Steel rail corrugation detection method and system based on AE-MMD algorithm

Abstract

The invention discloses a steel rail corrugation detection method and system based on an AE-MMD algorithm, and belongs to the technical field of data processing. The steel rail corrugation detection method based on the AE-MMD algorithm comprises the steps that a steel rail vibration acceleration signal is collected, and segmented processing is conducted on the signal to obtain segmented signals; constructing a phase space trajectory matrix for the segmented signals; performing singular value decomposition on the phase space trajectory matrix to obtain a singular mode component; screening effective singular mode components; a Teager energy operator is combined with a kurtosis characteristic to realize modal classification; the modals are superposed and compared with original signals; and a classification result is judged according to the combined criterion of the transient energy index, the characteristic kurtosis, the energy leakage rate and the SPI value, and the steel rail corrugation section is identified according to the impact mode. The steel rail corrugation detection method and system based on the AE-MMD algorithm can solve the problems that an existing detection method is low in steel rail corrugation detection accuracy and poor in interpretability.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and system for detecting rail corrugation based on the AE-MMD algorithm. Background Technology

[0002] Rail corrugation is a periodic wear phenomenon on the rail surface, characterized by uniform wavy wear along the direction of travel. The occurrence of corrugation leads to unevenness on the rail surface, inducing wheel-rail force fluctuations, accelerating fatigue damage to sleepers and fasteners, affecting ride smoothness and comfort, and generating multi-band responses during wheel-rail-track structure propagation: these may manifest as mid-to-high frequency contact impact components, or as modulation and structural resonance responses at low / mid frequencies. The frequency band is influenced by train speed, the spatial period of corrugation, and structural transmission characteristics. The formation mechanism of corrugation originates from dynamic processes such as wheel-rail friction self-excitation, structural coupling, and system energy redistribution. Its signals often exhibit strong non-stationarity, multi-scale modulation, and transient impact characteristics. Energy continuously migrates between different modes, and the spectral structure changes dynamically over time. Under traditional linear or steady-state methods, the dynamic evolution suffers from mode aliasing, energy leakage, and frequency distortion.

[0003] Traditional wave wear detection methods mainly include: time-domain envelope analysis and Fourier analysis, empirical mode decomposition and its improved algorithms, and spectral energy analysis. However, time-domain envelope analysis and Fourier analysis cannot distinguish between steady-state vibration and transient impact, empirical mode decomposition and its improved algorithms suffer from mode aliasing, spectral crossover, and energy leakage problems, and spectral energy analysis cannot maintain the phase space structure and energy conservation of the orbital system.

[0004] Existing detection methods generally ignore the structural characteristics of signals in phase space, resulting in inaccurate descriptions of the true dynamic energy distribution of the track system and making it difficult to accurately detect the corrugation characteristics of the rail. Summary of the Invention

[0005] The purpose of this invention is to provide a rail corrugation detection method and system based on the AE-MMD algorithm, which solves the problem of low accuracy in rail corrugation detection of existing detection methods.

[0006] To achieve the above objectives, this invention provides a rail corrugation detection method based on the AE-MMD algorithm, comprising the following steps: S1. Collect vertical or lateral vibration acceleration signals of the rail, preprocess the vibration acceleration signals, and perform sliding window segmentation on the preprocessed vibration acceleration signals to obtain segmented signals. S2. Construct the phase space trajectory matrix using an integration method with symplectic structure preservation properties for the segmented signal. ,in, The preprocessed segmented signal, It is generalized momentum, so as to maintain the energy conservation and phase space volume of the Hamiltonian system. S3. Perform singular value decomposition on the phase space trajectory matrix, and obtain several singular mode components based on the distribution characteristics of the singular value spectrum. ; S4. Calculate the Hilbert dominant frequency and energy proportion of the singular mode components. Based on the Hilbert dominant frequency difference constraint and energy accumulation rate constraint, select several effective singular mode components to eliminate modes with frequency crossover and energy redundancy. S5. Using the Teager energy operator combined with kurtosis features, the selected effective singular mode components are subjected to impulse feature identification to achieve classification of steady-state modes, modulation modes, and impulse modes; S6. Superimpose the separated steady-state mode, modulation mode and impulse mode and reconstruct and compare them with the original signal to calculate the symplectic structure retention index SPI value and energy leakage rate ELR; S7. Based on the combined criteria of transient energy index, characteristic kurtosis, energy leakage rate and SPI value, the classification result is determined, and the rail corrugation section is identified based on the impact mode.

[0007] Preferably, in step S1, the preprocessing includes denoising, normalizing, and zero-mean processing of the vibration acceleration signal to obtain a preprocessed segmented signal.

[0008] Preferably, in S2, the integration method with symplectic structure preservation characteristics is the second-order symplectic integration algorithm Stormer-Verlet method or the symplectic Euler method.

