A method for reconstructing and randomly generating three-dimensional profiles of ballast particles

Abstract

The present invention relates to the field of rail transit technology, and specifically discloses a method for reconstructing and randomly generating the three-dimensional profile of ballast particles. The current problems with the reconstruction and accurate characterization methods of ballast particle profiles are: the established three-dimensional ballast library contains limited ballast profile samples, and the three-dimensional profile is mainly acquired through three-dimensional scanning or two-dimensional profile inversion. In response to the above problems, the method of the present invention revolves around the two aspects of accurate characterization and random generation of ballast profiles, specifically including: first, a large number of ballast profile samples are acquired to form a ballast library, and the uncertainty of the ballast is described as much as possible; then the spherical harmonic function method is introduced into the three-dimensional profile characterization of ballast particles, aiming to achieve accurate reconstruction of the ballast particle profile; finally, a spherical harmonic function spectrum joint probability density function is established to achieve random generation of ballast particles.

Description

Technical Field

[0001] The present invention relates to the field of rail transit technology, and in particular to a method for reconstructing and randomly generating three-dimensional profiles of ballast particles. Background Art

[0002] The ballasted track bed is made up of ballast particles of a specific grade, and its mechanical properties play an important role in ensuring driving safety. Since indoor and outdoor tests have great limitations in studying the microscopic mechanical behavior of the track bed, the discrete element method can fully consider the contact characteristics between ballast particles. Therefore, domestic and foreign scholars have carried out a large number of numerical simulation studies on the mechanical properties of the ballasted track bed based on the discrete element method. As one of the most important basic characteristics of ballast particles, existing studies have found that the morphology of ballast particles has a significant impact on the interaction excitation between ballast particles and the macroscopic mechanical behavior of the track bed during discrete element simulation. The reconstruction and accurate characterization of the ballast particle profile have become important factors affecting the simulation accuracy.

[0003] At present, in the reconstruction of ballast particles, Indraratna used two-dimensional bonded disc particles to simulate the irregular shape of ballast, and studied the crushing mechanism of ballast particles under cyclic loads through triaxial tests. Lim simulated ballast using regular block units composed of multiple spheres. The above studies are all based on limited ballast profiles for particle reconstruction, but there is still a big difference from the real ballast particles, and the randomness of the ballast profile is ignored. Therefore, Zhao reconstructed the real two-dimensional profile of ballast particles based on the inverse discrete Fourier transform method. Zhang, Gao and others used digital imaging methods to obtain ballast profiles and realize ballasted track bed simulation modeling, but this method has a large scanning workload and low modeling efficiency. In response to the above problems, Huang inverted the contours of ballast particles based on the three-dimensional perspective reconstruction method, established a ballast library containing 11 typical ballast profiles, and randomly extracted discrete element models. Bian Xuecheng et al. proposed a method to obtain multi-angle images of the coarse aggregate to be measured through two plane mirrors based on the principle of mirror reflection, and then perform three-dimensional reconstruction after self-calibration according to the program algorithm to obtain a three-dimensional model that restores the shape of the coarse aggregate, and establish a conversion scheme between the model size and the actual geometric size, so as to complete the method of evaluating the geometric characteristics and gradation of the coarse aggregate. Xiao et al. proposed a new model called BallastGAN for randomly generating ballast particle contours. The model uses fractal dimension regularization and optimizes the loss function of the discriminator under the StyleGAN3 framework. The optimization effectively controls the roughness characteristics of the generated ballast particle image. By decoupling the latent space, the mutual transformation and style blending between different ballast particle contours are realized. Xu analyzed the characteristics of the two-dimensional ballast profile based on the normalized boundary chain code Fourier descriptor analysis method, and used the double plane mirror intersection method to combine the generated two-dimensional profile to obtain the three-dimensional ballast profile, and established a ballast library containing 28 ballasts.

