Research on signal enhancement technology of ultrasonic guided wave detection of rail crack based on spread spectrum technology

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This article proposes a signal enhancement technique for the processing of guided wave signals, aiming to improve the signal-to-noise ratio by enhancing the detection signals. Building upon traditional ultrasonic guided wave detection, this technique utilizes Barker codes as pseudo-random sequence codes and employs Binary Phase Shift Keying (BPSK) modulation to encode the original excitation signal, resulting in a new excitation signal. This achieves spread spectrum processing of the excitation signal and subsequent despreading of the received signals. An experimental platform for detecting subsoil cracks in rail tracks using ultrasonic guided waves was established. Comparative experiments were conducted on artificial cracks of different sizes at the bottom of rail tracks under both spread and non-spread conditions, calculating the attenuation coefficient of received guided wave signals. The results demonstrate that after applying this signal enhancement technique to guided wave signals, compared to unprocessed original guided wave signals, there is a significant reduction in attenuation coefficient when propagating over the same distance. As a result, ultrasonic guided wave signals can propagate over longer distances with increased sensitivity towards cracks of similar sizes at the bottom of rail tracks. These findings provide support for ultrasonic guided wave detection of subsoil cracks in rail tracks. Physical sciences/Physics/Techniques and instrumentation/Characterization and analytical techniques Physical sciences/Physics/Applied physics/Acoustics rail crack detection Barker code ultrasonic guided wave signal enhancement Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction With the development of high-speed and heavy-haul railways in China, under the environment of rapid economic development and the coexistence of various modes of transportation at the present stage, railway transportation still occupies an extremely important position in China's national economic system, which is called "the main artery of the national economy" [ 1 , 2 ] . It is increasingly urgent to carry out online non-destructive testing of rail to monitor rail quality. General rail cracks are easy to grow in the waist and bottom of the rail, with the development of cracks, cracks will reach a rapid expansion stage. When the crack area is large, the crack will develop to the surface of the rail head, so that the crack gradually develops into a broken rail, which is one of the important reasons affecting the normal operation of the rail. At present, Guided Wave Testing (GWT) is often used to detect rail cracks. Reference [ 3 ] gives an example of a classic trackside ultrasonic inspection system. On the basis of this system, a new ultrasonic guided-wave signal processing method based on SVD and independent component analysis is proposed for the remote detection and location of transverse defects of rail head. Reference [4] developed a 5% on-line defect detection system that can detect the cross-sectional area of the bottom rail of the switch. Hu Pan et al. [ 5 ] studied the method of active guided wave mode feature extraction and switch spallation damage location based on time-frequency analysis, and realized guided wave mode feature extraction and damage location of mild spallation damage. In the application of ultrasonic guided wave rail crack detection in the actual environment, the guided wave signal will inevitably be interfered by various noises, thus reducing the signal-to-noise ratio, which is not conducive to the identification of cracks in the rail. Therefore, it is necessary to conduct relevant signal processing for the guided wave in the rail [ 6 ] . The characteristic of spread spectrum technology is that it has strong anti-interference ability, and it has been widely used in radar field in the early days. Literature [ 7 ] et al. analyzed the anti-jamming mechanism of direct sequence spread spectrum system (DSSS) and analyzed and deduced the anti-jamming performance of radar communication, laying a foundation for the theoretical analysis of DSSS. Literature [ 8 ] defines the two indexes of energy efficiency and echo sequence correlation in ultrasonic spread spectrum applications. The Binary Phase Shift Keying (BPSK) and Binary Frequency Shift Keying (BFSK) are compared and discussed. Parameter configuration of three modulation methods, including BFSK and Binary Amplitude Shift Keying (BASK). Literature [ 9 ] et al. applied spread spectrum technology to the field of acoustic positioning to solve outdoor mechanical location, which can reduce the interference effects caused by wind speed and machine noise, proving that spread spectrum technology can ensure reliable signal transmission. Based on the pulse compression method in the communication principle, a single pulse signal or a short pulse signal is replaced by a multi-element encoding method. This method does not need to increase the excitation voltage of the excitation signal, but increases the average excitation power by increasing the excitation time of the signal. Then, the energy of the excitation signal is re-compressed and restored to a short-time pulse signal by relevant decoding methods, so that the resolution of the signal for crack identification is not affected by this method, and the signal-to-noise ratio of the system can be well improved [ 10 ] . In this paper, BPSK technology is applied to ultrasonic guided wave detection of rail bottom crack, and the anti-interference ability of spread spectrum technology is used to improve the propagation distance of ultrasonic guided wave signal, so as to improve the detection sensitivity of ultrasonic guided wave on rail bottom crack. 2. The selection of coding sequence and spread spectrum technique At present, the commonly used encoding can be divided into BinaryPhase Shift Keying (BPSK), linear frequency modulation signal (Chirp), etc. It can also be divided into multiple transmission coding and single transmission coding according to the transmission frequency of the encoded signal [ 11 ] . Phase coding, also known as binary coding, usually refers to a binary coding sequence composed of "1" and "-1" to achieve 180 on a single transmitted excitation signal. Phase coding; Frequency coding, also known as continuous wave coding [ 12 ], usually adds a guided wave signal to a signal with a continuously changing frequency [ 13 ] . According to these two classification methods, the common pseudoranding sequence codes are classified as shown in Table 1 . Barker code and M-sequence code belong to the single-emission coding mode in phase coding, while Golay code also belongs to phase coding but consists of a set of mutually complementary coding sequences. Chirp code, as a typical non-stationary signal, is a kind of linear frequency modulation signal coding method which is often used in radar and other fields. These common coding sequences can also be used as pseudo-random sequence codes of spread spectrum technology [ 14 ] , because the coding calculation method and spread spectrum method are similar, so the effect of both is the same. Table 1 Classification of common spread spectrum pseudorandom sequence codes Single launch Multiple launches Phase coding Barker code, M sequence Golay code Frequency coding Chirp coding As a phase encoding method, binary coding sequence is theoretically not limited by bandwidth. Compared with the phase coding method, Chirp signal is more sensitive to ambient noise and susceptible to interference, and its hardware implementation is more complicated than that of binary coding [ 15 ] . Compared with barker code, the main sidelobe of M sequence is worse. Table 2 Comparison of sequence codes of common spread spectrum techniques Encoding mode Advantage Disadvantage Barker Only need a single transmission, phase coding, hardware easy to implement The maximum code length is only 13 digits M sequence No code length limit, single transmission, phase coding, hardware easy to achieve The main sidelobe is poor Golay It reduces the sidelobe interference of aperiodic sequence, has no code length limitation, and is easy to implement in hardware Need two launches Chirp code Can control the range sidelobe level, single transmission, no code length limit Complex hardware design As shown in Table 2 , from the perspective of auto-correlation, the main lobe width and sidelobe level are used as measuring standards to make a comparative analysis of common sequence codes. In terms of sidelobe elimination, compared with Barker code, Golay code has better performance due to complementary coding sequences. Under the same code length, Barker code has the highest autocorrelation main sidelobe ratio [ 16 ] . In terms of the number of incentives, Golay code uses complementary coding sequences, so it needs two incentives, while Barker code only needs a single incentive, which is relatively easier in hardware implementation and has good autocorrelation characteristics, which is more suitable for practical application development. Therefore, this