Train bearing component load spectrum random inversion and tabulation method and system

Abstract

The present application relates to the field of rail vehicle structure strength, and discloses a train bearing component load spectrum random inversion music compilation method and system to improve the music compilation efficiency and ensure the accuracy. The method comprises the following steps: acquiring A mileage dynamic load time history of a train bearing component under multiple measuring points and multiple working conditions; calculating dynamic load coefficients of each working condition, and counting the mean value, root mean square, maximum and minimum boundary values of similar components. The normal distribution inverse cumulative function is obtained from the mean value and root mean square, and the real probability interval is obtained in combination with the boundary values. A uniform random array of each working condition of B mileage is generated, mapped to the real probability interval, and then converted to a dynamic load coefficient sequence of each working condition through the inverse cumulative function. The final sequence is spliced according to the working condition distribution of B mileage.

Description

Technical Field

[0001] This invention relates to the field of railway vehicle structural strength technology, and in particular to a method and system for random inversion and compilation of load spectrum of train load-bearing components. Background Technology

[0002] With the rapid development of modern rail transit technology, the operating speeds of transportation equipment such as high-speed trains and subway vehicles are constantly increasing, and the operating environment is becoming increasingly complex. During high-speed operation, these vehicles are subjected to various dynamic loads, including wheel-rail excitation and aerodynamic loads, which pose a serious threat to the structural safety and reliability of the vehicles. Therefore, accurate fatigue life assessment of key vehicle components has become an important means to ensure the safe operation of vehicles.

[0003] In fatigue life assessment, the compilation of dynamic load spectra is a crucial step. Dynamic load spectra reflect the dynamic load characteristics experienced by vehicles during actual operation, providing fundamental data for fatigue life prediction. However, traditional dynamic load spectrum compilation methods are often based on empirical formulas or simplified models, making it difficult to accurately reflect the complex load conditions encountered by vehicles in actual operation. Therefore, exploring a high-precision and high-efficiency dynamic load envelope random spectrum compilation technique is of great significance for improving the accuracy of fatigue life assessment for rail vehicles.

[0004] Currently, fatigue life assessment for rail vehicles still faces many challenges. Traditional dynamic load spectrum compilation methods are difficult to accurately reflect the complex load conditions of vehicles in actual operation, resulting in significant errors in fatigue life prediction results; improvements are needed. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for random inversion and compilation of load spectra of train load-bearing components, so as to improve compilation efficiency and ensure accuracy.

[0006] To achieve the above objectives, the random inversion and compilation method for the load spectrum of train load-bearing components disclosed in this invention includes:

[0007] Step S1: Obtain the dynamic load time history information corresponding to the operation of at least two measuring points of the target train's load-bearing components at at least two typical operating conditions at mileage A. Step S2: Calculate the dynamic load coefficient of each load-bearing component under each typical working condition at mileage A based on the dynamic load time history information, and obtain the boundary values ​​of the average, root mean square, maximum and minimum values ​​of the dynamic load coefficients of all load-bearing components of the same type after classifying and summarizing them according to working conditions. Step S3: Generate the corresponding normal distribution function based on the statistical mean and root mean square, and obtain the relationship between probability and coefficient quantile in the inverse cumulative distribution function through inverse transformation; Step S4: Obtain the probability interval within the true range using the inverse cumulative distribution function and the maximum and minimum values; Step S5: Generate a uniformly distributed random array of 0 to 1 with the required number of data for each working condition at the target mileage B. Step S6: Combine the probability interval within the true range to transform the uniformly distributed random array to obtain the true probability array. The calculation formula is: True probability array = (maximum probability within the probability interval - minimum probability within the probability interval) × uniformly distributed random array + minimum probability within the probability interval. Step S7: Transform the true probability array using the inverse cumulative distribution function to obtain the dynamic load coefficient sequence applicable to all similar load-bearing components of the target train under the corresponding working conditions; Step S8: Based on the distribution of working conditions of the target line B, splice and combine the dynamic load coefficient sequences of different working conditions to generate the dynamic load coefficient sequence of mileage B.

