Method for evaluating hunting of straddle-type monorail vehicle based on factor analysis

Abstract

The application discloses a kind of across seat type monorail vehicle shimmy evaluation method based on factor analysis method, comprising: S1. Vehicle shimmy parameter is collected, and vehicle shimmy parameter is standardized, and the parameter after processing is obtained;S2. The correlation coefficient matrix of processing parameter is calculated;S3. Whether correlation coefficient matrix is suitable for doing factor analysis, if yes, then enter step S4;If not, then return to step S1;S4. The factor loading matrix of correlation coefficient matrix is calculated;S5. Rotating factor loading matrix is obtained, and the shimmy factor model is obtained by rotating factor loading matrix;S6. Based on rotating factor loading matrix and shimmy factor model, calculate comprehensive factor score;And through comprehensive factor score, the shimmy degree of vehicle is evaluated.The application can quickly and effectively evaluate monorail vehicle shimmy state.

Description

Technical Field

[0001] This invention relates to the field of monorail vehicle transportation, and specifically to a method for evaluating the sway of straddle-type monorail vehicles based on factor analysis. Background Technology

[0002] Shimmy in straddle-type monorail vehicles is a highly complex vibration phenomenon, influenced by the coupled effects of vehicle structural parameters, tire parameters, and suspension parameters. This not only reduces passenger comfort but also significantly impacts operational stability, safety, and structural fatigue life. Therefore, conducting shimmy assessments during the vehicle development and design phases is crucial and plays a vital role in the development and design of straddle-type monorail vehicles.

[0003] Currently, there is a lack of methods or means to evaluate vehicle shimmy during the research and design phase of straddle-type monorail vehicles. Therefore, there is an urgent need for a shimmy evaluation method for straddle-type monorail vehicles based on factor analysis. Summary of the Invention

[0004] In view of this, the purpose of this invention is to overcome the deficiencies in the prior art and provide a method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis, which can quickly and effectively evaluate the shimmy state of monorail vehicles.

[0005] The method for evaluating the sway vibration of straddle-type monorail vehicles based on factor analysis of the present invention includes the following steps:

[0006] S1. Collect vehicle shimmy parameters and standardize the vehicle shimmy parameters to obtain the processed parameters;

[0007] S2. Calculate the correlation coefficient matrix of the processed parameters;

[0008] S3. Determine whether the correlation coefficient matrix is ​​suitable for factor analysis. If yes, proceed to step S4; otherwise, return to step S1.

[0009] S4. Calculate the factor loading matrix of the correlation coefficient matrix;

[0010] S5. Rotate the factor loading matrix to obtain the rotated factor loading matrix and the oscillation factor model;

[0011] S6. Calculate the comprehensive factor score based on the rotation factor load matrix and the shimmy factor model; and evaluate the degree of vehicle shimmy through the comprehensive factor score.

[0012] Furthermore, the sway parameters include the torsion shaft length, traction rod length, half-distance of the vehicle, vertical stiffness of the running wheel, vertical stiffness of the guide wheel, vertical stiffness of the stabilizer wheel, damping of the guide wheel, damping of the stability, lateral stiffness of the air spring, stiffness of the lateral damper, and damping of the lateral damper.

[0013] Furthermore, the correlation coefficient matrix R is determined according to the following formula:

[0014]

[0015] Where, r jk is the correlation coefficient between the j-th indicator and the k-th indicator; p is the number of indicators.

[0016] Furthermore, determining whether the correlation coefficient matrix is ​​suitable for factor analysis includes:

[0017] Calculate the KMO metric and perform the Bartlett's test for sphericity;

[0018] Calculate the significance level based on the Bartlett's test of sphericity;

[0019] Determine whether the KMO metric is greater than the metric threshold and whether the significance level is less than the level threshold. If yes, the correlation coefficient matrix is ​​suitable for factor analysis; otherwise, the correlation coefficient matrix is ​​not suitable for factor analysis.

[0020] Furthermore, the rotation factor loading matrix B is determined according to the following formula:

[0021] B = AΓ;

[0022] Where Γ is an orthogonal matrix. A is the factor loading matrix.