[0009] Preferably, in S4, the Hilbert frequency difference constraint is that the frequency difference between any two adjacent singular mode components is ≥5Hz, and the energy accumulation rate constraint is that the cumulative energy ratio of the effective singular mode components is ≥95%.

[0010] Preferably, in step S5, the specific method for classifying steady-state modes, modulation modes, and impulse modes is as follows: the energy mutation characteristics of each effective singular mode component are calculated using the Teager energy operator; mode classification is performed using the energy mutation characteristics and peak characteristics; and transient energy indices are used to characterize the degree of energy accumulation of the impulse mode on the time axis. The classification criterion for steady-state modes is: The eigenvalue kurtosis K < 3; The classification criteria for modulation modes are: The eigenvalue kurtosis is 3 ≤ K < 5; The classification criteria for impact modes are: The eigenkurtosis K ≥ 5.

[0011] Preferably, in step S6, the formula for calculating the symmetric structure retention index (SPI) value is as follows: ; in, For a symplectic matrix, The gradient of the Hamiltonian function. Represents the L2 norm; The formula for calculating the energy leakage rate (ELR) is as follows: ; in, The original signal energy, To reconstruct signal energy, This is a Jacobian correction term for the phase space.

[0012] Preferably, in step S7, the joint criterion for determining the rail corrugation section is the transient energy index. Characteristic kurtosis K≥5, energy leakage rate ELR≤10%, 0.98≤SPI value≤1.02.

[0013] The detection system for rail corrugation detection based on the AE-MMD algorithm includes: The signal acquisition module is used to acquire vertical and lateral vibration acceleration signals of the rail. The AE-MMD algorithm module executes the AE-MMD algorithm flow for acceleration signals, including a phase space embedding unit, a singular value decomposition and mode extraction unit, and a mode filtering unit. The phase space embedding unit is used to construct the phase space trajectory matrix; the singular value decomposition and mode extraction unit is used to perform singular value decomposition on the phase space trajectory matrix and obtain singular mode components; the mode filtering unit is used to filter valid singular mode components and perform mode classification and identification, classifying the modes into steady-state modes, modulation modes, and impulse modes. The index calculation module is used to calculate the SPI and ELR values ​​of the superimposed signals of the original signal and the steady-state mode, modulation mode and impulse mode; The corrugation identification module and the result output module are used to output results. They use the time-domain energy accumulation characteristics based on the impact mode to identify the rail corrugation section, and combine the energy leakage rate and symmetric structure retention index to constrain the effectiveness of the identification results. The rail corrugation section is judged based on the joint criteria of SPI value, ELR value, transient energy index and characteristic kurtosis.

[0014] The ripple recognition module is used to determine whether the energy leakage rate is less than a preset threshold. When the energy leakage rate exceeds the threshold, the ripple recognition module refuses to output the ripple recognition result. When the symplectic structure retention index deviates from the preset range, the ripple recognition module marks the mode decomposition result as invalid. The detection system is installed in the intelligent monitoring host of the running gear or the track detection equipment to realize online or quasi-online detection of rail corrugation.

[0015] Preferably, the AE-MMD algorithm module has an embedded sliding window segmentation unit for performing sliding window segmentation processing on long-time vibration acceleration signals.

[0016] Preferably, the result diagrams output by the wave polishing identification and result output module include modal spectrum diagrams, energy distribution diagrams, SPI-ELR joint curve diagrams, and original / reconstructed signal comparison diagrams.

[0017] The advantages and positive effects of the rail corrugation detection method and system based on the AE-MMD algorithm described in this invention are as follows: This invention introduces symplectic integrals to construct phase space embedding, and combines singular value decomposition (SVD) and Hilbert spectral analysis to achieve structure-preserving multimodal decomposition and energy decoupling of track signals; This invention introduces the symplectic structure preservation index SPI value and energy leakage rate to judge the identification results, ensuring the accuracy and stability of rail corrugation section identification.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart of the AE-MMD algorithm of the present invention; Figure 2 This is a diagram of the detection system of the present invention; Figure 3 The diagrams show the constructed and synthesized signals; a) is the 10Hz modulated signal, b) is the 50Hz carrier signal, c) is the exponentially decaying signal, and d) is the synthesized signal. Figure 4 The time-domain distributions of the six singular mode components selected for the synthesized signal; a) is the time-domain distribution of IMF1, b) is the time-domain distribution of IMF2, c) is the time-domain distribution of IMF3, d) is the time-domain distribution of IMF4, e) is the time-domain distribution of IMF5, and f) is the time-domain distribution of IMF71. Figure 5 Comparison of IMF component spectra and normalized energy distribution; a) IMF spectrum comparison, b) normalized energy distribution; Figure 6 A three-dimensional spectral waterfall plot of the IMF components of the synthesized signal; Figure 7 The original signals of the rails were collected; Figure 8 The RMSE and correlation coefficient of the segmented signal; Figure 9 This represents the total signal reconstruction error. Figure 10 A comparison diagram of the reconstructed signal and the original signal; Figure 11 Spectral comparison of the selected IMF components; a) original spectrum, b) magnified view of a portion; Figure 12 The temporal distribution of the selected IMF components; a) IMF77257, b) IMF53947, c) IMF79921, d) IMF78589, e) IMF31303, f) IMF60607; Figure 13 The energy percentage of the selected IMF components; Figure 14 This is a three-dimensional spectral waterfall of the real signal IMF. Detailed Implementation

[0020] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0021] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] The AE-MMD algorithm is an adaptive embedded multiscalemode decomposition method.

