An adaptive signal reconstruction method for rail weld joint damage detection based on VMD

Abstract

This invention discloses an adaptive signal reconstruction method based on VMD for detecting defects in rail welded joints, comprising: Variational Mode Decomposition (VMD): decomposing the acquired axial scan A-scan signal of the rail welded joint into multiple Intrinsic Mode Functions (IMFs) using VMD; removing low-frequency interference from the IMFs; Singular Value Decomposition (SVD): constructing a Hankel matrix H from the defect signal in the second-lowest frequency component, and performing singular value decomposition on H; and reconstructing the signal based on kurtosis. This invention improves the efficiency of ultrasonic detection of defects in rail welded joints.

Description

Technical Field

[0001] This invention relates to the field of rail welded joint technology, and in particular to an adaptive signal reconstruction method based on VMD for detecting damage to rail welded joints. Background Technology

[0002] Rail weld joints are vulnerable points in railways, and rail defects frequently occur at these joints. Ultrasonic testing is widely used in railway maintenance to detect these defects. However, the presence of coarse grains and inclusions in the weld joints results in significant backscattering noise in the ultrasonic signal, interfering with defect detection.

[0003] Because the rails are in direct contact with the wheels, they are subjected to high-frequency, high-intensity loads. These loads generate various forms of stress within the rails, leading to internal defects such as cracks; and welded joints are vulnerable points in the track system, especially in the case of thermoforming welding. (According to Yao N) 2 Studies have shown that approximately 52.6% of rail defects occur at weld points, although weld points only account for a small portion of the total rail length. This is primarily attributed to residual stress and the presence of non-metallic inclusions, such as silica and alumina within the weld point. If not detected in time, rail defects can develop into rail fractures.

[0004] Ultrasonic testing is commonly used in railway maintenance to detect internal defects in rails. However, its application to welded joints presents challenges. Inspectors report that echo signals from small internal defects in rail welded joints are often drowned out by echo signals from coarse particles and inclusions, especially in hot-melt welded joints. In many cases, these cracks are not small, but their echo signals are weak because the crack direction is not perpendicular to the ultrasonic incident direction. Therefore, the detector needs to repeatedly change the probe's direction and position to distinguish the defect signal, which increases the time required for weld defect detection.

[0005] For austenitic steels and high-alloy steels (such as stainless steel), the high anisotropy and inhomogeneity of their welded joints lead to energy attenuation, elastic wave deviation, and high noise. Several studies have proposed methods for assessing their internal acoustic fields. From a signal processing perspective, early researchers employed wavelet analysis for noise trimming and thresholding; another widely studied method is split-spectrum processing (SSP). This method uses multiple bandpass filters to separate the entire ultrasonic signal and applies nonlinear processing (such as minimization or polarity thresholding) to mitigate the effects of noise. In recent years, researchers have begun to use sparse signal representations. This includes deterministic methods, such as matched pursuit (MP) techniques, and Bayesian methods, such as sparse Bayesian learning.

[0006] The methods described above have all achieved good results on their respective datasets. However, they all require substantial prior knowledge, making them difficult to apply in practice. Another important fact is that these methods are tailored for stainless steel. Due to the heterogeneity of the material, these methods are not suitable for rail welded joints. As a type of low-alloy steel and high-carbon steel, rail steel welded joints do not exhibit as strong anisotropy and inhomogeneity, resulting in limited research on signal processing for defect detection in rail welded joints. Existing research primarily focuses on detecting inherent defects. Furthermore, the characteristics of noise signals in rail steel are not as unique as those in stainless steel, further complicating the differentiation between them.

[0007] Phased array ultrasonic testing (PAUT) has been used to address certain challenges associated with inspecting welded joints. However, PAUT equipment is significantly more expensive than conventional equipment, and its application in the railway industry has not yet taken off. Therefore, railway defect detection is expected to rely primarily on conventional testing equipment for the foreseeable future. Consequently, it is crucial in railway maintenance practice to adopt a method suitable for single-probe weld joint signal detection. This method should mitigate noise echo signals in the inspection of track welded joint defects. Summary of the Invention

[0008] To address the problems existing in the prior art, the purpose of this invention is to provide an adaptive signal reconstruction method based on VMD for detecting defects in rail welded joints. This invention improves the efficiency of ultrasonic detection of defects in rail welded joints.

