1. bookAHEAD OF PRINT
Détails du magazine
License
Format
Magazine
eISSN
2444-8656
Première parution
01 Jan 2016
Périodicité
2 fois par an
Langues
Anglais
Accès libre

Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function

Publié en ligne: 15 Jul 2022
Volume & Edition: AHEAD OF PRINT
Pages: -
Reçu: 15 Mar 2022
Accepté: 24 May 2022
Détails du magazine
License
Format
Magazine
eISSN
2444-8656
Première parution
01 Jan 2016
Périodicité
2 fois par an
Langues
Anglais
Introduction

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[3]. 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 [4]. 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 [5].

Model in this paper
Reconstructing the geometric model based on the image
Reconstructing the geometric model based on a single image

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 [6].

Using the stereo vision method to reconstruct the geometric model

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 [7].

Reconstructing the geometric model based on the depth image

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.

Design of prefabricated concrete composite beams

Essentially, the constant boundary layer thickness |φ| is the root cause of the poor performance of the saturation function method. Therefore, to improve the performance of the saturation function control method, a continuously variable |φ(·)| must be sought to replace the original |φ|, the boundary layer thickness |φ(·)| can be narrowed with the convergence of the system state trajectory, and finally coincides with the switching plane, so that the system trajectory converges asymptotically to the given switching plane s = 0. The approach angle θ is the angle between the system state trajectory and the switching plane, which decreases as the state trajectory approaches the switching plane, therefore, the approach angle θ is the most intuitive variable to measure the degree of state trajectory convergence. The approach angle θ can be used as a free variable of |φ(·)| to construct the boundary layer thickness function |φ(·)| = |φ(φ)|. Substitute φ(θ) to get (1) and (2) respectively: u=ueqksat(sφ(θ)) u = {u_{eq}} - ksat\left( {{s \over {\varphi \left( \theta \right)}}} \right) sat(sφ(θ))=sφ(θ)|sφ(θ)1| sat\left( {{s \over {\varphi \left( \theta \right)}}} \right) = {s \over {\varphi \left( \theta \right)}}\,\left| {{s \over {\varphi \left( \theta \right)}} \le 1} \right|

The introduction of the approach angle θ makes the switching function u have two characteristics: continuous function and discrete function. When the state trajectory enters the boundary layer, the approach angle θ will drive the boundary layer to shrink, so that the thickness of the boundary layer φ gradually decreases, until it coincides with the switching plane, this ensures that the system can reach the switching plane and also ensures the asymptotic stability of the system [8].

Figure 1 shows the relationship between the new saturation function sat(sφ(θ)) sat\left( {{s \over {\varphi \left( \theta \right)}}} \right) and the approach angle. It can be seen from the Figure that the slope of the new saturation function sat(sφ(θ)) sat\left( {{s \over {\varphi \left( \theta \right)}}} \right) increases as the approach angle decreases. When the slope becomes very large, the new switching function makes the system asymptotically stable. (3) can be obtained: lim|θ0|sat(sφ(θ))=sgn(s) \mathop {\lim }\limits_{\left| {\theta \to 0} \right|} sat\left( {{s \over {\varphi \left( \theta \right)}}} \right) = {\mathop{\rm sgn}} \left( s \right)

Figure 1

The relationship between sat(·) and θ

Let the equation of a second-order system be: x1=x2 {x_1} = {x_2} x2=g+u {x_2} = g + u y=x1 y = {x_1}

To make the system output y follow the given value yg, the switching function should be (7): s=y¯+my¯ s = \bar y + m\bar y

In the formula, y¯=yyg \bar y = y - {y_g} , when sliding motion is performed on the switching plane, the equivalent input ueg of the system is used to control the dynamic process of sliding mode motion, and the dynamic equation is (8): s˙=0 \dot s = 0

Substitute into the above formula to have (9): ueq=g+y¨gmy¯ {u_{eq}} = - g + {\ddot y_g} - m\bar y

The whole sliding mode control law is defined as (10): u=ueqnast(sφ(θ)) u = {u_{eq}} - nast\left( {{s \over {\varphi \left( \theta \right)}}} \right)

When the state trajectory (x1, x2) is not on the switching surface, the following control law is used to make the state trajectory move toward the switching surface as equation (11): ss<<ξ|s| ss < < - \xi \left| s \right|

In the formula: ξ represents the parameter of the proximity of the state trajectory to the switching surface, and the switching function is defined as follows (12): s(y¨y¨g+my¯)ξ|s| s\left( {\ddot y - {{\ddot y}_g} + m\bar y} \right) \le - \xi \left| s \right|

Design of prefabricated columns

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 [9]. (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 [10]. 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.

Experimental analysis

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.

Simulation instance generation method of geometric elements

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 [11]. 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 process of dimensional chain tolerance analysis

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 [12].

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.

