Rail short wave unevenness spectrum fitting method and device

Abstract

The application discloses a track short-wave unevenness spectrum fitting method and device, and relates to the field of track unevenness spectrum fitting. The method comprises the following steps: acquiring track surface roughness test data of a ballastless track high-speed rail line; performing power spectrum feature analysis on the track surface roughness test data to determine a mean spectrum, an upper limit spectrum and a lower limit spectrum of the track short-wave unevenness spectrum; performing segmented linear fitting processing on the mean spectrum according to the determined segmented features of the track short-wave unevenness spectrum to obtain a first fitting formula of the track short-wave unevenness spectrum; performing supplementary fitting processing on the first fitting formula according to the upper limit spectrum and the lower limit spectrum to obtain a second fitting formula of the track short-wave unevenness spectrum; and the supplementary fitting processing is used for describing the upper and lower boundary levels of the track short-wave unevenness spectrum. The application can realize segmented fitting of the mean spectrum of the track short-wave unevenness, improve the evaluation efficiency and accuracy of the track unevenness state, and perfect the evaluation of the high-speed track geometric state.

Description

Technical Field

[0001] This invention relates to the field of railway track technology, and in particular to a method and apparatus for fitting shortwave irregularity spectra of tracks. Background Technology

[0002] This section is intended to provide background or context for the embodiments of the invention 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] In high-speed railway systems, the track serves as a crucial support for train operation. Geometric irregularities in the track can exacerbate the dynamic interaction between the vehicle and the track, shorten the maintenance cycle and service life of both the train and track structures, and even affect the safety and stability of high-speed train operation. Therefore, scientifically and accurately evaluating track smoothness is an essential requirement for maintaining the service performance of high-speed railway tracks.

[0004] Among various methods for evaluating track smoothness, the track irregularity spectrum, as an indicator describing the change of track smoothness with spatial frequency, is an effective tool for characterizing the amplitude-frequency characteristics of track irregularities.

[0005] Currently, track irregularity spectra are mostly obtained by fitting test data from large-scale inspection equipment such as track inspection vehicles. Current research on high-speed railway track irregularity spectra focuses on wavelengths of 2 meters and above, as existing equipment struggles to accurately measure short-wavelength irregularities below 2 meters. Furthermore, as the operational lifespan of high-speed railways increases, the geometry of existing tracks gradually changes, and a track irregularity spectrum that accurately describes the current track geometry is still lacking. Moreover, due to increased train speeds, the excitation of wheel systems by short-wavelength track irregularities becomes increasingly prominent, and no solution currently exists for this problem. Summary of the Invention

[0006] This invention provides a method for fitting shortwave irregularity spectra of a track surface to achieve piecewise fitting of the mean spectrum of shortwave irregularities on the track surface, thereby improving the efficiency and accuracy of assessing track irregularity conditions and enhancing the evaluation of the geometric state of high-speed tracks. The method includes:

[0007] Obtain test data on the surface roughness of ballastless track high-speed railway lines;

[0008] Power spectrum characteristic analysis was performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum;

[0009] Based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to segmented linear fitting to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0010] Based on the upper limit spectrum and the upper limit spectrum, the first fitting formula is supplemented by a fitting process to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting process is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0011] This invention also provides a track shortwave irregularity spectrum fitting device for segmented fitting of the mean spectrum of track surface shortwave irregularities, improving the efficiency and accuracy of track irregularity assessment and perfecting the evaluation of high-speed track geometry. The device includes:

[0012] The test data acquisition module is used to acquire the track surface roughness test data of ballastless track high-speed railway lines;

[0013] The power spectrum feature analysis module is used to perform power spectrum feature analysis on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum.

[0014] The piecewise linear fitting module is used to perform piecewise linear fitting on the mean spectrum based on the determined piecewise characteristics of the orbital shortwave irregularity spectrum, so as to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0015] The supplementary fitting module is used to perform supplementary fitting processing on the first fitting formula based on the upper limit spectrum and the upper limit spectrum to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting processing is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0016] 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-described orbital shortwave irregularity spectrum fitting method.

[0017] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described orbital shortwave irregularity spectrum fitting method.

[0018] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described orbital shortwave irregularity spectrum fitting method.

[0019] In this embodiment of the invention, track surface roughness test data of a ballastless track high-speed railway line is acquired; power spectrum feature analysis is performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track short-wavelength irregularity spectrum; based on the determined segmented characteristics of the track short-wavelength irregularity spectrum, piecewise linear fitting processing is performed on the mean spectrum to obtain a first fitting formula for the track short-wavelength irregularity spectrum; based on the upper limit spectrum and the upper limit spectrum, supplementary fitting processing is performed on the first fitting formula to obtain a second fitting formula for the track short-wavelength irregularity spectrum; the supplementary fitting processing is used to describe the track surface short-wavelength irregularity spectrum. By establishing horizontal upper and lower boundaries, a piecewise fitting of the mean spectrum of short-wavelength irregularities on the track surface is achieved. This solves the problem of accurately measuring short-wavelength irregularities with wavelengths below 2m under existing technologies, making the analysis of track irregularities more accurate and the assessment of track irregularity conditions more efficient. Furthermore, by supplementing the fitting of the upper and lower bound spectra, the upper and lower boundary levels of the track surface short-wavelength irregularity spectrum can be further described. Therefore, it is possible to evaluate the short-wavelength irregularity condition of high-speed railway tracks more scientifically and accurately, improve the evaluation of the geometric state of high-speed tracks, and provide reference and guidance for wheel-rail vibration and noise analysis. Attached Figure Description

[0020] 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:

[0021] Figure 1 This is a flowchart illustrating a method for fitting the orbital shortwave irregularity spectrum in an embodiment of the present invention.

[0022] Figure 2 This is a schematic diagram comparing a short-wave roughness level with a standard limit in an embodiment of the present invention;

[0023] Figure 3 This is a specific example diagram of a shortwave irregularity spectrum of a high-speed railway ballastless track surface in an embodiment of the present invention;

[0024] Figure 4 This is a specific example diagram of a shortwave irregularity spectrum fitting method according to an embodiment of the present invention;

[0025] Figure 5 This is a schematic diagram of a short-wave irregularity fitting spectrum of a high-speed railway ballastless track surface in an embodiment of the present invention;

[0026] Figure 6 This is a structural example diagram of a shortwave irregularity spectrum fitting device according to an embodiment of the present invention;

[0027] Figure 7 This is a schematic diagram of the system composition structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0028] 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.

