A rail corrugation detection method based on enhanced time-frequency analysis

Abstract

This invention discloses a rail corrugation detection method based on enhanced time-frequency analysis. First, the axle box acceleration signal is input, the window function and window length are determined, and the parameter N is determined. The angle β∈(-π / 2,π / 2) is divided into N equal parts, resulting in N corresponding kernel functions. Then, the signal is subjected to N time-frequency transformations corresponding to the kernel functions, resulting in N time-frequency graphs. The kurtosis is calculated along the frequency direction at each time point of the N time-frequency graphs, yielding N kurtosis values. At each time point, the time-frequency representation corresponding to the maximum kurtosis value is retained to form a new time-frequency representation. The maximum value is then found in the frequency direction of the new time-frequency representation to determine the frequency redistribution operator f. L Based on the time-frequency representation of concentrated energy, an enhanced time-frequency representation is obtained using an improved local maximum synchronization compression operator. Finally, the location and frequency of wave-erosion are determined according to the energy intensity in the time-frequency representation, and the wave-erosion wavelength is calculated by combining the vehicle speed and frequency.

Description

Technical Field

[0001] This invention belongs to the field of rail transit fault detection, specifically relating to a wave wear detection method based on time-frequency analysis of axle box acceleration signals. Background Technology

[0002] In recent years, my country's intercity rail transit has developed rapidly, with subway vehicle operating speeds and traffic volumes continuously increasing. This has led to frequent occurrences of rail surface corrugation, affecting rail transit operations. Corrugation refers to the regular, wave-like unevenness on the surface of the track running section. When trains travel on corrugated sections, the unevenness causes abnormal vibrations between the wheel and rail, generating loud noise and easily damaging structural components in the track system, seriously affecting train operation safety and passenger comfort. Corrugation imposes high maintenance costs on the transportation system and poses significant safety hazards, making rail corrugation a pressing issue in the rail transit field. Currently, corrugation detection is mainly done by workers using corrugation trolleys. However, manual track inspection requires nighttime operation, making this method labor-intensive, inefficient, and unable to achieve all-weather inspection. Using a track inspection vehicle can avoid these problems and achieve all-weather inspection; however, this method has a long testing cycle and high cost, which do not meet the real-time requirements of rail transit inspection. The detection of axle box acceleration is simple and easy. By installing an acceleration sensor on the axle box, the vibration changes caused by the vehicle passing through the corrugated track section can be directly reflected in the axle box acceleration signal. Based on this characteristic of the axle box vibration acceleration signal, conditions are provided for the rapid and effective diagnosis of rail corrugation, which is of great significance for realizing rapid, real-time and effective diagnosis of corrugation.

[0003] In 2007, Caprioli A. et al. used wavelet packet transform with db10 wavelet as the basis function to analyze axle box vibration acceleration in order to extract the frequency response characteristics of shortwave irregularities in the track, and calculated the time-scale spectrum of axle box acceleration based on different bandwidths. In 2010, Gomes R. et al. used continuous wavelet transform and wavelet packet transform to analyze axle box acceleration. In 2018, Xu Xiaodi et al. used SST to detect high-speed rail track corrugation, which can extract the instantaneous frequency curve of the signal, but its application to noisy data has limitations. Although previous scholars have been able to use time-frequency analysis methods to detect corrugation, the poor time-frequency convergence and poor noise robustness of the methods used have affected the accuracy of corrugation detection. Time-frequency analysis methods, represented by STFT, are less effective when processing non-stationary signals. ΔR(u)The presence of [error term] is the main reason for inaccurate amplitude information. To improve the performance of existing time-frequency analysis methods and obtain accurate amplitude and frequency information, an improved enhanced time-frequency analysis method is proposed by introducing a kernel function to cancel the interference of the error term and introducing a local maximum synchronization compression operator. Summary of the Invention

[0004] To address the aforementioned problems, a rail corrugation detection method based on enhanced time-frequency analysis is proposed. This algorithm introduces a kernel function related to the rotation angle β and an improved synchronous compression operator. It uses a kurtosis index to select the best-matching angle parameters and employs the improved synchronous compression operator to obtain an enhanced time-frequency representation.

