Adaptive multi-resolution method and device for predicting wheel particle terrain traction performance

Abstract

This invention proposes an adaptive multi-resolution method and apparatus for predicting the traction performance of vehicle wheels on terrain. The method includes: generating a discrete unit set of the initial soil surface, setting the initial position of the wheel, identifying low-resolution and high-resolution regions, and updating the resolution boundary based on the wheel's position during travel. Discrete units cluster or split within different resolution regions according to a given particle size to meet simulation accuracy requirements. This invention is not only applicable to the analysis of the traction performance of off-road vehicle wheels on terrain but can also be extended to agricultural machinery, construction machinery, and other fields, possessing significant engineering application value and wide applicability. By dynamically changing the size and number of discrete units, this invention can achieve high-resolution simulation of soil particles in the vicinity of the wheel, improving simulation accuracy, while using low-resolution simulation in soil particle regions far from the wheel, thus improving simulation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of large-scale soil pavement mechanical analysis, specifically relating to an adaptive multi-resolution method and device for predicting the terrain traction performance of wheel particles. Background Technology

[0002] The unique characteristic of gravel roads lies in their composition of discontinuous gravel particles. These particles are prone to rotation and large displacement under the influence of vehicle wheels, leading to dynamic changes in the road surface structure and significantly impacting vehicle stability, passability, and energy efficiency. Therefore, deepening research in this area is not only crucial for promoting the leapfrog development of vehicle technology in my country, leading innovation in civilian industries, strengthening national defense capabilities, and advancing agricultural modernization, but also a key step in achieving efficient resource utilization, environmental protection, and sustainable development goals.

[0003] The Discrete Element Method (DEM), introduced by Cundall et al. in 1971, provides a powerful tool for exploring the complex mechanical behavior of granular media (Cundall PA, Strack OD L. (1979) A discrete numerical model for granular assemblies[J]. Geotechnique, 1979, 29(1):47-65.). This method can accurately simulate the dynamic processes of road material damage, particle splashing, and flow when a wheel travels on a gravel road, effectively overcoming the limitations of the traditional finite element method in dealing with discontinuous media, and is considered a highly promising analytical tool in the field of ground mechanics analysis. However, as the number of granular elements in the simulation increases, the computational efficiency of the Discrete Element Method (DEM) decreases significantly, becoming a key factor restricting its widespread application.

[0004] In recent years, in order to improve the computational efficiency of the Discrete Element Method (DEM), scholars at home and abroad have actively explored and proposed a variety of particle scaling strategies, including exact scaling, coarse-graining techniques, and truncation methods. Although these methods have improved computational efficiency to some extent, they still face many challenges. Specifically, although the exact scaling method can adjust the discrete element and the geometric model proportionally, it does not reduce the total number of elements in the system. Therefore, it has limited effectiveness in reducing computational load or shortening simulation time (Feng Y T, Owen DR J. (2014) Discrete element modelling of large scale particle systems-I: exact scaling laws[J]. Computational Particle Mechanics,1:159-168.). Coarse-graining techniques reduce the number of elements by merging small particles into larger ones. While this significantly improves computational speed, it sacrifices the system's microscopic degrees of freedom, altering the interparticle contact mechanism, limiting the direct application of existing microscopic parameters, and potentially affecting the accurate reproduction of minute road surface features (such as rut ​​clarity) in simulation results (Kanjilal S, Schneiderbauer S. (2021) A revised coarse-graining approach for simulation of highly poly-disperse granular flows[J]. Powder Technology, 385: 517-527.). Some researchers, in order to reasonably reproduce the true particle size distribution, apply coarse-graining techniques (methods) only to the smaller particles in the actual granular material (i.e., particles of a specified size are replaced with larger particles), and only consider the larger particle size distribution. This method is commonly referred to as the truncation method. Obviously, similar to coarse-graining technology, although this method reduces the degrees of freedom of the entire particle system, it ignores the influence of fine particles on the structure, such as vehicle driving behavior (Cleary PW, Sawley ML. (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge[J]. Applied Mathematical Modelling, 26(2):89-111.).

