A macroscopic free particle system velocity distribution law observation system

Abstract

This invention provides an observation system for the velocity distribution law of a macroscopic free particle system, comprising: a motion simulation device, a visual acquisition module, and a data processing module. The motion simulation device controls a rigid ball to perform horizontal motion in a non-equilibrium steady state on a horizontal rotating platform, simulating the thermal motion state of microscopic free particles under different driving conditions at a macroscopic scale. The visual acquisition module acquires continuous video data containing the motion process of the rigid ball and uploads it to the data processing module. The data processing module processes the video data into standard image frames, performs image detection and target tracking to obtain the motion trajectory data of each rigid ball, and analyzes the correlation between equivalent temperature and rotational speed based on the motion trajectory data to verify the physical effectiveness of the motion simulation device in simulating Maxwell's velocity distribution motion. Through this invention, the cross-scale universality of Maxwell's velocity distribution law can be intuitively verified at a macroscopic scale.

Description

Technical Field

[0001] This invention relates to the field of statistical physics experimental technology, specifically to an observation system for the velocity distribution law of a macroscopic free particle system. Background Technology

[0002] In the field of statistical physics experiments, the verification of Maxwell's velocity distribution law is mainly based on the study of microscopic particle systems (such as gas molecular beams). However, current experimental verification techniques for Maxwell's velocity distribution law primarily focus on microscopic particle systems, with typical schemes including:

[0003] Microscopic gas molecule experimental method: Traditional teaching demonstrations use the Miller-Kush experimental setup or modern molecular beam technology to verify microscopic particles (orders ≥ 10). 20 The Maxwell distribution characteristics under thermal equilibrium. Taking the Miller-Kush experiment as an example, a beam of metal vapor molecules is generated by a heated furnace, which is then collimated into a thin beam and enters a rotating cylindrical velocity selector. Only molecules with specific velocities can pass through the selector and reach the detector. By measuring the molecular flux at different selected velocities, the molecular velocity distribution curve is obtained. However, this method is only applicable to microscopic particle systems and cannot directly observe the statistical laws of macroscopic objects.

[0004] Brownian motion observation method: Some teaching experiments use a microscope to observe pollen grains (approximately 1-10 μm in diameter) suspended in liquid. By manually marking the positions of the grains and calculating their displacement distribution, statistical regularities are indirectly verified. However, this method has a small sample size (usually observing 10-20 grains), is time-consuming, and is easily affected by liquid viscosity and thermal convection.

[0005] Computer simulation method: This method uses Monte Carlo numerical simulation software to simulate the collision motion of a large number of particles in a virtual environment and generate velocity distribution histograms. However, this method relies entirely on software simulation and lacks the experience of real physical processes.

[0006] It is understandable that the aforementioned existing technologies generally have the following drawbacks: the experimental setup is complex and expensive (requiring a vacuum system and precision mechanical structure), making it unsuitable for widespread use in undergraduate teaching laboratories; the sample size is huge but cannot be visually displayed, making it difficult for students to understand the concept of "a large number of particles" in statistical physics; traditional image processing methods rely on manual labeling, which is inefficient, has large errors, and is difficult to process long-term sequence data.

[0007] To achieve more intuitive experimental teaching, a verification of Maxwell's velocity distribution law based on macroscopic scales is proposed. However, at macroscopic scales (millimeter level and above), the applicability of this law faces the following three fundamental challenges: The energy-dominated contradiction: the thermal motion energy of macroscopic particles at room temperature (approximately 10... -21 J) is far below the energy of environmental disturbance (approximately 10).-12 J), which leads to its motion being completely dominated by uncontrollable external disturbances, making it impossible to exhibit the random characteristics of microscopic thermal motion; dynamic equilibrium dilemma: the low frequency of macroscopic particle collisions (on the order of seconds) and the existence of inelastic losses cause the system energy to continuously decay, making it difficult to maintain a stable equilibrium state; insufficient statistical samples: the number of macroscopic particles available for experiments is usually only a few dozen to tens, with significant statistical fluctuations, making it impossible to obtain a convergent continuous distribution curve. Summary of the Invention

[0008] Therefore, this invention provides an observation system for the velocity distribution law of macroscopic free particle systems, aiming to solve the technical problems of existing technologies for verifying Maxwell's velocity distribution law, such as complex and expensive equipment, lack of intuitiveness, low image processing efficiency, insufficient statistical samples, and contradictions and dynamic equilibrium dilemmas caused by energy dominance.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides an observation system for the velocity distribution law of a macroscopic free particle system. The system includes: a motion simulation device, a visual acquisition module, and a data processing module; the visual acquisition module and the data processing module are communicatively connected. The motion simulation device is used to control multiple rigid balls to perform horizontal motion in a non-equilibrium steady state on a horizontal rotating platform, so as to simulate the thermal motion state of microscopic free particles under different driving conditions on a macroscopic scale; the driving conditions include at least the rotational speed of the horizontal rotating platform; The visual acquisition module is used to acquire continuous video data containing the motion process of the multiple rigid balls, and upload the video data to the data processing module; The data processing module is used to acquire the video data, process the video data into multiple consecutive standard image frames, perform image detection and target tracking on the multiple standard image frames to obtain the motion trajectory data of each rigid ball; and analyze the correlation between equivalent temperature and rotational speed based on the motion trajectory data to verify the physical effectiveness of the motion simulation device in simulating Maxwell's velocity distribution motion.

[0010] Furthermore, the motion simulation device includes the horizontal rotating platform, the rigid experimental box, the plurality of rigid balls, and the controllable speed-adjustable motor; the rigid experimental box is detachably fixed above the horizontal rotating platform, and when the rigid experimental box is fixed to the horizontal rotating platform, the central axis of the rigid experimental box coincides with the central axis of the horizontal rotating platform; The controllable speed-adjustable motor is connected to the horizontal rotating platform through an eccentric transmission mechanism, which is used to control the horizontal rotating platform to perform circular motion based on different speeds, so as to drive the rigid experimental box to rotate horizontally. The rigid experimental box is used to hold the plurality of rigid balls and rotates horizontally with the circular motion of the horizontal rotating platform to do work on the plurality of rigid balls. The multiple rigid spheres are used to acquire controllable kinetic energy by colliding with the inner wall of the rigid experimental box, which is performing translational rotation, and to perform two-dimensional planar motion inside the rigid experimental box, simulating the thermal motion state of microscopic free particles.

[0011] Furthermore, the visual acquisition module includes an adjustable cantilever bracket and a camera device; The camera device is detachably fixed to the end of the adjustable cantilever bracket and is used to capture video data from above. The adjustable cantilever bracket end is used to adjust the spatial position of the camera device so that the camera device is placed directly above the horizontal rotating platform; The adjustable cantilever bracket is equipped with a level at its end to ensure that the optical axis of the camera device is perpendicular to the plane of the horizontal rotating platform.

