A Method for Designing the Ultimate Envelope of a Solid-Surface Deployable Antenna Based on an Improved Particle Swarm Optimization Algorithm

Abstract

This invention discloses a method for designing the ultimate envelope of a solid-plane deployable antenna based on an improved particle swarm optimization algorithm. Considering the structural characteristics of solid-plane deployable antennas, the method utilizes the analytic hierarchy process (AHP) to divide the radius, height, and volume indices related to the antenna's containment envelope performance into different levels and weights, thereby establishing a single-objective optimization task. An optimization constraint function is constructed based on deployed geometric constraints, contracted envelope constraints, rigid body constraints, single-degree-of-freedom unfolding constraints, interference-free constraints, and structural parameter boundary constraints. Furthermore, structural parameters suitable for optimization are determined according to the requirements of the antenna design process. On this basis, a cross-platform, multi-threaded parallel solution process is constructed, enabling cross-iteration of the algorithm through information transfer between different computing platforms, ultimately completing the ultimate envelope design calculation for the solid-plane deployable antenna.

Description

Technical Field

[0001] This invention relates to the field of spaceborne antennas, and in particular to a method for designing the ultimate envelope of a solid-plane deployable antenna based on an improved particle swarm optimization algorithm. Background Technology

[0002] As humanity delves deeper into the mysteries of outer space, the development of ultra-large, high-precision satellites and space stations becomes increasingly urgent and necessary. Spaceborne antennas, as carriers of received signals, play a crucial role in fields such as wireless communication, deep space exploration, satellite remote sensing, and radio astronomy.

[0003] Due to space constraints on launch vehicles, large-aperture space antennas typically operate by retracting from the ground, transmitting into orbit, and then deploying. Therefore, space antennas are usually designed with deployable structures. Compared to mesh and thin-film reflector antennas, solid-state reflector antennas offer higher surface accuracy, better meeting the high-precision and wide-bandwidth performance requirements of fields such as space exploration and microwave remote sensing. Figure 2 As shown, a solid-surface deployable antenna mainly consists of a feed system, a reflector panel, a drive and transmission assembly, and a support and connection assembly. The antenna is mounted on the satellite via the support and connection assembly and stored in a collapsed state within the launch vehicle. After the satellite is launched into orbit, the reflector panel unfolds to its service attitude under the action of the drive and transmission assembly, cooperating with the feed system to achieve its intended service performance. However, research on large-aperture solid-surface deployable antennas is limited, especially regarding the storage problem that restricts their application, which urgently needs further research to provide technical reserves for solid-surface deployable antennas. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm. This method enables the design of structural parameters of the solid-surface deployable antenna and the evaluation of its ultimate storage performance, thereby solving the problem of improving the storage ratio of the solid-surface deployable antenna.

[0005] The technical solution of this invention is: a method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm, comprising the following steps:

[0006] S1. Using the analytic hierarchy process (AHP) to weight multiple indicators related to the antenna's coverage envelope performance according to task requirements, a single-objective optimization model is constructed to obtain the global optimization objective of the limit envelope of the solid-surface deployable antenna.

[0007] S2. Establish constraints for the optimization model, including expanded geometric surface constraints, contracted envelope surface constraints, rigid body constraints, single-degree-of-freedom expansion constraints, non-interference constraints, and structural parameter boundary constraints.

[0008] S3. Based on the antenna design requirements, determine the structural parameters to be solved in the optimization model;

[0009] S4. Initialize the structural parameters. Determine the dimension and scale of the particle swarm based on the number of structural parameters, and initialize the parameters of each particle swarm.

[0010] S5. Based on the global optimization objective, calculate the fitness of each particle swarm under the initial parameters, and update the particle velocity and spatial position; during the update process, the inertia coefficient is a non-fixed value.

[0011] S6. Correct the velocity and spatial position of particles that exceed the boundary conditions;

[0012] S7. Based on the structural parameters corresponding to the current position of the particle, construct a kinematic model of the antenna unfolding process, and determine whether the established constraints are met through kinematic analysis. If the constraints are met, execute S8.