[0005] Furthermore, the aforementioned particle magnification methods may struggle to accurately match the particle size distribution of the target research object in practical applications, thus affecting the precision and reliability of the simulation results. Particularly when the simulation involves fine particles, magnification can blur the clarity of subtle traces left on the road surface after a wheel passes, such as ruts, thereby reducing the accuracy of the simulation results in representing the actual physical phenomena. Therefore, how to maintain or improve simulation accuracy while enhancing computational efficiency remains a crucial problem that urgently needs to be addressed in current discrete element method research. Summary of the Invention

[0006] To address at least one of the problems existing in the prior art, this invention provides an adaptive multi-resolution method for predicting the traction performance of wheel particles on terrain. By controlling the size and number of discrete elements during the analysis process, discrete element simulation of large-scale soil pavements can be achieved.

[0007] The present invention is achieved by at least one of the following technical solutions.

[0008] An adaptive multi-resolution method for predicting wheel particle terrain traction performance includes the following steps:

[0009] Discrete elements are used to describe the initial granular soil pavement, generating a set of discrete elements and compacting it under its own weight to reach a stable state. The number, coordinates, radius, velocity and acceleration information of the discrete elements are stored.

[0010] The wheel is initially positioned on one side of the initial soil surface. Based on the wheel's position and size, low-resolution and high-resolution regions are identified to obtain the initial resolution boundary.

[0011] The initial resolution boundary remains unchanged. Discrete units are clustered or split according to their position and criteria in the resolution region to obtain high-resolution particles and low-resolution particles.

[0012] The wheel is directed to travel to the other side. When the distance traveled by the wheel is equal to the update length of the set resolution boundary, the resolution boundary is updated based on the position of the wheel's center of mass.

[0013] Furthermore, the generation of the initial granular soil pavement includes: firstly, generating a set of discrete unit particles with randomly distributed coordinates and set sizes within a specified area; then, adding rigid wall constraints around and at the bottom of the area, and adding a gravity field to make the discrete units compact under their own weight to reach a stable state, thus forming the initial granular soil pavement.

[0014] Furthermore, the resolution boundary is determined by the position, size radius and width of the wheel, and the radius coefficient and width coefficient of the resolution boundary.

[0015] Furthermore, the resolution boundary is a sector with the current wheel's center of mass as the center and a specified radius as the boundary. Areas within the sector are identified as high-resolution regions, while areas outside the sector are identified as low-resolution regions.

[0016] Furthermore, by using the number of splits, the resolution particle size constant, the maximum and minimum particle size coefficients of the low-resolution and high-resolution regions, and the radius of the discrete unit, the maximum and minimum particle sizes of the two different resolution regions are determined, thus obtaining the particle size range of the discrete units in the two different resolution regions.

[0017] Furthermore, in the discrete units of the high-resolution region, if the particle size does not meet the given particle size range of the high-resolution region, the discrete units will split or aggregate until the given particle size range is met.

[0018] In the discrete cells of the low-resolution region, if the particle size does not meet the given particle size range of the high-resolution region, the discrete cells will split or aggregate until the given particle size range is met.

[0019] Discrete units that are simultaneously in both low-resolution and high-resolution regions will not coalesce or split.

[0020] Furthermore, during the splitting process, the main discrete unit splits into a given number of sub-discrete units according to a given number of splits, and the volume of each sub-discrete unit is evenly distributed by the volume of the main discrete unit according to the number of splits.

[0021] Furthermore, during the coalescence process, the primary discrete unit searches for the nearest sub-discrete unit to coalesce into, and the volume of the coalesced discrete unit is equal to the sum of the volumes of the discrete units participating in the coalescence.

[0022] Furthermore, the wheel displacement length updated at the resolution boundary is affected by the radius coefficient of the resolution boundary, and the length required for the update is lower than that at the resolution boundary.

[0023] An apparatus for implementing the aforementioned adaptive multi-resolution method for predicting wheel particle terrain traction performance includes:

[0024] Input devices, including but not limited to input tools such as mice and keyboards, are used to input initial model data;

[0025] Output devices, including but not limited to monitors, printers, and other output tools, are used to display analysis results;

[0026] Internal storage devices, including random access memory (RAM) and read-only memory (ROM), are used to temporarily store data generated during the analysis process for further analysis and processing.

[0027] External storage devices, including hard disks, solid-state drives, optical disks, USB flash drives, etc., are used to store analysis results for a long time, facilitating subsequent data processing and analysis; the central processing unit (CPU) is the core of this device, responsible for handling data reading, analysis, updating and other operations, and executing the method steps of this invention.