[0009] To achieve the above objectives, the technical solution adopted by this invention is: an adaptive signal reconstruction method based on VMD for detecting damage at welded joints of rails, comprising the following steps:

[0010] Step 1, Variational Mode Decomposition: The acquired axial scan A-scan signal of the track welding joint is decomposed into multiple intrinsic mode functions (IMFs) using variational mode decomposition (VMD).

[0011] Step 2: Remove low-frequency interference from the intrinsic mode function (IMF);

[0012] Step 3, Singular Value Decomposition: Construct the defect signal in the second-lowest frequency component into a Hankel matrix H, and perform singular value decomposition on H;

[0013] Step 4: Reconstruct the signal using kurtosis as a guide.

[0014] As a further improvement of the present invention, in step 1, the number of intrinsic mode functions (IMFs) is determined according to the types of components that may exist in the signal, including: high-frequency noise, scatterer echoes, defect echoes, and interference signals.

[0015] As a further improvement of the present invention, in step 2, the first type of interference is the intrinsic mode function (IMF) with energy below a preset threshold, which is eliminated by calculating the energy ratio of the IMF:

[0016]

[0017] Where N is the number of sampling points, and A is the amplitude of each point; when the energy ratio of the IMF is less than a preset threshold, it is removed;

[0018] The second type of interference is the DC component generated inside the instrument, whose average value deviates from 0; therefore, when and If the magnitudes are the same, remove it.

[0019] As a further improvement to the present invention, step 3 is specifically as follows:

[0020] After removing interfering IMFs, the remaining IMF with the lowest center frequency is selected as the original target signal. Using the defect signal in the second-lowest frequency component, a Hankel matrix H is constructed with dimensions n×(n+1), where n is half the signal length. Then, singular value decomposition is performed on H to obtain: H = USV T , where U and V are orthogonal matrices, S is a diagonal matrix, and the elements on the diagonal are called singular values, arranged in descending order.

[0021] As a further improvement to the present invention, step 4 is specifically as follows:

[0022] The reconstruction work is based on the following formula:

[0023] H i =US i,i V T

[0024]

[0025] x recon =x i +x target

[0026] Where i≤n, j≤2n; S i,i Only the i-th value of the diagonal matrix S is retained, and all other elements are zero; x recon For reconstructing the signal; x target The target signal is equal to the residual IMF with the lowest center frequency when i=1;

[0027] If x recon If the kurtosis is greater than 0, then x target x recon It will become the next reconstruction of x target Otherwise, xtarget Will be retained.

[0028] As a further improvement of the present invention, in step 5, the orbital peak signal-to-noise ratio (RPSNR) is as follows:

[0029]

[0030] Among them, P defect P represents the peak amplitude of the defect echo. noise The peak amplitude represents the highest noise echo.

[0031] The beneficial effects of this invention are:

[0032] 1. This invention proposes using VSKR to reconstruct signals for defect detection in rail welded joints. It is adaptive and requires almost no prior knowledge. The effectiveness of VSKR was verified using finite element model data and experimental data from two different configurations, thus validating its credibility and feasibility.

[0033] 2. The RPSNR of this invention is designed based on the actual needs of railway maintenance practice. Compared with the traditional signal-to-noise ratio (SNR), RPSNR can better measure the signal quality in railway ultrasonic testing. Attached Figure Description

[0034] Figure 1 Schematic diagram of ultrasonic testing principle for welded joints;

[0035] Figure 2 This is a schematic diagram of the backscattering amplitude function of the grain;

[0036] Figure 3 This is a flowchart of VSK in an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the finite element model in an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the configuration for the first experiment in this embodiment of the invention;

[0039] Figure 6 This is a schematic diagram of the configuration for the second experiment in this embodiment of the invention;

[0040] Figure 7 The above are time and frequency waveforms of the original signal EXP2-1, the IMFs after VMD, and the reconstructed signal after VSKR in an embodiment of the present invention.

[0041] Figure 8 These are waveform diagrams of the original signal and the reconstructed signal under different conditions in embodiments of the present invention;

[0042] Figure 9 This is a schematic diagram comparing the RPSNR of the signals before and after VSKR in an embodiment of the present invention. Detailed Implementation

[0043] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0044] Example

[0045] An adaptive signal reconstruction method based on VMD for detecting damage at welded joints of rails includes:

[0046] A. Theoretical Basis:

[0047] 1) Overview of Ultrasonic Testing:

[0048] Because the vibration frequency and amplitude change over time, ultrasound can be considered an amplitude-frequency modulation (AM-FM) signal. During propagation, ultrasound may encounter discontinuous material interfaces, such as cracks, grains, and inclusions. These interfaces cause changes in acoustic impedance, leading to scattering, reflection, and refraction of the ultrasound waves. By analyzing these received echoes, internal information about the material can be obtained.

