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Extracting fiber paths from the optimized lamination parameters of variable-stiffness laminated shells based on physic-informed neural network 基于物理信息神经网络从可变刚度层压壳的优化层压参数中提取纤维路径
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-11-01 DOI: 10.1016/j.cad.2024.103821
Xinming Li, Lujie Ma, Bowen Ji, Kuan Fan, Zhengdong Huang
This paper presents a novel approach for extracting fiber paths from the optimized lamination parameters (LPs) of variable stiffness laminated shells, utilizing the framework of physics-informed neural network (PINN). In this methodology, each fiber layer is associated with a specific stream function, which is approximated by an independent neural network. The stream function is governed by a partial differential equation (PDE) derived from the fiber orientation field in the parameter space. Moreover, the isocontours of the stream function are transformed into the actual fiber paths in the physical space. To account for manufacturing constraints, Riemannian geometry serves as a computational tool to determine the intrinsic distance between adjacent fiber paths and the geodesic curvature of the isocontours. By incorporating regularization terms into the loss function based on the physical relationships, the constrained optimization problem is converted into an unconstrained one, making it more suitable for neural network training. Meanwhile, a fiber path extraction (FPE) algorithm is used to minimize the loss function at randomly sampled points through gradient descent. The numerical results suggest that the extraction of fiber paths using PINN can achieve satisfactory levels of accuracy while effectively satisfying the imposed constraints.
本文提出了一种新方法,利用物理信息神经网络(PINN)框架,从可变刚度层压壳的优化层压参数(LP)中提取纤维路径。在这种方法中,每个纤维层都与一个特定的流函数相关联,该流函数由一个独立的神经网络来近似。流函数受参数空间中纤维定向场衍生的偏微分方程(PDE)控制。此外,流函数的等值线被转换为物理空间中的实际纤维路径。为了考虑制造限制,黎曼几何是一种计算工具,用于确定相邻光纤路径之间的固有距离和等值线的大地曲率。通过在基于物理关系的损失函数中加入正则化项,有约束优化问题被转换为无约束优化问题,使其更适合神经网络训练。同时,采用光纤路径提取(FPE)算法,通过梯度下降法使随机采样点的损失函数最小化。数值结果表明,使用 PINN 提取光纤路径可以达到令人满意的精度水平,同时有效地满足所施加的约束条件。
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引用次数: 0
A Hybrid Recognition Framework for Highly Interacting Machining Features Based on Primitive Decomposition, Learning and Reconstruction 基于基元分解、学习和重构的高度交互加工特征混合识别框架
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-11-01 DOI: 10.1016/j.cad.2024.103813
Jianping Yang , Qiaoyun Wu , Yuan Zhang , Jiajia Dai , Jun Wang
For the highly interacting machining features, Layered Projection Decomposition Method presents inferior recognition efficiency and accuracy, due to its high-cost 3D projection and failures in determining projection faces for internal occluded faces. To address these issues, we propose a potential hybrid recognition framework. We first introduce a straightforward adjacent projection wire (APW) over UV wires, automatically restoring the full projection wires from highly interacting features. Building on APWs, an efficient hybrid boundary representation and its corresponding unambiguous primitive definitions are proposed by combining with graph-based boundary representations. Subsequently, we design an efficient primitive decomposition method by introducing primitive boundary matching to decide the initial projection faces, and introducing iterative projection boundary expansion to complete the full primitives from occluded faces. Moreover, we establish an efficient Graph Neural Network to learn the distinguishable distributions over the decomposed primitives. Specifically, an Adjacency Attention Unit is proposed to automatically perceive the influence weight of adjacent nodes, leading to more discriminative self-adaptive shape embedding for efficient primitive recognition. Finally, we summarize convenient reconstruction rules to correct the wrong predictions of feature faces with indistinguishable adjacent relationships. To evaluate the effectiveness of the proposed recognition framework, CAD models of complex aircraft structural parts are collected to present a challenging machining feature dataset. Extensive numerical experiments demonstrate that the proposed hybrid recognition framework enables significant improvements over the state-of-the-art machining feature recognition techniques.