[0028] Compared with the prior art, the present invention has at least the following advantages and technical effects:

[0029] This invention enables discrete element method (DEM) simulation of soil pavement in wheel performance analysis. It improves the resolution of the size and number of discrete elements within the range that significantly impacts wheel performance, while reducing the resolution of the size and number of discrete elements within the range that has a smaller impact. This approach reduces computational costs and improves computational efficiency while maintaining computational accuracy, thus making DEM valuable for engineering applications. The successful implementation of this invention is not only significant for studying vehicle performance on soil pavement, but also for researching ore crushing, sea ice dynamics, and the sedimentation and adsorption processes of pollutants. Attached Figure Description

[0030] Figure 1 This is a structural diagram of an implementation device for an adaptive multi-resolution method for predicting the traction performance of wheel particles in terrain, provided in an embodiment of the present invention.

[0031] Figure 2a This is a flowchart of an adaptive multi-resolution method for predicting wheel particle terrain traction performance according to an embodiment of the present invention.

[0032] Figure 2b This is a detailed flowchart of the adaptive multi-resolution method process C in the flowchart;

[0033] Figure 3 This is a schematic diagram of the initial soil pavement after the initial discrete unit set has been compacted by its own weight and the area it occupies.

[0034] Figure 4 This is a schematic diagram showing the position of the wheel in the left region of the discrete element set;

[0035] Figure 5 This is a schematic diagram illustrating the recognition of resolution boundaries and low / high resolution regions.

[0036] Figure 6a This is a schematic diagram illustrating the process of a discrete unit splitting.

[0037] Figure 6b This is a schematic diagram illustrating the coalescing process of discrete units;

[0038] Figure 6cThis is a schematic diagram of the road surface state after the adaptive transformation and change of the size and number of discrete unit particles before the wheels move;

[0039] Figure 7 This is a schematic diagram of the road surface state after updating the resolution boundary and performing adaptive transformation and changes in the size and number of discrete unit particles during wheel movement. Detailed Implementation

[0040] To enable those skilled in the art to better understand the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0041] An adaptive multi-resolution method for predicting wheel particle terrain traction performance according to the present invention is implemented by the following device, the structural diagram of which is shown below. Figure 1 As shown. The device comprises the following main components:

[0042] Input devices, including but not limited to input tools such as mice and keyboards, are used to input initial model data;

[0043] Output devices, including but not limited to monitors, printers, and other output tools, are used to display analysis results;

[0044] Internal storage devices, including random access memory (RAM) and read-only memory (ROM), are used to temporarily store data generated during the analysis process for further analysis and processing.

[0045] External storage devices, including hard drives, solid-state drives, optical discs, USB flash drives, etc., are used to store analysis results for a long time, facilitating subsequent data processing and analysis;

[0046] The central processing unit (CPU) is the core of this device, responsible for handling data reading, analysis, updating and other operations, and executing the method steps of this invention.

[0047] This invention provides an adaptive multi-resolution method for predicting the traction performance of wheel particles in terrain, such as... Figure 2a , Figure 2b As shown, the main steps include:

[0048] Step 1: Read in the initial discrete element model information. Use discrete elements to describe the initial soil pavement particles, generate a discrete element set, and let it compact under its own weight to reach a stable state. Store the numbers, coordinates, radii, velocities, and acceleration information of the discrete elements. The compacted discrete element set is the initial soil pavement.

[0049] This step specifically includes the following sub-steps:

[0050] Step 1.1: Establish a discrete element set and form a model of the initial soil pavement. Generate a discrete element set with a given low-resolution area within a given spatial region (the spatial range is: 0 to a in the X direction, 0 to b in the Y direction, where the X direction is the horizontal direction, the Y direction is the vertical direction, 0 is the lower boundary limit value in the X and Y directions, a is the upper boundary limit value in the X direction, b is the upper boundary limit value in the Y direction, and the sizes of a and b are determined according to specific parameters such as wheel size and pavement characteristics) with a discrete element radius r low of the discrete element set. The number of elements is denoted as N, and the element numbers are 1 to N.

[0051] Step 1.2: Add rigid wall constraints to the four perimeter boundaries and the bottom boundary of the given spatial region.

[0052] Step 1.3: Add a gravitational field, calculate the forces between the discrete elements under the action of the gravitational field, and make these discrete elements reach a stable state under their own gravity. At this time, the discrete element set that reaches the stable state is the initial soil pavement.

[0053] Among them, calculating the forces between discrete elements includes the following: contact search, calculating mutual forces such as tangential force and normal force according to the contact model used by the simulator, and updating the motion equations of the discrete elements according to the calculated forces.

