Construction method of subway track irregularity spectrum

Abstract

The invention discloses a construction method of a subway track irregularity spectrum, and aims to solve the technical problem that an existing classical track spectrum model is difficult to accurately and universally describe actual irregularity characteristics of subway lines in China. Comprising the following steps: a) acquiring actually measured track irregularity data of at least one subway line; b) based on the actually measured track irregularity data, calculating to obtain a power spectral density spectral line, the power spectral density spectral line representing a change relation of a power spectral density value along with a spatial frequency; c) preprocessing the power spectral density spectral line, wherein the preprocessing comprises identifying and eliminating periodic spectral peaks caused by track geometrical characteristics; d) the preprocessed power spectral density spectral line is converted to a logarithm-logarithm coordinate system, the abscissa is the logarithm value of the spatial frequency, and the ordinate is the logarithm value of the power spectral density value; and e) under the logarithm-logarithm coordinate system, establishing an analytical expression of the track irregularity power spectrum density through quintic polynomial fitting.

Description

Technical Field

[0001] This invention relates to the field of rail transit engineering, and specifically to a method for constructing a subway track irregularity spectrum. Background Technology

[0002] Track irregularities are the fundamental excitation source causing train vibrations, and their accurate modeling is a prerequisite for conducting vehicle system dynamics simulations, evaluating passenger comfort, and predicting component fatigue life. In engineering practice, track irregularities are usually statistically described by their power spectral density (PSD), i.e., the track irregularity spectrum.

[0003] To standardize the description of track irregularities, scholars and institutions both domestically and internationally have proposed several classic analytical spectral models, among which the American and German models are the most representative. The American model was proposed by the Federal Railroad Administration (FRA) of the U.S. Department of Transportation in the 1970s and 1980s, based on statistical analysis of extensive measured data from approximately 112,700 kilometers of track. This model classifies U.S. railroad tracks into six levels according to their irregularity safety limits and provides analytical expressions for the power spectral density of four types of irregularities—elevation, alignment, levelness, and gauge—under each level. These expressions are all given in the form of rational fractions; for example, for elevation irregularities, its power spectral density S... v (φ) is in the form of: S v (φ)=[A v ·φ v2 2 ·(φ²+φ v1 2 )] / [φ 4 ·(φ 2 +φ v2 2 In the formula, S v (φ) represents the power spectral density, in m³ / s. 2 / (1 / m); φ is the spatial frequency, in units of 1 / m; φ v1 and φ v2 The cutoff frequency is expressed in units of 1 / m; A v denoted as the roughness constant. The German spectrum was adopted in the early 1980s during high-speed train dynamics research in Germany. This model is generally divided into a "high-interference spectrum" suitable for conventional railways and a "low-interference spectrum" suitable for high-speed railways. Its analytical expression is also a rational fraction, but it employs a different mathematical structure than the American spectrum. These classic spectral models have provided an important theoretical foundation for the development of railway engineering.

[0004] However, with the rapid development of urban rail transit (subways) in my country, the inherent limitations of these existing models are becoming increasingly apparent when directly applied to subway systems. Firstly, existing spectral models differ significantly from the actual characteristics of subway lines. The aforementioned classic spectral models are mostly based on the operating conditions of trunk railways or high-speed railways, while subway systems have unique characteristics such as light axle load, low speed, small curve radius, and diverse track bed structures. Directly applying these models to subway vehicle dynamics simulations results in insufficient realism of the excitation inputs, potentially leading to distorted simulation results.

[0005] Secondly, and more importantly, the mathematical fitting methods of these models have fundamental flaws, making it difficult to balance fitting accuracy with model universality. Taking the German spectrum as an example, its fixed function structure determines the changing patterns of spectral line morphology. Although the function itself is smooth and continuous, its behavior in different frequency ranges is dominated by different power-law rules, and the transition regions between these rules are rigid and cannot be adjusted. This inherent "segmentation and splicing" logic makes it difficult to flexibly capture the diverse smooth transition patterns in actual spectral lines. On the other hand, the rational fractions used in the American spectrum, while uniform in form, have relatively fixed function shapes and low degrees of freedom. Extensive measured subway track spectrum data shows that the fixed-form rational fractions of the American spectrum, containing only a few parameters, lack sufficient function shaping ability and struggle to achieve high-precision fitting across the entire frequency band, especially in the mid-frequency region where the spectral shape undergoes bending changes, resulting in larger fitting errors.