[0049] Ultrasound waves propagate throughout the entire material domain in the form of a sound field. However, ultrasound waves are usually represented by a straight line, indicating the direction of maximum ultrasonic intensity. Figure 1 (a) illustrates a typical ultrasonic testing process for welded joints, including primary and secondary waves. Due to the presence of the near-field region, the primary echo method cannot effectively detect defects near the surface.

[0050] The transducer emits ultrasonic waves including longitudinal waves and transverse waves. Figure 1 (The red line in (a)). Due to the different velocities of transverse and longitudinal waves, when the incident angle α reaches the first critical angle, the refracted ultrasonic waves within the sample will be entirely transverse waves. Figure 1 (The blue line in (a)). When performing ultrasonic testing on welded joints of rails, transverse waves are primarily used. The refraction angle β of the wave determines the K value of the ultrasonic probe, which corresponds to the tangent value. For example, when the K value is 1, the refraction angle is 45°.

[0051] In an A-scan, the horizontal axis represents the signal reception time, and the vertical axis represents the signal reception amplitude. In an A-scan, a defect is determined when the peak value (maximum value) of the echo exceeds a predetermined threshold. Figure 1 (b) shows Figure 1 The A-scan detection in (a) shows the echoes from the two cracks and the echoes from the scatterer in the weld area.

[0052] In actual testing, the A-scan displays the absolute value of the amplitude. However, in this embodiment, to better display the waveform, the entire signal wave will be displayed. When discussing peak values, the absolute value will still be used.

[0053] 2) Signal texture features:

[0054] When ultrasound propagates through a material and encounters coarse particles or inclusions, these objects act as scatterers, causing the ultrasound waves to be scattered back to the probe, producing backscattered echo noise. The intensity of this scattered noise is affected by the ratio of the scatterer's diameter to the ultrasound wavelength, such as... Figure 2 As shown. In the case of rail-welded joints, the diameter of these scatterers is typically less than 300 μm. Since the commonly used ultrasonic wavelengths are between 1 and 2 mm, these scatterers fall within the Rayleigh scattering region. Within the Rayleigh scattering region, the scattering intensity is highly sensitive to changes in wavelength, roughly inversely proportional to the square of the wavelength.

[0055] Therefore, the backscattering of high-frequency components is more intense compared to low-frequency components. This causes the spectrum of the echo signal to shift to higher frequencies. It is important to note that when referring to the frequency of the probe, it refers to the probe's center frequency. The actual ultrasonic wave emitted by the probe consists of multiple components with different frequencies. Conversely, as a geometric reflector, the frequency of the reflected wave from a defect is independent of the frequency range. Therefore, the difference in frequency domain between the echo signals from defects and scatterers can be utilized.

[0056] 3) Variational pattern decomposition:

[0057] Dragonmiretskiy and Zosso proposed Variational Mode Decomposition (VMD) in 2014, introducing the fundamental concept of viewing a signal as a combination of intrinsic mode functions (IMFs) achieved through an optimization process. This method helps to decompose a signal into different modes, thereby obtaining smooth amplitudes and frequencies for each mode. Furthermore, the different modes are orthogonal to each other. Each mode corresponds to a vibrational component at a specific frequency and can be represented as an amplitude-modulated (AM-FM) signal.

[0058] h k (t)=A k (t)cos(φ k (t)) (1)

[0059] Among them, A k (t) is h k (t) and A k The amplitude envelope of the oscillation with t ≥ 0; φ k (t) is h k (t) and φ k The instantaneous phase when (t) ≥ 0. (and φ) k Compared to (t), A k (t) and instantaneous angular frequency ωk (t)=φ′ k The change in (t) is relatively slow.

[0060] Given the original signal x(t), find k narrowband IMFs. k (t), where the center frequency of each component is ω. k The corresponding constrained variational model is:

[0061]

[0062] Among them, {h k}={h1,h2,…,h k} is the set of all IMFs obtained by VMD; {ω k}={ω1,ω2,…,ω k} is the set of center angular frequencies for each IMF.

