Rail track vertical irregularity detection method based on FIR-wavelet transform

Abstract

The railway track vertical irregularity detection method based on FIR-wavelet transform disclosed by the present invention includes dividing the acceleration signal of the train into signals with the same length, performing denoising processing on the divided acceleration signals by using the ensemble empirical mode decomposition algorithm and the threshold selection method; resampling the denoised signals, and then processing them by using the double integration method based on the FIR filter to obtain the long-wave irregularity prediction result; extracting the high-frequency information of the divided acceleration signals by using the wavelet transform method to realize the short-wave irregularity prediction, and then superimposing it with the long-wave irregularity prediction result to obtain the railway track vertical irregularity detection result. The method of the present invention based on the ensemble empirical mode decomposition can effectively remove various interference noises in the acceleration signal; at the same time, the use of the FIR integral filter solves the problem of large interference of the trend term in the traditional integration method, and improves the accuracy of the railway track vertical irregularity prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of rail transit informatization and intelligent operation and maintenance, and specifically relates to a method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform. Background Art

[0002] In the 21st century, as an important part of transportation, railway transportation has an important impact on people's travel modes. The running safety and stability of trains not only depend on the performance of the trains themselves, but also are affected by the geometric state of the lines. As the fundamental cause of train vibration, the irregularity excitation of railway tracks not only generates impact forces on running trains, but also affects the running state of trains, causing vehicle tilt and roll motion, and has a great impact on the smoothness and comfort of trains. Therefore, realizing the monitoring of the geometric state of tracks is a key research direction for the daily operation and maintenance and intelligent development of national railways.

[0003] Traditional methods for detecting track irregularities mainly rely on expensive special high-precision attitude measurement equipment, which is detected in real time according to the plan during the dynamic operation of the inspection vehicle. The contradiction between the detection cost and detection efficiency still needs to be resolved through reasonable technical means. The current mainstream alternative solution is to install inertial sensors such as accelerometers and gyroscopes on in-service rail trains. The data obtained by the sensors can be used to realize the online monitoring of the geometric state of the tracks after appropriate processing. Compared with the traditional solution, the sensors are relatively cheap and easy to install, and can greatly save costs under the condition of effective monitoring, realize real-time detection of track irregularities, improve line safety, and meet the management requirements of the safety status of national railways. However, the acceleration signals obtained by the existing technology are affected by various noise interferences in the driving environment. How to effectively eliminate the noise interference in the signals and thus detect track irregularities with high precision is an urgent problem to be solved. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform, which solves the problem of low accuracy of the existing methods for detecting the vertical irregularity of railway tracks.

[0005] The technical solution adopted by the present invention is: a method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform, including the following steps:

[0006] Step 1: Divide the acceleration signal of the train into signals of the same length, and perform denoising processing on the divided acceleration signal by using the ensemble empirical mode decomposition algorithm and the threshold selection method;

[0007] Step 2: Resample the signal obtained after the denoising processing in Step 1, transform from the spatial domain to the time domain, and then process it by using the double integral method based on the FIR filter to obtain the prediction result of the long-wave irregularity;

[0008] Step 3: Use the wavelet transform method to extract the high-frequency information of the acceleration signal segmented in Step 1, realize the prediction of short-wave irregularities, and then superimpose it with the long-wave irregularity prediction result obtained in Step 2 to obtain the detection result of the vertical irregularity of the railway track.

[0009] The features of the present invention also lie in that

[0010] Step 1 specifically includes the following steps:

[0011] Step 1.1: Sequentially segment the acceleration signal of the train into signals with a length of 10,000, and similarly segment the vertical irregularity data of the railway track corresponding to the mileage of the acceleration signal into data with a length of 10,000;

[0012] Step 1.2: Perform ensemble empirical mode decomposition on the acceleration signal segmented in Step 1.1, and decompose it into multiple imf components. The decomposed imf components need to satisfy formula (1) and formula (2):

[0013] (N Z -1) ≤ N e ≤ (N Z +1) (1)

[0014] [f max (t) + f min (t)] ÷ 2 = 0 (2)