[0012] Furthermore, the data processing module includes a video processing unit, an image detection unit, a target tracking unit, a speed calculation unit, and a fitting verification unit connected in sequence; The video processing unit is used to acquire video data corresponding to different driving conditions, process the video data under each driving condition into multiple consecutive image frames, and perform size standardization and / or pixel normalization on each image frame to obtain the multiple standard image frames. The image detection unit is used to perform image detection on the multiple standard image frames using a target detection model to obtain the detection box information of each rigid ball; The target tracking unit is used to receive the detection frame information of each of the rigid balls, and determine the cross-frame identity information of the same rigid ball through cross-frame detection based on Kalman filter, so as to generate the motion trajectory data of each of the rigid balls. The speed calculation unit is used to calculate the motion speed data of each rigid ball based on the motion trajectory data, and to filter the valid trajectory data based on the motion speed data to obtain the target speed data corresponding to the valid trajectory data. The fitting analysis unit is used to fit a two-dimensional Maxwell distribution function based on the target speed data using the gradient descent method, and to analyze the correlation between equivalent temperature and rotational speed based on the target fitting parameters under different driving conditions.

[0013] Furthermore, the target detection model adopts a pre-trained YOLOv8 neural network architecture, including a backbone network, a neck network, and a head network; The backbone network integrates multiple CBS modules and multiple C2f modules to receive the multiple standard image frames, extract features from each standard image frame, and input multi-scale features into the neck network. The neck network adopts a PAN-FPN structure to perform feature fusion on the multi-scale features, and inputs the fused target features into the head network; The head network integrates multiple classification heads and multiple regression heads to output detection box information of the detected target; the detection box information includes the pixel coordinates of the upper left corner of the bounding box, the pixel coordinates of the lower right corner of the bounding box, the confidence score of the detected target, and the category label of the detected target.

[0014] Furthermore, the target tracking unit is also used for: Based on the historical motion trajectory determined by the detection box information of each rigid ball, a Kalman filter is used to predict the target position of the rigid ball in the current image frame, and the corresponding prediction box information is obtained. Based on the detection box information and the prediction box information, an IoU cost matrix between the detection box and the prediction box is constructed, and the Hungarian algorithm is used to perform optimal matching between the detection box and the prediction box to obtain the matching result; the matching result is used to determine the cross-frame identity information of the same rigid ball. The state of the Kalman filter is updated using the detection box that successfully matches the prediction box, and the motion trajectory data representing the unique identity information of each rigid ball is output.

[0015] Furthermore, the speed calculation unit is used for: Based on the motion trajectory data, the displacement difference and time interval of each rigid ball in adjacent image frames are determined; The instantaneous velocity vector of the rigid ball is calculated based on the displacement difference and the time interval, and the mathematical expression is as follows:

[0016]

[0017] in, Indicates the first The instantaneous velocity vector of the image frame; Indicates the first The position of the image frame; Indicates the first The position of the image frame; Indicates a time interval; The motion speed data of the rigid ball is calculated based on the instantaneous velocity vector, and the mathematical expression is as follows:

[0018] Among them, the Indicates the first The motion rate of the image frame.

[0019] Furthermore, the fitting verification unit is used for: Extract speed / rate samples from the target speed data; divide the speed / rate range of the speed / rate samples into multiple equal-width intervals, and calculate the probability density of each equal-width interval; The gradient descent method is used to fit the two-dimensional Maxwell distribution function, including: Define a loss function based on mean squared error, optimize the parameters to be fitted until the loss function is minimized, output the optimized target fitting parameters, and calculate the corresponding goodness of fit.

[0020] Furthermore, the fitting verification unit is also used for: Obtain the target fitting parameters under different driving conditions, and calculate the equivalent temperature value based on the target fitting parameters. The mathematical expression is as follows:

[0021] in, Indicates the first The equivalent temperature value corresponding to each driving condition; Indicates the first Target fitting parameters under each driving condition; Indicates the mass of the rigid ball; Represents the Boltzmann constant; Linear regression was used to analyze the correlation between the equivalent temperature value and the square of the rotational speed, and an equivalent temperature-rotational speed square relationship graph was plotted.

[0022] Furthermore, the system also includes a visualization module; the visualization module is communicatively connected to the data processing module. The visualization module is used to acquire experimental data from the data processing module and to visualize and display the experimental data. The experimental data includes at least one of the following: motion trajectory data, target velocity data, goodness of fit, and equivalent temperature-rotation square relationship graph.

[0023] The present invention, by adopting the above technical solution, has at least the following beneficial effects: This invention proposes an observation system for the velocity distribution law of a macroscopic free particle system, comprising: a motion simulation device, a visual acquisition module, and a data processing module; the visual acquisition module is communicatively connected to the data processing module; the motion simulation device controls multiple rigid spheres to perform horizontal motion in a non-equilibrium steady state on a horizontal rotating platform, simulating the thermal motion state of microscopic free particles under different driving conditions at a macroscopic scale; the visual acquisition module acquires continuous video data containing the motion process of the multiple rigid spheres and uploads the video data to the data processing module; the data processing module acquires the video data, processes it into multiple consecutive standard image frames, performs image detection and target tracking on the multiple standard image frames to obtain the motion trajectory data of each rigid sphere; and analyzes the correlation between equivalent temperature and rotational speed based on the motion trajectory data. This invention constructs a non-equilibrium steady-state system based on continuous energy injection, using a uniformly rotating reference frame to provide controllable kinetic energy to the macroscopic rigid spheres, and continuously compensating for the energy dissipation of the system through external driving to maintain the statistical steady state of the system. Meanwhile, a long-term sampling strategy is employed to compensate for the statistical deficiencies in instantaneous particle counts, thus reproducing the statistical distribution characteristics of microscopic thermal motion on a macroscopic scale. Combined with AI vision-based real-time multi-target tracking and automated data analysis, this invention can intuitively verify the cross-scale universality of Maxwell's velocity distribution law, providing an intuitive, reliable, and easily applicable experimental observation method for simulating microscopic statistical physical laws in macroscopic systems.