[0063] To transform a constrained variational problem into an unconstrained problem and solve for the optimal solution, the Lagrangian function is introduced. The Lagrangian function is a combination of the original objective function and the constraints imposed on the problem. Its expression is as follows:

[0064]

[0065] Here, α is a quadratic constraint operator; λ(t) is a Lagrange multiplication operator.

[0066] Solving constrained variational problems using Alternating Direction Multiplication (ADMM) involves alternating updates. and λ n+1 Find the saddle point of the Lagrange expression. The expression is:

[0067]

[0068] Use the Parseval Fourier transform to convert the above expression to the frequency domain:

[0069]

[0070] Using the same method, we can also obtain The expression:

[0071]

[0072] Then, the following iterative steps can be performed:

[0073] (1) Initialization,

[0074] (2) Update h according to formulas (5) and (6) k and ωk .

[0075] (3) According to Update λ.

[0076] (4) Repeat steps (2) and (3) until the convergence condition is met.

[0077] B. VMD-SVD-Kurtosis remodeling:

[0078] The purpose of this embodiment is to eliminate noise echo signals caused by coarse particles and inclusions in the defect detection of rail welded joints, while extracting echo signals caused by defects. To this end, this embodiment develops a reconstruction method called VMD-SVD-Kurtosis Reconstruction (VSKR). The steps are as follows: Figure 3 As shown.

[0079] (1) Modulation Decomposition: Since ultrasonic vibration can be considered as an amplitude-frequency modulation (AM-FM) signal, the acquired A-scan signal is decomposed into 5 IMFs using VMD. The number of IMFs is determined based on the types of components that may exist in the signal, such as high-frequency noise, scatterer echoes, defect echoes, and interference signals. The penalty factor α is set to 1000.

[0080] (2) Removing interference IMF: After VMD, the generated IMF may contain two types of low-frequency interference, which will affect the subsequent IMF selection.

[0081] Type I interference IMFs have low energy and can be considered insignificant. These interference IMFs can be eliminated by calculating their energy proportions.

[0082]

[0083] Where N is the number of sampling points, and A is the amplitude of each point. When the energy proportion of the IMF is less than 5%, it can be removed.

[0084] The second type of interference is the DC component generated inside the instrument. The average value of this component deviates from 0. Therefore, when and When the amount is of the same magnitude (i.e., greater than 10%), the component can be removed.

[0085] (3) Singular Value Decomposition: Because backscattered noise signals are mostly high-frequency components of the signal. After removing interfering IMFs, the remaining IMF with the lowest center frequency is selected as the original target signal. The second lowest frequency component contains important noise and defect signals.

[0086] To utilize the defect signal in the second-lowest frequency component, it can be constructed as a Hankel matrix H with dimensions n×(n+1), where n is half the signal length. Then, singular value decomposition (SVD) is performed on H to obtain:

[0087] H = USV T (8)

[0088] U and V are orthogonal matrices, and S is a diagonal matrix. The elements on the diagonal are called singular values ​​and are arranged in descending order.

[0089] (4) Kurtosis-oriented reconstruction: Since the distribution of scatterers in the material is relatively uniform, the signal caused by defects has a higher kurtosis than the signal caused by scatterers. It can be assumed that the signal with higher kurtosis contains more defect information.

[0090] The reconstruction work is based on the following formula:

[0091] H i =US i,i V T (9)

[0092]

[0093] x recon =x i +x target (11)

[0094] Where i≤n, j≤2n; S i,i Only the i-th value of the diagonal matrix S is retained, and all other elements are zero; x recon For reconstructing the signal; x target The target signal is equal to the residual IMF with the lowest center frequency when i=1.

[0095] If x recon If the kurtosis is greater than 0, then x target x recon It will become the next reconstruction of x target Otherwise, x target This will be retained. Since small singular values ​​contain very little information, it is feasible to compute only large singular values ​​(such as the first 50 singular values).

[0096] In the final reconstructed signal, the backscattered echo noise from the scatterer within the solder joint is significantly reduced. Although there is still some loss in the signal from the defect, its relative amplitude increases. VSKR has a simplified adaptive procedure that requires minimal prior knowledge.

