Railway track impact and corrugation combined disease time-frequency characteristic extraction method and device

Abstract

This invention provides a method and apparatus for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks. The method includes: determining a window length limit based on the discrete-time domain signal; using a third-order B-spline function as the window function for the Short-Time Fourier Transform (STFT) based on the discrete-time domain signal to determine the initial STFT time-frequency diagram and the initial Rayleigh entropy; utilizing the recursive property of the third-order B-spline function as the window function to determine the STFT result sequence and the Rayleigh entropy sequence of equal-length window sequences; determining the time-frequency transformation result and the optimal Rayleigh entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Rayleigh entropy, the STFT result sequence, and the Rayleigh entropy sequence; and determining the time-frequency characteristics of the impact signal and the corrugation signal based on the time-frequency transformation result and the optimal Rayleigh entropy. This invention can simultaneously, quickly, and effectively extract the time-frequency characteristics of the impact component and the corrugation component in railway track defects and express them on a time-frequency diagram.

Description

Technical Field

[0001] This invention relates to the field of track inspection technology, and in particular to a method and apparatus for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks. Background Technology

[0002] This section is intended to provide background or context for embodiments of the invention as set forth in the claims. The description herein is not an admission that it is prior art simply because it is included in this section.

[0003] The dynamic response signal of train vertical acceleration, collected by accelerometers mounted on the axle boxes of railway integrated inspection trains, may contain various high-frequency vibration components caused by short-wave irregularities in the railway track. Short-wave irregularities are a typical railway track defect, usually caused by factors such as bulges or depressions at rail welded joints, railhead corrugation, abrasion, or spalling. Its dynamic response has complex transient impact components and time-varying steady-state components. Defects such as poor welded joints, rail depressions, and spalling exhibit obvious transient impact characteristics in the acceleration time-domain signal; periodic defects such as rail corrugation and grinding marks show obvious peaks in the acceleration frequency-domain signal, corresponding to the wavelength of the defect. When the train is accelerating or braking, the frequency and amplitude of periodic defects change over time. Time-frequency analysis of this type of composite signal requires differentiation of signal components and characteristics at different time points to adopt an appropriate window length. Furthermore, in practical applications, it is necessary to obtain time-frequency analysis data quickly to promptly detect track defects.

[0004] Traditional time-frequency analysis methods have certain limitations when analyzing high-frequency dynamic response signals collected by accelerometers, and cannot simultaneously and quickly extract the time-frequency characteristics of impact and corrugation components in railway track defects.

[0005] Therefore, how to provide a new solution that can solve the above-mentioned technical problems is a technical challenge that urgently needs to be addressed in this field. Summary of the Invention

[0006] This invention provides a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks. This method can simultaneously, quickly, and effectively extract the time-frequency characteristics of both the impact and corrugation components in railway track defects and express them on a time-frequency graph. The method includes:

[0007] Determine the window length limit based on the discrete time domain signal;

[0008] Based on the discrete time domain signal, a third-order B-spline function is used as the window function of the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy.

[0009] By utilizing the recursive property of the third-order B-spline function as the window function, the STFT result sequence and Ruili entropy sequence of the equal-length window sequence are determined.

[0010] Based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence, determine the time-frequency transformation result and the optimal Ruili entropy;

[0011] Based on the time-frequency transformation results and the optimal Ruili entropy, the time-frequency characteristics of the impact signal and the wave milling signal are determined.

[0012] This invention also provides a device for extracting the time-frequency characteristics of combined track impact and corrugation defects, comprising:

[0013] The window length limit determination module is used to determine the window length limit based on the discrete time domain signal.

[0014] The module for determining the initial STFT time-frequency diagram and the initial Ruili entropy is used to determine the initial STFT time-frequency diagram and the initial Ruili entropy based on the discrete time domain signal and using a third-order B-spline function as the window function of the short-time Fourier transform STFT.

[0015] The module for determining the STFT result sequence and Ruili entropy sequence is used to determine the STFT result sequence and Ruili entropy sequence of the equal-length window sequence by utilizing the recursive property of the third-order B-spline function as the window function.

[0016] The module for determining the time-frequency transformation result and the optimal Ruili entropy is used to determine the time-frequency transformation result and the optimal Ruili entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence.

[0017] The module for determining the time-frequency characteristics of impact signals and wave milling signals is used to determine the time-frequency characteristics of impact signals and wave milling signals based on the time-frequency transformation results and the optimal Ruili entropy.

[0018] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0019] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0020] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-mentioned method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0021] This invention provides a method and apparatus for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks. The method includes: determining a window length limit based on a discrete-time domain signal; using a third-order B-spline function as the window function for the Short-Time Fourier Transform (STFT) based on the discrete-time domain signal to determine an initial STFT time-frequency diagram and an initial Rayleigh entropy; utilizing the recursive property of the third-order B-spline function as the window function to determine the STFT result sequence and Rayleigh entropy sequence of equal-length window sequences; determining the time-frequency transformation result and the optimal Rayleigh entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Rayleigh entropy, the STFT result sequence, and the Rayleigh entropy sequence; and determining the time-frequency characteristics of the impact signal and the corrugation signal based on the time-frequency transformation result and the optimal Rayleigh entropy. This invention provides a scheme for time-frequency analysis of high-frequency dynamic response signals in railways (Fast Adaptive Time-varying Window Length STFT, FATW-STFT), which can simultaneously, quickly, and effectively extract the time-frequency characteristics of the impact and corrugation components in railway track defects and express them on a time-frequency diagram. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0023] Figure 1 This is a schematic diagram of a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention.