[0024] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A structural block diagram of an observation system for the velocity distribution law of a macroscopic free particle system provided in an embodiment of the present invention is shown; Figure 2 A simplified structural schematic diagram of a motion simulation device provided in an embodiment of the present invention is shown; Figure 3 A schematic diagram of the rotation method of a rigid experimental box provided in an embodiment of the present invention is shown; Figure 4 A schematic diagram of the motion of a rigid ball according to an embodiment of the present invention is shown; Figure 5 A simplified structural diagram of a vision acquisition module provided in an embodiment of the present invention is shown; Figure 6 A structural block diagram of a data processing module provided in an embodiment of the present invention is shown; Figure 7 A schematic diagram of the principle of an image detection unit provided in an embodiment of the present invention is shown; Figure 8 A schematic diagram of the target tracking unit provided in an embodiment of the present invention is shown; Figure 9 A schematic diagram of the velocity / rate distribution fitting result provided by an embodiment of the present invention is shown; Figure 10 A graph showing the goodness of fit of the Maxwell velocity distribution provided by an embodiment of the present invention as a function of the number of observation frames is shown. Figure 11 A comparison graph showing the effect of rotational speed / number of balls on the goodness of fit of the Maxwell velocity distribution provided in an embodiment of the present invention is shown. Figure 12 A linear relationship between equivalent temperature and the square of rotational speed is shown in an embodiment of the present invention. Figure 13 A structural block diagram of an observation system for the velocity distribution law of a macroscopic free particle system provided in an embodiment of the present invention is shown. Detailed Implementation

[0027] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0028] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0029] This invention provides an observation system for the velocity distribution law of a macroscopic free particle system, such as... Figure 1 As shown, the system includes at least a motion simulation device 10, a vision acquisition module 20, and a data processing module 30.

[0030] The motion simulation device 10 can be used to control multiple rigid balls to perform horizontal motion in a non-equilibrium steady state on a horizontal rotating platform, so as to simulate the thermal motion state of microscopic free particles under different driving conditions on a macroscopic scale.

[0031] In a uniformly rotating reference frame, a system of free particles can reach a statistical equilibrium state, where its equivalent temperature is proportional to the square of the angular velocity. This invention transforms the difficult-to-observe microscopic thermal motion into macroscopic mechanical motion that can be precisely controlled by rotational speed, achieving the core innovation of "replacing uncontrollable thermal drive with controllable mechanical drive." Firstly, this invention constructs a "macroscopic simulation" device under non-equilibrium steady-state conditions, injecting up to 10 [units of measurement missing] into a rigid sphere. -6 The controllable kinetic energy of J is much higher than the energy of environmental disturbance (10). -12 J) and the thermal energy of macroscopic particles at room temperature (10 -21 J). This allows the motion of the rigid sphere to be dominated by controllable mechanical drive, rather than uncontrollable external disturbances, thus simulating the thermal motion of microscopic "free particles" using a macroscopic "rigid sphere." The construction of the motion simulation device 100 is described in detail below: like Figure 2 As shown, the motion simulation device 10 includes a horizontal rotating platform 11, a rigid experimental box 12, multiple rigid balls 13, and a controllable speed-adjustable motor (not shown in the figure).

[0032] In this embodiment of the invention, the horizontal rotating platform 11 can specifically be an orbital shaker. An orbital shaker is a commonly used laboratory device that uses a controllable speed-adjustable motor to drive the platform to perform horizontal circular motion. The rigid experimental box 12 is detachably fixed above the horizontal rotating platform 11. When the rigid experimental box 12 is fixed to the horizontal rotating platform 11, the central axis of the rigid experimental box 12 coincides with the central axis of the horizontal rotating platform 11. The controllable speed-regulating motor is connected to the horizontal rotating platform 11 through an eccentric transmission mechanism. The eccentric transmission mechanism consists of an eccentric shaft, an eccentric wheel, and an eccentric bearing. Its own central axis does not coincide with the rotation axis of the controllable speed-regulating motor, forming a small fixed eccentricity. When the controllable speed-regulating motor is running, it drives the eccentric transmission mechanism to make circular motion around the motor's main shaft, thereby driving the horizontal rotating platform 11 to achieve circular rocking. The rigid experimental box 12 is used to hold multiple rigid balls 13, and rotates horizontally with the circular rocking of the horizontal rotating platform 11 to do work on the multiple rigid balls 13. The multiple rigid balls 13 can obtain controllable kinetic energy by colliding with the inner wall of the rigid experimental box that performs the horizontal rotation, and perform two-dimensional planar motion inside the rigid experimental box 12 to simulate the thermal motion state of microscopic free particles.

[0033] In practical applications, the horizontal rotating platform 11 is placed on a horizontal support structure 14 (such as a horizontal tabletop). A controllable speed-regulating motor can be installed inside the horizontal rotating platform 11, driving it to rotate in a circular motion via an eccentric transmission mechanism. Different speeds of horizontal circular motion can be achieved by adjusting the motor speed. Specifically, the controllable speed-regulating motor has a built-in encoder, enabling closed-loop speed control of the angular velocity ω within the range of 0-600π rad / min, with an accuracy of ±5π rad / min. Concentric circular scale lines can be engraved on the upper surface of the horizontal rotating platform 11 for positioning the rigid experimental box 12. It is understandable that by using high-precision closed-loop speed control, the rigid ball 13 is ensured to undergo high-frequency inelastic collisions with the inner wall of the rigid experimental box. This process can obtain a precise and adjustable continuous kinetic energy injection to accurately compensate for the frictional dissipation between the rigid balls 13 and between the rigid balls 13 and the inner wall of the rigid experimental box, thereby achieving a statistically stable non-equilibrium steady state on a macroscopic level. The rigid experimental box 12 is set at the coaxial position of the horizontal rotating platform 11, and the structure is precisely and reliably assembled, avoiding additional shaking and motion interference caused by installation offset or loosening. This makes the motion trajectory of the rigid ball 13 inside the box regular and the motion state stable, thereby providing a stable and precise physical experimental environment for simulating the thermal motion of microscopic particles.

[0034] Preferably, the rigid experimental box 12 is a square metal box with dimensions of 20cm × 12cm × 5cm. To ensure that the horizontal rotating platform 11 is aligned with the central axis of the rigid experimental box 12, positioning posts (not shown in the figure) can be set at the four corners of the bottom of the rigid experimental box 12, and positioning holes (not shown in the figure) can be set on the upper surface of the horizontal rotating platform 11. The positioning posts and positioning holes form a clearance fit and are detachably fixed by a snap-fit ​​structure (not shown in the figure), achieving a central axis coincidence error of <2mm. In addition, to reduce the friction between the rigid balls 13 and the rigid experimental box 12, the inner wall of the rigid experimental box 12 needs to be polished to make its surface roughness Ra ≤ 0.8μm, thereby reducing friction. The rigid balls 13 are made of quartz, preferably with a diameter of 1.4cm, and number 2-10. Their surfaces are polished to reduce deformation and friction during movement. It is understandable that by polishing the inner wall of the rigid experimental box 12 and the surface of the rigid ball 13, the friction between the macroscopic particles and the box wall and the ball during the motion is significantly reduced, thereby minimizing energy loss and helping the system maintain a stable equilibrium state for a longer time. This more realistically simulates the frictionless motion characteristics of microscopic particles in an ideal state, thus better simulating Maxwell's velocity distribution motion.

