Then, the location of defect ${L_c}$ can be obtained according to Eq. (5).

Fig. 2. (a) ToA-location distribution of acoustic waves. (b) Phase noise induced error of ToA. (c) Sampling delay induced error of ToA

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In general, the acoustic velocity in the rail is a constant. Therefore, with a fixed velocity, ${L_c}$ can be obtained more easily as:

(7)$${L_c} = \frac{{\sum\nolimits_{i = 1}^N {[{({{L_{fi}} + {L_{bi}}} )- v \times ({To{A_{fi}} - To{A_{bi}}} )} ]} }}{{2N}}, $$

where $v = {v_f} ={-} {v_b}$ is the acoustic velocity in rail, and the symbol ${-}$ means the opposite propagation direction.

In order to discuss the location error of APF method, the errors of ToA is defined as ${E_{ToA}}$. Correspondingly, ${E_{ToA,fi}}$ and ${E_{ToA,bi}}$ are used to represent the error of $To{A_{fi}}$ and $To{A_{bi}}$ respectively. Therefore, the location error ${E_l}$ can be expressed as:

(8)$${E_l} = \frac{{v \times \left( {\sum\nolimits_{i = 1}^N {{E_{ToA,fi}}} + \sum\nolimits_{i = 1}^N {{E_{ToA,bi}}} } \right)}}{{2N}}. $$

Specifically, as described in Figs. 2(b) and 2(c), ${E_{ToA}}$ contains the phase noise induced error ${E_{ToA - n}}$ and sampling induced error ${E_{ToA - s}}$, where ${E_{ToA - n}}$ is related with system sampling rate f and the amplitude ratio of signal and phase noise(SNR), and ${E_{ToA - s}}$ is affected by f. Further, a numerical simulation is conducted to investigate the influence factors on ${E_l}$, which is described in Supplement 1. To characterize the effect of DAS noise, the parameter $\delta $ is presented, which is defined as the ratio of noise standard deviation to signal amplitude. As illustrated in Fig. 3(a) and 3(b), ${E_l}$ will decrease with the increase of N and f as well as the decrease of $\delta $. Since the limited transmission distance of sound waves will restrict the value of N, suppressing $\delta $ is an effective method to reduce the location error. Figure 3(b) shows that if $\delta $ is much less than 0.05, ${E_{ToA - n}}$ can be ignored, where ${E_l}$ can reach 0.179 m when f is 8kHz and N is 10. Another error reducing method is increasing f. As shown in Fig. 3(c), the error can be reduced to 0.09 m when f is 16kHz and N is 10. However, the increase of f will sacrifice the sensing distance of the railway, owing to the trade-off between the f and sensing range of fiber optic DAS [23]. Fortunately, there have been several effective methods to enhance the DAS bandwidth [24–26], which can ensure the location precision of the defect along the long-distance rail.

Fig. 3. Numerical simulation results. The relationship between (a) ${E_l}$, N and f when ${\boldsymbol \delta } = 0$; (b)${\; }{E_l}$ and ${\boldsymbol \delta }$ when f = 8kHz; (c)${\; }{E_l}$ and ${\boldsymbol N}$ when ${\boldsymbol \delta } = 0$.

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2.4 Dual-frequency joint-processing algorithm for higher location precision

Previous studies have shown that wheel-defect interaction has three dominate frequency bands with the central frequency around 40 Hz, 800 Hz and 1200 Hz, respectively [6,27]. Owing to the different propagation velocities, the different frequency signals will interfere with each other, leading to the ToA error. Therefore, the interference and white noise will be depressed by extracting a single frequency band. Due to the larger low-frequency noise in DAS, two higher frequency bands of 800 Hz and 1200 Hz are selected for further analysis.