[0029] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0030] In the description of this specification, the terms "comprising," "including," "having," and "containing" are open-ended terms, meaning that they include but are not limited to. The terms "an embodiment," "a specific embodiment," "some embodiments," and "for example," etc., refer to specific features, structures, or characteristics described in connection with that embodiment or example that are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. The order of steps involved in the various embodiments is used to illustrate the implementation of this application, and the order of steps is not limited and can be adjusted appropriately as needed.

[0031] The acquisition, storage, use, and processing of data in this application all comply with the relevant provisions of national laws and regulations.

[0032] In high-speed railway systems, the track serves as a crucial support for train operation. Geometric irregularities in the track can exacerbate the dynamic interaction between the vehicle and the track, shorten the maintenance cycle and service life of both the train and track structures, and even affect the safety and stability of high-speed train operation. Therefore, scientifically and accurately evaluating track smoothness is essential for maintaining the service performance of high-speed railway tracks. Among various track smoothness evaluation methods, the track irregularity spectrum, as an indicator describing the variation of track smoothness with spatial frequency, is an effective tool for characterizing the amplitude-frequency characteristics of track irregularities.

[0033] Track irregularity spectra are mostly obtained by fitting test data from large-scale inspection equipment such as track inspection vehicles. Current research on high-speed railway track irregularity spectra focuses on wavelengths of 2m and above, as existing equipment struggles to accurately measure short-wavelength irregularities below 2m. With the increasing operational lifespan of high-speed railways, the geometry of existing tracks gradually changes, and a track irregularity spectrum that accurately describes the current track geometry is still lacking. Furthermore, due to increased train speeds, the excitation of wheel systems by short-wavelength track irregularities becomes increasingly prominent. To address this issue, this invention, based on extensive high-speed railway track surface roughness test data, studies a fitting expression scheme for short-wavelength track irregularity spectra.

[0034] This invention provides a method for fitting shortwave irregularity spectra of a track surface, which is used to achieve piecewise fitting of the mean spectrum of shortwave irregularities on the track surface, improving the efficiency and accuracy of assessing track irregularity conditions and perfecting the evaluation of the geometric state of high-speed tracks. (See also...) Figure 1 The method may include:

[0035] Step 101: Obtain the track surface roughness test data for ballastless track high-speed railway lines;

[0036] Step 102: Perform power spectrum characteristic analysis on the above track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum;

[0037] Step 103: Based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, perform piecewise linear fitting on the mean spectrum to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0038] Step 104: Based on the above upper limit spectrum and upper limit spectrum, perform supplementary fitting processing on the above first fitting formula to obtain the second fitting formula for the orbital short-wave irregularity spectrum; the above supplementary fitting processing is used to describe the upper and lower boundary levels of the orbital short-wave irregularity spectrum.

[0039] In this embodiment of the invention, track surface roughness test data of a ballastless track high-speed railway line is obtained; power spectrum feature analysis is performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track short-wavelength irregularity spectrum; based on the determined segmented characteristics of the track short-wavelength irregularity spectrum, the mean spectrum is subjected to segmented linear fitting processing to obtain a first fitting formula for the track short-wavelength irregularity spectrum; based on the upper limit spectrum and the upper limit spectrum, the first fitting formula is subjected to supplementary fitting processing to obtain a second fitting formula for the track short-wavelength irregularity spectrum; the supplementary fitting processing is used to describe the track surface short-wavelength irregularity spectrum. By establishing horizontal upper and lower boundaries, a piecewise fitting of the mean spectrum of short-wavelength irregularities on the track surface is achieved. This solves the problem of accurately measuring short-wavelength irregularities with wavelengths below 2m under existing technologies, making the analysis of track irregularities more accurate and the assessment of track irregularity conditions more efficient. Furthermore, by supplementing the fitting of the upper and lower bound spectra, the upper and lower boundary levels of the track surface short-wavelength irregularity spectrum can be further described. Therefore, it is possible to evaluate the short-wavelength irregularity condition of high-speed railway tracks more scientifically and accurately, improve the evaluation of the geometric state of high-speed tracks, and provide reference and guidance for wheel-rail vibration and noise analysis.

[0040] In practice, the first step is to obtain the surface roughness test data of the ballastless track high-speed railway line.

[0041] In this embodiment, the test section of the above-mentioned rail surface roughness test data includes the main line of the section and the main line of the station area; the planar alignment of the above-mentioned rail surface roughness test data includes straight lines and curves; the rail surface state of the above-mentioned rail surface roughness test data includes corrugated condition data and non-corrugated condition data, and the corrugated condition data includes data before and after the grinding operation.

[0042] In one embodiment, rail surface roughness test data from multiple ballastless track high-speed railway lines can be collected, their power spectrum characteristics analyzed, and a piecewise power function can be used to fit the expression formula for the short-wave irregularity spectrum of the rail surface. In this embodiment, a rail corrugation testing trolley can be used to conduct measurement tests on multiple ballastless track high-speed railway lines, and the short-wave irregularity state of the rail surface can be recorded at 1mm sampling intervals. The test section can cover both the main line of the section and the main line of the station area; the planar alignment can include straight lines, large-radius curves, and small-radius curves; the rail surface condition can include corrugated and non-corrugated conditions, wherein the corrugated section can include test data before and after grinding operations.

[0043] The inventor discovered: Combining Figure 2 , Figure 2The short-wavelength roughness grades of the rail surface were given using a 1 / 3 octave band wavelength spectrum. Due to rail corrugation in some test sections, the roughness grade was particularly prominent at the center wavelength of 63 mm in the 1 / 3 octave band. Compared with the roughness grade limits specified in ISO 3095:2013, the measured data generally exceeded the limits when the center wavelength was greater than 4 mm; compared with the roughness grade limits specified in ISO 3095:2005, the measured data exceeded the limits when the center wavelength was between 5 and 31.5 mm and greater than 315 mm.