[0023] like Figure 1 As shown, a rail corrugation detection method based on the AE-MMD algorithm includes the following steps: S1. Acquire vertical or lateral vibration acceleration signals of the rail, preprocess the vibration acceleration signals, and perform sliding window segmentation on the preprocessed vibration acceleration signals to obtain segmented signals. Sliding window segmentation involves dividing the preprocessed vibration acceleration signals into segments with 20% overlap between windows to balance time-domain resolution and quasi-stationarity of the segmented signals.

[0024] Preprocessing includes denoising, normalization, and zero-mean processing of the vibration acceleration signal to obtain a preprocessed segmented signal. Preprocessing is used to suppress low-frequency drift components and high-frequency electrical noise interference.

[0025] S2. Construct the phase space trajectory matrix using an integration method with symplectic structure preservation properties for the segmented signal. ,in, The preprocessed segmented signal, It is generalized momentum, so as to maintain the energy conservation and phase space volume of the Hamiltonian system.

[0026] Integration methods that preserve symplectic structure are the second-order symplectic integration algorithms Stormer-Verlet or Ssymplectic Euler.

[0027] In constructing the phase space trajectory matrix, the embedding dimension is fixed at 40 to avoid information loss due to excessively low dimension and increased computational load due to excessively high dimension. Phase points are generated from the segmented signals according to time delays, and a symplectic integral algorithm is introduced to expand the phase points into a "position-momentum" phase space trajectory matrix. Thus, based on the time-delay embedding method combined with the second-order symplectic integral algorithm, a one-dimensional segmented signal is mapped to a high-dimensional trajectory matrix.

[0028] S3. Perform singular value decomposition on the phase space trajectory matrix, and obtain several singular mode components based on the distribution characteristics of the singular value spectrum. .

[0029] The formula for singular value decomposition is: ; in, It is a left singular matrix, corresponding to the characteristic direction of the phase space; It is a singular value diagonal matrix that reflects the magnitude of the mode energy; It is a right singular matrix.

[0030] Singular modal components are independent vibrational components of vibration acceleration signals at different scales, enabling multi-scale decoupling of complex orbital vibration signals. The effective modal order is initially determined based on the attenuation characteristics of singular values, and modal components with low energy proportions are further eliminated by combining the dominant frequency and energy proportion indices.

[0031] S4. Calculate the Hilbert dominant frequency and energy proportion of each singular mode component. Based on the Hilbert dominant frequency difference constraint and energy accumulation rate constraint, select several effective singular mode components to eliminate modes with frequency crossover and energy redundancy.

[0032] The Hilbert frequency difference constraint is that the frequency difference between any two adjacent singular mode components is ≥5Hz, and the energy accumulation rate constraint is that the cumulative energy ratio of the effective singular mode components is ≥95%. 3-12 effective modes are selected, and modes with lower energy are eliminated to avoid spectral overlap.

[0033] S5. Using the Teager energy operator combined with kurtosis features, the selected effective singular mode components are subjected to impulse feature identification to achieve classification of steady-state modes, modulation modes, and impulse modes.

[0034] In this invention, the identification of rail corrugation is not based on a single frequency threshold, but on the comprehensive characteristics of the impact mode in the time domain, frequency domain and structural retention.

[0035] Corrugation, as a spatially periodic wear defect, generates repetitive short-duration impacts during wheel-rail contact. These impacts manifest as impact modes in the AE-MMD decomposition results, with their time-domain energy significantly enhanced within the corrugated section. Therefore, this invention uses the energy accumulation interval of the impact mode on the time axis as the primary basis for determining the rail corrugated section. From a frequency domain perspective, the dominant frequency of the impact mode is related to the train speed and the wavelength characteristics of the rail corrugation. For short-wave corrugation, the energy of the impact mode exhibits stable accumulation within its passing frequency and modulation band, with the corresponding frequency determined by both the train speed and the spatial period of the corrugation, and not limited to a fixed frequency band. Simultaneously, the energy leakage rate (ELR) and the symplectic structure retention index (SPI) are introduced to effectively constrain the decomposition results, ensuring energy conservation and consistency of the phase space structure during mode decomposition.

