A shape-space joint feature based curved surface profile monitoring method

Abstract

The present application relates to a kind of based on shape-space joint feature's curved surface profile monitoring method, comprising obtaining point cloud data, the Laplace-Beltrami spectrum of workpiece is calculated as curved surface feature data, point cloud data is segmented into block point cloud with several different sizes, the minimum geodesic distance of any two point groups in block point cloud is calculated, space geodesic distance matrix is constructed, the statistical size is selected as the lowest Greary's G index by calculating, the clustering degree of each block point cloud is calculated according to statistical size;According to the Hotelling's T 2 statistic of each block point cloud is calculated according to clustering degree and Laplace-Beltrami spectrum, to detect abnormal curved surface.The method of the present application detects the slight change of workpiece surface by using the rich information in point cloud, and realizes the monitoring of workpiece surface quality change.

Description

Technical Field

[0001] This invention belongs to the field of surface monitoring technology, specifically relating to a surface contour monitoring method based on shape-space joint features. Background Technology

[0002] With the application and development of high-precision optical measurement and sensing technologies, the measurement of curved surfaces has moved from traditional single-point and segment measurement to high-density point cloud and full-contour measurement. For example, the widely used laser triangulation measuring instrument and high-precision composite 3D laser scanner can generate hundreds of thousands of point cloud data in tens of seconds to characterize the 3D curved surface contour of the entire workpiece.

[0003] Surface profile quality is a crucial indicator of workpiece machining quality. It reflects the impact of various factors such as equipment precision, raw material composition, and processing techniques on the workpiece during machining. Therefore, monitoring changes in surface profile quality can more accurately identify whether workpiece machining quality characteristics are within controllable limits. Current surface profile monitoring methods mainly include using tensor regression-based multivariate linear algebra methods to model and monitor the structure of point cloud data, and monitoring after converting 3D point clouds into 2D images. These methods only monitor a single variable, merely extracting discrete key quality characteristics from the surface point cloud, failing to fully utilize the rich intrinsic information of the point cloud, and thus unable to detect minor quality defects or faults. Furthermore, there is a strong spatial correlation between points in the surface point cloud, which existing methods cannot reflect. Therefore, false positives or false negatives often occur during monitoring, significantly impacting the workpiece manufacturing process.

[0004] Current commonly used surface contour monitoring methods are based on parametric modeling. This involves embedding point cloud data into their two-dimensional manifold space, inputting vectors to obtain low-dimensional manifold parameterization, and then monitoring the parametric model. Compared to traditional methods, this approach can describe changes in workpiece shape, but it requires registration of the surface point cloud before monitoring, resulting in high computational costs. Furthermore, its parametric model only considers changes in workpiece shape and does not account for the spatial correlation of the workpiece surface point cloud, making it unable to accurately monitor changes in workpiece processing quality. Therefore, a detection method is needed that can combine the spatial correlation of the workpiece surface point cloud to determine whether the surface contour is qualified. Summary of the Invention

[0005] Based on the aforementioned shortcomings and deficiencies in the prior art, one of the objectives of this invention is to at least solve one or more of the aforementioned problems in the prior art. In other words, one of the objectives of this invention is to provide a surface contour monitoring method based on shape-space joint features that satisfies one or more of the aforementioned requirements.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A surface contour monitoring method based on shape-space joint features, the method includes the following steps:

[0008] S1. Obtain point cloud data of the workpiece surface;

[0009] S2. Calculate the Laplace-Beltramian spectrum of the workpiece surface based on the point cloud data, and select the average value of the first few values ​​of the Laplace-Beltramian spectrum as the surface feature data of the workpiece surface.

[0010] S3. Divide the point cloud data into block point clouds using several different sizes;

[0011] S4. Calculate the minimum geodesic distance between any two point groups in the segmented point cloud, and construct a spatial geodesic distance matrix based on the minimum geodesic distance.

[0012] S5. Calculate Greary's C index for each block of point cloud based on the spatial geodesic distance matrix;

[0013] S6. Select the size of the point cloud block with the lowest Greary's C index as the statistical size, and calculate the clustering degree of each point cloud block based on the statistical size.

[0014] S7. Calculate the Hotelling's T for each point cloud segment based on the clustering degree and the Laplace-Beltramm spectrum. 2 Statistic;

[0015] S8, according to Hotelling's T 2 The statistical test revealed anomalies in the surface.

