Three-dimensional Coordinates Research Articles

Predicting transient wind loads on tall buildings in three-dimensional spatial coordinates using machine learning

Machine learning (ML) as a subset of artificial intelligence (AI), has gained significant attention in wind engineering applications over the past decade. Wind load predictions for tall buildings using ML studies presented in literature have always been limited to static pressure measurements or time history measurements without considering the spatial coordinates system. To design wind-sensitive tall buildings, ML models must be capable of estimating transient wind flow quantities along with its spatial distribution. Thus, in this study, for the first time, the authors used ML to model the transient wind pressure on a tall building using a three-dimensional (3D) spatial coordinates system. A series of Boundary Layer Wind Tunnel tests were performed to obtain the transient pressure readings on building surfaces, which were used to validate the Computational Fluid Dynamics (CFD) models. Turbulence was modelled using large eddy simulations and the data obtained through CFD simulations were utilised to generate the ML models. The popular Extreme Gradient Boosting (XGBoost) model was selected as the ML model due to its capability of efficient data handling. The trained XGBoost model accurately predicted the transient wind pressure throughout the flow time. The XGBoost model has captured the extreme values well, closely following the flow patterns. In addition, special flow features like flow separation, reattachment, and steep pressure gradients have been well captured over the corresponding surfaces. Therefore, this study showcases the ability to use ML to predict pressures on tall buildings, capturing all key flow features time-efficiently.

Quantum Value Valuation Continuum

Price, cost, and income (PCI) methods are traditionally used to approximate the value state of an economic commodity such as a property. Based on the estimates of these methods, we explore how quantum theory represents the fundamental process of value valuation in practice. We propose that the mathematical formalism of quantum theory is a promising view and measure of economic value. To ground our exploration, we first map traditional PCI estimates onto three-dimensional spherical coordinates, which were then transformed into two-dimensional quantum states using the Bloch sphere. This step enabled the computation of eigenvalues and eigenvectors of the Hamiltonian matrix, from which the value state measures were derived. The results exhibit practical applications as well as fundamental insights into potential connections between economic and quantum value states.

Characteristics of throwing arm movement for an elongated implement: a comparison of the javelin and baseball throwing.

In javelin, although many previous studies have examined throwing movements that can increase initial velocity, the characteristics of throwing arm movement an elongated implement have not been clarified. The purpose of the present study was to examine the characteristics of the throwing movement of an elongated implement by comparing throwing movement between a javelin and baseball. Twelve male javelin throwers were asked to perform a javelin throw (JT) and a baseball long toss (LT) twice. The three-dimensional coordinates of reflective markers attached to the athlete's body, javelin, and baseball were measured using an optical motion capture system. %Trajectory was used as an index to evaluate the degree to which the hand was moved linearly during the throw. A smaller value of this indicator meant that the hand was move closer to a straight line. The joint angles in the throwing arm were obtained by calculating the Euler angles between body segments. These data were used to compare JT and LT. %Trajectory showed that JT was significantly smaller than LT. Significant differences in the joint angles of the throwing arm were noted between JT and LT. JT showed a kinematic pattern in which the hand was moved more linearly than in baseball long toss.

Color-Based Object Tracking Using Forward and Inverse Kinematics

Nowadays, the current surge in diverse applications of robotic arms makes comprehending these concepts of paramount importance. Various studies have been conducted on the topic of robotic arms. However, little attention was paid to the coupling relationship between object tracking and kinematics. Therefore, this research paper delves into the intricacies of robotic arm dynamics, with a specific focus on the topics of Forward and Inverse Kinematics, alongside object tracking facilitated by color-based methodologies to deepen foundational insights into robotic arm functionality. Controlling the motion and movement of robotic arms is the initial step. Leveraging the capabilities of cutting-edge technologies such as OpenCV, Armpi, and Hiwonder, it becomes feasible to precisely rotate the servos to user-input degrees and accurately position the arm based on three-dimensional Cartesian coordinates. Additionally, cameras equipped in the system enable photographing and recognizing target objects. By analyzing various positions of the target object, the robotic arm can dynamically adjust multiple servos to maintain the object's relative position. This tracking mechanism relies on the Proportional-Integral-Derivative algorithm, incorporating a minimum valid area parameter to mitigate interferences. Harnessing these algorithms empowers the robotic arm to discern objects based on camera-detected colors, and is affected slightly by different angles or distances, meaning the system's error margin consistently resides within a favorable interval. The approach exhibits practical utility in daily life scenarios, such as drug classification and recognition.