[0005] The technical solution adopted in this invention is a rail corrugation detection method based on enhanced time-frequency analysis, which includes the following specific steps:

[0006] Step (1): Input the axle box acceleration signal, determine the window function and window length, determine the parameter N, divide the angle β∈(-π / 2,π / 2) into N equal parts, and obtain N corresponding kernel functions;

[0007] Step (2): Perform time-frequency transformation on the signal according to the corresponding kernel function N times to obtain N time-frequency graphs. Calculate the kurtosis along the frequency direction at each time point of the N time-frequency graphs to obtain N kurtosis values.

[0008] Step (3): At each time point, retain the time-frequency representation corresponding to the maximum kurtosis value to form a new time-frequency representation. Find the maximum value in the frequency direction of the new time-frequency representation and determine the frequency redistribution operator f. L ;

[0009] Step (4): Based on the time-frequency representation of energy concentration, an enhanced time-frequency representation is obtained using an improved synchronization compression operator;

[0010] Step (5): Determine the location and frequency of the wave grinding by the energy intensity in the time-frequency diagram, and calculate the wave grinding wavelength by combining the vehicle speed and frequency.

[0011] In step (1), the input signal is typically represented by a Gaussian window, and the window length and parameter N are determined based on the signal length. Let the signal be s(u), u be the time variable of the signal, and t be the time of the Taylor expansion. Performing a Taylor expansion at u = t yields:

[0012]

[0013] Where A is the amplitude of the signal, i is the imaginary unit, f(t) is the instantaneous frequency of the signal, f'(t) is the first derivative of the instantaneous frequency of the signal, ΔR1(u) is the Taylor expansion remainder term, and the amplitude of the signal at the instantaneous frequency position is:

[0014]

[0015] In the formula, g(ut) is a window function, since The influence of this factor causes the amplitude information to be smaller than the true value, and it can also be seen that... The existence of this is the main reason for the inaccuracy of amplitude information.

[0016] To reduce the interference of error terms, we introduce a kernel function. The expression for the time-frequency analysis method becomes:

[0017]

[0018] Where c(t) is the chirp rate. Based on this, the amplitude |Fm(t,f(t),c(t))| obtained at the instantaneous frequency is:

[0019]

[0020] When c(t) = f'(t), The obtained amplitude is approximately equal to the true value.

[0021] The key to obtaining accurate amplitude information is to determine the chirp rate c(t) that matches f'(t). This is considering the correspondence between the signal f'(t) and the angle β:

[0022] f'(t)=tan(β)·F s / (2T s )β∈(-π / 2,π / 2)

[0023] Where T s F is the sampling time of the signal. s Let c(t) = tan(β)·F. s / (2T s That is, the kernel function becomes The expression for the Matching Linear Chirplet Transform (MLCT) can be obtained as follows:

[0024]

[0025] MLCT transforms the chirp rate c(t) for finding a match into the angle β for finding a match. To determine the matching angle, β is discretized by dividing it into N equal parts:

[0026] β i =-π / 2+i·π / (N+1)i=1,2,...N

[0027] Let ci (t)=tan(β i )·F s / (2T s ), which can yield N corresponding kernel functions.

[0028] In step (2), the signal undergoes N time-frequency transformations to obtain N time-frequency representations. A kurtosis index is introduced to evaluate the energy concentration of the time-frequency representation at a given moment. The expression for kurtosis is:

[0029]

[0030] Where N a The frequency is represented by the number of frequency points at time t.

[0031] In step (3), the optimal rotation angle at each moment is found using the maximum kurtosis value:

[0032]

[0033] When N is larger The higher the accuracy, the better. When N=1, the algorithm degenerates into STFT.