[0006] Furthermore, the imperfections in the processing methods for measured track data also affect the accuracy of the model. The original track irregularity data not only contains random irregularities but also periodic components caused by fixed geometric structures such as rail joints and turnouts. Current technologies lack a clear and unified methodology for systematically processing these periodic disturbances to obtain a clean background spectrum of random irregularities when establishing the aforementioned analytical spectrum. This leads to the model potentially being contaminated by local features of specific lines, reducing the model's universality.

[0007] In summary, existing technologies have shortcomings in terms of the specificity of the metro spectrum, the accuracy and smoothness of the spectral model fitting method, and the rigor of the raw data processing. Therefore, there is an urgent need for a new technical solution to establish a track irregularity spectrum analytical model that can realistically reflect the common random irregularity characteristics of metro lines in my country, with a unified form, concise expression, smooth functions, and high accuracy across the entire frequency band. Summary of the Invention

[0008] The purpose of this invention is to provide a method for constructing a subway track irregularity spectrum, so as to solve the technical problem that existing classical track spectrum models are difficult to accurately and universally describe the actual irregularity characteristics of subway lines in my country.

[0009] This invention provides a method for constructing a subway track irregularity spectrum, comprising the following steps: a) acquiring measured track irregularity data for at least one subway line; b) calculating the power spectral density spectrum based on the measured track irregularity data, wherein the power spectral density spectrum represents the relationship between the power spectral density value and spatial frequency; c) preprocessing the power spectral density spectrum, wherein the preprocessing includes identifying and eliminating periodic spectral peaks caused by track geometric features; d) converting the preprocessed power spectral density spectrum to a log-log coordinate system, wherein the horizontal axis is the logarithm of the spatial frequency and the vertical axis is the logarithm of the power spectral density value; e) establishing an analytical expression for the track irregularity power spectral density in the log-log coordinate system by fitting a fifth-order polynomial: log 10 (S(f))=A0+A1·log 10 (f)+A2·(log 10 (f)) 2 +A3·(log 10 (f)) 3 +A4·(log 10 (f)) 4 +A5·(log 10 (f)) 5 Where: S(f) is the power spectral density obtained by the fifth-order polynomial fitting, f is the spatial frequency, and A0, A1, A2, A3, A4, and A5 are coefficients determined by the fifth-order polynomial fitting.

[0010] As an optimization and / or instantiation of the above method for constructing the subway track irregularity spectrum, further: in step a), measured track irregularity data from multiple subway lines are obtained, and in step b), the power spectral density spectrum line of each subway line is calculated.

[0011] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, it further includes: after step e), averaging multiple analytical expressions of power spectral density to establish a total track irregularity power spectral density model.

[0012] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, further: the coefficients A0, A1, A2, A3, A4, and A5 of the overall track irregularity power spectral density model are respectively: A0: -2.710±10%, A1: -5.977±10%, A2: -13.767±10%, A3: -24.045±10%, A4: -16.754±10%, A5: -3.928±10%.

[0013] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, it further includes step f): multiplying the analytical expression established by step e) by a transformation coefficient k to generate a quantile track irregularity power spectral density model with specific statistical percentiles.

[0014] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, the method is further used to generate a numerical simulation sample of track irregularities that integrates medium- and long-wavelength and short-wavelength characteristics, and includes the following subsequent steps: A. Using the inverse fast Fourier transform method, based on the analytical expression of the track irregularity power spectral density established in step e), a medium- and long-wavelength random irregularity displacement sequence is generated; B. Rail corrugation parameters representing short-wavelength characteristics are provided, including corrugation amplitude B and corrugation wavelength l; C. Based on the rail corrugation parameters, a short-wavelength periodic irregularity displacement sequence is generated using the cosine function y(x) = B·cos(2πx / l), where x is the mileage; D. The medium- and long-wavelength random irregularity displacement sequence is linearly superimposed with the short-wavelength periodic irregularity displacement sequence to obtain the final numerical simulation sample of track irregularities.