[0023] Furthermore, the oscillation factor model is determined using the following method:

[0024] x q =a q1 F1+a q2 F2+…+a qm F m ;

[0025] Where, x q For the factor model of the q-th factor, F m Let a be the m-th principal factor. qm The rotation factor loading coefficient of the m-th principal factor of the q-th factor.

[0026] Furthermore, the number of principal factors m is determined using the following method:

[0027] Calculate the eigenvalues ​​of the correlation coefficient matrix;

[0028] Incorporate oscillation parameters with eigenvalues ​​greater than 1 into the principal components;

[0029] Based on principal component analysis, the cumulative variance of the factors in the factor loading matrix is ​​calculated;

[0030] Factors with cumulative variance greater than the variance threshold are identified as principal components, and the number of principal components is counted.

[0031] Furthermore, the comprehensive factor score F is determined according to the following formula:

[0032]

[0033] Where m is the number of principal factors; λ i It is the principal factor F i The variance contribution rate; N is the number of factors, x j For the standardized data of factor j, b ij Is factor j relative to principal factor F i The score coefficient.

[0034] The beneficial effects of this invention are as follows: This invention discloses a shimmy assessment method for straddle-type monorail vehicles based on factor analysis. By employing factor analysis and dimensionality reduction techniques, the main influencing factors on vehicle shimmy are identified, transforming multiple indicators into a smaller set of assessment indicators. The weights of each principal factor are calculated based on the variance contribution rate, and the comprehensive factor score of shimmy is calculated using a shimmy factor model. This allows for a comprehensive assessment of vehicle shimmy and provides technical support for the development and design of straddle-type monorail vehicles. Attached Figure Description

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0036] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0037] Figure 2 This is a factor correlation coefficient matrix diagram of the present invention;

[0038] Figure 3 This is a feature value scree diagram of the present invention;

[0039] Figure 4 This is a time-domain plot of the vehicle body yaw angle acceleration of the present invention;

[0040] Figure 5 This is a time-domain diagram of the lateral acceleration of the vehicle body according to the present invention;

[0041] Figure 6 This is the root mean square plot of the yaw rate acceleration of the vehicle body according to the present invention;

[0042] Figure 7 This is the root mean square plot of the lateral acceleration of the vehicle body according to the present invention. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings, as shown in the figures:

[0044] The method for evaluating the sway vibration of straddle-type monorail vehicles based on factor analysis of the present invention includes the following steps:

[0045] S1. Collect vehicle shimmy parameters and standardize the vehicle shimmy parameters to obtain the processed parameters;

[0046] S2. Calculate the correlation coefficient matrix of the processed parameters;

[0047] S3. Determine whether the correlation coefficient matrix is ​​suitable for factor analysis. If yes, proceed to step S4; otherwise, return to step S1.

[0048] S4. Calculate the factor loading matrix of the correlation coefficient matrix;

[0049] S5. Rotate the factor loading matrix to obtain the rotated factor loading matrix and the oscillation factor model;

[0050] S6. Calculate the comprehensive factor score based on the rotation factor load matrix and the shimmy factor model; and evaluate the degree of vehicle shimmy through the comprehensive factor score.

[0051] In this embodiment, in step S1, raw data for shimmy evaluation is obtained through vehicle measurement and simulation. This raw data consists of shimmy parameters affecting vehicle shimmy. These shimmy parameters include the torsion shaft length, traction rod length, half-distance of the vehicle, vertical stiffness of the running wheels, vertical stiffness of the guide wheels, vertical stiffness of the stabilizing wheels, guide wheel damping, stability damping, lateral stiffness of the air spring, lateral damper stiffness, and lateral damper damping. The value ranges of these shimmy parameters are shown in Table 1.

[0052] Table 1

[0053]

[0054]

[0055] Standardize the vehicle shimmy parameters:

[0056] The formula for data standardization is:

[0057]

[0058] Where, x ijLet be the value of an indicator (the value of the j-th indicator in the i-th sample), where i = 1, 2, ..., n is the number of samples, and j = 1, 2, ..., p is the number of indicators. Let j be the sample mean of the j-th indicator. Let be the sample standard deviation of the j-th indicator. This is the value after standardization.