[0034] Frequency redistribution operator f L It can be represented as:

[0035]

[0036] For a multi-component signal, assume that any frequency component of the signal satisfies f k+1 (t)-f k (t)>4Δ, k is the k-th component, and Δ is the discrete frequency interval. The Fourier transform of the window function reaches its maximum value at 0 frequency, therefore we can obtain:

[0037]

[0038] In step (4), an improved synchronization compression operator can be obtained based on the frequency redistribution operator:

[0039]

[0040] This leads to the enhanced time-frequency expression:

[0041]

[0042] In step (5), the location and frequency of corrugation are determined based on the energy intensity in the time-frequency diagram. The formula for calculating the wavelength of rail corrugation is as follows:

[0043] λ=v / f

[0044] Where v is the vehicle speed and f is the corrugation frequency, the corrugation wavelength is calculated based on the vehicle speed information and the corrugation frequency in the time-frequency diagram, thereby realizing the detection of corrugation in subway rails. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method of the present invention;

[0046] Figure 2 This is an acceleration sensor installed on the axle box of a vehicle in this invention;

[0047] Figure 3 This is a time-domain waveform diagram of the axle box acceleration signal in this invention;

[0048] Figure 4 This is a graph showing the kurtosis values ​​of each N at t = 0.6s in this invention.

[0049] Figure 5 This is a time-frequency distribution diagram of the axle box acceleration signal obtained by the new method in this invention;

[0050] Figure 6 This is the time-frequency distribution diagram of the axle box acceleration signal obtained by STFT in this invention; Detailed Implementation

[0051] The present invention will now be further described in conjunction with the accompanying drawings and examples.

[0052] The method of this invention takes the axle box acceleration signal collected by the China Academy of Railway Sciences on a subway line as an example. The collected train speed is 46.5 km / h, the sampling frequency is Fs = 10000 Hz, and the number of data points is 12000.

[0053] Signal acquisition such as Figure 2 As shown in the diagram, the acceleration sensor is first installed on the vehicle's axle box. Then, acceleration data is collected using a data acquisition device and transmitted to a computer for subsequent data processing and analysis using MATLAB software.

[0054] Figure 3 The image shows the time-domain waveform of the acquired axle box acceleration signal.

[0055] The window function is set to a Gaussian window with a window length of 550 and a parameter N of 7, resulting in 7 corresponding kernel functions.

[0056] The signal is subjected to time-frequency transformation of the corresponding kernel function seven times to obtain seven time-frequency graphs. The kurtosis is calculated along the frequency direction at each time point of the seven time-frequency graphs to obtain seven kurtosis values.

[0057]

[0058] Figure 4The kurtosis polygon obtained at t = 0.6s is used to find the optimal rotation angle at each time step using the maximum kurtosis value. This step is repeated at each time step.

[0059]

[0060] For a multi-component signal, assume that any frequency component of the signal satisfies f k+1 (t)-f k (t) > 4Δ, where k is the k-th component and Δ is the discrete frequency interval. The Fourier transform of the window function reaches its maximum value at 0 frequency, therefore the frequency redistribution operator f can be obtained. L :

[0061]

[0062] An improved synchronization compression operator can be obtained based on the frequency redistribution operator:

[0063]

[0064] This leads to a high-resolution time-frequency expression:

[0065]

[0066] Depend on Figure 5 It can be seen that corrugation has occurred on the line. According to the formula for calculating the wavelength of rail corrugation, λ=v / f, the wavelength of corrugation is about 136mm, thus realizing the detection of rail corrugation in the subway.

[0067] Depend on Figure 6 The results of STFT time-frequency analysis show that due to poor time-frequency convergence, the warping wavelength is 117-172 mm. In comparison, the improved enhanced time-frequency analysis method can effectively detect warping and accurately obtain the warping wavelength.

