A steel rail fracture monitoring method based on barker code ultrasonic guided wave simulation optimization

Abstract

The application discloses a kind of steel rail fracture monitoring methods based on Barker code ultrasonic guided wave simulation optimization, first respectively generate 3, 5, 7, 11, 13 Barker code sequence, with Hamming window modulated sine single pulse signal is multiplied modulation, obtain different length coding excitation signal, get echo signal by simulation;Then the echo signal is pulse compression decoding, and the defect echo signal is extracted;Finally, through the defect echo peak value, time width, differential amplitude gain DAG, signal-to-noise ratio, defect discrimination coefficient DDC and other multi-dimensional evaluation indexes, the five kinds of coding length are compared comprehensively, and the best coding length is preferably selected.The application provides a scientific simulation optimization basis for the selection of coding length in the steel rail fracture monitoring system, and has obvious advantages in improving the response capability and noise resistance of the detection system to the steel rail fracture defect, and has remarkable effect on the optimization of coding excitation parameters.

Description

Technical Field

[0001] This invention belongs to the field of nondestructive testing and structural health monitoring technology, specifically relating to a rail fracture monitoring method based on Barker code-encoded excited ultrasonic guided waves and optimizing the code length through simulation. Background Technology

[0002] As the fundamental load-bearing component of railway rail transit, rails endure dynamic loads from trains, temperature stresses, and complex environmental conditions over long periods. The rail head, web, and base are highly susceptible to fatigue cracks and even sudden fractures. Once a rail fracture occurs, it can lead to anything from speed limits to train derailments and major safety accidents. Therefore, achieving highly reliable and sensitive online monitoring of rail fractures is of paramount importance.

[0003] Among existing non-destructive testing technologies for rails, ultrasonic guided wave testing has been widely used in the condition monitoring of long-distance structures such as rails and pipelines due to its advantages such as long propagation distance, coverage of several kilometers in a single test, and sensitivity to crack-like defects. However, ultrasonic guided waves still face several technical bottlenecks in practical applications: geometric diffusion and medium absorption occur during guided wave propagation, resulting in weak echo signals over long distances; strong background noise exists at the rail site, such as train vibration and ballast impact; and increasing the transmission voltage is limited by the transducer's withstand voltage and heating characteristics.

[0004] Encoding excitation and pulse compression techniques are effective ways to solve the above problems. This technique increases the average transmit energy under a limited peak voltage, and the receiver uses matched filtering to focus the dispersed energy into a narrow-bandwidth, high-peak-value main lobe pulse, thereby improving the signal-to-noise ratio and range resolution. Barker codes are binary phase-coded sequences with excellent autocorrelation, and their theoretical lengths are limited to a few, such as 3, 5, 7, 11, and 13 bits. The longer the code length, the greater the signal-to-noise ratio gain, but the range resolution decreases, and the higher the requirements for the transient response of the transducer are placed.

[0005] In existing research based on Barker codes, the code length is often selected empirically, lacking a systematic optimization method, and the evaluation indicators are relatively singular. To address these shortcomings, this invention proposes a rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization. It compares the performance of the entire encoding and decoding process of all finite-length Barker codes through a three-dimensional finite element simulation system, introduces multi-dimensional evaluation indicators, and employs a comprehensive scoring method to achieve scientific optimization of the code length. Summary of the Invention

[0006] Purpose of the invention: This invention proposes a rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization, which improves the response capability and noise resistance of the detection system to rail fracture defects.

[0007] Technical solution: The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization described in this invention is implemented as follows:

[0008] (1) Generate Barker code sequences of different lengths; (2) Design a sinusoidal single-pulse signal modulated by a Hamming window;

[0009] (3) Multiply and modulate the Barker code sequence generated in step (1) with the single pulse signal designed in step (2) to generate an coded excitation signal, and load it into the rail finite element model for simulation to receive the defect echo signal; (4) Perform pulse compression decoding on the defect echo signal to obtain the decoded signal;

[0010] (5) Perform multi-dimensional performance evaluation on the decoded signal and calculate evaluation indicators including defect echo peak, time width, differential amplitude gain (DAG), signal-to-noise ratio, and defect discrimination coefficient (DDC). (6) Based on the calculation results of step (5), Barker codes of different lengths are compared and the Barker code length most suitable for rail fracture monitoring is selected.