[0016] As a preferred embodiment, the steps following step S1 and before step S2 include:

[0017] S11. Remove outliers and redundant points from the point cloud data.

[0018] As a preferred option, step S2 specifically includes the following steps:

[0019] S21. Generate the corresponding surface model based on each point cloud data;

[0020] S22. Define the surface of the surface model as a Riemannian manifold;

[0021] S23. Calculate the Laplace-Beltramm spectrum of each point cloud data based on the Riemannian manifold;

[0022] S24. Select the average of the first few values ​​in the Laplace-Beltramm spectrum of each point cloud data as the surface feature data of the workpiece surface corresponding to the point cloud data.

[0023] As a further preferred option, in step S24, the average value of the first 50 values ​​in the Laplace-Beltramm spectrum of each point cloud data is selected as the surface feature data of the workpiece surface.

[0024] As a preferred embodiment, the steps following step S5 and before step S6 include:

[0025] S51. Calculate the z-test value of each point cloud block based on the spatial geodesic distance matrix, and delete the point cloud block sizes whose z-test values ​​are lower than the preset value.

[0026] As a preferred option, step S8 specifically includes:

[0027] S81, according to Hotelling's T 2 Hotelling's T Statistical Generation 2 Control charts;

[0028] S82, according to Hotelling's T 2 The control chart detected an abnormal surface.

[0029] 7. A surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that,

[0030] In step S3, the dimensions include 5×5mm, 10×10mm, 15×15mm, 20×20mm, 25×25mm, 30×30mm, 35×35mm, 40×40mm, 45×45mm, and 50×50mm.

[0031] Compared with the prior art, the beneficial effects of this invention are:

[0032] The method of this invention utilizes the rich information inherent in point clouds to detect minute changes on the workpiece surface, thereby enabling monitoring of changes in workpiece surface quality.

[0033] The method of this invention eliminates the traditional registration step before surface monitoring, reduces the time for point cloud preprocessing, and lowers the cost of surface monitoring. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of a segmented point cloud according to an embodiment of the present invention;

[0035] Figure 2 This is a line graph of Greary's C-index of the segmented point cloud according to an embodiment of the present invention;

[0036] Figure 3 This is a Hotelling's T of the segmented point cloud in an embodiment of the present invention. 2 Control chart. Detailed Implementation

[0037] To more clearly illustrate the embodiments of the present invention, specific implementation methods will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0038] Example: This example provides a surface contour monitoring method based on shape-space joint features, specifically including the following steps:

[0039] First, execute S1 to acquire point cloud data of the workpiece surface. The point cloud data can be acquired using a laser scanning camera. In this embodiment, ten curved surfaces are artificially generated using MATLAB as hypothetical workpiece surfaces, so that subsequent steps can use these ten curved surfaces to illustrate the specific implementation of the present invention.

[0040] The ten generated point clouds are Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, and Q10, respectively. The surface point cloud model is shown below. Figure 1 As shown. The curvature of surfaces Q1-Q8 has slight variations, but is still within a controlled range; the curvature of surface Q9 is significantly different from that of surfaces Q1-Q8, and is out of control; although the curvature of surface Q10 is similar to that of surfaces Q1-Q8, it has a hole with a radius of 20mm, and is therefore also out of control.

[0041] Furthermore, after step S1, step S11 is also included: removing outliers and redundant points from each point cloud data to improve surface accuracy and eliminate scanning errors.

[0042] S2. After obtaining the point cloud data, use the linear finite element method to calculate the Laplace-Beltramm spectrum of the corresponding workpiece surface based on the point cloud data.

[0043] Point cloud data cannot be directly used in the linear finite element method for curved surfaces. This embodiment provides an implementation method for step S2, including the following steps:

[0044] S21. Generate a corresponding surface model based on each point cloud data. Use the meshing function in engineering modeling software such as SolidWorks to connect the point cloud data to generate a triangular mesh. Then, use the surface generation function to fit the triangular mesh into a surface model.

[0045] S22. Read the surface model file and define the surface as a Riemannian manifold. ;

[0046] S23. Calculate the Laplace-Beltramm spectrum of each point cloud data based on the Riemannian manifold;

[0047] Specifically, the Laplace-Beltrami spectrum in step S23 is calculated as follows: The Riemannian manifold is obtained. Helmholtz equations on The set of eigenvalues This is the Laplace-Beltrami spectrum of a curved surface.