[0015] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, further: the corrugation amplitude B and the corrugation wavelength l are determined according to the track structure type of the line.

[0016] As an optimization and / or instantiation of the above-mentioned method for constructing the irregularity spectrum of subway tracks, further: when the track structure type is "18mm elastic short sleeper + integral track bed" and is located on a small radius curve, the value range of the corrugation wavelength l is 63mm to 100mm.

[0017] As an optimization and / or instantiation of the above-mentioned method for constructing the irregularity spectrum of subway tracks, further: when the track structure type is "ordinary fastener + ordinary integral track bed" and is located on a straight section, the value range of the corrugation wavelength l is 160mm to 250mm.

[0018] As an optimization and / or instantiation of the above-mentioned method for constructing the subway track irregularity spectrum, the constructed track irregularity spectrum further includes at least one of the following: elevation irregularity spectrum, track alignment irregularity spectrum, horizontal irregularity spectrum, and track gauge irregularity spectrum.

[0019] The method for constructing the subway track irregularity spectrum of the present invention has the following beneficial effects: First, it solves the technical problems of the fixed form and low degree of freedom of the American spectrum function in the prior art, and the non-smoothness of the function caused by the piecewise idea of ​​the German spectrum. Existing classical spectrum models (such as the American spectrum) pre-set rational fractions with specific physical meanings as function structures. This fixed function form leads to insufficient degree of freedom and makes it difficult to accurately fit the complex curvature of the measured spectrum of subway lines. The present invention no longer insists on finding function forms with specific physical meanings, but adopts a series of combined steps to improve the adaptability and accuracy of the model: First, the power spectral density spectrum is preprocessed before fitting. By identifying and eliminating periodic spectral peaks caused by track geometry features, it is ensured that the constructed model is a pure random irregularity background spectrum. This avoids the model being contaminated by the local features of specific lines, significantly enhancing the model's universality and representativeness as a standard spectrum. Secondly, the log-log coordinate transformation significantly reduces the complexity of the spectral line morphology, making it easier to perform mathematical fitting. Finally, based on this, a high-degree-of-freedom fifth-order polynomial is used for fitting. The fifth-order polynomial not only has sufficient flexibility to accurately capture and fit the complex bending morphology in a large number of measured data spectral lines, thus greatly improving the model's fitting accuracy across the entire frequency band, but its inherent continuous and smooth property also solves the inherent defect of the German spectrum in the non-smoothness at the segmented connection points.

[0020] Secondly, by acquiring a large amount of measured track irregularity data from multiple subway lines and averaging the model coefficients of each line, a comprehensive track irregularity power spectral density model is established. This method fundamentally solves the deficiency of existing technologies in terms of poor universality caused by the single or unrepresentative data source. Because this model is built on massive and diverse real-world subway operation data, it can truly and comprehensively reflect the common and widespread irregularity characteristics of my country's subway lines, making it highly representative and authoritative as a standardized stimulus input.

[0021] Third, the values ​​of coefficients A0, A1, A2, A3, A4, and A5 for specific irregularity types (such as high-low irregularity left rail) in the overall track irregularity power spectral density model are given. This provides a standardized set of subway track irregularity spectral model parameters that can be directly applied by those skilled in the art, greatly facilitating engineering applications and avoiding users having to repeatedly perform complex data collection and modeling processes. Furthermore, the determined coefficient ranges themselves constitute a quantitative characterization of the general irregularity state of subway lines in my country, and have significant reference value.

[0022] Fourth, by introducing a transformation coefficient k, a quantile track irregularity power spectral density model with specific statistical percentiles can be generated. This greatly expands the application scope of the model and overcomes the limitation that existing models usually only represent average conditions. Users can easily generate track irregularity spectra representing different maintenance levels according to their needs (such as extreme condition analysis, fatigue life assessment, or reliability design), providing a powerful tool for more refined and targeted vehicle system dynamics simulation.