[0015] Formula (1) represents the relationship satisfied by the number of extreme points of the imf component, where N Z is the number of extreme points of the zero-crossing of the separated imf component, and N e is the number of extreme points that do not cross the zero; formula (2) represents the relationship between the upper and lower envelope lines determined by the extreme points of the signal, f max (t) is the mean value of the upper envelope line of the imf component, and f min (t) is the mean value of the lower envelope line. The imf component x(t) shown in formula (3) is obtained through formula (1) and formula (2):

[0016]

[0017] In formula (3), x(t) is the data segmented in Step 1.1, n is the number of imf components decomposed from the signal segmented in Step 1.1, and r n (t) is the remaining residual component;

[0018] After obtaining the imf component imf(t) through Step 1.2, perform discrete Fourier transform on each component x[k] of it to obtain X[k], as shown in formula (4):

[0019]

[0020] In formula (4), N is the signal length of 10,000 in step 1.1, and j is the complex number flag;

[0021] Step 1.4: Obtain the frequency-domain signal of the imf component through step 1.3, perform threshold screening on the frequency fluctuation range of the frequency-domain signal, and use whether the maximum frequency amplitude point in the imf component is within the threshold range as the screening condition to remove the imf components outside the threshold range, and recombine the remaining components to obtain the denoised signal.

[0022] When performing threshold screening on the frequency fluctuation range of the frequency-domain signal in step 1.4, it is first necessary to determine the threshold. Perform prior data analysis on the imf components obtained from multiple groups of decomposed data, and select the threshold by calculating the influence factor of each imf component on the long-wave irregularity prediction result; the influence factor needs to remove the current imf component and the signal without removing the current imf component respectively, calculate the long-wave irregularity prediction result using the subsequent steps, and then calculate the Pearson correlation coefficient between the previous and subsequent long-wave irregularity prediction results and the prediction target, and obtain the ratio of the two coefficients as the influence factor. The calculation process is shown in formulas (5) and (6):

[0023]

[0024]

[0025] In formula (5), r is the calculated influence factor, and p k represents the Pearson correlation coefficient calculated after removing the k-th imf component, and p0 is the Pearson correlation coefficient calculated without removing any component; formula (6) is the Pearson correlation coefficient calculation formula, X and Y are the prediction result and the prediction target respectively. Find the imf components with an influence factor greater than 1, divide them into high-frequency and low-frequency signal parts, and find the maximum frequency amplitude point and the minimum frequency amplitude point close to the center frequency respectively. The average of the two points is the minimum frequency threshold and the maximum frequency threshold.

[0026] Step 2 specifically includes the following steps:

[0027] Step 2.1: Resample the denoised signal obtained in step 1.4, resample the distance-based acceleration signal into a time-based acceleration signal a(τ), the signal frequency is 400Hz, and the sampling formula is shown in formula (7):

[0028]

[0029] In formula (7), y represents the amplitude of the resampled point, t1, t2, and t3 represent the times of the previous point, the resampled point, and the next point respectively, and y1 and y2 represent the amplitudes of the previous point and the next point;

[0030] Step 2.2: Perform time-domain integration on the resampled acceleration signal a(τ) obtained in Step 2.1, as shown in formula (8):

[0031]

[0032] In formula (8), v(0) is the initial acceleration, and dτ is the signal time difference;

[0033] After obtaining the velocity signal by integration, perform FIR filtering to remove the low-frequency trend term, as shown in formula (9):

[0034]

[0035] In formula (9), N is the length of the signal, h(t) is the FIR filter coefficient, and * is the convolution identifier;

[0036] Step 2.3: Perform a second time-domain integration on the velocity signal obtained after removing the trend term in Step 2.2 to obtain the displacement signal y(x) of the train, as shown in formula (10):

[0037]

[0038] In formula (10), y(0) is the initial velocity;

[0039] Perform first-order least squares calculation on the displacement signal y(x), as shown in formula (11):

[0040]

[0041] In formula (11), L is the obtained minimum difference; f(x) is the first-order fitting function, as shown in formula (12):

[0042] f(x) = kx + b (12)

[0043] In formula (12), k is the first-order coefficient and b is the constant;

[0044] Remove the first-order fitting signal f(x) from the displacement signal y(x) to obtain the long-wave irregularity prediction result Y(x), as shown in formula (13):

[0045] Y(x) = y(x) - f(x) (13).