[0004] As one of the most important basic characteristics of ballast particles, the shape of ballast particles has a significant impact on the interaction excitation between ballast particles and the macroscopic mechanical behavior of the roadbed during discrete element simulation. Therefore, it is necessary to carry out corresponding research on the reconstruction and precise characterization of the ballast particle profile.

[0005] Although the existing technology has preliminarily achieved the characterization of the randomness of the ballast profile, the ballast profile samples obtained based on scanning are relatively small, making it difficult to describe the uncertainty of the ballast; at the same time, if the three-dimensional profile is inverted through the two-dimensional profile, the error will be amplified, and it is difficult to ensure the consistency of the generated profile with the actual ballast profile characteristics, and the restoration accuracy is limited.

[0006] Therefore, in view of the fact that the current particle profile characterization methods are difficult to quantify the uncertainty of particle morphology and the limitations of the established three-dimensional ballast library in generating ballast profiles, it is urgent to propose a method for reconstructing and randomly generating the three-dimensional profile of ballast particles. Summary of the invention

[0007] In order to solve the problems existing in the prior art, the present invention provides a method for reconstructing and randomly generating the three-dimensional profile of ballast particles. Firstly, a large number of ballast profile samples are obtained to form a ballast library to describe the uncertainty of the ballast as much as possible; then, the spherical harmonic function method is introduced into the three-dimensional profile characterization of the ballast particles, aiming to achieve accurate reconstruction of the profile of the ballast particles; finally, a spherical harmonic function spectrum combined with a probability density function is established to achieve random generation of ballast particles, thereby solving the problems mentioned in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solution: a method for reconstructing and randomly generating a three-dimensional profile of ballast particles, comprising the following steps:

[0009] S1. Obtaining 3D profile data of ballast;

[0010] S2, reconstructing the ballast profile based on the spherical harmonic function method;

[0011] S3, probabilistic characterization of ballast particles;

[0012] S4. Ballast particles are randomly generated.

[0013] Preferably, in step S1, the following is specifically included: 300 ballasts are randomly selected, and the ballasts are rotated 360° along an axis perpendicular to the base by rotating the base, and target points are set on the ballast surface at the same time, and the ballast particles are rotated multiple times and scanned multiple times at different angles, and the multiple scanning results are spliced ​​by target point positioning, and finally the spatial coordinate information set of the surface point cloud in the Cartesian coordinate system is obtained. And transform to the spatial coordinate information set in the spherical coordinate system Where j is the particle number and k is the point cloud number.

[0014] Preferably, in step S2, the following is specifically included: according to the spatial coordinate information set of the surface point cloud in the spherical coordinate system Based on the spherical harmonic function theory method, N = 15 was selected for research, and the spherical harmonic function coefficients of each ballast particle were solved by least squares fitting, and finally a spherical harmonic function coefficient set with a sample number of 300 was obtained. The formula is as follows:

[0015]

[0016] In the formula, j is the particle number, n and m correspond to the expansion order and degree of the spherical harmonic function respectively;

[0017] The obtained spherical harmonic coefficient set Substituting the following formula into the ballast particle reconstruction can be achieved; the formula is as follows:

[0018]

[0019]

[0020]

[0021]

[0022] Where θ is the co-latitude angle, and its domain is [0, π], is the azimuth, with the domain being [0, 2π], is the coefficient corresponding to the spherical series of spherical harmonics of order n and degree m, and are the real and imaginary parts of the spherical harmonic coefficients, respectively, (·) * is the conjugate transpose, is the spherical harmonic series of order n and degree m.