[0036] It should be noted that the low-frequency or mid-frequency characteristic components appearing in the measured signal (such as modulation or resonance response in the range of 0–100Hz) are the result of the transmission and modulation of high-frequency wave grinding impact in the wheel-rail-track system. These characteristics are mainly used for wave grinding mechanism explanation and result cross-verification, and are not a necessary condition for wave grinding segment determination.

[0037] The formula for calculating the Teager energy operator is: ; The specific method for classifying steady-state modes, modulation modes, and impulse modes is to calculate the energy mutation characteristics of each effective singular mode component using the Teager energy operator, and then classify the modes based on the energy mutation characteristics and peak characteristics.

[0038] Using transient energy indicators Characterizes the degree of energy accumulation of the impact mode along the time axis. The mean value of the transient energy index of the impact mode is statistically analyzed within a reference section without significant erosion. with standard deviation And set the threshold as follows: ; ; in, This is an empirical coefficient, with a value range of 2–4; The transient energy threshold, This is the low threshold for transient energy. The transient energy threshold is adaptively determined based on actual engineering data.

[0039] The classification criterion for steady-state modes is: The characteristic kurtosis K < 3. The steady-state mode has low energy concentration, uniform distribution, and no single spike, indicating the natural vibration of the track and the response of the background structure, without any undulation components.

[0040] The classification criteria for modulation modes are: The characteristic kurtosis is 3≤K<5. The energy concentration of the adjustment mode is moderate, with multiple secondary peaks or lateral peaks, indicating sleeper pitch excitation, fastener stiffness changes, and intermediate frequency modulation. It is the precursor mode of corrugation impact.

[0041] The classification criteria for impact modes are: The characteristic kurtosis K≥5. It has high energy concentration, with a single narrowband peak accounting for a significant proportion, corresponding to short-wave ripple in the orbit, which is the body characteristic mode of the ripple.

[0042] For impact mode signals Its discrete Teager energy is defined as: ; in, Let Teager be the energy function under the impact mode. For the first n Teager energy function values ​​at each sampling point under the impact mode.

[0043] The Teager energy operator outputs energy values ​​at discrete sampling points, reflecting only abrupt energy changes at a single sampling point and failing to directly characterize energy accumulation trends over a period of time. In contrast, rail corrugation is characterized by continuous / periodic energy accumulation over time. Therefore, within the sliding time window... Within the window, the transient energy index is represented as a statistical measure of the Teager energy. This invention uses the mean or peak value of the Teager energy within the window, defined as follows: ; ; in, For the first k The mean of the Teager energy in each mode. For the first k Peak values ​​of Teager energy in each mode.

[0044] S6. The separated steady-state mode, modulation mode and impulse mode are superimposed according to the original time sequence and reconstructed and compared with the original signal. The reconstructed signal is compared and analyzed with the original signal, and the reconstruction error, correlation coefficient, energy leakage rate and symplectic structure preservation index are calculated.

[0045] The formula for calculating the SPI (Structure Retention Index) value is as follows: ; in, J For a symplectic matrix, The gradient of the Hamiltonian function. This represents the L2 norm.

[0046] The formula for calculating the energy leakage rate (ELR) is: ; in, As primordial energy, To reconstruct energy, This is a Jacobian correction term for the phase space.

[0047] S7. Based on the combined criteria of transient energy index, characteristic kurtosis, energy leakage rate, and SPI value, rail corrugation sections are identified. Rail corrugation sections are identified based on the energy accumulation characteristics of the impact mode on the time axis, and the energy leakage rate and symplectic structure retention index are used to constrain the effectiveness of the identification results. Furthermore, by combining train speed and the spatial periodic characteristics of corrugation, a mapping relationship between the frequency of corrugation passage is established to achieve stable identification and interpretable diagnosis of corrugation sections.

[0048] When the transient energy index of the impact mode significantly increases and forms a stable cluster within a continuous window, the corresponding time segment is identified as the rail corrugation segment. ELR and SPI are introduced as validity constraints: ELR is used to measure the degree of energy closure in the decomposition and reconstruction process, and SPI is used to measure the degree of preservation of the phase space structure; when ELR exceeds the threshold or SPI deviates from the preset range, the identification result is marked as invalid or rejected.

[0049] The transient energy index range is Characteristic kurtosis K≥5, energy leakage rate ELR≤10%, 0.98≤SPI value≤1.02. The closer the SPI value is to 1, the more intact the signal structure is.

[0050] like Figure 2 As shown, a detection system for rail corrugation detection based on the AE-MMD algorithm includes: The signal acquisition module is used to acquire vertical and lateral vibration acceleration signals of the rail. The AE-MMD algorithm module executes the AE-MMD algorithm flow for acceleration signals, including a phase space embedding unit, a singular value decomposition and mode extraction unit, and a mode filtering unit. The phase space embedding unit is used to construct the phase space trajectory matrix; the singular value decomposition and mode extraction unit is used to perform singular value decomposition on the phase space trajectory matrix and obtain singular mode components; the mode filtering unit is used to filter valid singular mode components and perform mode classification and recognition. The index calculation module is used to calculate the SPI and ELR values ​​of the superimposed signals of the original signal and the steady-state mode, modulation mode and impulse mode; The corrugation identification module and the result output module are used to output results and determine the classification result based on the joint criteria of SPI value, ELR value, transient energy index, and characteristic kurtosis. The rail corrugation section is determined based on the time-domain energy accumulation characteristics of the impact mode and the structural preservation constraints of SPI and ELR; the dominant modal frequency is used for result interpretation and consistency verification.