paper chooses Barker code as the pseudo-random sequence code of spread spectrum technology. An n-bit Barker code element [x0,x1,...,x(N-1)] consists of "1" or "-1". When the code element is "1", the waveform obtained is in the same phase as the original waveform. When the code element is "-1" [ 17 ] , the waveform obtained is opposite to the original waveform, and the phase difference of the original waveform after the two code elements is π, and several Barker codes form the pseudo-random binary spread spectrum code required by signal spread spectrum technology. B[N]=[x 0 ,x 1 ,…,x (N−1) ],x i ∈{-1,1} (1) The decoding process after encoding is also called pulse compression. According to the principle of pulse compression, the product of the actual time-bandwidth is equivalent to the signal-to-noise ratio gain after signal compression [ 18 ] . The signal-to-noise ratio gain of the encoded signal is related to the length N of the coded code, so the signal-to-noise ratio gain ASNR after Barker code processing can be expressed as follows: A SNR =10logN, N∈{2,3,4,5,7,11,13} (2) According to formula (2), in order to obtain the maximum SNR gain, 13-bit Barker code should be selected as the coded element. At present, the common Spread Spectrum technologies include direct sequence Spread Spectrum, Frequency Hopping Spread Spectrum (FH-SS), and Time Hopping Spread Spectrum (TH-SS) [ 19 ] . Direct spread spectrum (DSS) technique is to extend the bandwidth of the transmitted signal by injecting the signal to a higher rate pseudo-random sequence code. Frequency hopping spread spectrum (FSS) is a technique that discretely selects the output spectrum of the carrier oscillator using pseudoranity codes, so that the frequency of the transmitted signal changes with the change of the binary pseudoranity sequence. Time-hopping spread spectrum is similar to frequency-hopping spread spectrum in that the signal to be transmitted is divided into multiple time slots in the timing [ 20 ] , and the pseudo-random spread spectrum code controls the signal in which time slot, because the time slot is much narrower than the original frame in the timing, so as to achieve the purpose of broadening the spectrum. Since FH-SS uses pseudoranity sequence to perform frequency shift keying (FSK) on the carrier, the carrier frequency keeps hopping with the sequence to achieve the purpose of spectrum expansion, and the hardware design is relatively complicated [ 21 ] . Therefore, DS-SS direct sequence spread spectrum method is chosen in this paper, which is a technology that multiplies pseudo-random sequences directly with baseband signals to realize spectrum spread [ 22 ] . Direct sequence spread spectrum signals are generated by direct sequence code modulation. Compared with frequency shift keying and amplitude keying, phase shift keying is the modulation mode with the lowest bit error rate among the three modes under the same conditions [ 23 ] . The pseudorandom sequence used for spread spectrum is also called spread spectrum code [ 24 ] . In this paper, Barker code is used as the pseudorandom sequence in spread spectrum technology. 3. Simulation verifies the feasibility of the spread spectrum method The finite element simulation software ABAQUS/CAE was used for analysis, and the rail model CHN60AT was selected. The rail simulation model and cross section were shown in Fig. 1 , and the three-dimensional rail model with a length of 1m was selected. The material properties of the model are: density P = 7840kg/m3, Poisson ratio σ = 0.29, elastic modulus E = 210GPa. The blue mark simulates the probe installed at the bottom of the rail, the excitation probe in the middle, the receiving probe on both sides, and the cut artificial rail bottom crack in the red frame,as shown in Fig. 2 and Fig. 3 . A simulated crack is made at a distance of L1 = 423mm from the rail end face. The crack length is 150mm, the depth is 10mm, and the width is 1.5mm. The R-E spacing is changed by changing the length of LR − E while keeping L2 = 5mm unchanged. According to the current inspection requirements of the railway department, the inspection depth required for the bottom crack of the rail is 10mm. Theoretically, the detected crack size should be ensured to be greater than half of the detection frequency wavelength [ 25 ] , so the guided wave frequency of 200kHz is selected. The simulation parameters of HWS excitation waveform are shown in Table 3 ,the Hanning window modulated signal (HWS) is used as the guided wave excitation signal. The initial interval of the R-E pitch is 40mm, and the step size is 20mm each time, until the R-E pitch is 140mm. Table 3 Simulation parameters of HWS excitation waveform No. R − E interval (mm) Excitation waveform No. R − E interval (mm) Excitation waveform 1 40 HWS 4 100 HWS 2 60 HWS 5 120 HWS 3 80 HWS 6 140 HWS As shown in Fig. 4 , V pnd represents the non-damaged waveform, and V pd represents the waveform after the crack. Cracks cause significant amplitude attenuation for the propagation of guided wave signals. With the gradual increase of the R-E distance, the propagation distance increases, and the amplitude of the received signal also decreases. In order to describe the attenuation degree of guided wave signal in the propagation process, the attenuation coefficient α is used to represent it, and its formula is shown in Eq. (3) [ 25 ] . α = 20log 10 (v 0 /v 1 ) (3) Where, v 0 represents the amplitude of the signal without attenuation, v 1 represents the amplitude of the signal after attenuation. Here, V pd is used to represent the peak value of guided wave signal passing through the rail bottom crack, and V pnd is used to represent the peak value of guided wave signal not passing through the crack at the same distance. αpd = 20log 10 (V pnd /V pd ) (4) Table 4 Vpnd and Vpd of HWS excitation waveform varying with distance No. (S0 ) Interval(mm) Vpnd Vpd αpd (dB) 1 40 2031.49 711.054 9.118 2 60 2030.34 719.075 9.016 3 80 2083.17 732.387 9.079 4 100 1509.10 656.726 7.227 5 120 1284.37 367.039 10.879 6 140 1107.31 440.769 8.001 As can be seen from Table 4 , the average attenuation coefficient α pd of signal S0 without spread spectrum processing is about 8.89dB. In addition, the increase of the propagation distance will also cause the attenuation of the guided wave signal. In order to describe the attenuation degree of guided wave propagation distance, the attenuation coefficient αL is expressed as: α L = 20log 10 \(\:\frac{\begin{array}{c}Vpnd(R-Emin)\\\:\end{array}}{Vpd(R-Emax)}\) (5) V pnd (R-Emax) indicates the V pnd amplitude at a distance of 140mm, and Vpnd (R-Emin) indicates the V pnd amplitude at a distance of 40mm. The simulation results in Table 4 were analyzed, and the attenuation coefficient α L was calculated to be 5.271dB. The greater the attenuation coefficient α L , the more serious the attenuation, that is, the more serious the influence of distance attenuation on the guided wave signal. Barker code is used as the spread spectrum code to process the HWS excitation mode, and the processed Signal is used as the Direct Sequence spread spectrum signal (DSS). The simulation parameters are the same as Table 3 except for the excitation signal. The received signal is de-amplified and related processing is carried out, and the processed signal is denoted as S1. The processed signal is shown in Fig. 5 . After the de-amplification process, an obvious correlation peak is obtained, which is the information code of "1" in the excitation signal. After the signal passes through the crack, the crack reflects and scatters the guided wave signal to a certain extent, resulting in obvious distortion and energy attenuation of the guided wave signal. Therefore, the correlation between the signal after deamplification and the original excitation signal is weakened, and the information code "1" in the excitation signal cannot be fully recovered, and there is no high correlation peak in the signal. It is in sharp contrast to the direct wave processing signal without crack. As can be seen from Fig. 6 , when the distance is 100mm, V pnd attenuates significantly, but there is still a large difference between V pd and V pnd , which reduces the influence caused by the increase of the propagation distance and further improves the detection range of cracks in the rail. Calculated from Table 5 , the mean attenuation coefficient α pd of signal S1 is 17.198dB, while the mean attenuation coefficient α pd of signal S0 without spread spectrum processing is 8.887dB, which increases the mean value of α pd by 8.311dB. The larger the attenuation coefficient α pd is, the more serious the amplitude attenuation of the signal after the crack, indicating that the crack in the bottom of the rail is more easily detected after the DSS signal is processed by spread spectrum. As can be seen from Table 5 , the calculated amplitudes of V pnd at 40mm spacing and 140mm spacing show that the guided wave attenuation coefficient α L of this frequency is 4.977dB, which is 0.574dB lower than the signal attenuation coefficient α L = 5.271dB without spread spectrum processing. Table 5 V pnd and V pd of DSS excitation waveform varying with distance No. (S1 ) Interval(mm) Vpnd Vpd αpd (dB) 1 40 54.985 8.811 15.904 2 60 54.635 5.791 19.494 3 80 53.273 5.978 18.999 4 100 32.003 5.781 14.864 5 120 31.891 3.769 18.549 6 140 31.003 5.278 15.379 The simulation results show that the spread spectrum technique can reduce the influence of distance attenuation on crack identification. At the same time, the amplitude of the signal decreases more after the crack, which increases the sensitivity of crack detection. 