Deformed workpiece twinning modeling method based on matching of measuring point cloud and three-dimensional CAD (computer-aided design) model

Abstract

The invention discloses a deformed workpiece twin modeling method based on measurement point cloud and three-dimensional CAD model matching. The deformed workpiece twin modeling method comprises the steps that an improved GFO-ICP registration algorithm is adopted to solve the initial coarse registration problem of the measurement point cloud and a CAD model in combination with geometric feature constraint and self-adaptive step length optimization; extracting a key geometric curved surface of the point cloud by adopting a clustering-based plane segmentation algorithm, and extracting a semantic feature vector of a segmented region in combination with a Pointnet + + network; a cosine similarity matching mechanism is constructed by integrating mixed descriptors of geometric features (areas and normal vectors) and semantic features, and accurate binding of a point cloud curved surface and a curved surface of a CAD model is achieved. According to the method, the problem of assembly geometric deviation caused by workpiece deformation due to manufacturing errors in compressor and fan rotor assembly is solved, multi-link error accumulation is effectively processed, digital twin modeling of high-precision deformed workpieces is achieved, and the assembly simulation effect and intelligent manufacturing application are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of digital twin intelligent manufacturing and deep learning, and relates to point cloud processing, point cloud registration, feature matching and binding, and in particular to a deformed workpiece twin modeling method based on matching of measured point clouds and three-dimensional CAD models. BACKGROUND

[0002] In the field of industrial assembly, high-precision modeling of deformed parts is always one of the core challenges to be broken through in the process of intelligent manufacturing. With the development of modern products towards high performance, miniaturization and multi-function, their structure and shape are increasingly complex, the types of materials are diverse, and the machining precision requirements are continuously improved, so that the parts are prone to elastic-plastic deformation, thermal deformation or geometric deviation caused by residual stress during machining, handling, storage and assembly. These small but non-negligible deformations often lead to mismatching of gaps, difficulty in cooperation and even assembly failure during assembly, thereby seriously affecting product quality and manufacturing efficiency.

[0003] Traditional modeling methods are usually based on CAD models or tolerance design concepts, assuming that the parts have ideal geometric shapes and ignoring their real deformation behavior during the manufacturing process. However, with the increasing uncertainty of the production environment and the acceleration of the assembly rhythm, this static modeling method based on ideal geometric assumptions cannot accurately reflect the actual state of the parts, thereby affecting the reliability of assembly path planning, interference detection and cooperation analysis. In addition, the traditional method has limited support for real-time and multi-source data collection, and it is also difficult to meet the needs of "data-driven modeling" in intelligent manufacturing. SUMMARY

[0004] In view of the above shortcomings of the prior art, the present application aims to provide a deformed workpiece twin modeling method based on matching of measured point clouds and three-dimensional CAD models, which aims to solve the problem that in the assembly process of a compressor rotor, manufacturing errors cause workpiece deformation, which leads to deviation of assembly characteristics from the design expectation, and the traditional modeling method is difficult to establish a high-precision double model due to the accumulation of multi-link errors.

[0005] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions: A deformed workpiece twin modeling method based on matching of measured point clouds and three-dimensional CAD models, comprising the following steps: Step 1: Obtain CAD model point cloud data and measured point cloud data of the part; Step 2: Use a statistical filtering algorithm to denoise the original measured point cloud data, output denoised point cloud data, and perform voxel downsampling on the denoised point cloud data to reduce the data size; Step three: the pre-processed measured point cloud data and the CAD model point cloud data of the part are registered using the GFO-ICP algorithm, the nearest point pairs meeting the geometric characteristics are screened, and the dynamic registration adjustment iteration step is adopted to obtain the registered point cloud data; Step four: for the registered point cloud data, the normal vector and the curvature of each point are obtained through PCA, the candidate plane points are screened according to the normal vector consistency and the low curvature characteristics, and the Euclidean clustering classification is performed on the candidate points based on the k-d tree, the points with a spatial distance less than a set threshold are classified into the same cluster, and the surface data is obtained; Step five: based on the surface data obtained in step four and the segmented surface and the CAD ideal surface, the deep feature vector is extracted through the PointNet++ network, and the geometric features and the deep features of each surface are spliced and fused in the last dimension to form a composite feature vector; then, the cosine similarity matching is performed between all the measured surface and the CAD surface feature vectors, the accurate corresponding relationship is established, the feature matching and binding function is realized, the surface-level matching from the segmented area to the CAD model is completed, and the workpiece modeling is realized.

