| CPC G06F 30/13 (2020.01) [G06F 30/17 (2020.01); G06N 7/01 (2023.01)] | 2 Claims |
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1. A method of reconstructing and randomly generating realistic three-dimensional (3D) profiles of railway ballast particles, comprising the following steps:
S1: obtaining three-dimensional profile data of railway ballasts;
S2: reconstructing railway ballast profiles based on a spherical harmonic function method;
wherein step S2 comprises: selecting N=15 to carry out research work based on a theoretical method of a spherical harmonic function, according to space coordinate information set
 of a surface point cloud in a spherical coordinate system, solving a spherical harmonic function coefficient of each of the railway ballast particles by least square fitting, and obtaining a spherical harmonic function coefficient set
 with 300 samples, wherein the spherical harmonic function coefficient set
 is defined by a following formula:
 wherein j is a particle number, and n and m correspond to an order and degree of expansion of the spherical harmonic function, respectively; and
reconstructing the railway ballast particles by substituting the spherical harmonic function coefficient set
 into a following formula defined by a following formula:
 wherein θ is a colatitude angle having a domain of definition of [0, π], φ is an azimuth angle having a domain of definition of [0, 2π],
 is a coefficient corresponding to a spherical series of an n-order and m-degree spherical harmonic function,
 and
 are a real part and an imaginary part of the spherical harmonic function coefficient, respectively, (⋅)* is a conjugate transpose, and
 is the spherical series of the n-order and m-degree spherical harmonic function;
S3: characterizing a probability of the railway ballast particles; and
S4: randomly generating the railway ballast particles;
wherein step S4 comprises:
S41: establishing a joint probability density function of a spherical harmonic function spectrum through Nataf theory according to a marginal probability density function ƒ=ƒ1(l1), ƒ2(l2), . . . , ƒn(ln) of a spherical harmonic function spectrum of each order to obtain the joint probability density function of the spherical harmonic function defined by formula (7):
 wherein ϕn(y, ρ0) is a joint probability density function of a standard normal distribution, and ρ0 is a correlation coefficient of an n-dimensional standard normal distribution;
S42: obtaining a spherical harmonic function spectrum Lq=[L1,q, L2,q, . . . , Ln,q]T of a target number NL according to the joint probability density function, q=1, 2, . . . , NL;
establishing a relationship between 16 spherical harmonic function spectra and 256 spherical harmonic function coefficients to generate particles, wherein conversion formulas are as shown in formula (8) and formula (9):
 wherein
 and
 are random numbers following a uniform distribution from 0 to 1;
S43: generating the 3D railway ballast particles rapidly and randomly according to the spherical harmonic function coefficient
 in combination with formula (2) to formula (5) to be used in a discrete element simulation; wherein the result of the simulation is used to evaluate an interaction between railway ballasts and macroscopic mechanical behavior of a ballast bed to ensure physical railway safety;
wherein step S1 comprises: randomly selecting 300 railway ballasts, rotating a base to rotate railway ballasts by 360 degrees along an axis perpendicular to the base, setting target points on surfaces of the railway ballasts at a same time, rotating the railway ballast particles for a plurality of times and scanning the railway ballast particles at different angles for a plurality of times, splicing results of scanning for a plurality of times in a target point positioning manner, and obtaining a space coordinate information set
 of a surface point cloud in a Cartesian coordinate system, and converting the space coordinate information set of the surface point cloud in the Cartesian coordinate system into the space coordinate information set
 in the spherical coordinate system, wherein j is the particle number, and k is a point cloud number.
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