[0059] In this embodiment, the formula for calculating the correlation coefficient in step S2 is as follows:

[0060]

[0061] Furthermore,

[0062] Where, r jk Let p be the correlation coefficient between the j-th and k-th indicators, and r be the number of indicators. ii =1,r jk =r kj Therefore, the correlation coefficient matrix R is:

[0063]

[0064] Factor correlation coefficient matrix obtained from standardized data, such as Figure 2 As shown in the figure. Using the oscillation parameters as the aforementioned indicators, the correlation coefficient matrix corresponding to the oscillation parameters can be obtained.

[0065] In this embodiment, in step S3, before extracting the principal factors, it is necessary to test the validity of the correlation coefficient matrix to determine whether it is suitable for factor analysis.

[0066] Validity tests include the KMO measure and the Bartlett test for sphericity.

[0067] The KMO metric is used to compare simple correlation coefficients and partial correlation coefficients between variables, requiring a correlation coefficient greater than 0.6 (the metric threshold). A higher KMO value indicates a stronger correlation between variables, making the original variables more suitable for factor analysis.

[0068] Bartlett's test of sphericity indicates that each variable is independent. When the test result shows a significance level of less than 0.05 (the threshold level), the data exhibits a spherical distribution, and the variables are independent to a certain extent, making it suitable for factor analysis.

[0069] In this embodiment, the validity test results show that the KMO value is 0.792, the approximate chi-square value of Bartlett's test of sphericity is 1203.995, and the significance level is 0. Therefore, the KMO value is greater than 0.7 and the significance level is less than 0.05, indicating that factor analysis is suitable.

[0070] In this embodiment, in step S4, the eigenvalues, variance contribution rate, cumulative contribution rate, and factor loading matrix of the correlation coefficient matrix R are calculated based on principal component analysis, thereby extracting each principal factor; here, the factor is the oscillation parameter; wherein, the factor eigenvalues ​​and cumulative variance contribution rate are shown in Table 2:

[0071] Table 2

[0072]

[0073] Based on the characteristic equation |R-λE|=0, the eigenvalues ​​λ of the correlation coefficient matrix are obtained. i (i = 1, 2, ..., p), and the corresponding orthogonalized eigenvectors U i (i = 1, 2, ..., p). Where λ1 ≥ λ2 ≥ ... ≥ λ p ≥0;

[0074] The factor loading matrix can be obtained from the eigenvalues ​​and eigenvectors:

[0075]

[0076] The formulas for calculating the variance contribution rate and the cumulative contribution rate are as follows:

[0077]

[0078]

[0079] If the cumulative contribution ratio is greater than 70% or the eigenvalue is greater than 1, the first q common factors can be determined and extracted.

[0080] Specifically, the eigenvalues ​​of the correlation coefficient matrix represent the degree to which the principal components are explained. If the eigenvalue is greater than 1, it indicates that the principal components have greater explanatory power than the original variables, and therefore variables with eigenvalues ​​greater than 1 are included in the principal components.

[0081] The factor loading matrix is ​​derived from the eigenvalues ​​of the correlation coefficient matrix. The cumulative variance of the first four factors in Table 3 is 72.722%, which satisfies the condition that the cumulative variance of the principal components is greater than 70% (variance threshold). Therefore, the first four variables are extracted as principal components. The factor loading matrix is ​​shown in Table 3.

[0082] Table 3

[0083]

[0084]

[0085] like Figure 3As shown, the scree plot can visually represent the eigenvalues. The eigenvalue of the first principal component is 4.111, the second principal component is 1.633, the third principal component is 1.212, and the fourth principal component is 1.044. Since the eigenvalues ​​of the first four principal components are less than 1, they are not suitable for principal component extraction, indicating that only the first four principal components were extracted for vehicle shimmy.

[0086] In this embodiment, in step S5, the factor loading matrix is ​​rotated based on the maximum variance method to obtain the rotated factor loading matrix and the oscillation factor model.