[0006] Further, in step three, the pre-processed measured point cloud data and the CAD model point cloud data of the part are registered using the GFO-ICP algorithm, which includes: Step 3-1: the point cloud data in step two is obtained, and the KD-Tree search method and the Euclidean distance are used to search the nearest point pairs in the measured point cloud data and the CAD model point cloud data; Step 3-2: based on step 3-1, the point cloud geometric feature normal vector and the curvature are obtained, and the nearest point pairs with an angle between the normal vectors and a curvature difference less than a set threshold are screened out; Step 3-3: according to the nearest point pairs screened out in step 3-2, a step dynamic adjustment mechanism is introduced to adjust the registration iteration, the target of iteration is to find the optimal rotation matrix R and translation vector t to make the Euclidean square sum of the nearest point pairs of the measured point cloud and the target point cloud minimum, the step is dynamically updated based on the iteration change of each error, the step is reduced or increased according to the error change, and finally the optimal transformation parameter and the transformed point cloud are obtained.

[0007] Further, in step 3-2, the screening condition of the nearest point pairs is: In the formula, are a pair of nearest points , , is the angle between the normal vectors, and are respectively and the curvature points of and are threshold values for controlling the strictness of the normal vector consistency and the curvature similarity.

[0008] Further, in step 3-3, the objective function error of each iteration is: wherein, is the number of matched point pairs, and are the rotation and translation parameters of the i-th iteration; the error rate, i.e. the error change, is: When the error rate is large, it indicates that the current step size is large and needs to be reduced, and when the error rate is small and tends to be stable, the step size is increased to speed up the convergence. The initial step size is then The step size of the iteration is updated as: wherein, is the step size adjustment factor, is the threshold value of the error rate for determining whether the step size needs to be adjusted.

[0009] Further, the step four comprises: Step 4-1: First, calculate the normal vector and curvature of each point in the point cloud, the normal vector reflects the local direction information of the point cloud surface, and the curvature describes the curvature degree of the surface. For point , its normal vector is obtained by the characteristic vector corresponding to the minimum eigenvalue of the covariance matrix by PCA, and the curvature is calculated by the ratio of the minimum eigenvalue to the sum of all eigenvalues, and then according to the normal vector consistency and low curvature characteristics, the points that may belong to the plane are screened out, and the screening formula is as follows: ; ; wherein is the normal vector of point i, is the curvature of point i, and according to the normal vector consistency and low curvature characteristics, the points that may belong to the plane can be screened out.

[0010] ​​​Step 4-2: Construct a kd-tree for the selected planar points in Step 1 to accelerate the nearest neighbor search. Use Euclidean clustering algorithm to segment the point cloud into several independent planar regions, and group the points with a distance less than a specified threshold. The points are grouped into the same cluster, and the above process is repeated until all points are assigned to a cluster or labeled as noise. By combining geometric feature filtering and spatial distance clustering, multiple planar regions in the point cloud are extracted.