对于高度交互的加工特征,分层投影分解法的识别效率和准确性较低,原因是其三维投影成本较高,且无法确定内部遮挡面的投影面。为了解决这些问题,我们提出了一种潜在的混合识别框架。首先,我们在 UV 线之上引入了直接的相邻投影线(APW),自动从高度交互的特征中恢复完整的投影线。在 APW 的基础上,我们结合基于图的边界表示法,提出了一种高效的混合边界表示法及其相应的无歧义基元定义。随后,我们设计了一种高效的基元分解方法,通过引入基元边界匹配来决定初始投影面,并引入迭代投影边界扩展来完成从遮挡面到完整基元的分解。此外,我们还建立了一个高效的图神经网络来学习分解基元的可区分分布。具体来说,我们提出了一个邻接注意单元,用于自动感知相邻节点的影响权重,从而实现更具辨别力的自适应形状嵌入,以实现高效的基元识别。最后,我们总结了方便的重构规则,以纠正对相邻关系无法区分的特征面的错误预测。为了评估所提出的识别框架的有效性,我们收集了复杂飞机结构部件的 CAD 模型,以提供一个具有挑战性的加工特征数据集。广泛的数值实验证明,与最先进的加工特征识别技术相比,所提出的混合识别框架能够实现显著的改进。
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引用次数: 0
SITF: A Self-Supervised Iterative Training Framework for Point Cloud Denoising SITF:用于点云去噪的自监督迭代训练框架
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-10-18 DOI: 10.1016/j.cad.2024.103812
Zhiyong Su , Changchang Wang , Kun Jiang , Kai Jiang , Weiqing Li
Despite existing supervised point cloud denoising methods having made great progress, they require paired ideal noisy-clean datasets for training which is expensive and impractical in real-world applications. Moreover, they may perform the denoising process multiple times with fixed network parameters for better denoising results at test time. To address above issues, this paper proposes a self-supervised iterative training framework (SITF) for point cloud denoising, which only requires single noisy point clouds and a noise model. Given an off-the-shelf denoising network and original noisy point clouds, firstly, an intermediate noisier-noisy dataset is created by adding additional noises from the known noise model to noisy point clouds (i.e. learning targets). Secondly, after training on the noisier-noisy dataset, the denoising network is employed to denoise the original noisy point clouds to obtain the learning targets for the next iteration. The above two steps are iteratively and alternatively performed to get a better and better trained denoising network. Furthermore, to get better learning targets for the next round, this paper also proposes a novel iterative denoising network (IDN) architecture of stacked source attention denoising modules. The IDN explicitly models the iterative denoising process internally within a single network via reforming the given denoising network. Experimental results show that existing supervised networks trained through the SITF can achieve competitive denoising results and even outperform supervised networks under high noise conditions. The source code can be found at: https://github.com/VCG-NJUST/SITF.