[0008] Preferably, the dynamic load factor The calculation formula is: ;in, This refers to the instantaneous vertical or lateral contact force between the wheel and rail when the vehicle is in motion. The vertical contact force between the wheel and rail when the vehicle is stationary, indicated by the superscript. Indicates vertical direction, superscript It refers to the horizontal direction.

[0009] Preferably, the operating conditions are any one of open track operation, open track intersection, tunnel intersection, and single vehicle passing through a tunnel.

[0010] Preferably, under high-speed operating conditions where the speed exceeds a set threshold, the constant mean load spectrum method is used to compile the load spectrum.

[0011] Preferably, in step S1, the dynamic load time history information corresponding to mileage A is determined by actual measurement or simulation based on multibody dynamics.

[0012] Typically, the number of elements from 0 to 1 in the uniformly distributed random array expected for any operating condition at the target mileage B is the product of the sampling frequency and the mileage. Further, the method of this invention also includes step S9: calculating the statistics of the generated dynamic load coefficient sequence of mileage B and comparing it with the statistical value from step S2 to complete data verification, ensuring the generated data is within acceptable limits; and performing spectrum compilation and comparison with existing load spectra to verify that the generated data is within acceptable limits; and verifying the dynamic load coefficient sequence of mileage B through time series indicators such as autocorrelation function, power spectral density, and / or damage equivalence under representative SN curves.

[0013] For example, the comparative data verification in step S9 specifically includes: comparing the four statistical features of the generated dynamic load coefficient sequence of mileage B with the statistical features of step S2, and judging that the standard within the acceptable range is that the error of each statistical feature is within 5%, and the comparison with the existing load spectrum is in the form of probability density spectrum.

[0014] To achieve the above objectives, the present invention also discloses a random inversion and compilation system for the load spectrum of train load-bearing components, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0015] The present invention has the following beneficial effects: Based on statistical principles, a dynamic load statistical envelope model was constructed. Monte Carlo and other random generation methods were used to invert the dynamic load time history and randomly compile the spectrum, thus generating a dynamic load spectrum that reflects the actual operating load characteristics of the vehicle and can flexibly adapt to splicing different mileages and operating conditions. The results show that the generated dynamic load spectrum is consistent with the measured data in statistical characteristics and can accurately simulate the dynamic load variation patterns of the vehicle under different operating conditions. Furthermore, the load spectrum obtained through statistical envelope can reflect the most severe dynamic loads that key vehicle components may encounter during service, providing important basis for the design and evaluation of vehicle structural strength.

[0016] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the random inversion and compilation method for the load spectrum of train load-bearing components disclosed in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of the distribution of dynamic load time history disclosed in an embodiment of the present invention.

[0019] Figure 3 and Figure 4 These are schematic diagrams showing the relationship between the dynamic load coefficient disclosed in the embodiments of the present invention and each statistical parameter based on separate vertical or horizontal statistics and the quadrant.

[0020] Figure 5 This is a schematic diagram showing the distribution of the vertical dynamic load coefficient of the open line generated by the random algorithm disclosed in the embodiments of the present invention as a function of mileage.

[0021] Figure 6This is a schematic diagram showing the distribution of the lateral dynamic load coefficient of the open line as a function of mileage, generated by the random algorithm disclosed in this embodiment of the invention.

[0022] Figure 7 This is a schematic diagram comparing the wheel vertical dynamic load coefficient generated by the inversion method disclosed in this embodiment of the invention with the measured results.

[0023] Figure 8 This is a schematic diagram of the vertical and lateral wheel load spectra generated by the method disclosed in the embodiments of the present invention under three working conditions: open road, intersection, and tunnel. Detailed Implementation

[0024] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0025] Example 1 This embodiment discloses a method for random inversion and compilation of load spectrum of train load-bearing components, which aims to provide a basis for the design of wheels under complex load spectrum by generating dynamic load coefficient mileage curve data in reverse.