Sex estimation based on mandibular measurements.

Medical imaging and machine learning are beneficial approaches in physical and forensic anthropology. They are particularly useful for the development of models for sex identification based on bone remains. The present study uses machine learning algorithms to create models for sex estimation based on mandibular measurements. The sample included head CT scans of 239 adult Bulgarians (116 males and 123 females). Three-dimensional coordinates of 45 landmarks of the mandible were acquired from segmented polygonal models of the skulls of these individuals. Two datasets of mandibular measurements were assembled. The first dataset included 51 measurements: linear, projective, and angular measurements. The second dataset included 990 interlandmark distances. Seven machine learning algorithms (Support Vector Machines, Neural Network, Naïve Bayes, Random Forest, J48, JRip, and Logistic Regression) were applied to the two datasets, and the classification accuracy was evaluated by 10x5-cross-validation. The selection of the best subsets of attributes specific to each of the abovementioned algorithms was done based on the attribute importance evaluated by an attribute selection scheme. In general, the sub-symbolic algorithms achieved higher results than the symbolic ones, except for the logistic regression. The best classification model was learnt by the Support Vector Machines algorithm, which achieved an accuracy of 95.3% on a dataset described by 19 interlandmark distances. In both datasets, the application of advanced attribute selection has led to an increase in the classification accuracy of all algorithms used in the experiments.

3D vision technologies for a self-developed structural external crack damage recognition robot

Persistent cracking and progressive damage can weaken the operational performance of structures such as bridges, dams, and concrete buildings. Consequently, research into automated, high-precision crack detection methods remains pivotal within the realm of structural health monitoring (SHM). Presently, scholars predominantly rely on two-dimensional (2D) image-based algorithms for crack detection. However, these methods commonly struggle to accurately locate the three-dimensional (3D) coordinates of cracks on large structures and to extract the 3D contours of cracks. To address this challenge, this study proposes an automated 3D crack detection system for structures based on high-precision Light Detection and Ranging (LiDAR) and camera fusion. Firstly, precise registration of images and LiDAR point clouds was achieved through accurate extrinsic calibration of the sensors. Secondly, the lightweight MobileNetV2_DeepLabV3 crack semantic segmentation network was employed to detect and locate cracks. Finally, by automatically guiding the robotic arm, an industry-standard depth camera was able to capture high-precision 3D information about the crack at close observation points. Compared with the existing studies, this study emphasizes the extraction of high-precision 3D crack features and verifies the validity of the method by comparing the measurement results with those of the traditional method, demonstrating a remarkable measurement accuracy reaching sub-millimeter levels (0.1 mm). Moreover, the study introduces a comprehensive hardware platform and algorithmic framework, offering pioneering theoretical methodologies and replicable equipment references for automated surveillance and monitoring systems dedicated to structural health.

Rapid and Precise Measurement Method for Track Static Geometry of Large-Span Bridge Railway

Track geometry is an important parameter reflecting the safety of bridge railway, which is of great significance for the structure control of railway track. The measurement of track geometry is an indispensable part of structural health monitoring for bridge railway. However, existing methods for track static track geometry measurement are inadequate in terms of accuracy and efficiency. In order to improve the measurement method, this paper proposes a rapid and precise measurement method based on IMU/odometer aided by multiple total stations, which has the advantages of high efficiency, high accuracy, and is less affected by the environment. The proposed method uses a track measurement trolley (TMT) integrated with IMU and an odometer to collect railway track data on the bridge, and multiple total stations are used to synchronously measure the three-dimensional coordinates of the TMT. After coordinate system registration and time synchronisation, the data are then fused using a filtering algorithm to finally obtain the static geometry of the railway track. The proposed method was validated on the NanSha Port Railway Bridge across the Xijiang River in Foshan, China, and the results showed that the proposed method can make a single on-orbit measurement of a 1000 m length of large-span bridge railway track within half an hour, with an accuracy on the order of millimetres. The proposed method has obvious advantages in terms of efficiency and accuracy and is therefore an effective new measurement method with practical significance.

