VMD-based self-adaptive signal reconstruction method for rail welded joint damage detection

Abstract

The invention discloses a VMD-based self-adaptive signal reconstruction method for rail welded joint damage detection. The method comprises the following steps: variable mode decomposition: decomposing an obtained rail welded joint axial scanning A-scan signal into a plurality of intrinsic mode functions IMF by using variable mode decomposition VMD; removing an intrinsic mode function (IMF) of low-frequency interference; singular value decomposition: constructing defect signals in the sub-low frequency component into a Hankel matrix H, and performing singular value decomposition on the H; performing signal reconstruction by taking kurtosis as guidance; the method improves the efficiency of ultrasonic detection of steel rail welded joint defects.

Description

Technical Field

[0001] The invention relates to the technical field of rail welding joints, and in particular to an adaptive signal reconstruction method for damage detection of rail welding joints based on VMD. Background Art

[0002] Rail welding points are vulnerable points in railways, and rail defects often occur at welding points. To detect these defects, ultrasonic testing is widely used in railway maintenance practices. However, due to the presence of coarse grains and inclusions in the welds, there is a lot of backscattered noise in the ultrasonic signal, which interferes with defect detection.

[0003] Since the rails are in direct contact with the wheels, they are subject to high-frequency and high-intensity loads. These loads will generate various forms of stress inside the rails, leading to internal defects such as cracks; and the welding points are the vulnerable points of the rail system, especially in the case of hot melt welding. According to Yao N 2 According to a study conducted by the National Railway Administration (NTRA), about 52.6% of rail defects occur at welds, even though welds only account for a small portion of the entire rail length. This is mainly attributed to residual stress and the presence of non-metallic inclusions such as silica and alumina within the welds. If not detected in time, rail defects may develop into rail fractures.

[0004] Ultrasonic testing is commonly used in railway maintenance practice to detect internal defects of rails. However, there are difficulties when applying it to welded joints. Inspectors report that the echo signals caused by small internal defects in rail welded joints are often drowned out by the echo signals caused by 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 direction and position of the probe to distinguish the defect signal, which increases the time required for weld defect detection.

[0005] For austenitic steel and high alloy steel (such as stainless steel), the high anisotropy and inhomogeneity of their welded joints can lead to energy attenuation, elastic wave deviation and high noise. Several studies have proposed methods to evaluate their internal acoustic fields. From a signal processing perspective, early researchers used wavelet analysis for noise trimming and threshold processing; 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 polar threshold processing) to mitigate the impact of noise. In recent years, researchers have begun to use sparse signal representation methods. This includes deterministic methods, such as matching pursuit (MP) techniques, and Bayesian methods, such as sparse Bayesian learning.

[0006] The above methods have achieved good results in their respective data. But they all require a lot of prior knowledge. This makes it difficult to apply these methods in actual operations. Another important fact is that these methods are tailored for stainless steel. Due to the heterogeneity of the material, these methods are not applicable to rail welded joints. As a case of low-alloy steel and high-carbon steel, the welded joints of rail steel do not have such strong anisotropy and inhomogeneity, and there are fewer studies on the signal processing of defect detection of rail welded joints. Existing research mainly focuses on detecting inherent defects. In fact, the characteristics of noise signals in rail steel are not as unique as those of stainless steel. This increases the difficulty of distinguishing them.

[0007] Phased array ultrasonic testing (PAUT) has been used to address some of the challenges associated with inspecting welded joints. However, PAUT equipment is much more expensive than conventional equipment, and its application in the railway industry has not yet developed. Therefore, rail defect detection is expected to continue to rely primarily on conventional inspection equipment for the foreseeable future. Therefore, it is critical to adopt a method suitable for single-probe weld signal detection in railway maintenance practices. This method should be able to mitigate the noise echo signal in rail weld joint defect detection. Summary of the invention

[0008] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide an adaptive signal reconstruction method for rail weld joint damage detection based on VMD, which improves the efficiency of ultrasonic detection of rail weld joint defects.