[0044] Therefore, in order to quantitatively describe the severity of rail wear in high-speed railways, the inventors used the modified periodogram method proposed by Welch to calculate the short-wave irregularity spectrum of the rail surface. Each calculation unit is 4.096m long, and the results are plotted on... Figure 3 In the next step, the shortwave irregularity spectrum values ​​of each computational unit under each wavelength condition are sorted, and the 1% and 99th percentiles can be selected as the lower and upper limits of the shortwave irregularity spectrum. It can be seen that the overall amplitude of the mean spectrum lies between the upper and lower limit spectra, and is closer to the upper limit spectrum.

[0045] In practice, after obtaining the track surface roughness test data of the ballastless track high-speed railway line, the power spectrum characteristic analysis is performed on the above track surface roughness test data to determine the mean spectrum, upper limit spectrum and lower limit spectrum of the track short-wave irregularity spectrum.

[0046] In this embodiment, power spectrum characteristic analysis is performed on the above-mentioned track surface roughness test data to determine the upper and lower limits of the track shortwave irregularity spectrum, including:

[0047] Using the periodogram method, the short-wave irregularity spectrum of the rail surface is calculated based on the above rail surface roughness test data;

[0048] The shortwave irregularity spectral values ​​under different wavelength conditions are sorted, and the shortwave irregularity spectral values ​​of the first preset value and the second preset value are selected as the upper limit spectrum and lower limit spectrum of the shortwave irregularity spectrum.

[0049] In the above embodiments, by determining the upper and lower limit spectra and performing supplementary fitting in subsequent steps, the upper and lower boundary levels of the short-wave irregularity spectrum of the track surface can be further described. Therefore, the short-wave irregularity state of high-speed railway tracks can be evaluated more scientifically and accurately, the evaluation of the geometric state of high-speed tracks can be improved, and references and lessons can be provided for wheel-rail vibration and noise analysis.

[0050] In practice, after analyzing the power spectrum characteristics of the above-mentioned track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track short-wave irregularity spectrum, the mean spectrum is subjected to piecewise linear fitting based on the determined segmented characteristics of the track short-wave irregularity spectrum to obtain the first fitting formula for the track short-wave irregularity spectrum.

[0051] The embodiment also includes:

[0052] The mean spectrum, upper limit spectrum, and lower limit spectrum of the shortwave irregularity spectrum are transformed into a double logarithmic coordinate system;

[0053] Linear fitting and data analysis were performed on the mean spectrum, upper limit spectrum, and lower limit spectrum in a double logarithmic coordinate system within the preset band to determine the segmentation characteristics of the orbital shortwave irregularity spectrum.

[0054] In one embodiment, based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to piecewise linear fitting to obtain a first fitting formula for the orbital shortwave irregularity spectrum, including:

[0055] The mean spectrum in the double logarithmic coordinate system is subjected to equal-interval resampling and peak elimination processing to obtain the processed mean spectrum data;

[0056] Using a power function, the shortwave irregularity spectrum of the orbital surface is fitted based on the processed mean spectrum data to obtain the first fitting formula for the shortwave irregularity spectrum of the orbital surface; the first fitting formula includes the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency.

[0057] Based on the segmentation points corresponding to the segmentation characteristics of the orbital shortwave irregularity spectrum, the processed mean spectrum data is subjected to piecewise linear fitting to determine the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency.

[0058] In the above embodiments, the power spectrum amplitude coefficient and the power spectrum rate coefficient with spatial frequency can be determined by performing piecewise linear fitting on the processed mean spectrum data, thereby determining the coefficients of the orbital shortwave irregularity spectrum fitting line.

[0059] In one embodiment, based on the segmentation points corresponding to the segmentation characteristics of the orbital shortwave irregularity spectrum, piecewise linear fitting is performed on the processed mean spectrum data to determine the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency, including:

[0060] Using the least squares method, based on the segmentation points corresponding to the segmentation characteristics of the shortwave irregularity spectrum, the processed mean spectrum data is subjected to piecewise linear fitting to obtain two fitting lines.

[0061] When the difference between the spatial frequency at the intersection of the two fitted lines and the second spatial frequency at the segmentation point is greater than a preset value, the intersection of the two fitted lines is taken as a new segmentation point, and piecewise linear fitting is performed on the processed mean spectrum data to obtain two fitted lines again. The above steps are repeated until the difference between the spatial frequency at the intersection of the two target fitted lines obtained again and the spatial frequency at the intersection of the two fitted lines obtained previously is less than a preset value.

[0062] Based on the two target fitting lines obtained again, the power spectrum amplitude coefficient and the power spectrum rate coefficient with spatial frequency are determined.

[0063] In the above embodiment, by repeating the above steps until the difference between the spatial frequency at the intersection of the two target fitting lines obtained again and the spatial frequency at the intersection of the two fitting lines obtained previously is less than a preset value, and based on the two target fitting lines obtained again, the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency are determined, and the two fitted target fitting lines can also be obtained, which are the target orbit shortwave irregularity spectrum fitting lines.

[0064] In the above embodiments, a power function is used to fit the short-wave irregularity spectrum of the orbital surface based on the processed mean spectrum data, resulting in the first fitting formula for the short-wave irregularity spectrum of the orbital surface:

[0065] s(f)=Af -k

[0066] Where s(f) represents the first fitting formula for the orbital shortwave irregularity spectrum; A is the power spectrum amplitude coefficient; k is the power spectrum rate coefficient with respect to spatial frequency; and f is the spatial frequency.

[0067] For example, considering the testing accuracy of the corrugated test trolley and the application scenarios of the short-wave irregularity spectrum of the rail surface in simulation calculations, the fitting wavelength range can be taken as 0.002 to 1 m.

[0068] The short-wave irregularity spectrum of the track surface was fitted using a power function, as shown in equation (1).

[0069] s(f)=Af -k (1)

[0070] Where s(f) represents the first fitting formula for the orbital shortwave irregularity spectrum, with units of mm. 2 / m -1 A is the power spectral amplitude coefficient; k is the power spectral density coefficient as a function of spatial frequency; f is the spatial frequency in meters (m). -1 .