Influence of the radius of Monson’s sphere and excursive occlusal contacts on masticatory function of dentate subjects

ObjectiveTo determine the influence of the radius of Monson’s sphere, the number of posterior laterotrusive, mediotrusive, and protrusive contacts, and the chewing rate on food comminution. DesignSixty healthy dentate subjects, aged 21.22 ± 2.30 years, were selected. The three-dimensional coordinates of the cusp tips of the lower canine, premolar, and molar teeth were identified from the subjects’ digital models. Monson’s sphere was designed using the simplex method for function minimisation by adjusting the coordinates on its surface. The contacts were verified using 12 µm metal strips in jaw excursions at 0.5, 1.0, 2.0, and 3.0 mm. The masticatory performance and efficiency, swallowing threshold, and chewing rate were assessed through particle size fractionation. Data were analysed with multiple linear regression (α = 0.05). ResultsThe sphere’s radius, laterotrusive and protrusive contacts at 0.5 mm, and chewing rate were found to be negative predictor variables for masticatory performance until 20 chewing cycles (R2 = 0.429). For 40 cycles, the radius and total contacts (0.5 mm) were also explanatory factors (R2 = 0.223). Only the radius (R2 = 0.176) and the chewing rate (R2 = 0.082) were found to be significant for 60 cycles and swallowing threshold, respectively. Masticatory efficiency was influenced by masticatory performance until 40 and 60 cycles, as well as the radius and total contacts at 2.0 and 3.0 mm (R2 = 0.958). ConclusionA larger radius of Monson’s sphere and a greater number of posterior excursive contacts were found to be related to better masticatory function.

Development and Innovation of Chinese Classical Dance Teaching Mode in the Background of Internet

Abstract Since the development of Chinese classical dance, its dance technology and dance skills have been maturing for a long time, but the innovation and development of classical dance teaching mode needs to be improved. In this paper, OptiTrack is used to capture the dance movement data of classical dancers, transform the data into three-dimensional coordinates, and extract the features of classical dance data through direction normalization. The Hidden Markov Model obtains the time series information in the features and constructs the correlation model. Using the skeletal model data to get the center of mass of the human body, the convolution-gated recurrent unit network structure is used to improve the accuracy of the classical dance score generation results. Combining the above methods, a new teaching model framework for classical dance is proposed from three aspects and empirically analyzed. The empirical results show that the mean value of each dimension of classical dance teachers’ teaching ability ranges from 3.4562-4.3621, which is an excellent overall performance. In the comparison between students’ classical dance movements and standard movements, there existed higher scores than traditional movements in the two time periods within 20 minutes, which were 30 and 5 points higher than the conventional scores, respectively. The rest of the time was slightly lower than the regular movements, which shows that the innovation effect of classical dance teaching is better, and optimizes students’ classical dance movements to a certain extent.

UAV-Based High-Throughput Phenotyping to Segment Individual Apple Tree Row Based on Geometrical Features of Poles and Colored Point Cloud

Highlights Integrating RGB values and 3D coordinates of fruit trees provided phenotype-related data. The use of point clouds projection in tree rows segmentation has been confirmed. Using geometric features increased the accuracy of removing poles in an orchard. Segmenting fruit trees after removing poles on a single tree row was more accurate than traditional segmentation method. UAV equipped with LiDAR and a camera is promising for orchard high-throughput phenotyping. Abstract. High-throughput phenotyping (HTP) of fruit trees is important for providing crop geometrical information to evaluate their high yield genotypes. Unmanned aerial vehicle (UAV) is suitable for HTP by obtaining remote sensing data of large modern apple orchards, where each tree row needs to be segmented before segmenting a single tree. This study aims to develop a method for segmenting each row without noise (ERWON) of apple trees based on integrating RGB values and three-dimensional coordinates by UAV. A robust, real-time, RGB-colored, and LiDAR-inertial-visual tightly-coupled state estimation network was used to form a dense map of the orchard, which provided datasets of colored point clouds. Supporting poles were removed from the point clouds based on the consistent number of half upper parts and lower parts. Random sampling and an effective local feature aggregator were trained to segment ERWON after pole segmentation. Results showed that a precision of 0.971, a recall of 0.984, and an intersection-over-union of 0.817 for ERWON segmentation were achieved. This method proposed a potential solution for addressing the challenge of accurately and efficiently segmenting ERWON in large orchards. It is expected to be helpful for obtaining general parameters, such as geometric, morphological, and textural characteristics, as well as more specific parameters relevant to a particular phenotyping task. Keywords: Apple trees, Detection, Point cloud, RGB-colored, Segmentation.