Example of dimensional tolerance analysis of precision mechanical assembly

(1) The nominal centerline coordinate system x4 y4 z4 of the tailstock hole, the transformation matrix of the base coordinate system x3 y3 z3 of the tailstock base. Mpnb={01027300150002800001} M_p^{n - b} = \left\{ {\matrix{ 0 & 1 & 0 & { - 273} \cr 0 & 0 & 1 & { - 5} \cr 0 & 0 & 0 & {280} \cr 0 & 0 & 0 & 1 \cr } } \right\}

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 [13]. The tailstock supports the actual surface coordinate system x3 y3 z3, the coordinates of the nominal surface coordinate system x2 y2 z2 of the tailstock support are transformed into formula (4), the parameters t and α in the formula, all are determined by the plane control point parameters t1, t2, and t3.

The transformational translation transformation of the nominal surface of the tailstock support to the tailstock support datum surface, the transformation matrix: Mpnb={100001000011100001} M_p^{n - b} = \left\{ {\matrix{ 1 & 0 & 0 & 0 \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 1 & {110} \cr 0 & 0 & 0 & 1 \cr } } \right\}

When the two control points of the center line of the tailstock hole change to any position (x4, y4, −355) and (x4, y4, 355), the positions of the two points in the tailstock support reference coordinate system can be obtained by formula (15) respectively: (x1y1z11)=MpnbMMnb(x4y4z41) \left( {\matrix{ {{x_1}} \cr {{y_1}} \cr {{z_1}} \cr 1 \cr } } \right) = M_p^{n - b}M{M^{n - b}}\left( {\matrix{ {{x_4}} \cr {{y_4}} \cr {{z_4}} \cr 1 \cr } } \right)

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 z1 coordinate values of the two ends, it is the dimensional error of the center line of the tailstock hole relative to the bottom surface of the tailstock support, and the statistical analysis result of the difference between the z1 coordinate values of the two ends is the parallelism error. The following table shows the statistical calculation results under different simulation times, among them, x and z represent the coordinate value of the left end point, x′, z′ represents the coordinate value of the right end point, and zz′ represents the parallelism of the centerline of the tailstock hole relative to the bottom surface of the tailstock support[14]. The mean value of the x1-coordinate samples at both ends is 273mm, and the mean value of the z1-coordinate samples is 370mm. It can be seen from Table 1 that the dimensional error of the tailstock hole centerline relative to the tailstock support bottom surface is ±0.0546mm, and the parallelism error of the tailstock hole centerline relative to the tailstock support bottom surface is ±0.015mm.

Position and parallelism error of tailstock hole axis

Simulation times x coordinate z coordinate x′ coordinate z′ coordinate zz′ Coordinate difference
20000 0.1358 0.0548 0.1452 0.0845 0.0148
30000 0.1249 0.0871 0.1781 0.0549 0.0153
90000 0.2100 0.0487 0.1453 0.0371 0.0182
100000 0.1573 0.1524 0.1620 0.0551 0.0151
Conclusion

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.

Figure 1

The relationship between sat(·) and θ
The relationship between sat(·) and θ

Position and parallelism error of tailstock hole axis

Simulation times x coordinate z coordinate x′ coordinate z′ coordinate zz′ Coordinate difference
20000 0.1358 0.0548 0.1452 0.0845 0.0148
30000 0.1249 0.0871 0.1781 0.0549 0.0153
90000 0.2100 0.0487 0.1453 0.0371 0.0182
100000 0.1573 0.1524 0.1620 0.0551 0.0151

Collins J A, Heiselman J S, Clements L W, et al. Toward Image Data-Driven Predictive Modeling for Guiding Thermal Ablative Therapy[J]. IEEE Transactions on Biomedical Engineering, 2020, 67(6):1548–1557. CollinsJ A HeiselmanJ S ClementsL W Toward Image Data-Driven Predictive Modeling for Guiding Thermal Ablative Therapy [J] IEEE Transactions on Biomedical Engineering 2020 67 6 1548 1557 10.1109/TBME.2019.2939686736526431494543 Search in Google Scholar

Mang A, Bakas S, Subramanian S, et al. Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology[J]. Annual Review of Biomedical Engineering, 2020, 22(1):309–341. MangA BakasS SubramanianS Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology [J] Annual Review of Biomedical Engineering 2020 22 1 309 341 10.1146/annurev-bioeng-062117-121105752088132501772 Search in Google Scholar

Li M, Ma K, You J, et al. Efficient and Effective Context-Based Convolutional Entropy Modeling for Image Compression[J]. IEEE Transactions on Image Processing, 2020, PP(99):1–1. LiM MaK YouJ Efficient and Effective Context-Based Convolutional Entropy Modeling for Image Compression [J] IEEE Transactions on Image Processing 2020 PP 99 1 1 10.1109/TIP.2020.298522532305914 Search in Google Scholar

Kolb J, Hameyer K. Sensitivity Analysis of Manufacturing Tolerances in Permanent Magnet Synchronous Machines With Stator Segmentation[J]. IEEE Transactions on Energy Conversion, 2020, PP(99):1–1. KolbJ HameyerK Sensitivity Analysis of Manufacturing Tolerances in Permanent Magnet Synchronous Machines With Stator Segmentation [J] IEEE Transactions on Energy Conversion 2020 PP 99 1 1 10.1109/TEC.2020.3017279 Search in Google Scholar