[0071] Where A and k are the coefficients to be fitted.

[0072] Taking the logarithm to base 10 of equation (1) yields...

[0073] q=-kp+lg(A) (2)

[0074] In the formula: p = lg(f), the unit is m -1 q = lg(S(f)), in mm 2 / m -1 .

[0075] As shown in (2), fitting the power spectrum using a power function in a double logarithmic coordinate system can be transformed into a linear fit of the independent variable p and the dependent variable q. The coefficient A describes the amplitude of the power spectrum, and k describes the rate of change of the power spectrum with spatial frequency. When directly performing linear fitting on the mean spectrum, upper limit spectrum, and lower limit spectrum in a double logarithmic coordinate system within the 0.002–1 m band, it was found that at a spatial frequency of 20 m… -1 There are relatively obvious segmentation characteristics in the vicinity. Therefore, the shortwave irregularity spectrum of the high-speed railway track surface is fitted as a power function in two segments.

[0076] In one embodiment, the fitting process for the mean spectrum of short-wave irregularities on the track surface can be as follows: Figure 4 As shown. First, the mean spectrum can be transformed to a double logarithmic coordinate system; then, it can be resampled at equal intervals to balance the fitting weights of the mean spectrum at each wavelength; then, peak elimination processing is performed to extract the random components of short-wavelength irregularities on the orbital surface; with a spatial frequency of 20m... -1 The first segmentation point is used as the first segmentation point. The least squares method is used to perform linear fitting in two segments. The intersection of the two fitted lines is the new segmentation point. It is determined whether the spatial frequency of the two segmentation points is less than the given threshold. Otherwise, the segments are re-fitted according to the new segmentation point until the threshold condition is met. The coefficient fitting results are shown in Table 1.

[0077] Table 1. Coefficients of the Fitting Formula for Shortwave Irregularity Spectrum of High-Speed ​​Railway Track Surface

[0078]

[0079] In specific implementation, after performing piecewise linear fitting on the mean spectrum based on the determined segmented characteristics of the orbital shortwave irregularity spectrum to obtain the first fitting formula for the orbital shortwave irregularity spectrum, a supplementary fitting process is performed on the first fitting formula based on the upper limit spectrum and the upper limit spectrum to obtain the second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting process is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0080] In the above embodiments, by supplementing the upper and lower limit spectra with fitting, the upper and lower boundary levels of the short-wave irregularity spectrum of the track surface can be further described. Therefore, the short-wave irregularity state of high-speed railway tracks can be evaluated more scientifically and accurately, the evaluation of the geometric state of high-speed tracks can be improved, and references and lessons can be provided for wheel-rail vibration and noise analysis.

[0081] In this embodiment, based on the aforementioned upper limit spectrum and upper limit spectrum, the first fitting formula is supplemented with a second fitting formula to obtain the orbital shortwave irregularity spectrum, including:

[0082] The first fitting formula above is supplemented by fitting to obtain the second fitting formula for the orbital shortwave irregularity spectrum; the second fitting formula includes upper and lower limit spectrum transformation coefficients.

[0083] Based on the upper limit spectrum and the upper limit spectrum mentioned above, determine the upper and lower limit spectrum transformation coefficients.

[0084] In one embodiment, the first fitting formula described above is supplemented with the following formula to obtain a second fitting formula for the orbital shortwave irregularity spectrum:

[0085] S(f) = 10 b Af -k

[0086] Where S(f) represents the second fitting formula for the orbital shortwave irregularity spectrum; A is the power spectrum amplitude coefficient; k is the power spectrum rate coefficient with respect to spatial frequency; f is the spatial frequency; and b is the upper and lower limit spectrum transformation coefficient.

[0087] In the above embodiments, in order to describe the upper and lower boundary levels of the short-wave irregularity spectrum of the track surface, a coefficient b (i.e., the upper and lower limit spectrum transformation coefficient) is introduced to supplement the fitting of the upper and lower limit spectra. The final fitting formula of the short-wave irregularity spectrum of the high-speed railway track surface is shown in Equation (3). The coefficient b represents the difference in amplitude between the upper and lower limit spectra and the mean spectrum. The introduction of b can ensure that the fitting form and change trend of these three spectra are consistent. By transforming the coefficient b, when the fitting error between the upper limit spectrum (or lower limit spectrum) after peak elimination and the piecewise power function in the double logarithmic coordinate system is minimized, the fitting result of the upper limit spectrum (or lower limit spectrum) coefficient b is obtained as shown in Table 1. The coefficient b of the mean spectrum is 0.

[0088] S(f) = 10 b Af -k

[0089] Where S(f) represents the second fitting formula for the orbital shortwave irregularity spectrum; A is the power spectrum amplitude coefficient; k is the power spectrum rate coefficient with respect to spatial frequency; f is the spatial frequency; and b is the upper and lower limit spectrum transformation coefficient.

[0090] Where b is the coefficient to be fitted.

[0091] The following is a specific embodiment to illustrate the application of the method of the present invention. In this embodiment, track surface roughness test data from multiple ballastless track high-speed railway lines can be collected, and their power spectrum characteristics can be analyzed. A piecewise power function is used to fit the expression formula of the track surface short-wavelength irregularity spectrum. The details are as follows:

[0092] (1) Test methods and data samples

[0093] A rail corrugation testing trolley was used to conduct measurement tests on multiple ballastless track high-speed railway lines. Short-wave irregularities on the rail surface were recorded at 1mm sampling intervals. On-site test photos are shown below. Figure 1 As shown. The test section covers both the main line of the section and the main line of the station area, and the horizontal alignment includes straight lines, large-radius curves, and small-radius curves. The rail surface condition includes corrugated and non-corrugated conditions, and the corrugated section includes test data before and after grinding operations.

[0094] (2) Analysis of power spectrum characteristics of shortwave irregularities on the track surface

[0095] Figure 2 The short-wavelength roughness grades of the rail surface were given using a 1 / 3 octave band wavelength spectrum. Due to rail corrugation in some test sections, the roughness grade was particularly prominent at the center wavelength of 63 mm in the 1 / 3 octave band. Compared with the roughness grade limits specified in ISO 3095:2013, the measured data generally exceeded the limits when the center wavelength was greater than 4 mm; compared with the roughness grade limits specified in ISO 3095:2005, the measured data exceeded the limits when the center wavelength was between 5 and 31.5 mm and greater than 315 mm.