4. Experimental method and result analysis 4.1 Ultrasonic guided wave detection platform for rail bottom cracks In this paper, an ultrasonic transducer based on piezoelectric effect is selected as the excitation and receiving device of ultrasonic guided wave. The whole ultrasonic guided wave detection system consists of ultrasonic transducer, signal generator, power amplifier, oscilloscope and rail to be detected. On a rail with a length of 1100 mm, an artificial crack with the length of the rail x axis being long, the width of the rail z axis being wide, and the depth of the rail y axis being deep is manufactured at the positions of the bottom of the rail 300 mm, 600 mm, and 900 mm from the end face of the rail respectively, subject to the restriction of the crack manufacturing conditions. The crack depth is 3 mm, 6 mm, 9 mm, width is 0.5 mm, length is 150 mm. Piezoelectric ceramics are used as ultrasonic guided wave transducers to generate and receive ultrasonic guided waves. By observing the direct waveform propagated through the rail, if the guided wave signal passes through the crack, the signal energy attenuates obviously, the waveform mode changes, and the amplitude of the signal waveform decreases and the signal waveform will be distorted. According to the experimental platform construction method described above, the rail artificial crack samples are divided into 3 different depths, 3 mm, 6 mm, 9 mm, and the crack width and length are the same. Gathered round two methods, the use of three 200 kHz ultrasonic guided wave transducer R pd , E and R pnd , E said excitation probe, R pd and R pnd said receiving probe. The three kinds of transducers are installed near the rail artificial crack to be detected, and the rail is divided into two detection areas: there is artificial crack between R pd and E, and there is no crack between R pnd and E, and the spacing is consistent with the spacing between R pd and E. In order to form a comparative experiment, the spacing between R pd and E is the same as that between R pnd and E, which is expressed by the R-E spacing for convenience. The relative positions of the probe and the crack are shown in FIG. 7 . Using the Direct Sequence Spread Spectrum (DSSS) technique, the composite code d(t) is obtained by multiplying the sent information code a n with the pseudo-random binary spread spectrum code c(t). The carrier signal is modulated with the composite code sequence d(t) to obtain the transmitted signal s(t), and the pseudo-random code is used to have a higher rate to achieve the effect of broadening the spectrum. At this time, the signal s(t) is the signal with spread spectrum, and its bandwidth is determined by the code rate of c(t) of the pseudo-random spread spectrum code, but has almost nothing to do with the code rate of a n [ 11 ] . In an ideal case, the information code a n is modulated to obtain the transmitted signal s(t), whose formula is: s(t) = d(t)cos(2πfct) = Aa n c(t)cos(2πfct) (3) In formula (3), A represents the amplitude and fc represents the center frequency of the carrier. After receiving the signal, the receiving end will calculate the received signal with the local reference spread spectrum code, and through software filtering, you can restore the sent data code a n . In this paper, the signal code is "1", and the pseudo-random spread spectrum code uses 13-bit Barker code. The composite code is obtained after the multiplication of the signal code and pseudo-random code, and its frequency is expanded to 13 times of the original frequency. Since the signal code is "1", the composite code and the spread spectrum code are the same. Then the sequence obtained after spread spectrum is used as modulation code, and is modulated with 200 kHz carrier signal sin (t) to obtain the carrier signal s(t) modulated after spread spectrum sequence, that is, as excitation signal. The above spread spectrum and unspread process are calculated by MATLAB. The original Signal is HWS (Hanning Window Signal) wave. DSSS technology is used to spread spectrum HWS wave in MATLAB, and a new signal is obtained, which is called DSS(Direct-Sequence signal) wave. The received signal r(t) is correlated with the local reference spread spectrum code, the peak value is restored according to the correlation, and the rail bottom crack is judged according to the amplitude information of the peak value.The ideal spread spectrum process waveform is shown in Fig. 8 . 4.2 Rail bottom crack experiment and data analysis Using ordinary HWS signal and DSS signal as excitation signal, three different R-E spacing experiments were carried out on the rail bottom crack detection platform. As shown in Fig. 9 , the waveforms after de-expanding of DSS received signals are statistically measured under different R-E spacing conditions, and the amplitudes of the normal guided wave propagation and the direct wave (marked with boxes) propagated through cracks are V pnd and V pd . It is considered that the reduced amplitude of V pd is compared with that of V pnd . Is the attenuation caused by cracks under these conditions and is described by the attenuation coefficient α pd Similarly, the direct wave peak value of guided wave during normal propagation of 100 mm and 150 mm is collected, and the amplitude reduced at 150 mm compared with 100 mm is the attenuation of guided wave during normal propagation of 50 mm, and is described by the distance attenuation coefficient α L . After repeated experiments, when the crack depth is 3 mm, 6 mm and 9 mm, the guided wave attenuation coefficients α pd of HWS signal under excitation are 4.774 dB, 7.819 dB and 11.058 dB respectively, and when the crack depth is 50 mm normally transmitted. The distance attenuation coefficient α L . is 4.007 dB. When DSS signal is excited, the mean attenuation coefficients of guided wave α pd are 6.439 dB, 7.189 dB and 14.905 dB respectively, and the distance attenuation coefficient α L is 1.702dB. Experiments with crack depth of 9 mm were selected to show the amplitude changes of guided waves stimulated by HWS signal and DSS signal through the same crack size. As shown in Fig. 3 , Figure (a) is the HWS signal without spread spectrum processing, and Figure (b) is the calculated waveform DSS after spread spectrum processing. As can be seen in Table 6 , for the detection result of the rail bottom crack with a depth of 9 mm, the attenuation coefficient α pd increases by 4.35dB, 1.601dB and 5.6dB respectively at the R-E spacing of 100 mm, 120 mm and 150 mm. Compared with the HWS excitation waveform, After being processed by spread spectrum technology, the attenuation coefficient α pd of the signal subjected to cracks in the bottom of the rail is increased by 3.847dB on average, which proves that the proposed method can make the guided wave signal more easily detect cracks in the bottom of the rail. Table 6 Changes of different guided wave attenuation coefficients after 9 mm cracking Interval /mm Crack depth/mm HWS Signal attenuation coefficient α pd /dB DSS Signal attenuation coefficient α pd /dB 100 9 9.715 14.065 120 9 13.156 14.757 150 9 10.303 15.903 5. Conclusion Based on the traditional ultrasonic guided wave detection, this paper uses Barker code as pseudo-random sequence code, and uses BPSK technology to encode and modulated the original HWS excitation signal to obtain a new excitation signal, and realizes the spread spectrum processing of the excitation signal. The feasibility of the proposed method is verified by simulation experiments. The artificial cracks at the bottom of rails with different depths such as 3 mm, 6 mm and 9 mm were verified by setting up an experimental platform. Guided wave crack attenuation coefficients α pd and distance attenuation coefficients α L are calculated by experiments with raw excitation signal HWS signal and DSS signal using the coded spread spectrum technology proposed in this paper respectively. Experiments show that the distance attenuation coefficient of guided wave signal is reduced by about 2.3dB after using the signal enhancement technique in this paper, and the guided wave signal can propagate longer distance. The attenuation coefficient of guided wave cracks is significantly increased by about 3.8dB, and the attenuation effect of cracks of the same size is more significant, which improves the sensitivity of guided wave rail bottom crack detection and provides strong support for small crack detection of rail bottom. Declarations Author Contribution Wenhao Guo wrote the main manuscript text and prepared figures 1-9. All authors reviewed the manuscript. