Railway rail corrugation detection method under variable speed conditions based on multi-window spectrogram

Abstract

The application provides a rail corrugation detection method under variable speed conditions based on a multi-window spectrogram, which adopts a time-frequency analysis method of a multi-window re-distribution spectrogram, and optimizes re-distribution coordinates so that they are gathered on the instantaneous frequency of a transient signal, and the obtained rail corrugation fault frequency has high time-frequency gathering, strong anti-interference ability and clear identification degree. In the rail corrugation damage fault detection under variable speed conditions, the application verifies the simulation signal and the field measured signal. The results show that the time-frequency method of the multi-window coordinate re-distribution spectrogram has excellent application effect in the rail corrugation detection, can accurately analyze the fault frequency of the rail corrugation excitation under the traction and braking conditions, and obtains relatively accurate results when applied to the field measured data, which reflects the high resolution, high time-frequency gathering and strong anti-interference ability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of subway train fault diagnosis, and in particular to a rail corrugation detection method under variable speed working condition based on multi-window spectrogram. BACKGROUND

[0002] Subway trains will appear rail corrugation due to frequent braking and starting, which will cause safety hazards to train operation. Effectively detecting the generation of rail corrugation under variable speed working condition helps to improve the safety and operation comfort of metro rail vehicles. When the metro vehicle passes through the rail corrugation section, the dynamic response between the wheel and the rail is more significant, which intensifies the vibration and noise between the wheelset and the track. The vibration phenomenon causes disturbance to the safety and comfort of the passengers. The formation of rail corrugation also leads to the deterioration of the wheel-rail relationship during normal operation of the train, reduces the service life of the vehicle and track components, and intensifies the fatigue wear of the wheel and track surface. In severe cases, it even affects the normal operation of the metro vehicle and causes derailment. Therefore, detecting the existing rail corrugation on the existing track through the existing various methods is also a hot and difficult problem that has not been completely solved, and there is a more specific and detailed demand for the detection and diagnosis of rail corrugation in actual engineering.

[0003] At present, among the many detection methods of rail corrugation, the methods that have been applied in actual engineering mainly include two categories: direct detection method and indirect detection method. However, in today's rapid development of rail transit, the direct detection method adopts traditional manual detection, which has the disadvantages of heavy workload, low detection efficiency and high labor cost; the indirect detection method has less accurate results than the direct detection method, and has the disadvantages of long test time and high cost. Moreover, the above two methods cannot provide fast and effective detection for the problems of metro lines in China, and cannot meet the real-time detection needs of rail transit.

[0004] The dynamic characteristics of the wheel-rail system with rail corrugation damage are analyzed, and an algorithm for effectively detecting the generation of rail corrugation under variable speed working condition is proposed for the detection and diagnosis of rail corrugation. This algorithm plays a significant role in detecting and identifying rail corrugation, stabilizing the dynamic characteristics of the wheel-rail system, ensuring the performance of metro vehicles and track structures, improving driving safety and smoothness, and laying a foundation for the prevention and control of rail corrugation. It has important engineering significance for the design, operation and track maintenance of metro lines. SUMMARY

[0005] Since the existence of rail corrugation will aggravate the vibration response between the wheel and the rail of the urban rail vehicle, and then cause the vibration of the axle box, the axle box acceleration data can reflect the damage of the rail to a certain extent. In order to solve the above existing problems, the rail corrugation signal is input into the track according to the metro vehicle dynamics model, so as to obtain the axle box acceleration data under the variable speed working condition. Since the information of the wavelength of the rail corrugation cannot be described by the time domain data or the frequency domain data of the track irregularity with the existence of the corrugation, the application proposes to use the multi-window spectrum algorithm after the optimization of the coordinate redistribution to perform time-frequency analysis on the collected vibration acceleration data, and finally uses the simulation signal and the field measured corrugation signal to analyze and verify. The application specifically adopts the following technical scheme:

[0006] A rail corrugation detection method under variable speed working condition based on multi-window spectrum, the method comprising the following specific steps:

[0007] (1) Rail corrugation model establishment

[0008] The input model of the rail corrugation is as follows:

[0009]