[0026] First, based on a large amount of measured data, analysis revealed that the wheel dynamic load coefficient follows a normal distribution. As a common continuous probability distribution, the shape of the normal distribution is completely determined by two parameters: the mean (expectation) and the standard deviation. This allows this embodiment to directly construct the corresponding normal distribution function based on existing statistical characteristic parameters.

[0027] Based on statistical analysis, the expected value μ and standard deviation σ of the dynamic load coefficient of each wheel can be obtained, and the corresponding normal distribution function can be written. The probability density function of the normal distribution function for: in, Represents the dynamic load coefficient. The mean, The standard deviation is denoted as .

[0028] After determining the fitting method, the Monte Carlo method is used to generate a random sequence conforming to the above-mentioned normal distribution. The Monte Carlo method, as an algorithm for approximating mathematical problems through random sampling, is suitable for simulating processes with stochastic properties. The specific implementation process is as follows: First, using the obtained statistical characteristics of the boundary loads, such as the mean and standard deviation, and the corresponding normal distribution function, the maximum and minimum values ​​of the dynamic load coefficients are used to limit the probability interval of the data to be generated. Then, a uniform sequence of 0 to 1 is randomly generated using the uniform distribution function U(0,1). Finally, values ​​meeting the conditions are selected using boundary probability values ​​as the probability distribution under the normal distribution. After obtaining the random numbers, the random sequence is mapped to these probability intervals according to the inverse cumulative distribution function (ICDF, also known as the inverse cumulative distribution function). Through this mapping, a random sequence of dynamic load coefficients corresponding to the original normal distribution can be obtained. Each value in this sequence is randomly sampled according to the probability density function of the normal distribution, thus effectively simulating dynamic load changes in actual operation.

[0029] In this embodiment, to ensure that the generated random sequence of dynamic load coefficients also meets the actual requirements in the frequency domain, the maximum frequency in the frequency domain can be controlled by limiting the sampling frequency. In other words, when generating the random sequence, this embodiment needs to consider the rate of change of the dynamic load coefficients under actual operating conditions to ensure that the simulation results are not only consistent with the original data in terms of statistical characteristics, but also similar in terms of the dynamic characteristics of the time series.

[0030] In summary, the random inversion and compilation method for the load spectrum of train load-bearing components disclosed in this embodiment is applicable to the processing of load spectra at various speed levels up to 600 km / h, and can be summarized as follows: Figure 1 The following is a more simplified series of steps: Step S1: Obtain the dynamic load time history information corresponding to the running distance A of at least two wheels of the target train under the target working condition.

[0031] In this step, "same type of load-bearing components" specifically refers to components such as wheels or air springs under the same bogie, with the same load type and almost identical load conditions; the target operating condition can be any one of open track operation, open track intersection, tunnel intersection, and single vehicle passing through a tunnel; the dynamic load time history information corresponding to mileage A is determined through actual measurement (based on sensors for some or all wheels) or simulation based on multibody dynamics (usually, the dynamic load time history information corresponding to all wheels can be obtained at once); and one optional dynamic load time history information is as follows: Figure 2 As shown.

[0032] Step S2: Calculate the dynamic load coefficient of each load-bearing component under each typical working condition at mileage A based on the dynamic load time history information, and obtain the boundary values ​​of the average, root mean square, maximum and minimum values ​​of the dynamic load coefficients of all load-bearing components of the same type after classifying and summarizing them according to working conditions.

[0033] In this step, the dynamic load factor is determined based on the relationship between the statistical parameters and the quadrants, calculated separately for the vertical or lateral directions. Figure 3 and Figure 4 Among them, the dynamic load factor The calculation formula is: ;in, This refers to the instantaneous vertical or lateral contact force between the wheel and rail when the vehicle is in motion. The vertical contact force between the wheel and rail when the vehicle is stationary, indicated by the superscript. Indicates vertical direction, superscript The horizontal direction refers to the superscript in the calculation formula. Indicates vertical or horizontal direction.