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4715741","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":335751422,"identity":"66a7f552-968a-49f9-8a2d-00bc59be6f20","order_by":0,"name":"Guo Wenhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYBACefbmA4f/VEjI8bM3EKnFsOdY4gGeMzbGkj0HiLXmRo7xAd62tMQNMxKI1ME4I8fggATbYWMDyccbbzDU2EQT1MLO86zggAHPYTlz6bRiC4ZjabkNBG1pT95wIEHisLHl7BwzCcaGw4S1MBxIMDhwwOBw4oabZ4jVciLF4GBDAtD7N3iI1AIM5ITDDAdAgQz0SwIxfgFG5eHPjP9AUXl4440PNTZEOAwJGEgkkKIcooVUHaNgFIyCUTAyAAAuSkZfnapmOgAAAABJRU5ErkJggg==","orcid":"","institution":"China Railway Fourth Survey and Design Institute Group Co., LTD","correspondingAuthor":true,"prefix":"","firstName":"Guo","middleName":"","lastName":"Wenhao","suffix":""}],"badges":[],"createdAt":"2024-07-10 05:32:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4715741/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4715741/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61937313,"identity":"6fe35171-84ef-487c-b7ab-044afbda8641","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":55036,"visible":true,"origin":"","legend":"\u003cp\u003eRail simulation model and cross-section\u003c/p\u003e","description":"","filename":"Figure1Railsimulationmodelandcrosssection.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/e134ac1670d0fffcec1755b3.png"},{"id":61938429,"identity":"1f12ff51-ce27-4eb4-93da-cc207932d770","added_by":"auto","created_at":"2024-08-07 09:41:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":104439,"visible":true,"origin":"","legend":"\u003cp\u003eUltrasonic guided wave rail bottom crack detection mode\u003c/p\u003e","description":"","filename":"Figure2.Ultrasonicguidedwaverailbottomcrackdetectionmode.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/f95e98f28a11a630a52a33f6.png"},{"id":61937867,"identity":"4d7d7112-8177-42d0-8f35-664c35ebd98e","added_by":"auto","created_at":"2024-08-07 09:33:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":63685,"visible":true,"origin":"","legend":"\u003cp\u003eInstallation diagram of the simulated probe\u003c/p\u003e","description":"","filename":"Figure3Installationdiagramofthesimulatedprobe.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/06c96cc6c63840054949988e.png"},{"id":61937322,"identity":"40523d05-e405-4e55-a720-198ed8131706","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":131139,"visible":true,"origin":"","legend":"\u003cp\u003eV\u003csub\u003epnd\u003c/sub\u003e and V\u003csub\u003epd\u003c/sub\u003e waveforms of HWS signals at different distances\u003c/p\u003e","description":"","filename":"Figure4VpndandVpdwaveformsofHWSsignalsatdifferentdistances.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/cdf49efacbae1c2b2c5c0f64.png"},{"id":61937319,"identity":"739fbd9f-b385-407a-8e54-19639a3bc237","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":159400,"visible":true,"origin":"","legend":"\u003cp\u003eV\u003csub\u003epnd\u003c/sub\u003e and V\u003csub\u003epd\u003c/sub\u003e waveforms without de-amplifications of the received signal\u003c/p\u003e","description":"","filename":"Figure5VpndandVpdwaveformswithoutdeamplificationsofthereceivedsignal.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/5894877286cb02ecb949bdb3.png"},{"id":61937318,"identity":"ad3f33f8-1609-4140-8e02-30a444594e9d","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":115283,"visible":true,"origin":"","legend":"\u003cp\u003eV\u003csub\u003epnd\u003c/sub\u003e and V\u003csub\u003epd\u003c/sub\u003e waveforms of the received signal with de-amplification processing\u003c/p\u003e","description":"","filename":"Figure6VpndandVpdwaveformsofthereceivedsignalwithdeamplificationprocessing.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/283c4ab97629362b7298d0dd.png"},{"id":61937316,"identity":"f0de9f59-38fb-4cde-91f7-a3407f8bedd0","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":463974,"visible":true,"origin":"","legend":"\u003cp\u003eThe probe is positioned relative to the crack\u003c/p\u003e","description":"","filename":"Figure7Theprobeispositionedrelativetothecrack.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/1e9a61f8355d6ededb96292f.png"},{"id":61937869,"identity":"c04f7fd4-e58f-48f8-80e7-f617ae8a5b22","added_by":"auto","created_at":"2024-08-07 09:33:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":160031,"visible":true,"origin":"","legend":"\u003cp\u003eWaveform diagram of ideal spread spectrum process\u003c/p\u003e","description":"","filename":"Figure8Waveformdiagramofidealspreadspectrumprocess.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/1b134113e3a48311e2dbd5b7.png"},{"id":61937868,"identity":"16c15693-32f4-4586-b9d5-d907f97c04df","added_by":"auto","created_at":"2024-08-07 09:33:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":149415,"visible":true,"origin":"","legend":"\u003cp\u003eWaveform after despreading the DSS received signal\u003c/p\u003e","description":"","filename":"Figure9WaveformafterdespreadingtheDSSreceivedsignal.png","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/d3ac22b54923c6a192bfff97.png"},{"id":62246786,"identity":"6ed217b5-944d-4b33-8c7e-f64fffca65dd","added_by":"auto","created_at":"2024-08-12 05:05:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2246153,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/7719b261-783b-4a77-ae95-3f6b6e6aa803.pdf"},{"id":61937315,"identity":"9d30dc54-37cf-43fb-9d37-2b72b482e709","added_by":"auto","created_at":"2024-08-07 09:25:18","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":22675,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-4715741/v1/a14e48ce9ee8303c84a9caff.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Research on signal enhancement technology of ultrasonic guided wave detection of rail crack based on spread spectrum technology","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWith the development of high-speed and heavy-haul railways in China, under the environment of rapid economic development and the coexistence of various modes of transportation at the present stage, railway transportation still occupies an extremely important position in China's national economic system, which is called \"the main artery of the national economy\" \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e. It is increasingly urgent to carry out online non-destructive testing of rail to monitor rail quality.\u003c/p\u003e \u003cp\u003eGeneral rail cracks are easy to grow in the waist and bottom of the rail, with the development of cracks, cracks will reach a rapid expansion stage. When the crack area is large, the crack will develop to the surface of the rail head, so that the crack gradually develops into a broken rail, which is one of the important reasons affecting the normal operation of the rail.\u003c/p\u003e \u003cp\u003eAt present, Guided Wave Testing (GWT) is often used to detect rail cracks. Reference \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e gives an example of a classic trackside ultrasonic inspection system. On the basis of this system, a new ultrasonic guided-wave signal processing method based on SVD and independent component analysis is proposed for the remote detection and location of transverse defects of rail head. Reference [4] developed a 5% on-line defect detection system that can detect the cross-sectional area of the bottom rail of the switch. Hu Pan et al. \u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e studied the method of active guided wave mode feature extraction and switch spallation damage location based on time-frequency analysis, and realized guided wave mode feature extraction and damage location of mild spallation damage.\u003c/p\u003e \u003cp\u003eIn the application of ultrasonic guided wave rail crack detection in the actual environment, the guided wave signal will inevitably be interfered by various noises, thus reducing the signal-to-noise ratio, which is not conducive to the identification of cracks in the rail. Therefore, it is necessary to conduct relevant signal processing for the guided wave in the rail \u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe characteristic of spread spectrum technology is that it has strong anti-interference ability, and it has been widely used in radar field in the early days. Literature \u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e et al. analyzed the anti-jamming mechanism of direct sequence spread spectrum system (DSSS) and analyzed and deduced the anti-jamming performance of radar communication, laying a foundation for the theoretical analysis of DSSS. Literature \u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e defines the two indexes of energy efficiency and echo sequence correlation in ultrasonic spread spectrum applications. The Binary Phase Shift Keying (BPSK) and Binary Frequency Shift Keying (BFSK) are compared and discussed. Parameter configuration of three modulation methods, including BFSK and Binary Amplitude Shift Keying (BASK). Literature \u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e et al. applied spread spectrum technology to the field of acoustic positioning to solve outdoor mechanical location, which can reduce the interference effects caused by wind speed and machine noise, proving that spread spectrum technology can ensure reliable signal transmission.