[0097] C. Railway peak signal-to-noise ratio:

[0098] Setting an appropriate threshold becomes challenging when the level of scattered echoes from scatterers is high. A threshold that is too high may fail to detect actual defects, while a threshold that is too low may falsely report scattered echoes as defects. Therefore, for orbital ultrasonic testing, an important metric for signal quality is the ratio of the peak amplitude of the defect echo to the noise echo. With a high ratio, the threshold can be set lower while avoiding false alarms. This allows for a wider range of detection locations and orientations, thereby improving overall efficiency. Based on this idea, this embodiment introduces the orbital peak signal-to-noise ratio (RPSNR):

[0099]

[0100] Among them, P defect P represents the peak amplitude of the defect echo. noise The peak amplitude represents the highest noise echo.

[0101] The finite element model and experimental configuration of this embodiment are described below:

[0102] A. Finite element model:

[0103] Most studies using finite element method (FEM) simulations of ultrasonic detection simulate the excitation and incidence of ultrasound by manipulating mechanical quantities at the boundary (such as velocity, displacement, and force). The received ultrasonic signal is also reflected through changes in these mechanical quantities. However, in reality, both the incident and received ultrasonic signals are electrical signals, converted into mechanical effects through the piezoelectric effect. To better represent the actual situation and directly obtain voltage values ​​(A-scan), the finite element model established in this embodiment incorporates the piezoelectric effect. Both the incident and received signals are treated as voltage values. To achieve this, an ultrasonic transducer is constructed in the finite element model, consisting of three basic components: a piezoelectric layer, a matching layer, and an absorbing layer.

[0104] To prevent significant ultrasonic wave loss during propagation due to the high impedance of the solid-gas interface, a coupling medium, such as oil or water, is required between the probe and the rail in practical track ultrasonic testing. This coupling layer eliminates air from the gap between the probe and the rail. Furthermore, this layer involves fluid-structure coupling. Therefore, the coupling layer affects the received ultrasonic signal. In the finite element model established in this study, a water coupling layer with a thickness of 0.3 mm was created.

[0105] In this finite element model, the scatterer is simulated as aluminum oxide mixed in steel. Considering computation time and memory consumption, the scatterer is represented as a square with a side length of 0.5 mm. This side length allows the scatterer to be within the Rayleigh region of the longitudinal waves without resulting in an overly dense mesh. According to the DhuaSK standard, the area of ​​the scatterer is equivalent to 0.5% of the total cross-sectional area.

[0106] Two crack conditions were designed, each with a crack length of 1 mm and an angle of 60 degrees to the horizontal plane. The difference lies in the crack location: one is located in the middle of the track network, and the other is located on the left side of the track network. In addition, a control condition without scatterers and cracks was calculated. The signal obtained under the crack condition was subtracted from the signal obtained under the control condition to highlight the echo characteristics of scatterers and cracks. The overall finite element model is as follows: Figure 4 As shown. The absorption layer is brown, the piezoelectric layer is purple, the matching layer is pink, the coupling layer is blue, the scatterer is green, and the crack is in bold.

[0107] Finite element method (FEM) was used in COMSOL Multiphysics 6.1 for modeling and solving. The computer's CPU was an Intel Core I9-11900KF. When the modeling range was a total height of 95 mm from the top of the rail to the middle of the rail network on the cross section, and the simulation process took 6.5 microseconds, the required computation time was approximately 7 hours, and the memory consumption was approximately 8 GB.

[0108] B. Experimental Setup:

[0109] This method was tested on signals collected from two different experimental configurations. One experiment involved artificially created defects, while the other involved actual defects occurring during orbital servicing. All acquired defect signals passed through weld points during propagation, and the location of the defects in the signals was confirmed by experts.

[0110] The track segment used in the first experiment is as follows Figure 6 As shown, this was manufactured for testing the inspection process of hot-melt welded joints. Figure 5 In (a), a semi-circular slit with a diameter of 12 mm was artificially created on the surface. Figure 5 In (b), another semi-circular slit with a diameter of 5 mm was created at the center of the bottom. The secondary echo method was used to detect cracks on the rail surface. The core instrument used in this experiment was a JSR Ultrasonics DPR300. Analog signals were sent to an oscilloscope for display, then converted into digital signals and stored in a USB flash drive for computer processing. The signal sampling frequency was 100 MHz. The probe used to detect crack echoes had a K value of 1 and emitted ultrasonic waves at a frequency of 2.5 MHz. Experimental images are shown below. Figure 6 .