[0010] Wherein, Z0(t) is the vertical position of the corrugation on the rail surface; L is the irregularity wavelength; a is the irregularity wave depth; v is the normal running speed of the train; t is the time variable, and ω is the angular velocity;

[0011] When the vehicle passes through the rail corrugation section, high-frequency excitation vibration is generated between the wheel and the rail, and the excitation frequency f is represented as

[0012]

[0013] Wherein, f is the excitation frequency of the rail corrugation; v' is the speed of the vehicle passing through the rail corrugation section; λ is the wavelength of the track irregularity in the rail corrugation section;

[0014] (2) Rail corrugation working condition setting

[0015] Based on the established rail corrugation model, by changing the wavelength and depth of the rail corrugation on the track and the variable speed interval of the vehicle passing through the corrugation existing section, a plurality of rail corrugation damage working conditions are established, and the rail corrugation model is combined with the German track spectrum as the track irregularity excitation signal input;

[0016] (3) Multi-window spectrum rail corrugation detection under variable speed working condition

[0017] The Hermite function is used as the window function, and the new reassignment coordinates are optimized to concentrate on the instantaneous frequency of the transient signal. The multi-window spectrum algorithm after coordinate reassignment is used to diagnose the rail corrugation fault under variable speed conditions.

[0018] Preferably, step (3) specifically adopts the following steps:

[0019] (3.1) Reassignment spectrum

[0020] For a complex-valued signal x(t) and a time window function h(t), the short-time Fourier transform is

[0021] F h (t,f) = ∫x(v)h * (v-t)e -i2πfv dv

[0022] Where * indicates that the complex conjugate of the signal is taken to be the conjugate signal.

[0023] The corresponding spectrum is obtained as

[0024] S(t,f) = |F h (t,f)| 2

[0025] By introducing and calculating the reassignment coordinates and the two-dimensional Dirac impulse δ(t,f), the spectrum after reassignment is obtained:

[0026]

[0027] The reassignment coordinates depend on the signal x(t) and the window function h(t) and are calculated as

[0028]

[0029] Where c t and c f are scale constants, and R and I represent the real and imaginary parts, respectively, F h (t,f), F th (t,f) and are calculated using the complex-valued signal x(t) and the window function h(t), t·h(t) and dh(t) / dt, respectively;

[0030] (3.2) Multi-window coordinate reassignment

[0031] The Hermite function is used as the window function, and the new reassignment coordinates are optimized to concentrate on the instantaneous frequency of the transient signal. The multi-window spectrum algorithm after coordinate reassignment is used to diagnose the rail corrugation fault under variable speed conditions.

[0032] (3.2.1) Coordinate reassignment

[0033] The general oscillatory transient response with a Gaussian envelope is as follows:

[0034]

[0035] The above response has a fixed amplitude A, a time-frequency domain center (t0, f0), and a phase φ, which can be simplified to obtain

[0036]

[0037] The standard Hermite polynomial is as follows:

[0038]

[0039] Scaling weight function

[0040]

[0041] Where σ is the estimation factor;

[0042] After defining the scaling Hermite function, it is determined that orthogonality applies to any pair of orthogonal systems.

[0043]

[0044] In this step, we make the assumption that the window set h k (t) Assuming the scaling estimation factor σ of the window set is the same as the scaling estimation factor σ of the envelope signal, we obtain...

[0045]

[0046] Signal s(t) and any window set h k (t) after performing a short-time Fourier transform is expressed as:

[0047]

[0048] Change the variable according to the following conditions.

[0049]

[0050] After that, I received

[0051]

[0052] Then it can be expanded to

[0053]

[0054] at this time,

[0055] The result of using the short-time Fourier transform with multiple time windows is as follows:

[0056]

[0057] The last expression Converging to 0;

[0058] Then, using the definition of the Hermite polynomial derivative.

[0059]

[0060] get

[0061]

[0062] For the special case of k=0, when the window is a Gaussian function and the polynomial is therefore equal to 1, we get...

[0063]

[0064] Simplified to

[0065]

[0066] when When choosing the short-time Fourier transform with a time-derived window, we obtain:

[0067]

[0068] The transformation when k = 0 is as follows:

[0069]

[0070] Therefore, the formula for the short-time Fourier transform is:

[0071]

[0072] Considering the short-time Fourier transform and Based on the interrelationships between them, a new set of redistributed coordinates is proposed.