[0051] The wave pattern recognition module determines whether the energy leakage rate is less than a preset threshold. If the energy leakage rate exceeds the threshold, the wave pattern recognition module refuses to output the wave pattern recognition result. When the symplectic structure preservation index deviates from the preset range, the wave pattern recognition module marks the modal decomposition result as invalid. Through interaction with the structure preservation constraint parameters, the wave pattern recognition module enables dynamic feedback on the decomposition quality during the modal screening process, thereby improving the stability of the wave pattern recognition result.

[0052] The detection system is installed in the intelligent monitoring host of the running gear or the track inspection equipment to realize online or quasi-online detection of rail corrugation. The AE-MMD algorithm module has an embedded sliding window segmentation unit for processing long-time vibration acceleration signals by sliding window segmentation.

[0053] The results output by the wave polishing identification and result output module include modal spectrum diagrams, energy distribution diagrams, SPI-ELR joint curve diagrams, and original / reconstructed signal comparison diagrams.

[0054] Unlike existing signal analysis methods based on empirical mode decomposition or statistical decomposition, this invention does not merely improve decomposition results by adjusting decomposition parameters or adding post-processing steps. Instead, it introduces structure preservation constraints during the signal phase space construction stage, ensuring that the energy distribution and geometric structure of the rail vibration signal remain consistent during embedding, decomposition, and reconstruction. Specifically, this invention constructs phase space trajectories based on approximate symplectic structures and introduces symplectic structure preservation indices and structure-preserving energy leakage rates as joint constraints during mode decomposition and screening. This avoids the mode aliasing and energy distortion problems that easily occur in traditional mode decomposition methods under the strong impact conditions of urban rail transit. Through this structure preservation mechanism, this invention can highlight the impact modes corresponding to short-wave corrugation of the rail while ensuring decomposition stability, giving the corrugation identification results clear physical meaning and engineering repeatability.

[0055] To verify the effectiveness of the method described in this invention, three typical signal components were constructed, all with normalized waveform amplitudes and dimensionless dimensions. For example... Figure 3 As shown, the three typical signal components are: (1) Low-frequency modulation signal: ,in =10Hz, characterizing the periodic modulation features of the mechanical system; (2) Carrier signal: ,in =50Hz, simulating the high-frequency vibration component during equipment operation; (3) transient impact signal: , where the attenuation constant =0.5s, reflecting the nonlinear decay characteristics of the system after being subjected to an impact. The synthesized signal is represented as: ,in, This is for measuring the noise term.

[0056] The method described in this invention is used to process the signal. A phase space trajectory matrix is ​​constructed with a delay time of 1 second. Singular value decomposition is performed on the phase space trajectory matrix to select six IMF components, and their energy distributions are calculated. The temporal distributions of the six IMF components are as follows: Figure 4 As shown, the amplitude is the normalized waveform amplitude, which is dimensionless. The dominant frequency, energy percentage, and physical meaning of the six IMF components are shown in Table 1.

[0057] Table 1 Energy distribution and physical significance of IMF components

[0058] To further quantify the decomposition accuracy and energy preservation, the six IMF components were superimposed and reconstructed compared with the original signal. RMSE, CC, energy leakage rate, and SPI were calculated. RMSE reflects the mean square error between the original and reconstructed signals, while CC measures the degree of linear correlation between the two. The AE-MMD algorithm described in this invention is compared with existing EMD and CEEMDAN algorithms, and the results are shown in Table 2.

[0059] Table 2 Comparison of Indicators between AE-MMD, EMD, and CEEMDAN Methods

[0060] As shown in Table 2, the ELR of AE-MMD is approximately 0.06, significantly lower than that of EMD (0.19) and CEEMDAN (0.18); meanwhile, the symplectic structure retention index (SPI) of AE-MMD is 1.00, demonstrating good structural consistency. AE-MMD's... , This indicates that the decomposed signal maintains a high degree of consistency with the original signal in terms of phase and amplitude. The energy leakage rate (ELR) of AE-MMD is reduced by an average of about 68% compared with traditional methods (relative to EMD / CEEMDAN), indicating that AE-MMD achieves better energy containment and structure preservation in mode separation, significantly suppressing spectral spread and high-frequency noise leakage, thereby maintaining both the reconstruction and physical consistency of non-stationary signals.