[0035] In practical applications, such as Figure 3 As shown, this is a schematic diagram (top view) of the rotation method of the rigid experimental box 12. A controllable speed-regulating motor drives a circular shaking table to perform circular shaking, causing the rigid experimental box 12 to perform horizontal circular motion through "parallel rotation." This ensures that the rigid balls 13 inside the rigid experimental box 12 continue to roll, resulting in more uniform movement and preventing impact and accumulation. Figure 4 The diagram shows the motion of rigid balls 13 when a controllable speed-regulating motor drives a circular shaking table. Multiple rigid balls 13 undergo two-dimensional planar motion inside the rigid experimental box 12. It can be understood that by changing the driving conditions (rotary shaking table speed), the speed and equivalent temperature of the rigid balls 13 will also change. Therefore, by collecting the motion states of the rigid balls 13 under different driving conditions, the physical effectiveness of the motion simulation device 10 in simulating Maxwell's velocity distribution motion can be analyzed and verified.

[0036] Furthermore, the visual acquisition module 20 can be used to acquire continuous video data of the motion process of multiple rigid balls 13, and upload the video data to the data processing module 30. For example... Figure 5 As shown, the visual acquisition module 20 includes at least an adjustable cantilever bracket 21 and a camera device 22.

[0037] The adjustable cantilever bracket 21 adopts a three-degree-of-freedom adjustable cantilever structure, and its first end can be fixed to the horizontal support structure 14 (such as a horizontal table). The camera device 22 (such as a mobile phone or camcorder) can be detachably fixed to the end of the adjustable cantilever bracket 21 through the clamping device 23 for capturing video data from above. The adjustable cantilever bracket 21 can be used to adjust the spatial position of the camera device 22 after it is fixed, so that the camera device 22 is placed directly above the horizontal rotating platform 11. The end of the adjustable cantilever bracket 21 is equipped with a level (not shown in the figure), which can be used to ensure that the optical axis of the camera device 22 is perpendicular to the plane of the horizontal rotating platform 12. As an optional embodiment, an LED supplementary light source (not shown in the figure) can also be set at the end of the adjustable cantilever bracket 21 to provide uniform illumination. In practical applications, the camera preferably uses a frame rate of 240fps and a resolution of 1920. A 1080 resolution video stream was acquired to perform high-precision observation of the motion of the rigid ball 13.

[0038] Furthermore, in this embodiment of the invention, the visual acquisition module 20 and the data processing module 30 can be connected via USB or wirelessly to upload video data to the data processing module 30 in real time. The data processing module 30 employs a high-performance GPU (such as an NVIDIA RTX 3070) to execute processing steps for the video data through preset algorithm code, including acquiring video data, processing the video data into multiple consecutive standard image frames, performing image detection and target tracking on the multiple standard image frames to obtain the motion trajectory data of each rigid ball; and analyzing the correlation between equivalent temperature and rotational speed based on the motion trajectory data to verify the physical effectiveness of the motion simulation device 10 in simulating Maxwell's velocity distribution motion.

[0039] Specifically, such as Figure 6 As shown, the data processing module 30 includes multiple functional units to collaboratively perform data processing and verification analysis of video data, including a video processing unit 31, an image detection unit 32, a target tracking unit 33, a speed calculation unit 34, and a fitting verification unit 35 connected in sequence. The working principles of each functional unit are explained in detail below: The video processing unit 31 can be used to acquire video data corresponding to different driving conditions, process the video data under each driving condition into multiple consecutive image frames, and perform image standardization processing on each image frame, including size standardization (such as scaling the size to 640×640) and pixel normalization to [0,1]; and then input the obtained standard image frames to the image detection unit 32.

[0040] Furthermore, the image detection unit 32 is equipped with an object detection model, which can be used to perform image detection on multiple standard image frames to obtain the detection box information of each rigid ball. Specifically, the object detection model adopts a pre-trained YOLOv8 neural network architecture, and outputs the bounding box coordinates, confidence score, and class label of each rigid ball by performing forward inference on each standard image frame.

[0041] like Figure 7 The diagram shown is a schematic representation of the principle of the image detection unit 32. Figure 7 As can be seen, the target detection model employs a backbone network, a neck network, and a head network. The backbone network integrates multiple CBS modules and multiple C2f modules, which can receive multiple standard image frames and extract features from each frame, inputting multi-scale features into the neck network. The neck network uses a PAN-FPN structure to fuse multi-scale features, inputting the fused target features into the head network. The head network integrates multiple classification heads and multiple regression heads, which can output the detection box information of the detected target after filtering by confidence threshold and non-maximum suppression. This includes the pixel coordinates of the top-left corner (x1, y1), the pixel coordinates of the bottom-right corner (x2, y2), the target detection confidence (0-1), and the target category label (0 represents a rigid sphere, 1 represents a rigid experimental box boundary).

[0042] In practical applications, the image detection unit 32 undergoes thorough pre-training (trained on 467 labeled images) to achieve high-precision model performance (mAP@0.5=99.5%), ensuring real-time, accurate, and high-confidence detection of macroscopic rigid balls. This provides high-quality data input for subsequent target tracking, significantly reducing errors that may be introduced in the target detection process, thereby improving the accuracy and reliability of the entire system in tracking the trajectory of the ball.

[0043] Furthermore, the target tracking unit 33 is used to receive the detection frame information of each rigid ball, and determine the cross-frame identity information of the same rigid ball through cross-frame detection based on Kalman filter, so as to generate the motion trajectory data of each rigid ball.

[0044] like Figure 8The diagram shows the principle of the target tracking unit 33. After receiving the detection box information of each rigid ball, the target tracking unit 33 determines its historical motion trajectory, uses a Kalman filter to predict the target position where the rigid ball should appear in the current image frame, and obtains the corresponding prediction box information; it constructs the IoU cost matrix between the detection box and the prediction box based on the detection box information and the prediction box information, and uses the Hungarian algorithm to perform optimal matching between the detection box and the prediction box to obtain the matching result; the matching result is used to determine the cross-frame identity information of the same rigid ball; the state of the Kalman filter is updated using the detection box that successfully matches the prediction box, and the motion trajectory data representing the unique identity information of each rigid ball is output.