[0023] Fifth, by linearly superimposing the medium- and long-wavelength random irregularity displacement sequences generated based on the analytical expression of this invention with the short-wavelength periodic irregularity displacement sequences generated based on rail corrugation parameters, the technical challenge of accurately describing short-wavelength periodic irregularities such as rail corrugation using traditional spectral models is solved. The numerical simulation samples generated by this method simultaneously include background random irregularities and key periodic excitations, and their realism is far superior to samples generated solely based on power spectra. This is crucial for accurately predicting high-frequency vibrations, wheel-rail impacts, and noise caused by rail corrugation.

[0024] Sixth, the corrugation amplitude B and corrugation wavelength l are correlated with specific track structure types (such as "18mm elastic short sleepers + integral track bed" or "ordinary fasteners + ordinary integral track bed") and track conditions (such as small-radius curves or straight sections). This refined approach makes the simulation of short-wave irregularities no longer a general discussion, but rather has a clear physical background and engineering basis. This further enhances the realism and relevance of the final numerical simulation samples of track irregularities, making the simulation results more valuable for reference.

[0025] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages provided by the present invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice. Attached Figure Description

[0026] The accompanying drawings, which form part of this specification, are used to aid in understanding the invention. The contents provided in the drawings and their related descriptions in this specification can be used to explain the invention, but do not constitute an undue limitation of the invention.

[0027] Figure 1 This is a schematic diagram of the power spectral density spectrum obtained by calculating the data of the uneven left rail of a subway track in Embodiment 1 of the present invention. It shows the spectral characteristics under different curve radii (represented by R, in meters).

[0028] Figure 2This is a schematic diagram of the power spectral density obtained from the calculation of data on the irregular left rail of a subway track in Embodiment 1 of the present invention, showing the spectral characteristics under different track structures. "WJ-2 + elastic support block + ordinary integral track bed elastic support block" means: WJ-2 type fasteners are used, the rail is fixed to the elastic support block, and the elastic support block is installed on the ordinary integral track bed. "WJ-2 + embedded support block + ordinary integral track bed ordinary support block" means: WJ-2 type fasteners are used, but the rail support is an embedded support block, which is anchored in the ordinary integral track bed. "SD-1 + elastic support block + ordinary integral track bed elastic support block" means: SD-1 type fasteners are used, the rail is fixed to the elastic support block, and the elastic support block is installed on the ordinary integral track bed. "SD-1 + concrete long sleeper + concrete long sleeper integral track bed" means: SD-1 type fasteners are used, the rail is fixed to the concrete long sleeper, and the concrete long sleeper is cast together with the integral track bed. "LORD + Elastic Support Block + Ordinary Integral Track Elastic Support Block" refers to the use of high-performance vibration-damping fasteners manufactured by LORD, with the rail fixed to the elastic support block, which is then installed on the ordinary integral track bed. "DTⅢ-2 + Concrete Long Sleeper + Concrete Long Sleeper Integral Track Bed" refers to the use of DTⅢ-2 type fasteners, with the rail fixed to the concrete long sleeper, which is cast integrally with the integral track bed. All of the above fastener types are known and commonly used in this field.

[0029] Figure 3 This is a schematic diagram showing the result of fitting the average power spectral density spectrum of a subway line in an embodiment of the present invention. Figure 3 (a) is the result of fitting the power spectral density spectrum obtained from the data of the irregular left rail of the high and low track of the subway. Figure 3 (b) is the result of fitting the power spectral density spectrum obtained from the data of the irregular right rail of the high and low track of the subway. Figure 3 (c) is the result of fitting the power spectral density spectrum obtained from the data of the irregular left rail of the subway track; Figure 3 (d) is the result of fitting the power spectral density spectrum obtained from the data of the right rail with track irregularity of the subway; Figure 3 (e) is the result of fitting the power spectral density spectrum obtained from the calculation of the subway track gauge irregularity data; Figure 3 (f) shows the result of fitting the power spectral density curve calculated from the subway level irregularity data. In each figure, "original spectrum" refers to the initial power spectral density curve; "peak-removed spectrum" is the spectrum obtained after identifying and removing periodic spectral peaks (and preprocessing) based on the "original spectrum"; "fitted spectrum" refers to the power spectral density curve of the track irregularity established after fitting with the fifth-order polynomial in this invention.