[0061] Figure 5 A comparison of the spectra of the six IMF components and their normalized energy distribution. Figure 6 This is a three-dimensional spectral waterfall plot of the IMF components of the synthesized signal. (Example:) Figure 5 , Figure 6 As shown, each IMF exhibits significant band-limiting characteristics in the frequency domain: IMF1, IMF2 (total energy percentage) ) Main frequency 10Hz, corresponding IMF3 and IMF4 (total energy share) ) Main frequency 50Hz, corresponding IMF5 and IMF71 (combined energy percentage 8.7%) are distributed between 8 and 60 Hz, characterizing signal modulation effects and The transient impact response was obtained. The above results show that AE-MMD can effectively separate three typical components: low-frequency modulation (10Hz), high-frequency carrier (50Hz), and transient impact signal, and separate vibration modes generated by different physical mechanisms, laying the foundation for subsequent feature extraction.

[0062] The technical effects of the present invention will be explained below with reference to examples.

[0063] This invention collects measured data of rails from a subway line with typical complex operating conditions as a verification sample. The total operating mileage of the line is 31.04km, including 23 stations and 2 depot facilities. The track system is divided into 312 standard unit sections (200m each) in the up and down directions.

[0064] Experimental data were directly acquired using a high-precision uniaxial piezoelectric accelerometer. The sensor was mounted longitudinally along the rail at the axle position of the tested vehicle, and the sampling frequency was set to 2000Hz to ensure full coverage of the corrugation characteristics within the wavelength range of 10-1000mm. The original signal time series is as follows: Figure 7 As shown, the signal duration is 138s, and the sampling frequency is f. s =2000Hz, with 276,000 valid data points. To adapt to the algorithm's computational efficiency and ensure time-frequency resolution, the signal is divided into 138 segments (2000 points per segment, corresponding to a 1s time window), and a sliding window strategy (20% overlap) is used for segmentation.

[0065] Analysis of the time domain characteristics shows that the measured corrugation signal exhibits significant non-stationary characteristics. Its dynamic response includes multi-scale coupled vibration components: ① quasi-steady-state fluctuation components caused by the periodic surface deformation of the rail (main frequency band 0.5-50Hz); ② high-frequency disturbances generated by random vibration of the vehicle-track coupling system (frequency band 50-500Hz); ③ inherent noise of the detection system and environmental interference (frequency band >500Hz).

[0066] The AE-MMD algorithm was used to process 138 segmented signals. Through experimental results and analysis of synthesized and real signals, the performance advantages of AE-MMD in modal aliasing suppression and endpoint effect control were systematically evaluated, providing a new theoretical tool for intelligent diagnosis of track conditions.

[0067] The distribution of RMSE and correlation coefficient of segmented signals is as follows: Figure 8 As shown, the RMSE is generally low and changes gradually in the first 0–30 segments, then rises significantly in the middle and later segments with stronger fluctuations. The maximum error is concentrated around segment number 80, indicating that the signal has significant nonlinear characteristics or noise interference in this period. The global mean of the correlation coefficient is 0.72, and it reaches a peak of 0.95 at segment 80, while the coefficient in the segment 30–50 interval is below 0.6, which may be related to the fact that the transient impact component is not completely decomposed.

[0068] All signal reconstruction errors are as follows Figure 9 As shown, the error amplitude shows a significant negative shift at 80 seconds, corresponding to the RMSE peak of segment 80, suggesting the presence of high-amplitude transient components that were not effectively separated during this period. Figure 10 The image shows a comparison between the reconstructed signal and the original signal. The amplitude fluctuates wildly in the 60-80 second interval, but the reconstructed curve still tracks the main peaks (correlation coefficient > 0.9), demonstrating that the method described in this invention has strong robustness to steady-state vibration components.

[0069] Figure 11 For the spectral comparison of the selected IMF components, such as Figure 11 As shown, the IMF number is a unique identifier within the algorithm and does not indicate the order of decomposition. The spectral energy of each IMF is highly concentrated in the low-frequency range of 0–5Hz, where the spectral amplitude reaches its maximum, indicating that the dominant component of the signal exhibits significant low-frequency modulation characteristics. As the frequency increases, the spectral amplitude decays rapidly, retaining only low-amplitude fluctuations in the 5–100Hz range, reflecting the limited contribution of mid-frequency dynamic components to the overall energy; while in the high-frequency range above 150Hz, the spectral amplitude further decreases, and its energy proportion is negligible. This spectral characteristic indicates that the analyzed signal is dominated by low-frequency non-stationary modulation, a result consistent with the aforementioned piecewise error analysis and the phenomenon of low-frequency energy consistently dominating in the subsequent three-dimensional spectral waterfall plot.