[0054] Store the numbers, coordinates, radii, velocities, and acceleration information of the discrete elements after reaching the stable state. The discrete element set that reaches the stable state is the initial soil pavement. The spatial region range of the initial soil pavement becomes X: 0 to a, Y: 0 to b', where b' < b, and b' is the upper boundary limit value when the discrete element set compacts under its own weight and reaches the stable state.

[0055] In some embodiments of the present invention, the contact determination between discrete units during the self-weight compaction process adopts the C-grid method (Williams JR, Perkins E, Cook B. (2004) A contact algorithm for partitioning N arbitrary sized objects[J]. Engineering Computations, 2004, 21(2 / 3 / 4):235-248.), and the discrete unit contact determination search is X: 0~a, Y: 0~b, that is, the region where the discrete unit set is located before self-weight compaction.

[0056] Step 2: Place the wheel at its initial position on one side of the initial soil surface. Identify the low-resolution and high-resolution areas based on the wheel's position and size to obtain the initial resolution boundary.

[0057] In some embodiments of the present invention, the wheel is initially positioned on the left side of the initial soil surface, with the leftmost edge of the wheel aligned as closely as possible with the left edge of the surface. Subsequently, based on the number of splits q and the resolution particle size constant γ1 of the low-resolution region and the resolution particle size constant γ2 of the high-resolution region, the maximum particle size coefficient β for each of the low-resolution and high-resolution regions is determined. low_max β high_max and minimum particle size coefficient β low_min β high_min Then, based on the radius r of the generated discrete unit particle Furthermore, the maximum particle size r in the low-resolution region and the high-resolution region were obtained respectively. low_max r high_ma and minimum particle size r low_min r high_min Next, based on the wheel radius r... tire The radius coefficient α1 of the resolution boundary and the wheel displacement length l required for resolution boundary update. update The system determines whether the resolution boundary needs updating and identifies low-resolution and high-resolution regions (the first update occurs after the wheel is placed). The resolution boundary is a sector centered on the current wheel's centroid and bounded by the wheel's radius. Regions within this boundary are identified as high-resolution, while regions outside are identified as low-resolution. The resolution boundary radius coefficient is determined based on the required simulation accuracy.

[0058] Step 3: Apply an angular velocity ω to the wheel, causing it to travel in the positive X direction. Simultaneously, modify the search range for the discrete element contact judgment (to: X: 0~a, Y: 0~b'). Before and during wheel travel, adaptive transformations and changes in the size and number of discrete element particles will occur.

[0059] Step 4: Adaptive Multi-Resolution Prediction of Wheel Particle Terrain Traction Performance: The resolution region to which a discrete unit belongs is identified by the resolution boundary. This region is divided into a low-resolution region (regions of discrete units that have no impact on wheel traction performance) and a high-resolution region (regions of discrete units that do impact wheel traction performance). Discrete units entirely within either the low-resolution or high-resolution region will be judged based on the given particle size range of their respective resolution region. Units larger than the given particle size range will split, while those smaller will aggregate, until the particle size meets the given range of the resolution region. Whether a discrete unit aggregates or splits depends on its location and the given particle size range of its resolution region. Both the low-resolution and high-resolution regions have their own given particle size ranges. Discrete units whose particle size falls within the given range of their respective resolution regions will not split or aggregate; those whose particle size does not fall within the given range of their respective resolution regions will split or aggregate.

[0060] When a discrete unit splits, the main discrete unit splits into a corresponding number of sub-discrete units according to a given number of splits. The volume of each sub-discrete unit is evenly distributed by the volume of the main discrete unit according to the number of splits. When a discrete unit coalesces, the main discrete unit searches for the nearest sub-discrete unit to coalesce. The volume of the coalesced discrete unit is equal to the sum of the volumes of the participating discrete units, satisfying the conservation of mass and momentum.

[0061] Step 5: During the wheel's movement, the forces between discrete elements are continuously calculated to update the force conditions and motion equations of the particles and the wheel. When the displacement length in the X direction equals the wheel displacement length l required for updating the resolution boundary... updat When the resolution is multiple of that, the resolution boundary is updated based on the current position of the wheel's center of mass, and then the low-resolution and high-resolution regions are re-identified.

