In recent years, with the continuous development of computer software and hardware technology, the real-time display of large-scale complex phenomena has become possible, which puts forward new requirements for the complexity and authenticity of the design. Although traditional 3D modeling tools are improving, creating more complex 3D models is still a very time-consuming and labor-intensive task. Given that many of the 3D models we want to create can be found or shaped in the real world, 3D scanner technology and image-based modeling have come to mind as the most appropriate modeling techniques; the former is often a hotspot in computer graphics, Because the latter provides a natural way to create realistic composite images, since only the geometric information of the phenomenon is available. In fact, obtaining 3D information from real-time images has always been an important research topic in the field of computer vision, and its main applications are visual control and machine navigation, so automation and real-time performance are the main topics of these researches. Learn. Although there are many 3D vision systems that have achieved good results, it is difficult for researchers to predict when and when they will be able to find algorithms that automatically restore 3D scenes at will.
The tolerance of the part controls the degree to which the target geometric elements deviate from the ideal state in size, position and shape, the mathematical model of the tolerance is the mathematical description and representation of the tolerance information, consistently explain the meaning of each member of the tolerance information through the mathematical model of the tolerance, and obtain the numerical relationship between the geometric size change and the shape change between the datum element and the measured element, etc., the mathematical model of tolerance is the basis of related technologies such as tolerance analysis, tolerance design, and tolerance inspection. The mathematical model of the tolerance must conform to the GPS standard system in terms of design, and must include at least: ①All tolerance types corresponding to all valid geometric features; ②All valid or possible interaction relationships; ③Be able to identify the datum priority relationship and datum order; ④It is easy to combine with the CAD entity model, and the tolerance model must contain the reference information, which can not only express the tolerance, but also facilitate the accumulation of tolerance and the conversion of tolerance; ⑤ It must be applicable to various tolerance analysis methods including extreme value method and probability statistics method. According to the above goals, this paper proposes a mathematical model of tolerance representation based on control point representation.
Li M et al. found that for most image-based modeling tasks, the image or image sequence should be calibrated first, so as to determine the orientation and viewing parameters of the camera relative to the 3D scene during the shooting of each image; The framing parameters of the camera are called internal parameters, and the orientation and position of the camera are called external parameters. Kolb J Research found that there is often a certain constraint relationship between several images of the same scene. Epipolar geometry is an important tool for developing such constraints, it points out the epipolar constraints that exist between corresponding feature points on two or more images, such constraints can be obtained by camera calibration or even just by a given set of corresponding feature points . Braga D et al. proposed a tolerance map model (Tolerance. Map, T-Map) compatible with ASME standard, T-Map is an imaginary convex polyhedron shape point set space, its shape and size reflect the type and various possible changes of the target object, so that the various tolerance changes of the target object have a one-to-one correspondence with the points in the T-Map .
Traditional methods in computer vision perform geometric reconstruction of a single image based on clues such as shading, texture, and focal length, since these methods usually have strict restrictions on the shape, reflection properties, and exposure of the scene in the picture, therefore, it is only suitable for the reconstruction of some special scenes. Recent research work in the field of computer graphics shows that, introducing proper user interaction can simplify the single image reconstruction problem very effectively. For example, many researchers utilize vanishing point information and geometric invariants specified by user interaction, the geometric reconstruction of the sliced plane model is realized; The authors et al recovered a similar geometric model from the panorama using a constraint system based on user input; The interactive modeling of the architectural scene is realized from some parametric basic geometric shapes. The above methods also have certain limitations, that is, only scenes composed of planes and basic geometric shapes can be reconstructed. In order to realize the reconstruction of a curved scene based on a single image, two methods are generally used: Bring in a knowledge base. For example, starting from a database of human head models and using a single image for face reconstruction has achieved good results. Introduce a larger amount of interaction. As we all know, the human visual system has a strong ability to understand the depth information contained in a single image, this inspires us to directly use traditional image editing methods to interactively specify the depth value of each point in the image; Similarly, the human eye can also estimate the normal direction of the object surface sampling point corresponding to a certain point in the image, therefore, as long as the user interactively specifies the corresponding normals of several points in the image, a better estimate of the curved object can be obtained. Practice has shown that the surface normal is easier to specify interactively than the depth of field, and can provide a more intuitive surface control method .