[0011] Further, the generation of Barker code sequences of different lengths in step (1) specifically refers to 3, 5, 7, 11, and 13-bit Barker code sequences, all with values ​​of +1 or -1; wherein:

[0012] 3-bit Barker code: BK(3) = [1, 1, -1] 5-bit Barker code: BK(5) = [1, 1, 1, -1, 1] 7-bit Barker code: BK(7) = [1, 1, 1, -1, -1, 1, -1] 11-bit Barker code: BK(11) = [1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1] 13-bit Barker code: BK(13) = [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1].

[0013] 3. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that the sinusoidal single-pulse signal in step (2) is:

[0014]

[0015] Where f is the center frequency of the sine wave. A is the number of cycles of the Hamming window modulated sine wave; A is the signal amplitude.

[0016] Furthermore, the implementation process of step (3) is as follows:

[0017] Barker code sequence and Product modulation is performed by sequentially multiplying each symbol with a single pulse and then concatenating the results to obtain the coded excitation signal. :

[0018]

[0019] In the formula, BK(i) is the i-th symbol of the Barker code sequence, with a value of +1 or -1; five different lengths of coded excitation signals are generated and loaded into the rail finite element model for simulation, and defect echo signals are received.

[0020] Furthermore, the implementation process of step (4) is as follows:

[0021] Read the received signal file output from the finite element simulation, calculate the average time interval of the received signal, and determine the sampling rate:

[0022]

[0023] Set carrier frequency The number of sine wave cycles for each symbol is The Hamming window function is After generating individual symbol templates, they are concatenated according to the Barker code sequence to obtain the reference signal. ;

[0024] The original received signal is preprocessed by using the detrend function to remove DC drift and linearity, and then interpolated to a value determined by the sampling rate. On a defined uniform time axis, we obtain ;

[0025] The preprocessed received signal is cross-correlated with the reference signal, and the decoded signal is the cross-correlation result.

[0026]

[0027] The time axis of the cross-correlation results is determined by the sampling rate and the cross-correlation length, converted to milliseconds:

[0028]

[0029] Where lags is the delayed index for cross-correlation operation;

[0030] Based on the defect location and the guided wave propagation velocity, a time window for the defect echo is pre-set. Extract a segment of the signal within the gate from the decoded signal, and calculate the maximum absolute value within that segment and its corresponding position:

[0031] .

[0032] Furthermore, the calculation of the defect echo duration in step (5) is implemented as follows:

[0033] The envelope signal is intercepted within the defect echo time window to locate the main lobe peak and calculate the half-amplitude threshold. The search proceeds point by point from the peak position to the left. When a point is found to be below the threshold, the signal within the fixed window is checked forward. If all points within the window are below the threshold, the left boundary is confirmed; otherwise, the search continues. The right boundary is determined in the same way. The defect echo time width is the time difference between the left and right boundaries.

[0034] Furthermore, the differential amplitude gain (DAG) in step (5) is calculated using the benchmark difference method to quantify the signal change intensity caused by the defect, reflecting the sensitivity of the detection system to the defect; specifically as follows:

[0035] The healthy and damaged signals are cross-correlated with a reference signal and decoded, then the envelopes are extracted using Hilbert transform and normalized.

[0036]

[0037] The DAG is calculated within the defect echo time gate by subtracting the normalized damage signal envelope from the healthy signal envelope.

[0038]

[0039] In the formula, multiply by 10 6 For dimensionless processing, the unit of DAG is dB.

[0040] Further, step (5) of calculating the signal-to-noise ratio (SNR) includes: performing maximum value normalization processing on the decoded envelope signal, setting defect area gate and noise area gate, and extracting peak amplitude values ​​respectively. and And calculate SNR:

[0041]

[0042] like ,but SNR is measured in decibels.

[0043] Furthermore, the defect discrimination coefficient (DDC) mentioned in step (5) is used to comprehensively measure the discrimination between the defect signal and the background noise. The ratio of the peak difference in the defect region to the fluctuation range of the noise region is calculated using the benchmark difference method; specifically as follows:

[0044] The health signal and damage signal are cross-correlated and decoded with the reference signal, and the envelope is extracted by Hilbert transform and globally normalized. Defect area gate and noise area gate are then set.