[0062] In some embodiments of the present invention, if the discrete unit is simultaneously in a low-resolution region and a high-resolution region, it will not coalesce or split; coalesce or split will only occur when the entire discrete unit completely enters the new resolution region.

[0063] When the wheel's displacement satisfies the resolution boundary update condition, the resolution boundary is updated based on the wheel's current position. This process is repeated along the wheel's direction of travel, dynamically realizing the adaptive transformation and change of the discrete unit particle size and quantity during the analysis of the wheel's driving performance on the soil surface.

[0064] In some embodiments of the present invention, the wheel displacement length updated by the resolution boundary is affected by the radius coefficient of the resolution boundary. That is, the length required for the update must be less than or equal to the resolution boundary, and can be determined within the range of 0 (not 0) to the resolution boundary according to the simulation accuracy requirements.

[0065] In some embodiments of the present invention, the following specific examples illustrate an adaptive multi-resolution method for predicting wheel particle terrain traction performance, the specific steps of which include:

[0066] 1. First, generate a discrete unit set with a radius of 3.5 mm in the region range X: 0~600mm, Y: 0~100mm, with a number of 1560 units, and store them in an external storage device.

[0067] 2. Using the aforementioned discrete element set as initial input, after reading it through the input device, rigid walls are added around and to the bottom of the region where the discrete element set is located. Simultaneously, a gravity field is added to allow the discrete elements to reach a stable state under their own weight. The element number, coordinates, radius, velocity, and acceleration information at this moment are stored in the internal storage device. The discrete element set that has reached a stable state is the initial soil pavement. Figure 3 As shown. At this time, the discrete unit numbers are 1 to 1560, and the contact judgment search range is X: 0 to 600 mm, Y: 0 to 95 mm.

[0068] 3. Adjust the radius r tire Place a 30mm wheel on the left side of the initial soil surface, aligning the leftmost edge of the wheel as closely as possible with the left edge of the surface. The initial position of the wheel is as follows: Figure 4 As shown, the coordinates of the wheel's center of mass O are (30, 125).

[0069] 4. Determine the radius coefficient α1 of the resolution boundary as 1.2. Therefore, the resolution boundary is a circle with a radius of 36mm centered on the current wheel's center of mass. Areas within this boundary are identified as high-resolution regions, while areas outside the boundary are identified as low-resolution regions. The identification of the resolution boundary and resolution regions is as follows: Figure 5 As shown.

[0070] 5. Determine the number of splits q as 7 and the resolution particle size constant γ1 as... and γ2 are Further determine the maximum grain size coefficient β for the low-resolution and high-resolution regions. low_max for β high_max for and minimum particle size coefficient β low_min for β high_min for The maximum grain size r in both the low-resolution and high-resolution regions can be obtained. low_max It is 6.125mm, r high_max With a particle size of 0.875 mm and a minimum particle size r low_min 0.875mm, r high_min The particle size is 0.125mm. Before the wheel travels, an adaptive transformation and change in the size and number of discrete unit particles occurs: Discrete units entirely in the high-resolution region will aggregate if their particle size is less than 0.125mm, and split if their particle size is greater than 0.875mm; Discrete units entirely in the low-resolution region will aggregate if their particle size is less than 0.875mm, and split if their particle size is greater than 6.125mm; Discrete units simultaneously in both low-resolution and high-resolution regions will not aggregate or split. The aggregation and splitting processes of discrete units and the road surface conditions before the wheel travels are as follows: Figure 6a , Figure 6b , Figure 6c As shown.

[0071] 6. Determine the wheel X-direction displacement length l for resolution boundary update. upddte The radius is 18mm. An angular velocity ω = 0.5 rad / s is applied to the wheel, which begins to travel along the positive X-axis. During this process, the discrete element contact judgment search range is X: 0–600mm, Y: 0–95mm, and adaptive transformations and changes occur in the size and number of discrete element particles. As the wheel travels, the forces between discrete elements are continuously calculated to update the force conditions and motion equations of the particles and the wheel. When the displacement length of the wheel in the X direction is equal to 18mm or a multiple of 18, the resolution boundary is updated based on the current position of the wheel's center of mass, and then the low-resolution and high-resolution regions are re-identified. The road surface state after re-identifying the low-resolution and high-resolution regions is as follows. Figure 7 As shown.

[0072] Repeat the above steps along the direction of wheel travel to solve the discrete elements, and output and store the analysis results in an external storage device, thereby realizing the simulation analysis of the wheel's driving performance on soil roads. Each time the size and number of discrete element particles are adaptively transformed and changed, the number and coordinates of the discrete elements that undergo the transformation and change are updated.