尽管现有的有监督点云去噪方法取得了巨大进步,但它们需要成对的理想噪声-清洁数据集进行训练,这在实际应用中既昂贵又不切实际。此外,为了在测试时获得更好的去噪效果,它们可能会在网络参数固定的情况下多次执行去噪过程。为解决上述问题,本文提出了一种用于点云去噪的自监督迭代训练框架(SITF),它只需要单个噪声点云和噪声模型。给定一个现成的去噪网络和原始噪声点云,首先,通过向噪声点云(即学习目标)添加已知噪声模型中的额外噪声,创建一个中间噪声-噪声数据集。其次,在噪声数据集上进行训练后,利用去噪网络对原始噪声点云进行去噪,以获得下一次迭代的学习目标。以上两个步骤交替迭代进行,以获得更好的去噪网络。此外,为了获得下一轮更好的学习目标,本文还提出了一种新颖的叠加源注意力去噪模块的迭代去噪网络(IDN)架构。IDN 通过重构给定的去噪网络,在单个网络内部明确模拟了迭代去噪过程。实验结果表明,通过 SITF 训练的现有监督网络可以获得有竞争力的去噪结果,甚至在高噪声条件下优于监督网络。源代码见:https://github.com/VCG-NJUST/SITF。
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引用次数: 0
Two-Level High-Resolution Structural Topology Optimization with Equilibrated Cells 利用平衡单元进行两级高分辨率结构拓扑优化
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-10-17 DOI: 10.1016/j.cad.2024.103811
Rafael Merli , Antolín Martínez-Martínez , Juan José Ródenas , Marc Bosch-Galera , Enrique Nadal
In today’s industry, the rapid evolution in the design and development of optimized mechanical components to meet customer requirements represents a significant challenge for companies. These companies seek efficient solutions to enhance their products in terms of stiffness and strength. One powerful approach is Topology Optimization, which aims to determine the optimal material distribution within a predefined domain to maximize the overall component’s stiffness. Achieving high-resolution solutions is also crucial for accurately defining the final material distribution. While standard Topology Optimization tools can propose optimal solutions for entire components, they struggle with small-scale details (such as trabecular structures) due to prohibitive computational costs. To address this issue, our proposed approach introduces a two-level topology optimization methodology considering density-based techniques. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution, assigning a different density to each cell. Since the output stresses from the coarse problem are not equilibrated into each cell, they must not be directly used in the fine level. Thus, the second step uses the equilibrating traction recovery approach to convert the cell nodal forces into equilibrated lateral tractions over the cell boundary. Finally, taking as input data the densities from the coarse optimization and imposing these lateral tractions as Neumann boundary conditions, each cell is optimized at fine level. The main goal of this work is to efficiently solve high-resolution topology optimization problems using a two-level mechanically-continuous method, which would be unaffordable with standard computing facilities and the current techniques.
在当今的工业领域,为满足客户要求而进行的优化机械部件的设计和开发工作发展迅速,这对企业来说是一项重大挑战。这些公司寻求高效的解决方案,以提高产品的刚度和强度。拓扑优化是一种强有力的方法,其目的是确定预定域内的最佳材料分布,以最大限度地提高整个部件的刚度。实现高分辨率解决方案对于准确定义最终材料分布也至关重要。虽然标准的拓扑优化工具可以为整个部件提出最佳解决方案,但由于计算成本过高,它们在处理小尺度细节(如小梁结构)时显得力不从心。为解决这一问题,我们提出了一种两级拓扑优化方法,其中考虑了基于密度的技术。建议的方法包括三个步骤:第一步,将整个部件细分为单元,生成粗略优化的低定义材料分布,并为每个单元分配不同的密度。由于粗略问题的输出应力没有均衡到每个单元,因此不能直接用于精细层面。因此,第二步使用平衡牵引恢复法将单元节点力转换为单元边界上的平衡横向牵引力。最后,将粗优化的密度作为输入数据,并将这些横向牵引力作为新曼边界条件,对每个单元进行精细优化。这项工作的主要目标是使用两级机械连续方法高效地解决高分辨率拓扑优化问题,而标准计算设施和现有技术是无法负担这一工作的。
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引用次数: 0
SplineGen: Approximating unorganized points through generative AI SplineGen:通过生成式人工智能逼近无组织点
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-10-10 DOI: 10.1016/j.cad.2024.103809
Qiang Zou, Lizhen Zhu, Jiayu Wu, Zhijie Yang
This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. Parameters and knots are generated in an associative way to attain better parameter-knot alignment, and therefore a higher approximation accuracy. These features are attained by using a new generative model SplineGen, which casts the parameterization and knot placement problems as a sequence-to-sequence translation problem. It first adopts a shared autoencoder model to learn a 512-D embedding for each input point, which has the local neighborhood information implicitly captured. Then these embeddings are autoregressively decoded into parameters and knots by two associative decoders, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. The two decoders are made to work in a coordinated manner by a new network module called internal cross-attention. Once trained, SplineGen demonstrates a notable improvement over existing methods, with one to two orders of magnitude increase in approximation accuracy on test data.
