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
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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