Estimation of Three-dimensional Glass Coordinates with a LiDAR and a Polarization Camera for Indoor SLAM

Estimation of Three-dimensional Glass Coordinates with a LiDAR and a Polarization Camera for Indoor SLAM

Multi-ion magnetized sheath properties with non-extensive electron distribution

Magnetized plasma sheath plays an important role in semiconductor processing, material surface modification, film deposition, etc. In plasma experiments and discharge applications, multi-ion plasma consisting of more than two kinds of ions often exists. For a long range interacting plasma system, non-Maxwellian electrons can be described by the non-extensive distribution of Tsallis. In this work, a fluid model with one-dimensional spatial coordinates and three-dimensional velocity coordinates is established for the multi-ion plasma sheath. It is assumed that the electron velocity in the sheath follows a non-extensive distribution, and the background helium ions and different kinds of impurity ions are magnetized in a magnetic field with a certain tilt angle. The effects of non-extensive parameters, impurity ions and oblique magnetic field on the number density, velocity, wall potential and kinetic energy of ions in the multi-ion magnetic sheath are investigated by numerical simulation. The results show that in the helium-hydrogen or helium-argon mixed plasma sheath, the ionic velocity along the vertical wall direction decreases with the increase of the non-extensive parameters, the number density of ions and electrons in the sheath, the sheath thickness , and the kinetic energy of ions at the wall decrease. When the concentration of impurity ions increases, the kinetic energy of ions on the wall is independent of the type of ions. With the increase of magnetic field intensity, the number density of helium ions and the velocity along the vertical wall fluctuate along the sheath edge, and the fluctuation amplitude increases with the decrease of non-extensive parameters, while the heavy ions have no obvious fluctuation. In addition, the effects of the types and concentrations of impurity ions on the related properties of the sheath are also analyzed. With the increase of the magnetic field intensity, the number density and the velocity along the vertical wall direction fluctuate at the sheath edge, and the fluctuation amplitude increases with the decrease of the non-extensive parameter, whereas there are no significant fluctuations for heavy ions. In addition, when impurity ions are heavy ions, the absolute value of wall potential increases with the increase of impurity ion concentration and the decrease of non-extensibility parameters, and the kinetic energy of background ions increases at the wall surface. When the impurity ion is a light ion, the absolute value of the wall potential decreases with the increase of the impurity ion concentration and the decrease of the non-extensibility parameter, and the kinetic energy of the background ion at the wall decreases.

Estimating the location of the hook-wire used in breast-conserving surgery using a magnetometer

In the surgical treatment of nonpalpable breast lesions, such as in early-stage cancer, a hook-wire is inserted into the lesion as a marker to enable surgeons to excise the tissue, along with the hook-wire, with a good margin. However, a benchmark technique for intraoperatively determining whether the excised tissue has an appropriate margin around the lesion has not yet been established. In this study, a method for locating a ferromagnetic stainless steel hook-wire inside the excised tissue using a magnetometer is proposed. The magnetometer is placed around a phantom along with the hook-wire at varied locations to map the magnetic field distribution. The three-dimensional coordinates of hook-wire are obtained by executing an optimization algorithm. The experimental results indicate that the location of the hook-wire is successfully obtained. Based on the information regarding the margin around the hook-wire, the surgeon can immediately evaluate the risk of whether some cancer cells still remain in the body.

Research on the Innovation of Physical Education and Physical Education Teaching Based on Big Data Analysis

Abstract In this paper, Openpose is used to process the sports teaching video to get the coordinates data of the human body joint point positions in each frame of the video, and Kalman filter data fusion is used to establish the human skeleton model. According to the results of the division of the five major parts of the human body, after establishing the limb vectors of the human body’s torso, left arm, right arm, left leg, and right leg in three-dimensional spatial coordinates, the distances between the joints of the five human body skeletons based on the DTW posture matching algorithm were used to extract the characteristics of the sports error technical movements. From the demand of sports digital teaching, the design and implementation of sports basic movement teaching evaluation system based on the DTW posture matching algorithm, and the research and analysis of sports teaching under the background of big data. The results show that the IoU values of batting action localization in 6 segments of physical education teaching are 85.6%, 91.6%, 77.7%, 75.1%, 87.4% and 77.7%, respectively, and the average reach 82.5%, i.e., it shows that the research on action localization and recognition based on the DTW posture matching algorithm has a good performance. In the assessment of movement standardization in physical education, the maximum moment of stretching angle corresponds to the moment of hitting the ball, and its value reaches 3.79, i.e., it reflects that the evaluation system of physical education basic movement teaching can accurately determine whether the students’ movements are accurate or not, and make timely feedbacks to carry out the corrections of physical education movements. This study has the potential to enhance students’ interest and performance in sports and contribute to the advancement of digital sports teaching.