[0009] To achieve the above object, the technical solution adopted by the present invention is: an adaptive signal reconstruction method for rail weld joint damage detection based on VMD, comprising the following steps:

[0010] Step 1, variable mode decomposition: The acquired orbital weld joint axial scanning A-scan signal is decomposed into multiple intrinsic mode functions IMF using variable mode decomposition VMD;

[0011] Step 2, removing the intrinsic mode function IMF of low frequency interference;

[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 based on kurtosis.

[0015] As a further improvement of the present invention, in step 1, the number of the intrinsic mode functions IMF is determined according to the types of components that may exist in the signal, including: high-frequency noise, scatterer echo, defect echo and interference signal.

[0016] As a further improvement of the present invention, in step 2, the first type of interference is an intrinsic mode function IMF whose energy is lower than a preset threshold, and is eliminated by calculating the energy ratio of the intrinsic mode function IMF:

[0017]

[0018] Where N is the number of sampling points, A is the amplitude of each point; when the energy ratio of IMF is less than the preset threshold, it is removed;

[0019] The second type of interference is the DC component generated inside the instrument, whose average value deviates from 0; therefore, when and If they are of the same magnitude, remove them.

[0020] As a further improvement of the present invention, the step 3 is specifically as follows:

[0021] After removing the interfering IMF, the remaining IMF with the lowest center frequency is selected as the original target signal; the defect signal in the sub-low frequency component is used to construct it into a Hankel matrix H with a dimension of n×(n+1), where n is half the signal length; then H is subjected to singular value decomposition 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.

[0022] As a further improvement of the present invention, the step 4 is specifically as follows:

[0023] The reconstruction is based on the following formula:

[0024] H i =US i,i V T

[0025]

[0026] x recon =x i +x target

[0027] Where i≤n, j≤2n; S i,i Only the i-th value of the diagonal matrix S is retained, and the other elements are zero; x recon is the reconstructed signal; x target is the target signal, which is equal to the residual IMF with the lowest center frequency when i=1;

[0028] If x recon If the kurtosis is greater than target x recon Will be the next reconstruction of x target Otherwise, xtarget Will be retained.

[0029] As a further improvement of the present invention, in step 5, the track peak signal-to-noise ratio RPSNR is as follows:

[0030]

[0031] Among them, P defect Represents the peak amplitude of the defect echo, P noise Represents the peak amplitude of the highest noise echo.

[0032] The beneficial effects of the present invention are:

[0033] 1. The present invention proposes to reconstruct signals using VSKR for rail weld joint defect detection. It is adaptive and requires little prior knowledge. The effectiveness of VSKR is verified by using finite element model data and experimental data of two different configurations, thereby verifying its credibility and feasibility.

[0034] 2. The RPSNR of the present invention is designed according to the actual needs of railway maintenance practice. Compared with the traditional signal-to-noise ratio (SNR), the RPSNR can better measure the signal quality in railway ultrasonic detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is the principle diagram of ultrasonic testing of welding joints. This is the principle diagram of ultrasonic testing of welding joints;

[0036] Figure 2 is a schematic diagram of the grain backscattering amplitude function;

[0037] Figure 3 Flow chart of VSK in an embodiment of the present invention;

[0038] Figure 4 A schematic diagram of a finite element model in an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram of the configuration of the first experiment in an embodiment of the present invention;

[0040] Figure 6 Schematic diagram of the configuration of the second experiment in an embodiment of the present invention;

[0041] Figure 7 It is a time and frequency waveform diagram of the original signal EXP2-1, the IMFs after VMD, and the reconstructed signal after VSKR in an embodiment of the present invention;

[0042] Figure 8 are waveform diagrams of original signals and reconstructed signals under different conditions in the embodiments of the present invention;

[0043] Fig. 9 Schematic diagram of RPSNR comparison of signals before and after VSKR in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0045] Example

[0046] An adaptive signal reconstruction method for rail welding joint damage detection based on VMD, comprising:

[0047] A. Theoretical basis:

[0048] 1) Overview of ultrasonic testing:

[0049] Since the vibration frequency and amplitude change over time, ultrasound can be considered an amplitude modulation-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, resulting in scattering, reflection, and refraction of ultrasound. By analyzing the received echoes of these ultrasounds, internal information of the material can be obtained.