[0045] Specifically, the target tracking unit 33 employs multi-target tracking based on the SORT tracker. It predicts the location of the rigid ball across frames based on historical positions and matches this location with the detection location in the current frame to identify the same rigid ball in both the current and historical frames, establishing a unique ID for each. Through continuous multi-frame processing, the continuous motion trajectory of the same rigid ball in different frames can be obtained. In practical applications, new trajectories can be created for unmatched detection boxes, and lost trajectories can be retained for 100 frames before being deleted. This improves the robustness and fault tolerance of the tracking algorithm, effectively addressing potential brief occlusions, lighting changes, or occasional missed detections by the detection model during the ball's movement. It reduces trajectory interruptions and ID switching errors, ensuring the integrity and accuracy of long-term continuous trajectory data and providing a more reliable data foundation for subsequent velocity calculations and distribution fitting.

[0046] Furthermore, the velocity calculation unit 34 is used to calculate the motion velocity data of each rigid ball based on the motion trajectory data, and to filter the valid trajectory data based on the motion velocity data to obtain the target velocity data corresponding to the valid trajectory data.

[0047] In this embodiment of the invention, the motion trajectory data (including center coordinates) of each rigid ball are obtained. timestamp Afterwards, it is recorded to a data file. For each rigid ball, its velocity is calculated using the velocity calculation unit 34. Specifically, the displacement difference and time interval of each rigid ball in adjacent image frames can be determined based on the motion trajectory data; the instantaneous velocity vector of the rigid ball is calculated based on the displacement difference and time interval, and the mathematical expression is as follows:

[0048]

[0049] in, Indicates the rigid ball in the first... The instantaneous velocity vector of the image frame; Indicates the rigid ball in the first... The position of the image frame; Indicates the rigid ball in the first... The position of the image frame; This represents a time interval, which can be 1 / 240s.

[0050] Subsequently, the motion speed data of the rigid ball is calculated based on the instantaneous velocity vector, and the mathematical expression is as follows:

[0051] in, Indicates the rigid ball in the first... The motion rate of the image frame.

[0052] It should be noted that after obtaining the velocity data of each rigid ball, it is automatically stored in a CSV data file, and a preset Python script automatically filters valid motion trajectory data (e.g., length > 50 frames, outlier removal based on quartiles, etc.). This achieves automated cleaning and preprocessing of the raw motion trajectory data, eliminating invalid data caused by brief detection or unstable tracking, thus ensuring the data quality and accuracy used for Maxwell distribution fitting.

[0053] Furthermore, the fitting analysis unit 35 is used to fit a two-dimensional Maxwell distribution function based on the target velocity data using the gradient descent method, and to analyze the correlation between equivalent temperature and rotational speed based on the target fitting parameters under different driving conditions. The specific functions of the fitting analysis unit 35 include the following: First, the velocity (including direction information) / rate samples extracted from all velocity data after the start of steady state are fitted, and the goodness of fit is calculated. The specific execution steps include: ① Extract velocity / rate samples from the target velocity data; ② Histogram preparation: Divide the velocity / rate range of the velocity / rate samples into... For each equal-width interval, calculate the probability density to obtain the velocity components. and rate The distribution histogram; ③ Determine the theoretical model: To describe the driving effect of the circular shaking table on the rigid ball 13, an equivalent temperature is introduced. This characterizes the average kinetic energy of a particle under steady-state conditions. The mathematical expression is: ;in, For the mass of a single particle, It is the average of the squares of the motion speeds of all particles.

[0054] Based on this, embodiments of the present invention have fitted the velocity distribution and velocity components respectively. Specifically, the velocity distribution fitting function is expressed as:

[0055] in, This represents the theoretical probability density corresponding to the velocity distribution. Indicates the speed of motion; These are the parameters that need to be adjusted during the fitting process to make the fitting function match the experimental data points; Indicates the equivalent temperature value; This indicates the mass of the ball.

[0056] The velocity component fitting function is expressed as:

[0057] in, This represents the theoretical probability density corresponding to the velocity component; Indicates speed of motion ; These are the parameters to be fitted.

[0058] ④ Define the loss function based on mean squared error: To quantify the fitting effect, this invention introduces a loss function, which represents the predicted value of the fitted curve. Compared with the true value The difference between them is represented by the mean squared error value as the loss function.

[0059] in, This represents the value of the loss function; Indicates the number of equal-width intervals; Indicates the first The theoretical probability density of equal-width intervals; Indicates the first The actual probability density of equal-width intervals; This represents the parameters to be fitted.

[0060] ⑤ Perform gradient descent optimization until the loss function is minimized, output the optimized target fitting parameters, and calculate the goodness of fit based on the probability density.

[0061] Specifically, the gradient descent optimization algorithm is used to obtain... The minimum point of the curve is found, which minimizes the loss function and makes the fitted curve most closely resemble the real data. The gradient descent optimization algorithm may include the following steps: initializing the parameters to be fitted. (like ); Calculate the gradient; the gradient direction of the fitted function at each point should be:

[0062] In practical applications, to achieve accurate and efficient local minima search, this invention employs the optimizer from the SciPy library to perform gradient descent optimization, which can automatically determine the learning rate for each step based on a given loss function. Specifically, the parameters to be fitted Iterative updates will be performed in the following manner:

[0063] in, loss function For the parameters to be fitted The gradient; This represents the learning rate. The optimization process will repeatedly perform gradient calculations and parameter updates until the model converges, i.e., satisfies the condition. Or, if the number of iterations reaches a preset upper limit, the loss function is finally obtained. The minimum point, that is, the point where the fitted curve most closely approximates the data points. Find the optimal value. Substitute this optimal parameter into the Maxwell theory curve. Then the final fitted curve can be obtained.

[0064] At the same time, the goodness of fit is calculated using the following formula:

[0065] in, Represents the sum of squared residuals; Represents the total sum of squares; This represents the mean of the actual probability density. Therefore, it allows for a quantitative assessment of the degree of agreement between experimental data and theoretical distributions, providing students with objective and immediate feedback on experimental results, thus enhancing the scientific rigor of the experiment and the effectiveness of teaching.

[0066] Rigorous particle dynamics theory shows that inelastic dissipation causes the high-energy tail of the distribution to deviate slightly from the Gaussian form, but based on the system characteristics (small number of particles, high-frequency random boundary driving), this deviation is extremely weak and negligible. Therefore, under steady-state conditions, the velocity / rate distribution macroscopically exhibits a two-dimensional Maxwell distribution that is highly consistent with that of an ideal gas.

[0067] Finally, based on the fitted two-dimensional Maxwell distribution function, an equivalent temperature-rotational speed relationship analysis is performed to verify the physical effectiveness of the motion simulation device 10 proposed in this embodiment of the invention for simulating Maxwell velocity distribution motion.