[0030] Figure 4 This is a schematic diagram of the overall orbital irregularity power spectral density model established by averaging multiple power spectral density analytical expressions in an embodiment of the present invention.

[0031] Figure 5 This is a schematic diagram of a quantile orbital irregularity power spectral density model with specific statistical percentiles generated by introducing a conversion coefficient k in an embodiment of the present invention.

[0032] Figure 6 This is a schematic diagram illustrating the process of linearly superimposing a sequence of random irregular displacements of medium and long waves with a sequence of periodic irregular displacements of short waves in an embodiment of the present invention to generate a numerical simulation sample of track irregularities that integrates the characteristics of medium and long waves and short waves.

[0033] Figure 7 This is a comparison chart used in this embodiment of the invention to verify the accuracy of the Inverse Fast Fourier Transform (IFFT) method. Figure 7 (a) is a contrast of spatial domain irregularities. Figure 7 (b) is a comparison of power spectral density. Detailed Implementation

[0034] The present invention will now be clearly and completely described in conjunction with the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0035] The technical solutions and features provided in the various sections, including the following description, can be combined with each other without conflict. Furthermore, where possible, these technical solutions, features, and related combinations can be given specific technical subject matter and protected by relevant patents.

[0036] The embodiments of the present invention described below are generally only some embodiments and not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of patent protection.

[0037] The term "comprising," and any variations thereof, in this specification, the corresponding claims, and related sections are intended to cover a non-exclusive inclusion. Other related terms and units can be reasonably interpreted based on the relevant content provided in this specification.

[0038] Example 1

[0039] This embodiment provides a method for constructing a subway track irregularity spectrum. Taking subway line data of a single city as an example, the steps of the core technical solution of this invention are explained in detail.

[0040] Step a): Obtain measured track irregularity data.

[0041] In this step, measured track irregularity data were obtained from multiple subway lines in the city during different operating hours, measured by track inspection vehicles. Data types include elevation irregularities (left and right rails), track alignment irregularities (left and right rails), horizontal irregularities, and track gauge irregularities.

[0042] Step b): Calculate the power spectral density lines.

[0043] Based on the measured track irregularity data obtained in step a), power spectral density estimation methods known in the art, such as the Welch method, are used to calculate the power spectral density spectral lines for each line and various irregularity types. Figure 1 and Figure 2 As shown, preliminary analysis indicates that the curve shape and orbital structure have little impact on the overall trend of the spectral lines, which provides a basis for averaging data from different lines to obtain a universal model.

[0044] Step c): Preprocess the power spectral density lines.

[0045] To obtain a clean background of random irregularities, the power spectral density lines obtained in step b) need to be preprocessed. This preprocessing mainly includes identifying and eliminating periodic spectral peaks caused by track geometry features (such as a standard rail length of 25m, a simply supported beam bridge length of 30m, etc.), as well as attenuation values ​​or spikes caused by data acquisition anomalies. Elimination methods can employ local interpolation or smoothing algorithms. This step ensures that the subsequently fitted model is specific to random irregularities, avoiding contamination of the model by the periodic characteristics of a particular track.

[0046] Step d): Convert to log-log coordinate system.

[0047] The purified power spectral density lines obtained after preprocessing in step c) are transformed to a log-log coordinate system. In this coordinate system, the horizontal axis represents the logarithm of the spatial frequency f. 10 (S(f)), the vertical axis is the logarithm of the power spectral density value S (log 10 (S)). This transformation can effectively reduce the complexity of spectral morphology, compressing a curve with a very large dynamic range into a curve with a smoother shape that is easier to describe with a simple function.

[0048] Step e): Establish an analytical expression by fitting a fifth-order polynomial.

[0049] In a log-log coordinate system, a nonlinear least squares method is used to fit the transformed data points using a fifth-order polynomial, thereby establishing an analytical expression for the power spectral density of track irregularities.