本文提出了一种基于学习的方法,用于解决 B-样条逼近中的传统参数化和节点放置问题。与传统的启发式方法或最新的基于人工智能的方法不同,本文提出的方法不假定有序或固定大小的数据点作为输入。此外,也无需手动设置节点数量。参数和节点以关联方式生成,以实现更好的参数-节点对齐,从而提高近似精度。这些特点是通过使用新的生成模型 SplineGen 实现的,该模型将参数化和节点放置问题视为序列到序列的转换问题。它首先采用共享自动编码器模型,为每个输入点学习 512-D 嵌入,其中隐含了本地邻域信息。然后,由两个关联解码器将这些嵌入自回归解码为参数和结点,一个生成过程自动决定结点的数量、位置、参数值及其排序。这两个解码器通过一个称为内部交叉注意的新网络模块协调工作。经过训练后,SplineGen 与现有方法相比有了显著改进,测试数据的近似精度提高了一到两个数量级。
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引用次数: 0
Minimal surface-guided higher-order mesh generation for CAD models 为 CAD 模型生成最小曲面引导的高阶网格
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-10-01 DOI: 10.1016/j.cad.2024.103810
Kaixin Yu , Bohan Wang , Xuejuan Chen , Ying He , Jianjun Chen
This paper presents a novel method for generating higher-order meshes for CAD surfaces by leveraging minimal surface theory to improve element shapes. We explore the concept of higher-order mesh distortion through deformation gradients and introduce an energy function designed to minimize the surface area of these meshes, providing a theoretical justification for its effectiveness in untangling. The process of mesh generation starts with segmenting CAD surfaces into linear elements, followed by the insertion of higher-order nodes within these elements. These nodes are then projected onto the CAD surface to form the initial higher-order elements. By optimizing energy functions related to minimal surfaces and the projection distances, we achieve high-quality, geometrically accurate higher-order surface meshes. Our method has been validated on complex geometries, showcasing its potential in creating effective higher-order meshes for industrial CAD models.
本文提出了一种新方法,利用最小曲面理论改进元素形状,为 CAD 曲面生成高阶网格。我们通过变形梯度探索了高阶网格变形的概念,并引入了旨在最小化这些网格表面积的能量函数,为其在解缠方面的有效性提供了理论依据。网格生成过程首先是将 CAD 表面分割成线性元素,然后在这些元素中插入高阶节点。然后将这些节点投影到 CAD 表面,形成初始高阶元素。通过优化与最小曲面和投影距离相关的能量函数,我们获得了高质量、几何精度高的高阶曲面网格。我们的方法已在复杂几何图形上得到验证,展示了其为工业 CAD 模型创建有效高阶网格的潜力。
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引用次数: 0
Boundary recognition of ship planar components from point clouds based on trimmed delaunay triangulation 基于修剪三角测量法的点云船舶平面部件边界识别
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-09-27 DOI: 10.1016/j.cad.2024.103808
Puhao Lei , Zhen Chen , Runli Tao , Jun Li , Yuchi Hao
A vision-based boundary detector is crucial for intelligent processing of ship planar components due to its automatically identifying workpiece edges. However, traditional methods suffer from many issues such as low accuracy and excessive detection errors for these workpieces with complex shape profiles. This paper proposes a trimmed Delaunay triangulation method (TDT) for recognizing boundary edges of planar workpieces from point clouds. It begins by distinguishing the difference of binary image pixel generated from point cloud to eliminate redundant points far away from plane boundary. Then, a triangulation trimming algorithm is developed to extract the edge points from the simplified points. Finally, complete plane boundary is reconstructed by a clustering-and-fitting method from the extracted edge points. Experimental results from multiple angles show that average absolute errors of straight edges and angles recognition are 1.29 mm and 1.04° respectively, which demonstrate that TDT has a high identification accuracy and robustness of plane boundary edge.
