Part surface contour reconstruction method based on global fitting optimization

Abstract

The invention belongs to the technical field of high-precision scanning intelligent equipment, and particularly relates to a part surface contour reconstruction method based on global fitting optimization. A high-precision three-dimensional contour is generated for fitting of a large free-form surface, firstly, a preliminary curved surface is generated by adopting a curved surface contour fitting optimization algorithm according to data acquired based on a laser two-way point cloud scanning technology, then smoothing processing of the curved surface contour is realized based on a fairing optimization algorithm, and finally, the generated curved surface is evaluated. And if the precision is within the deviation range, taking the curved surface as a final curved surface. The fairing optimization algorithm is put forward to carry out overall fairing processing on the fitted initial curved surface from the overall situation aiming at the condition that the curved surface is in non-fairing forms such as local unevenness, violent normal vector jitter and overlarge curvature change, and the high-precision fitting requirement of the large free-form curved surface can be met.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-precision scanning intelligent equipment, and particularly relates to a method for reconstructing the surface contour of parts based on global fitting optimization. Background Art

[0002] In the field of industrial manufacturing, such as the processing, grinding, non-destructive testing, measurement, and equipment of large metal parts, there is a need for 3D modeling and positioning of workpieces. Based on the need for non-destructive testing of large free-form surface parts, such as propeller blades and turbine blades, the present technology develops a method for reconstructing the surface contour of parts by laser scanning to meet the high-precision positioning requirements for automatic detection of irregular parts during automatic detection. This technology is also applied to the processing, grinding, non-destructive testing, measurement, and equipment of any other irregular parts to achieve the three-dimensional space positioning function during the implementation of the system.

[0003] Currently, for the fitting of large free-form surfaces, such as propeller blades and turbine blades, surface skinning technology is usually used to generate surfaces, but it often encounters the situation where the cross-sectional line family used to express the surface shape is uneven. The present invention mainly solves two types of problems: 1) fitting a high-precision contour surface of the object to be detected based on a series of spatially discrete points; 2) the surface presents non-smooth forms such as local concavity and convexity, severe jitter of normal vectors, and excessive curvature changes. Summary of the Invention

[0004] Aiming at the problems to be solved in generating high-precision three-dimensional contours by fitting large free-form surfaces, the present invention proposes a method for reconstructing the surface contour of parts based on global fitting optimization on the basis of the least squares method. Aiming at non-smooth forms such as local concavity and convexity, severe jitter of normal vectors, and excessive curvature changes on the surface, a smoothing optimization algorithm is proposed to perform overall smoothing processing on the initially fitted surface from a global perspective, which can meet the high-precision fitting requirements of large free-form surfaces.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for reconstructing the surface contour of parts based on global fitting optimization, for generating high-precision three-dimensional contours by fitting large free-form surfaces. First, a preliminary surface is generated by using a surface contour fitting optimization algorithm according to the data obtained by the laser bidirectional point cloud scanning technology, then the smoothing processing of the surface contour is realized by using a smoothing optimization algorithm, and finally the generated surface is evaluated. If the accuracy is within the deviation range, the surface is used as the final surface.

[0007] The specific steps are as follows:

[0008] (1) Obtain large free-form surface contour data: Obtain the real-time data of the Renishaw probe and the ranging probe; Generate a scanning strategy, create scanning path and sampling interval data; Execute the generation of scanning contour data and save the rough contour point cloud data;

[0009] (2) Calculate and generate the initial surface data: Execute the operation of loading the rough contour point cloud data; Judge the construction of the constraint condition set data, including one-to-one correspondence, shape similarity, and fairness constraints; Execute the solution of the parameter values of the data points on the initial surface; Execute the establishment of an overdetermined linear equation system and use the Householder transformation method to execute the solution; Execute the calculation of the error vector, compare and iterate the error threshold to generate the initial surface;

[0010] (3) Perform optimization processing on the initial surface and save the optimized data: Load the initial surface data and store it in the initial surface data repository; Execute the fairness constraint and curvature change constraint of the surface; Establish a simplified expression of the surface strain energy; Establish and solve the surface curvature change expression; Based on the surface strain energy change and curvature change, establish a generalized energy expression including the surface fairness criterion; Execute the solution of the surface fairness model to obtain the optimized data; Execute the construction of the evaluation benchmark, calculate the average error, and provide comprehensive deviation feedback; Execute the establishment of the tangent plane equation; Calculate the shortest distance from the sampling point to the surface; Execute the calculation of the surface fitting error and feedback the calculation evaluation result; Execute the storage of the optimized surface data.