[0050] The parsing expression is in the form of:

[0051] log 10 (S(f))=A0+A1·log 10 (f)+A2·(log 10 (f)) 2 +A3·(log 10 (f)) 3 +A4·(log 10 (f)) 4 +A5·(log 10 (f)) 5 ,in:

[0052] S(f) is the power spectral density obtained by the fifth-order polynomial fitting, f is the spatial frequency, and A0, A1, A2, A3, A4, and A5 are the coefficients determined by the fifth-order polynomial fitting.

[0053] Figure 3 The fitting results are shown using the average power spectral density spectrum of the uneven left rail of a subway line (specifically the Shanghai Metro) as an example. As can be seen from the figure, the analytical expression curve (solid line) obtained by the fifth-order polynomial fitting closely matches the preprocessed discrete spectral data (dots), demonstrating that this method has extremely high fitting accuracy.

[0054] The coefficients A0 to A5 obtained by fitting the average spectrum of various irregularities in the Shanghai Metro are shown in Table 1.

[0055] Table 1: Fitting coefficients of the average spectrum of track irregularities in Shanghai Metro

[0056] Uneven <![CDATA[A0]]> <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[A4]]> <![CDATA[A5]]> High / Low - Left Rail -4.051 -21.107 -59.358 -84.878 -52.933 -11.643 High / Low - Right Rail -4.478 -24.372 -68.785 -96.859 -59.798 -13.100 Track direction - left track -5.104 -30.367 -87.523 -123.710 -77.330 -17.282 Track direction - right rail -5.554 -33.826 -96.106 -133.100 -82.047 -18.172 gauge -1.962 2.153 18.031 22.690 11.717 2.243 level -2.340 -3.303 0.011 1.304 1.112 0.337

[0057] Example 2

[0058] Based on Example 1, this embodiment further describes how to construct a more representative overall orbital irregularity power spectral density model and provides specific model parameter ranges.

[0059] First, repeat steps a) to e) in Example 1 to process the subway line data from multiple cities (such as Shanghai, Wuhan, Wuxi, Guangzhou, Chongqing, Lanzhou, Dalian, Ningbo, etc.) separately, establish an independent analytical expression for each city and each type of irregularity, and obtain its corresponding coefficients A0 to A5.

[0060] Then, following step e), an averaging process is performed: the coefficients (A0 to A5) of the same type of irregularity (e.g., all cities with high and low irregular left rails) of the analytical expressions from the aforementioned cities are arithmetically averaged. Through this averaging of the model parameters, a final overall track irregularity power spectral density model is established.

[0061] Figure 4 This paper presents a power spectral density model for the overall unevenness of the left rail, obtained by averaging data from all cities. This model integrates common characteristics of subway lines in several representative Chinese cities, demonstrating high universality and authority.

[0062] Table 2 presents the fitting coefficients for the overall average spectrum of track irregularities.

[0063] Table 2: Overall average spectrum fitting coefficients for track irregularities

[0064] Uneven <![CDATA[A0]]> <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[A4]]> <![CDATA[A5]]> High / Low - Left Rail -2.710 -5.977 -13.767 -24.045 -16.754 -3.928 High / Low - Right Rail -3.045 -8.685 -20.369 -30.960 -20.037 -4.510 Track direction - left track -3.512 -11.168 -25.533 -36.929 -23.312 -5.159 Track direction - right rail -3.345 -10.053 -22.406 -32.861 -20.903 -4.633 gauge -2.259 1.159 15.591 19.608 9.620 1.684 level -2.146 0.358 7.612 6.483 1.844 0.097

[0065] Based on the data in Table 2, this invention provides the preferred value ranges for the coefficients A0 to A5 of the high and low irregularities on the left track in the overall track irregularity power spectral density model. For example, a fluctuation range of ±10% can be set based on the center value of -2.710, that is, the value range of A0 is -2.710 ± 10%. Similarly, the ranges of other coefficients can be obtained, which provides direct and reliable standardized parameters for engineering applications.

[0066] Example 3

[0067] This embodiment describes how to generate a quantile orbital irregularity power spectral density model with specific statistical percentiles.

[0068] Based on the analytical expression established in Example 1 or Example 2 (which is obtained from the average value of the power spectrum, and in random processes such as orbital irregularities that follow a specific statistical distribution, the average value usually corresponds to about the 63.2 percentile, rather than the 50th percentile corresponding to the median), step f) is performed: multiply the analytical expression by a conversion coefficient k.