[0046] Step 3 specifically includes the following steps:

[0047] Step 3.1: Extract the signals segmented in Step 1.1, perform wavelet decomposition on the segmented signals to obtain multi-layer high-frequency wavelet signals DWT(x), as shown in Formulas (14) and (15):

[0048]

[0049]

[0050] In Formula (14), ψ is the wavelet basis function, a and b are time and frequency respectively, m and n are wavelet basis transformation coefficients, k is the number of wavelet decomposition layers; Z is an integer;

[0051] In Formula (15), f is the acceleration signal segmented in Step 1.1;

[0052] After wavelet decomposition, extract the first two layers of high-frequency wavelet signals DWT1(x) and DWT2(x), and then perform wavelet reconstruction to obtain high-frequency information H(x), as shown in Formula (16):

[0053]

[0054] In Formula (16), m1 and n1 are the wavelet basis transformation coefficients of the first-layer signal, and m2 and n2 are the wavelet basis transformation coefficients of the second-layer signal;

[0055] Step 3.2: Superimpose the high-frequency information H(x) obtained in Step 3.1 with Y(x) obtained in Step 2.4, as shown in Formula (17), to obtain the railway track vertical irregularity detection result A(x):

[0056] A(x) = H(x) + Y(x) (17).

[0057] The beneficial effects of the present invention are as follows: The railway track vertical irregularity detection method based on FIR-wavelet transform of the present invention, based on the ensemble empirical mode decomposition method, can effectively remove various interference noises in the acceleration signal; at the same time, the use of the FIR integral filter solves the problem of large trend term interference in the traditional integration method, and improves the accuracy of railway track vertical irregularity prediction. Brief Description of the Drawings

[0058] Figure 1 is a schematic flow chart of the railway track vertical irregularity detection method based on FIR-wavelet transform of the present invention;

[0059] Figure 2 is a schematic diagram of the vertical acceleration data input in the embodiment of the railway track vertical irregularity detection method based on FIR-wavelet transform of the present invention;

[0060] Figure 3It is a schematic diagram of the result after ensemble empirical mode decomposition and Fourier transform in the embodiment of the method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform of the present invention;

[0061] Figure 4 It is a schematic diagram of the result of signal processing by removing noise and then using the double integral method based on the FIR filter in the embodiment of the method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform of the present invention;

[0062] Figure 5 It is a schematic diagram of the detection result of the vertical irregularity of railway tracks obtained in the embodiment of the method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform of the present invention. Detailed implementation manners

[0063] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0064] The present invention provides a method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform, as Figure 1 shown, including the following steps:

[0065] Step 1: Use the measured vertical acceleration data of the track inspection vehicle as the data to be measured. As Figure 2 shown, first input the vertical acceleration data, and then divide it into signals with the same length. Use the ensemble empirical mode decomposition algorithm and the threshold selection method to denoise the acceleration signal. Specifically as follows:

[0066] Step 1.1: First, sequentially divide the input original acceleration signal into signals with a length of 10,000, and similarly divide the track vertical irregularity data corresponding to the mileage of the acceleration signal into data with a length of 10,000.

[0067] Step 1.2: Perform CEEMDAN (ensemble empirical mode decomposition) processing on the acceleration signal divided in Step 1.1 to decompose it into multiple imf components. The decomposed imf components need to satisfy the formulas (1) and (2) shown:

[0068] (N Z -1) ≤ N e ≤ (N Z +1) (1)

[0069] [f max (t) + f min (t)] ÷ 2 = 0 (2)

[0070] Formula (1) represents the relationship satisfied by the number of extreme points of the imf component. Where N Z is the number of extreme points of the zero-crossing of the separated imf component, and N eis the number of extreme points that do not cross the zero point; Equation (2) represents the relationship between the upper and lower envelope lines determined by the extreme points of the signal, f max (t) is the mean value of the upper envelope line of the imf component, f min (t) is the mean value of the lower envelope line. By satisfying the two equations, the imf component as shown in Equation (3) can be obtained:

[0071]

[0072] where x(t) is the data obtained by segmentation in Step 1.1, n is the number of imf components decomposed from the original signal, and r n (t) is the remaining residual component.