[0011] By performing constraint processing on the surface fairness and curvature change, the contour data collected is converted into optimized ideal surface information; The surface fairness constraint condition set is used for the centralized storage of constraint condition data, including position constraint conditions and boundary constraint conditions. The position constraint conditions are used to ensure the approximation accuracy of the surface to the original data points, and the boundary constraint conditions are used to ensure that the boundary conditions of the surface along the isoparametric line direction remain unchanged during the surface fairness processing; Establish a simplified surface strain energy model, which has good calculation stability and fairness, and realizes the surface fairness constraint function through this model; Establish a surface curvature change model, which uses the second-order difference of the surface curvature along the double isoparametric directions to represent the two partial derivatives of the surface curvature, and solves the partial derivatives by fitting the surface expression. The curvature change constraint function is realized through this model;

[0012] Based on the surface fairness constraint and curvature change constraint models, solve the surface fairness model. Use the quadratic programming method with linear constraints with the surface control vertices as variables to execute the solution calculation of the model expression, establish a surface optimization model including the surface fairness constraint criterion, and realize the optimization calculation of the surface result.

[0013] Perform quality evaluation and comprehensive error optimization calculation on the surface generated by fitting operation, determine the surface fitting accuracy by collecting sampling points to evaluate the distance error, and feedback the evaluation result of the overall deviation of the fitting surface; perform the establishment of the evaluation benchmark, construct the tangent plane equation of the fitting surface passing through the corresponding points on the fitting surface after matching the plane projection points of the collected points, and solve the tangent plane equation by substituting the normal vector of the corresponding points for calculation to obtain the evaluation benchmark model; establish the tangent plane equation, and the coordinate set of the collected points is P i (x i ,y i ,z i ), obtain the corresponding point set P0(x0, y0, z0) on the surface according to its projection point on the XOY plane, and then make a tangent plane of the surface through the P0 set, and the normal vector is the partial derivative of the surface with respect to (x0, y0, z0), and the obtained tangent plane equation is:

[0014] F x0 (X - x0)+F y0 (Y - y0)+F z0 (Z - z0)=0;

[0015] Calculate the shortest distance from the sampling point to the fitting surface; the straight line equation perpendicular to the tangent plane passing through the point set P i is:

[0016]

[0017] The projection point set of the point set P i to the tangent plane is P i ′(x′ i , y ′ i ,z′ i ), then the distance (i.e., the deviation value) from the point set P i to the point set P i ′ is:

[0018]

[0019] Calculate the overall fitting error of the surface; calculate the fitting error of the surface based on the average error;

[0020]

[0021] When the fitting deviation meets the detection requirements, the surface generated by fitting is the contour of the scanned part.

[0022] The beneficial effects achieved by the present invention are:

[0023] The two-way laser probe is combined with a ranging probe to achieve rapid acquisition of three-dimensional point cloud data of the contour through optimal fitting and trajectory planning. The teaching scanning measurement accuracy is better than ±0.5 cm. A least squares problem is constructed to find the optimal matching coordinate system, and a multi-function surface fitting algorithm based on the weighted least squares method and an energy method surface fairing algorithm are combined to generate the workpiece contour surface. The surface fitting error is not greater than 1 mm. The surface fitting technology is evaluated and optimized under the quadratic basis. The partial derivative is calculated through the collected points and the tangent plane, and then the surface fitting deviation is calculated based on the tangent plane equation, the normal vector, and the projection point. Through optimization, it is ensured that the average distance from the data point set at an interval of 1 second to the surface W does not exceed 0.6 mm. Description of the Drawings

[0024] Figure 1 is the global surface optimization algorithm;

[0025] Figure 2 is the fitting surface evaluation and optimization algorithm;

[0026] Figure 3 is the system structure diagram;

[0027] Figure 4 is the overall process diagram;

[0028] Figure 5 is the rough contour data generation process;

[0029] Figure 6 is the initial surface generation process;

[0030] Figure 7 is the surface optimization process. Detailed Implementation Manner

[0031] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0032] The present invention designs two key technologies, namely, the global surface optimization algorithm and the fitting surface evaluation and optimization algorithm. At the same time, it designs a rough contour data generation module, an initial surface generation module, and a surface optimization module that cover the entire process of contour reconstruction. The following is the detailed content of the technical solution.