基于视觉的边界检测器可自动识别工件边缘,对船舶平面部件的智能加工至关重要。然而,传统的方法存在许多问题,例如精度低、检测误差过大,无法识别形状复杂的工件。本文提出了一种修剪德劳内三角测量法(TDT),用于从点云中识别平面工件的边界边缘。该方法首先区分由点云生成的二值图像像素的差异,以消除远离平面边界的冗余点。然后,开发一种三角形修剪算法,从简化点中提取边缘点。最后,通过聚类和拟合方法从提取的边缘点重建完整的平面边界。多角度的实验结果表明,直线边缘和角度识别的平均绝对误差分别为 1.29 mm 和 1.04°,这表明 TDT 对平面边界边缘具有较高的识别精度和鲁棒性。
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引用次数: 0
eCAD-Net: Editable Parametric CAD Models Reconstruction from Dumb B-Rep Models Using Deep Neural Networks eCAD-Net:利用深度神经网络从呆板的 B-Rep 模型重建可编辑的参数化 CAD 模型
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-09-24 DOI: 10.1016/j.cad.2024.103806
Chao Zhang , Arnaud Polette , Romain Pinquié , Gregorio Carasi , Henri De Charnace , Jean-Philippe Pernot
This paper introduces a novel framework capable of reconstructing editable parametric CAD models from dumb B-Rep models. First, each B-Rep model is represented with a network-friendly formalism based on UV-graph, which is then used as input of eCAD-Net, the new deep neural network-based algorithm that predicts feature-based CAD modeling sequences from the graph. Then, the sequences are scaled and fine-tuned using a feature matching algorithm that retrieves the exact parameter values from the input dumb CAD model. The output sequences are then converted in a series of CAD modeling operations to create an editable parametric CAD model in any CAD modeler. A cleaned dataset is used to learn and validate the proposed approach, and is provided with the article. The experimental results show that our approach outperforms existing methods on such reconstruction tasks, and it outputs editable parametric CAD models compatible with existing CAD modelers and ready for use in downstream engineering applications.
本文介绍了一种能够从哑巴 B-Rep 模型重建可编辑参数化 CAD 模型的新型框架。首先,每个 B-Rep 模型都使用基于 UV 图的网络友好形式表示,然后将其作为 eCAD-Net 的输入,eCAD-Net 是一种基于深度神经网络的新算法,可从图中预测基于特征的 CAD 建模序列。然后,使用特征匹配算法对序列进行缩放和微调,该算法可从输入的哑计算机辅助设计模型中检索精确的参数值。然后在一系列 CAD 建模操作中转换输出序列,在任何 CAD 建模器中创建可编辑的参数化 CAD 模型。本文提供了一个经过清理的数据集,用于学习和验证所提出的方法。实验结果表明,在此类重建任务中,我们的方法优于现有方法,而且它输出的可编辑参数化 CAD 模型与现有 CAD 建模器兼容,可用于下游工程应用。
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引用次数: 0
Numerical integration on 2D/3D arbitrary domains: Adaptive quadrature/cubature rule for domains with curved boundaries 二维/三维任意域的数值积分:具有弯曲边界的域的自适应正交/余角规则
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-09-24 DOI: 10.1016/j.cad.2024.103807
Nafiseh Niknejadi, Bijan Boroomand
This paper introduces an efficient quadrature rule for domains with curved boundaries in 2D/3D. Building upon our previous work focused on polytopes (Comput. Methods Appl. Mech. Engrg. 403 (2023) 115,726), we extend this method to handle volume/boundary integration on domains with general configurations and boundaries. In this method, we approximate a generic function using a finite number of orthogonal polynomials, and we obtain the coefficients of these polynomials through the integration points. The physical domain is enclosed by a fictitious rectangular/cuboidal domain, where a tensor-product of Gauss quadrature points is primarily considered. To locate the integration points that are strictly within the domain under consideration (e.g., the physical 3D domain itself or its mapped boundaries), we form a system of algebraic equations whose dimensions depend solely on the number of polynomials, not the number of quadrature points which may be significantly larger. This allows us to construct a full-rank square coefficient matrix, leading to the uniqueness of the solution, and the system of equations is then solved through a straightforward inverse process. To evaluate the integral of the polynomials, we transform the integration over the domain under consideration into an equivalent integration along the domain's boundaries using the divergence theorem. For 2D cases, we perform the boundary integration using Gauss points along the curved lines. In 3D cases, we provide an efficient algorithm for computing the boundary integrals over curved surfaces. We present several integration problems involving two and three-dimensional curved regions to demonstrate the accuracy and efficiency of the proposed method.