[0011] Furthermore, in step five, the feature matching and binding steps are as follows: Step 5-1: Input the segmented surface regions of the measured point cloud obtained in Step 4 and their corresponding surfaces in the CAD model into the PointNet++ model for depth feature extraction, and output a 256-dimensional high-dimensional feature vector for each surface region. ; Step 5-2: To enhance the representational ability of the features, obtain the centroid of each surface region. Center of mass This represents the average position of the surface in space. Principal component analysis (PCA) is used to obtain the eigenvalues ​​of the covariance matrix of the surface point cloud, thus yielding the flatness characteristics. ; measures the degree to which the surface region is nearly flat, and the radius of the surface region. :radius For all points in the surface region to their centroid The maximum value of the distance represents the spatial extent of the surface; Step 5-3: Extract the high-dimensional feature vector from Step 5-1. and the three geometric features obtained in step 5-2 , , The last dimension is concatenated to return the fused 261-dimensional hybrid features. ; Step 5-4: Combine the fused feature vector of the i-th surface of the measured point cloud obtained in Step 5-3. The fused feature vector of the j-th surface of the CAD model Cosine similarity is calculated, with the result ranging from [-1, 1]. The closer the value is to 1, the more similar the two vectors are. For each surface i of the measured point cloud, all surfaces j of the CAD model are traversed to find the match with the highest similarity. The measured surface i and the ideal surface are then output. Establish a one-to-one matching relationship.

[0012] Furthermore, in step 5-2, the centroid The formula is: In the formula, where It is the surface The number of points on; flatness The formula is: In the formula , , These are the three eigenvalues ​​of the covariance matrix, satisfying... ; The maximum variance represents the variance of the main directions of the point cloud distribution. and Variance representing the secondary direction; The larger the value, the flatter the surface region. The smaller the value, the less flat the surface region is; The formula for obtaining the radius is: .

[0013] Furthermore, in step 5-4: The formula for calculating cosine similarity is: In the formula, The fused feature vector of the i-th surface of the measured point cloud. Let be the fused feature vector of the j-th surface of the ideal CAD model. represents the inner product of vectors, and || represents the L2 norm of the vectors; Feature matching formula: In the formula, The surface represented by i in the ideal CAD model has the highest cosine similarity to the surface in the measured point cloud. Finally, the surface i of the observed point cloud is compared with the surface of the ideal point cloud. Matching.

[0014] The technical solution adopted in this invention has the following beneficial effects: This invention presents a method for digital twin modeling of deformable workpieces based on matching measured point clouds with 3D CAD models. It introduces an improved GFO-ICP registration algorithm for initial registration, followed by a clustering-based planar segmentation algorithm to extract key geometric surfaces from the point cloud. Then, it combines this with a PointNet++ network to extract semantic feature vectors from the segmented regions. Finally, by integrating a hybrid descriptor of geometric features (area, normal vector) and semantic features, a cosine similarity matching mechanism is constructed to achieve precise binding between the point cloud surfaces and the CAD model surfaces. This invention addresses the problems of traditional modeling methods, which struggle to effectively handle the accumulation of errors across multiple stages and thus fail to achieve high-precision digital twin modeling of deformable workpieces. Attached Figure Description

[0015] Figure 1 This is an overall framework diagram of the present invention; Figure 2 This is a flowchart of the present invention; Figure 3 This is a registration result image using the GFO-ICP algorithm in this invention; Figure 4 This is a diagram showing the result of point cloud surface segmentation in this invention. Figure 5 This is a network structure diagram of the PointNet++ model used for feature extraction in this invention; Figure 6 This is a flowchart of the feature matching and binding process of the present invention; Figure 7 Comparison chart of high-precision industrial parts dataset; Figure 8 A comparison chart of road vehicle datasets; Figure 9 Comparison chart of complex indoor scene datasets; Figure 10 This is a diagram showing the results of feature matching and binding. Detailed Implementation

[0016] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0017] In recent years, digital twin technology, as a key enabling technology for intelligent manufacturing, is providing a new paradigm for modeling and optimizing complex systems. Through mechanisms such as virtual-physical fusion, data-driven approaches, and dynamic mapping, digital twins can build a continuous feedback loop between physical entities and their digital models, enabling real-time state perception and dynamic modeling of parts throughout the entire manufacturing and assembly process. Current research mainly focuses on geometric feature extraction, multi-source data fusion, and physical behavior simulation: In compressor assembly, measured point cloud data is used to construct virtual pre-assembled models of key geometric features. Through digital mapping of contours and contact features, assembly accuracy has been significantly improved. The development of fan rotors has exposed the shortcomings of traditional modeling methods in terms of high fidelity and cyber-physical integration, necessitating the use of digital twins to achieve closed-loop optimization of the design.