[0034] The boundary value in this step is selected by taking the extreme value of the same characteristic value of all similar load-bearing components. This extreme value is a reasonable extreme value after the preprocessing of equalization.

[0035] Step S3: Generate the corresponding normal distribution function based on the statistical mean and root mean square, and obtain the relationship between the probability and coefficient quantiles in the inverse cumulative distribution function through inverse transformation.

[0036] Step S4: Obtain the probability interval within the true range using the inverse cumulative distribution function and the maximum and minimum values.

[0037] Step S5: Generate a uniformly distributed random array of 0 to 1 with the required amount of data for each working condition at the target mileage B. Preferably, this step generates the uniformly distributed random array of 0 to 1 with the same sampling frequency as the time history data in mileage A.

[0038] Step S6: Combine the probability interval within the true range to transform the uniformly distributed random array to obtain the true probability array. The calculation formula is: True probability array = (maximum probability within the probability interval - minimum probability within the probability interval) × uniformly distributed random array + minimum probability within the probability interval.

[0039] Step S7: Transform the true probability array using the inverse cumulative distribution function to obtain the dynamic load coefficient sequence applicable to all similar load-bearing components of the target train under the corresponding working conditions.

[0040] Step S8: Based on the distribution of working conditions of the target line B, splice and combine the dynamic load coefficient sequences of different working conditions to generate the dynamic load coefficient sequence of mileage B.

[0041] The distribution of working conditions for the target line B in this step mainly includes the distribution order of each working condition and the mileage information corresponding to each working condition.

[0042] The essence of the above steps in this embodiment is to first segment the dynamic load time history information of each working condition from mileage A, then summarize and statistically analyze the dynamic load coefficients of all similar load-bearing components according to working conditions, and then obtain simulation data of other mileages under the same working conditions for the user based on the inversion model of the Monte Carlo method (based on probability and statistical theory and using random numbers to solve the calculation problem). Finally, the complete dynamic load coefficient sequence of the target line B is obtained by splicing the data of different working conditions.

[0043] Step S9 (not shown in the figure): Calculate the statistics of the generated dynamic load coefficient sequence of mileage B and compare them with the statistical values ​​from step S2 to complete data verification, ensuring that the generated data is within the acceptable range. Then, perform spectral analysis and compare it with existing load spectra for verification. For example, compare the four statistical features of the generated dynamic load coefficient sequence of mileage B with the statistical features from step S2. The standard for determining if it is within the acceptable range is that the error of each statistical feature is within 5%, and the comparison with existing load spectra is performed in the form of probability density spectrum.

[0044] In the above steps, step S1 acquires real random load data, step S2 extracts random features from the data, step S3 constructs a random control function, step S4 generates random boundary constraints, step S5 generates pseudo-random numbers, and steps S6 and S7 generate random samples. Steps S3-S7 are inversion models using the Monte Carlo method (based on probability and statistical theory, using random numbers to solve computational problems). If necessary, verification can be performed in step S9 based on the time series index autocorrelation function and power spectral density, and the damage equivalence of the dynamic load coefficient sequence of mileage B obtained in this step under the representative SN curve can be studied. Furthermore, the key statistics (mean, standard deviation, maximum value, minimum value) of the generated dynamic load coefficient sequence of mileage B can be calculated and compared with the given data to complete data verification. If the verification fails, the above steps are returned and / or the preprocessing process is corrected, and this process is repeated until the verification passes, thereby realizing the verification of randomly generated data and ensuring that the generated data is within an acceptable range.

[0045] In this step, the distribution of the generated vertical and lateral dynamic load coefficients of the open line with mileage is respectively referred to Figure 5 and Figure 6Among them, the statistical parameters of the vertical or lateral dynamic load coefficients under each working condition are basically consistent with the statistical parameters of mileage A.