Reconstructing 3D geometry based on stereo vision is a classic problem in the field of computer vision, it is widely used in automatic navigation devices. In recent years, stereo vision methods have also been favored by graphics researchers, where two or more scaled images are used to reconstruct the geometric model of the scene. The basic principle of stereo vision is the principle of triangulation: For the two images that have been scaled (that is, both the intrinsic and extrinsic parameters of the camera are known), suppose we find a pair of corresponding points on two images (i.e. they are projections of the same point on the surface of an object in the scene), starting from the projection centers of the two images, the two straight lines passing through the pair of corresponding points will intersect at one point in space, in this way, we get the three-dimensional coordinates of a point on the surface of the object in the scene. If we can get the three-dimensional coordinates of all points on the surface of the object, the shape and position of the three-dimensional object are uniquely determined. In some simple occasions, such as a three-dimensional object is a polyhedron, we only need to know the three-dimensional coordinates and adjacent relations of its various vertices, and the shape and position of the polyhedron are also uniquely determined. Finding correspondence matches is the most important and also the most difficult task in stereo vision methods. Considering that most object surfaces are not ideal surfaces, therefore, the brightness values of the projected points of the same spatial point on different images are not exactly the same; Conversely, image points with the same luminance value are not necessarily projections of the same point in space. In addition, due to the existence of various occlusion relationships in the scene space, the corresponding points of adjacent pixels on the image in the three-dimensional space are often discontinuous. These factors make the correspondence matching algorithm relying solely on the comparison of luminance values encounters great difficulties. At present, people mainly obtain more robust matching by introducing epipolar constraints, which reduce the search range of corresponding points from two-dimensional to one-dimensional, thus greatly improving the accuracy of feature detection and matching .
The several methods described above are all methods of reconstructing geometric models by using luminance images, in some occasions where there are high requirements for model accuracy and model complexity, the method of reconstructing geometric models from depth images has been widely used. The depth image is similar to an ordinary image with pixels, the difference is that each pixel position stores not the color value, but the depth value of each sampling point on the surface of the object in the scene. Depth images can be generated in a variety of ways, including structured light sources, laser transit time measurement, radar, sonar, and other computer vision methods. Since there are often multiple occlusion relationships in the scene, it is often necessary to stitch together multiple depth images to obtain a complete representation of an object.
For the case where there is only a single object in the scene, it is generally necessary to combine multiple depth images through two steps of registration and merging. Registration refers to matching the overlapping parts of the two depth images through coordinate transformations such as rotation and translation; Merging refers to the use of two or more registered depth images to generate a single representation of an object. The single representation here is usually a polygon mesh representation, or a parametric surface or an implicit surface representation! There are two commonly used merging methods: Merging using the adjacency relationship between pixels on the depth image and merging directly in the form of spatially scattered point reconstruction. The mesh model generated by merging is usually too complicated, which reduces the drawing efficiency. Therefore, the mesh model generally needs to be simplified after merging. In addition, in the case of multiple objects in the scene, it is often necessary to segment the objects in the depth image after registration, and then merge each segmented object, so that the scene can be edited or edited. An object is parameterized. Considering the existing automatic segmentation methods, it is difficult to obtain satisfactory results even for the simplest plane object segmentation. Most of the practical segmentation algorithms require some scene information and manual interaction. Furthermore, in some cases, we cannot or inconveniently obtain depth samples of all surfaces in the scene, resulting in incomplete or even incorrect reconstructed models. In order to overcome this problem, the researchers also proposed some algorithms to compensate for the flaws in the reconstruction results.
Essentially, the constant boundary layer thickness |
The introduction of the approach angle
Figure 1 shows the relationship between the new saturation function
Let the equation of a second-order system be:
To make the system output
In the formula,
Substitute into the above formula to have (9):
The whole sliding mode control law is defined as (10):
When the state trajectory (
In the formula:
The Tolerance coordinate system is used to determine the orientation of the natural degrees of freedom and represents the change in the position and orientation of the connecting element relative to the nominal position relative to the tolerance. The tolerance coordinate system is related to the geometry type, the relative position of geometric elements and data, and the special rules for establishing the tolerance coordinate system are as follows. (1) The tolerance coordinate system shall be determined at the nominal position of the geometric element. (2) The Z axis of the tolerance coordinate system is the integration direction of the geometric elements, that is, the Z axis direction is the same free direction, which coincides with the Oxy coordinate plane of the tolerance coordinate system. There is a vertical plane of degrees of freedom . (3) The origin of the tolerance coordinate system coincides with the center of the target geometric element, that is, the coordinate origin of the point, line, and surface geometric elements is the point itself, the midpoint of the line, the center of the circle. The plane constraint box. (4) The X-axis direction of the tolerance coordinate system is the direction of the degree of freedom of the reference constraint. The datum standard is judged one by one according to the datum principle. If the current datum limits the vertical translation degree of freedom or the vertical rotation degree of freedom, the degree of freedom limitation direction is X. - Axial.