[0073]

[0074] Using this set of coordinates, the redistribution coordinates of the transient signal with its frequency domain center at (0,0) can be obtained as follows:

[0075]

[0076] Preferably, step (3) further includes the following steps:

[0077] (3.2.2) Multi-window coordinate reallocation and coordinate optimization

[0078] The multi-window coordinate redistribution spectrum algorithm optimizes the resulting redistributed coordinates by averaging them, resulting in:

[0079]

[0080] The multi-window spectrum is as follows:

[0081]

[0082] The optimized multi-window coordinate reassignment is

[0083]

[0084] The present invention has the following specific beneficial effects:

[0085] This invention employs a time-frequency analysis method based on multi-window coordinate redistribution spectra and optimizes the redistribution coordinates to focus on the instantaneous frequency of transient signals. The resulting fault frequencies exhibit high time-frequency concentration, strong anti-interference capability, and clear identification. The invention was validated using simulated signals and field-measured signals in the detection of rail corrugation damage under variable speed conditions. Results show that the time-frequency method based on multi-window coordinate redistribution spectra has excellent application effects in rail corrugation detection. It can accurately analyze the fault frequencies of rail corrugation excitation under traction and braking conditions. Applying it to field-measured data also yielded relatively accurate results, demonstrating its high resolution, high time-frequency concentration, and strong anti-interference capability. Attached Figure Description

[0086] Figure 1 It is a simple harmonic excitation diagram.

[0087] Figure 2 It is a time-frequency graph with different window numbers.

[0088] Figure 3 (a) in the figure is the global time-domain plot of the axle box acceleration of the simulated signal.

[0089] Figure 3 (b) in the figure is a time-domain diagram of the rail corrugation section of the simulated signal at a certain moment.

[0090] Figure 4 This is a comparison chart of the calculation and detection frequency of rail corrugation faults under traction conditions.

[0091] Figure 5 (a) in the figure is the global time-domain plot of axle box acceleration under braking conditions.

[0092] Figure 5 (b) in the diagram represents the time-domain and frequency-domain plots of the rippled section.

[0093] Figure 6(a) in the figure is the vibration acceleration waveform of the section with rail corrugation.

[0094] Figure 6 (b) in the diagram is the vibration acceleration waveform of the non-erosion section.

[0095] Figure 7 (a) in the diagram is a time-frequency diagram under a certain traction condition.

[0096] Figure 7 (b) Time-frequency diagram under a certain braking condition. Detailed Implementation

[0097] 1. Establishment of rail corrugation model

[0098] Rail corrugation is a type of uneven, wavy wear phenomenon that occurs on the surface of rails, such as... Figure 1 As shown, this is a typical excitation with continuous harmonic characteristics, which mainly has two characteristic quantities: wavelength and wave depth.

[0099] This invention provides a method for simulating rail corrugation excitation using a displacement input function. Since rail corrugation is a typical continuous harmonic disturbance and exhibits periodicity, this invention addresses rail corrugation with a constant wavelength. The input function used is shown in the following equation:

[0100]

[0101] Where Z0(t) is the vertical position of the corrugation on the rail surface; L is the wavelength of the irregularity; a is the depth of the irregularity; v is the normal operating speed of the train; t is the time variable; and ω is the angular velocity.

[0102] When a vehicle passes through a section of corrugated rails, high-frequency excitation vibrations are generated between the wheel and rail. The excitation frequency f is denoted as...

[0103]

[0104] Where f is the excitation frequency of rail corrugation; v′ is the speed of the vehicle when passing through the rail corrugation section; and λ is the wavelength of track irregularity in the rail corrugation section.