[0024] Figure 2 This is a flowchart of a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention.

[0025] Figure 3 The image shows the time-domain plot and FFT spectrum of a method for extracting the time-frequency characteristics of combined track impact and corrugation defects in railways, according to an embodiment of the present invention.

[0026] Figure 4 This invention provides a normalized fourth-order central moment and optimal window length diagram for a method of extracting time-frequency characteristics of combined railway track impact and corrugation defects.

[0027] Figure 5 This is a diagram showing the final time-frequency transformation result of a method for extracting the time-frequency characteristics of combined track impact and corrugation defects according to an embodiment of the present invention.

[0028] Figure 6A schematic diagram of a computer device used to run a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to the present invention.

[0029] Figure 7 This is a schematic diagram of a device for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0031] Figure 1 This is a schematic diagram of a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention. Figure 1 As shown, this embodiment of the invention provides a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks. This method can simultaneously, quickly, and effectively extract the time-frequency characteristics of both the impact and corrugation components in railway track defects and express them on a time-frequency graph. The method includes:

[0032] Step 101: Determine the window length limit based on the discrete time domain signal;

[0033] Step 102: Based on the discrete time domain signal, a third-order B-spline function is used as the window function of the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy.

[0034] Step 103: Using the recursive property of the third-order B-spline function as the window function, determine the STFT result sequence and Ruili entropy sequence of the equal-length window sequence;

[0035] Step 104: Determine the time-frequency transformation result and the optimal Ruili entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence;

[0036] Step 105: Determine the time-frequency characteristics of the impact signal and the wave milling signal based on the time-frequency transformation results and the optimal Ruili entropy.

[0037] This invention provides a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks, comprising: determining a window length limit based on a discrete-time domain signal; determining an initial STFT time-frequency diagram and an initial Rayleigh entropy based on the discrete-time domain signal using a third-order B-spline function as the window function for the Short-Time Fourier Transform (STFT); determining the STFT result sequence and Rayleigh entropy sequence of equal-length window sequences using the recursive property of the third-order B-spline function as the window function; determining the time-frequency transformation result and the optimal Rayleigh entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Rayleigh entropy, the STFT result sequence, and the Rayleigh entropy sequence; and determining the time-frequency characteristics of the impact signal and the corrugation signal based on the time-frequency transformation result and the optimal Rayleigh entropy. This invention provides a scheme for time-frequency analysis of high-frequency dynamic response signals of railways (Fast Adaptive Time-varying Windowlength STFT, FATW-STFT), which can simultaneously, quickly, and effectively extract the time-frequency characteristics of the impact and corrugation components in railway track defects and express them on a time-frequency diagram.

[0038] The Short-Time Fourier Transform (STFT), developed from the classical Fourier Transform (FT), provides a powerful tool for time-frequency analysis of transient signals. However, STFT cannot adaptively select the window length, and using the same window length for time-varying signals can easily lead to the loss of signal components. The Wigner-Ville Distribution (WVD) eliminates the windowing operation in the calculation, improving the accuracy and energy concentration of time-frequency analysis. However, it only performs well for single signals and can introduce interference from cross-terms for complex signals with multiple components. With the development of wavelet transform (WT) theory, the wavelet basis form has solved the problem of the lack of flexibility in window length selection in STFT. However, selecting a wavelet basis is not easy. For complex high-frequency dynamic response signals of tracks, it is difficult to find a wavelet basis applicable to all types of track defect signals. Therefore, wavelet transform only performs well for stationary signals and is less effective at representing transient impact signals. Synchrosqueezing Transforms (SST) significantly improves the time-frequency analysis accuracy of STFT and WT, effectively separating and representing multi-component time-varying steady-state periodic signals. To express the transient characteristics of signals, a second-order adaptive synchronous synchrosqueezing transform (ASST) based on time-domain adaptive parameters is proposed. By introducing a time-varying frequency as a parameter for adaptive window length selection, it achieves extremely high analytical accuracy in the time-frequency analysis of multi-component linear frequency modulation (LFM) signals. However, when applied to high-frequency dynamic response signal analysis, it still cannot express the transient impact component. Furthermore, the energy and spectral components of periodic erosion and grinding marks in shortwave irregularities exhibit nonlinear changes over time, causing significant aliasing in the time-frequency representation results of ASST. Various time-domain adaptive time-frequency analysis algorithms developed from SST employ extensive and complex calculations in selecting time-domain adaptive parameters, resulting in a substantial increase in computation time. Therefore, research on time-frequency analysis methods applied to high-frequency dynamic response signals requires a new algorithm for fast adaptive selection of the window length in the time domain. To maximize computational speed while maintaining analytical accuracy, it is necessary not only to distinguish steady-state signals but also to provide a good representation of transient signals. Many scholars have proposed variable window length calculation methods and their algorithmic acceleration methods based on the original STFT.Furthermore, based on STFT, a fast time-frequency representation algorithm (Adaptive Fast Time-frequency Representation, AFTFR) is proposed. It utilizes the superior properties of the third-order B-spline function (Cubic B-Spline) as a window function, which greatly improves the calculation speed without sacrificing time-frequency resolution and performs well for analyzing signals with a certain degree of separation in the frequency domain. However, when processing high-frequency dynamic response signals, due to the high energy concentration and full-frequency domain characteristics of impulse signals, the method of analyzing each frequency point is prone to losing time-varying steady-state signals. Moreover, this method has strong frequency domain discontinuity when processing such mixed signals.