[0023] Preferably, in step S3, the following is specifically included:

[0024] S31. Combined with the obtained spherical harmonic coefficient set Substitute into formula (6) to calculate the spherical harmonic spectrum L j,n ;

[0025]

[0026] Where, L j,n is the nth-order spherical harmonic spectrum of the jth particle, is the spherical harmonic coefficient of the jth particle of order n and degree m, ||·|| is the second-order Euclidean norm of the spherical harmonic coefficient vector;

[0027] S32, L1-L for 300 ballast particles 15 Conduct frequency histogram statistical analysis, its distribution approximately obeys the gamma distribution, and select the gamma distribution to fit it;

[0028] S33, select gamma distribution to construct the marginal probability density function of the spherical harmonic function spectrum of each order f = f1(l1), f2(l2),…, f n (l n ), thereby realizing the probabilistic characterization of the spherical harmonic function spectra of ballast particles of various orders.

[0029] Preferably, in step S4, the following is specifically included:

[0030] S41, according to the marginal probability density function of the spherical harmonic function spectrum of each order obtained, f=f1(l1),f2(l2),…,f n (l n), the joint probability density function of the spherical harmonic function spectrum is established through the Nataf theory, and the joint probability density function of the spherical harmonic function is obtained, as shown in formula (7):

[0031]

[0032] In the formula, φ n (y,ρ0) is the joint probability density function of the standard normal distribution, ρ0 is the correlation coefficient of the n-dimensional standard normal distribution;

[0033] S42. Obtain the target number N according to the obtained joint probability density function L The spherical harmonic spectrum of

[0034] In order to realize the generation of particles, the relationship between 16 spherical harmonic function spectra and 256 spherical harmonic function coefficients is established. The specific conversion formula is as follows:

[0035]

[0036]

[0037] In the formula, and is a random number from 0 to 1 that follows a uniform distribution;

[0038] S43, based on the generated spherical harmonic coefficients Combining formula (2)-formula (5) can finally realize the rapid random generation of ballast particles.

[0039] The beneficial effects of the present invention are as follows: the method of the present invention randomly selects 300 ballasts for scanning to obtain ballast profile samples, describing the uncertainty of the ballast as much as possible; and introduces the spherical harmonic function theory to reconstruct the ballast profile in three dimensions. When the order of the spherical harmonic function reaches 15, the restored ballast profile is relatively accurate, and the accurate reconstruction of the ballast particle profile is achieved. At the same time, based on the Nataf change, the joint probability density function of the spherical harmonic function spectrum is established to characterize the uncertainty of the ballast profile, and the rapid random generation of ballast particles is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the steps of the method for reconstructing and randomly generating the three-dimensional profile of ballast particles of the present invention;

[0041] Figure 2 A schematic diagram showing the comparison of the profile reconstructions of different spherical harmonic function orders;

[0042] Figure 3 Schematic diagram of randomly generated ballast particles. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] See also Figure 1-Figure 3 The present invention provides a technical solution: a method for reconstructing and randomly generating the three-dimensional profile of ballast particles, such as Figure 1 As shown, the following steps are included:

[0045] S1. Obtain 3D ballast profile data

[0046] 300 ballasts are randomly selected, and the ballast is rotated 360° along an axis perpendicular to the base by rotating the base. At the same time, target points are set on the ballast surface. The ballast particles are rotated multiple times and scanned multiple times at different angles. The multiple scanning results are spliced ​​through target positioning, and finally the spatial coordinate information set of its surface point cloud in the Cartesian coordinate system is obtained. And transform to the spatial coordinate information set in the spherical coordinate system Where j is the particle number and k is the point cloud number.

[0047] S2. Reconstruction of ballast profile based on spherical harmonic function method

[0048] The spatial coordinate information set of the surface point cloud obtained in step S1 in the spherical coordinate system Based on the spherical harmonic function theory method, the profile reconstruction comparison of different spherical harmonic function orders is as follows: Figure 2 As shown, the present invention selects the spherical harmonic function order N = 15 to carry out research work, and solves the spherical harmonic function coefficient of each ballast particle by least square fitting, and finally obtains a spherical harmonic function coefficient set with a sample number of 300 The formula is as follows:

[0049]