Moreover, the structures’ difference between different defects brings a different energy and a different energy distribution at various frequency bands, which may cause a poor SNR and further bring a larger error ${E_l}$. To improve the locating accuracy, a $\kappa $-index method is proposed, in which signals in two frequency bands are used to locate defects independently, and the result with higher precision is selected according to the following evaluation parameter:

(9)$$\kappa \textrm{ = }\frac{{{\textrm{R}_f}^2\textrm{ + }{\textrm{R}_\textrm{b}}^2}}{2}, $$

where $R_f^2$ and $R_b^2$ are the regression coefficients ${R^2}$ of the fitted forward and backward propagation lines, respectively, which are defined as

(10)$$\left\{ \begin{array}{l} {\textrm{R}_f}^2 = 1 - \frac{{\sum {[{To{A_{fi}} - ({{L_{fi}} - {L_{f0}}} )/v} ]} }}{{\sum {({To{A_{fi}} - \overline {To{A_f}} } )} }}\\ {\textrm{R}_b}^2 = 1 - \frac{{\sum {[{To{A_{bi}} - ({{L_{bi}} - {L_{b0}}} )/v} ]} }}{{\sum {({To{A_{bi}} - \overline {To{A_b}} } )} }} \end{array} \right.$$

where $\overline {To{A_f}} $ and $\overline {To{A_b}} $ are the average values of $To{A_{fi}}$ and $To{A_{bi}}$ for i ranging from 1 to N, respectively. According to Eqs. (8) and (10), a larger ${R^2}$ means a lower ${E_{ToA}}$ and a smaller ${E_l}$. Therefore, the defect location will be optimized with the $\kappa $-index method.

3. Field test

To verify the practicability of the proposed defect detection method, a field test was conducted in a test rail. In the test, the self-developed DAS system based on coherent detection and polarization diversity reception is used as interrogator. The schematic diagram is shown in Fig. 4(a) [28] and its principle is introduced in Supplement 1. Specially, the BEOF is used as the sensing cable, in which a series of scattering enhanced points (SEPs) is inscribed through UV exposure. The SEPs can enhance the power of the backscattered light and suppress the coherent fading noise [11]. The sampling frequency of DAS was set as 8kHz and a 250 m BEOF cable with a 2 m spatial resolution was fixed on the waist of rail, which is depicted in Fig. 4(b). There are 5 defects with the size of $7\textrm{cm}({length} )\times 1\textrm{cm}({width} )\times 3\textrm{cm}({depth} )$ along the tested rail, locating at about 81 m, 104 m, 129 m, 155 m and 204 m, respectively. As displayed in Fig. 4(d), a GC-270 heavy rail car was driven along the tested rail with a speed of 30 km/h.

Fig. 4. (a) Schematic diagram of DAS system. Photographs of the field test environment: (b) Optical Fiber cable laying on the rail waist. (c) The vertical view of a defect. (d) The side view of a defect. (e) The field test environment and test train.

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Firstly, taking the defect at 204 m as an example, we recorded and plotted acoustic signals of two typical sensing channels as shown in Figs. 5(a). One channel is close to the defect and another is far away from the defect. It can be seen that the precise ToAs cannot be obtained due to the strong noise. Then, band-pass filter (BPF) with the passbands of 600Hz-800 Hz and 1100Hz-1300 Hz are respectively adopted to extract the effective signals. As plotted in Figs. 5(b) and 5(c), the signal-to-noise ratio is significantly improved.

Fig. 5. The temporal waveforms of (a) original acoustic signal and filtered acoustic signals through (b)600Hz-800Hz BPF and (c)1100Hz-1300Hz BPF. Space-time distribution of acoustic signals filtered by (d) 600Hz-800Hz BPF and (e)1100Hz-1300Hz BPF.

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In the following, the signal space-time distributions of two frequency bands are plotted in Fig. 5(d) and Fig. 5(e), respectively, where the signals of different channels are added with different bias. Taking the signal within 600Hz-800 Hz as an example, the sensing channel positions and the corresponding ToAs are extracted and listed in Table 1. Then, the backward (${\mathrm{{\cal L}}_b}$) and forward $({{\mathrm{{\cal L}}_f}} )$ propagation lines are fitted as

(11)$$\left\{ \begin{array}{l} {\mathrm{{\cal L}}_f}:\textrm{L}(m )= 5263.72820 \times t(s )- 6.19670479 \times {10^5}\\ {\mathrm{{\cal L}}_b}:\textrm{L}(m )= \textrm{ - }5\textrm{357}.\textrm{50719} \times t(s )\textrm{ + }6.\textrm{31123757} \times {10^5} \end{array} \right.$$