本文介绍了一种适用于二维/三维曲面域的高效正交规则。基于我们之前专注于多边形的工作(Comput.Methods Appl.Engrg.403 (2023) 115,726)的基础上,我们扩展了这一方法,以处理具有一般配置和边界的域的体积/边界积分。在这种方法中,我们使用有限个正交多项式逼近一个通用函数,并通过积分点获得这些多项式的系数。物理域由一个虚构的矩形/立方体域所包围,主要考虑高斯二次积分点的张量乘积。为了确定严格位于所考虑的域(例如物理三维域本身或其映射边界)内的积分点,我们形成了一个代数方程系统,其维度仅取决于多项式的数量,而不是正交点的数量,后者可能大得多。这样,我们就可以构建一个全秩平方系数矩阵,从而得到唯一的解,然后通过直接的逆过程求解方程组。为了评估多项式的积分,我们利用发散定理将考虑域的积分转换为沿域边界的等效积分。在二维情况下,我们使用沿曲线的高斯点进行边界积分。在三维情况下,我们提供了计算曲面边界积分的高效算法。我们提出了几个涉及二维和三维曲面区域的积分问题,以证明所提方法的准确性和效率。
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引用次数: 0
Multi-part kinematic constraint prediction for automatic generation of CAD model assemblies using graph convolutional networks 利用图卷积网络自动生成 CAD 模型装配的多部分运动学约束预测
IF 3 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2024-09-21 DOI: 10.1016/j.cad.2024.103805
Lucas Vergez, Arnaud Polette, Jean-Philippe Pernot
This paper presents a machine learning-based approach to predict kinematic constraints between CAD models that have potentially never been assembled together before. During the learning phase, the algorithm is trained to predict the next-possible-constraints between a set of parts candidate to the assembly. Assemblies are represented in a new graph-based formalism that is capable of capturing features associated with parts, interfaces between parts and constraints between them. Using such a multi-level feature extraction strategy coupled to a state-by-state graph decomposition, the approach does not need to be trained on a large database. This formalism is used to model both the network input and output where the next-possible-constraints appear after evaluation. The core of the approach relies on a series of networks based on a link-prediction encoder–decoder architecture, integrating the capabilities of several convolutional networks trained in an end-to-end manner. A decision-making algorithm is added to post-process the output and drive the prediction process in finding one among the set of next-possible-constraints. This process is repeated until no more constraints can be added. The experimental results show that the proposed approach outperforms state-of-the-art methods on such assembly tasks. Although the state-by-state assembly algorithm is iterative, it still takes into account the whole set of parts as well as the whole set of constraints already predicted, and this makes it possible to handle constraint cycles, which is generally not possible when not considering multiple parts as input.
本文提出了一种基于机器学习的方法,用于预测可能从未组装在一起的 CAD 模型之间的运动学约束。在学习阶段,对算法进行训练,以预测装配体候选零件集之间的下一个可能约束。装配体用一种新的基于图形的形式来表示,这种形式能够捕捉与零件相关的特征、零件之间的接口以及它们之间的约束。利用这种多层次特征提取策略和逐状态图分解,该方法无需在大型数据库中进行训练。这种形式主义既可用于网络输入建模,也可用于评估后出现下一个可能约束的输出建模。该方法的核心依赖于一系列基于链接预测编码器-解码器架构的网络,整合了以端到端方式训练的多个卷积网络的功能。此外,还添加了一种决策算法,用于对输出进行后处理,并驱动预测过程,从一组下一个可能的约束条件中找到一个。这一过程不断重复,直到无法再添加更多的约束条件为止。实验结果表明,在此类装配任务中,所提出的方法优于最先进的方法。虽然逐状态装配算法是迭代式的,但它仍然考虑到了整套零件以及已预测的整套约束,这使得它可以处理约束循环,而这在不考虑多个零件作为输入时通常是不可能的。
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引用次数: 0
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Computer-Aided Design
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