[0039] The aforementioned time-frequency analysis methods are all unable to simultaneously and rapidly extract the time-frequency characteristics of both impact and corrugation components in railway track defects. This invention proposes a fast method (Fast Adaptive Time-varying Window Length STFT, FATW-STFT) for time-frequency analysis of high-frequency dynamic response signals from railway tracks. This method can simultaneously and rapidly extract the time-frequency characteristics of both impact and corrugation components in railway track defects and express them on a time-frequency plot.

[0040] Figure 2 This is a flowchart illustrating a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention. Figure 2 As shown, in one embodiment of the method for extracting the time-frequency characteristics of combined impact and corrugation defects of railway tracks provided by the present invention, the method includes:

[0041] Determine the window length limit based on the discrete time domain signal;

[0042] Based on the discrete time domain signal, a third-order B-spline function is used as the window function of the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy.

[0043] By utilizing the recursive property of the third-order B-spline function as the window function, the STFT result sequence and Ruili entropy sequence of the equal-length window sequence are determined.

[0044] Based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence, determine the time-frequency transformation result and the optimal Ruili entropy;

[0045] Based on the time-frequency transformation results and the optimal Ruili entropy, the time-frequency characteristics of the impact signal and the wave milling signal are determined.

[0046] The main technical implementation process of this invention includes: firstly, using a third-order B-spline function β with an initial window length l0 = 5. 3(k) is used as the window function for the short-time Fourier transform, and the initial STFT result X0(k, ω) of the discrete-time signal x(k) is calculated. j ) and the initial Ruili entropy R0(k)

[13] ; at the same time, the normalized fourth-order central moment K of the discrete-time signal is calculated. N (k)

[14] and the boundary function f L [K N (k)]、f U [K N (k)]; then, using the recursive property of the third-order B-spline function as the window function, the STFT result {X} under the equal-length sequence window is quickly calculated. d (k, ω) j )} and the corresponding Ruili entropy R d (k); then, based on the window length limit and the minimum entropy of Ruili, determine the optimal window length corresponding to the d value at each time point. opt (k). The final time-frequency transformation result X(k, ω) j This involves splicing the STFT results under the optimal window length at each time point to obtain the time-frequency transformation result and the optimal Ruili entropy, and then analyzing the time-frequency characteristics of the impact signal and the wave milling signal.

[0047] In a specific implementation of the time-frequency characteristic extraction method for combined impact and corrugation defects of railway tracks provided in this invention, in one embodiment, determining the window length limit based on the discrete time-domain signal includes:

[0048] Determine the normalized fourth-order central moments based on the discrete-time domain signal;

[0049] Determine the boundary function based on the normalized fourth-order central moments;

[0050] Determine the window length limit based on the boundary function.

[0051] In a specific implementation of the time-frequency characteristic extraction method for combined railway track impact and corrugation defects provided in this invention, in one embodiment, the normalized fourth-order central moment is determined as follows:

[0052]

[0053]

[0054]

[0055]

[0056] Among them, K N(k) represents the normalized fourth-order central moment; k = 1, 2, ..., L are discrete time points; L is the time domain length of the signal; D is the data half-width of the moving average; K(k) reflects the discreteness of the dataset, with the half-width D (taking...) near time point k as... K(k) calculated from the data (where Fs is the sampling frequency of x(k)) reflects the degree of dispersion of the data in the range [kD, k+D]. The greater the degree of dispersion, the stronger the impact characteristics of the data, and the larger the value of K(k).

[0057] The aforementioned expression for determining the normalized fourth central moment is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0058] In the embodiment, the above formula (1) is the normalized fourth-order central moment K of the discrete-time domain signal x(k). N K(k) reflects the discreteness of the dataset, with the half-width D (taking k) around time point k as an example. K(k), calculated from data where Fs is the sampling frequency of x(k), reflects the dispersion of the data within the range [kD, k+D]. The greater the dispersion, the stronger the impulse characteristic, and the larger the value of K(k). For signals containing both transient impulse components and time-varying steady-state components, the duration of the impulse signal is relatively small compared to the total signal duration; therefore, the overall average K(k) value can be used. As the normalized denominator, and taking the logarithm to the base 10 as K. N (k) is used to evaluate the signal impact characteristics.

[0059] In a specific implementation of the time-frequency characteristic extraction method for combined impact and corrugation defects of railway tracks provided in this invention, in one embodiment, the boundary function is determined as follows:

[0060]

[0061]

[0062] Among them, K N (k) represents the normalized fourth-order central moment; f L [K N [(k)] is the minimum value of the bounding function; f U [K N [(k)] represents the maximum value of the limit function; M represents the total number of different window lengths used in the signal time-frequency analysis; j represents the amplitude constant; v represents the scaling constant; λ represents the bias constant; j, δ, and λ characterize the shape of the limit function.