Claims

1. A method for rail corrugation detection based on enhanced time-frequency analysis, characterized in that: The method includes the following steps: Step (1): input the axle box acceleration signal, determine the window function and window length, determine the parameter N, determine the angle Divide the average into N parts to obtain N corresponding kernel functions; Step (2): Perform N time-frequency transformations on the signal according to the corresponding kernel function to obtain N time-frequency graphs. Calculate the kurtosis along the frequency direction at each time point of the N time-frequency plots to obtain N kurtosis values; Step (3): At each time point, the time-frequency representation corresponding to the maximum kurtosis is reserved to form a new time-frequency representation, and the maximum value in the frequency direction of the new time-frequency representation is found to determine the frequency reassignment operator ; Step (4): Based on the time-frequency representation of energy concentration, an enhanced time-frequency representation is obtained using an improved synchronization compression operator; Step (5): Determine the location and frequency of the wave grinding by the energy intensity in the time-frequency graph, and calculate the wave grinding wavelength by combining the vehicle speed and frequency; Step (3): At each time point, retain the time-frequency representation corresponding to the maximum kurtosis value to form a new time-frequency representation. Find the maximum value in the frequency direction of the new time-frequency representation to determine the frequency redistribution operator. ; Find the optimal rotation angle at each moment using the maximum kurtosis value: K is the kurtosis; t is the time of the Taylor expansion; To Discretization is performed, that is... Divide into N equal parts; when When it is larger, The higher the accuracy; when At that time, the algorithm degenerates into STFT; Frequency redistribution operator Represented as: To match the linear Chirplet transform; The instantaneous frequency of the signal; For a multi-component signal, assume that any frequency component of the signal satisfies , For the first One portion, For the discrete frequency range; the Fourier transform of the window function reaches its maximum value at 0 frequency, therefore we can obtain: Step (4): Based on the time-frequency representation of energy concentration, an enhanced time-frequency representation is obtained using an improved synchronization compression operator; An improved synchronization compression operator is derived based on the frequency redistribution operator: This leads to the enhanced time-frequency expression: It is the first derivative of the instantaneous frequency of the signal.

2. The rail corrugation detection method based on enhanced time-frequency analysis as described in claim 1, characterized in that: Step (1): Input the axle box acceleration signal, determine the window function and window length, determine the parameter N, and set the angle. Divide the data into N equal parts to obtain N corresponding kernel functions; For the input signal, a Gaussian window is typically chosen as the window function. The window length and parameter N are determined based on the signal length. Let the signal be... , For the time variable of this signal, When the time of Taylor expansion is given, the signal is at... Performing Taylor series, we get: in, The amplitude of the signal. The imaginary unit, The instantaneous frequency of the signal. The remainder of the Taylor expansion gives the amplitude of the signal at the instantaneous frequency position as: In the formula, For window functions; To reduce interference from error terms, a kernel function is introduced. The expression for the time-frequency analysis method becomes: in The chirp rate; based on this, the amplitude is obtained at the instantaneous frequency. for: when hour, The obtained amplitude is approximately equal to the true value; The key to obtaining accurate amplitude information is to determine and Matching chirp rate Considering the signal With angle There is a corresponding relationship: in The sampling time of the signal. Let be the sampling frequency; That is, the kernel function becomes The expression for the matched linear Chirplet transform is obtained as follows: Matching the linear Chirplet transform will find the matching chirp rate. Transformed into finding a matching angle To determine the matching angle, for Discretization is performed, that is... Divide into N equal parts: make This yields N corresponding kernel functions.

3. The rail corrugation detection method based on enhanced time-frequency analysis as described in claim 1, characterized in that: Step (2): Perform time-frequency transformation on the signal according to the corresponding kernel function N times to obtain N time-frequency graphs. Calculate the kurtosis along the frequency direction at each time point of the N time-frequency graphs to obtain N kurtosis values. Perform N time-frequency transformations on the signal to obtain N time-frequency representations; introduce a kurtosis index to evaluate the energy concentration of the time-frequency representation at a certain moment; the expression for kurtosis is: in For time-frequency representation in Frequency points at any given moment.

4. The rail corrugation detection method based on enhanced time-frequency analysis as described in claim 1, characterized in that: Step (5): Determine the location and frequency of the wave grinding by the energy intensity in the time-frequency graph, and calculate the wave grinding wavelength by combining the vehicle speed and frequency; The location of rail corrugation is detected based on the energy intensity in the time-frequency graph. The formula for calculating the wavelength of rail corrugation is as follows: in For vehicle speed, The corrugation frequency is used to calculate the corrugation wavelength based on the vehicle speed information and the corrugation frequency in the time-frequency diagram, thereby realizing the detection of corrugation in subway rails.

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