\u003c/p\u003e \u003cp\u003eBased on the pulse compression method in the communication principle, a single pulse signal or a short pulse signal is replaced by a multi-element encoding method. This method does not need to increase the excitation voltage of the excitation signal, but increases the average excitation power by increasing the excitation time of the signal. Then, the energy of the excitation signal is re-compressed and restored to a short-time pulse signal by relevant decoding methods, so that the resolution of the signal for crack identification is not affected by this method, and the signal-to-noise ratio of the system can be well improved \u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this paper, BPSK technology is applied to ultrasonic guided wave detection of rail bottom crack, and the anti-interference ability of spread spectrum technology is used to improve the propagation distance of ultrasonic guided wave signal, so as to improve the detection sensitivity of ultrasonic guided wave on rail bottom crack.\u003c/p\u003e"},{"header":"2. The selection of coding sequence and spread spectrum technique","content":"\u003cp\u003eAt present, the commonly used encoding can be divided into BinaryPhase Shift Keying (BPSK), linear frequency modulation signal (Chirp), etc. It can also be divided into multiple transmission coding and single transmission coding according to the transmission frequency of the encoded signal \u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e. Phase coding, also known as binary coding, usually refers to a binary coding sequence composed of \"1\" and \"-1\" to achieve 180 on a single transmitted excitation signal. Phase coding; Frequency coding, also known as continuous wave coding \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e],\u003c/sup\u003e usually adds a guided wave signal to a signal with a continuously changing frequency \u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e. According to these two classification methods, the common pseudoranding sequence codes are classified as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Barker code and M-sequence code belong to the single-emission coding mode in phase coding, while Golay code also belongs to phase coding but consists of a set of mutually complementary coding sequences. Chirp code, as a typical non-stationary signal, is a kind of linear frequency modulation signal coding method which is often used in radar and other fields. These common coding sequences can also be used as pseudo-random sequence codes of spread spectrum technology\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e, because the coding calculation method and spread spectrum method are similar, so the effect of both is the same.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eClassification of common spread spectrum pseudorandom sequence codes\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle launch\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMultiple launches\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhase coding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBarker code, M sequence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGolay code\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency coding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eChirp coding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs a phase encoding method, binary coding sequence is theoretically not limited by bandwidth. Compared with the phase coding method, Chirp signal is more sensitive to ambient noise and susceptible to interference, and its hardware implementation is more complicated than that of binary coding\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e. Compared with barker code, the main sidelobe of M sequence is worse.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of sequence codes of common spread spectrum techniques\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEncoding mode\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAdvantage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDisadvantage\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBarker\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOnly need a single transmission, phase coding, hardware easy to implement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe maximum code length is only 13 digits\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eM sequence\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo code length limit, single transmission, phase coding, hardware easy to achieve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe main sidelobe is poor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGolay\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIt reduces the sidelobe interference of aperiodic sequence, has no code length limitation, and is easy to implement in hardware\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNeed two launches\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eChirp code\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCan control the range sidelobe level, single transmission, no code length limit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComplex hardware design\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, from the perspective of auto-correlation, the main lobe width and sidelobe level are used as measuring standards to make a comparative analysis of common sequence codes. In terms of sidelobe elimination, compared with Barker code, Golay code has better performance due to complementary coding sequences. Under the same code length, Barker code has the highest autocorrelation main sidelobe ratio \u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. In terms of the number of incentives, Golay code uses complementary coding sequences, so it needs two incentives, while Barker code only needs a single incentive, which is relatively easier in hardware implementation and has good autocorrelation characteristics, which is more suitable for practical application development. Therefore, this paper chooses Barker code as the pseudo-random sequence code of spread spectrum technology.\u003c/p\u003e \u003cp\u003eAn n-bit Barker code element [x0,x1,...,x(N-1)] consists of \"1\" or \"-1\". When the code element is \"1\", the waveform obtained is in the same phase as the original waveform. When the code element is \"-1\"\u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e, the waveform obtained is opposite to the original waveform, and the phase difference of the original waveform after the two code elements is π, and several Barker codes form the pseudo-random binary spread spectrum code required by signal spread spectrum technology.\u003c/p\u003e \u003cp\u003eB[N]=[x\u003csub\u003e0\u003c/sub\u003e,x\u003csub\u003e1\u003c/sub\u003e,\u0026hellip;,x\u003csub\u003e(N\u0026minus;1)\u003c/sub\u003e ],x\u003csub\u003ei\u003c/sub\u003e\u0026isin;{-1,1} (1)\u003c/p\u003e \u003cp\u003eThe decoding process after encoding is also called pulse compression. According to the principle of pulse compression, the product of the actual time-bandwidth is equivalent to the signal-to-noise ratio gain after signal compression\u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e. The signal-to-noise ratio gain of the encoded signal is related to the length N of the coded code, so the signal-to-noise ratio gain ASNR after Barker code processing can be expressed as follows:\u003c/p\u003e \u003cp\u003eA\u003csub\u003eSNR\u003c/sub\u003e=10logN, N\u0026isin;{2,3,4,5,7,11,13} (2)\u003c/p\u003e \u003cp\u003eAccording to formula (2), in order to obtain the maximum SNR gain, 13-bit Barker code should be selected as the coded element.\u003c/p\u003e \u003cp\u003eAt present, the common Spread Spectrum technologies include direct sequence Spread Spectrum, Frequency Hopping Spread Spectrum (FH-SS), and Time Hopping Spread Spectrum (TH-SS)\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. Direct spread spectrum (DSS) technique is to extend the bandwidth of the transmitted signal by injecting the signal to a higher rate pseudo-random sequence code. Frequency hopping spread spectrum (FSS) is a technique that discretely selects the output spectrum of the carrier oscillator using pseudoranity codes, so that the frequency of the transmitted signal changes with the change of the binary pseudoranity sequence. Time-hopping spread spectrum is similar to frequency-hopping spread spectrum in that the signal to be transmitted is divided into multiple time slots in the timing\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e, and the pseudo-random spread spectrum code controls the signal in which time slot, because the time slot is much narrower than the original frame in the timing, so as to achieve the purpose of broadening the spectrum. Since FH-SS uses pseudoranity sequence to perform frequency shift keying (FSK) on the carrier, the carrier frequency keeps hopping with the sequence to achieve the purpose of spectrum expansion, and the hardware design is relatively complicated \u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e. Therefore, DS-SS direct sequence spread spectrum method is chosen in this paper, which is a technology that multiplies pseudo-random sequences directly with baseband signals to realize spectrum spread \u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDirect sequence spread spectrum signals are generated by direct sequence code modulation. Compared with frequency shift keying and amplitude keying, phase shift keying is the modulation mode with the lowest bit error rate among the three modes under the same conditions \u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e. The pseudorandom sequence used for spread spectrum is also called spread spectrum code\u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e. In this paper, Barker code is used as the pseudorandom sequence in spread spectrum technology.