[0105] 2. Rail Corrugation Condition Settings

[0106] The maximum operating speed of subways is generally less than 80 km / h. Furthermore, due to the frequent braking and starting of subway vehicles and the prevalence of small-radius curves, the rail corrugation damage on subway lines is primarily characterized by short wavelengths. Therefore, based on the established rail corrugation simulation model, various rail corrugation damage conditions were established by varying the rail corrugation wavelength and depth on the track, as well as the speed variation range of the vehicle passing through corrugated sections. The rail corrugation model was then combined with the German track spectrum as a track irregularity excitation and imported into the vehicle dynamics model. For the wavelength of rail corrugation, a wavelength depth of 0.1mm was set, and 40mm, 60mm, 80mm, 100mm, and 120mm were selected as five different rail corrugation wavelengths for comparison. For the wavelength depth of rail corrugation, a wavelength of 100mm was set, and 0.08mm, 0.10mm, 0.12mm, 0.14mm, and 0.16mm were selected as five different rail corrugation depths for comparison. For different vehicle operating speed ranges, a wavelength of 80mm and a wavelength depth of 0.12mm were set, and the operating speed ranges of 0km / h-45km / h, 0km / h-50km / h, 0km / h-60km / h, and 0km / h-70km / h were selected as four different speed ranges for comparison.

[0107] (1) Firstly, under traction and braking conditions, as the vehicle speed increases or decreases, the dynamic response between the wheel and rail fluctuates more significantly than when the speed is constant. Among them, the vertical force between the wheel and rail and the wheel load reduction rate are more significantly affected by the rail corrugation damage and are more likely to exceed the safety limit.

[0108] (2) Regarding the characteristics of rail corrugation, both the decrease in wavelength and the increase in wave depth exacerbate the impact of rail corrugation on the dynamic response of the wheel-rail system. The decrease in wavelength has a weaker impact on the lateral force of the wheel axle and the derailment coefficient, and all working condition indicators are within the safety limits. However, the impact on the vertical and lateral force of the wheel and the wheel load reduction rate is more significant and is more likely to exceed the safety limits of the evaluation indicators.

[0109] (3) Regarding the track layout, the wheel-rail interaction is more significant on small-radius curved tracks compared to straight tracks, and the influence on the inner side of the track is deeper. The dynamic response of the wheel-rail system on the inner side of the track surface is stronger than that on the outer side.

[0110] (4) As the speed range of subway trains increases, while keeping other settings unchanged, the dynamic response between wheels and rails becomes more intense and the fluctuation amplitude gradually increases.

[0111] 3. Rail corrugation detection method under variable speed conditions using multi-window spectra

[0112] The redistribution spectrum is a classic time-frequency signal analysis method. The multi-window redistribution algorithm of this invention has the advantages of low variance and high resolution of the multi-window spectrum analysis method, while maintaining the high time-frequency clustering of redistribution. At the same time, it can effectively reduce cross terms and fluctuations caused by rearrangement and noise, and clearly show the modulation phenomenon of the signal. It is suitable for processing strong vibration and strong noise signals. This invention uses the Hermite function as the window function and optimizes the new redistribution coordinates to focus on the instantaneous frequency of the transient signal. Furthermore, the multitaper reassigned spectrogram (MTRS) algorithm after coordinate redistribution is applied to the fault diagnosis of rail corrugation under variable speed conditions. The analysis and verification are carried out by using simulated rail corrugation signals and field measured corrugation signals.

[0113] (1) Redistribution spectrum

[0114] For a complex-valued signal x(t) and a time window function h(t), the short-time Fourier transform (STFT) is:

[0115] F h (t,f)=∫x(v)h * (vt)e -i2πfv dv (1)

[0116] The asterisk (*) indicates that the signal is conjugated to become a conjugate signal. Furthermore, all integral symbols in this invention range from positive infinity to negative infinity.

[0117] Therefore, the corresponding spectrum is defined as follows.

[0118] S(t,f)=|F h (t,f)| 2 (2)

[0119] Because the spectrum exhibits a bilinear energy distribution, reducing cross terms and improving the time-frequency convergence of the signal become key issues in spectrum time-frequency analysis methods. This is addressed by introducing and calculating redistributed coordinates. And the two-dimensional Dirac impulse δ(t,f), to obtain the redistributed spectrum, can be defined as formula (3):

[0120]

[0121] That is, the redistribution method maps the signal energy (t1,f1) at any given point in S(t,f) to another corresponding point. This point is the centroid of the signal energy near the given point (t1, f1). Redistributing the spectrum yields a more localized time-frequency representation, making its instantaneous frequencies easier to obtain and interpret. The redistributed coordinates depend on the signal x(t) and the window function h(t) and can be calculated as follows:

[0122]

[0123] Where c t and c f F is a scaling constant, and R and I represent the real and imaginary parts, respectively. In the short-time Fourier transform, F... h (t,f), F th (t,f) and The calculations are performed using the complex-valued signal x(t) and the window functions h(t), t·h(t), and dh(t) / dt, respectively.