[0073] Step 1.3: After obtaining the imf components through Step 1.2, perform discrete Fourier transform (DFT) on each component as shown in Equation (4), and the obtained result is as Figure 3 shown. It can be seen that the CEEMD decomposition method can have a good separation effect on signals in different frequency domains:

[0074]

[0075] where N is the signal length of 10000 in Step 1.1.

[0076] Step 1.4: Obtain the frequency-domain signals of the imf components through Step 1.3, and perform threshold screening on the frequency fluctuation range of the frequency-domain signals. First, it is necessary to determine an appropriate threshold. Conduct prior data analysis on the imf components obtained from multiple groups of decomposed data, and select the threshold by calculating the influence factor of each imf component on the long-wave irregularity prediction result. The influence factor requires removing the current imf component and the signal without removing the current imf component, respectively calculating the long-wave irregularity prediction results using the subsequent steps, and then calculating the Pearson correlation coefficient between the long-wave irregularity prediction results before and after and the prediction target, and obtaining the ratio of the two coefficients as the influence factor. The calculation process is shown in Equations (5) and (6):

[0077]

[0078]

[0079] where r is the calculated influence factor, p kIt represents the Pearson correlation coefficient calculated after removing the k-th IMF component, and p0 is the Pearson correlation coefficient calculated without removing any components. Formula (6) is the formula for calculating the Pearson correlation coefficient, where X and Y are the prediction result and the prediction target respectively. Find the IMF components with influence factors greater than 1, divide them into high-frequency and low-frequency signal parts, find the maximum point of the frequency amplitude and the minimum point of the frequency amplitude close to the center frequency respectively, and the average of the two points is the minimum frequency threshold and the maximum frequency threshold. The calculated maximum and minimum frequency thresholds of the retained IMF components can achieve the maximum removal of noise signals on the premise of retaining the effective signals, and have strong universality.

[0080] Taking whether the maximum point of the frequency amplitude in the IMF component is within the threshold range as the screening condition, remove the IMF components outside the threshold range, and the remaining components can be recombined to obtain the target denoised signal.

[0081] Step 2: First, resample the denoised signal, convert it from the spatial domain to the time domain, and then use the double integral method based on the Finite Impulse Response (FIR) filter to process the signal to obtain the prediction results of the vertical irregularity. Specifically as follows:

[0082] Step 2.1: Resample the signal obtained in Step 1.4, resample the acceleration signal based on distance to the acceleration signal a(τ) based on time, and the signal frequency is 400Hz. The sampling formula is as shown in Formula (7):

[0083]

[0084] Where y represents the amplitude of the resampled point, t1, t2, and t3 represent the time of the previous point, the resampled point, and the next point respectively, and y1 and y2 represent the amplitudes of the previous point and the next point.

[0085] Step 2.2: In the field of predicting the vertical irregularity of the track, integrating the acceleration signal in the time domain or frequency domain is a common method. Among them, removing the trend term generated during the integration process is crucial. Here, a time-domain integration method based on the FIR filter is introduced, which can well remove the trend term. The obtained result is as Figure 4 shown. The speed signal is relatively stable after removing the low-frequency trend term. First, perform time-domain integration on the resampled acceleration signal a(τ), as shown in Formula (8):

[0086]

[0087] Where v(0) is the initial speed. After obtaining the speed signal by integration, perform FIR filtering on it to remove the low-frequency trend term, as shown in Formula (9):

[0088]

[0089] Where N is the length of the signal, and h(t) is the filtering coefficient of the FIR filter.

[0090] Step 2.3: Perform a second-time domain integration process on the velocity signal obtained after removing the trend term according to formula (6), and the displacement signal y(x) of the train can be obtained, as shown in formula (10):

[0091]

[0092] In formula (10), y(0) is the initial velocity;

[0093] Perform a first-order least squares calculation on the displacement signal y(x), as shown in formula (11):

[0094]

[0095] Where L is the obtained minimum difference, and f(x) is the first-order fitting function, as shown in formula (12):

[0096] f(x) = kx + b (12)

[0097] Where k is the first-order coefficient and b is the constant.

[0098] Subtracting the fitted first-order signal f(x) from the displacement signal y(x) can obtain the final result, as shown in formula (13):

[0099] Y(x) = y(x) - f(x) (13)

[0100] As shown above, Y(x) is the predicted value of the long-wave unevenness obtained.