[0111] In the second experiment, Figure 6The rail segment in (a) was taken from an active railway line in China. During routine ultrasonic testing, the detector detected a crack in the rail head at the weld point. Subsequently, this section of rail was removed. The core instrument used in the experiment was the CTS-08UT, manufactured by Guangdong Guohuan Co., Ltd. Digital signal acquisition was achieved by connecting this instrument to a personal computer. Other configurations were the same as in the first experiment. Experimental images are shown below. Figure 6 (b) Multiple signals were acquired from different probe positions and orientations.

[0112] The results section used the following seven signals obtained from the finite element model and experiments: (1) FEM1: Finite element with a crack in the middle of the rail network. (2) FEM2: FEM with a crack on the left side of the rail network. (3) EXP1-1: Artificial defects on the surface of the rail. (4) EXP1-2: Artificial defects at the bottom of the rail. (5) EXP2-1: Actual defects in the disused rail. (6) EXP2-2: Actual defects on the disused rail. (7) EXP2-3: Actual defects in the disused rail.

[0113] Results and Discussion:

[0114] To illustrate VSKR, this embodiment uses signal EXP2-1 for a comprehensive demonstration. Figure 7 The original signal and the time and frequency waveforms of the five IMFs after VMD are shown, along with the final reconstructed signal. The locations of the defect echoes are marked with dashed boxes in all figures. Table 1 calculates several metrics for IMF removal. It is clear that IMF5 represents the DC component. After removing IMF5, the IMF with the lowest center frequency, IMF4, is selected as the target signal.

[0115] This embodiment does not provide specific units for the physical quantities derived from signal amplitude. This is because different experiments and simulations employ different signal gains. Amplitude values ​​are only applicable for relative comparisons within the same set of signals. In such cases, units may lead to misunderstandings.

[0116] Compared to the original signal, the peak signal caused by the crack is more prominent in IMF4, while other peaks in the signal are suppressed. In the original signal, the peak value of the crack echo is 48, while the peak value of other echoes is 40, resulting in an RPSNR of 1.58 dB. In the reconstructed signal, the peak value of the crack echo is 30, while the peak value of other echoes is relatively small at 14.5, resulting in an RPSNR of 6.32 dB. This represents an increase of 4.74 dB.

[0117] Table 1. Calculation results for interference removal

[0118]

[0119]

[0120] Figure 8 The VSKR results for other signals are shown. Figure 8 In (a), the first row is FEM1, where the original signal's RPSNR is 4.68 dB and the reconstructed signal's RPSNR is 11.64 dB, an increase of 6.96 dB. It can be seen that due to the simplification of FEM, the echo range caused by the crack is wider, but VSKR still achieves suppression of the scattering signal. The second row is FEM2, where the original signal's RPSNR is 0.79 dB and the reconstructed signal's RPSNR is 7.32 dB, an increase of 6.53 dB.

[0121] Figure 8 (b) shows the VSKR results of the experiment in Figure 5. The first row is EXP1-1, where the RPSNR of the original signal is 2.27 dB and the RPSNR of the reconstructed signal is 11.21 dB, an increase of 8.94 dB. The second row is EXP1-2, where the RPSNR of the original signal is 4.81 dB and the RPSNR of the reconstructed signal is 6.96 dB, resulting in an increase of 2.15 dB.

[0122] Figure 8 (c) shows from Figure 6 Two different results were obtained in the experiment. The first line is EXP2-2, where the RPSNR of the original signal is 2.50 dB, and the RPSNR of the reconstructed signal is 9.43 dB, an increase of 6.93 dB. The second line is EXP2-3, which illustrates an extreme case where the defect echo is completely submerged, resulting in an RPSNR of -0.23 dB for the original signal. Based on prior knowledge, it is known that a defect echo exists in this signal. In the reconstructed signal, the submerged defect echo is revealed, leading to an RPSNR of 2.00 dB. This extreme case demonstrates the potential of VSKR.

[0123] at last, Figure 9 This visually demonstrates the improvement in RPSNR after VSKR in this embodiment.