[0124] The original formula for the redistribution spectrum applies to longer signals, sine waves, or FM / AM linear frequency modulated signals. In this case, to obtain the optimal energy localization around the instantaneous frequency, the formula for calculating the redistribution scaling constant is defined as c. t =c f =1. For oscillating transient signals, if the window function h(t) matches the signal envelope, and , then c... t =c f =2 can achieve excellent energy location capability at the instantaneous frequency of transient signals.

[0125] (2) Multi-window coordinate reassignment

[0126] This invention extends the spectrum redistribution algorithm by using the Hermite function as the window function, combining multi-window and spectrum redistribution, and optimizing the new redistribution coordinates. This makes the optimized method robust to noise while still improving the energy localization of the spectrum.

[0127] (2.1) Coordinate Reassignment

[0128] The redistributed coordinates are invariant to time and frequency shifts. Therefore, the general oscillatory transient response with a Gaussian envelope is studied by the following formula (5):

[0129]

[0130] This formula has a fixed amplitude A, a time-frequency domain center (t0, f0), and a phase φ, so formula (5) can be simplified to obtain

[0131]

[0132] The simplified version of formula (5-6) is to set the amplitude A to a unit amplitude, the time-frequency domain center (t0,f0) to (0,0), and to have no phase.

[0133] The Hermite function is selected as the window function in the multi-window coordinate redistribution spectrum method because they are orthogonal in the time-frequency plane and provide good time-frequency energy localization capability. The standard Hermite polynomial is as follows (7):

[0134]

[0135] Orthogonal to the weighting function, i.e., formula (8)

[0136]

[0137] If the Hermite polynomials are scaled using an estimation factor σ, then to maintain orthogonality, the weight functions should be scaled with the same estimation factor. The scaled weight functions are shown in formula (9).

[0138]

[0139] After defining the scaling Hermite function, it can be determined that orthogonality applies to any pair of orthogonal systems.

[0140]

[0141] In this step, we make the assumption that the window set h k (t) Assume that the scaling estimation factor σ of the window set is the same as the scaling estimation factor σ of the envelope signal, that is, σ in formulas (6) and (11) is the same. Formula (11) is shown below:

[0142]

[0143] This is the same matching required for scaling redistribution and matching window reallocation. Therefore, achieving good time-frequency convergence at the instantaneous frequency requires precise matching; when the matching is inaccurate, the localization capability will significantly decrease. Thus, if a signal has multiple components with different scaling ratios, matching the window with a specific component can be used as a detection method. In practical applications, if the scaling estimation factor is unknown, it must be estimated for successful signal detection.

[0144] The window sets obtained from Hermite are all real-valued, therefore the signal s(t) in equation (6) and any window set h in equation (11) are real-valued. k (t) can be expressed as follows after performing a short-time Fourier transform:

[0145]

[0146] To simplify calculations, the variables are changed according to the following conditions.

[0147]

[0148] Then we get formula (14).

[0149]

[0150] Then it can be expanded to

[0151]

[0152] at this time,

[0153] The solution to this integral depends on the order of the Hermite polynomial. Calculating the integral of a higher-order polynomial requires a direct but decomposition into multiple parts for integration. However, for the purposes of these calculations, further simplification of this integral is unnecessary.

[0154] The short-time Fourier transform using multiple time windows can be programmed in a similar way, with the result shown in the following formula.

[0155]

[0156] The last expression It converges to 0. Then, using the definition of the Hermite polynomial derivative, i.e.

[0157]

[0158] It can be obtained

[0159]

[0160] For the special case of k=0, when the window is a Gaussian function and the polynomial is therefore equal to 1, we can obtain...

[0161]

[0162] This means that formula (16) can be simplified to...

[0163]

[0164] when At that time, by applying a similar method to the short-time Fourier transform with a time-derived window, we can obtain:

[0165]

[0166] The transformation when k = 0 is as follows:

[0167]

[0168] Therefore, the formula for the short-time Fourier transform is:

[0169]

[0170] Considering the short-time Fourier transform and Based on the interrelationships between them, a new set of redistributed coordinates is proposed.