[0033] (1) Global Surface Optimization Algorithm

[0034] By performing constraint processing on the surface fairness and curvature change, the contour data acquired is converted into optimized ideal surface information. The global surface optimization tool includes: a surface fairness constraint condition set, a surface fairness constraint sub-module, a curvature change constraint sub-module, and an optimization result calculation sub-module;

[0035] Set of surface fairing constraint conditions: Used for centralized storage of constraint condition data, including position constraint conditions and boundary constraint conditions. The position constraint conditions are used to ensure the approximation accuracy of the surface to the original data points, and the boundary constraint conditions are used to ensure that the boundary conditions of the surface remain unchanged along the isoparametric line direction during the surface fairing process;

[0036] Surface fairing constraint sub-module: Used to establish a simplified surface strain energy model. The model has good calculation stability and fairing property, and realizes the surface fairing constraint function through this model;

[0037] Curvature change constraint sub-module: Used to establish a surface curvature change model. The model uses the second-order difference of the surface curvature along the bi-isoparametric direction to approximately represent the two partial derivatives of the surface curvature, and solves the partial derivatives by fitting the surface expression. The curvature change constraint function is realized through this model;

[0038] Optimization result calculation sub-module: Based on the surface fairing constraint and curvature change constraint models, solve the surface fairing model. Use the quadratic programming method with linear constraints with the surface control vertices as variables to perform the solution calculation of the model expression, establish a surface optimization model including the surface fairing constraint criterion, and realize the surface result optimization calculation function.

[0039] (2) Fitting surface evaluation and optimization algorithm

[0040] Used to perform quality evaluation and comprehensive error optimization calculation on the surface generated by the fitting operation. Determine the surface fitting accuracy by collecting sampling points to evaluate the distance error, and finally feedback the overall deviation evaluation result of the fitting surface; including an evaluation benchmark construction sub-module, an average error calculation sub-module, and a comprehensive deviation feedback sub-module.

[0041] Evaluation benchmark construction sub-module: Used to establish the evaluation benchmark. Construct the tangent plane equation of the fitting surface corresponding to the matching points of the plane projection points of the collection points on the fitting surface. Solve the tangent plane equation by substituting the normal vector of the corresponding points (for the fitting surface). Obtain the evaluation benchmark model; establish the tangent plane equation, and the coordinate set of the collection points is P i (x i , y i , z i ). Obtain the corresponding point set P0(x0, y0, z0) on the surface according to its projection points on the XOY plane, and then make the tangent plane of the surface through the P0 set. The normal vector Is the partial derivative of the surface with respect to (x0, y0, z0), and the obtained tangent plane equation is

[0042] F x0 (X - x0)+F y0 (Y - y0)+F z0 (Z - z0) = 0;

[0043] Average error calculation sub-module: used to calculate the shortest distance from the sampling point to the fitted surface; for the point set P i The equation of the line perpendicular to the tangent plane is

[0044]

[0045] Point set P i The set of projection points onto the tangent plane is P i ′(x′ i ,y′ i ,z′ i ), then the distance from the point set P i to the point set P i ′ (i.e., the deviation value) is

[0046]

[0047] Comprehensive deviation feedback sub-module: used to calculate the overall error of surface fitting; based on the average error, the fitting error of the surface can be calculated

[0048]

[0049] When the fitting deviation meets the detection requirements, the fitted surface is the contour of the scanned part.

[0050] (3) Structural description of each module

[0051] Rough contour data generation module (RFG): used to perform raw data acquisition and data normalization using sensors, obtain real-time data of Renishaw probes and ranging probes through the sensor data interface, and then create a scanning path and set sampling interval data through the scanning strategy generation sub-module. The generated data can be called by an external motion control system to achieve point cloud data acquisition and generation; the rough contour data generation module includes a sensor data interface, a scanning strategy generation sub-module, and a scanning contour generation sub-module;

[0052] Initial surface generation module (ICG): used to process the rough contour data and generate initial surface data; the initial surface generation module includes a rough contour data loading interface, a judgment constraint condition set, an initial surface parameter calculation sub-module, and an error calculation sub-module; among them, the rough contour data loading interface is used to perform data loading operations, the judgment constraint condition set includes one-to-one matching conditions, shape similarity conditions, and smoothness judgment conditions, the initial surface parameter calculation sub-module is used to solve the parameter values of data points on the initial surface, and the error calculation sub-module is used to establish an overdetermined linear equation system and use the Householder transformation method to perform the solution, as well as error vector calculation and error threshold comparison iteration;