[0050] Ultrasonic waves propagate throughout the material in the form of a sound field. However, ultrasonic waves are usually represented by a straight line, indicating the direction of maximum ultrasonic intensity. Figure 1 (a) shows a typical ultrasonic testing process for welded joints, including primary and secondary waves. Due to the existence of the near-field region, the primary echo method cannot effectively detect defects near the surface.

[0051] The ultrasonic waves emitted by the transducer include longitudinal waves and transverse waves ( Figure 1 (a)). Due to the different velocities of shear waves and longitudinal waves, when the incident angle α reaches the first critical angle, the ultrasonic wave refracted in the sample will be completely shear waves ( Figure 1 (a) (blue line). When ultrasonic testing rail weld joints, shear waves are mainly 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°.

[0052] The A-scan represents the signal reception time on the horizontal axis and the signal reception amplitude on the vertical axis. In the A-scan, when the peak value (highest value) of the echo exceeds a predetermined threshold, it can be determined that a defect exists. Figure 1 (b) shows Figure 1 A-scan test in (a). From the figure, we can see the echoes from the two cracks and the echoes from the scatterers in the welding area.

[0053] In actual detection operation, the A scan displays the absolute value of the amplitude. However, in this embodiment, in order to better display the waveform, the full wave of the signal will be displayed. When discussing the peak value, the absolute value is still used.

[0054] 2) Signal texture features:

[0055] When ultrasound propagates in a material and encounters coarse particles or inclusions, these objects act as scatterers, causing the ultrasound to scatter back to the probe, generating backscattered echo noise. The intensity of this scattered noise is affected by the ratio of the scatterer diameter to the ultrasound wavelength, such as Figure 2 As shown. In the case of orbital welded joints, these scatterers are usually less than 300 μm in diameter. Since the commonly used ultrasonic wavelength is between 1 and 2 mm, these scatterers belong to the Rayleigh scattering region. In the Rayleigh scattering region, the scattering intensity is very sensitive to changes in wavelength and is roughly inversely proportional to the square of the wavelength.

[0056] Therefore, the high-frequency components are backscattered more strongly than the low-frequency components. This causes the spectrum of the echo signal to shift toward high frequencies. It is worth noting that when the frequency of the probe is mentioned, it refers to the center frequency of the probe. The actual ultrasonic wave emitted by the probe consists of multiple components with different frequencies. In contrast, as a geometric reflector, the frequency of the defect reflection wave is independent of the frequency. Therefore, the difference in the frequency domain between the echo signals of defects and scatterers can be used.

[0057] 3) Variational mode decomposition:

[0058] The variational mode decomposition (VMD) proposed by Dragonmiretskiy and Zosso in 2014 proposed the basic concept of considering the signal as a combination of intrinsic mode functions (IMFs) realized through an optimization process. This approach helps to decompose the signal into different modes, thereby obtaining a smooth amplitude and frequency of each mode. Moreover, different modes are orthogonal to each other. Each mode corresponds to a vibration component of a specific frequency and can be represented as an AM-FM signal:

[0059] h k (t) = A k (t)cos(φ k (t)) (1)

[0060] Among them, A k (t) is h k (t) and A k (t) ≥ 0 amplitude envelope; φ k (t) is h k (t) and φ k (t)≥0. k (t) Compared with A k (t) and instantaneous angular frequency ωk (t) = φ′ k (t) changes slowly.