[0171]

[0172] Using the coordinates from formula (24), we can obtain the following coordinates for the redistribution of the transient signal with its frequency domain center at (0,0):

[0173]

[0174] Furthermore, it achieves clear energy localization of transient signals at instantaneous frequencies. The proposed new coordinate redistribution method contrasts with the traditional coordinate redistribution spectrum method using Equation (11), which uses a Hermite window with a Gaussian envelope signal to redistribute the signal to an ellipse around the center of the time-frequency domain.

[0175] By combining h0(t) with the newly proposed coordinate equation formula (11), the multi-window reassigned spectrogram (MWRS) algorithm is derived.

[0176] (2.2) Multi-window coordinate reallocation and coordinate optimization

[0177] When computation is performed using any Hermite window function, the redistributed coordinates redistribute the signal energy of a Gaussian envelope transient to its instantaneous frequency. Therefore, the average of the redistributed coordinates calculated using the same transient signal and different Hermite windows can still redistribute the instantaneous frequency of the transient signal.

[0178] Therefore, this invention optimizes the obtained redistributed coordinates by calculating the average value, i.e., using a multi-window coordinate redistribution spectrum algorithm. The MTRS algorithm yields:

[0179]

[0180] The multi-window spectrum is as follows:

[0181]

[0182] The optimized multi-window coordinate reassignment is

[0183]

[0184] It can be observed that averaging the redistributed coordinates in formula (24) yields a better time-frequency representation than directly using these coordinates.

[0185] (2.3) Optimal k value selection

[0186] Since multiple Hermite window functions can be used in the time domain to truncate the signal, making the heights of the side lobes approach zero and concentrating the energy relatively in the main lobe, the spectrum can be closer to the true spectrum. However, windowing itself also increases the error, and it is expected that the time-frequency resolution of MTRS will decrease as the number of windows increases. Therefore, for the multi-window redistribution method, a trade-off between resolution and accuracy needs to be struck.

[0187] The simulated vertical acceleration signal of the axle box was selected under traction conditions, with rail corrugation set to a wavelength of 80 mm, a corrugation depth of 0.2 mm, and a speed range of 0 km / h-70 km / h. Figure 2 The time-frequency curves for different window numbers at a given 2-second time point show that the curve obtained when k=4 is significantly clearest. While the time-frequency curve for k=0 can still cluster and locate fault frequencies, its clarity is weaker than that obtained with other k values ​​greater than 0. In other words, as the number of windows increases, the MTRS algorithm slightly improves both the resolution and energy clustering of the time-frequency map, and its ability to identify second harmonics also gradually strengthens.

[0188] 4. Simulation signal verification

[0189] (1) Time-frequency characteristics of rail corrugation under traction conditions

[0190] Figure 3 The data includes the global time-domain plot, the time-domain plot of the corrugated section, and the frequency-domain plot of the axle box acceleration signal under traction conditions with a wavelength of 60 mm, a wave depth of 0.1 mm, and a speed range of 0 km / h-50 km / h. The sampling frequency is 2000 Hz.

[0191] Figure 3 (a) in the figure is the global time-domain plot of the axle box acceleration of the simulated signal. Figure 3 (b) in the figure shows the time-domain plot of the rail corrugated section of the simulated signal at a certain moment. It can be seen that the amplitude of the section with rail corrugation is greater than that of the section without rail corrugation, and the waveform of the section exhibits a periodic fluctuation. At the same time, the amplitude and frequency of the signal are highly time-varying. Next, the multi-window coordinate redistribution spectrum algorithm is used to process the time-frequency characterization results.

[0192] A 2-second segment of the ripple zone in the simulated signal of this traction condition was selected for multi-window coordinate redistribution spectrum processing. Due to the characteristics of continuous wavelet transform, both before and after CWT optimization, there is some energy frequency dispersion and poor clustering performance, with distortion boundary effects appearing at the second harmonic. The WSST algorithm has excellent anti-interference ability and good ridge effect, but its frequency resolution is not high and the amplitude is not obvious. The frequency curve obtained by the multi-window coordinate redistribution spectrum method has the advantages of strong anti-interference ability and high resolution, while maintaining high time-frequency clustering.