[0063] The above-mentioned expression for determining the boundary function is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0064] In a specific implementation of the time-frequency characteristic extraction method for combined impact and corrugation defects of railway tracks provided in this embodiment of the invention, the window length limit is determined as follows:

[0065] f L [K N [(k)]<d(k)<f U [K N (k)] (7)

[0066] Among them, f L [K N [(k)] is the minimum value of the bounding function; f U [K N [(k)] is the maximum value of the limit function; d(k) is the window length limit, and d is the length of the window function.

[0067] The above-mentioned expression for determining the window length limit is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0068] In the embodiment, K at each time point is used N The value of (k) is used to initially filter the applicable window length, and two boundary functions f are constructed. L [K N (k)](Equation (5)), f U [K N (k) (Equation (6)) restricts the length of the window function, and the range of values ​​of d should satisfy equation (7).

[0069] Equation (7) above is the window length limit proposed in the embodiments of the present invention, where h, v, and λ are the amplitude constant, scale constant, and bias constant, respectively, representing the shape of the limit function. The present invention adopts v=2 and λ=0.75 are suitable for dynamic response signal analysis. The normalized fourth-order central moment and window length limit are calculated only once for the time-domain signal during the calculation process, resulting in a small overall computational load. The window length limit determines the applicable window length range at each time point.

[0070] In a specific implementation of the method for extracting the time-frequency characteristics of combined track impact and corrugation defects provided in this invention, in one embodiment, based on the discrete time-domain signal, a third-order B-spline function is used as the window function for the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy, including:

[0071] Based on the discrete-time domain signal, determine the time-frequency representation of the short-time Fourier transform (STFT);

[0072] A third-order B-spline function is used as the window function for the short-time Fourier transform to determine the initial STFT time-frequency diagram;

[0073] The initial Ruili entropy is determined based on the STFT time-frequency diagram.

[0074] In a specific implementation of the method for extracting the time-frequency characteristics of combined track impact and corrugation defects provided in this invention, in one embodiment, the time-frequency representation of the short-time Fourier transform (STFT) is determined as follows:

[0075]

[0076] Where X(k, ω) j ω represents the time-frequency representation of the Short-Time Fourier Transform (STFT); j =2πj / N, j = 0, 1, ..., N-1, N is the number of spectral lines; w(k) is the window function, k = 1, 2, ..., L is the discrete time point; L is the time domain length of the signal; l is the window length; Z is the total number of window lengths.

[0077] The above-mentioned expression for determining the time-frequency representation of the Short-Time Fourier Transform (STFT) is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0078] In the embodiment, the time-frequency expression of the discrete short-time Fourier transform of the discrete time-domain signal x(k) is given by the above equation (8).

[0079] In a specific implementation of the time-frequency characteristic extraction method for combined impact and corrugation defects of railway tracks provided in this invention, one embodiment utilizes the recursive property of a third-order B-spline function as a window function to determine the STFT result sequence and Ruili entropy sequence of equal-length window sequences, including:

[0080] Using the recursive property of the third-order B-spline function as the window function, and based on the time-frequency representation of the short-time Fourier transform (STFT), the recursive property of the window function is determined.

[0081] Based on the recursive property of the window function, calculate the STFT result sequence of the geometric window length sequence;

[0082] Based on the STFT result sequence, the Ruili entropy at each time point is determined, forming the Ruili entropy sequence.

[0083] In a specific implementation of the method for extracting the time-frequency characteristics of combined track impact and corrugation defects provided in this invention, in one embodiment, the window function is determined to apply recursive properties in the following manner:

[0084]

[0085] Among them, X 2m (k, ω) j Applying recursive properties to window functions; The time-domain discrete third-order B-spline function with integer scale m≥1 is: ω j =2πj / N, j = 0, 1, ..., N-1, N is the number of spectral lines; k = 1, 2, ..., L are discrete time points; L is the time domain length of the signal.

[0086] The above-mentioned expression for determining the window function using recursive properties is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0087] Considering the need for a time-domain variable window length and fast computation capability in this invention, a third-order B-spline function is used as the window function for the STFT. Due to the applications and advantages of B-spline functions in signal processing and time-frequency analysis, the theoretical and application basis for accelerating the algorithm using a third-order B-spline function is presented, and a time-domain discrete third-order B-spline function with integer scale m≥1 is derived. The recursive properties applied to the window function w(k) in equation (8) are shown in equation (9).

[0088] Equation (9) shows that the short-time Fourier transform X of the signal, with a time-domain discrete third-order B-spline function of scale 2m as the window function, is... 2m (k, ω) j The short-time Fourier transform X of the signal can be derived from a time-domain discrete third-order B-spline function with scale m as the window function. m (k, ω) j After performing four complex number additions, multiply by the coefficient. Thus, it is only necessary to calculate the STFT result X0(k, ω) with an initial window length l0 = 5. j Then, the recursive formula (9) can be used to quickly calculate the geometric window length sequence of l. d =5×2d (d = 1, 2, ..., M-1, l) d The STFT result sequence {X ≤ L, M is the total number of different window lengths used in the time-frequency analysis of this signal) d (k, ω) j )}.