[0013] S8. Update the particle swarm optimization solution and the global optimal solution;

[0014] S9. Repeat S5 to S8 until the set iteration conditions are met. The final global optimal solution is the structural parameter that satisfies the limiting envelope of the solid-surface deployable antenna.

[0015] Furthermore, in step S1, the indicator is the storage diameter D. max Storage height H max and storage volume V max The single-objective optimization model is constructed as follows:

[0016] min:ζ(u)=α1D max +α2H max +α3V max

[0017] In the formula, the parameters [α1, α2, α3] represent the storage diameter D determined using the analytic hierarchy process (AHP). max Storage height H max and storage volume V max The weight vector is determined by selecting specific data based on the actual task requirements; u represents the structural parameters to be solved, and ζ() represents the antenna convergence rate.

[0018] Furthermore, in step S2, the specific form of the constraint is as follows:

[0019] st:G D (x D y D z D ) = 0

[0020] G F (xF y F z F )≤0

[0021] δ=0

[0022] DOF=1

[0023] d min ≥d0

[0024] u min ≤u≤u max

[0025] In the formula, G D Let x be the expanded antenna surface function. D y D z D For the expanded panel coordinates, by setting G D =0 indicates that the expanded surface satisfies the expanded geometric surface constraints;

[0026] G F For the convergent envelope surface function, x F y F z F To determine the coordinates of the collapsed panel, set G... F ≤0 indicates that the collapsed surface satisfies the collapsed envelope surface constraint;

[0027] δ represents the deformation of the antenna panel. Setting δ = 0 indicates that the antenna panel has no deformation, thus satisfying the rigid body constraint.

[0028] DOF represents the antenna unfolding degree of freedom. Setting DOF=1 indicates that the antenna unfolding process has only one degree of freedom, satisfying the single degree of freedom constraint.

[0029] d min This represents the minimum distance between adjacent antenna panels during antenna movement. d0 is the set distance threshold, which is determined by setting d... min ≥d0 indicates that the distance between adjacent panels is always greater than the distance threshold during the antenna unfolding process, satisfying the no-interference constraint;

[0030] u max and u min This represents the upper and lower limits of the structural parameters to be solved, which are set by u. min ≤u≤u max This indicates that the antenna structural parameters are always within the design range and satisfy the structural parameter boundary constraints.

[0031] Furthermore, in step S3, the structural parameter u includes the expanded diameter D. a The diameter of the center panel is D. iFocal length f, number of petals n, structural parameters of drive transmission rod L, structural parameters of reflector panel and back frame B, and structural parameters of feed assembly F.

[0032] Furthermore, in step S4, when initializing the parameters of each particle group, the initial position and initial velocity of each particle group are assigned random values ​​within the constraints.

[0033] Furthermore, in step S5, the particle velocity and spatial position are updated, specifically as follows:

[0034] v i (k+1)=wv i (k)+c1r1(P Best,i (k)-s i (k))+c2r2(G Best (k)-s i (k))

[0035] s i (k+1)=s i (k)+v i (k+1)

[0036] In the formula, v is the particle's velocity; s is the particle's spatial position; k is the number of iterations; w is the inertia coefficient; c1 and c2 are the acceleration coefficients; r1 and r2 are random numbers; P Best,i The optimal solution for particle swarm optimization; G Best This is the globally optimal solution;

[0037] The inertia coefficient is a non-fixed value and is used in the iterative calculation according to the following formula:

[0038]

[0039] In the formula, w max The maximum inertia coefficient; w min is the minimum inertia coefficient; N is the maximum number of iterations.

[0040] Furthermore, in step S8, the particle swarm optimization solution and the global optimization solution are updated, specifically as follows:

[0041] P Best,i (k+1)=min(P Best,i (k),s i (k+1))

[0042] G Best (k+1)=min(P Best,i (k+1)) i＝1.2....

[0043] In the formula, i represents the number of particles in the swarm, and the specific value is selected by comprehensively considering the calculation accuracy and the computing power of the platform.