[0096] Therefore, in order to quantitatively describe the severity of rail wear in high-speed railways, the inventors used the modified periodogram method proposed by Welch to calculate the short-wave irregularity spectrum of the rail surface. Each calculation unit is 4.096m long, and the results are plotted on... Figure 3 In the next step, the shortwave irregularity spectrum values ​​of each computational unit under each wavelength condition are sorted, and the 1% and 99th percentiles can be selected as the lower and upper limits of the shortwave irregularity spectrum. It can be seen that the overall amplitude of the mean spectrum lies between the upper and lower limit spectra, and is closer to the upper limit spectrum.

[0097] (3) Formula for fitting short-wave irregularity spectrum of the track surface

[0098] Considering the testing accuracy of the corrugated test trolley and the application scenarios of the short-wave irregularity spectrum of the rail surface in simulation calculations, the fitting wavelength range can be taken as 0.002~1m.

[0099] The short-wave irregularity spectrum of the track surface was fitted using a power function, as shown in equation (1).

[0100] s(f)=Af -k (1)

[0101] Where s(f) represents the first fitting formula for the orbital shortwave irregularity spectrum, with units of mm. 2 / m -1 A is the power spectral amplitude coefficient; k is the power spectral density coefficient as a function of spatial frequency; f is the spatial frequency in meters (m). -1 .

[0102] Where A and k are the coefficients to be fitted.

[0103] Taking the logarithm to base 10 of equation (1) yields...

[0104] q=-kp+lg(A) (2)

[0105] In the formula: p = lg(f), the unit is m -1 q = lg(S(f)), in mm 2 / m -1 .

[0106] As shown in (2), fitting the power spectrum using a power function in a double logarithmic coordinate system can be transformed into a linear fit of the independent variable p and the dependent variable q. The coefficient A describes the amplitude of the power spectrum, and k describes the rate of change of the power spectrum with spatial frequency. When directly performing linear fitting on the mean spectrum, upper limit spectrum, and lower limit spectrum in a double logarithmic coordinate system within the 0.002–1 m band, it was found that at a spatial frequency of 20 m… -1 There are relatively obvious segmentation characteristics in the vicinity. Therefore, the shortwave irregularity spectrum of the high-speed railway track surface is fitted as a power function in two segments.

[0107] In one embodiment, the fitting process for the mean spectrum of short-wave irregularities on the track surface can be as follows: Figure 4 As shown. First, the mean spectrum can be transformed to a double logarithmic coordinate system; then, it can be resampled at equal intervals to balance the fitting weights of the mean spectrum at each wavelength; then, peak elimination processing is performed to extract the random components of short-wavelength irregularities on the orbital surface; with a spatial frequency of 20m... -1 The first segmentation point is used as the first segmentation point. The least squares method is used to perform linear fitting in two segments. The intersection of the two fitted lines is the new segmentation point. It is determined whether the spatial frequency of the two segmentation points is less than the given threshold. Otherwise, the segments are re-fitted according to the new segmentation point until the threshold condition is met. The coefficient fitting results are shown in Table 1.

[0108] To describe the upper and lower boundary levels of the short-wave irregularity spectrum of the track surface, a coefficient b (i.e., the upper and lower limit spectrum transformation coefficient) is introduced to supplement the fitting of the upper and lower limit spectra. The final fitting formula for the short-wave irregularity spectrum of the high-speed railway track surface is shown in Equation (3). The coefficient b represents the difference in amplitude between the upper and lower limit spectra and the mean spectrum. The introduction of b ensures that the fitting form and trend of these three spectra are consistent. By transforming the coefficient b, when the overall fitting error between the upper limit spectrum (or lower limit spectrum) after peak elimination and the piecewise power function in the double logarithmic coordinate system is minimized, the fitting result of the upper limit spectrum (or lower limit spectrum) coefficient b is obtained as shown in Table 1. The coefficient b of the mean spectrum is 0.

[0109] S(f) = 10 b Af -k

[0110] Where S(f) represents the second fitting formula for the orbital shortwave irregularity spectrum; A is the power spectrum amplitude coefficient; k is the power spectrum rate coefficient with respect to spatial frequency; f is the spatial frequency; and b is the upper and lower limit spectrum transformation coefficient.

[0111] Where b is the coefficient to be fitted.

[0112] Based on the above method, the fitting results of the short-wavelength irregularity spectrum of the high-speed railway track surface are obtained, such as... Figure 5 As shown, the piecewise power function can effectively describe the variation trend of the random component of shortwave irregularities on the track surface. Comparison with commonly used shortwave irregularity spectra in the 0.002–1 m band reveals that: the upper limit amplitude of the shortwave irregularity spectrum for high-speed railway track surfaces is generally smaller than the upper limit amplitude of the Stato spectrum; when the wavelength is less than 0.025 m, the upper limit amplitude is greater than the lower limit amplitude of the Stato spectrum; when the wavelength is less than 0.045 m, the upper limit amplitude is greater than the Wang Lan spectrum; for other bands, the upper limit amplitude is smaller than both the lower limit amplitude of the Stato spectrum and the Wang Lan spectrum. The mean amplitude is generally smaller than the Stato spectrum; when the wavelength is less than 0.006 m, the mean amplitude is greater than the Wang Lan spectrum; for other bands, the mean amplitude is smaller than the Wang Lan spectrum. The lower limit amplitude is smaller than both the Stato and Wang Lan spectra.

[0113] Of course, it is understood that there may be other variations of the above detailed process, and all such variations should fall within the protection scope of this invention.

