CN112686799A - Annular forging section line extraction method based on normal vector and L1 median - Google Patents
Annular forging section line extraction method based on normal vector and L1 median Download PDFInfo
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Abstract
The invention provides a method for extracting a section line of an annular forging based on a normal vector and an L1 median, which comprises the following steps: carrying out down-sampling on the annular forging point cloud based on curvature to obtain a sampling point set; accurately selecting the neighborhood of the sampling points in the set in the source input point set; combining a normal vector-based projection operator with a local L1 median value to create an iterative shrinkage optimization model; performing iterative shrinkage on the accurately selected sampling points according to the created iterative shrinkage optimization model; and connecting the sampling points subjected to iterative shrinkage to obtain the section lines of the annular forging. The invention can directly process point cloud with a large amount of noise and extract the section line of the annular forging with higher precision.
Description
Technical Field
The invention relates to the technical field of computer graphic processing, in particular to a method for extracting section lines of an annular forging based on normal vectors and an L1 median.
Background
The annular forging is a basic component of various equipment, is widely applied in the fields of ships, nuclear power, aerospace and the like, and along with the development of science and technology, the requirement of industrial application on the production quality of the annular forging is higher and higher, and the performance and the quality of the annular forging are influenced when the geometric dimension of the annular forging in the forming process cannot reach the deformation amount required by the process, so that the annular forging is scrapped due to low precision, and the accurate control of the dimensional parameters of the annular forging has very important significance.
In the rolling process of the annular forging, the shape of the section line of the annular forging determines the key size of the annular forging, and the key size of the annular forging can be obtained by measuring the section line, so that the section line extraction in the rolling process of the annular forging is of great significance.
The cross-section line extraction algorithm of the annular forging at home and abroad mainly comprises the following four algorithms: a moving least squares method, a field-represented curve reconstruction method, a model-based curve reconstruction, and a skeleton extraction method. These methods extract curves from point clouds containing a small amount of noise. However, due to the strong interference environment of the ring rolling field, the point cloud data obtained by laser scanning contains a large amount of noise, and how to extract the section lines with higher precision from the point cloud containing a large amount of noise is a difficult problem.
Disclosure of Invention
Aiming at the difficulty in the extraction of the section lines of the annular forging, the point clouds are down-sampled according to the curvature, the projection operator based on the normal vector is combined with the local L1 median value, an iterative contraction optimization model of the sampling points is created, the sampling points are iteratively contracted, and then the sampling points are connected to obtain the section lines of the annular forging.
Specifically, the invention discloses a method for extracting a section line of an annular forging based on a normal vector and an L1 median, which comprises the following steps:
s1, down-sampling the annular forging point cloud based on curvature to obtain a sampling point set, wherein the method specifically comprises the following steps;
s11, constructing a local quadric surface of each data point in the annular forging point cloud, and taking the average curvature of the local quadric surface as the curvature of the point;
s12, calculating a curvature threshold value H of the annular forging point cloud, putting points with curvature values larger than the threshold value H into a large curvature value area, and putting points with curvature values smaller than the threshold value H into a small curvature value area;
s13, curvature sampling is conducted on the sampling points in the large curvature value area, average sampling is conducted on the sampling points in the small curvature value area, and a sampling point set I of the annular forging is obtained;
s2, accurately selecting the neighborhood of the sampling point in the source input point set, which comprises the following steps;
s21, obtaining a normal vector of each sampling point according to a principal component analysis method;
s22, selecting a source input point with the distance x from the sampling point in the source input point set smaller than the neighborhood radius h as an initial neighborhood point;
s23, calculating an included angle beta between the initial neighborhood point and a normal vector of the sampling point, selecting the initial neighborhood point with beta being less than or equal to 90 degrees as a final neighborhood point of the sampling point, and obtaining an accurate neighborhood of the sampling point;
s3, combining a projection operator based on a normal vector with a local L1 median value to create an iterative shrinkage optimization model, and specifically, the steps are as follows;
s31, obtaining a normal vector of the source input data point according to a principal component analysis method;
s32, obtaining a projection operator according to the normal vector of the source input data point:
where x is the sampling point, qjIs the jth neighbor, n, of the sample point in the source input point set JjIs qjThe corresponding consistent outward normal vector,
for projection operator, it is the projection point of sampling point on the tangent line of jth adjacent point in its source input point neighborhood, and this point is named as sampling pointPredicting points in a sample point neighborhood;
s33, adding shape control parameters into the projection operator to obtain the projection operator with controllable shape:
where s is a shape control parameter,
the neighborhood prediction points with controllable positions of sampling points;
s34, local L1 median definition according to L1 median theory:
the median of local L1 is defined as:
wherein the content of the first and second substances,
as a weight function, r is the distance between the sampling point and the source input point, and h is the neighborhood radius; x is the number ofiIs the ith sample point in the set of sample points I, qjIs the jth neighborhood point of the sampling point in the neighborhood of the source input point set J;
s35, combining the projection operator with the controllable shape with the local L1 median value to create an iterative shrinkage optimization model, wherein the expression is as follows:
wherein the content of the first and second substances,
as a weight function, r is the distance between the sampling point and the source input point, and h is the neighborhood radius; x is the number ofiIs the ith sampling point in the sampling point set I, s is the shape control parameter,
is the sampling point xiA projection point with controllable position on the tangent line of the jth neighborhood point of the neighborhood in the source input point set J;
s4, performing iterative shrinkage on the sampling points obtained in the step S2 according to an iterative shrinkage optimization model, wherein the specific steps are as follows;
s41, setting an iterative contraction stopping condition, and beginning to contract each point in the sampling point set;
s42, calculating a distribution metric value sigma of the contracted sampling points;
s43, judging whether the distribution metric value sigma of the sampling points meets the iterative contraction stopping condition, and if the distribution metric value sigma of the sampling points does not meet the iterative contraction stopping condition, performing the step S44; when the condition is satisfied, proceed to step S45;
s44, continuing to shrink each point in the sampling point set, and repeating the steps S42 and S43;
s45, stopping contraction of the sampling points, and finishing iterative contraction of the sampling points;
s5, connecting sampling points after iterative contraction to obtain section lines of the annular forging, and specifically comprising the following steps:
s51, connecting the sampling points after iterative contraction to construct a curve branch;
simply connecting sampling points which are obviously distributed in a curve to form a curve branch, roughly screening candidate sampling points from the rest sampling points, and screening and connecting the candidate sampling points by using a hard constraint rule to construct the curve branch;
s52, connecting the curve branches according to a connection rule to form a one-dimensional curve;
s53, smoothing the one-dimensional curve according to a quadrilateral subdivision rule and a Laplace smoothing theory to obtain a smooth one-dimensional curve;
and S54, projecting the smooth one-dimensional curve to a two-dimensional plane to obtain a section line of the annular forging.