\u003c/p\u003e"},{"header":"3. Simulation verifies the feasibility of the spread spectrum method","content":"\u003cp\u003eThe finite element simulation software ABAQUS/CAE was used for analysis, and the rail model CHN60AT was selected. The rail simulation model and cross section were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and the three-dimensional rail model with a length of 1m was selected.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe material properties of the model are: density P\u0026thinsp;=\u0026thinsp;7840kg/m3, Poisson ratio σ\u0026thinsp;=\u0026thinsp;0.29, elastic modulus E\u0026thinsp;=\u0026thinsp;210GPa.\u003c/p\u003e \u003cp\u003eThe blue mark simulates the probe installed at the bottom of the rail, the excitation probe in the middle, the receiving probe on both sides, and the cut artificial rail bottom crack in the red frame,as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. A simulated crack is made at a distance of L1\u0026thinsp;=\u0026thinsp;423mm from the rail end face. The crack length is 150mm, the depth is 10mm, and the width is 1.5mm. The R-E spacing is changed by changing the length of LR\u0026thinsp;\u0026minus;\u0026thinsp;E while keeping L2\u0026thinsp;=\u0026thinsp;5mm unchanged.\u003c/p\u003e \u003cp\u003eAccording to the current inspection requirements of the railway department, the inspection depth required for the bottom crack of the rail is 10mm. Theoretically, the detected crack size should be ensured to be greater than half of the detection frequency wavelength \u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e, so the guided wave frequency of 200kHz is selected.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe simulation parameters of HWS excitation waveform are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e,the Hanning window modulated signal (HWS) is used as the guided wave excitation signal. The initial interval of the R-E pitch is 40mm, and the step size is 20mm each time, until the R-E pitch is 140mm.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSimulation parameters of HWS excitation waveform\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u0026thinsp;\u0026minus;\u0026thinsp;E interval (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExcitation waveform\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026thinsp;\u0026minus;\u0026thinsp;E interval (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eExcitation waveform\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHWS\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, V\u003csub\u003epnd\u003c/sub\u003e represents the non-damaged waveform, and V\u003csub\u003epd\u003c/sub\u003e represents the waveform after the crack. Cracks cause significant amplitude attenuation for the propagation of guided wave signals. With the gradual increase of the R-E distance, the propagation distance increases, and the amplitude of the received signal also decreases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to describe the attenuation degree of guided wave signal in the propagation process, the attenuation coefficient α is used to represent it, and its formula is shown in Eq.\u0026nbsp;(3) \u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eα\u0026thinsp;=\u0026thinsp;20log\u003csub\u003e10\u003c/sub\u003e (v\u003csub\u003e0\u003c/sub\u003e /v\u003csub\u003e1\u003c/sub\u003e) (3)\u003c/p\u003e \u003cp\u003eWhere, v\u003csub\u003e0\u003c/sub\u003e represents the amplitude of the signal without attenuation, v\u003csub\u003e1\u003c/sub\u003e represents the amplitude of the signal after attenuation. Here, V\u003csub\u003epd\u003c/sub\u003e is used to represent the peak value of guided wave signal passing through the rail bottom crack, and V\u003csub\u003epnd\u003c/sub\u003e is used to represent the peak value of guided wave signal not passing through the crack at the same distance.\u003c/p\u003e \u003cp\u003eαpd\u0026thinsp;=\u0026thinsp;20log\u003csub\u003e10\u003c/sub\u003e(V\u003csub\u003epnd\u003c/sub\u003e/V\u003csub\u003epd\u003c/sub\u003e) (4)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVpnd and Vpd of HWS excitation waveform varying with distance\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. (S0 )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInterval(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVpnd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVpd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eαpd (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2031.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e711.054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.118\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2030.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e719.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2083.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e732.387\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.079\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1509.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e656.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.227\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1284.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e367.039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10.879\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1107.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e440.769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the average attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e of signal S0 without spread spectrum processing is about 8.89dB.\u003c/p\u003e \u003cp\u003eIn addition, the increase of the propagation distance will also cause the attenuation of the guided wave signal. In order to describe the attenuation degree of guided wave propagation distance, the attenuation coefficient αL is expressed as:\u003c/p\u003e \u003cp\u003eα\u003csub\u003eL\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;20log\u003csub\u003e10\u003c/sub\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\begin{array}{c}Vpnd(R-Emin)\\\\\\:\\end{array}}{Vpd(R-Emax)}\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e \u003cp\u003eV\u003csub\u003epnd\u003c/sub\u003e (R-Emax) indicates the V\u003csub\u003epnd\u003c/sub\u003e amplitude at a distance of 140mm, and Vpnd (R-Emin) indicates the V\u003csub\u003epnd\u003c/sub\u003e amplitude at a distance of 40mm.\u003c/p\u003e \u003cp\u003eThe simulation results in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e were analyzed, and the attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e was calculated to be 5.271dB.\u003c/p\u003e \u003cp\u003eThe greater the attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e, the more serious the attenuation, that is, the more serious the influence of distance attenuation on the guided wave signal.\u003c/p\u003e \u003cp\u003eBarker code is used as the spread spectrum code to process the HWS excitation mode, and the processed Signal is used as the Direct Sequence spread spectrum signal (DSS). The simulation parameters are the same as Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e except for the excitation signal.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe received signal is de-amplified and related processing is carried out, and the processed signal is denoted as S1. The processed signal is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. After the de-amplification process, an obvious correlation peak is obtained, which is the information code of \"1\" in the excitation signal. After the signal passes through the crack, the crack reflects and scatters the guided wave signal to a certain extent, resulting in obvious distortion and energy attenuation of the guided wave signal. Therefore, the correlation between the signal after deamplification and the original excitation signal is weakened, and the information code \"1\" in the excitation signal cannot be fully recovered, and there is no high correlation peak in the signal. It is in sharp contrast to the direct wave processing signal without crack.\u003c/p\u003e \u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, when the distance is 100mm, V\u003csub\u003epnd\u003c/sub\u003e attenuates significantly, but there is still a large difference between V\u003csub\u003epd\u003c/sub\u003e and V\u003csub\u003epnd\u003c/sub\u003e, which reduces the influence caused by the increase of the propagation distance and further improves the detection range of cracks in the rail.