[0069] S_p(f) = k·S_avg(f)

[0070] Where S_avg(f) is the power spectral density of the average spectrum, and S_p(f) is the power spectral density of the quantile spectrum corresponding to the target percentile p. The values ​​of the conversion coefficient k can be found in Table 3. By selecting different k values, track irregularity spectra representing different maintenance levels or statistical significance can be easily generated, such as the 30th percentile spectrum (representing a better condition) or the 90th percentile spectrum (representing a poor condition).

[0071] Table 3: Conversion coefficients between the mean spectrum and percentile spectrum of orbital irregularities

[0072] parameter 10% 20% 30% 39.4% 50% 63.2% 70% 80% 90% K median 0.152 0.322 0.515 0.722 1.000 1.443 1.737 2.322 3.322 K average 0.105 0.223 0.357 0.5 0.693 1.000 1.204 1.609 2.303

[0073] Figure 5 A series of quantile spectra generated based on the average spectrum of Shanghai Metro were demonstrated, which greatly expanded the application scenarios of the model and can be used for extreme condition analysis, fatigue life assessment, etc.

[0074] Example 4

[0075] This embodiment describes how to use the spectral model constructed in this invention to generate numerical simulation samples of orbit irregularities that are closer to reality and incorporate characteristics of medium- and long-wavelengths and short-wavelengths.

[0076] Step A: Using the Inverse Fast Fourier Transform (IFFT) method, based on the analytical expression for the power spectral density of track irregularities established in Example 1 or Example 2, a sequence of medium-to-long-wavelength random irregular displacements is generated. The accuracy of the IFFT method can be verified by... Figure 7 Verification, from Figure 7 (a) and Figure 7 (b) It can be seen that the inverted samples are highly consistent with the measured samples in both the time and frequency domains.

[0077] Step B: Set the rail corrugation parameters that represent the short-wave characteristics, including the corrugation amplitude B and the corrugation wavelength l. These parameters are determined based on the actual conditions of the track (such as track structure type, curve radius, etc.).

[0078] Step C: Based on the rail corrugation parameters set in Step B, a short-wave periodic irregular displacement sequence is generated using the cosine function y(x)=B·cos(2πx / l), where x is the mileage.

[0079] Step D: Linearly superimpose the medium- and long-wave random irregular displacement sequence generated in Step A with the short-wave periodic irregular displacement sequence generated in Step C to obtain the final numerical simulation sample of track irregularities.

[0080] Figure 6 This superposition process is clearly demonstrated, and the final sample (the black line at the top) contains both background random irregularities and key periodic ripple excitations, making it far more realistic than samples containing only random components.

[0081] Example 5

[0082] This embodiment provides a specific basis for determining the parameters in step B of embodiment 4, and further explains how to associate the corrugation parameters with the specific track structure type and track conditions.

[0083] To establish this correlation, the inventors conducted extensive statistical analysis of measured data. The results show that the rail corrugation characteristics differ significantly under different working conditions. Two typical examples are provided below: Statistical data shows that when simulating track irregularities in a "18mm elastic short sleeper + integral track bed" configuration on a small-radius curve (such as R350), the typical range of the corrugation wavelength l is 63mm to 100mm, and the amplitude B (half of the peak value) can reach a maximum of 0.35mm. This provides direct data support for the present invention's definition of "the range of the corrugation wavelength l being 63mm to 100mm." Similarly, when simulating track irregularities in a "standard fastener + standard integral track bed" configuration on a straight section, the typical range of the corrugation wavelength l is 160mm to 250mm, and the amplitude B (half of the peak value) can reach a maximum of 0.215mm. This also provides direct data support for the present invention's definition of "the range of the corrugation wavelength l being 160mm to 250mm."

[0084] This refined parameter setting provides a clear engineering basis for simulating shortwave irregularities, significantly improving the realism and relevance of the final generated samples.