[0018] However, current research still faces three major challenges. First, the fusion of multi-source heterogeneous data in industrial scenarios presents a feature-level matching problem, and traditional ICP algorithms are prone to getting trapped in local optima when dealing with complex surfaces such as thin-walled parts. Second, it is difficult to simultaneously consider the real-time performance and accuracy of geometric-physical coupled modeling. Case studies in the oil and gas drilling field show that existing methods experience response delays of up to seconds under dynamic loads. Finally, maintaining semantic consistency across different levels of models is challenging; 26% of errors in aircraft assembly are caused by semantic discrepancies between design models and measurement data. The root cause of these problems lies in the separation of geometric modeling from data-driven methods, urgently requiring breakthroughs in feature representation and algorithm structure.

[0019] Based on the above research, this invention proposes a twin modeling method for deformable workpieces based on matching measurement point clouds with 3D CAD models. The overall framework is as follows: Figure 1 As shown in the diagram. First, the measured point cloud and the ideal CAD point cloud of the part are obtained. Then, they are processed by denoising, etc. The processed point cloud is then registered, surface segmented, and point cloud surface feature matched and bound using an improved GFO-ICP algorithm. The entire process is as follows: Figure 2 As shown.

[0020] A twin modeling method for deformable workpieces based on matching measurement point clouds with 3D CAD models, the main steps of which are as follows: Step 1: Obtain the CAD data and measured point cloud data of the part; Acquire measured point cloud data and CAD data of the compressor and fan rotor, and convert the CAD model STL file into a PLY point cloud file.

[0021] Step 2: Use statistical filtering algorithm to denoise the original point cloud data and output the denoised clean point cloud. Voxel downsampling is performed on the denoised point cloud data to reduce the data size and improve the efficiency of subsequent processing. The process of denoising the original point cloud data using statistical filtering algorithms is as follows: Step 2-1: Calculate the average distance from each point in the point cloud to all its neighboring points within a specified search radius. The calculation formula is: (1) Step 2-2: Calculate the global mean distance based on the average distance of all points ( ) and standard deviation ( The calculation formula is: (2) (3) Steps 2-3: Set a threshold interval, iterate through each point, and if its average distance ( Points exceeding this threshold range are identified as noise and removed. Points within the range are retained as valid data. The determination formula is as follows: (4) Steps 2-4: Input the original number of point cloud points, determine the target number of points (m) or sampling ratio for random sampling, then randomly generate m unique indices within the original point cloud index range, and finally extract the corresponding points according to the indices to form a new point cloud. The sampling formula is as follows: (5) (6) Step 3: Register the preprocessed measured point cloud data from Step 2 with the point cloud data of the part's CAD model using the improved GFO-ICP algorithm. This algorithm adds steps to calculate the normal vector and curvature geometric features of each point, constraining the selection of matching point pairs and filtering out the closest point pairs that meet the geometric features, thus reducing the mismatch rate. Dynamic registration adjusts the iteration step size. To accelerate convergence and avoid getting trapped in local optima, the registered point cloud data is obtained, and the registration is performed using the improved GFO-ICP algorithm. The registration process is as follows: Step 3-1: Obtain the ideal point cloud data and measured point cloud data from Step 2. Similar to the traditional ICP algorithm, use the KD-Tree search method and Euclidean distance to search for the closest point pair between the measured point cloud and the CAD ideal point cloud.