[0114] In this embodiment of the invention, track surface roughness test data of a ballastless track high-speed railway line is acquired; power spectrum feature analysis is performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track short-wavelength irregularity spectrum; based on the determined segmented characteristics of the track short-wavelength irregularity spectrum, piecewise linear fitting processing is performed on the mean spectrum to obtain a first fitting formula for the track short-wavelength irregularity spectrum; based on the upper limit spectrum and the upper limit spectrum, supplementary fitting processing is performed on the first fitting formula to obtain a second fitting formula for the track short-wavelength irregularity spectrum; the supplementary fitting processing is used to describe the track surface short-wavelength irregularity spectrum. By establishing horizontal upper and lower boundaries, a piecewise fitting of the mean spectrum of short-wavelength irregularities on the track surface is achieved. This solves the problem of accurately measuring short-wavelength irregularities with wavelengths below 2m under existing technologies, making the analysis of track irregularities more accurate and the assessment of track irregularity conditions more efficient. Furthermore, by supplementing the fitting of the upper and lower bound spectra, the upper and lower boundary levels of the track surface short-wavelength irregularity spectrum can be further described. Therefore, it is possible to evaluate the short-wavelength irregularity condition of high-speed railway tracks more scientifically and accurately, improve the evaluation of the geometric state of high-speed tracks, and provide reference and guidance for wheel-rail vibration and noise analysis.

[0115] As described above, this invention proposes a short-wavelength irregularity spectrum characterization method, which enriches the formulation of short-wavelength irregularity spectra for high-speed railways. It can more scientifically and accurately evaluate the short-wavelength irregularity state of high-speed railway tracks. Based on the test data of track surface roughness of high-speed railways, the short-wavelength irregularity spectrum of the track surface can be determined. The research results of the short-wavelength irregularity spectrum of high-speed railway tracks improve the evaluation of the geometric state of high-speed tracks and can also provide reference and guidance for wheel-rail vibration and noise analysis.

[0116] This invention also provides a track shortwave irregularity spectrum fitting device to achieve piecewise fitting of the mean spectrum of track surface shortwave irregularities, thereby improving the efficiency and accuracy of track irregularity assessment and perfecting the evaluation of the geometric state of high-speed tracks. Figure 6 As shown, the device includes:

[0117] Test data acquisition module 601 is used to acquire track surface roughness test data of ballastless track high-speed railway lines;

[0118] The power spectrum feature analysis module 602 is used to perform power spectrum feature analysis on the track surface roughness test data to determine the mean spectrum, upper limit spectrum and lower limit spectrum of the track shortwave irregularity spectrum.

[0119] The piecewise linear fitting module 603 is used to perform piecewise linear fitting on the mean spectrum based on the determined piecewise characteristics of the orbital shortwave irregularity spectrum to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0120] The supplementary fitting module 604 is used to perform supplementary fitting processing on the first fitting formula based on the upper limit spectrum and the upper limit spectrum to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting processing is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0121] This invention provides an orbital shortwave irregularity spectrum fitting device, as described in the above embodiments. Since the principle by which this device solves the problem is similar to that of the orbital shortwave irregularity spectrum fitting method, the implementation of this device can refer to the implementation of the orbital shortwave irregularity spectrum fitting method; repeated details will not be elaborated further.

[0122] In this embodiment of the invention, track surface roughness test data of a ballastless track high-speed railway line is acquired; power spectrum feature analysis is performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track short-wavelength irregularity spectrum; based on the determined segmented characteristics of the track short-wavelength irregularity spectrum, piecewise linear fitting processing is performed on the mean spectrum to obtain a first fitting formula for the track short-wavelength irregularity spectrum; based on the upper limit spectrum and the upper limit spectrum, supplementary fitting processing is performed on the first fitting formula to obtain a second fitting formula for the track short-wavelength irregularity spectrum; the supplementary fitting processing is used to describe the track surface short-wavelength irregularity spectrum. By establishing horizontal upper and lower boundaries, a piecewise fitting of the mean spectrum of short-wavelength irregularities on the track surface is achieved. This solves the problem of accurately measuring short-wavelength irregularities with wavelengths below 2m under existing technologies, making the analysis of track irregularities more accurate and the assessment of track irregularity conditions more efficient. Furthermore, by supplementing the fitting of the upper and lower bound spectra, the upper and lower boundary levels of the track surface short-wavelength irregularity spectrum can be further described. Therefore, it is possible to evaluate the short-wavelength irregularity condition of high-speed railway tracks more scientifically and accurately, improve the evaluation of the geometric state of high-speed tracks, and provide reference and guidance for wheel-rail vibration and noise analysis.

[0123] Based on the same inventive concept, this embodiment of the invention also provides a computer device embodiment for implementing all or part of the above-described orbital shortwave irregularity spectrum fitting method. This computer device specifically includes the following:

[0124] The computer device comprises a processor, memory, a communications interface, and a bus; wherein the processor, memory, and communications interface communicate with each other via the bus; the communications interface is used to realize information transmission between related devices; the computer device can be a desktop computer, tablet computer, or mobile terminal, etc., and this embodiment is not limited to these. In this embodiment, the computer device can be implemented with reference to the embodiments for implementing the above-mentioned orbital shortwave irregularity spectrum fitting method and the embodiments for implementing the above-mentioned orbital shortwave irregularity spectrum fitting device, the contents of which are incorporated herein, and repeated parts will not be described again.

[0125] Figure 7 This is a schematic diagram of the system composition structure of a computer device provided in an embodiment of the present invention. Figure 7 As shown, the computer device 70 may include a processor 701 and a memory 702; the memory 702 is coupled to the processor 701. It is worth noting that... Figure 7 This is an example; other types of structures can also be used to supplement or replace this structure to achieve telecommunications functions or other functions.

[0126] In one embodiment, the functionality implemented by the orbital shortwave irregularity spectrum fitting method can be integrated into the processor 701. The processor 701 can be configured to perform the following control:

[0127] Obtain test data on the surface roughness of ballastless track high-speed railway lines;

[0128] Power spectrum characteristic analysis was performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum;

[0129] Based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to segmented linear fitting to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0130] Based on the upper limit spectrum and the upper limit spectrum, the first fitting formula is supplemented by a fitting process to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting process is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0131] As can be seen from the above, the computer equipment provided in the embodiments of the present invention realizes the segmented fitting of the mean spectrum of short-wavelength irregularities on the track surface, solving the problem that it is difficult to accurately measure short-wavelength irregularities with wavelengths below 2m under the prior art. This makes the analysis of track irregularities more accurate and the evaluation efficiency of track irregularity status higher. At the same time, by supplementing the fitting processing of the upper and lower limit spectra, the upper and lower boundary levels of the short-wavelength irregularity spectrum on the track surface can be further described. Therefore, it can more scientifically and accurately evaluate the short-wavelength irregularity status of high-speed railway tracks, improve the evaluation of the geometric state of high-speed tracks, and also provide reference and guidance for wheel-rail vibration and noise analysis.