[0193] Under traction conditions, as the speed of urban rail vehicles gradually increases, the vertical vibration response caused by track irregularities due to rail corrugation gradually intensifies, and its fault frequency also shows an upward trend. Since the speed range of the 2-second corrugated section extracted in this simulation signal is 5.63 m / s-6.02 m / s, the theoretical value of the main frequency of the rail corrugation vibration signal under this condition is calculated to be 93.82 Hz-102.38 Hz. However, due to fitting errors and other issues, there is a small error between the extracted detection frequency value and the theoretical calculation value. Figure 4 As shown, the error value is approximately 2Hz. It can be seen that this method can also accurately locate the fault frequency under traction conditions and accurately diagnose rail corrugation defects.

[0194] (2) Time-frequency characteristics of rail corrugation under braking conditions

[0195] Figure 5 (a) in the figure is the global time-domain plot of axle box acceleration under braking conditions. Figure 5 (b) shows the time-domain and frequency-domain plots of the corrugated section. The sampling frequency is 2000 Hz.

[0196] The simulated rail corrugation signal was set to a wavelength of 100 mm, a wave depth of 0.1 mm, and a speed range of 0 km / h to 50 km / h. The time-frequency characterization results were then processed using a multi-window coordinate redistribution spectrum algorithm.

[0197] A 2-second segment from the ripple zone of the simulated signal under this braking condition was selected and processed using time-frequency analysis methods such as multi-window coordinate redistribution spectrum. The time-frequency graph obtained by the multi-window coordinate redistribution spectrum is significantly superior to other algorithms in both energy localization capability and clustering. Furthermore, traditional time-frequency analysis methods such as CWT and WSST mostly focus energy localization on the second harmonic, while the MTRS algorithm clusters the time-frequency curve around its accurate fault frequency.

[0198] Under braking conditions, as the speed of the urban rail vehicle gradually decreases, the vertical vibration response caused by track irregularities due to rail corrugation gradually weakens, and the fault frequency shows a downward trend. Since the speed range of the 2-second corrugation section extracted in this simulation signal is 9.39 m / s-8.69 m / s, the theoretical value of the main frequency of the rail corrugation vibration signal under this condition is calculated to be 93.89 Hz-86.87 Hz. Similar to the traction condition, the frequency value detected by MTRS also has an error compared to the theoretical calculation value, but this error is negligible. This shows that the MTRS algorithm can accurately locate the fault frequency under braking conditions. In summary, the MTRS algorithm using the new coordinates can diagnose rail corrugation defects from the model simulation signal under variable speed conditions.

[0199] Subways experience frequent starts and stops during actual operation, resulting in a near-constant speed change during signal measurement. This leads to inconsistent frequency characteristics of rail corrugation. Furthermore, numerous impact signals are distributed throughout the time-domain signal, making it difficult to clearly identify and separate the fault components caused by rail corrugation. Considering these factors, the measured signal contains noise and other signal interference, making it challenging to accurately locate and detect rail corrugation.

[0200] Identify the sections in the measured section where rail corrugation exists, and perform waveform analysis on the sections where rail corrugation exists and the sections where rail corrugation was not detected. Figure 6 (a) in the figure represents the vibration acceleration waveform of the section with rail corrugation. Figure 6 (b) in the figure shows the vibration acceleration waveform of the non-corrugated section. It can be seen that the waveform amplitude of the corrugated section is large and periodic, while the acceleration of the non-corrugated section exhibits a random and irregular fluctuation. Next, the signal will be processed based on the MTRS algorithm.

[0201] The measured time-frequency diagram of the corrugated section is as follows: Figure 7 As shown, the proposed MTRS algorithm for time-frequency analysis of the measured data not only accurately analyzes the frequency variation of the signal over time but also maintains high concentration and high resolution. Based on a fixed wavelength, the passing frequency of the corresponding corrugation is calculated from the measured track surface irregularity wavelength. Figure 7 The consistent frequencies shown indicate that the MTRS algorithm can also accurately analyze the rail corrugation excitation frequency under vehicle speed change conditions and perform precise diagnosis of the corrugation wavelength.