[0061] Given the original signal x(t), find k narrowband IMFh k (t), the center frequency of each component is ω k , the corresponding constrained variational model is:

[0062]

[0063] 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 central angular frequencies of each IMF.

[0064] In order to transform the constrained variation problem into an unconstrained problem and solve 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:

[0065]

[0066] Among them, α is the quadratic constraint operator; λ(t) is the Lagrange multiplication operator.

[0067] Solve constrained variational problems using alternating direction multiplication (ADMM), alternating updates, and λ n+1 , find the saddle point of the Lagrangian expression. The expression is:

[0068]

[0069] The above expression is converted to the frequency domain using the Parseval Fourier transform:

[0070]

[0071] Using the same method, we can also get The expression is:

[0072]

[0073] Afterwards, the following iterative steps can be performed:

[0074] (1) Initialization,,

[0075] (2) Update h according to formulas (5) and (6) k and ωk .

[0076] (3) Based on Update λ.

[0077] (4) Repeat steps (2) and (3) until the convergence condition is met.

[0078] B.VMD-SVD-Kurtosis reconstruction:

[0079] The purpose of this embodiment is to eliminate the noise echo signals caused by coarse particles and inclusions in the defect detection of rail welding joints, and at the same time extract the 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 shown.

[0080] (1) Variable mode decomposition: Since ultrasonic vibration can be regarded as an amplitude-frequency modulation signal, the acquired A-scan signal is decomposed into five IMFs using VMD. The number of IMFs here is determined according to the types of components that may exist in the signal, such as high-frequency noise, scatterer echo, defect echo, and interference signal. The penalty factor α is set to 1000.

[0081] (2) Removing interfering IMFs: After VMD, the generated IMFs may contain two kinds of low-frequency interferences, which will affect the subsequent IMF selection.

[0082] The first type of interfering IMF has low energy and can be considered unimportant. This type of interfering IMF can be eliminated by calculating its energy ratio.

[0083]

[0084] Where N is the number of sampling points and A is the amplitude of each point. When the energy proportion of an IMF is less than 5%, it can be removed.

[0085] 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 magnitude of is the same as that of (i.e., greater than 10%), the component can be removed.

[0086] (3) Singular value decomposition: Because the backscattered noise signal is more manifested as the high-frequency component of the signal. After removing the interfering IMF, 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.

[0087] To utilize the defect signal in the sub-low frequency component, it can be constructed as a Hankel matrix H with a dimension of n×(n+1), where n is half the length of the signal. Then perform singular value decomposition (SVD) on H to obtain:

[0088] H=USV T (8)

[0089] Where U and V are orthogonal matrices, S is a diagonal matrix, and the elements on the diagonal are called singular values ​​and are arranged in descending order.

[0090] (4) Kurtosis-guided 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 considered that the signal with higher kurtosis contains more defect information.

[0091] The reconstruction is based on the following formula:

[0092] H i =US i,i V T (9)

[0093]

[0094] x recon =x i +x target (11)

[0095] Where i≤n, j≤2n; S i,i Only the i-th value of the diagonal matrix S is retained, and the other elements are zero; x recon is the reconstructed signal; x target is the target signal, which is equal to the residual IMF with the lowest center frequency when i=1.

[0096] If x recon If the kurtosis is greater than target x recon Will be the next reconstruction of x target Otherwise, x target Since small singular values ​​contain little information, it is feasible to calculate only large singular values ​​(such as the first 50 singular values).

[0097] In the final reconstructed signal, the backscatter echo noise from the scatterers in the solder joint will be significantly reduced. Although there will still be some loss of the signal from the defect, its relative amplitude will increase. VSKR has a simplified adaptive procedure and requires minimal prior knowledge.