[0070] Figure 12 The time-domain distribution of the selected IMF components, such as Figure 12As shown, the time-domain waveform of IMF77257 exhibits a slowly changing trend component. The initial segment maintains a relatively stable negative bias level, followed by a significant rise after approximately 100 seconds, gradually approaching zero. This reflects the enhancement of the low-frequency baseline / operating condition gradual change component. IMF60607 similarly shows a smooth drift throughout the entire time period, with a rapid rise at the end, indicating that it primarily carries a gradually changing background rather than a typical narrow pulse impact. IMF78589, on the other hand, exhibits a certain degree of slow bending in the middle segment and rises in the latter part, reflecting the non-stationary evolution of the low-frequency modulation or trend term over time. Figure 12 The key IMFs are closer to the separation results of low-frequency background and slowly changing operating conditions than obvious high-amplitude transient impact sequences. The time-domain waveform of IMF77257 shows a quasi-periodic impact sequence, with the amplitude envelope gradually increasing after 100s, which is related to the time-varying characteristics of train load; IMF60607 shows abrupt amplitude changes in the 100-120s range, with a pulse width of 2.5s, characterizing the impact response of the track joint; IMF78589 shows a gradual amplitude modulation phenomenon (modulation period ≈40s), which may be related to the periodic vibration caused by wheelset eccentric wear.

[0071] Figure 13 The energy percentage of the selected IMF components is shown. IMF77257 is dominant (approximately 35% of the sector area), followed by IMF60607 (approximately 22%) and IMF53947 (18%), totaling 75% and forming the main signal energy backbone. IMF31303 and IMF79921 together account for less than 15%, mainly carrying broadband noise and environmental interference, with energy concentrated in high-frequency IMFs. The frequency band distribution of each IMF may reflect potential modal coupling. Figure 14 middle.

[0072] Figure 14 This is a three-dimensional spectral waterfall of the real signal from the IMF. (Example:) Figure 14 As shown, the energy exhibits a significant low-frequency dominance along the frequency axis: a large area of ​​high-amplitude "spectral ridges / curtains" appears in the low-frequency range near 0, spreading continuously along the IMF number direction, indicating that the low-frequency (gradually varying / baseline) components contribute the most significantly to the overall spectral amplitude in the decomposition results; in the mid-to-high frequency region (above approximately several hundred Hz), only sporadic peak-like components appear, exhibiting a sparse distribution, suggesting that the high-frequency components are more representative of local transients or weak-amplitude details rather than the energy backbone. Combined with... Figure 13 It can be seen that the energy share of the selected key IMFs does not differ significantly, while Figure 14 The wide distribution of mid-to-low frequency amplitudes further confirms that the signal is mainly composed of multiple low-frequency / gradually varying modes; at the same time, sporadic spikes in the mid-to-high frequency region may reflect the mixing of weak coupling or local disturbance components, but their overall contribution is relatively limited.

[0073] In this embodiment, AE-MMD can stably separate key modes dominated by low-frequency slowly varying and modulated components, and the decomposition results maintain good consistency in the time domain, frequency domain, and energy distribution. Spectral analysis shows that the measured signal energy is mainly concentrated in the low-frequency modulation range, while mid-to-high frequency components appear in a weak and sparse manner, reflecting the non-stationary and multi-source coupling characteristics of the wheel-rail system dynamic response under real-world conditions. Several high-energy IMFs occupy a major proportion in the energy distribution, indicating that AE-MMD has good energy concentration and mode differentiation capabilities under complex backgrounds.

[0074] Therefore, the rail corrugation detection method and system based on the AE-MMD algorithm described in this invention can improve the stability and reliability of rail corrugation detection.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A rail corrugation detection method based on AE-MMD algorithm, characterized in that, The method comprises the following steps: S1, collecting a rail vertical or lateral vibration acceleration signal, preprocessing the vibration acceleration signal, and performing sliding window segmentation processing on the preprocessed vibration acceleration signal to obtain a segmented signal; S2, constructing phase space trajectory matrix by integral method with symplectic structure preserving property for the segmented signal wherein, is the pre-processed segmented signal, is the generalized momentum, to maintain the energy conservation and the phase space volume of the Hamiltonian system. S3, singular value decomposition is performed on the phase space trajectory matrix, and a plurality of singular mode components are obtained according to the distribution characteristics of the singular value spectrum ; S4, calculating the Hilbert dominant frequency and energy proportion of the singular modal component, and screening a plurality of effective singular modal components based on the Hilbert dominant frequency difference constraint and the energy accumulation rate constraint to eliminate modal components with frequency crossing and energy redundancy; S5, using the Teager energy operator combined with kurtosis characteristics to identify the impact characteristics of the screened effective singular modal components, and realizing the classification of steady-state modal, modulated modal and impact modal; S6, superimposing the divided steady-state modal, modulated modal and impact modal, and comparing the superimposed signal with the original signal to calculate the symplectic structure preservation index SPI value and the energy leakage rate ELR; S7, judging the classification result according to the joint criterion of the transient energy index, the characteristic kurtosis, the energy leakage rate and the SPI value, and identifying the rail corrugation section according to the impact modal.