[0046] Furthermore, to further verify whether the simulation data is consistent with the actual situation, the vertical dynamic load coefficient generated at 400km / h was compared with the measured line spectrum. The results are as follows: Figure 7 As shown in the figure, the trend of data variation at 400 km / h in the comparison graph shows a high degree of consistency with the measured data at 350 km / h and 330 km / h. The maximum frequency load coefficient is not affected by the speed level change; the generated data comparison uses a 16-level mean-frequency spectrum. As the speed increases, the maximum frequency load appears more frequently in each load level. This impact state is generated by the train's serpentine motion and high-frequency wheel-rail impact caused by the increase in wheel and axle speed. Under high-speed conditions, the high-frequency load will be closer to the mean and more concentrated, and the root mean square will be smaller, which is consistent with the characteristics of the randomly generated data curve. Therefore, the model data and the measured data are highly consistent in statistical characteristics, verifying the accuracy and reliability of the simulation model, and providing a solid foundation for subsequent high-speed train dynamics analysis and optimization design.

[0047] In applications based on the aforementioned reverse-generated dynamic load coefficient mileage curve data, the train load spectrum can be compiled using the rainflow counting method. The principle is that when the stress-strain relationship corresponding to a random load forms a hysteresis loop, a cycle is constituted. This counting method assumes that extracting a hysteresis loop from a small range will not affect the damage caused by the entire large range. Therefore, small cycles from multiple hysteresis loops can be extracted from the entire large range and combined. After processing using this method, the time history data can be converted into mean and amplitude values.

[0048] After obtaining the mean amplitude, to construct a one-dimensional load spectrum, the data needs to be simplified to a univariate random variable, which is where the wave center method comes in. The static load component of the load cycle is replaced by the wave center, which is considered a fixed parameter. The dynamic load component of the load cycle is replaced by its amplitude, which is then superimposed on the wave center. If the mean is a specific value, a constant mean load spectrum can be obtained. This method ignores changes in the mean and is suitable for situations where the data mean is relatively stable. For example, in high-speed conditions, the higher the speed level, the greater the load concentration, making the constant mean load spectrum method more suitable.

[0049] The load data obtained from line testing are all acquired within a certain line length. For example, the line spectrum used in the model also uses irregularity data from a 4km ballasted track. If we consider the amplitude and mean of the load data as random variables, and their correspondence with the frequency as a frequency distribution, then the population distribution function can be estimated and inferred from the frequency distribution of the sample. The load amplitude generally follows a three-parameter Weibull distribution.

[0050] Based on the data calculated under the three working conditions, this embodiment can use the above method to compile a 16-level constant-mean amplitude spectrum and fit it according to a three-parameter Weibull distribution. The load spectrum compilation results for the three working conditions can be referred to respectively. Figure 8 .

[0051] In summary, in this embodiment, the dynamic model obtained from the time history data of mileage A using existing methods based on multibody dynamics is very complex. This results in very low efficiency in reconstructing the dynamic load coefficient mileage curves of other mileages under the same operating conditions based on the dynamic model. However, the method disclosed in this embodiment can quickly and accurately reconstruct the dynamic load coefficient curves of other flexibly set mileages from the measured dynamic load time history data or the dynamic load time history data of the target operating conditions based on multibody dynamics models under a limited mileage. This achieves the effect of improving the efficiency of spectrum compilation and ensuring accuracy.

[0052] Example 2 Corresponding to the above embodiments, this embodiment discloses a random inversion and compilation system for the load spectrum of train load-bearing components, 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 aforementioned method. The core of this method is: acquiring the dynamic load time history of train load-bearing components at multiple measurement points and under multiple operating conditions at mileage A; calculating the dynamic load coefficients for each operating condition; and statistically analyzing the mean, root mean square, and maximum and minimum boundary values ​​of similar components. The inverse cumulative function of the normal distribution is obtained from the mean and root mean square, combined with the true probability interval of the boundary values. A uniform random array of each operating condition at mileage B is generated, mapped to the true probability interval, and then transformed using the inverse cumulative function to obtain the dynamic load coefficient sequence for each operating condition. The final sequence is generated by splicing the load condition distributions at mileage B.