[0068] In this embodiment of the invention, since the rigid experimental box 12 is driven by a circular shaker, the speed of the "container" can be expressed as: ( Let the radius of the circular motion be . (This refers to the rotational speed of the circular shaking table). It can be understood that, under steady-state conditions, the velocity characteristic scale acquired by the rigid ball 13 upon collision will necessarily be proportional to the velocity of the container wall, that is, the square root mean square velocity of the rigid ball 13 is proportional to the square of the velocity of the circular shaking table. Therefore, theoretically, the equivalent temperature and the rotational speed of the circular shaking table follow the following relationship: .

[0069] To verify whether the actual motion state of the rigid ball 13 matches the theory, this embodiment of the invention obtains target fitting parameters under different driving conditions (platform speed), and calculates the equivalent temperature value based on the target fitting parameters. The mathematical expression is as follows:

[0070] in, Indicates the first The equivalent temperature value corresponding to each driving condition; Indicates the first Target fitting parameters under each driving condition; This represents the mass of the rigid ball. Linear regression analysis was then used to examine the relationship between the equivalent temperature and the square of the rotational speed, and an equivalent temperature-rotational speed square relationship graph was plotted.

[0071] In practical applications, by changing the platform rotation speed By repeating the experiment, a set of results can be obtained. Data, fitted parameters based on the target Calculate the corresponding equivalent temperature value Therefore, linear regression can be used to fit and plot the graph. and Relationship diagram, i.e. This verifies the physical effectiveness of the motion simulation device 10 in simulating Maxwell's velocity distribution motion.

[0072] To verify the physical effectiveness and measurement accuracy of the observation system for the velocity distribution law of macroscopic free particle systems proposed in this invention, a specific embodiment is given below: Researchers confirmed that the system can accurately reproduce the statistical laws of microscopic thermal motion on a macroscopic scale by conducting actual measurements and data analysis on the motion state of a rigid ball under different driving conditions, thus providing reliable experimental support for practical applications.

[0073] First, based on the following experimental preparations and variable conditions, the motion data of the rigid ball were obtained: Rigid spheres: made of quartz, with a diameter of 1.4 cm and a polished surface, were used in quantities of 2, 4, 6, 8, and 10 to investigate the effect of different particle numbers on the experimental results.

[0074] Rigid experimental box: Made of aluminum with a smooth inner wall to minimize friction interference during the movement of rigid balls. Its dimensions are 20cm×12cm×5cm, providing a stable space for the rigid balls to move.

[0075] Horizontal rotary platform (circular shaking table): driven by a controllable speed-adjustable motor, with a speed adjustment range of 80π rad / min to 400π rad / min, supporting continuous adjustment, adopting a closed-loop control mode, and achieving a control accuracy of ±5π rad / min to ensure the stability and accuracy of driving conditions.

[0076] Visual acquisition: A smartphone is used as a camera device to capture overhead video at a frame rate of 240fps and a resolution of 1920×1080. The optical axis of the camera device is strictly perpendicular to the plane of the circular rocking table to ensure that the position of the ball is accurately captured.

[0077] Image detection and target tracking: A YOLOv8 model is used for ball detection, combined with a SORT tracker for multi-target tracking, accurately extracting the position coordinates of each ball in each frame; the instantaneous velocity of the ball is calculated based on the position difference between adjacent frames, with a sampling time interval... =1 / 240s, ensuring the timeliness and accuracy of speed calculation.

[0078] Furthermore, based on the motion data, the following experimental verifications were conducted: ①Fitting accuracy verification: This embodiment uses rotational speeds of 200π rad / min and 240π rad / min as examples to specifically process the motion data of 10 rigid balls, obtaining velocity components respectively. and rate The distribution histogram was obtained, and the two-dimensional Maxwell distribution function was fitted using the gradient descent method. Specifically, the velocity distribution and velocity component were fitted using the aforementioned velocity distribution fitting function and velocity component fitting function, respectively, and the fitting results are shown below. Figure 9 As shown in the figure, under both rotational speed conditions, the velocity component distribution exhibits a Gaussian distribution with a mean of zero, while the speed distribution displays a typical Maxwell's bell curve. Furthermore, the goodness of fit... The calculation results are shown in Table 1 below:

[0079] As can be seen from the above data, the velocity distribution and velocity components measured by the observation system of this invention are in high agreement with the theoretical Maxwell distribution, and the goodness of fit is greater than 0.98. This fully demonstrates the accuracy of the system in reproducing the statistical laws of microscopic thermal motion on a macroscopic scale and meets the accuracy requirements of experimental measurement.

[0080] ② Determination of minimum effective sampling size: To investigate the minimum number of video frames (i.e., the minimum effective sample size) required to obtain a stable statistical distribution, this embodiment extracts subsets of different sizes from the complete experimental dataset at intervals of 100 frames, 200 frames, ..., 20,000 frames. Distribution fitting is then performed on each subset, and the goodness of fit is calculated. The value was determined. This experiment was conducted under the conditions of a fixed rotational speed of 160π rad / min and the number of rigid balls being 2, 4, 6, 8, and 10, respectively, to ensure the influence of a single variable on the experimental results. The experimental results are as follows: Figure 10 As shown, it can be seen that when the video frame rate exceeds 1500 frames, the number of balls under all conditions... The values ​​remained consistently above 0.95, indicating that the sampling rate at this point met the stability requirements of the statistical distribution; when the number of frames further increased to over 15,000 frames, The value gradually approaches 1.0, further improving the statistical accuracy. This result verifies that the core strategy of this invention, which uses "time averaging instead of spatial averaging," can obtain statistically significant sample data by extending the observation time under conditions of a limited number of particles (as low as 2), effectively overcoming the statistical fluctuation problem caused by insufficient particle numbers in macroscopic experiments, and further demonstrating the practicality of the system.

[0081] ③ Parameter universality verification: To verify the robustness and applicability of the observation system under different rotational speeds and different numbers of balls, this embodiment employs a full-parameter combination experiment. Independent experiments were conducted under full combinations of rotational speeds of 80π, 120π, 160π, 200π, 240π, 280π, 320π, 360π, and 400π rad / min (covering the entire adjustable rotational speed range) and ball numbers of 2, 4, 6, 8, and 10 (covering all set quantities). Maxwell fit was applied to the ball velocity distribution under each parameter combination, and the goodness of fit was calculated. Values, and draw Value heatmaps visually represent system performance under different conditions, such as Figure 11 As shown. Experimental results show that, under all test parameter combinations, the goodness of fit of the rate distribution is... All were above 0.90, under most conditions The results are consistent with those from the fitting accuracy verification stage. This indicates that the macroscopic free particle system velocity distribution law observation system described in this invention can stably and accurately reproduce Maxwell's velocity distribution within a wide range of rotational speeds (80π~400π rad / min) and particle numbers (preferably 2~10), demonstrating good parameter universality and adaptability to the needs of different experimental scenarios.