According to Eqs. (4) and (5), the defect location can be calculated as 204.8375 m with the evaluation parameter $\mathrm{\kappa }$ of 0.996. Similarly, the defect location can be calculated as 204.9592 m with the $\mathrm{\kappa }$ of 0.992 by using the signals of 1100Hz-1300 Hz. For the higher $\mathrm{\kappa },{\; }$ the corresponding defect location of 204.8375 m is selected as the final defect location. To evaluate the stability of the method, ten tests are carried out for 5 defects, and the results are displayed in Table 2. It can be seen that all the tests for defects can be detected with the recognition rate of 100%.

Table 1. The locations of channels and their ToA

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Table 2. The locations result of five crack in ten tests

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Furthermore, we analyzed the performance of dual-frequency joint-processing algorithm. The location errors of 10 tests are presented in Fig. 6(a), where the black points represent the 1100Hz-1300 Hz results, the red points represent 700Hz-900 Hz result, and the blue points are the optimized results through $\kappa $-index method. It is obvious that the optimized results are more centralized than single frequency results. Figure 6(b) presents the location standard deviations obtained from Fig. 6(a), which proves that the $\kappa $-index method can effectively improve the localization accuracy with the maximum standard deviation of only 0.314 m. What’s more, the defect location error can be further optimized through increasing the sampling rate and reducing the noise.

Fig. 6. (a)The defect-location error results from a single frequency and ${\; }\kappa $-index method. (b) The standard deviations of defect-location results.

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4. Discussion

In the field test, our method can distributedly detect defects with a 100% recognition rate and a sub-meter location accuracy. Compared with previous methods, our method has the improvement in terms of detection range, location precision and portability capability.

a. The AE detection and ultrasonic detection methods can only cover a few meters, which is usually used for local damage detection. In our method, the DAS system can record the wheel-rail interaction signals over ten kilometers and the defeats over ten kilometers can be found.
b. There is a trade-off between detection accuracy and detection range in defeat detection field. More precise detection needs denser sensors and suffers greater data pressure. In our method, the location precision was improved to much less than acoustic acquisition spatial resolution and we realized the high precision defeat location.
c. Some defect identification method with machine learning has been reported [29], while the methods usually have a poor portability and need accumulate a lot of data to improve recognition accuracy in new environment. Our method is based on the wheel-rail interaction, a physical law applicable to all tracks. Therefore, our method can work on different rail environments.

Although our method is still conducted in a non commercial track with large size and dense defects, the test can also verify the effectiveness. Compared with the train running signal, the elastic wave has unique frequency band and unique space-time distribution, which can be easily identified and extracted even in the commercial tracks. Besides, the small cracks can also excite elastic waves by the wheel-rail interaction and the elastic waves can be tracked by DAS, although the energy may be smaller. Finally, the defects farther away each other will make our method perform better, since the elastic waves will avoid overlapping each other and bringing crosstalk.

5. Conclusion

A high-precision, distributed and on-line track defect recognition scheme based on fiber optic DAS system is proposed and demonstrated. When a train goes through defects, the wheel-rail interaction will generate instantaneous elastic waves. Through the fiber DAS system with the sensing fiber cable mounting along the railway, the bidirectional propagation of elastic waves can be detected. Then, the defects can be detected and located by solving intersection of two propagation traces. Theoretical analysis shows that the location error is related to the DAS noise and sampling frequency. Further, the dual-frequency joint-processing algorithm is adopted to depress the phase noise and improve the location precision. The experiments in the test rail proves that APF with dual-frequency joint-processing algorithm can detect defects with a 100% recognition rate and a sub-meter location accuracy. To the best of our knowledge, this study firstly reported a method for distributed and on-line defects recognition with a sub meter location accuracy and up to tens of kilometers. The proposed method offers a new insight for high-precision structural damage detection and can provide a reference for the infrastructures safety monitoring such as the railway, pipeline, tunnel.