[0085] The foregoing has described the relevant content of the present invention. Those skilled in the art will be able to implement the present invention based on these descriptions. All other embodiments obtained by those skilled in the art based on the foregoing content of this specification without inventive effort should fall within the scope of the present invention.

Claims

1. A method for constructing a subway track irregularity spectrum, characterized in that: Includes the following steps: a) Obtain measured track irregularity data for at least one subway line; b) Based on the measured track irregularity data, the power spectral density line is calculated, which represents the relationship between the power spectral density value and the spatial frequency. c) Preprocessing the power spectral density lines, the preprocessing including identifying and eliminating periodic spectral peaks caused by orbital geometry features; d) Convert the preprocessed power spectral density lines to a log-log coordinate system, where the horizontal axis represents the logarithmic value of the spatial frequency and the vertical axis represents the logarithmic value of the power spectral density. e) In the aforementioned log-log coordinate system, an analytical expression for the power spectral density of orbital irregularities is established through fifth-order polynomial fitting: log 10 (S(f)) = A0 + A1·log 10 (f) + A2·(log 10 (f)) 2 + A3·(log 10 (f)) 3 + A4·(log 10 (f)) 4 + A5·(log 10 (f)) 5 , where: S(f) is the power spectral density obtained by the fifth-order polynomial fitting, f is the spatial frequency, and A0, A1, A2, A3, A4, and A5 are the coefficients determined by the fifth-order polynomial fitting.

2. The method for constructing the subway track irregularity spectrum according to claim 1, characterized in that: In step a), measured track irregularity data from multiple subway lines are obtained, and in step b), the power spectral density line of each subway line is calculated.

3. The method for constructing the subway track irregularity spectrum according to claim 2, characterized in that: Also includes: After step e), the multiple analytical expressions for power spectral density are averaged to establish a total orbital irregularity power spectral density model.

4. The method for constructing the subway track irregularity spectrum according to claim 3, characterized in that: The coefficients A0, A1, A2, A3, A4, and A5 of the overall track irregularity power spectral density model are as follows: A0: -2.710±10%, A1: -5.977±10%, A2: -13.767±10%, A3: -24.045±10%, A4: -16.754±10%, A5: -3.928±10%.

5. The method for constructing the subway track irregularity spectrum according to claim 1, characterized in that: It also includes step f): multiplying the analytical expression established in step e) by a transformation coefficient k to generate a quantile orbital irregularity power spectral density model with specific statistical percentiles.

6. The method for constructing the subway track irregularity spectrum according to claim 1, characterized in that: The method is also used to generate numerical simulation samples of track irregularities that incorporate characteristics of medium- and long-wavelengths and short-wavelengths, and includes the following subsequent steps: A. Using the inverse fast Fourier transform method, based on the analytical expression of the power spectral density of track irregularities established in step e), a medium- and long-wavelength random irregular displacement sequence is generated; B. Provide rail corrugation parameters that represent short-wave characteristics, including corrugation amplitude B and corrugation wavelength l; C. Based on the rail corrugation parameters, a short-wave periodic irregular displacement sequence is generated using the cosine function y(x)=B·cos(2πx / l), where x is the mileage; D. The medium- and long-wave random irregular displacement sequence is linearly superimposed with the short-wave periodic irregular displacement sequence to obtain the final numerical simulation sample of track irregularity.

7. The method for constructing the subway track irregularity spectrum according to claim 6, characterized in that: The corrugation amplitude B and corrugation wavelength l are determined based on the track structure type of the line.

8. The method for constructing the subway track irregularity spectrum according to claim 7, characterized in that: When the track structure type is "18mm elastic short sleeper + integral track bed" and it is located on a small radius curve, the value range of the corrugation wavelength l is 63mm to 100mm.

9. The method for constructing the subway track irregularity spectrum according to claim 7, characterized in that: When the track structure type is "ordinary fastener + ordinary integral track bed" and it is located on a straight section, the value range of the corrugated wavelength l is 160mm to 250mm.

10. The method for constructing the subway track irregularity spectrum according to claim 1, characterized in that: The constructed track irregularity spectrum includes at least one of the following: elevation irregularity spectrum, directional irregularity spectrum, horizontal irregularity spectrum, and gauge irregularity spectrum.

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