[0098] C. Railway Peak Signal-to-Noise Ratio:

[0099] When the level of scattered echoes caused by scatterers is high, setting an appropriate threshold becomes challenging. A threshold that is too high may result in failure to detect actual defects, while a threshold that is too low may misreport scattered echoes as defects. Therefore, for rail ultrasonic testing, an important indicator of signal quality is the ratio of the peak amplitude of the defect echo to the noise echo. In the case of a high ratio, the threshold can be set lower while avoiding false alarms. This will allow a wider range of detection positions and directions, thereby improving overall efficiency. Based on this idea, this embodiment introduces the rail peak signal-to-noise ratio (RPSNR):

[0100]

[0101] Among them, P defect Represents the peak amplitude of the defect echo, P noise Represents the peak amplitude of the highest noise echo.

[0102] The finite element model and experimental configuration of this embodiment are introduced below:

[0103] A. Finite element model:

[0104] Most studies using finite elements to simulate ultrasonic detection simulate the excitation and incidence of ultrasonic waves by manipulating the mechanical quantities of the boundary (such as velocity, displacement, and force). The received ultrasonic signal is also reflected by the changes in these mechanical quantities. But in fact, both the incident and received signals of the ultrasonic wave are electrical signals, which are converted into mechanical effects through the piezoelectric effect. In order to better represent the actual situation and directly obtain the voltage value (A-scan), the finite element model established in this embodiment incorporates the piezoelectric effect. Both the incident signal and the received signal are regarded as voltage values. To achieve this goal, an ultrasonic transducer is established in the finite element, which consists of three basic components: a piezoelectric layer, a matching layer, and an absorption layer.

[0105] In order to prevent the huge loss of ultrasonic waves due to the high impedance of the solid-gas interface during propagation, a coupling medium such as oil or water is required between the probe and the rail in actual rail ultrasonic testing. This coupling layer can exclude the air in the gap between the probe and the rail. In addition, this layer also involves fluid-structure coupling. Therefore, the coupling layer will have an impact on 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.

[0106] In this finite element model, the scatterer is simulated as aluminum oxide mixed in steel. Considering the computational time and memory consumption, the scatterer is represented as a square with a side length of 0.5 mm. Such a side length allows the scatterer to be in the Rayleigh region of longitudinal waves without causing the mesh to be too dense. According to the DhuaSK standard, the area of ​​the scatterer is equivalent to 0.5% of the total cross-sectional area.

[0107] Two crack conditions were designed, each with a length of 1 mm and an angle of 60 degrees to the horizontal plane. The difference lies in the location of the crack, one is located in the middle of the track grid and the other is located on the left side of the track grid. 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 shown in Figure 1. Figure 4 The absorber is in brown, the piezoelectric layer is in purple, the matching layer is in pink, the coupling layer is in blue, the scatterer is in green, and the crack is in bold.

[0108] Finite element modeling and solving were performed using dG-FEM in COMSOL Multiphysics 6.1. The computer CPU was 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 was 6.5 microseconds, the required computing time was about 7 hours and the memory consumption was about 8 GB.

[0109] B. Experimental configuration:

[0110] The method was tested on signals collected from two different experimental configurations. One experiment involved artificially created defects, and the other involved real defects that occurred during track service. All acquired defect signals passed through the weld during propagation, and the defect locations in the signals were confirmed by experts.

[0111] The track segments used in the first experiment are as follows Figure 6 As shown, it is manufactured for testing the hot melt welding joint inspection process. Figure 5 In (a), a semicircular gap with a diameter of 12 mm is artificially created on the surface. Figure 5 In (b), another semicircular gap with a diameter of 5 mm is made in the middle of the bottom. In order to detect cracks on the surface of the rail, the secondary echo method is used. The core instrument used in this experiment is the DPR300 produced by JSR Ultrasonics. The analog signal is sent to the oscilloscope for display, then converted into a digital signal and stored in a USB flash drive for computer processing. The signal sampling frequency is 100MHz. The probe K value used to detect crack echoes is 1, and the ultrasonic wave with a transmission frequency of 2.5MHz. Experimental pictures are shown in Figure 6 .