[0101] Step 3: Extract the high-frequency information in the original acceleration signal by using the wavelet transform method, and superimpose it with the prediction result of the unevenness to obtain the final prediction result. As Figure 5 shown, there is a relatively accurate prediction effect in the low-frequency part, and the prediction in the high-frequency part also has a good supplementary effect on the result. Specifically as follows:

[0102] Step 3.1. Since the integration process of the signal in Step 2 suppresses the high-frequency information of the signal, it is necessary to add high-frequency information to the predicted result to achieve short-wave irregularity prediction. Here, a signal extraction method based on wavelet transform is adopted. This method is a local transform in space (time) and frequency, so it can effectively extract information from the signal and can extract high-frequency information in the signal more effectively than the filter method. Extract the signal segmented in Step 1.1, perform wavelet decomposition on the signal, and obtain multi-layer high-frequency wavelet signals DWT(x), as shown in Formulas (14) and (15):

[0103]

[0104]

[0105] where ψ is the wavelet basis function, a and b are time and frequency respectively, m and n are wavelet basis transformation coefficients, k is the number of wavelet decomposition layers, Z is an integer, and f is the acceleration signal segmented in Step 1.1.

[0106] After extracting the first two layers of high-frequency wavelet signals DWT1(x) and DWT2(x) after wavelet decomposition, and then performing wavelet reconstruction, the high-frequency information H(x) is obtained:

[0107]

[0108] In Formula (16), ψ is the wavelet basis function, m1 and n1 are the wavelet basis transformation coefficients of the first-layer signal, and m2 and n2 are the wavelet basis transformation coefficients of the second-layer signal.

[0109] Step 3.2. Superimpose the high-frequency information H(x) and the result Y(x) obtained in Step 2.4 to obtain the final prediction result A(x):

[0110] A(x) = H(x) + Y(x) (17)

[0111] This result is the prediction result of the track vertical irregularity corresponding to the mileage of the vehicle vertical acceleration signal.

[0112] Through the above method, the railway track vertical irregularity detection method based on FIR-wavelet transform of the present invention, based on the ensemble empirical mode decomposition method, can effectively remove various interference noises in the acceleration signal; at the same time, using the FIR integration filter solves the problem of large trend term interference in the traditional integration method and improves the accuracy of railway track vertical irregularity prediction.

Claims

1. A method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform, characterized in that, Including the following steps: Step 1: Divide the acceleration signal of the train into signals with the same length, and perform denoising processing on the divided acceleration signal by using the ensemble empirical mode decomposition algorithm and the threshold selection method; specifically including the following steps: Step 1.1: Divide the acceleration signal of the train into signals with a length of 10,000 in sequence, and similarly divide the railway track unevenness data corresponding to the mileage of the acceleration signal into data with a length of 10,000; Step 1.

2. Perform ensemble empirical mode decomposition on the acceleration signals segmented in Step 1.1, and decompose them into multiple components. The decomposed components need to satisfy Formula (1) and Formula (2): （1） （2） Formula (1) represents the relationship satisfied by the number of extreme points of the component, where is the separated number of extreme points of the zero-crossing of the component, is the number of extreme points that do not cross the zero point; Formula (2) represents the relationship between the upper and lower envelope lines determined by the extreme points of the signal, is the mean value of the upper envelope line of the component, is the mean value of the lower envelope line, and Formula (3) shown below is obtained through Formula (1) and Formula (2) for the component : （3） In formula (3), is the data obtained by segmentation in step 1.1, n is the number of components decomposed from the signal obtained by segmentation in step 1.1, is the remaining residual component; Step 1.

3. After obtaining component , perform discrete Fourier transform on each of its components to obtain , as shown in formula (4): （4） In formula (4), is the signal length 10000 in step 1.1, j is the complex flag; Step 1.