An improved phase-field algorithm for simulating the impact of a drop on a substrate in the presence of surfactants

This paper is devoted to the numerical study of droplet impact on solid substrates in the presence of surfactants. We formulate the problem in an energetically variational framework and introduce an incompressible Cahn-Hilliard-Navier-Stokes system for the phase-field modeling of two-phase flows. Flory-Huggins potential and generalized Navier boundary condition are used to account for soluble surfactants and moving contact lines. Based on the convex splitting and pressure stabilization technique, we develop unconditionally energy stable schemes for this model. The discrete energy dissipation law for the original energy is rigorously proved for the first-order scheme. The numerical methods are implemented using finite difference method in three-dimensional cylindrical coordinates with axisymmetry. Using the proposed methods for this model, we systematically study the impact dynamics of both clean and contaminated droplets (with surfactants) in a series of numerical experiments. In general, the dissipation in the impact dynamics of a contaminated drop is smaller than that in the clean case, and topological changes are more likely to occur for contaminated drops. Adding surfactants can significantly influence the impact phenomena, leading to the enhancement of adherence effect on hydrophilic surfaces and splashing on hydrophobic surfaces. Some qualitative agreements with experiments are also obtained.

Global joint information extraction convolution neural network for Parkinson’s disease diagnosis

Parkinson’s Disease (PD) is a prevalent neurodegenerative condition, ranking second in incidence only to Alzheimer’s disease. Presently, the diagnosis of PD using sensors and computer vision can recognize characteristics like speech, respiration, and gait in patients. However, these methods typically require the use of complex hardware systems or extensive data analysis when collecting or processing motion data from various joints of the patients. In this research, an efficient diagnostic system for PD is introduced, which utilizes common smartphones to capture videos of 42 healthy volunteers and 30 Parkinson’s patients walking under different conditions. The system utilizes human pose estimation technology to extract three-dimensional joint coordinates, simplifying the data collection process. Afterward, joint coordinates are transformed into two-dimensional images using color mapping techniques, thus converting the diagnosis into an image recognition challenge. In contrast to video processing, this approach reduces 6.51 million parameters (22%) and reduces testing time by 62.92%. Finally, by combining ResNet50 and random forest algorithms, decision accuracy is improved using two-dimensional images. Experimental evidence substantiates the system’s capability to efficiently identify Parkinsonian gait. The recognition rate for the leg joint group is 88.89%, and it would increase to 91.67% when factoring in the four-limb joint group. The system provides the potential for preliminary at-home diagnosis, holding significant clinical application potential, and diagnostic value for other movement-related disorders.

Sexual dimorphism in the three-dimensional detailed crown structure of maxillary first premolars

Maxillary first premolars have a unique shape because of their curvature features, positional relationship of the cusps, and most prominent points, making them different from other teeth. This study aimed to quantitatively analyze the detailed three-dimensional morphometric structure of maxillary first premolars and sexual dimorphism. The study participants were 60 elementary and junior high school students (30 boys and 30 girls) in Japan. The distance between landmarks was measured using the three-dimensional coordinates of plaster casts, and the data collected was statistically analyzed. Sexual dimorphism was greater in the lingual cusp, showing greater variation in size than the buccal cusp. Boys exhibited significantly larger relative distances in the mesiodistal and buccolingual directions than girls; particularly, regarding mesiodistal diameter of the central groove, mesial slope of the buccal cusp, and distal slope of the lingual cusp. These results may be due to a slight difference in the timing of secondary enamel knots between boys and girls during the developmental stage, which was reflected in the sexual dimorphism of the completed teeth. Curvature features, cusp positions, and most prominent points were considered individual traits because they were not interrelated. Subtle differences during the developmental stage may lead to sexual dimorphism of the completed crown. Furthermore, the morphological characteristics of the maxillary first premolars may be related to their location in the dental arch.