[0124] This embodiment proposes the VMD-SVD-Kurtosis Reconstruction (VSKR) method to address the backscattering noise signal problem caused by coarse grains and inclusions in rail welded joint defect detection. This method effectively suppresses noise and improves defect detection capabilities by utilizing the different frequency characteristics between VMD and noise / defect signals. This embodiment also introduces a new index called RPSNR to better measure signal quality in railway ultrasonic testing. This index is then used to evaluate the effectiveness of VSKR. Applying VSKR to finite element models and actual experiments yielded encouraging results, with a significant improvement in RPSNR, averaging 5.50 dB under all conditions.

[0125] These findings demonstrate that VSKR can improve the efficiency of ultrasonic testing of railway welded joints by expanding the range of probe positions and orientations for defect detection. This makes VSKR an important tool in railway maintenance practice. The effectiveness of VSKR can be further improved by adaptively optimizing the penalty factor of VMD and the number of IMFs, which can be investigated in future work. Through further research and field validation, this method is expected to be applied to practical railway defect detection.

[0126] This embodiment proposes an adaptive ultrasonic signal reconstruction method, VSKR (VMD-SVD-Kurtosis Reconstruction), and introduces a new metric called Track Peak Signal-to-Noise Ratio (RPSNR) to measure the effectiveness of the method. This method utilizes the different frequency characteristics between noise and defect signals, employing a Variational Mode Decomposition (VMD) algorithm. VSKR has been successfully applied to signals obtained from finite element models and actual experiments, highlighting defect echoes and demonstrating its effectiveness. Under specific conditions, the RPSNR value improved by 8.94 dB. The average increase in RPSNR was 5.50 dB. This indicates that VSKR can expand the probe location and orientation range for defect detection, thereby improving the efficiency of ultrasonic detection of defects in welded rail joints.

[0127] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. An adaptive signal reconstruction method based on VMD for detecting damage at welded joints of rails, characterized in that, Includes the following steps: Step 1, Modular Decomposition: The acquired axial scan A-scan signal of the track welding joint is decomposed into multiple intrinsic mode functions (IMFs) using modular decomposition (VMD). In Step 1, the number of IMFs is determined according to the types of components present in the signal, including: high-frequency noise, scatterer echo, defect echo, and interference signal. Step 2: Remove low-frequency interference from the intrinsic mode function (IMF); Step 3, Singular Value Decomposition: Construct the defect signal in the second-lowest frequency component into a Hankel matrix H, and perform singular value decomposition on H; Step 4: Reconstruct the signal using kurtosis as a guide.

2. The adaptive signal reconstruction method for detecting damage at welded rail joints based on VMD according to claim 1, characterized in that, In step 2, the first type of interference is the intrinsic mode function (IMF) with energy below a preset threshold, which is eliminated by calculating the energy ratio of the IMF: Where N is the number of sampling points, and A is the amplitude of each point; when the energy ratio of the IMF is less than a preset threshold, it is removed; The second type of interference is the DC component generated inside the instrument, whose average value deviates from 0; therefore, when and If the magnitudes are the same, remove it.

3. The adaptive signal reconstruction method for detecting damage at welded rail joints based on VMD according to claim 2, characterized in that, Step 3 is described in detail below: After removing interfering IMFs, the remaining IMF with the lowest center frequency is selected as the original target signal. Using the defect signal in the second-lowest frequency component, a Hankel matrix H is constructed with dimensions n×(n+1), where n is half the signal length. Then, singular value decomposition is performed on H to obtain: H = USV T , where U and V are orthogonal matrices, S is a diagonal matrix, and the elements on the diagonal are called singular values, arranged in descending order.

4. The adaptive signal reconstruction method for detecting damage at welded rail joints based on VMD according to claim 3, characterized in that, Step 4 is as follows: The reconstruction work is based on the following formula: H i =US i,i V T x recon =x i +x target Where i≤n, j≤2n; S i,i Only the i-th value of the diagonal matrix S is retained, and all other elements are zero; x recon For reconstructing the signal; x target The target signal is equal to the residual IMF with the lowest center frequency when i=1; If x recon The kurtosis is greater than x target Then x recon It will become the next reconstruction of x target Otherwise, x target Will be retained.

5. The adaptive signal reconstruction method for detecting damage at welded rail joints based on VMD according to claim 4, characterized in that, It also includes introducing the orbital peak signal-to-noise ratio (RPSNR) to measure the effectiveness of the method, wherein the orbital peak signal-to-noise ratio (RPSNR) is as follows: Among them, P defect P represents the peak amplitude of the defect echo. noise The peak amplitude represents the highest noise echo.

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