[0053] Surface Optimization Module (CM): It is used to read the initial surface data, respectively call the global surface optimization tool and the fitting surface evaluation and optimization tool to perform fitting surface optimization and evaluation operations, and finally feedback the optimized surface data; the surface optimization module includes a data transmission interface, an initial surface data repository, and an optimized surface data repository;

[0054] To generate a high-precision three-dimensional contour for the fitting of a large freeform surface, first generate a preliminary surface using a surface contour fitting and optimization algorithm based on the data obtained by the laser bidirectional point cloud scanning technology, then perform smoothing processing of the surface contour using a fairing optimization algorithm, and finally evaluate the generated surface. If the accuracy is within the deviation range, the surface is used as the final surface for the next process. The following is a specific description of the implementation method:

[0055] (1) Profile Data Sampling

[0056] It is used to obtain the contour data of a large freeform complex surface; the content of each sub-step includes data channel construction, data framework construction, and data content generation in sequence.

[0057] 1.1 Data Channel Construction: Initialize the sensor interface to obtain real-time data of the Renishaw probe and the ranging probe;

[0058] 1.2 Data Framework Construction: Generate a sub-module through the scanning strategy to generate a scanning strategy and create scanning path and sampling interval data;

[0059] 1.3 Data Content Saving: Generate a sub-module through the scanning profile to execute the generation of scanning profile data and save the rough contour point cloud data.

[0060] (2) Initial Surface Generation

[0061] It is used to perform the calculation and generation of the initial surface data; the content of each sub-step includes rough data loading, constraint condition construction, initial surface parameter calculation, solution of overdetermined linear equations, and error comparison calculation in sequence.

[0062] 2.1 Data Loading: Call the rough contour data loading interface to execute the data loading operation;

[0063] 2.2 Constraint Condition Construction: Judge the construction of the constraint condition set data, including constraints such as one-to-one correspondence, shape similarity, and fairness;

[0064] 2.3 Initial Surface Parameter Calculation: Call the initial surface parameter calculation sub-module to execute the solution of the data points at the initial surface parameter values;

[0065] 2.4 Solution of Overdetermined Linear Equations: Call the error calculation sub-module to execute the establishment of overdetermined linear equations and use the Householder transformation method to execute the solution;

[0066] 2.5 Error comparison calculation: Perform error vector calculation and error threshold comparison iteration to generate the initial surface.

[0067] (3) Surface contour fitting optimization

[0068] Used to perform optimization processing on the initial surface and save the optimized data; the content of each sub-step includes data loading, global surface optimization, fitting surface optimization, and data storage in sequence.

[0069] 3.1 Data loading: Load the initial surface data and store it in the initial surface data repository;

[0070] 3.2 Global surface optimization: Call the global surface optimization tool to perform surface fairing constraint and curvature change constraint; call the surface fairing constraint sub-module to establish a simplified expression of the surface strain energy; call the curvature change constraint sub-module to establish and solve the surface curvature change expression; call the optimization result calculation sub-module to establish a generalized energy expression including the surface fairing criterion based on the surface strain energy change and curvature change; call the optimization result calculation sub-module to perform surface fairing model solution to obtain the optimized data;

[0071] 3.3 Fitting surface optimization: Call the fitting surface evaluation and optimization tool to perform evaluation criterion construction, average error calculation, and comprehensive deviation feedback; call the evaluation criterion construction sub-module to establish the tangent plane equation; call the average error calculation sub-module to calculate the shortest distance from the sampling point to the surface; call the comprehensive deviation feedback sub-module to perform surface fitting error calculation and feedback the calculation evaluation result.

[0072] 3.4 Data storage: Perform optimized surface data storage.

Claims

1. A method for reconstructing the surface profile of a part based on global fitting optimization, characterized in that: To generate a high-precision three-dimensional contour by fitting a large free-form surface, first, a preliminary surface is generated using a surface contour fitting optimization algorithm based on the data obtained by the laser bidirectional point cloud scanning technology. Then, a smoothing process of the surface contour is realized using a fairing optimization algorithm. Finally, the generated surface is evaluated. If the accuracy is within the deviation range, the surface is used as the final surface.