[0082] ④ Verification of the linear relationship between equivalent temperature and the square of rotational speed: Based on theoretical derivation, under non-equilibrium steady state, the equivalent temperature of the system is... It should be the square of the rotational speed of the circular shaking table. Proportional, that is This relationship is one of the core theoretical bases for verifying the physical effectiveness of the system. This embodiment modifies the rotational speed of the circular shaking table. (Setting the speeds sequentially to 80π, 120π, 160π, 200π, 240π, 280π, 320π, 360π, and 400π rad / min, covering all adjustable speeds), and recording the fitting parameters at each speed. and using relational expressions The equivalent temperature of the system at the corresponding rotational speed was calculated. .

[0083] Furthermore, the calculated With the corresponding A linear regression fit was performed, and the fitting result is as follows: Figure 12 As shown. The regression analysis results show: The fitting coefficients (Units omitted), linear fit goodness of fit The results show a highly significant linear positive correlation between the system's equivalent temperature and the square of the circular shaking table's rotational speed, accurately verifying the theoretical prediction. The regularity further proves, from a quantitative perspective, the physical effectiveness of the motion simulation device of this invention in simulating Maxwell's velocity distribution motion, and also confirms the reliability of the measurement data of the observation system.

[0084] In summary, this embodiment, through four verification tests, fully demonstrates that the macroscopic free particle system velocity distribution law observation system of the present invention has high measurement accuracy, good parameter universality, and reliable physical validity. It can accurately reproduce the statistical laws of microscopic thermal motion at the macroscopic scale and can meet the needs of related experiments and practical applications.

[0085] As an optional embodiment, such as Figure 13As shown in the embodiment of the present invention, the observation system for the velocity distribution law of a macroscopic free particle system may further include a visualization module 40. The visualization module 40 is communicatively connected to the data processing module 30 and is used to acquire experimental data from the data processing module 30 and to visualize and display the experimental data. The experimental data includes trajectory data, target velocity data, goodness of fit, and equivalent temperature-rotational square relationship graphs, etc. Thus, by automatically generating intuitive visualization charts and real-time fitting results, abstract statistical physics concepts (such as the bell curve of Maxwell's velocity distribution law) are presented to students in an intuitive and easy-to-understand way, enabling students to observe the degree of agreement between experimental results and theory, enhancing the intuitiveness, interactivity, and interest of teaching, and helping students to understand statistical laws more deeply.

[0086] This invention provides an observation system for the velocity distribution law of a macroscopic free particle system, which, compared with the prior art, has at least the following advantages: 1) This invention enables intuitive verification of Maxwell's distribution law on a macroscopic scale: Traditional experiments can only indirectly measure microscopic molecules, and students cannot intuitively "see" the statistical regularity. This invention transforms abstract concepts into visible millimeter / centimeter-level ball motion, and achieves goodness-of-fit through real-time AI tracking and fitting result display. (Under certain conditions >0.98), the bell-shaped distribution curve is visually presented directly, significantly enhancing the intuitiveness of teaching. The experiment confirms that macroscopic particles also follow the Maxwell distribution under specific conditions, breaking down the cognitive barrier that "this law only applies to microscopic systems" and providing cross-scale experimental evidence for the teaching of statistical physics.

[0087] 2) This invention addresses the statistical fluctuation problem caused by insufficient sample size of macroscopic particles: Macroscopic experimental systems typically contain fewer than 10 particles, making it difficult to obtain a convergent statistical distribution using traditional methods. This invention innovatively proposes a "time-average instead of spatial-average" approach, acquiring 20,000 frames of data within 20 minutes through high-speed 240fps acquisition and AI-automated processing. Each frame contains a maximum of 10 particles, accumulating over 10000 samples. 5 1500 independent velocity samples. Experiments show that when the number of frames > 1500, It can be stabilized above 0.95, which effectively suppresses statistical fluctuations, proves the effectiveness of the ensemble hypothesis in the macroscopic system, and provides a reusable paradigm for finite sample statistical experiments.

[0088] 3) A low-cost, highly compatible intelligent teaching platform has been constructed: Compared to traditional molecular beam devices (cost > 100,000 RMB), the core components of this invention are a commercially available rotating platform (350 RMB) and a regular smartphone (2,000 RMB), with a total cost < 10,000 RMB, making it suitable for mass deployment in undergraduate teaching laboratories. Furthermore, the system supports a wide range of adjustments for 2-10 or more particles and a rotational speed of 0-600π rad / min, allowing for the exploration of the influence of different variables on distribution, and possesses "out-of-the-box" teaching friendliness.

[0089] 4) This invention achieves interdisciplinary integration of statistical physics and artificial intelligence in teaching: It integrates cutting-edge AI technologies such as object detection (YOLOv8), multi-object tracking (SORT), and gradient descent optimization into classic physics experiments. Students can not only verify Maxwell's distribution but also intuitively understand the impact of algorithms on data quality by adjusting confidence thresholds and IoU matching parameters. This cross-disciplinary design of "physics + AI" cultivates students' computational thinking and data literacy in the context of new engineering disciplines, which aligns with the national strategy for digital transformation of higher education.

[0090] Those skilled in the art will clearly understand that the specific working process of the systems, devices, modules and units described above can be referred to the corresponding process in the foregoing method embodiments. For the sake of brevity, it will not be repeated here.

[0091] Furthermore, the functional units in the various embodiments of the present invention can be physically independent of each other, or two or more functional units can be integrated together, or all functional units can be integrated into one processing unit. The integrated functional units described above can be implemented in hardware, or in software or firmware.

[0092] Those skilled in the art will understand that if the integrated functional unit is implemented in software and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or all or part of it, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computing device (e.g., a personal computer, server, or network device) to execute all or part of the steps of the methods described in the embodiments of the present invention when running the instructions. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0093] Alternatively, all or part of the steps of the foregoing method embodiments can be implemented by hardware (such as a computing device, personal computer, server, or network device) related to program instructions. The program instructions can be stored in a computer-readable storage medium. When the program instructions are executed by the processor of the computing device, the computing device executes all or part of the steps of the methods described in the various embodiments of the present invention.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that within the spirit and principles of the present invention, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the corresponding technical solutions to depart from the protection scope of the present invention.