[0112] In the second experiment, Figure 6The rail section in (a) was taken from an active railway line in China. During routine ultrasonic testing, the detector detected cracks in the rail head at the weld. The rail section was then removed. The core instrument used in the experiment was CTS-08UT, produced by Guangdong Guohuan Co., Ltd. Digital signal acquisition was achieved by connecting the instrument to a personal computer. The other configurations were the same as the first experiment. Experimental pictures are shown in Figure 6 (b) Acquire multiple signals from different probe positions and orientations.

[0113] The following seven signals obtained from the finite element model and experiments are used in the results section. (1) FEM1: finite element of a rail network with cracks in the middle. (2) FEM2: FEM of a rail network with cracks on the left side. (3) EXP1-1: artificial defects on the rail surface. (4) EXP1-2: artificial defects on the bottom of the rail. (5) EXP2-1: actual defects on a decommissioned rail. (6) EXP2-2: actual defects on a decommissioned rail. (7) EXP2-3: actual defects on a decommissioned rail.

[0114] Results and Discussion:

[0115] In order to illustrate VSKR, this embodiment uses signal EXP2-1 for comprehensive demonstration. Figure 7 The time and frequency waveforms of the original signal and five IMFs after VMD are shown, as well as the final reconstructed signal. The location of the defect echo is marked with a dotted box in all figures. Table 1 calculates several indicators for removing IMFs. It is obvious that IMF5 represents the DC component. After removing IMF5, the IMF with the lowest center frequency, IMF4, is selected as the target signal.

[0116] This embodiment does not provide specific units for physical quantities derived from signal amplitudes. This is because different experiments and simulations use different signal gains. Amplitude values ​​are only applicable to relative comparisons of the same set of signals. In this case, units may lead to misunderstandings.

[0117] Compared with the original signal, the peak signal caused by the crack in IMF4 is more prominent, while other peaks in the signal are suppressed. The peak of the crack echo in the original signal is 48, while the peak of other echoes is 40, so the RPSNR is 1.58dB. The peak of the crack echo in the reconstructed signal is 30, and the peak of other echoes is not large, at 14.5, so the RPSNR is 6.32dB. This means an increase of 4.74 decibels.

[0118] Table 1. Calculation results of removing interference

[0119]

[0120]

[0121] Figure 8 VSKR results for other signals are shown. Figure 8 In (a), the first row is FEM1, the RPSNR of the original signal is 4.68dB, and the RPSNR of the reconstructed signal is 11.64dB, an increase of 6.96dB. It can be seen that due to the simplification of FEM, the echo range caused by the crack is wider, but VSKR still achieves the suppression of the scatterer signal. The second row is FEM2, the RPSNR of the original signal is 0.79dB, and the RPSNR of the reconstructed signal is 7.32dB, an increase of 6.53dB.

[0122] Figure 8 (b) shows the VSKR results of the experiment in Figure 5. The first row is EXP1-1, the RPSNR of the original signal is 2.27dB, and the RPSNR of the reconstructed signal is 11.21dB, which is an increase of 8.94dB. The second row is EXP1-2, the RPSNR of the original signal is 4.81dB, and the RPSNR of the reconstructed signal is 6.96dB, resulting in an increase of 2.15dB.

[0123] Figure 8 (c) shows the Figure 6 Two different results obtained in the experiment. The first row is EXP2-2, the RPSNR of the original signal is 2.50dB, and the RPSNR of the reconstructed signal is 9.43dB, an increase of 6.93dB. The second row is EXP2-3, which illustrates an extreme case where the defect echo is completely submerged and the RPSNR of the original signal is -0.23dB. Based on previous knowledge, it can be known that there is a defect echo in this signal. In the reconstructed signal, the submerged defect echo is revealed, resulting in an RPSNR of 2.00dB. This extreme case demonstrates the potential of VSKR.

[0124] at last, Fig. 9 The improvement of RPSNR after VSKR in this embodiment is intuitively demonstrated.