4. Obtain through Step 1.3 the frequency-domain signal of the component, and perform threshold screening on the frequency fluctuation range of the frequency-domain signal, so as to use whether the maximum frequency amplitude point in the component is within the threshold range as the screening condition, and remove the components not within the threshold range, and recombine the remaining components to obtain the denoised signal; Step 2: Resample the denoised signal obtained in Step 1, transform from the spatial domain to the time domain, and then use the double integration method based on the FIR filter to process to obtain the long-wave unevenness prediction result; Step 3: Use the wavelet transform method to extract the high-frequency information of the acceleration signal divided in Step 1 to realize the short-wave unevenness prediction, and then superimpose it with the long-wave unevenness prediction result obtained in Step 2 to obtain the railway track unevenness detection result.

2. The method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform according to claim 1, wherein, When performing threshold screening on the frequency fluctuation range of the frequency-domain signal in Step 1.4, it is first necessary to determine the threshold and conduct prior data analysis on the components obtained from multiple sets of decomposed data. The threshold is selected by calculating the influence factor of each component on the prediction result of long-wave irregularity; The influence factor needs to remove the current component and the signal without removing the current component are respectively used in the subsequent steps to calculate the long-wave irregularity prediction results. Then, the Pearson correlation coefficients between the front and rear long-wave irregularity prediction results and the prediction target are calculated, and the ratio of the two coefficients is obtained as the influence factor. The calculation process is shown in Formulas (5) and (6): （5） （6） In formula (5), is the calculated influence factor, represents the Pearson correlation coefficient calculated after removing the th component, is the Pearson correlation coefficient calculated without removing any components; formula (6) is the calculation formula of the Pearson correlation coefficient, and are the prediction result and the prediction target respectively. Find the components with an influence factor greater than 1, which are divided into high-frequency and low-frequency signal parts. The maximum points of the frequency amplitudes and the minimum points of the frequency amplitudes close to the center frequency are found respectively. The average of the two points is the minimum frequency threshold and the maximum frequency threshold.

3. The method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform according to claim 2, wherein The specific steps of Step 2 include the following steps: Step 2.1: Resample the denoised signal obtained in Step 1.4 to resample the distance-based acceleration signal into a time-based acceleration signal , with a signal frequency of 400 Hz. The sampling formula is as shown in Equation (7): （7） In formula (7), represents the amplitude of the resampled point, respectively represent the time of the previous point, the resampled point, and the next point, represent the amplitudes of the previous point and the next point; Step 2.

2. Perform time-domain integration on the resampled acceleration signal obtained in Step 2.1 as shown in Equation (8): （8） In formula (8), is the initial acceleration, is the signal time difference; After integrating to obtain the velocity signal, perform FIR filtering to remove the low-frequency trend term, as shown in Equation (9): （9） In formula (9), is the length of the signal, are the filtering coefficients of the FIR filter, is the convolution identifier; Step 2.3: Perform a second time-domain integration on the velocity signal obtained after removing the trend term in Step 2.2 to obtain the displacement signal of the train , as shown in Equation (10): （10） In formula (10), is the initial velocity; For the displacement signal perform first-order least squares calculation as shown in Equation (11): （11） In formula (11), is the obtained minimum difference; is a first-order fitting function, as shown in formula (12): （12） In formula (12), is the first-order coefficient, is a constant; Displacement signal Remove the first-order fitting signal Obtain the long-wave irregularity prediction result , as shown in Equation (13): （13）。 4. The method for detecting the vertical irregularity of railway tracks based on FIR-wavelet transform according to claim 3, characterized in that, The specific steps of Step 3 include the following steps: Step 3.1: Extract the signals segmented in Step 1.1, perform wavelet decomposition on the segmented signals, and obtain multi-layer high-frequency wavelet signals , as shown in Formulas (14) and (15): （14） （15） In formula (14), is a wavelet basis function, and are time and frequency respectively, and are wavelet basis transform coefficients, is the number of wavelet decomposition levels; is an integer; In formula (15), is the acceleration signal obtained by segmentation in step 1.1; Extract the first two layers of high-frequency wavelet signals after wavelet decomposition and After that, perform wavelet reconstruction to obtain high-frequency information , as shown in formula (16): （16） In formula (16), and the wavelet basis transform coefficients of the first-layer signal, and the wavelet basis transform coefficients of the second-layer signal; Step 3.2: Superimpose the high-frequency information obtained in Step 3.1 with that obtained in Step 2.4 as shown in Formula (17) to obtain the detection result of the vertical irregularity of the railway track : （17）。

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