[0073] In summary, this invention continuously adapts and changes the size and number of discrete element particles during wheel movement, reducing the accuracy of regions of discrete elements that do not affect wheel performance (i.e., reducing the total number of discrete elements and increasing their size), while increasing the accuracy of regions of discrete elements that do affect wheel performance (i.e., increasing the total number of discrete elements and decreasing their size). This reduces computational costs and improves computational efficiency while maintaining computational accuracy as much as possible, making discrete element simulation of large-scale soil pavements possible. Furthermore, this invention is also applicable to the simulation of the working processes of other loose pavement equipment, such as agricultural machinery, construction machinery, and mining machinery.

[0074] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, enabling those skilled in the art to better understand and utilize the invention.

Claims

1. An adaptive multi-resolution method for predicting the traction performance of a vehicle wheel on granular terrain, characterized in that, Includes the following steps: Discrete elements are used to describe the initial granular soil pavement, generating a set of discrete elements and compacting it under its own weight to reach a stable state. The number, coordinates, radius, velocity and acceleration information of the discrete elements are stored. The wheel is initially positioned on one side of the initial soil surface. Based on the wheel's position and size, low-resolution and high-resolution regions are identified to obtain the initial resolution boundary. The initial resolution boundary remains unchanged. Discrete units are clustered or split according to their position and criteria in the resolution region to obtain high-resolution particles and low-resolution particles. The wheel is directed to travel to the other side. When the distance traveled by the wheel is equal to the set resolution boundary update length, the resolution boundary is updated based on the position of the wheel's center of mass. The resolution boundary is a sector centered on the centroid of the current wheel and bounded by the wheel radius. Areas within the sector are identified as high-resolution regions, while areas outside the sector are identified as low-resolution regions. By determining the number of splits, the resolution particle size constant, and the maximum and minimum particle size coefficients of the low-resolution and high-resolution regions, the maximum and minimum particle sizes of the low-resolution and high-resolution regions are obtained, thus yielding the particle size range of the discrete units in the low-resolution and high-resolution regions.

2. The adaptive multi-resolution method for predicting wheel particle terrain traction performance according to claim 1, characterized in that, The generation of the initial granular soil pavement includes: firstly, generating a set of discrete elements with randomly distributed coordinates and set dimensions within a specified area; then, adding rigid wall constraints around and at the bottom of the specified area, and adding a gravity field to make the discrete elements compact under their own weight to reach a stable state, thus forming the initial granular soil pavement.

3. The adaptive multi-resolution method for predicting wheel particle terrain traction performance according to claim 1, characterized in that, In the discrete unit of the high-resolution region, if the particle size does not meet the given particle size range of the high-resolution region, the discrete unit will split or aggregate until the given particle size range is met. In discrete units in the low-resolution region, if the particle size does not meet the given particle size range in the low-resolution region, the discrete units will split or aggregate until the given particle size range is met. Discrete units that are simultaneously in both low-resolution and high-resolution regions will not coalesce or split.

4. The adaptive multi-resolution method for predicting wheel particle terrain traction performance according to claim 3, characterized in that, During the splitting process, the main discrete unit splits into a corresponding number of sub-discrete units according to the calculated or given number of splits, and the volume of each sub-discrete unit is evenly distributed by the volume of the main discrete unit according to the number of splits.

5. The adaptive multi-resolution method for predicting wheel particle terrain traction performance according to claim 3, characterized in that, During the coalescence process, the primary discrete unit searches for the nearest sub-discrete unit to coalesce with, and the volume of the coalesced discrete unit is equal to the sum of the volumes of the discrete units that participated in the coalescence.

6. An adaptive multi-resolution method for predicting wheel particle terrain traction performance according to any one of claims 1-5, characterized in that, The wheel displacement length required for resolution boundary updates is less than or equal to the resolution boundary.

7. An apparatus for implementing an adaptive multi-resolution method for predicting wheel particle terrain traction performance according to any one of claims 1-6, characterized in that, include: Input device, used to input initial data; Output devices are used to display the analysis results; Internal storage devices are used for temporary storage of data generated during the analysis process; External storage devices are used to store analysis results for a long time, facilitating subsequent data processing and analysis. The central processing unit (CPU) is responsible for handling data reading, analysis, and update operations.

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