Funding

National Natural Science Foundation of China (61775072, 61922033); the Wuhan Science and Technology Bureau Achievement Conversion Project (2018010403011330); Fundamental Research Funds for the Central Universities (HUST:2021JYCXJJ036); the Young Eagle Program Cultivation Program from Zhejiang Provincial Market Supervision and Administration Bureau (CY2022228); Optics Valley Laboratory, Hubei 430074, China; the Innovation Fund of WNLO.

Acknowledgments

We thank China Railway SIYUAN survey and design group CO.,LTD for providing field trial environments.

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.

Supplemental document

See Supplement 1 for supporting content.

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Backward propagation direction		Forward propagation direction
Location/m	ToA/s	Location/m	ToA/s
173.8451599	117.769500	207.2469233	117.764000
176.8168696	117.768500	209.246955	117.764375
180.5760069	117.768000	211.3022729	117.764750
183.4382522	117.767500	213.0443617	117.765125
185.7608405	117.767125	214.8733776	117.765500
187.821577	117.766750	216.9201251	117.765875
189.3916841	117.766375	218.9702757	117.766250
191.5840073	117.766000	221.2779683	117.766625
193.5471346	117.765750	223.149352	117.767000
195.2784821	117.765250	224.8773548	117.767375

Location result/m	Crack 1	Crack2	Crack 3	Crack 4	Crack 5
Test 1	80.48417	104.4077	129.5298	154.9968	204.3436
Test 2	80.73452	104.2227	128.8849	155.1731	204.5797
Test 3	80.88238	104.2874	128.8169	155.2168	204.0725
Test 4	80.63754	104.6090	128.7008	155.3502	204.0474
Test 5	81.00013	104.9134	129.4304	155.3191	204.5722
Test 6	80.58026	104.5024	129.3957	155.4378	204.8375
Test 7	81.00029	104.8020	129.1564	155.0678	204.5185
Test 8	80.73468	104.8591	128.5670	154.9527	204.5447
Test 9	80.34482	104.5002	129.0492	155.0937	204.4012
Test 10	80.19296	104.3098	128.8406	155.3664	204.6249

Backward propagation direction		Forward propagation direction
Location/m	ToA/s	Location/m	ToA/s
173.8451599	117.769500	207.2469233	117.764000
176.8168696	117.768500	209.246955	117.764375
180.5760069	117.768000	211.3022729	117.764750
183.4382522	117.767500	213.0443617	117.765125
185.7608405	117.767125	214.8733776	117.765500
187.821577	117.766750	216.9201251	117.765875
189.3916841	117.766375	218.9702757	117.766250
191.5840073	117.766000	221.2779683	117.766625
193.5471346	117.765750	223.149352	117.767000
195.2784821	117.765250	224.8773548	117.767375

Location result/m	Crack 1	Crack2	Crack 3	Crack 4	Crack 5
Test 1	80.48417	104.4077	129.5298	154.9968	204.3436
Test 2	80.73452	104.2227	128.8849	155.1731	204.5797
Test 3	80.88238	104.2874	128.8169	155.2168	204.0725
Test 4	80.63754	104.6090	128.7008	155.3502	204.0474
Test 5	81.00013	104.9134	129.4304	155.3191	204.5722
Test 6	80.58026	104.5024	129.3957	155.4378	204.8375
Test 7	81.00029	104.8020	129.1564	155.0678	204.5185
Test 8	80.73468	104.8591	128.5670	154.9527	204.5447
Test 9	80.34482	104.5002	129.0492	155.0937	204.4012
Test 10	80.19296	104.3098	128.8406	155.3664	204.6249

High-precision distributed detection of rail defects by tracking the acoustic propagation waves

Abstract

1. Introduction

2. Principle

2.1 Wheel-rail interaction characteristics at the defect area

2.2 Rail defect recognition based on elastic wave propagation

2.3 Rail defect location based on APF algorithm

2.4 Dual-frequency joint-processing algorithm for higher location precision

3. Field test

4. Discussion

5. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (6)

Tables (2)

Equations (11)

Optics Express