[0132] In another embodiment, the orbital shortwave irregularity spectrum fitting device can be configured separately from the processor 701. For example, the orbital shortwave irregularity spectrum fitting device can be configured as a chip connected to the processor 701, and the function of the orbital shortwave irregularity spectrum fitting method can be realized through the control of the processor.

[0133] like Figure 7 As shown, the computer device 70 may also include: a communication module 703, an input unit 704, an audio processing unit 705, a display 706, and a power supply 707. It is worth noting that the computer device 70 does not necessarily need to include these components. Figure 7 All components shown; in addition, computer device 70 may also include Figure 7 For components not shown, please refer to existing technologies.

[0134] like Figure 7As shown, processor 701, sometimes also referred to as controller or operation control, may include a microprocessor or other processor device and / or logic device, which receives input and controls the operation of various components of computer device 70.

[0135] The memory 702 may be, for example, one or more of a cache, flash memory, hard drive, removable media, volatile memory, non-volatile memory, or other suitable device. It may store the aforementioned failure-related information, and also store a program for executing that information. The processor 701 may execute the program stored in the memory 702 to perform information storage or processing, etc.

[0136] Input unit 704 provides input to processor 701. This input unit 704 may be, for example, a keypad or touch input device. Power supply 707 provides power to computer device 70. Display 706 displays images and text, etc. This display may be, for example, an LCD display, but is not limited thereto.

[0137] The memory 702 can be a solid-state memory, such as a read-only memory (ROM), random access memory (RAM), a SIM card, etc. It can also be a memory that retains information even when power is off, can be selectively erased, and contains more data; examples of this type of memory are sometimes referred to as EPROMs. The memory 702 can also be some other type of device. The memory 702 includes a buffer memory 7021 (sometimes referred to as a buffer). The memory 702 may include an application / function storage unit 7022 for storing application programs and function programs or processes for executing operations of the computer device 70 via the processor 701.

[0138] The memory 702 may also include a data storage unit 7023 for storing data, such as contacts, digital data, pictures, sounds, and / or any other data used by the computer device. The driver storage unit 7024 of the memory 702 may include various drivers for the computer device for communication functions and / or for performing other functions of the computer device (such as messaging applications, address book applications, etc.).

[0139] The communication module 703 is a transmitter / receiver that transmits and receives signals via the antenna 708. The communication module (transmitter / receiver) 703 is coupled to the processor 701 to provide input signals and receive output signals, which is the same as in a conventional mobile communication terminal.

[0140] Based on different communication technologies, multiple communication modules 703 can be configured in the same computer device, such as cellular network modules, Bluetooth modules, and / or wireless LAN modules. The communication module (transmitter / receiver) 703 is also coupled to a speaker 709 and a microphone 710 via an audio processing unit 705 to provide audio output via the speaker 709 and receive audio input from the microphone 710, thereby realizing typical telecommunications functions. The audio processing unit 705 may include any suitable buffer, decoder, amplifier, etc. Additionally, the audio processing unit 705 is also coupled to a processor 701, enabling on-device recording via the microphone 710 and on-device playback of stored audio via the speaker 709.

[0141] In embodiments of the present invention, a computer-readable storage medium is also provided for implementing all steps of the orbital shortwave irregularity spectrum fitting method in the above embodiments. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements all steps of the orbital shortwave irregularity spectrum fitting method in the above embodiments. For example, when the processor executes the computer program, it implements the following steps:

[0142] Obtain test data on the surface roughness of ballastless track high-speed railway lines;

[0143] Power spectrum characteristic analysis was performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum;

[0144] Based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to segmented linear fitting to obtain the first fitting formula for the orbital shortwave irregularity spectrum.

[0145] Based on the upper limit spectrum and the upper limit spectrum, the first fitting formula is supplemented by a fitting process to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting process is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum.

[0146] As can be seen from the above, the computer-readable storage medium provided in the embodiments of the present invention realizes the piecewise fitting of the mean spectrum of short-wavelength irregularities on the track surface, solving the problem that it is difficult to accurately measure short-wavelength irregularities with wavelengths below 2m under the prior art. This makes the analysis of track irregularities more accurate and the evaluation efficiency of track irregularity status higher. At the same time, by supplementing the fitting processing of the upper and lower limit spectra, the upper and lower boundary levels of the short-wavelength irregularity spectrum on the track surface can be further described. Therefore, it can more scientifically and accurately evaluate the short-wavelength irregularity status of high-speed railway tracks, improve the evaluation of the geometric state of high-speed tracks, and also provide reference and guidance for wheel-rail vibration and noise analysis.

[0147] Embodiments of the present invention also provide a computer program product, the computer program product including a computer program, which, when executed by a processor, implements the above-described orbital shortwave irregularity spectrum fitting method.

[0148] It should be noted that the acquisition, storage, use, and processing of data in the technical solution of this application all comply with the relevant provisions of national laws and regulations.

[0149] While this invention provides the method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only possible execution order. In actual device or client product execution, the methods shown in the embodiments or drawings can be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0150] 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.

[0151] 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.

[0152] 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.

[0153] 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.

[0154] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0155] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. The terms "upper," "lower," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0156] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0157] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention is not limited to any single aspect, nor to any single embodiment, nor to any combination and / or substitution of these aspects and / or embodiments. Each aspect and / or embodiment of the present invention can be used alone, or in combination with one or more other aspects and / or other embodiments.