[0089] In a specific implementation of the time-frequency characteristic extraction method for combined railway track impact and corrugation defects provided in this invention, in one embodiment, the Ruili entropy at each time point is determined as follows:

[0090]

[0091] Among them, R d (k) represents the Ruili entropy at each time point; X d (i, ω) j ) is the STFT result sequence {X d (k, ω) j The time-frequency plane corresponding to the d-value in )}; ω j =2πj / N, j = 0, 1, ..., N-1, N is the number of spectral lines; D is the half-width of the moving average data; k = 1, 2, ..., L are discrete time points; L is the signal time domain length; constant α = 2.5.

[0092] The above-mentioned expression for determining the Ruili entropy at each time point is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0093] In this embodiment, Ruili entropy is a commonly used method for evaluating the concentration of time-frequency distributions. To adaptively select the optimal window length for each time point, the Ruili entropy at each time point is used as the evaluation parameter for the STFT result sequence {X}. d (k, ω) j A measure of concentration. For a given d, X d (k, ω) j The entropy R of Ruili at each time point d (k) can be expressed as equation (10).

[0094] R d The smaller the value of (k), the higher the time-frequency resolution of the data. This means that for time point k, using R... d (k) The window length l corresponding to the minimum value d (k) enables the most concentrated energy in the time-frequency representation at that point in time. For the STFT result sequence {X} d (k, ω) jFor each time-frequency plane of {R}, the corresponding Ruili entropy is calculated according to equation (10), thus obtaining the Ruili entropy sequence {R}. d (k)}.

[0095] In a specific implementation of the time-frequency characteristic extraction method for combined impact and corrugation defects of railway tracks provided in this invention, in one embodiment, the time-frequency transformation result and the optimal Ruili entropy are determined based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence, including:

[0096] Based on the initial Ruili entropy and the Ruili entropy sequence, the optimal Ruili entropy value is determined. Combined with the window length limit, a double screening is performed to determine the window function value corresponding to the optimal window length at each time point.

[0097] Based on the optimal window length corresponding to the window function value at each time point, determine the initial STFT time-frequency diagram and the time-frequency plane corresponding to the STFT result sequence at each time point under the optimal window length, and stitch the time-frequency planes together to determine the time-frequency transformation result.

[0098] In a specific implementation of the time-frequency characteristic extraction method for combined railway track impact and corrugation defects provided in this invention, in one embodiment, the window function value corresponding to the optimal window length at each time point is determined as follows:

[0099]

[0100] Where, d opt (k) represents the window function value corresponding to the optimal window length at each time point; R d (k) represents the Ruili entropy at each time point; f L [K N [(k)] is the minimum value of the bounding function; f U [K N [(k)] is the maximum value of the limit function; d(k) is the window length limit, and d is the length of the window function.

[0101] The aforementioned expression for determining the window function value corresponding to the optimal window length at each time point is for illustrative purposes only. Those skilled in the art will understand that, in practice, the above formula can be modified in a certain way and other parameters or data can be added, or other specific formulas can be provided. All such variations should fall within the protection scope of this invention.

[0102] In the embodiments, as shown in equation (11), the present invention uses the optimal values ​​of window length limits and Ruili entropy to pair {X}. d (k, ω) j Double filtering is performed to obtain the optimal window length d value for each time point. opt (k); Final time-frequency transformation result X final(k, ω) j This can be viewed as the optimal window length at each time point. STFT results The spliced ​​result represents the Fourier transform result performed with the corresponding optimal window length at each time point, which has the most concentrated energy and the highest time-frequency resolution.

[0103] In a specific implementation of the method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks provided by this invention, in one embodiment, the time-frequency characteristics of the impact signal and the corrugation signal are determined based on the time-frequency transformation results and the optimal Ruili entropy, including:

[0104] Based on the time-frequency transformation results and the optimal Ruili entropy, the time point of the impact component, the characteristic frequency of the erosion component, and the energy change of the erosion component over time are determined.

[0105] The time-frequency characteristics of the impact signal and the erosion signal are determined based on the time point of the impact component, the characteristic frequency of the erosion component, and the change of the energy of the erosion component over time.

[0106] The following is a brief description of a method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks, provided by an embodiment of the present invention, using a specific scenario as an example:

[0107] The specific calculation process of the time-frequency transformation method FATW-STFT proposed in this embodiment of the invention can be described as follows:

[0108] (a) For the discrete-time domain signal x(k), calculate K N (k), f L [K N (k)] and f U [K N (k)];

[0109] (b) β with an initial window length l0 = 5 3 Using (k) as the window function of the STFT, the initial time-frequency plane X0(k, ω) of x(k) is calculated. j (At this point, d = 0), and a copy of this data is made to store the final time-frequency transformation result X. final (k, ω) j ), denoted as X (0) (k, ω) j );

[0110] (c) For X0(k, ω) j Calculate the initial Ruili entropy R0(k) as it changes over time, and then make a copy of this data to store the optimal Ruili entropy R at each time point in the final result. opt (k), denoted as R (0) (k);

[0111] (d) Step, d increases by 1;

[0112] (e) Quickly calculate the next window long sequence l d STFT results X d (k, ω) j At this point, the result X of the previous long sequence... d-1 (k, ω) j (This can be deleted to save storage space;)

[0113] (f) For X d (k, ω) j Calculate the time-varying entropy R of Ruili. d (k), and determine R d (k) Does it satisfy the window length limit and R? d (k)<R d-1 (k), the time point at which the two conditions are satisfied is denoted as k. i (i = 1, 2, ...);