2. The method for reconstructing the surface profile of a part based on global fitting optimization according to claim 1, characterized in that: The specific steps are as follows: (1) Obtain the contour data of the large free-form surface: Obtain the real-time data of the Renishaw probe and the ranging probe; Generate a scanning strategy, create scanning paths and sampling interval data; Execute the generation of scanning contour data and save the rough contour point cloud data. (2) Calculate and generate the initial surface data: Execute the loading operation of the rough contour point cloud data; Judge the construction of the constraint condition set data, including one-to-one correspondence, shape similarity, and fairing constraint conditions; Execute the solution of the parameter values of the data points on the initial surface; Execute the establishment of an overdetermined linear equation system and use the Householder transformation method to execute the solution; Execute the calculation of the error vector and the comparison and iteration of the error threshold to generate the initial surface. (3) Perform optimization processing on the initial surface and save the optimized data: Load the initial surface data and store it in the initial surface data repository; Execute the surface fairing constraint and the curvature change constraint; Establish a simplified expression of the surface strain energy; Establish and solve the surface curvature change expression; Based on the surface strain energy change and the curvature change, establish a generalized energy expression including the surface fairing criterion; Execute the solution of the surface fairing model to obtain the optimized data. Execute the construction of the evaluation benchmark, the calculation of the average error, and the comprehensive deviation feedback; Execute the establishment of the tangent plane equation. Calculate the shortest distance from the sampling point to the surface; Execute the calculation of the surface fitting error and feedback the calculation evaluation result; Execute the storage of the optimized surface data.

3. The method for reconstructing the surface profile of a part based on global fitting optimization according to claim 2, characterized in that: By performing constraint processing on the surface fairing degree and the curvature change, the contour data collected is converted into optimized ideal surface information; The surface fairing constraint condition set is used for the centralized storage of constraint condition data, including position constraint conditions and boundary constraint conditions. Among them, the position constraint conditions are used to ensure the approximation accuracy of the surface to the original data points, and the boundary constraint conditions are used to ensure that the boundary conditions of the surface along the isoparametric line direction remain unchanged during the surface fairing process; Establish a simplified surface strain energy model, which has good calculation stability and fairing. The surface fairing constraint function is realized through this model; Establish a surface curvature change model. The model uses the second-order difference of the surface curvature along the double isoparametric directions to represent the two partial derivatives of the surface curvature, and solves the partial derivatives by fitting the surface expression. The curvature change constraint function is realized through this model; Based on the surface fairing constraint and the curvature change constraint models, the surface fairing model is solved. The model expression solution calculation is executed using the quadratic programming method with the surface control vertices as variables and linear constraints. A surface optimization model including the surface fairing constraint criterion is established to realize the optimized calculation of the surface result.

4. The method for reconstructing the surface profile of a part based on global fitting optimization according to claim 2, characterized in that: Perform quality evaluation and comprehensive error optimization calculation on the surface generated by the fitting operation. Determine the surface fitting accuracy by collecting sampling points to evaluate the distance error, and feedback the evaluation result of the overall deviation of the fitting surface; Establish the evaluation benchmark, construct the tangent plane equation of the fitting surface passing through the corresponding points on the fitting surface by matching the plane projection points of the collected points, and solve the tangent plane equation by substituting the normal vector of the corresponding points for calculation to obtain the evaluation benchmark model; Establish the tangent plane equation, and the coordinate set of the collected points is P i (x i , y i , z i ). Obtain the corresponding point set P0(x0, y0, z0) on the surface according to its projection point on the XOY plane, and then make a tangent plane of the surface through the P0 set. The normal vector is the partial derivative of the surface with respect to (x0, y0, z0), and the obtained tangent plane equation is: F x0 (X - x0) + F y0 (Y - y0) + F z0 (Z - z0) = 0; Calculate the shortest distance from the sampling point to the fitted surface; for the point set P i The equation of the line perpendicular to the tangent plane is: Point set P i The projected point set onto the tangent plane is P' i (x' i , y' i , z' i ), then the distance (i.e., the deviation value) from the point set P i to the point set P' i is: Calculate the overall error of the surface fitting; Calculate the fitting error of the surface based on the average error. When the fitting deviation meets the detection requirements, the surface generated by fitting is the contour of the scanned part.

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