[0044] This invention also provides a system for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm, comprising:

[0045] The main control module is used to execute S1: Multiple indicators related to the antenna's containment envelope performance are weighted according to task requirements using the analytic hierarchy process (AHP) to construct a single-objective optimization model, obtaining the global optimization objective of the fixed-surface deployable antenna's limiting envelope; S2: Optimization model constraints are established, including expanded-state geometric constraints, contracted-state envelope constraints, rigid body constraints, single-degree-of-freedom unfolding constraints, interference-free constraints, and structural parameter boundary constraints; S3: Based on antenna design requirements, the structural parameters to be solved in the optimization model are determined; After step S3 is completed, the particle swarm optimization module is called; Based on feedback from the particle swarm optimization module, S9 is executed: S5-S8 are repeated until the set iteration conditions are met, and the final globally optimal solution is the structural parameter that satisfies the limiting envelope of the fixed-surface deployable antenna, until the process ends;

[0046] The particle swarm optimization module performs the following steps: S4: Initializes the structural parameters, determines the dimension and scale of the particle swarm based on the number of structural parameters, and initializes the parameters of each particle swarm; S5: Calculates the fitness of each particle swarm under the initial parameters based on the global optimization objective, and updates the particle velocity and spatial position. During the update process, the inertia coefficient is a non-fixed value; S6: Corrects the velocity and spatial position of particles that exceed the boundary conditions; After step S6 is completed, the kinematics module is called; Based on the feedback from the kinematics module, S8 is executed: Updates the optimal solution for the particle swarm and the global optimal solution; After step S8 is completed, the module returns to the main control module.

[0047] The kinematics module is used to execute S7: Based on the structural parameters corresponding to the current position of the particle, construct a kinematic model of the antenna unfolding process, and determine whether the established constraints are met through kinematic analysis. If the constraints are met, execute S8. After the execution of step S7, return to the particle swarm optimization module.

[0048] Furthermore, the main control module and particle swarm optimization module are implemented on the Python platform, using multi-threaded parallel computing to achieve parallel motion of multiple groups of particles; the kinematics module is implemented on the ADAMS platform to complete kinematic analysis.

[0049] The present invention also provides a computer program product that, when executed by a processor, implements the steps of the method as described in any of the preceding claims.

[0050] The advantages of this invention compared to the prior art are:

[0051] 1) This invention proposes a method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm, which can realize the evaluation of the antenna's ultimate storage performance and the design of structural parameters.

[0052] 2) This invention proposes a cross-platform multi-threaded optimization algorithm architecture, which can solve the problem of low efficiency of serial calculation in the extreme envelope calculation process. Attached Figure Description

[0053] Figure 1 This is a flowchart of a method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to the present invention.

[0054] Figure 2 This is a schematic diagram of the solid-surface deployable antenna structure involved in this invention. Detailed Implementation

[0055] To better understand the technical solution of the present invention, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0056] Reference Figure 1 This invention discloses a method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm. The specific steps are as follows:

[0057] Step 1: Determine the global optimization objective for the limiting envelope of the solid-surface deployable antenna. Using the analytic hierarchy process (AHP), multiple indices related to the antenna's coverage envelope performance are divided into different levels and weights, thus establishing a single-objective optimization task. For the antenna's coverage envelope, the key indicator is the coverage diameter D. max Storage height H max Storage volume V max Based on different task requirements, the three indicators are weighted and planned to construct a single-objective optimization model, the mathematical expression of which is as follows:

[0058] min:ζ(u)=α1D max +α2H max +α3V max (1)

[0059] In the formula, the parameters [α1, α2, α3] are the antenna envelope index weight vectors determined by the analytic hierarchy process (AHP). The specific data need to be selected according to the actual task index requirements; u is the structural parameter that affects the antenna coverage envelope, and it is also the solution of the objective function.