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCalculated from Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the mean attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e of signal S1 is 17.198dB, while the mean attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e of signal S0 without spread spectrum processing is 8.887dB, which increases the mean value of α\u003csub\u003epd\u003c/sub\u003e by 8.311dB. The larger the attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e is, the more serious the amplitude attenuation of the signal after the crack, indicating that the crack in the bottom of the rail is more easily detected after the DSS signal is processed by spread spectrum.\u003c/p\u003e \u003cp\u003eAs can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the calculated amplitudes of V\u003csub\u003epnd\u003c/sub\u003e at 40mm spacing and 140mm spacing show that the guided wave attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e of this frequency is 4.977dB, which is 0.574dB lower than the signal attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;5.271dB without spread spectrum processing.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eV\u003csub\u003epnd\u003c/sub\u003e and V\u003csub\u003epd\u003c/sub\u003e of DSS excitation waveform varying with distance\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo. (S1 )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInterval(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVpnd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVpd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eαpd (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.985\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.904\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.635\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19.494\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e53.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.978\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.999\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e32.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.781\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14.864\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e31.891\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.549\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e31.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.379\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe simulation results show that the spread spectrum technique can reduce the influence of distance attenuation on crack identification. At the same time, the amplitude of the signal decreases more after the crack, which increases the sensitivity of crack detection.\u003c/p\u003e"},{"header":"4. Experimental method and result analysis","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Ultrasonic guided wave detection platform for rail bottom cracks\u003c/h2\u003e \u003cp\u003eIn this paper, an ultrasonic transducer based on piezoelectric effect is selected as the excitation and receiving device of ultrasonic guided wave. The whole ultrasonic guided wave detection system consists of ultrasonic transducer, signal generator, power amplifier, oscilloscope and rail to be detected.\u003c/p\u003e \u003cp\u003eOn a rail with a length of 1100 mm, an artificial crack with the length of the rail x axis being long, the width of the rail z axis being wide, and the depth of the rail y axis being deep is manufactured at the positions of the bottom of the rail 300 mm, 600 mm, and 900 mm from the end face of the rail respectively, subject to the restriction of the crack manufacturing conditions. The crack depth is 3 mm, 6 mm, 9 mm, width is 0.5 mm, length is 150 mm.\u003c/p\u003e \u003cp\u003ePiezoelectric ceramics are used as ultrasonic guided wave transducers to generate and receive ultrasonic guided waves. By observing the direct waveform propagated through the rail, if the guided wave signal passes through the crack, the signal energy attenuates obviously, the waveform mode changes, and the amplitude of the signal waveform decreases and the signal waveform will be distorted.\u003c/p\u003e \u003cp\u003eAccording to the experimental platform construction method described above, the rail artificial crack samples are divided into 3 different depths, 3 mm, 6 mm, 9 mm, and the crack width and length are the same. Gathered round two methods, the use of three 200 kHz ultrasonic guided wave transducer R\u003csub\u003epd\u003c/sub\u003e, E and R\u003csub\u003epnd\u003c/sub\u003e, E said excitation probe, R\u003csub\u003epd\u003c/sub\u003e and R\u003csub\u003epnd\u003c/sub\u003e said receiving probe.\u003c/p\u003e \u003cp\u003eThe three kinds of transducers are installed near the rail artificial crack to be detected, and the rail is divided into two detection areas: there is artificial crack between R\u003csub\u003epd\u003c/sub\u003e and E, and there is no crack between R\u003csub\u003epnd\u003c/sub\u003e and E, and the spacing is consistent with the spacing between R\u003csub\u003epd\u003c/sub\u003e and E. In order to form a comparative experiment, the spacing between R\u003csub\u003epd\u003c/sub\u003e and E is the same as that between R\u003csub\u003epnd\u003c/sub\u003e and E, which is expressed by the R-E spacing for convenience. The relative positions of the probe and the crack are shown in FIG. \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUsing the Direct Sequence Spread Spectrum (DSSS) technique, the composite code d(t) is obtained by multiplying the sent information code a\u003csub\u003en\u003c/sub\u003e with the pseudo-random binary spread spectrum code c(t). The carrier signal is modulated with the composite code sequence d(t) to obtain the transmitted signal s(t), and the pseudo-random code is used to have a higher rate to achieve the effect of broadening the spectrum. At this time, the signal s(t) is the signal with spread spectrum, and its bandwidth is determined by the code rate of c(t) of the pseudo-random spread spectrum code, but has almost nothing to do with the code rate of a\u003csub\u003en\u003c/sub\u003e \u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e. In an ideal case, the information code a\u003csub\u003en\u003c/sub\u003e is modulated to obtain the transmitted signal s(t), whose formula is:\u003c/p\u003e \u003cp\u003es(t)\u0026thinsp;=\u0026thinsp;d(t)cos(2πfct)\u0026thinsp;=\u0026thinsp;Aa\u003csub\u003en\u003c/sub\u003ec(t)cos(2πfct) (3)\u003c/p\u003e \u003cp\u003eIn formula (3), A represents the amplitude and fc represents the center frequency of the carrier. After receiving the signal, the receiving end will calculate the received signal with the local reference spread spectrum code, and through software filtering, you can restore the sent data code a\u003csub\u003en\u003c/sub\u003e. In this paper, the signal code is \"1\", and the pseudo-random spread spectrum code uses 13-bit Barker code. The composite code is obtained after the multiplication of the signal code and pseudo-random code, and its frequency is expanded to 13 times of the original frequency. Since the signal code is \"1\", the composite code and the spread spectrum code are the same. Then the sequence obtained after spread spectrum is used as modulation code, and is modulated with 200 kHz carrier signal sin (t) to obtain the carrier signal s(t) modulated after spread spectrum sequence, that is, as excitation signal.\u003c/p\u003e \u003cp\u003eThe above spread spectrum and unspread process are calculated by MATLAB. The original Signal is HWS (Hanning Window Signal) wave. DSSS technology is used to spread spectrum HWS wave in MATLAB, and a new signal is obtained, which is called DSS(Direct-Sequence signal) wave. The received signal r(t) is correlated with the local reference spread spectrum code, the peak value is restored according to the correlation, and the rail bottom crack is judged according to the amplitude information of the peak value.The ideal spread spectrum process waveform is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Rail bottom crack experiment and data analysis\u003c/h2\u003e \u003cp\u003eUsing ordinary HWS signal and DSS signal as excitation signal, three different R-E spacing experiments were carried out on the rail bottom crack detection platform.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the waveforms after de-expanding of DSS received signals are statistically measured under different R-E spacing conditions, and the amplitudes of the normal guided wave propagation and the direct wave (marked with boxes) propagated through cracks are V\u003csub\u003epnd\u003c/sub\u003e and V\u003csub\u003epd\u003c/sub\u003e. It is considered that the reduced amplitude of V\u003csub\u003epd\u003c/sub\u003e is compared with that of V\u003csub\u003epnd\u003c/sub\u003e. Is the attenuation caused by cracks under these conditions and is described by the attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e Similarly, the direct wave peak value of guided wave during normal propagation of 100 mm and 150 mm is collected, and the amplitude reduced at 150 mm compared with 100 mm is the attenuation of guided wave during normal propagation of 50 mm, and is described by the distance attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e. After repeated experiments, when the crack depth is 3 mm, 6 mm and 9 mm, the guided wave attenuation coefficients α\u003csub\u003epd\u003c/sub\u003e of HWS signal under excitation are 4.774 dB, 7.819 dB and 11.058 dB respectively, and when the crack depth is 50 mm normally transmitted. The distance attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e. is 4.007 dB. When DSS signal is excited, the mean attenuation coefficients of guided wave α\u003csub\u003epd\u003c/sub\u003e are 6.439 dB, 7.189 dB and 14.905 dB respectively, and the distance attenuation coefficient α\u003csub\u003eL\u003c/sub\u003e is 1.702dB.