[0053] In summary, the methods and systems disclosed in the two embodiments of the present invention have at least the following beneficial effects: Based on statistical principles, a dynamic load statistical envelope model was constructed. Monte Carlo and other random generation methods were used to invert and stochastically compile the dynamic load time history, thereby generating a dynamic load spectrum that reflects the actual operating load characteristics of the vehicle and can flexibly adapt to splicing different mileages and operating conditions. The results show that the generated dynamic load spectrum is consistent with the measured data in statistical characteristics and can accurately simulate the dynamic load variation patterns of the vehicle under different operating conditions. Furthermore, the load spectrum obtained through statistical envelope can reflect the most severe dynamic loads that key vehicle components may encounter during service, providing an important basis for the design and evaluation of vehicle structural strength; and it can be extended to the stochastic inversion and compilation of load spectra for other load-bearing components of trains.

[0054] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for stochastic inversion and compilation of load spectra for train load-bearing components, characterized in that, include: Step S1: Obtain the dynamic load time history information corresponding to the operation of at least two measuring points of the target train's load-bearing components at at least two typical operating conditions at mileage A. Step S2: Calculate the dynamic load coefficient of each load-bearing component under each typical working condition at mileage A based on the dynamic load time history information, and obtain the boundary values ​​of the average, root mean square, maximum and minimum values ​​of the dynamic load coefficients of all load-bearing components of the same type after classifying and summarizing them according to working conditions. Step S3: Generate the corresponding normal distribution function based on the statistical mean and root mean square, and obtain the relationship between probability and coefficient quantile in the inverse cumulative distribution function through inverse transformation; Step S4: Obtain the probability interval within the true range using the inverse cumulative distribution function and the maximum and minimum values; Step S5: Generate a uniformly distributed random array of 0 to 1 with the required number of data for each working condition at the target mileage B. Step S6: Combine the probability interval within the true range to transform the uniformly distributed random array to obtain the true probability array. The calculation formula is: True probability array = (maximum probability within the probability interval - minimum probability within the probability interval) × uniformly distributed random array + minimum probability within the probability interval. Step S7: Transform the true probability array using the inverse cumulative distribution function to obtain the dynamic load coefficient sequence applicable to all similar load-bearing components of the target train under the corresponding working conditions; Step S8: Based on the distribution of working conditions of the target line B, splice and combine the dynamic load coefficient sequences of different working conditions to generate the dynamic load coefficient sequence of mileage B.

2. The method for random inversion and compilation of load spectrum of train load-bearing components according to claim 1, characterized in that, The operating conditions are any one of the following: running on open track, meeting on open track, meeting in a tunnel, and single vehicle passing through a tunnel.

3. The method for random inversion and compilation of load spectrum of train load-bearing components according to claim 1 or 2, characterized in that, Also includes: Step S9: Calculate the statistics of the generated dynamic load coefficient sequence of mileage B and compare it with the statistics of step S2 to complete the data verification, ensure that the generated data is within the acceptable range, and perform spectrum compilation and comparison verification with the existing load spectrum.

4. The method for random inversion and compilation of load spectrum of train load-bearing components according to claim 3, characterized in that, The comparative data verification in step S9 specifically includes: comparing the four statistical features of the generated dynamic load coefficient sequence of mileage B with the statistical features of step S2, and judging that the standard within the acceptable range is that the error of each statistical feature is within 5%, and the comparison with the existing load spectrum is in the form of probability density spectrum.

5. The method for random inversion and compilation of load spectrum of train load-bearing components according to claim 1 or 2, characterized in that, The number of 0 to 1 elements in the uniformly distributed random array expected for any operating condition at target mileage B is the product of the sampling frequency and the mileage.

6. A random inversion and compilation system for the load spectrum of a train load-bearing component, 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 described in any one of claims 1 to 5.

Images