The control points of basic geometric elements include orientation control points and shape control points, the orientation control points determine the position of the ideal geometry (fitting components) of the elements, and the shape control points are the extraction elements of the control object. The azimuth control point of a point element is the point itself, the azimuth control point of a line element is the two endpoints of the line, and the azimuth control point of a plane element is any three vertices of the plane bounding box, and the bounding box is the boundary parallel to the coordinate axis of the tolerance coordinate system. and the smallest rectangle enclosing the target plane.
A shape control point is a collection of points that make up a geometric element, that is, the shape control point of a line and a plane element is a point located inside and on the boundary of the geometric element, shape control points for curves and surfaces are points located inside and on the boundaries of curves and surfaces. The change direction of the shape control point is the normal direction of the geometric feature or the specified direction of the tolerance. The number of change parameters of basic geometric element orientation control point is the same as the number of degrees of freedom, and the number of change parameters of point element, line element and plane element are 3, 4, and 3 respectively. The change of the orientation control point can represent the change of the natural degree of freedom direction of the geometric element, the absolute variation of the azimuth control point in a given direction represents the variation range of the translational degrees of freedom of the geometric element, and the relative variation of the azimuth control point in a given direction can represent the variation range of the rotational degree of freedom of the geometric element. Orientation control points can represent various types of tolerances, the azimuth control point is used to indicate that the change of geometric elements is consistent with the meaning of the tolerance, and the maximum change of the control point is the tolerance value of the geometric element. Therefore, the positional variation of geometric elements can be simulated by the variation of the azimuth control point. According to the definition of natural degrees of freedom, tolerance coordinate system and orientation control points, the space swept by the geometric elements with the movement of the changing points is the tolerance field of the geometric elements. The changing spatial shapes of point, line and area geometric elements are as follows: ① The changing space shape of a point is sphere, cylinder and cube in spherical coordinate system, cylindrical coordinate system and rectangular coordinate system respectively; ② The shape of the changing space of the straight line can be a cylinder, a long cube (the length of the cube is absolutely larger than the width and height) and a rectangle; ③ The shape of the changing space of the plane is a flat cube (the height dimension of the cube is absolutely smaller than the length and width dimensions). The relative position between the azimuth control points represents the direction error of the geometric element, and the bounding box and bounding volume formed by the largest relative position between the azimuth control points is the directional tolerance zone of the geometric element, therefore, the position of the directional tolerance zone has a floating characteristic and floats within the position tolerance zone . The shape control point change space of geometric elements constitutes the shape tolerance domain. For example, according to the tolerance requirements, the shape control point change direction of a straight line has a circumferential direction and an orthogonal direction, and the corresponding shape control point change space is a cylinder and a rectangular cube. The change direction of the shape control point of the plane is along the plane normal direction, so the change space of the shape control point of the plane is a flat cube; The change direction of the shape control points of curves and surfaces is generally the normal direction or a specific direction, and the change space of their shape control points is the area enclosed by the equidistant lines and equidistant surfaces of the nominal curve or surface. Shape control points vary relative to the ideal geometry, so the shape tolerance field is attached to the ideal geometry of the feature. The relationship between the absolute variation range of geometric element control points and the relative variation range between control points, it is the interaction relationship between the position tolerance and the direction tolerance, so there is a corresponding relationship between the interaction of different types of tolerances and the change of control points, for example, the two azimuth control points of a straight line, the absolute range of variation along a certain coordinate direction, and the relative range of variation can represent the relationship between the position tolerance (dimensional tolerance) of the straight line in this direction, and the direction tolerance.
The core content of the tolerance analysis method based on Monte Carlo simulation is to use a random number generator, generate an instance of the azimuth control point position of all geometric elements on the dimension chain, and calculate the closed loop size for each generated precision mechanical instance sample, statistical analysis method is used to calculate the error distribution law and statistical characteristics of the closed ring size, to estimate the qualification rate of assembly, and to analyze the rationality of part tolerance setting.