[0022] Step 3-2: Based on Step 3-1, calculate the geometric feature normal vectors of the point cloud. and curvature and set a threshold and The nearest point pairs are selected based on their normal vector angle and curvature difference being less than a set threshold. The selection formula is as follows: (7) (8) Step 3-3: Based on the selected nearest point pairs, a dynamic step size adjustment mechanism is introduced to adjust the registration iteration. The goal of the iteration is to find the optimal rotation matrix R and translation vector t such that the sum of the squares of the Euclidean distances of the nearest point pairs between the measured point cloud and the target point cloud is minimized. The step size is dynamically updated based on the iteration change of the error. If the error changes drastically, decrease the step size; otherwise, increase the step size appropriately. Finally, obtain the optimal transformation parameters and the transformed point cloud. The final registration result is as follows: Figure 3 As shown: The traditional ICP registration process is as follows: (9) R belongs to a special orthogonal group. The three-dimensional rotation matrix satisfies the formula: (10) Similar to traditional ICP, the objective function error of the improved GFO-ICP algorithm in each iteration is: (11) The error rate (error variation) is: (12) initial step size ,but Iteration step size Updated to: (13) Step 4: Calculate the normal vector and curvature of each point in the input point cloud using PCA, and filter candidate planar points based on the consistency of normal vectors and low curvature characteristics; perform Euclidean clustering on the candidate points based on kd-tree, and group points with a spatial distance less than a set threshold into the same cluster, and finally output independent planar regions and noise points.

[0023] To extract planar regions from point clouds, this invention employs a multi-plane segmentation method based on Euclidean clustering. Compared to traditional single-plane fitting methods, this method can simultaneously handle multiple planes in complex scenes, making it suitable for high-precision point cloud analysis tasks.

[0024] The point cloud surface segmentation process is as follows: Step 4-1: First, calculate the normal vector and curvature of each point in the point cloud. The normal vector reflects the local orientation information of the point cloud surface, while the curvature describes the degree of curvature of the surface. For a point... Its normal vector The curvature can be obtained by finding the eigenvector corresponding to the smallest eigenvalue of the covariance matrix using PCA. The ratio of the minimum eigenvalue to the sum of all eigenvalues ​​can be used to calculate the value, and then points that may belong to the plane can be selected based on the consistency of the normal vector and the low curvature feature.

[0025] The calculation formula is as follows: (14) (15) Step 4-2: Construct a kd-tree for the selected planar points in Step 1 to accelerate the nearest neighbor search. Use Euclidean clustering to segment the point cloud into several independent planar regions. Euclidean clustering is a spatial distance-based clustering method whose core idea is to cluster regions with a distance less than a specified threshold. Points are grouped into the same cluster. This process is repeated until all points are assigned to a cluster or labeled as noise. By combining geometric feature filtering and spatial distance clustering, this method can efficiently and accurately extract multiple planar regions from a point cloud. The segmentation results are as follows: Figure 4 As shown.

[0026] Step 5: For the surface data obtained in Step 4, extract 256-dimensional depth feature vectors from the measured point cloud segmented surface and the CAD ideal surface using the PointNet++ network. Then, calculate the centroid, flatness, radius, and other geometric features of each surface's feature vector. Simultaneously, calculate and fuse the geometric and depth features of each surface in the last dimension to form a composite feature vector containing spatial location, shape characteristics, and semantic information. Subsequently, perform pairwise cosine similarity calculations on the feature vectors of all measured surfaces and CAD surfaces, and select the CAD surface with the highest cosine similarity as the matching result to establish a precise correspondence, realize feature matching and binding functions, and complete the surface-level matching from the segmented region to the CAD model. The specific process of feature matching and binding is as follows: Step 5-1: Input the segmented surface regions of the measured point cloud from Step 4 and their corresponding surfaces in the ideal point cloud (CAD model) into the PointNet++ model for depth feature extraction, and output a 256-dimensional high-dimensional feature vector for each surface region. The network structure for feature extraction using the PointNet++ model is as follows: Figure 5 As shown.