[0048] Therefore, the Helmholtz equation can be transformed using the Galerkin variational formula:

[0049] ,in It is a surface element on the manifold.

[0050] because ,in For the manifold surface metric tensor, A linear combination of N shape functions:

[0051] .

[0052] Finally obtained .

[0053] Representing it as a generalized eigenvalue problem in matrix form: ,in and The Laplace-Beltrami spectrum can be obtained by solving for matrices A and B.

[0054] The process of solving matrices A and B is as follows:

[0055] The surface is divided into several triangular meshes, and the local coordinates are first parametrically described by three special coordinates (the special coordinates are respectively...). A specific triangle is formed by ( ), and the coordinates of the points in this triangle are ( ). ,in .

[0056] Calculate the metric tensor of this plane. First, calculate the partial derivatives of the two vertices P2 and P3 of this triangle in the u and v directions. ;

[0057] Then the components of the planar metric tensor are obtained. ;

[0058] The metric tensor of the plane is thus calculated. .

[0059] Calculate the shape function of the three points on the triangle above. The expression for the shape function is: The shape function of point P1 For example, it only takes the value 1 at P1, and takes the value 0 elsewhere.

[0060] Therefore, the following system of equations can be obtained. ;

[0061] Solving for the results The shape function of point P1 is obtained. .

[0062] Similarly, the shape function of point P2 can be obtained. The shape function of point P3 .

[0063] Consider ordinary points on the surface , , The triangular plane formed by this process transforms ordinary point coordinates into special coordinates through surface parameterization:

[0064] .

[0065] in Planar metric tensor components ,get .

[0066] At this point, matrices A and B become:

[0067] ;

[0068] .

[0069] Substitute the above matrices A and B The Laplace-Beltrami spectrum can then be calculated.

[0070] After obtaining the Laplace-Beltrami spectrum, step S24 is executed: the average of the first few values ​​in the Laplace-Beltrami spectrum of each point cloud data is selected as the surface feature data of the workpiece surface corresponding to the point cloud data. In this embodiment, the average of the first 50 values ​​is selected.

[0071] Based on the point cloud data of Q1-Q10 above, the obtained Laplace-Beltrami spectra are 0.005069837, 0.005092308, 0.005114155, 0.00513565, 0.00513565, 0.005227028, 0.005274232, 0.00531914, 0.005913554, and 0.005913554, respectively.

[0072] After the Laplace-Beltrami spectrum calculation in step S2 is completed, step S3 is executed to divide the point cloud data into block point clouds of several different sizes. In this embodiment, the division sizes are 5×5mm, 10×10mm, 15×15mm, 20×20mm, 25×25mm, 30×30mm, 35×35mm, 40×40mm, 45×45mm, and 50×50mm.

[0073] S4. Calculate the minimum geodesic distance between any two point groups in the segmented point cloud, and construct a spatial geodesic distance matrix from all the minimum geodesic distance data.

[0074] Specifically, when calculating the minimum geodesic distance between each block, the centroid of each point group is used as the feature point, and the distance between the centroids of the point group is used as the point group distance.

[0075] S5. Calculate the Greary's C exponent for each point cloud segment based on the minimum geodesic distance data in the aforementioned spatial geodesic distance matrix. The Greary's C exponents for point clouds of various sizes are as follows: Figure 2 As shown, the following method is used for calculation:

[0076] ,in The number of blocks in the point cloud. This is the geodesic distance matrix. It is the index of any two blocks in the point cloud. The first Block, number Clustering degree of point clouds; , It is the aggregation degree of the entire point cloud.

[0077] In addition, to further screen point clouds with significant spatial correlation, step S51 is included after step S5: calculating the z-test value of each point cloud block and deleting block sizes with z-test values ​​lower than a preset value. When the Z-test value is greater than 1.96, the spatial correlation of the point cloud segment is considered significant, and point clouds with Z-test values ​​less than 1.96 are deleted.

[0078] S6. Select the size of the point cloud segment with the lowest Greary's C exponent as the statistical size, and calculate the clustering degree of each point cloud segment based on the statistical size. In the Q1-Q10 surface of the above example, select the segment size with the smallest Greary's C exponent, i.e., 15×15mm, to calculate the clustering degree of the point cloud segments.