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eExperiments with crack depth of 9 mm were selected to show the amplitude changes of guided waves stimulated by HWS signal and DSS signal through the same crack size. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, Figure (a) is the HWS signal without spread spectrum processing, and Figure (b) is the calculated waveform DSS after spread spectrum processing.\u003c/p\u003e \u003cp\u003eAs can be seen in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, for the detection result of the rail bottom crack with a depth of 9 mm, the attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e increases by 4.35dB, 1.601dB and 5.6dB respectively at the R-E spacing of 100 mm, 120 mm and 150 mm. Compared with the HWS excitation waveform, After being processed by spread spectrum technology, the attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e of the signal subjected to cracks in the bottom of the rail is increased by 3.847dB on average, which proves that the proposed method can make the guided wave signal more easily detect cracks in the bottom of the rail.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChanges of different guided wave attenuation coefficients after 9 mm cracking\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterval\u003c/p\u003e \u003cp\u003e/mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCrack depth/mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHWS Signal attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e /dB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDSS Signal attenuation coefficient α\u003csub\u003epd\u003c/sub\u003e /dB\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.715\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e14.065\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e14.757\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.903\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eBased on the traditional ultrasonic guided wave detection, this paper uses Barker code as pseudo-random sequence code, and uses BPSK technology to encode and modulated the original HWS excitation signal to obtain a new excitation signal, and realizes the spread spectrum processing of the excitation signal. The feasibility of the proposed method is verified by simulation experiments. The artificial cracks at the bottom of rails with different depths such as 3 mm, 6 mm and 9 mm were verified by setting up an experimental platform. Guided wave crack attenuation coefficients α\u003csub\u003epd\u003c/sub\u003e and distance attenuation coefficients α\u003csub\u003eL\u003c/sub\u003e are calculated by experiments with raw excitation signal HWS signal and DSS signal using the coded spread spectrum technology proposed in this paper respectively. Experiments show that the distance attenuation coefficient of guided wave signal is reduced by about 2.3dB after using the signal enhancement technique in this paper, and the guided wave signal can propagate longer distance. The attenuation coefficient of guided wave cracks is significantly increased by about 3.8dB, and the attenuation effect of cracks of the same size is more significant, which improves the sensitivity of guided wave rail bottom crack detection and provides strong support for small crack detection of rail bottom.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eWenhao Guo wrote the main manuscript text and prepared figures 1-9. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data generated or analysed during this study are included in this published article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eZhang Hui, Song Yaonan, Wang Yaonan et al. Review of Non-destructive Testing and Evaluation Techniques for Rail Defects [J]. Chinese Journal of Scientific Instrument,2019,40(02):11\u0026ndash;25.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLOVEDAY P W,LONG C S,RAMATLO D A.Ultrasonic guided wave monitoring of an operational rail track:[J].Structural Health Monitoring, 2020, 12 (6): 1666\u0026ndash;1684.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHU P,WANG H,TIAN G,et al.Wireless localization of spallings in switch-rails with guided waves based on a time-frequency method[J].IEEE Sensors Journal,2019,19(23):11050\u0026ndash;11062. (in Chinese)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYUAN Qi. Design and Hardware Implementation of ultrasonic guided Wave Broken Track Detection Algorithm [D]. Xi 'an University of Technology,2018.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao Huawei, Cui Jianhua. Research on anti-radar pulse interference of direct sequence spread spectrum System [J]. Communications Technology,2008(04):38\u0026ndash;41. (in Chinese\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Haozhen. Research on track failure detection Algorithm based on Barker coding excitation [D]. Xi 'an University of Technology,2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMalo S, Fateri S, Livadas M, et al. Wave Mode Discrimination of Coded Ultrasonic Guided Waves Using Two-Dimensional Compressed Pulse Analysis[J]. 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Trans IEEE, 1992, 14(7):710\u0026ndash;732.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDragomiretskiy K, Zosso D. Variational Mode Decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62 (3) : 531\u0026ndash;544.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen Jiaxing, Liu Zhihua. Spread Spectrum Communication [M]. Beijing University of Posts and Telecommunications Press Co., LTD.,2013\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZHANG Qinghua, ZHANG Dengke, CUI Chuang, et al. Fatigue Crack Detection Method of longitudinal butt seam of Steel bridge panel based on ultrasonic guided wave [J]. China Journal of Highway and Highway, 2022,35(06): 101\u0026ndash;112.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"rail crack detection, Barker code, ultrasonic guided wave, signal enhancement","lastPublishedDoi":"10.21203/rs.3.rs-4715741/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4715741/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDuring the propagation of guided waves in rail tracks, there are issues such as poor anti-interference ability and severe signal attenuation. This article proposes a signal enhancement technique for the processing of guided wave signals, aiming to improve the signal-to-noise ratio by enhancing the detection signals.\u003c/p\u003e \u003cp\u003eBuilding upon traditional ultrasonic guided wave detection, this technique utilizes Barker codes as pseudo-random sequence codes and employs Binary Phase Shift Keying (BPSK) modulation to encode the original excitation signal, resulting in a new excitation signal. This achieves spread spectrum processing of the excitation signal and subsequent despreading of the received signals. An experimental platform for detecting subsoil cracks in rail tracks using ultrasonic guided waves was established. Comparative experiments were conducted on artificial cracks of different sizes at the bottom of rail tracks under both spread and non-spread conditions, calculating the attenuation coefficient of received guided wave signals.\u003c/p\u003e \u003cp\u003eThe results demonstrate that after applying this signal enhancement technique to guided wave signals, compared to unprocessed original guided wave signals, there is a significant reduction in attenuation coefficient when propagating over the same distance. As a result, ultrasonic guided wave signals can propagate over longer distances with increased sensitivity towards cracks of similar sizes at the bottom of rail tracks. These findings provide support for ultrasonic guided wave detection of subsoil cracks in rail tracks.\u003c/p\u003e","manuscriptTitle":"Research on signal enhancement technology of ultrasonic guided wave detection of rail crack based on spread spectrum technology","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-07 09:25:13","doi":"10.21203/rs.3.rs-4715741/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3bb4925a-c6ae-4565-8a84-88dfd0a1a4d2","owner":[],"postedDate":"August 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":35557672,"name":"Physical sciences/Physics/Techniques and instrumentation/Characterization and analytical techniques"},{"id":35557673,"name":"Physical sciences/Physics/Applied physics/Acoustics"}],"tags":[],"updatedAt":"2024-08-12T04:57:18+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-07 09:25:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4715741","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4715741","identity":"rs-4715741","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}