[0050] In the formula, j is the particle number, n and m correspond to the expansion order and degree of the spherical harmonic function respectively;

[0051] The obtained spherical harmonic coefficient set Substituting the following formula into the ballast particle reconstruction can be achieved. The formula is as follows:

[0052]

[0053]

[0054]

[0055]

[0056] Where θ is the co-latitude angle, and its domain is [0, π], is the azimuth, with the domain being [0, 2π], is the coefficient corresponding to the spherical series of spherical harmonics of order n and degree m, and are the real and imaginary parts of the spherical harmonic coefficients, respectively, (·) * is the conjugate transpose, is the spherical harmonic series of order n and degree m. is the corresponding Legendre polynomial; is the coefficient corresponding to the spherical series of spherical harmonics of order n-m; i is the imaginary unit.

[0057] S3. Probabilistic characterization of ballast particles

[0058] The probabilistic characterization of ballast particles specifically includes the following:

[0059] S31, combined with the spherical harmonic coefficient set obtained in step S2 Substitute into formula (6) to calculate the spherical harmonic spectrum L j,n ;

[0060]

[0061] Where, L j,n is the nth-order spherical harmonic spectrum of the jth particle, is the spherical harmonic coefficient of the jth particle of order n and degree m, ||·|| is the second-order Euclidean norm of the spherical harmonic coefficient vector;

[0062] S32, L1-L for 300 ballast particles 15 Conduct frequency histogram statistical analysis, its distribution may approximately obey the gamma distribution, and select the gamma distribution to fit it;

[0063] S33. After comparative analysis, the gamma distribution is selected to construct the marginal probability density functions of the spherical harmonic function spectra of each order f = f1(l1), f2(l2),…, f n (l n ), the shape parameter (α) and scale coefficient (β) of the gamma distribution are shown in Table 1, thereby realizing the probabilistic characterization of the spherical harmonic function spectra of each order of ballast particles.

[0064] Table 1 Parameters of spherical harmonics spectrum gamma distribution

[0065]

[0066] S4. Random generation of ballast particles

[0067] The random generation of ballast particles includes the following:

[0068] S41, according to the marginal probability density function of the spherical harmonic function spectrum of each order obtained, f=f1(l1),f2(l2),…,f n (l n ), the joint probability density function of the spherical harmonic function spectrum is established through the Nataf theory, and the joint probability density function of the spherical harmonic function is obtained, as shown in formula (7):

[0069]

[0070] In the formula, φ n (y,ρ0) is the joint probability density function of the standard normal distribution, ρ0 is the correlation coefficient of the n-dimensional standard normal distribution;

[0071] S42. Obtain the target number N according to the obtained joint probability density function L The spherical harmonic spectrum of

[0072] In order to realize the generation of particles, the relationship between 16 spherical harmonic function spectra and 256 spherical harmonic function coefficients is established. The specific conversion formula is as follows:

[0073]

[0074]

[0075] In the formula, and is a random number from 0 to 1 that follows a uniform distribution;

[0076] S43, based on the generated spherical harmonic coefficients Combining formula (2)-formula (5) to finally realize the rapid random generation of ballast particles, the generated ballast profile is as follows: Figure 3 shown.

[0077] The method of the present invention will be compared with the current ballast particle profile reconstruction and accurate characterization methods from the two aspects of accurate characterization and random generation of ballast profile. The currently established ballast profile sample library only contains dozens of typical ballast profiles, which is difficult to describe the uncertainty of ballast. In order to achieve the generation of three-dimensional profiles, three-dimensional inversion is mainly performed through two-dimensional, and the error will be amplified, making it difficult to ensure the consistency of the generated ballast profile with the actual ballast profile characteristics. The method of the present invention randomly selected 300 ballasts for scanning to obtain ballast profile samples, and introduced spherical harmonic function theory to reconstruct the ballast profile in three dimensions. When the order of the spherical harmonic function reaches 15, the restored ballast profile is more accurate. At the same time, based on the Nataf change, the joint probability density function of the spherical harmonic function spectrum is established to characterize the uncertainty of the ballast profile, and realize the rapid random generation of ballast particles.