[0087] The rotation factor loading matrix B is obtained by left-multiplying the factor loading matrix A by the orthogonal matrix Γ (of any order q×q);

[0088] B = AΓ;

[0089] Here, the elements in the i-th row and j-th column of B are represented as b. ij ,Then:

[0090]

[0091] Where r, g = 1, 2, ..., q, and θ is the orthogonal rotation angle. From ΓΓ T =I q The oscillation factor model can be expressed as:

[0092] X=AΓΓ T F+ε

[0093] X=(AΓ)(Γ T F)+ε

[0094] Among them, Γ T F can be used as the principal factor, AΓ is the corresponding rotated factor loading matrix, and ε is a special factor.

[0095] Specifically, to clarify the principal factors, the factor loading matrix is ​​rotated using the maximum variance method. After rotation, the cumulative variance contribution rate of the factors remains unchanged, and the factor loadings are closer to 1 or 0. This simplifies the structure of the factor loading matrix and facilitates a more practical interpretation.

[0096] The factor loadings of each principal factor after rotation are shown in Table 4:

[0097] Table 4

[0098]

[0099]

[0100] Based on the rotation factor load matrix, the vehicle shimmy factor model is established as follows:

[0101] x q =a q1 F1+a q2 F2+…+a qm F m

[0102] Where, x q For the factor model of the q-th factor, F m Let a be the m-th principal factor. qm The rotation factor loading coefficient of the m-th principal factor of the q-th factor.

[0103] It can be seen from the rotated factor loadings and factor model that:

[0104] The absolute value of the factor load of the principal factor F1 is greater than 0.5. It mainly consists of the vertical stiffness of the stabilizing wheel, the vertical stiffness of the running wheel, the stiffness of the lateral damper, the length of the traction rod, and the damping of the stabilizing wheel. It is called the vertical stiffness factor of the space wheel system.

[0105] Similarly, the factors in the main factor F2 include the vertical stiffness of the guide wheel, the torsional shaft length, and the half-move of the vehicle, which are called bogie structural parameter factors;

[0106] The factors in the main factor F3 include the lateral damper damping and the lateral stiffness of the air spring, which are called suspension parameter factors;

[0107] The factors in the principal factor F4 include guide wheel damping, which is called the guide wheel damping factor.

[0108] In this embodiment, in step S6, the factor scoring function is established based on the rotated factor loading matrix, and the factor scoring coefficient matrix is ​​obtained, as shown in Table 5:

[0109] Table 5

[0110]

[0111] Based on the factor score coefficients in Table 5, the formulas for the scores of each principal factor can be obtained:

[0112] N is the number of factors, and N takes the value of 11; x j For the standardized data of factor j, b ij Is factor j relative to principal factor F i The score coefficient.

[0113] To comprehensively evaluate the advantages and disadvantages of different design schemes, the ratio of the variance contribution rate to the cumulative variance contribution rate of each main factor is used as the weight. The scores of each factor are weighted, and the number of main factors m is set to 4 to obtain the comprehensive factor score. The calculation formula is as follows:

[0114]

[0115] Where F is the composite score (oscillation score); λ i It is the principal factor F i The variance contribution rate.

[0116] The comprehensive factor score is negatively correlated with the degree of oscillation; the higher the score, the greater the degree of oscillation; the lower the score, the smaller the degree of oscillation.

[0117] To better understand the vehicle shimmy evaluation method of this invention, a comprehensive scoring formula was used to verify the vehicle design scheme. To verify the advantages and disadvantages of the vehicle design scheme, three structural design schemes were selected, and the design parameters are shown in Table 6.

[0118] Table 6

[0119]

[0120] Based on the design parameters of the three monorail vehicle design schemes mentioned above, standardization was performed. Using the factor score coefficient matrix in Table 5, the factor score formula was substituted into the factor score formula to obtain the scores of the four main factors. The comprehensive factor score was obtained through weighted synthesis, as shown in Table 7.

[0121] Table 7

[0122]

[0123] The comprehensive factor score is negatively correlated with the degree of shimmy. The comprehensive factor scores for the three design schemes were calculated. Table 7 shows that design scheme 1 has a comprehensive score of 1.922, design scheme 2 has a factor score of 0.958, and design scheme 3 has a factor score of 0.379. Among the three design schemes, design scheme 3 has the lowest comprehensive score, indicating it is the optimal design with the lowest degree of shimmy. Design scheme 1 has the highest factor score, indicating it is the worst design with the highest degree of shimmy. To minimize vehicle shimmy, the design scheme with the lowest comprehensive factor score, i.e., the third design scheme, is the optimal design scheme.