[0027] Step 5-2: To enhance the representational power of the features, calculate the centroid of each surface region. The flatness feature represents the average position of the surface in space. The eigenvalues ​​of the covariance matrix of the surface point cloud are calculated using principal component analysis (PCA) to obtain the flatness feature. Defined as the second largest eigenvalue and With the largest eigenvalue The ratio: measures how close the surface region is to flatness, and the radius of the surface region. : All points in the surface region from their centroid The maximum distance represents the spatial extent of the surface. Calculate the centroid. Flatness characteristics ,radius The formula is as follows: (16) (17) (18) Step 5-3: Extract the deep learning feature vectors from Step 5-1 (256 dimensions) and the three geometric features calculated in step 5-2 ( - 3D, -1 dimension, - (1-dimensional) Concatenate along the last dimension to return the fused hybrid features. (261 dimensions). The formula is as follows: (19) Step 5-4: Surface Matching Stage. To achieve surface matching between the measured point cloud and the ideal point cloud, the fused feature vector of the i-th surface of the measured point cloud obtained in Step 5-3 is... The fused feature vector of the j-th surface of the ideal point cloud The cosine similarity is calculated, and the result ranges from [-1, 1]. The closer the value is to 1, the more similar the directions of the two vectors are (the closer the included angle is). The formula for calculating cosine similarity is as follows: (20) For each surface i in the measured point cloud, iterate through all surfaces j in the ideal point cloud, find the match with the highest similarity, and output the measured surface i and the ideal surface j. To establish a one-to-one matching relationship, the calculation formula is as follows: (twenty one) The overall process of feature matching and binding is as follows: Figure 6 As shown.

[0028] Experimental results The present invention conducted the following comparative experiments: (1) Comparisons were carried out in different complex scenarios, and the results are as follows. Figure 7 High-precision industrial parts Figure 8 Road vehicles, Figure 9 (2) Comparison of complex indoor scenes and different registration methods, the experimental results are shown in Table 1 below. (3) Visualization of feature matching and binding Table 1 Comparison of experimental results In point cloud registration, evaluating the accuracy of the estimated transformation requires metrics for rotation and translation errors. These metrics can be categorized into isotropic (orientation-agnostic) and anisotropic (orientation-aware) metrics. Using both isotropic and anisotropic metrics provides a comprehensive understanding of registration accuracy. Anisotropic error offers a concise overall performance score and helps diagnose orientation biases or weaknesses in the registration algorithm. Furthermore, the evaluation is conducted under two different conditions: using the original point cloud (noise-free) and using a point cloud corrupted by synthetic noise, thus assessing the robustness of each method.

[0029] As shown in Table 1, under noise-free point cloud conditions, compared to the traditional ICP, GFO-ICP exhibits significantly lower values ​​(anisotropic R: 0.005, T: 0.0; isotropic R: 0.008, T: 0.3). In contrast, the standard ICP has an anisotropic rotation error of 0.934, a translation error of 0.023, and corresponding isotropic errors of 1.32 and 69.633, respectively. GFO-ICP not only significantly outperforms the standard ICP, but its variants, Robust ICP and Fast ICP, also show larger errors, particularly in translation. Compared to the deep learning method Rpmnet, GFO-ICP demonstrates a clear advantage. Rpmnet produces the largest error among all tested methods. GFO-ICP, with its isotropic rotation and translation errors, not only significantly outperforms the standard ICP, but its variants, Robust ICP and Fast ICP, also show larger errors. Compared to the deep learning method Rpmnet, GFO-ICP shows a clear advantage. Rpmnet produced the largest error among all testing methods, with isotropic rotation and translation errors of 2.22 and 142.8, respectively.