[0079] Clustering degree is calculated using the following method:

[0080] ,in , The size of the entire point cloud is , , The size of each small block after the dot cloud is divided is , For all points in the point cloud, This indicates the number of small blocks that fall within it. Indicates the total number of blocks. This refers to the number of points within each small block after the point cloud is divided into blocks. This represents the block index, i.e., the index located in the point cloud. OK Small blocks in a column.

[0081] After calculating the Laplace-Beltrami spectrum and clustering degree, proceed to step S7: calculate Hotelling's T for each block of point cloud based on the clustering degree and the Laplace-Beltrami spectrum. 2 Statistics.

[0082] Specifically, Hotelling's T 2 Statistic ,in For sample size, Let be the sample mean of the t-th sample. and Let be the mean vector and covariance matrix under controlled conditions.

[0083] Finally, execute step S8, according to Hotelling's T 2 Statistical analysis revealed anomalous surface block point clouds. Specifically, the detection was performed using the following method:

[0084] S81, according to Hotelling's T 2 Statistics generation such as Figure 3 The Hotelling's T shown 2 Control charts;

[0085] S82, according to Figure 3 Hotelling's T 2 Control charts identify outliers, thereby detecting patch point clouds with anomalous surfaces. Figure 3 Based on the broken line detection, Q9 and Q10 were identified as abnormal surfaces.

[0086] It should be noted that the above embodiments are merely detailed descriptions of preferred embodiments and principles of the present invention. For those skilled in the art, there may be changes in specific implementation methods based on the ideas provided by the present invention, and these changes should also be considered within the scope of protection of the present invention.

Claims

1. A method for monitoring surface contours based on shape-space joint features, characterized in that, The method includes the following steps: S1. Obtain point cloud data of the workpiece surface; S2. Calculate the Laplace-Beltramian spectrum of the workpiece surface based on the point cloud data, and select the average value of the first few values ​​of the Laplace-Beltramian spectrum as the surface feature data of the workpiece surface. S3. Divide the point cloud data into block point clouds using several different sizes; S4. Calculate the minimum geodesic distance between any two point groups in the segmented point cloud, and construct a spatial geodesic distance matrix based on the minimum geodesic distance; S5. Calculate Greary's C index for each of the segmented point clouds based on the spatial geodesic distance matrix; S6. Select the size of the point cloud segment with the lowest Greary's C index as the statistical size, and calculate the clustering degree of each point cloud segment based on the statistical size. S7. Calculate the Hotelling's T for each of the segmented point clouds based on the clustering degree and the Laplace-Beltramian spectrum. 2 Statistic; S8, according to the Hotelling's T 2 The statistical test revealed anomalies in the surface. Step S2 specifically includes the following steps: S21. Generate a corresponding surface model based on each point cloud data; S22. Define the surface of the surface model as a Riemannian manifold; S23. Calculate the Laplace-Beltramm spectrum of each point cloud data according to the Riemannian manifold; S24. Select the average of the first few values ​​in the Laplace-Beltramm spectrum of each point cloud data as the surface feature data of the workpiece surface corresponding to the point cloud data; The Greary's C exponent of the segmented point cloud is calculated using the following method: ,in The number of blocks in the point cloud. This is the geodesic distance matrix. It is the index of any two blocks in the point cloud. The first Block, number Clustering degree of point clouds; , It is the clustering degree of the entire point cloud.

2. The surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that, The steps following step S1 and before step S2 include: S11. Remove outliers and redundant points from the point cloud data.

3. The surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that, In step S24, the average value of the first 50 values ​​in the Laplace-Beltramm spectrum of each point cloud data is selected as the surface feature data of the workpiece surface.

4. The surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that, The steps following step S5 and before step S6 include: S51. Calculate the z-test value of each block point cloud according to the spatial geodesic distance matrix, and delete the block size of the point cloud with a z-test value lower than the preset value.

5. The surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that, Step S8 specifically includes: S81, according to the Hotelling's T 2 Hotelling's T Statistical Generation 2 Control charts; S82, according to the Hotelling's T 2 The control chart detected an abnormal surface.

6. The surface contour monitoring method based on shape-space joint features as described in claim 1, characterized in that, In step S3, the dimensions include 5×5mm, 10×10mm, 15×15mm, 20×20mm, 25×25mm, 30×30mm, 35×35mm, 40×40mm, 45×45mm, and 50×50mm.

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