[0114] (g) X d (k i ω j Replace X with data (d-1) (k i ω j The corresponding data in ) are used to form a new time-frequency plane X. (d) (k, ω) j );

[0115] (h) R d (k i Replace R with data (d-1) (k i The corresponding data in the () are used to form a new Ruili entropy optimization result R. (d) (k), at this time, R d-1 (k) can be deleted to save storage space;

[0116] (i) Repeat steps (d) to (h) until d traverses from 1 to M-1, and finally obtain the time-frequency transformation result X. final (k, ω) j That is, X when d = M-1. (M-1) (k, ω) j The final entropy optimization result R for Ruili is... opt (k) is R (M-1) (k);

[0117] (j) Based on the time-frequency transformation result X final (k, ω) j ) and the optimal Ruili entropy R opt(k) determines the time point of the impact component, the characteristic frequency of the erosion component, and the change of the energy of the erosion component over time, thereby determining the time-frequency characteristics of the impact signal and the erosion signal.

[0118] The proposed time-frequency characteristic extraction method for combined rail impact and corrugation defects based on Time-Frequency Transform (FATW-STFT) was applied to the analysis of measured axle box acceleration signals on a heavy-haul railway line. This signal, a vibration signal, was acquired by a vertical acceleration sensor installed on the left axle box of a heavy-haul integrated testing train. The train's speed was 67 km / h, the selected signal length was 1000 ms, and the acceleration sensor's sampling frequency Fs = 2000 Hz. This section contained rail corrugation of varying intensities, interspersed with a transient rail joint impact.

[0119] The time-domain plot and FFT spectrum of the signal are as follows: Figure 3 As shown, where, Figure 3 In the diagram, (a) represents the time-domain plot and (b) represents the FFT spectrum, characterizing the measured acceleration signal of the left axle box on a heavy-load track. The time-domain plot shows rail joint impact around t = 491.7 ms, with varying degrees of rail corrugation in other sections, and stronger corrugation energy between t = 250 ms and 650 ms. The spectrum shows a dominant frequency component f = 131 Hz, corresponding to a corrugation wavelength λ = 142.1 mm, and local spectral peaks at f = 768 Hz and f = 860 Hz, possibly indicating other types of damage.

[0120] The graphs showing the changes in the normalized central moment and the optimal window length over time during the calculation process of the method of this invention are shown below. Figure 4 As shown, where, Figure 4 In the diagram, (a) represents the normalized fourth central moment, and (b) represents the optimal window length. The graphs showing the changes of the normalized central moment and the optimal window length over time during the calculation process of the method of this invention are shown below. Figure 4 As shown, it can be seen that the impact characteristics are stronger in the segment around t=495ms, K N The value of (k) reaches 1.754, therefore the optimal window length in this vicinity is relatively small. The final time-frequency transform result is as follows: Figure 5 As shown.

[0121] from Figure 5 As can be seen, applying the method of this invention to the dynamic response signal analysis of the axial acceleration of the comprehensive inspection vehicle, the analysis results clearly express the time-frequency characteristics of the impact signal and the pulsation signal in the time-frequency diagram. An impact signal exists near t = 495 ms, and... Figure 3 (a) and Figure 4The results are consistent with (a) in the above. The main frequency component of the wave-scraping signal is f = 131 Hz, corresponding to a wave-scraping wavelength λ = 142.1 mm, and there is a certain energy concentration at f = 768 Hz and f = 860 Hz, which is consistent with... Figure 3 The result is consistent with (b) in the text. From Figure 5 The varying shades of grayscale gradients indicate different degrees of energy change in the wave-mold signal over time. The wave-mold signal energy is stronger in the t = 250ms to 650ms range. Figure 3 (a) and Figure 4 The results are consistent with (a) in the previous section. The analysis of this group of signals took 1.45 seconds, which is a relatively fast calculation speed. Therefore, the method of this invention can quickly and effectively extract the time-frequency characteristics of the combined defects of railway track impact and corrugation.

[0122] The core of this invention lies in a time-frequency representation method that splices together the short-time Fourier transform results of the optimal window length at each time point, based on the boundary function and window length boundary proposed by the normalized fourth-order central moment, and by combining the window length boundary and Ruili entropy to evaluate the time-domain impact characteristics and energy concentration of the signal.

[0123] This invention uses time-frequency transformation to represent the time point where the impact component is located on the time-frequency graph; it also uses time-frequency transformation to represent all characteristic frequencies of the erosion component on the time-frequency graph; and it uses time-frequency transformation to represent the energy change of the erosion component over time on the time-frequency graph. The time-frequency transformation method has a relatively fast calculation speed.

[0124] Figure 6 A schematic diagram of the computer equipment used to run the method for extracting the time-frequency characteristics of combined impact and corrugation defects of railway tracks according to the present invention is shown below. Figure 6 As shown, this embodiment of the invention also provides a computer device 600, including a memory 610, a processor 620, and a computer program 630 stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0125] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0126] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-mentioned method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects.

[0127] This invention also provides a device for extracting the time-frequency characteristics of combined railway track impact and corrugation defects, as described in the following embodiments. Since the principle by which this device solves the problem is similar to that of a method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects, the implementation of this device can refer to the implementation of a method for extracting the time-frequency characteristics of combined railway track impact and corrugation defects; therefore, repeated details will not be elaborated upon.