An Error Estimation System for Close-Range Photogrammetric Systems and Algorithms.

Close-range photogrammetry methods are widely used for non-contact and accurate measurements of surface shapes. These methods are based on calculating the three-dimensional coordinates of an object from two-dimensional images using special digital processing algorithms. Due to the relatively complex measurement principle, the accurate estimation of the photogrammetric measurement error is a non-trivial task. Typically, theoretical estimations or computer modelling are used to solve this problem. However, these approaches cannot provide an accurate estimate because it is impossible to consider all factors that influence the measurement results. To solve this problem, we propose the use of physical modelling. The measurement results from the photogrammetric system under test were compared with the results of a more accurate reference measurement method. This comparison allowed the error to be estimated under controlled conditions. The test object was a flexible surface whose shape could vary smoothly over a wide range. The estimation of the measurement accuracy for a large number of different surface shapes allows us to obtain new results that are difficult to obtain using standard approaches. To implement the proposed approach, a laboratory system for the error estimation of close-range photogrammetric measurements was developed. The paper contains a detailed description of the developed system and the proposed technique for a comparison of the measurement results. The error in the reference method, which was chosen to be phasogrammetry, was evaluated experimentally. Experimental testing of the stereo photogrammetric system was performed according to the proposed technique. The obtained results show that the proposed technique can reveal dependencies that may not be detected by standard approaches.

Real-Time Recognition and Localization of Apples for Robotic Picking Based on Structural Light and Deep Learning

The apple is a delicious fruit with high nutritional value that is widely grown around the world. Apples are traditionally picked by hand, which is very inefficient. The development of advanced fruit-picking robots has great potential to replace manual labor. A major prerequisite for a robot to successfully pick fruits the accurate identification and positioning of the target fruit. The active laser vision systems based on structured algorithms can achieve higher recognition rates by quickly capturing the three-dimensional information of objects. This study proposes to combine the laser active vision system with the YOLOv5 neural network model to recognize and locate apples on trees. The method obtained accurate two-dimensional pixel coordinates, which, when combined with the active laser vision system, can be converted into three-dimensional world coordinates for apple recognition and positioning. On this basis, we built a picking robot platform equipped with this visual recognition system, and carried out a robot picking experiment. The experimental findings showcase the efficacy of the neural network recognition algorithm proposed in this study, which achieves a precision rate of 94%, an average precision mAP% of 92.86%, and a spatial localization accuracy of approximately 4 mm for the visual system. The implementation of this control method in simulated harvesting operations shows the promise of more precise and successful fruit positioning. In summary, the integration of the YOLOv5 neural network model with an active laser vision system presents a novel and effective approach for the accurate identification and positioning of apples. The achieved precision and spatial accuracy indicate the potential for enhanced fruit-harvesting operations, marking a significant step towards the automation of fruit-picking processes.

Pressure-dependent characteristics of the diffusion coefficient during the gas desorption process in coal cuttings: Numerical modelling and analysis

Determining the diffusion coefficient is crucial in coalbed methane development. Existing models have limitations, as they often apply only to spherical systems, cannot describe nonlinear adsorption, and do not quantify the impact of gas pressure on diffusion coefficients. Additionally, traditional trial methods struggle to accurately compute diffusion coefficients in numerical solutions. To address these challenges, our study builds two unipore diffusion models (EPDDM and PPDDM) by introducing exponential and power pressure-dependent diffusion coefficients, considering three-dimensional coordinates and Langmuir adsorption. And then proposes a diffusion coefficient determination method using a particle swarm optimization algorithm. Through desorption experiments, numerical modelling, and model comparisons, we analyze the evolution law of diffusion coefficient, gas pressure, and desorption volume during the desorption process. Our results show that the proposed models quantitatively depict the positive correlation between diffusion coefficient and gas pressure. Furthermore, they accurately reflect changes in desorption volume. During early-stage desorption, the diffusion coefficient of EPDDM is 1.63–1.85 times greater than that of PPDDM, while their desorption volumes are similar. This observation motivates the proposal of a more versatile Logistic pressure-dependent diffusivity model, aiming to unify the above two models. These achievements are anticipated to serve as a foundational framework for exploring the mechanisms governing gas diffusion.