[0045]

[0046] Extract the maximum value of the lossy and lossless signal envelopes within the defective region gate, and calculate the difference D. 1；

[0047]

[0048] Extract the maximum and minimum values ​​of the lossy and lossless signal envelopes within the noise zone gate, calculate the fluctuation ranges R1 and R2, and take the maximum value of the two noise fluctuation ranges as the denominator.

[0049]

[0050] Calculate DDC:

[0051]

[0052] like If the noise fluctuation is too small and the DDC approaches infinity, it indicates that the detection system has an extremely high signal-to-noise ratio and detection reliability.

[0053] Furthermore, the implementation process of step (6) is as follows:

[0054] The overall score is calculated after normalizing each indicator using the adjustable weight method; let there be a total of M evaluation indicators. Let k be the normalized value of the k-th index for the i-th coding type at the j-th track break depth. The weighting coefficients for each indicator are given, and the comprehensive score for the i-th coding type at the j-th track break depth is:

[0055]

[0056] The weighting coefficients satisfy the following constraints:

[0057]

[0058] Then calculate the average overall score:

[0059]

[0060] The higher the average overall score, the better the overall performance of the coding type across the five track break depths;

[0061] The normalization methods for the various evaluation indicators are as follows: for DAG, SNR, DDC, and peak value, a normalization method that is as large as possible is adopted; for time width, a normalization method that is as small as possible is adopted.

[0062] Beneficial Effects: Compared with the prior art, the beneficial effects of this invention are as follows: This invention systematically compares the encoding and decoding performance of all finite-length Barker codes (3-bit, 5-bit, 7-bit, 11-bit, and 13-bit) in rail fracture monitoring, filling the technical gap of lacking a systematic basis for optimizing encoding length; This invention introduces five indicators: defect echo peak value, duration, DAG, and SNR, to evaluate encoding performance from multiple dimensions such as sensitivity, resolution, and noise immunity, overcoming the limitations of traditional single indicators; This invention provides a complete signal processing flow, including steps such as received signal import and sampling rate determination, reference signal generation, detrending and resampling preprocessing, cross-correlation matched filtering, time axis conversion, and defect segment peak detection, ensuring the accuracy and repeatability of pulse compression decoding. Attached Figure Description

[0063] Figure 1 This is a flowchart of the present invention;

[0064] Figure 2 A five-cycle sine wave signal modulated by a 60kHz Hamming window;

[0065] Figure 3 It is a 3-bit Barker code symbol sequence;

[0066] Figure 4 It is a 5-bit Barker code symbol sequence;

[0067] Figure 5 It is a 7-bit Barker code symbol sequence;

[0068] Figure 6 It is a codeword sequence of an 11-bit Barker code;

[0069] Figure 7 It is a 13-bit Barker code symbol sequence;

[0070] Figure 8 The excitation signal is encoded using a 3-bit Barker code.

[0071] Figure 9 The excitation signal is encoded using a 5-bit Barker code.

[0072] Figure 10 The excitation signal encoded with 7-bit Barker code;

[0073] Figure 11 The excitation signal encoded with 11-bit Barker code;

[0074] Figure 12 The excitation signal encoded with 13-bit Barker code;

[0075] Figure 13 To obtain the original waveform of the echo signal in the simulation;

[0076] Figure 14 This is the preprocessed signal after detrending, resampling, and alignment.

[0077] Figure 15 The waveform after pulse compression decoding;

[0078] Figure 16 The graph shows the variation of the peak values ​​of five Barker codes with the degree of track breakage;

[0079] Figure 17 The graph shows the variation of the width of five Barker codes with the degree of track breakage.

[0080] Figure 18 The graph shows the variation of five Barker code DAGs with the degree of rail breakage;

[0081] Figure 19 The graph shows the variation of SNR for five Barker codes with the degree of track breakage.