[0030] Crucially, experiments with noise highlight the robustness of our proposed algorithm. While adding noise typically increases the error of all methods, GFO-ICP maintains its high accuracy and significantly outperforms baseline techniques. In contrast, other methods, including Robust ICP and Rpmnet, exhibit more significant performance degradation. Comparisons with and without noisy point clouds demonstrate that our invention can better achieve high-precision registration in complex scenes, effectively addressing the problem that workpiece deformation caused by manufacturing errors leads to deviations from design expectations in assembly characteristics. Traditional modeling methods, due to the accumulation of errors from multiple stages, struggle to establish high-precision dual models.

[0031] In the feature matching and binding stage, by adjusting the cosine similarity threshold and through manual statistics and calculation, the matching accuracy was 100% on the 27 feature surfaces of the three-part segmentation, which is sufficient to prove the effectiveness of the method proposed in this invention. The visualization results are as follows: Figure 10 As shown.

[0032] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the solutions disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

Claims

1. A method for twin modeling deformable workpieces based on matching measurement point clouds with 3D CAD models, characterized in that, The steps are as follows: Step 1: Obtain the point cloud data of the CAD model and the measured point cloud data of the part; Step 2: Use statistical filtering algorithm to denoise the original measured point cloud data, output the denoised point cloud data, and perform voxel downsampling on the denoised point cloud data to reduce the data size; Step 3: Register the preprocessed measured point cloud data with the CAD model point cloud data of the part using the GFO-ICP algorithm, select the nearest point pairs that meet the geometric features, and use dynamic registration to adjust the iteration step size to obtain the registered point cloud data. Step 4: For the registered point cloud data, obtain the normal vector and curvature of each point through PCA, and filter candidate plane points based on the consistency of normal vectors and low curvature characteristics; perform Euclidean clustering classification on the candidate points based on kd-tree, and classify the points with spatial distance less than a set threshold into the same cluster to obtain surface data; Step 5: Based on the surface data obtained in Step 4, as well as the measured point cloud segmented surface and the CAD ideal surface, depth feature vectors are extracted using the PointNet++ network. The geometric features and depth features of each surface are then concatenated and fused in the last dimension to form a composite feature vector. Subsequently, pairwise cosine similarity matching is performed on the feature vectors of all measured surfaces and CAD surfaces to establish an accurate correspondence, realize feature matching and binding functions, complete the surface-level matching from the segmented region to the CAD model, and realize workpiece modeling.

2. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 1, characterized in that, In step three, the preprocessed measured point cloud data and the CAD model point cloud data of the part are registered using the GFO-ICP algorithm, including: Step 3-1: Obtain the point cloud data from Step 2, and use the KD-Tree search method and Euclidean distance to search for the nearest point pair between the measured point cloud data and the CAD model point cloud data; Step 3-2: Based on Step 3-1, obtain the geometric feature normal vectors of the point cloud. and curvature Filter out the closest point pairs whose normal vector angle and curvature difference are less than a set threshold; Step 3-3: Based on the nearest point pairs selected in Step 3-2, a dynamic step size adjustment mechanism is introduced to adjust the registration iteration. The goal of the iteration is to find the optimal rotation matrix R and translation vector t such that the sum of the squares of the Euclidean distances of the nearest point pairs between the measured point cloud and the target point cloud is minimized. The step size is dynamically updated based on the iteration change of the error. By adjusting the step size according to the error changes, the optimal transformation parameters and the transformed point cloud can be obtained.

3. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 2, characterized in that, In step 3-2, the filtering criteria for the nearest point pair are: In the formula, They are a pair of closest points , , It is the angle between the normal vectors. and They are and The curvature point, and The threshold is used to control the strictness of normal vector consistency and curvature similarity.

4. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 2, characterized in that, In step 3-3, the objective function error for each iteration is: In the formula, It is the number of matching point pairs. and It is the first The rotation and translation parameters for the next iteration; Error rate, i.e., error change, is: when A larger value indicates that the current step size is too large and needs to be reduced. If the value is small and tends to be stable, increase the step size to accelerate convergence; initial step size ,but Iteration step size Updated to: In the formula, It is the step size adjustment factor. It is the threshold for the error rate, used to determine whether the step size needs to be adjusted.

5. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 1, characterized in that, Step four includes: Step 4-1: First, calculate the normal vector and curvature of each point in the point cloud. The normal vector reflects the local orientation information of the point cloud surface, while the curvature describes the degree of curvature of the surface. For a point... Its normal vector The curvature is obtained by finding the eigenvector corresponding to the smallest eigenvalue of the covariance matrix using PCA. The calculation is performed by taking the ratio of the smallest eigenvalue to the sum of all eigenvalues. Then, based on the consistency of the normal vector and the low curvature characteristic, points that may belong to the plane are selected. The selection formula is as follows: ； ； In the formula It is the normal vector of point i. Let i be the curvature of point i. Based on the consistency of the normal vector and the low curvature characteristic, points that may belong to this plane can be selected. Step 4-2: Construct a kd-tree for the selected planar points in Step 1 to accelerate the nearest neighbor search. Use Euclidean clustering algorithm to segment the point cloud into several independent planar regions, and group the points with a distance less than a specified threshold. The points are grouped into the same cluster, and the above process is repeated until all points are assigned to a cluster or labeled as noise. By combining geometric feature filtering and spatial distance clustering, multiple planar regions in the point cloud are extracted.

6. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 1, characterized in that, In step five, the feature matching and binding steps are as follows: Step 5-1: Input the segmented surface regions of the measured point cloud obtained in Step 4 and their corresponding surfaces in the CAD model into the PointNet++ model for depth feature extraction, and output a 256-dimensional high-dimensional feature vector for each surface region. ; Step 5-2: To enhance the representational ability of the features, obtain the centroid of each surface region. Center of mass This represents the average position of the surface in space. Principal component analysis (PCA) is used to obtain the eigenvalues ​​of the covariance matrix of the surface point cloud, thus yielding the flatness characteristics. ; measures the degree to which the surface region is nearly flat, and the radius of the surface region. :radius For all points in the surface region to their centroid The maximum value of the distance represents the spatial extent of the surface; Step 5-3: Extract the high-dimensional feature vector from Step 5-1. and the three geometric features obtained in step 5-2 , , The last dimension is concatenated to return the fused 261-dimensional hybrid features. ; Step 5-4: Combine the fused feature vector of the i-th surface of the measured point cloud obtained in Step 5-3. The fused feature vector of the j-th surface of the CAD model Cosine similarity is calculated, with the result ranging from [-1, 1]. The closer the value is to 1, the more similar the two vectors are. For each surface i of the measured point cloud, all surfaces j of the CAD model are traversed to find the match with the highest similarity. The measured surface i and the ideal surface are then output. Establish a one-to-one matching relationship.

7. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 6, characterized in that, In step 5-2, the centroid The formula is: In the formula, where It is the surface The number of points on; flatness The formula is: In the formula , , These are the three eigenvalues ​​of the covariance matrix, satisfying... ; The maximum variance represents the variance of the main directions of the point cloud distribution. and Variance representing the secondary direction; The larger the value, the flatter the surface region. The smaller the value, the less flat the surface region is; The formula for obtaining the radius is: 。 8. The method for twin modeling of deformable workpieces based on matching measurement point clouds with 3D CAD models according to claim 7, characterized in that, In step 5-4: The formula for calculating cosine similarity is: In the formula, The fused feature vector of the i-th surface of the measured point cloud. Let be the fused feature vector of the j-th surface of the ideal CAD model. represents the inner product of vectors, and || represents the L2 norm of the vectors; Feature matching formula: In the formula, The surface represented by i in the ideal CAD model has the highest cosine similarity to the surface in the measured point cloud. Finally, the surface i of the observed point cloud is compared with the surface of the ideal point cloud. Matching.

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