[0078] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for reconstructing and randomly generating three-dimensional profiles of ballast particles, characterized in that: The steps include: S1. Obtaining 3D profile data of ballast; S2. Reconstruct the ballast profile based on the spherical harmonic function method; specifically, the following steps are performed: Based on the spherical harmonic function theory method, N = 15 was selected for research, and the spherical harmonic function coefficients of each ballast particle were solved by least squares fitting, and finally a spherical harmonic function coefficient set with a sample number of 300 was obtained. The formula is as follows: In the formula, j is the particle number, n and m correspond to the expansion order and degree of the spherical harmonic function respectively; The obtained spherical harmonic coefficient set Substituting the following formula into the ballast particle reconstruction can be achieved; the formula is as follows: Where θ is the co-latitude angle, and its domain is [0, π], is the azimuth, with the domain being [0, 2π], is the coefficient corresponding to the spherical series of spherical harmonics of order n and degree m, and are the real and imaginary parts of the spherical harmonic coefficients, respectively, (·) * is the conjugate transpose, is the spherical harmonic series of order n and degree m; S3, probabilistic characterization of ballast particles; S4. Ballast particles are randomly generated, including the following: S41, according to the marginal probability density function of the spherical harmonic function spectrum of each order obtained, f=f1(l1),f2(l2),…,f n (l n ), the joint probability density function of the spherical harmonic function spectrum is established through the Nataf theory, and the joint probability density function of the spherical harmonic function is obtained, as shown in formula (7): In the formula, φ n (y,ρ0) is the joint probability density function of the standard normal distribution, ρ0 is the correlation coefficient of the n-dimensional standard normal distribution; S42. Obtain the target number N according to the obtained joint probability density function L The spherical harmonic spectrum of In order to realize the generation of particles, the relationship between 16 spherical harmonic function spectra and 256 spherical harmonic function coefficients is established. The specific conversion formula is as follows: In the formula, and is a random number from 0 to 1 that follows a uniform distribution; S43, based on the generated spherical harmonic coefficients Combining formula (2)-formula (5) can finally realize the rapid random generation of ballast particles.

2. The method for reconstructing and randomly generating three-dimensional profiles of ballast particles according to claim 1, characterized in that: In step S1, the following is specifically included: 300 ballasts are randomly selected, and the ballast is rotated 360° along an axis perpendicular to the base by rotating the base, and target points are set on the ballast surface. The ballast particles are rotated multiple times and scanned multiple times at different angles, and the multiple scanning results are spliced ​​through target point positioning, and finally the spatial coordinate information set of its surface point cloud in the Cartesian coordinate system is obtained. And transform to the spatial coordinate information set in the spherical coordinate system Where j is the particle number and k is the point cloud number.

3. The method for reconstructing and randomly generating three-dimensional profiles of ballast particles according to claim 1, characterized in that: In step S3, the specific steps include: S31. Combined with the obtained spherical harmonic coefficient set Substitute into formula (6) to calculate the spherical harmonic spectrum L j,n ; Where, L j,n is the nth-order spherical harmonic spectrum of the jth particle, is the spherical harmonic coefficient of the jth particle of order n and degree m, ||·|| is the second-order Euclidean norm of the spherical harmonic coefficient vector; S32, L1-L for 300 ballast particles 15 Conduct frequency histogram statistical analysis, its distribution approximately obeys the gamma distribution, and select the gamma distribution to fit it; S33, select gamma distribution to construct the marginal probability density function of the spherical harmonic function spectrum of each order f = f1(l1), f2(l2),…, f n (l n ), thereby realizing the probabilistic characterization of the spherical harmonic function spectra of ballast particles of various orders.

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