Braga D, Maciel R, Bergmann L, et al. Fatigue performance of hybrid overlap friction stir welding and adhesive bonding of an Al-Mg-Cu alloy[J]. Fatigue & Fracture of Engineering Materials & Structures, 2019, 42(6):1262–1270. BragaD MacielR BergmannL Fatigue performance of hybrid overlap friction stir welding and adhesive bonding of an Al-Mg-Cu alloy [J] Fatigue & Fracture of Engineering Materials & Structures 2019 42 6 1262 1270 10.1111/ffe.12933 Search in Google Scholar

Kim K H, Lee Y, Kim S, et al. Ramp Tolerance Analysis Considering Geometric Errors[J]. IEEE Transactions on Magnetics Mag, 2009, 45(5):2284–2287. KimK H LeeY KimS Ramp Tolerance Analysis Considering Geometric Errors [J] IEEE Transactions on Magnetics Mag 2009 45 5 2284 2287 10.1109/TMAG.2009.2016459 Search in Google Scholar

Teng, Kai, Wang, et al. Graphene-coated nanowire dimers for deep subwavelength waveguiding in mid-infrared range.[J]. Optics express, 2019, 27(9):12458–12469. Teng WangKai Graphene-coated nanowire dimers for deep subwavelength waveguiding in mid-infrared range [J] Optics express 2019 27 9 12458 12469 10.1364/OE.27.01245831052785 Search in Google Scholar

Stals L. Algorithm-based fault recovery of adaptively refined parallel multilevel grids[J]. Experimental Mechanics, 2019, 33(1):189–211. StalsL Algorithm-based fault recovery of adaptively refined parallel multilevel grids [J] Experimental Mechanics 2019 33 1 189 211 10.1177/1094342017720801 Search in Google Scholar

Jmca B, Mzaa B, Ran H, et al. Experimental demonstration of suppressing residual geometric dephasing[J]. Science Bulletin, 2019, 64(23):1757–1763. JmcaB MzaaB RanH Experimental demonstration of suppressing residual geometric dephasing [J] Science Bulletin 2019 64 23 1757 1763 10.1016/j.scib.2019.09.007 Search in Google Scholar

Huang L, Huang Y, Ouyang W, et al. Modeling Sub-Actions for Weakly Supervised Temporal Action Localization[J]. IEEE Transactions on Image Processing, 2021, PP(99):1–1. HuangL HuangY OuyangW Modeling Sub-Actions for Weakly Supervised Temporal Action Localization [J] IEEE Transactions on Image Processing 2021 PP 99 1 1 10.1109/TIP.2021.307832433983884 Search in Google Scholar

Bhatt R, Naik N, Subramanian V K. SSIM Compliant Modeling Framework With Denoising and Deblurring Applications[J]. IEEE Transactions on Image Processing, 2021, PP(99):1–1. BhattR NaikN SubramanianV K SSIM Compliant Modeling Framework With Denoising and Deblurring Applications [J] IEEE Transactions on Image Processing 2021 PP 99 1 1 10.1109/TIP.2021.305336933502978 Search in Google Scholar

Gan B, Zhang C, Chen Y, et al. Research on role modeling and behavior control of virtual reality animation interactive system in Internet of Things[J]. Journal of Real-Time Image Processing, 2020(1):1–15. GanB ZhangC ChenY Research on role modeling and behavior control of virtual reality animation interactive system in Internet of Things [J] Journal of Real-Time Image Processing 2020 1 1 15 10.1007/s11554-020-01046-y Search in Google Scholar

Wang Chunping Song Lilison glili2013@yeah.net Kunming University of Science and Technology, Kunming 650500, Yunnan, P. R. China School of Economics and Management, Chongqing Three Gorges Vocational College, Chongqing 404155, Chongqing, P. R. China. Compensation incentive contract of the subject librarians based on the H-M model[J]. Applied Mathematics and Nonlinear Sciences, 2021, 6(2):553–562. WangChunping SongLilison glili2013@yeah.net Kunming University of Science and Technology, Kunming 650500, Yunnan, P. R. China School of Economics and Management, Chongqing Three Gorges Vocational College, Chongqing 404155, Chongqing, P. R. China. Compensation incentive contract of the subject librarians based on the H-M model [J]. Applied Mathematics and Nonlinear Sciences 2021 6 2 553 562 10.2478/amns.2021.2.00106 Search in Google Scholar

Yildirim Furkan furkan.yildirim@atauni.edu.tr Narman Vocational Training School, Ataturk University, 25530 Erzurum, Turkey. On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle[J]. Applied Mathematics and Nonlinear Sciences, 2021, 6(1):421–428. YildirimFurkan furkan.yildirim@atauni.edu.tr Narman Vocational Training School, Ataturk University, 25530 Erzurum, Turkey. On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle [J] Applied Mathematics and Nonlinear Sciences 2021 6 1 421 428 10.2478/amns.2020.2.00066 Search in Google Scholar

Articles recommandés par Trend MD

Planifiez votre conférence à distance avec Sciendo