Claims

1. A system for observing the velocity distribution law of a macroscopic free particle system, characterized in that, The system includes: a motion simulation device, a vision acquisition module, and a data processing module; the vision acquisition module is communicatively connected to the data processing module. The motion simulation device is used to control multiple rigid balls to perform horizontal motion in a non-equilibrium steady state within a horizontal rotating platform, so as to simulate the thermal motion state of microscopic free particles under different driving conditions on a macroscopic scale; the driving conditions include at least the rotational speed of the horizontal rotating platform; The visual acquisition module is used to acquire continuous video data containing the motion process of the multiple rigid balls, and upload the video data to the data processing module; The data processing module is used to acquire the video data, process the video data into multiple consecutive standard image frames, perform image detection and target tracking on the multiple standard image frames to obtain the motion trajectory data of each rigid ball; and analyze the correlation between equivalent temperature and rotational speed based on the motion trajectory data to verify the physical effectiveness of the motion simulation device in simulating Maxwell's velocity distribution motion.

2. The system according to claim 1, characterized in that, The motion simulation device includes the horizontal rotating platform, the rigid experimental box, the plurality of rigid balls, and the controllable speed-adjustable motor; the rigid experimental box is detachably fixed above the horizontal rotating platform, and when the rigid experimental box is fixed to the horizontal rotating platform, the central axis of the rigid experimental box coincides with the central axis of the horizontal rotating platform; The controllable speed-adjustable motor is connected to the horizontal rotating platform through an eccentric transmission mechanism, which is used to control the horizontal rotating platform to perform circular motion based on different speeds, so as to drive the rigid experimental box to rotate horizontally. The rigid experimental box is used to hold the plurality of rigid balls and rotates horizontally with the circular motion of the horizontal rotating platform to do work on the plurality of rigid balls. The multiple rigid spheres are used to acquire controllable kinetic energy by colliding with the inner wall of the rigid experimental box, which is performing translational rotation, and to perform two-dimensional planar motion inside the rigid experimental box, simulating the thermal motion state of microscopic free particles.

3. The system according to claim 2, characterized in that, The visual acquisition module includes an adjustable cantilever bracket and a camera device; The camera device is detachably fixed to the end of the adjustable cantilever bracket and is used to capture video data from above. The adjustable cantilever bracket is used to adjust the spatial position of the camera device so that the camera device is positioned directly above the horizontal rotating platform; The adjustable cantilever bracket is equipped with a level at its end to ensure that the optical axis of the camera device is perpendicular to the plane of the horizontal rotating platform.

4. The system according to claim 1, characterized in that, The data processing module includes a video processing unit, an image detection unit, a target tracking unit, a speed calculation unit, and a fitting verification unit connected in sequence. The video processing unit is used to acquire video data corresponding to different driving conditions, process the video data under each driving condition into multiple consecutive image frames, and perform size standardization and / or pixel normalization on each image frame to obtain the multiple standard image frames. The image detection unit is used to perform image detection on the multiple standard image frames using a target detection model to obtain the detection box information of each rigid ball; The target tracking unit is used to receive the detection frame information of each of the rigid balls, and determine the cross-frame identity information of the same rigid ball through cross-frame detection based on Kalman filter, so as to generate the motion trajectory data of each of the rigid balls. The speed calculation unit is used to calculate the motion speed data of each rigid ball based on the motion trajectory data, and to filter the valid trajectory data based on the motion speed data to obtain the target speed data corresponding to the valid trajectory data. The fitting analysis unit is used to fit a two-dimensional Maxwell distribution function based on the target speed data using the gradient descent method, and to analyze the correlation between equivalent temperature and rotational speed based on the target fitting parameters under different driving conditions.

5. The system according to claim 4, characterized in that, The target detection model adopts a pre-trained YOLOv8 neural network architecture, including a backbone network, a neck network, and a head network. The backbone network integrates multiple CBS modules and multiple C2f modules to receive the multiple standard image frames, extract features from each standard image frame, and input multi-scale features into the neck network. The neck network adopts a PAN-FPN structure to perform feature fusion on the multi-scale features, and inputs the fused target features into the head network; The head network integrates multiple classification heads and multiple regression heads to output detection box information of the detected target; the detection box information includes the pixel coordinates of the upper left corner of the bounding box, the pixel coordinates of the lower right corner of the bounding box, the confidence score of the detected target, and the category label of the detected target.

6. The system according to claim 4, characterized in that, The target tracking unit is also used for: Based on the historical motion trajectory determined by the detection box information of each rigid ball, a Kalman filter is used to predict the target position of the rigid ball in the current image frame, and the corresponding prediction box information is obtained. Based on the detection box information and the prediction box information, an IoU cost matrix between the detection box and the prediction box is constructed, and the Hungarian algorithm is used to perform optimal matching between the detection box and the prediction box to obtain the matching result; the matching result is used to determine the cross-frame identity information of the same rigid ball. The state of the Kalman filter is updated using the detection box that successfully matches the prediction box, and the motion trajectory data representing the unique identity information of each rigid ball is output.

7. The system according to claim 4, characterized in that, The speed calculation unit is used for: Based on the motion trajectory data, the displacement difference and time interval of each rigid ball in adjacent image frames are determined; The instantaneous velocity vector of the rigid ball is calculated based on the displacement difference and the time interval, and the mathematical expression is as follows: in, Indicates the first The instantaneous velocity vector of the image frame; Indicates the first The position of the image frame; Indicates the first The position of the image frame; Indicates a time interval; The motion speed data of the rigid ball is calculated based on the instantaneous velocity vector, and the mathematical expression is as follows: Among them, the Indicates the first The motion rate of the image frame.

8. The system according to claim 4, characterized in that, The fitting verification unit is used for: Extract speed / rate samples from the target speed data; divide the speed / rate range of the speed / rate samples into multiple equal-width intervals, and calculate the probability density of each equal-width interval; The gradient descent method is used to fit the two-dimensional Maxwell distribution function, including: Define a loss function based on mean squared error, optimize the parameters to be fitted until the loss function is minimized, output the optimized target fitting parameters, and calculate the corresponding goodness of fit.

9. The system according to claim 8, characterized in that, The fitting verification unit is also used for: Obtain the target fitting parameters under different driving conditions, and calculate the equivalent temperature value based on the target fitting parameters. The mathematical expression is as follows: in, Indicates the first The equivalent temperature value corresponding to each driving condition; Indicates the first Target fitting parameters under each driving condition; Indicates the mass of the rigid ball; Represents the Boltzmann constant; Linear regression was used to analyze the correlation between the equivalent temperature value and the square of the rotational speed, and an equivalent temperature-rotational speed square relationship graph was plotted.

10. The system according to any one of claims 1 to 9, characterized in that, The system also includes a visualization module; the visualization module is communicatively connected to the data processing module. The visualization module is used to acquire experimental data from the data processing module and to visualize and display the experimental data. The experimental data includes at least one of the following: motion trajectory data, target velocity data, goodness of fit, and equivalent temperature-rotation square relationship graph.

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