[0082] Figure 20 The graph shows the variation of DDC for five Barker codes with the degree of track breakage;

[0083] Figure 21 A graph showing how the overall score changes with the degree of track breakage;

[0084] Figure 22 This is a comparison chart of the average comprehensive scores for each encoding length. Detailed Implementation

[0085] The invention will now be further described with reference to the accompanying drawings.

[0086] like Figure 1 As shown, this invention proposes a rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization. Long-distance propagation of ultrasonic guided waves is achieved through Barker code encoding excitation. Pulse compression decoding technology is used to perform matched filtering on the echo signal to extract the defect echo signal. Subsequently, 3-bit, 5-bit, 7-bit, 11-bit, and 13-bit Barker codes are comprehensively compared using multi-dimensional performance evaluation indicators to select the optimal encoding length. The specific steps are as follows:

[0087] Step 1: Generate Barker code sequences of different lengths.

[0088] When ultrasonic guided waves propagate in steel rails, the echo signal energy attenuates significantly over long distances due to geometric diffusion and medium absorption, making it easily submerged by environmental noise. To increase the transmitted energy without increasing the peak voltage, this invention employs Barker code encoding excitation technology. Barker code is a binary phase coding sequence with excellent autocorrelation characteristics; the absolute values ​​of the sidelobe amplitudes of its aperiodic autocorrelation function are all no greater than 1, enabling the achievement of low peak sidelobe levels after pulse compression. Figure 2 As shown, a sinusoidal single-pulse signal with a center frequency of 60kHz and a 5-cycle Hamming window modulation is generated. The amplitude A = 1V. For example... Figures 3 to 7 As shown, 3-bit, 5-bit, 7-bit, 11-bit, and 13-bit Barker code sequences are generated, each with a value of +1 or -1:

[0089] 3-bit Barker code: BK(3)=[1, 1, -1]; 5-bit Barker code: BK(5)=[1, 1, 1, -1, 1]; 7-bit Barker code: BK(7)=[1, 1, 1, -1, -1, 1, -1]; 11-bit Barker code: BK(11)=[1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1]; 13-bit Barker code: BK(13)=[1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1].

[0090] Step 2: Design a Hamming window modulated sinusoidal single-pulse signal;

[0091]

[0092] Where f is the center frequency of the sine wave, taken as 60kHz. The number of cycles for the Hamming window modulated sine wave is 5; A is the signal amplitude, which is 1V.

[0093] Step 3: Generate Barker code-encoded excitation signals.

[0094] Barker code sequence and Product modulation is performed by multiplying each symbol (+1 or -1) with a single pulse in sequence and then concatenating the results to obtain the coded excitation signal. :

[0095]

[0096] In the formula, BK(i) is the i-th symbol of the Barker code sequence, with a value of +1 or -1. Five different lengths of coded excitation signals are generated and loaded into the rail finite element model for simulation, and defect echo signals are received.

[0097] Connect each Barker code sequence with Product modulation is performed to obtain the coded excitation signal. , Figures 8 to 12 The time-domain waveforms are obtained after modulation with 3, 5, 7, 11, and 13-bit Barker codes. After the Barker code is modulated with a single-pulse signal, the phase of the waveform corresponding to different code elements is maintained or flipped. As the code length increases, the duration of the coded excitation signal increases significantly, and the total energy injected into the system also increases accordingly. The generated coded excitation signal is loaded into a finite element model for simulation, and the defect echo signal is received, such as... Figure 13 As shown, the original echo signal obtained from the simulation has obvious attenuation oscillations. The defect-related echo is mixed with the background fluctuation, making it difficult to identify the defect features directly from the original waveform. Therefore, subsequent preprocessing and pulse compression decoding are required.

[0098] Step 4: Pulse compression decoding.

[0099] Pulse compression decoding involves matching and filtering the received defect echo signal with the original encoded reference signal to focus the encoded energy dispersed in the time domain into a main lobe pulse with narrow bandwidth and high peak value.

[0100] Received signal import and sampling rate determination: Read the received signal file output from the finite element simulation, calculate the average time interval of the received signal, and determine the sampling rate.

[0101]

[0102] Reference signal generation: Setting the carrier frequency =60 kHz, the number of sine wave cycles per symbol is =5, Hamming window function is After generating individual symbol templates, they are concatenated according to the Barker code sequence to obtain the reference signal. .