[0158] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of fitting a short wave irregularity spectrum of a rail, characterized by, include: Obtain test data on the surface roughness of ballastless track high-speed railway lines; Power spectrum characteristic analysis was performed on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum; Based on the determined segmentation characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to segmented linear fitting to obtain the first fitting formula for the orbital shortwave irregularity spectrum. Based on the upper and lower limit spectra, the first fitting formula is supplemented by a fitting process to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting process is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum. Based on the upper and lower limit spectra, the first fitting formula is supplemented with a second fitting formula to obtain the orbital shortwave irregularity spectrum. This includes: supplementing the first fitting formula to obtain the second fitting formula for the orbital shortwave irregularity spectrum; the second fitting formula includes upper and lower limit spectrum transformation coefficients; and determining the upper and lower limit spectrum transformation coefficients based on the upper and lower limit spectra. The first fitting formula is supplemented by a second fitting process to obtain the second fitting formula for the orbital shortwave irregularity spectrum, as follows: wherein, represents a second fitting formula for the track short-wave irregularity spectrum; is a power spectrum amplitude coefficient; is a power spectrum rate of change with spatial frequency coefficient; is a spatial frequency; is an upper and lower spectrum transform coefficient.

2. The method as described in claim 1, characterized in that, The test section for the track surface roughness test data includes the main line of the section and the main line of the station area. The planar linearity of the rail surface roughness test data includes straight lines and curves; The rail surface roughness test data includes rail surface conditions: corrugated condition data and non-corrugated condition data, wherein the corrugated condition data includes data before and after the grinding operation.

3. The method as described in claim 1, characterized in that, Power spectrum characteristic analysis is performed on the track surface roughness test data to determine the upper and lower limits of the track shortwave irregularity spectrum, including: The short-wave irregularity spectrum of the rail surface is calculated using the periodogram method based on the rail surface roughness test data. The shortwave irregularity spectral values ​​under different wavelength conditions are sorted, and the shortwave irregularity spectral values ​​of the first preset value and the second preset value are selected as the upper limit spectrum and lower limit spectrum of the shortwave irregularity spectrum.

4. The method as described in claim 1, characterized in that, Also includes: The mean spectrum, upper limit spectrum, and lower limit spectrum of the shortwave irregularity spectrum are transformed into a double logarithmic coordinate system; Linear fitting and data analysis were performed on the mean spectrum, upper limit spectrum, and lower limit spectrum in a double logarithmic coordinate system within the preset band to determine the segmentation characteristics of the orbital shortwave irregularity spectrum.

5. The method as described in claim 1, characterized in that, Based on the determined segmented characteristics of the orbital shortwave irregularity spectrum, the mean spectrum is subjected to piecewise linear fitting to obtain the first fitting formula for the orbital shortwave irregularity spectrum, including: The mean spectrum in the double logarithmic coordinate system is subjected to equal-interval resampling and peak elimination processing to obtain the processed mean spectrum data; Using a power function, the shortwave irregularity spectrum of the orbital surface is fitted based on the processed mean spectrum data to obtain the first fitting formula for the shortwave irregularity spectrum of the orbital surface; the first fitting formula includes the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency. Based on the segmentation points corresponding to the segmentation characteristics of the orbital shortwave irregularity spectrum, the processed mean spectrum data is subjected to piecewise linear fitting to determine the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency.

6. The method as described in claim 5, characterized in that, Based on the segmentation points corresponding to the segmentation characteristics of the shortwave irregularity spectrum, piecewise linear fitting is performed on the processed mean spectrum data to determine the power spectrum amplitude coefficient and the power spectrum rate of change coefficient with spatial frequency, including: Using the least squares method, based on the segmentation points corresponding to the segmentation characteristics of the shortwave irregularity spectrum, the processed mean spectrum data is subjected to piecewise linear fitting to obtain two fitting lines. When the difference between the spatial frequency at the intersection of the two fitted lines and the second spatial frequency at the segmentation point is greater than a preset value, the intersection of the two fitted lines is taken as a new segmentation point, and the processed mean spectrum data is subjected to piecewise linear fitting to obtain two fitted lines again. The above steps are repeated until the difference between the spatial frequency at the intersection of the two target fitted lines obtained again and the spatial frequency at the intersection of the two fitted lines obtained previously is less than a preset value. Based on the two target fitting lines obtained again, the power spectrum amplitude coefficient and the power spectrum rate coefficient with spatial frequency are determined.

7. The method as described in claim 5, characterized in that, Using a power function, the short-wave irregularity spectrum of the orbital surface is fitted based on the processed mean spectrum data, resulting in the first fitting formula for the short-wave irregularity spectrum of the orbital surface, as follows: in, The first fitting formula for representing the orbital shortwave irregularity spectrum; The power spectral amplitude coefficient; This is the rate coefficient of change of the power spectrum with spatial frequency; This refers to the spatial frequency.

8. A device for fitting shortwave irregularity spectra in orbits, characterized in that, include: The test data acquisition module is used to acquire the track surface roughness test data of ballastless track high-speed railway lines; The power spectrum feature analysis module is used to perform power spectrum feature analysis on the track surface roughness test data to determine the mean spectrum, upper limit spectrum, and lower limit spectrum of the track shortwave irregularity spectrum. The piecewise linear fitting module is used to perform piecewise linear fitting on the mean spectrum based on the determined piecewise characteristics of the orbital shortwave irregularity spectrum, so as to obtain the first fitting formula for the orbital shortwave irregularity spectrum. The supplementary fitting module is used to perform supplementary fitting processing on the first fitting formula based on the upper limit spectrum and the lower limit spectrum to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the supplementary fitting processing is used to describe the upper and lower boundary levels of the orbital shortwave irregularity spectrum. The supplementary fitting module is specifically used to: perform supplementary fitting processing on the first fitting formula to obtain a second fitting formula for the orbital shortwave irregularity spectrum; the second fitting formula includes upper and lower limit spectrum transformation coefficients; and determine the upper and lower limit spectrum transformation coefficients based on the upper and lower limit spectra. The first fitting formula is supplemented by a second fitting process to obtain the second fitting formula for the orbital shortwave irregularity spectrum, as follows: in, The second fitting formula represents the orbital shortwave irregularity spectrum; The power spectral amplitude coefficient; This is the rate coefficient of change of the power spectrum with spatial frequency; Spatial frequency; These are the upper and lower limit spectral transformation coefficients.

9. 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 7.

10. 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 7.

11. 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 7.

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