2. The rail corrugation detection method based on AE-MMD algorithm according to claim 1, characterized in that: In S1, the preprocessing includes denoising, normalization and zero mean processing of the vibration acceleration signal to obtain the preprocessed segmented signal.

3. The rail corrugation detection method based on AE-MMD algorithm according to claim 2, characterized in that: In S2, the integral method with the symplectic structure preservation characteristic is the second-order symplectic integral algorithm Stormer-Verlet method or the symplectic Euler method.

4. The rail corrugation detection method based on AE-MMD algorithm according to claim 3, characterized in that: In S4, the Hilbert dominant frequency difference constraint is that the dominant frequency difference of any adjacent singular modal component is greater than or equal to 5 Hz, and the energy accumulation rate constraint is that the cumulative energy proportion of the effective singular modal component is greater than or equal to 95%.

5. The rail corrugation detection method based on AE-MMD algorithm according to claim 4, characterized in that: The specific method of the classification of the steady-state mode, the modulation mode and the impact mode in S5 is to calculate the energy mutation characteristics of each effective singular modal component by the Teager energy operator, to classify the modes by the energy mutation characteristics and the peak value characteristics, and to use the transient energy index characterizes the energy aggregation degree of the impact mode on the time axis; Statistical impact modal transient energy index is calculated in the reference section without visible wave wear with standard deviation and the threshold is set to: ； ； wherein, is an empirical coefficient, having a value ranging from 2 - 4; is a transient energy threshold, is a transient energy low threshold; The classification criterion of the steady-state mode is: , characteristic peak degree K < 3; The classification criterion of the modulation mode is: , the characteristic kurtosis 3≤K<5; The classification criterion of the impact mode is: characteristic kurtosis K≥5; where, for the impact modal signal its discrete Teager energy is defined as: ； wherein, is the Teager energy function in the impact mode, is the Teager energy function in the impact mode for the n th sample point; In the sliding time window Within the sliding time window, the transient energy index adopts the mean or peak value of Teager energy within the window, which are defined as: ； ； wherein, is the mean value of the Teager energy in the k th mode, is the peak value of the Teager energy in the k th mode.

6. The rail corrugation detection method based on AE-MMD algorithm according to claim 5, characterized in that, In S6, the calculation formula of the symplectic structure preservation index SPI value is: ； wherein is an octonion, is the gradient of the Hamiltonian function, denotes the L2 norm; The calculation formula of the energy leakage rate ELR is: ； wherein, is the original signal energy, is the reconstructed signal energy, is the phase space Jacobian correction term.

7. The rail corrugation detection method based on AE-MMD algorithm according to claim 6, characterized in that: In the S7, the joint criterion of the rail corrugation section is that the transient energy index is , the characteristic peak degree K is greater than or equal to 5, the energy leakage rate ELR is less than or equal to 10%, and the SPI value is greater than or equal to 0.98 and less than or equal to 1.

02.

8. A detection system based on the AE-MMD algorithm-based rail corrugation detection method according to any one of claims 1 to 7, characterized in that, It comprises: A signal acquisition module for acquiring rail vertical and lateral vibration acceleration signals; An AE-MMD algorithm module for executing the AE-MMD algorithm process of the acceleration signal, including a phase space embedding unit, a singular value decomposition and modal extraction unit, and a modal screening unit; The phase space embedding unit is used to construct a phase space trajectory matrix; the singular value decomposition and modal extraction unit is used to perform singular value decomposition on the phase space trajectory matrix and obtain singular modal components; and the modal screening unit is used to screen effective singular modal components and perform modal classification and identification, and classify the modal into steady-state modal, modulated modal and impact modal; An index calculation module for calculating the SPI value and the ELR value of the original signal and the superimposed signal of the steady-state modal, the modulated modal and the impact modal; A corrugation identification module and a result output module for outputting results, identifying the rail corrugation section based on the time domain energy accumulation characteristics of the impact modal, and judging the effectiveness of the identification results by combining the energy leakage rate and the symplectic structure preservation index to identify the rail corrugation section; The corrugation identification module is used to judge whether the energy leakage rate is less than a preset threshold value, and when the energy leakage rate exceeds the threshold value, the corrugation identification module refuses to output the corrugation identification result; when the symplectic structure preservation index deviates from a preset range, the corrugation identification module invalidates the modal decomposition result. The detection system is arranged in a running part intelligent monitoring host or a track detection device, and is used for realizing online or quasi-online detection of rail corrugation.

9. The detection system of claim 8, wherein: The AE-MMD algorithm module is embedded with a sliding window segmentation unit, which is used for sliding window segmentation processing of long-time vibration acceleration signals.

10. The detection system of claim 8, wherein: The result graph output by the corrugation identification and result output module includes a modal spectrum graph, an energy distribution graph, an SPI-ELR joint curve graph and an original / reconstructed signal comparison graph.

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