[0103] The raw received signal is preprocessed as follows:

[0104] Detrend: Use the detrend function to remove DC drift and linear trend from the signal.

[0105] Resampling alignment: interpolating the signal to the order determined by the sampling rate. On a defined uniform time axis, we obtain ,like Figure 14As shown, after detrending and resampling, the baseline drift of the echo signal is suppressed and the time sampling is more uniform, providing a more stable data foundation for subsequent matched filtering and defect echo peak extraction.

[0106] Cross-correlation operation (matched filtering): The preprocessed received signal is cross-correlated with the reference signal, and the decoded signal is the cross-correlation result.

[0107]

[0108] Time axis conversion: The time axis of the cross-correlation results is determined by the sampling rate and cross-correlation length, and is converted to milliseconds:

[0109]

[0110] Here, lags is the delayed index for cross-correlation operations.

[0111] Defect segment peak detection: Based on the defect location and guided wave propagation velocity, a time window for the defect echo is pre-set. (Unit: ms). Extract a segment of the signal within the gate from the decoded signal, and calculate the maximum absolute value within that segment and its corresponding position:

[0112]

[0113] Figure 15 The waveform after pulse compression decoding is as follows: After pulse compression decoding, the encoded energy that was originally dispersed in the time domain is compressed into a more concentrated peak response. The defect echo is more prominent within the set time window, which is beneficial for calculating evaluation indicators such as peak value, time width, and signal-to-noise ratio.

[0114] Step 5: Performance Evaluation: Calculate the following parameters for the echo signals of 3-, 5-, 7-, 11-, and 13-bit Barker codes under the same simulation conditions (rail length 11m, defect location 4.25m, defect depth 30%-70% of rail height):

[0115] (5.1) The peak value of the defect echo signal, i.e. the maximum amplitude of the defect echo after pulse compression (unit: V), directly reflects the sensitivity of the detection system to the defect, and the larger the better.

[0116] (5.2) Calculate the defect echo duration: The defect echo duration is defined as the duration of the main lobe of the defect echo at -6dB (half amplitude) after pulse compression, and is used to evaluate the distance resolution of the detection system.

[0117] This method employs a look-ahead fault-tolerant algorithm: It extracts signal segments within the defect echo gate and calculates the half-amplitude threshold; it searches point by point from the peak position to the left and right, looking back 50 degrees when encountering a point below the half-amplitude threshold. The signal within a fixed tolerance window is considered a boundary if all points within that window are below half the amplitude; otherwise, it is considered noise fluctuation, and the search continues. The defect echo duration is the time difference between the left and right boundaries, in microseconds.

[0118] (5.3) Calculate the differential amplitude gain (DAG) to quantify the signal change intensity caused by the defect and reflect the sensitivity of the detection system to the defect. This method uses the benchmark difference method for calculation.

[0119] The healthy and damaged signals are cross-correlated with a reference signal and decoded, then the envelopes are extracted using Hilbert transform and normalized.

[0120]

[0121] The DAG is calculated within the defect echo time gate by subtracting the normalized damage signal envelope from the healthy signal envelope.

[0122]

[0123] In the formula, multiply by 10 6 For dimensionless processing, the unit of DAG is dB.

[0124] (5.4) Calculate the signal-to-noise ratio (SNR): The signal-to-noise ratio is used to measure the energy difference between the defect echo signal and the background noise after the coded excitation pulse is compressed. The maximum value of the decoded envelope signal is normalized, and the defect area gate and noise area gate are set to extract the peak amplitude respectively. and And calculate SNR.

[0125]

[0126] like ,but The unit of SNR is decibel (dB).

[0127] (5.5) The Defect Discrimination Coefficient (DDC) is used to comprehensively measure the distinguishability between the defect signal and the background noise. The ratio of the peak difference in the defect area to the fluctuation range of the noise area is calculated using the benchmark difference method.

[0128] The health signal and the damage signal are cross-correlated with the reference signal and decoded. The envelope is extracted by Hilbert transform and then globally normalized. Defect area gate and noise area gate are set.

[0129]

[0130] Extract the maximum value of the lossy and lossless signal envelopes within the defective gate area and calculate the difference D1.