[0128] Figure 7 This is a schematic diagram of a device for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks according to an embodiment of the present invention. Figure 7 As shown in the figure, this embodiment of the invention also provides a device for extracting the time-frequency characteristics of combined defects of railway track impact and corrugation.

[0129] In one embodiment of the present invention, a device for extracting the time-frequency characteristics of combined track impact and corrugation defects is provided.

[0130] The window length limit determination module 701 is used to determine the window length limit based on the discrete time domain signal.

[0131] The initial STFT time-frequency diagram and initial Ruili entropy determination module 702 is used to determine the initial STFT time-frequency diagram and initial Ruili entropy based on the discrete time domain signal and using a third-order B-spline function as the window function of the short-time Fourier transform STFT.

[0132] The STFT result sequence and Ruili entropy sequence determination module 703 is used to determine the STFT result sequence and Ruili entropy sequence of the equal window length sequence by utilizing the recursive property of the third-order B-spline function as the window function.

[0133] The time-frequency transformation result and optimal Ruili entropy determination module 704 is used to determine the time-frequency transformation result and optimal Ruili entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence and the Ruili entropy sequence;

[0134] The time-frequency characteristic determination module 705 for impact signal and wave milling signal is used to determine the time-frequency characteristics of impact signal and wave milling signal based on the time-frequency transformation result and the optimal Ruili entropy.

[0135] In summary, the present invention provides a method and apparatus for extracting the time-frequency characteristics of combined impact and erosion defects in railway tracks, comprising: determining a window length limit based on a discrete-time domain signal; determining an initial STFT time-frequency diagram and an initial Rayleigh entropy based on the discrete-time domain signal using a third-order B-spline function as the window function for the Short-Time Fourier Transform (STFT); determining the STFT result sequence and Rayleigh entropy sequence of equal-length window sequences using the recursive property of the third-order B-spline function as the window function; determining the time-frequency transformation result and the optimal Rayleigh entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Rayleigh entropy, the STFT result sequence, and the Rayleigh entropy sequence; and determining the time-frequency characteristics of the impact signal and the erosion signal based on the time-frequency transformation result and the optimal Rayleigh entropy. The present invention provides a scheme for time-frequency analysis of high-frequency dynamic response signals of railways (Fast Adaptive Time-varying Window Length STFT, FATW-STFT), which can simultaneously, quickly, and effectively extract the time-frequency characteristics of the impact and erosion components in railway track defects and express them on a time-frequency diagram.

[0136] The acquisition, storage, use, and processing of data in this application comply with the relevant provisions of national laws and regulations. All types of data, including personal identity data, operational data, and behavioral data related to individuals, customers, and groups, obtained in this application have been authorized.

[0137] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0138] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0139] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0140] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0141] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks, characterized in that, include: Determine the window length limit based on the discrete time domain signal; Based on the discrete time domain signal, a third-order B-spline function is used as the window function of the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy. By utilizing the recursive property of the third-order B-spline function as the window function, the STFT result sequence and Ruili entropy sequence of the equal-length window sequence are determined. Based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence, determine the time-frequency transformation result and the optimal Ruili entropy; Based on the time-frequency transformation results and the optimal Ruili entropy, the time-frequency characteristics of the impact signal and the wave milling signal are determined; Based on the window length limit, initial STFT time-frequency plot, initial Rayli entropy, STFT result sequence, and Rayli entropy sequence, the time-frequency transformation result and optimal Rayli entropy are determined, including: determining the optimal Rayli entropy value based on the initial Rayli entropy and Rayli entropy sequence; performing double screening based on the window length limit to determine the window function value corresponding to the optimal window length at each time point; determining the time-frequency plane corresponding to the initial STFT time-frequency plot and STFT result sequence at each time point under the optimal window length based on the optimal window function value corresponding to the optimal window length at each time point; and stitching the time-frequency planes to determine the time-frequency transformation result. Based on the time-frequency transformation results and the optimal Ruili entropy, the time-frequency characteristics of the impact signal and the ripple signal are determined, including: based on the time-frequency transformation results and the optimal Ruili entropy, determining the time point where the impact component is located, the characteristic frequency of the ripple component, and the change of the energy of the ripple component over time; and based on the time point where the impact component is located, the characteristic frequency of the ripple component, and the change of the energy of the ripple component over time, determining the time-frequency characteristics of the impact signal and the ripple signal.

2. The method as described in claim 1, characterized in that, Based on the discrete-time domain signal, determine the window length limits, including: Determine the normalized fourth-order central moments based on the discrete-time domain signal; Determine the boundary function based on the normalized fourth-order central moments; Determine the window length limit based on the boundary function.

3. The method as described in claim 2, characterized in that, The normalized fourth central moments are determined as follows: in, Normalized fourth-order central moments; For discrete time points; The signal's time domain length; The data width is half the width of the moving average. This reflects the degree of dispersion of the dataset, in terms of discrete time points. Nearby half width D Calculated from discrete-time signals Reflects [ kD , k+D The degree of discreteness of a discrete-time signal within a given range; the greater the degree of discreteness, the stronger its impulse characteristics. The larger the value, the better. Discrete time points The discrete-time domain signal at that location.