Since the shape tolerance zone does not participate in the analysis of the dimensional chain, it is not necessary to simulate the shape tolerance when generating instances of geometric elements based on the Monte Carlo simulation method, therefore, it is only necessary to discuss the relationship between the control point position variation of the simulation direction tolerance and position tolerance. The absolute position of the azimuth control point is used to represent the dimensional tolerance and position tolerance of the geometric element, and the relative positional relationship of the azimuth control point is used to represent the direction tolerance of the geometric element . In the process of tolerance analysis, when the direction error and position error of a geometric element need to be considered at the same time, firstly, according to the probability distribution law of the direction error and the direction tolerance value, for each azimuth control point, a random number generator is used to generate a random change position of the azimuth control point. Then, according to the distribution law of the direction tolerance zone in the position tolerance zone, the random number generator is used to generate the position instance of the center of the direction tolerance zone in the position tolerance zone. Finally, the random variation of the azimuth control point is superimposed with the random position of the center of the orientation tolerance zone in the position tolerance zone, and the random position of the control point in the position tolerance zone is obtained, a random position of the geometric element is determined according to all the control points, that is, an instance sampling of the geometric element is obtained.
The simulation method based on azimuth control point representation is different from the simulation method of parametric representation, the parametric simulation method is based on parameter constraints to solve, and the established dimensional chain assembly function is a nonlinear equation system, which is very expensive to solve. Dimensional chain tolerance analysis based on azimuth control points, in fact, the closed loop is calculated according to the position instance of the geometric element obtained by simulation, that is, the vector algebraic calculation is performed on the position vector of the geometric element on the dimension chain through the coordinate transformation, so there is no need to solve the nonlinear equation, and the calculation cost is very small. The specific process of the Monte Carlo simulation method of tolerance accumulation based on control point representation is as follows.
Determine the closed loop variable on the dimension chain and its tolerance requirements.
Determine all related geometric elements on the dimension chain and the direction tolerance, position tolerance (dimensional tolerance) and corresponding error distribution law of each geometric element.
According to the assembly relationship of the dimension chain, the transformation relationship between the part tolerance coordinate systems is established, and the assembly function of the target variable and the related geometric elements is obtained, that is, the relationship between the closed loop variable and the related dimensions of the geometric elements .
A single instance of the location of all geometric elements in the dimension chain is obtained using a Monte Carlo simulation method.
Calculates a sample value for the closed loop from the assembly function.
Steps (4) and (5) are repeated until a sufficient number of sampling samples of the closed loop are obtained, and a sample distribution diagram is drawn to calculate the pass rate and analyze the rationality of the tolerance design of the relevant geometric elements on the dimension chain.
(1) The nominal centerline coordinate system
Since the nominal dimensions of the two mating surfaces of the tailstock bottom surface and the actual surface of the tailstock support are equal, it can be approximately considered that the two coordinate systems coincide, and the coordinate transformation of the tailstock bottom surface and the actual surface of the tailstock support is an identity transformation . The tailstock supports the actual surface coordinate system
The transformational translation transformation of the nominal surface of the tailstock support to the tailstock support datum surface, the transformation matrix:
When the two control points of the center line of the tailstock hole change to any position (
The above process is simulated, and the two ends of the center line of the tailstock hole are obtained respectively, the coordinate change in the coordinate system of the bottom surface of the tailstock support, statistical analysis results of the
Position and parallelism error of tailstock hole axis
The author proposes a mathematical model of tolerance based on precision mechanical control points. The model conforms to the current tolerance standard, the control point coordinate parameter definition domain is the tolerance zone, and the geometric elements defined by the control point position can reach any position in the tolerance domain, the absolute position of the control point position in the tolerance coordinate system, the relative positional relationship between the control points, the position of the component point relative to the fitting component can directly represent the size and position tolerance, direction tolerance and shape tolerance, by establishing the control point parameter relationship between the benchmark and the measured target, the independent principle and related principle of tolerance can be expressed.
Image-based modeling tasks usually contain a large number of complex data processing algorithms, such as the decomposition of large matrices, the solution of large-scale equations, and many nonlinear optimization problems, in the past, these operations can only be performed on the CPU, which requires a long processing time, so the expected execution speed cannot be achieved in some occasions requiring real-time interaction.
Position and parallelism error of tailstock hole axis
|100000||0.1573||0.1524||0.1620||0.0551||0.0151|Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Industrial transfer and regional economy coordination based on multiple regression model Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe80Si10Nb6B2Cu2 Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations Application research on piano teaching in colleges and universities based on remote wireless network communication Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x p m− x+ δ) s+ ax p m+ bxover F p2 m The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphyllavar. nullopetalina(Trilliaceae) Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G) on the set of maximal subgroups of p-groups The internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H2-N2 atmosphere Algorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model