[0125] This embodiment proposes a VMD-SVD-Kurtosis Reconstruction (VSKR) method to solve the problem of backscattered noise signals caused by coarse grains and inclusions in rail weld joint defect detection. This method uses VMD and the different frequency characteristics between noise signals and defect signals to effectively suppress noise and improve defect detection capabilities. This embodiment also introduces a new indicator called RPSNR to better measure the signal quality in railway ultrasonic testing. This indicator is then used to evaluate the effectiveness of VSKR. The application of VSKR to finite element models and actual experiments has achieved gratifying results, with a significant improvement in RPSNR, reaching an average of 5.50dB under all conditions.

[0126] These findings suggest that VSKR can improve the efficiency of ultrasonic inspection of railway welded joints by expanding the range of probe positions and orientations to detect defects. 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 studied in future work. With more research and field validation, this method is expected to be applied in actual railway defect detection.

[0127] This embodiment proposes an adaptive ultrasonic signal reconstruction method VSKR (VMD-SVD-KurtosisReconstruction), and introduces a new indicator called rail peak signal-to-noise ratio (RPSNR) to measure the effectiveness of the method. This method uses the different frequency characteristics between noise signals and defect signals and adopts the variable mode decomposition (VMD) algorithm. VSKR has been successfully applied to signals obtained from finite element models and actual experiments, and the defect echoes in these signals are highlighted, which proves the effectiveness of VSKR. Under specific conditions, the RPSNR value is improved by 8.94dB. The average increase in RPSNR is 5.50dB. This shows that VSKR can expand the probe position and direction range for detecting defects, thereby improving the efficiency of ultrasonic detection of defects in rail welded joints.

[0128] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. An adaptive signal reconstruction method for rail weld joint damage detection based on VMD, characterized in that: The following steps are involved: Step 1, variable mode decomposition: The acquired orbital weld joint axial scanning A-scan signal is decomposed into multiple intrinsic mode functions IMF using variable mode decomposition VMD; Step 2, removing the intrinsic mode function IMF of low frequency interference; 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 based on kurtosis.

2. The adaptive signal reconstruction method for rail weld joint damage detection based on VMD according to claim 1 is characterized in that: In step 1, the number of the intrinsic mode functions IMF is determined according to the types of components that may exist in the signal, including: high-frequency noise, scatterer echo, defect echo and interference signal.

3. The adaptive signal reconstruction method for rail weld joint damage detection based on VMD according to claim 1, characterized in that: In step 2, the first type of interference is the intrinsic mode function IMF whose energy is lower than the preset threshold, which is eliminated by calculating the intrinsic mode function IMF energy ratio: Where N is the number of sampling points, A is the amplitude of each point; when the energy ratio of IMF is less than the 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 they are of the same magnitude, remove them.

4. The adaptive signal reconstruction method for rail weld joint damage detection based on VMD according to claim 3 is characterized in that: The step 3 is as follows: After removing the interfering IMF, the remaining IMF with the lowest center frequency is selected as the original target signal; the defect signal in the sub-low frequency component is used to construct it into a Hankel matrix H with a dimension of n×(n+1), where n is half the signal length; then H is subjected to singular value decomposition 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.

5. The VMD-based adaptive signal reconstruction method for rail weld joint damage detection according to claim 4, characterized in that: The step 4 is specifically as follows: The reconstruction 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 the other elements are zero; x recon is the reconstructed signal; x target is the target signal, which is equal to the residual IMF with the lowest center frequency when i=1; If x recon If the kurtosis is greater than target x recon Will be the next reconstruction of x target Otherwise, x target Will be retained.

6. The VMD-based adaptive signal reconstruction method for rail weld joint damage detection according to claim 5, characterized in that: In step 5, the track peak signal-to-noise ratio RPSNR is as follows: Among them, P defect Represents the peak amplitude of the defect echo, P noise Represents the peak amplitude of the highest noise echo.

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