[0060] Step 2: Establish the constraints for the optimization model. For the solid-plane deployable antenna described in this patent, the constraints are manifested as geometric surface constraints in the deployed state, envelope surface constraints in the contracted state, rigid body constraints, single-degree-of-freedom unfolding constraints, interference-free constraints, and structural parameter boundary constraints.

[0061]

[0062] In the formula, G D Let x be the expanded antenna surface function. D y D z D For the expanded panel coordinates, by setting G D =0 indicates that the unfolded surface meets the preset, that is, it meets the geometric surface constraints of the unfolded state, such as... Indicates parabolic surface constraints;

[0063] G F For the convergent envelope surface function, x F y F z F To determine the coordinates of the collapsed panel, set G... F ≤0 indicates that all converged surfaces are within the preset envelope, i.e., satisfying the converged envelope surface constraint, such as... and These represent cylindrical and conical envelopes, respectively.

[0064] δ represents the deformation of the antenna panel. Setting δ = 0 indicates that the antenna panel has no deformation, which satisfies the rigid body constraint. DOF represents the antenna unfolding degree of freedom. Setting DOF = 1 indicates that the antenna unfolding process has only one degree of freedom, which satisfies the single degree of freedom constraint.

[0065] d min This represents the minimum distance between adjacent antenna panels during antenna movement. d0 is the set distance threshold, which is determined by setting d... min ≥d0 indicates that the distance between adjacent panels is always greater than the distance threshold during the antenna unfolding process, which means that the no-interference constraint is satisfied;

[0066] u max and u min This represents the upper and lower limits of the structural parameters to be solved, which are set by u. min ≤u≤u max This indicates that the antenna structural parameters are always within the design range, that is, they meet the structural parameter boundary constraints.

[0067] Step 3: Determine the structural parameters to be solved. Based on the requirements of the antenna design process, determine the structural parameters that can be used for optimization.

[0068] u(D a D i In equation (3), D a D is the diameter of the expanded state. i Where is the diameter of the center panel, f is the focal length, n is the number of petals, L is the structural parameter of the drive transmission rod, B is the structural parameter of the reflector panel and back frame, and F is the structural parameter of the feed assembly.

[0069] Step 4: Initialize the particle swarm parameters. Based on the task requirements, initialize the antenna structure parameters involved in Step 3. Determine the dimension and scale of the particle swarm based on the number of structure parameters. Assign initial positions and velocities of various swarms randomly within constraints.

[0070] Step 5: Begin the particle swarm search process. Based on the global optimization objective, calculate the fitness of various swarms under given initial parameters, and update their spatial positions based on the calculation results.

[0071]

[0072] In the formula, v is the particle's velocity; s is the particle's spatial position; k is the number of iterations; w is the inertia coefficient; c1 and c2 are the acceleration coefficients; r1 and r2 are random numbers; P Best,i The optimal solution for the population; G Best This is the globally optimal solution.

[0073]

[0074] In the formula, w max The maximum inertia coefficient; w min is the minimum inertia coefficient; k is the number of iterations; N is the maximum number of iterations.

[0075] Step 6, Particle velocity and position correction. The velocity and spatial position of the particles are determined, and particles exceeding the boundary conditions are corrected.

[0076]

[0077] In the formula, [v min , v max ] and [s min s max [ ] represents the boundaries of particle velocity and spatial position, respectively.

[0078] Step 7, Constraint Determination. Construct a kinematic model of the antenna unfolding process based on the structural parameters corresponding to the particle positions. Determine whether the constraints are met through kinematic analysis. If the constraints are met, proceed to Step 8; otherwise, do not update the optimal solution for the population.

[0079] Step 8, Optimal Solution Update. Update the population optimum and the global optimum based on the fitness function calculated from the particle positions.

[0080]

[0081] Step 9, iterate repeatedly. Based on the set number of iterations, repeat steps 5 through 8 until you obtain G. bestIt is the globally optimal solution, that is, the structural parameters that satisfy the limiting envelope of a solid-surface deployable antenna.