Claims

1.A method for rail corrugation detection under variable speed conditions based on multi-window spectrogram, characterized in that, The method comprises the following specific steps: (1) Rail corrugation model establishment The input model of rail corrugation is as follows: Wherein, Z0(t) is the vertical position of the corrugation on the rail surface; L is the wavelength of the irregularity; a is the irregularity wave depth; v is the normal running speed of the train; t is the time variable, and ω is the angular velocity; When the vehicle passes through the rail corrugation section, high-frequency excitation vibration is generated between the wheel and the rail, and the excitation frequency f is represented as Wherein, f is the rail corrugation excitation frequency; v' is the speed of the vehicle passing through the rail corrugation section; λ is the wavelength of the rail corrugation section track irregularity; (2) Rail corrugation condition setting Based on the established rail corrugation model, by changing the wavelength and depth of the rail corrugation on the track and the variable speed interval of the vehicle passing through the corrugation existing section, a plurality of rail corrugation damage conditions are established, and the rail corrugation model is combined with the German track spectrum as the track irregularity excitation signal input; (3) Multi-window spectrogram rail corrugation detection under variable speed conditions The Hermite function is used as the window function, and the new reassignment coordinates are optimized to be concentrated on the instantaneous frequency of the transient signal, and the multi-window spectrogram algorithm after coordinate reassignment is used for fault diagnosis of the rail corrugation under variable speed conditions; Step (3) specifically adopts the following steps: (3.1) Reassignment spectrogram For a complex-valued signal x(t) and a time window function h(t), the short-time Fourier transform is F h (t,f) = ∫ x (v)h * (v-t)e -i2πfv dv Wherein * represents the complex conjugate of the signal to make it a conjugate signal; The corresponding spectrogram is S(t,f) = |F h (t,f)| 2 By introducing and calculating the redistribution coordinates and the two-dimensional Dirac impulse δ(t,f), the redistributed spectrogram is obtained: The reassignment coordinates depend on the complex-valued signal x(t) and the time window function h(t) and are calculated as where c t and c f are scale constants and R and I represent the real and imaginary parts, respectively, F h (t,f) is computed using a complex-valued signal x(t) and a time window function h(t), F th (t,f) is computed using a complex-valued signal x(t) and the function t-h(t), is computed using a complex-valued signal x(t) and the function dh(t) / dt; (3.2) Multi-window coordinate reassignment The Hermite function is used as the window function, the multi-window and reassignment spectrogram are combined, and the new reassignment coordinates are optimized; (3.2.1) Coordinate reassignment The oscillatory transient response with a Gaussian envelope is as follows: The above response has a certain fixed amplitude A, a time-frequency domain center (t0, f0) and a phase φ, and is simplified to obtain The standard Hermite polynomial is as follows: The scaling weight function is Wherein σ is an estimation factor; After defining the scaled Hermite function, the orthogonality is applicable to any pair of orthogonal systems At this step, the hypothesis window set h k (t) The scaling estimation factor σ of the hypothesis window set is the same as the scaling estimation factor σ of the envelope signal The signal s(t) and any window set h k After a short-time Fourier transform of s(t) is represented as According to the following conditions, the variables are changed Then it is extended to The result of the short-time Fourier transform using multiple time windows is as follows At this time, Then, using the definition of the Hermite polynomial derivative where the last expression converges to 0 converges to 0; The result is For the special case of k = 0, when the window is a Gaussian function and the polynomial therefore equals 1, the result is Simplified as Where the transformation is as follows when k = 0: When the short-time Fourier transform with time derivative windows is chosen, one obtains: Therefore, for the short-time Fourier transform, the formula is: Through this set of coordinates, when the transient signal reassignment coordinates are as follows when the time-frequency domain center is (0, 0): Taking into account the interrelation between the short-time Fourier transform and a new set of reassignment coordinates is proposed Step (3) further comprises the following steps: (3.2.2) Multi-window coordinate reassignment and optimized coordinates The multi-window coordinate reassignment spectrogram algorithm optimizes the reassignment coordinates obtained, and the average value is calculated to obtain: Wherein the multi-window spectrogram is: The optimized multi-window reassignment coordinates are ​

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