4. The method as described in claim 2, characterized in that, Determine the boundary function as follows: in, Normalized fourth-order central moments; This represents the minimum value of the bounding function; This represents the maximum value of the bounding function; The total number of different window lengths used for signal time-frequency analysis; It is the amplitude constant; It is a scale constant; This is the bias constant; , and Characterizes the shape of the bounding function.

5. The method as described in claim 2, characterized in that, Determine the window length limits as follows: in, This represents the minimum value of the bounding function; This represents the maximum value of the bounding function; As the boundary of the window, The value for the length of the window function.

6. The method as described in claim 1, characterized in that, Based on the discrete-time signal, a third-order B-spline function is used as the window function for the short-time Fourier transform (STFT) to determine the initial STFT time-frequency diagram and the initial Ruili entropy, including: Based on the discrete-time domain signal, determine the time-frequency representation of the short-time Fourier transform (STFT); A third-order B-spline function is used as the window function for the short-time Fourier transform to determine the initial STFT time-frequency diagram; The initial Ruili entropy is determined based on the STFT time-frequency diagram.

7. The method as described in claim 6, characterized in that, The time-frequency representation of the Short-Time Fourier Transform (STFT) is determined as follows: in, This is the time-frequency representation of the Short Time Fourier Transform (STFT). , N This represents the number of spectral lines. For window functions, For discrete time points; The signal's time domain length; For window length; The total length of the window.

8. The method as described in claim 6, characterized in that, Using the recursive properties of the third-order B-spline function as the window function, the STFT result sequence and Ruili entropy sequence of the geometrically long window sequence are determined, including: Using the recursive property of the third-order B-spline function as the window function, and based on the time-frequency representation of the short-time Fourier transform (STFT), the recursive property of the window function is determined. Based on the recursive property of the window function, calculate the STFT result sequence of the geometric window length sequence; Based on the STFT result sequence, the Ruili entropy at each time point is determined, forming the Ruili entropy sequence.

9. The method as described in claim 8, characterized in that, Determine the application of recursive properties to window functions as follows: in, For scale 2 m The time-domain discrete third-order B-spline function is used as the window function for the short-time Fourier transform of the signal. For scale m The time-domain discrete third-order B-spline function is used as the window function for the short-time Fourier transform of the signal; Integer scale m The time-domain discrete third-order B-spline function with ≥1 is: ; , N This represents the number of spectral lines. For discrete time points; The time domain length of the signal.

10. The method as described in claim 8, characterized in that, The Ruili entropy at each point in time is determined as follows: in, The entropy of Ruili at each point in time; STFT result sequence Chinese correspondence The time-frequency plane of the value; , N This represents the number of spectral lines. The data width is half the width of the moving average. For discrete time points; The time domain length of the signal; a constant. .

11. The method as described in claim 1, characterized in that, The optimal window length for each time point is determined as follows: in, The window function values ​​corresponding to the optimal window length at each time point are determined. The entropy of Ruili at each point in time; This represents the minimum value of the bounding function; This represents the maximum value of the bounding function; As the boundary of the window, The value for the length of the window function.

12. A device for extracting the time-frequency characteristics of combined impact and corrugation defects in railway tracks, characterized in that, include: The window length limit determination module is used to determine the window length limit based on the discrete time domain signal. The module for determining the initial STFT time-frequency diagram and the initial Ruili entropy is used to determine the initial STFT time-frequency diagram and the initial Ruili entropy based on the discrete time domain signal and using a third-order B-spline function as the window function of the short-time Fourier transform STFT. The module for determining the STFT result sequence and Ruili entropy sequence is used to determine the STFT result sequence and Ruili entropy sequence of the equal-length window sequence by utilizing the recursive property of the third-order B-spline function as the window function. The module for determining the time-frequency transformation result and the optimal Ruili entropy is used to determine the time-frequency transformation result and the optimal Ruili entropy based on the window length limit, the initial STFT time-frequency diagram, the initial Ruili entropy, the STFT result sequence, and the Ruili entropy sequence. The module for determining the time-frequency characteristics of impact signals and wave-swelling signals is used to determine the time-frequency characteristics of impact signals and wave-swelling signals based on the time-frequency transformation results and the optimal Ruili entropy. Based on the window length limit, initial STFT time-frequency plot, initial Rayli entropy, STFT result sequence, and Rayli entropy sequence, the time-frequency transformation result and optimal Rayli entropy are determined, including: determining the optimal Rayli entropy value based on the initial Rayli entropy and Rayli entropy sequence; performing double screening based on the window length limit to determine the window function value corresponding to the optimal window length at each time point; determining the time-frequency plane corresponding to the initial STFT time-frequency plot and STFT result sequence at each time point under the optimal window length based on the optimal window function value corresponding to the optimal window length at each time point; and stitching the time-frequency planes to determine the time-frequency transformation result. Based on the time-frequency transformation results and the optimal Ruili entropy, the time-frequency characteristics of the impact signal and the ripple signal are determined, including: based on the time-frequency transformation results and the optimal Ruili entropy, determining the time point where the impact component is located, the characteristic frequency of the ripple component, and the change of the energy of the ripple component over time; and based on the time point where the impact component is located, the characteristic frequency of the ripple component, and the change of the energy of the ripple component over time, determining the time-frequency characteristics of the impact signal and the ripple signal.

13. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 11.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 11.

15. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 11.

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