[0082] In one possible implementation, the aforementioned method is achieved by building a cross-platform, multi-threaded optimization architecture. For the object of this invention, kinematic analysis is involved in determining constraints, and the computational load of kinematic analysis itself can even exceed that of the optimization process. However, in the particle swarm optimization algorithm, different groups only exchange information after each optimization, and are independent of each other during the optimization process. Therefore, to address the low efficiency of serial computation, this invention builds a cross-platform, multi-threaded optimization architecture to improve computational efficiency. Specifically, a Python program is used as the main control program for the particle swarm algorithm, enabling parallel motion of multiple groups of particles; secondary program development is conducted based on the ADAMS platform to perform kinematic analysis, thereby determining constraints such as single-degree-of-freedom, geometric surfaces, and non-interference constraints.

[0083] It is understood that this invention has been described through embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of this invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific circumstances without departing from the spirit and scope of this invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are protected by this invention.

[0084] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm, characterized in that, Includes the following steps: S1. Using the analytic hierarchy process (AHP) to weight multiple indicators related to the antenna's coverage envelope performance according to task requirements, a single-objective optimization model is constructed to obtain the global optimization objective of the limit envelope of the solid-surface deployable antenna. S2. Establish constraints for the optimization model, including expanded geometric surface constraints, contracted envelope surface constraints, rigid body constraints, single-degree-of-freedom expansion constraints, non-interference constraints, and structural parameter boundary constraints. S3. Based on the antenna design requirements, determine the structural parameters to be solved in the optimization model; S4. Initialize the structural parameters. Determine the dimension and scale of the particle swarm based on the number of structural parameters, and initialize the parameters of each particle swarm. S5. Based on the global optimization objective, calculate the fitness of each particle swarm under the initial parameters, and update the particle velocity and spatial position; during the update process, the inertia coefficient is a non-fixed value. S6. Correct the velocity and spatial position of particles that exceed the boundary conditions; S7. Based on the structural parameters corresponding to the current position of the particle, construct a kinematic model of the antenna unfolding process, and determine whether the established constraints are met through kinematic analysis. If the constraints are met, execute S8. S8. Update the particle swarm optimization solution and the global optimal solution; S9. Repeat S5 to S8 until the set iteration conditions are met. The final global optimal solution is the structural parameter that satisfies the limiting envelope of the solid-surface deployable antenna.

2. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step S1, the indicator is the storage diameter D. max Storage height H max and storage volume V max The single-objective optimization model is constructed as follows: min:ζ(u)=α1D max +α2H max +α3V max In the formula, the parameters [α1, α2, α3] represent the storage diameter D determined using the analytic hierarchy process (AHP). max Storage height H max and storage volume V max The weight vector is determined by selecting specific data based on the actual task requirements; u represents the structural parameters to be solved, and ζ() represents the antenna convergence rate.

3. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 2, characterized in that: In step S2, the specific form of the constraint is as follows: s.t.:G D (x D y D z D )=0 G F (x F y F z F )≤0 δ=0 DOF=1 d min ≥d0 in min Oh, oh. max In the formula, G D Let x be the expanded antenna surface function. D y D z D For the expanded panel coordinates, by setting G D =0 indicates that the expanded surface satisfies the expanded geometric surface constraints; G F For the convergent envelope surface function, x F y F z F To determine the coordinates of the collapsed panel, set G... F ≤0 indicates that the collapsed surface satisfies the collapsed envelope surface constraint; δ represents the deformation of the antenna panel. Setting δ = 0 indicates that the antenna panel has no deformation, thus satisfying the rigid body constraint. DOF represents the antenna unfolding degree of freedom. Setting DOF=1 indicates that the antenna unfolding process has only one degree of freedom, satisfying the single degree of freedom constraint. d min This represents the minimum distance between adjacent antenna panels during antenna movement. d0 is the set distance threshold, which is determined by setting d... min ≥d0 indicates that the distance between adjacent panels is always greater than the distance threshold during the antenna unfolding process, satisfying the no-interference constraint; u max and u min This represents the upper and lower limits of the structural parameters to be solved, which are set by u. min ≤u≤u max This indicates that the antenna structural parameters are always within the design range and satisfy the structural parameter boundary constraints.

4. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 2, characterized in that: In step S3, the structural parameter u includes the expanded diameter D. a The diameter of the center panel is D. i Focal length f, number of petals n, structural parameters of drive transmission rod L, structural parameters of reflector panel and back frame B, and structural parameters of feed assembly F.

5. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step S4, when initializing the parameters of each particle group, the initial position and initial velocity of each particle group are assigned random values ​​within the constraints.

6. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step S5, the particle velocity and spatial position are updated, specifically as follows: v i (k+1)=wv i (k)+c1r1(P Best,i (k)-s i (k))+c2r2(G Best (k)-s i (k)) with i (k+1)=s i (k)+v i (k+1) In the formula, v is the particle's velocity; s is the particle's spatial position; k is the number of iterations; w is the inertia coefficient; c1 and c2 are the acceleration coefficients; r1 and r2 are random numbers; P Best,i The optimal solution for particle swarm optimization; G Best This is the globally optimal solution; The inertia coefficient is a non-fixed value and is used in the iterative calculation according to the following formula: In the formula, w max The maximum inertia coefficient; w min is the minimum inertia coefficient; N is the maximum number of iterations.

7. The method for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm according to claim 6, characterized in that: In step S8, the particle swarm optimization solution and the global optimization solution are updated, specifically as follows: P Best,i (k+1)=min(P Best,i (k),s i (k+1)) G Best (k+1)=min(P Best,i (k+1)) i＝1.2.... In the formula, i represents the number of particles in the swarm, and the specific value is selected by comprehensively considering the calculation accuracy and the computing power of the platform.

8. A system for designing the ultimate envelope of a solid-surface deployable antenna based on an improved particle swarm optimization algorithm, characterized in that, include: The main control module is used to execute S1: It uses the analytic hierarchy process (AHP) to perform weight planning on multiple indicators related to the antenna's receiving envelope performance according to the task requirements, constructs a single-objective optimization model, and obtains the global optimization objective of the limit envelope of the solid-surface deployable antenna. S2: Establish constraints for the optimization model, including expanded geometric surface constraints, contracted envelope surface constraints, rigid body constraints, single-degree-of-freedom unfolding constraints, non-interference constraints, and structural parameter boundary constraints; S3: Determine the structural parameters to be solved in the optimization model according to the antenna design requirements; After step S3 is completed, call the particle swarm optimization module; Based on the feedback from the particle swarm optimization module, execute S9: Repeat S5 to S8 until the set iteration conditions are met, and finally obtain the global optimal solution, which is the structural parameter that satisfies the limiting envelope of the solid-surface deployable antenna, until the end; The particle swarm optimization module performs the following steps: S4: Initializes the structural parameters, determines the dimension and scale of the particle swarm based on the number of structural parameters, and initializes the parameters of each particle swarm; S5: Calculates the fitness of each particle swarm under the initial parameters based on the global optimization objective, and updates the particle velocity and spatial position. During the update process, the inertia coefficient is a non-fixed value; S6: Corrects the velocity and spatial position of particles that exceed the boundary conditions; After step S6 is completed, the kinematics module is called; Based on the feedback from the kinematics module, S8 is executed: Updates the optimal solution for the particle swarm and the global optimal solution; After step S8 is completed, the module returns to the main control module. The kinematics module is used to execute S7: Based on the structural parameters corresponding to the current position of the particle, construct a kinematic model of the antenna unfolding process, and determine whether the established constraints are met through kinematic analysis. If the constraints are met, execute S8. After the execution of step S7, return to the particle swarm optimization module.

9. The design system according to claim 8, characterized in that: The main control module and particle swarm optimization module are implemented on the Python platform and use multi-threaded parallel computing to realize the parallel motion of multiple groups of particles; the kinematics module is implemented on the ADAMS platform to complete kinematic analysis.

10. A computer program product, characterized in that: When the computer program product is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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