[0124] To verify whether the comprehensive factor scores of the three design schemes can accurately reflect the degree of vehicle yaw, the design parameters of the three schemes were input into the vehicle dynamics model for simulation calculations. From the vehicle dynamics calculation results, the yaw acceleration, lateral acceleration, root mean square yaw acceleration, and root mean square lateral acceleration of the three design schemes were obtained and compared. The comparison results are as follows: Figure 4-7 As shown.

[0125] Depend on Figure 4-7It can be seen that among the three design schemes, design scheme 3, with the lowest comprehensive factor score, has the smallest yaw acceleration, lateral acceleration, root mean square yaw acceleration, and root mean square lateral acceleration, indicating the least wobbling. Design scheme 1, with the highest comprehensive factor score, has the largest yaw acceleration, lateral acceleration, root mean square yaw acceleration, and root mean square lateral acceleration, indicating the most severe wobbling. The wobbling degree of design scheme 2 falls between that of design schemes 1 and 3. The results verify that the calculated results of the comprehensive factor score formula are in good agreement with the dynamic simulation results, and the factor analysis model is accurate.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis, characterized in that: Includes the following steps: S1. Collect vehicle shimmy parameters and standardize the vehicle shimmy parameters to obtain the processed parameters; S2. Calculate the correlation coefficient matrix of the processed parameters; S3. Determine whether the correlation coefficient matrix is ​​suitable for factor analysis. If yes, proceed to step S4; otherwise, return to step S1. S4. Calculate the factor loading matrix of the correlation coefficient matrix; S5. Rotate the factor loading matrix to obtain the rotated factor loading matrix and the oscillation factor model; S6. Based on the rotation factor load matrix and the shimmy factor model, calculate the comprehensive factor score; and evaluate the degree of vehicle shimmy through the comprehensive factor score; The oscillation factor model is determined using the following method: ； in, For the first A factor model with 1 factor. For the first One principal factor, For the first The factor of the first Rotation factor loadings of each principal factor; The number of principal factors is determined using the following method. : Calculate the eigenvalues ​​of the correlation coefficient matrix; Incorporate oscillation parameters with eigenvalues ​​greater than 1 into the principal components; Based on principal component analysis, the cumulative variance of the factors in the factor loading matrix is ​​calculated; Factors with cumulative variance greater than the variance threshold are identified as principal components, and the number of principal components is counted. The composite factor score is determined using the following formula. : ； in, Number of principal factors; It is the principal factor The variance contribution rate; , The number of factors. As a factor Standardized data, It is a factor For principal factors The score coefficient.

2. The method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis according to claim 1, characterized in that: The sway parameters include the torsion shaft length, traction rod length, half the vehicle distance, vertical stiffness of the running wheel, vertical stiffness of the guide wheel, vertical stiffness of the stabilizer wheel, guide wheel damping, stability damping, lateral stiffness of the air spring, lateral damper stiffness, and lateral damper damping.

3. The method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis according to claim 1, characterized in that: The correlation coefficient matrix is ​​determined using the following formula. : ； in, For the first The first indicator and the first The correlation coefficient of each indicator; Number of indicators.

4. The method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis according to claim 1, characterized in that: Determining whether a correlation coefficient matrix is ​​suitable for factor analysis includes: Calculate the KMO metric and perform the Bartlett's test for sphericity; Calculate the significance level based on the Bartlett's test of sphericity; Determine whether the KMO metric is greater than the metric threshold and whether the significance level is less than the level threshold. If yes, the correlation coefficient matrix is ​​suitable for factor analysis; otherwise, the correlation coefficient matrix is ​​not suitable for factor analysis.

5. The method for evaluating the shimmy of straddle-type monorail vehicles based on factor analysis according to claim 1, characterized in that: The rotation factor loading matrix is ​​determined according to the following formula. : ； in, It is an orthogonal matrix. ; This is the factor loading matrix.

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