[0131]

[0132] Extract the maximum and minimum values ​​of the lossy and lossless signal envelopes within the noise zone gate, calculate the fluctuation ranges R1 and R2, and take the maximum value of the two noise fluctuation ranges as the denominator.

[0133]

[0134] DDC calculation:

[0135]

[0136] like If the noise fluctuation is too small, the DDC approaches infinity, indicating that the detection system has an extremely high signal-to-noise ratio and detection reliability. The larger the DDC, the higher the distinction between the defect signal and the background noise, and the stronger the identification capability.

[0137] Step 6: Compare the 3-bit, 5-bit, 7-bit, 11-bit, and 13-bit Barker codes to select the most suitable Barker code length for rail fracture monitoring.

[0138] The overall score is calculated after normalizing each indicator using an adjustable weighting method. Let there be a total of M evaluation indicators. Let k be the normalized value of the k-th index for the i-th coding type at the j-th track break depth. The weighting coefficients for each indicator are given, and the comprehensive score for the i-th coding type at the j-th track break depth is:

[0139]

[0140] The weighting coefficients satisfy the following constraints:

[0141]

[0142] Taking the equal-weighted method as an example, the comprehensive score is calculated after normalizing each indicator. Figures 16 to 21 The figure shows a comparison of performance metrics for five Barker code lengths under different track break depths. Significant differences exist in peak value, duration, DAG, SNR, DDC, and overall score among Barker codes of different lengths. Let the overall score of the i-th coding type at the j-th track break depth be:

[0143]

[0144]

[0145] , , , , These are the normalized values ​​of DAG, SNR, time width, and DDC, respectively.

[0146] The normalization methods for each indicator are as follows:

[0147] DAG: The larger the better.

[0148] SNR: The higher the better

[0149] Width: The smaller the better.

[0150] DDC: The larger the better.

[0151] Peak value: the higher the better.

[0152] Average overall score; the average overall score for the i-th encoding type is:

[0153]

[0154] A higher average overall score indicates better overall performance of the coding type across the five track break depths. The weighting coefficients can be adjusted according to actual engineering needs. It can be flexibly adapted to different application scenarios.

[0155] like Figure 22 As shown in the simulation results, the 11-bit Barker code ranks first in comprehensive score and has the highest average comprehensive score under the five rail breakage depths. It is recommended as the most suitable coding excitation scheme for the 11m long rail breakage monitoring system.

[0156] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization, characterized in that, Includes the following steps: (1) Generate Barker code sequences of different lengths; (2) Design a sinusoidal single-pulse signal modulated by a Hamming window; (3) Multiply and modulate the Barker code sequence generated in step (1) with the single pulse signal designed in step (2) to generate an coded excitation signal, and load it into the rail finite element model for simulation to receive the defect echo signal; (4) Perform pulse compression decoding on the defect echo signal to obtain the decoded signal; (5) Perform multi-dimensional performance evaluation on the decoded signal and calculate evaluation indicators including defect echo peak, time width, differential amplitude gain (DAG), signal-to-noise ratio, and defect discrimination coefficient (DDC). (6) Based on the calculation results of step (5), Barker codes of different lengths are compared and the Barker code length most suitable for rail fracture monitoring is selected.

2. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, Step (1) generates Barker code sequences of different lengths, specifically 3, 5, 7, 11, and 13-bit Barker code sequences, each with a value of +1 or -1; where: 3-bit Barker code: BK(3) = [1, 1, -1] 5-bit Barker code: BK(5) = [1, 1, 1, -1, 1] 7-bit Barker code: BK(7) = [1, 1, 1, -1, -1, 1, -1] 11-bit Barker code: BK(11) = [1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1] 13-bit Barker code: BK(13) = [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1].

3. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The sinusoidal single-pulse signal mentioned in step (2) is: Where f is the center frequency of the sine wave. A is the number of cycles of the Hamming window modulated sine wave; A is the signal amplitude.

4. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The implementation process of step (3) is as follows: Barker code sequence and Product modulation is performed by sequentially multiplying each symbol with a single pulse and then concatenating the results to obtain the coded excitation signal. : In the formula, BK(i) is the i-th symbol of the Barker code sequence, with a value of +1 or -1; five different lengths of coded excitation signals are generated and loaded into the rail finite element model for simulation, and defect echo signals are received.

5. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The implementation process of step (4) is as follows: Read the received signal file output from the finite element simulation, calculate the average time interval of the received signal, and determine the sampling rate: Set carrier frequency The number of sine wave cycles for each symbol is The Hamming window function is After generating individual symbol templates, they are concatenated according to the Barker code sequence to obtain the reference signal. ; The original received signal is preprocessed by using the detrend function to remove DC drift and linearity, and then interpolated to a value determined by the sampling rate. On a defined uniform time axis, we obtain ; The preprocessed received signal is cross-correlated with the reference signal, and the decoded signal is the cross-correlation result. The time axis of the cross-correlation results is determined by the sampling rate and the cross-correlation length, converted to milliseconds: Where lags is the delayed index for cross-correlation operation; Based on the defect location and the guided wave propagation velocity, a time window for the defect echo is pre-set. Extract a segment of the signal within the gate from the decoded signal, and calculate the maximum absolute value within that segment and its corresponding position: 。 6. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The process for calculating the defect echo duration in step (5) is as follows: The envelope signal is intercepted within the defect echo time window to locate the main lobe peak and calculate the half-amplitude threshold. The search proceeds point by point from the peak position to the left. When a point is found to be below the threshold, the signal within the fixed window is checked forward. If all points within the window are below the threshold, the left boundary is confirmed; otherwise, the search continues. The right boundary is determined in the same way. The defect echo time width is the time difference between the left and right boundaries.

7. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, Step (5) involves calculating the differential amplitude gain (DAG) using the benchmark difference method to quantify the signal change intensity caused by the defect, reflecting the sensitivity of the detection system to the defect; specifically as follows: The healthy and damaged signals are cross-correlated with a reference signal and decoded, then the envelopes are extracted using Hilbert transform and normalized. The DAG is calculated within the defect echo time gate by subtracting the normalized damage signal envelope from the healthy signal envelope. In the formula, multiply by 10 6 For dimensionless processing, the unit of DAG is dB.

8. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, Step (5) of calculating the signal-to-noise ratio (SNR) includes: normalizing the maximum value of the decoded envelope signal, setting a defect area gate and a noise area gate, and extracting the peak amplitude respectively. and And calculate SNR: like ,but SNR is measured in decibels.

9. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The Defect Differentiation Coefficient (DDC) mentioned in step (5) is used to comprehensively measure the distinguishability between the defect signal and the background noise. The ratio of the peak difference in the defect region to the fluctuation range of the noise region is calculated using the benchmark difference method; specifically as follows: The health signal and damage signal are cross-correlated and decoded with the reference signal, and the envelope is extracted by Hilbert transform and globally normalized. Defect area gate and noise area gate are then set. Extract the maximum value of the lossy and lossless signal envelopes within the defective region gate, and calculate the difference D. 1； Extract the maximum and minimum values ​​of the lossy and lossless signal envelopes within the noise zone gate, calculate the fluctuation ranges R1 and R2, and take the maximum value of the two noise fluctuation ranges as the denominator. Calculate DDC: like If the noise fluctuation is too small and the DDC approaches infinity, it indicates that the detection system has an extremely high signal-to-noise ratio and detection reliability.

10. The rail fracture monitoring method based on Barker code ultrasonic guided wave simulation optimization according to claim 1, characterized in that, The implementation process of step (6) is as follows: The overall score is calculated after normalizing each indicator using the adjustable weight method; let there be a total of M evaluation indicators. Let k be the normalized value of the k-th index for the i-th coding type at the j-th track break depth. The weighting coefficients for each indicator are given, and the comprehensive score for the i-th coding type at the j-th track break depth is: The weighting coefficients satisfy the following constraints: Then calculate the average overall score: The higher the average overall score, the better the overall performance of the coding type across the five track break depths; The normalization methods for the various evaluation indicators are as follows: for DAG, SNR, DDC, and peak value, a normalization method that is as large as possible is adopted; for time width, a normalization method that is as small as possible is adopted.

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