Preferably, the specific steps of step S21 are as follows:
s211, constructing a covariance matrix of sampling points:
wherein q isjIs the source input point, k is the neighborhood number,
is the neighborhood mean of the sampling point; selecting a neighborhood of the sampling point from a source input point set J, and selecting a source input point with a distance sampling point less than a neighborhood radius h as a neighborhood point;
s212, calculating an eigenvalue and an eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is a normal vector of a sampling point;
s213, adjusting the directions of the normal vectors of the sampling points according to the minimum spanning tree theory to enable all the normal vectors to be consistent in direction.
Preferably, the specific steps of step S31 are as follows:
s311, constructing a covariance matrix of the source input data points:
wherein q isjIs the source input point, k is
The number of neighborhood points is the neighborhood average value of the source input point; selecting a neighborhood of the source input point from a source input point set J;
s312, calculating an eigenvalue and an eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is a normal vector of a sampling point;
and S313, adjusting the directions of the normal vectors of the source input points according to the minimum spanning tree theory to enable all the normal vectors to be consistent in orientation.
Preferably, the concrete solving step of the distribution metric σ of the sampling points in the step S41 is as follows:
p1, establishing a covariance matrix of the sampling points according to a principal component analysis method:
wherein the content of the first and second substances,
as a function of weight, xiIs the ith sample point, x, in the set of sample points IiIs sample point xiThe average value in the neighborhood of the sampling point set, at the moment, the neighborhood of the sampling point is selected from the sampling point set I, and the distance sampling point x is selectediOther sampling points smaller than the neighborhood radius h are neighborhood points; ciIs the sampling point xiThe covariance matrix of (a);
p2, obtaining a distribution metric value sigma of the sampling point according to the eigenvalue of the covariance matrix:
wherein λ isi 0，λi 1，λi 2Covariance matrix Ci3 of a characteristic value, and λi 0＜λi 1＜λi 2，σi＝σ(xi) Is the sampling point xiThe distribution metric value of (2).
Preferably, the step S53 is implemented as follows:
s531, for each node v1 except the head and tail points of each curve, calculating a corresponding included angle between the node v0 and the front node v2 and the rear node v0 and v2, and if the included angle is more than 50 degrees, performing one-dimensional Laplace smoothing on the node, namely v 1-v 0/4+ v1/4+ v 2/4;
s532, four-point interpolation subdivision is carried out on each curve until the longest subsection of the curve is smaller than a threshold value;
s533, carrying out down-sampling on the subdivided curve, namely, gradually taking out the next point from the first point as a sampling node, wherein the node just meets the condition that the distance between the node and the previous point is more than a threshold value; a smooth one-dimensional curve with substantially the same segment length is obtained.
Preferably, the interpolation subdivision method in step S532 is as follows: assuming that v0, v1, v2 and v3 are four points in succession on the curve, the rule for inserting new points is as follows: if neither v1 nor v2 is an endpoint, the new insertion point is v ═ v0+9v1+9v2-v 3)/16; if v1 is an endpoint, i.e., v1 has no point before: the new insertion point is v ═ 3v1+6v2-v 3)/8; if v2 is an endpoint, i.e., there is no point after v 2: the new insertion point is v ═ v0+6v1+3v 2)/8.
Preferably, the iterative shrinkage stop condition set in step S41 is that the distribution metric value σ of all sampling points is > 0.9.
Preferably, the connection rule in step S52 is: when only two head and tail points exist in a certain area range and the directions of the two branches are more than 155 degrees, the two branches are connected into a long branch; when there are three or more head and tail points in a certain area, the middle point of the head branch is solved and the nearest branch is moved to the middle point, the middle point of the tail point corresponding branch is solved and the nearest branch is moved to the middle point, and the two branches are connected into a long branch.
The invention has the following beneficial effects:
aiming at annular forging point cloud which is scanned by laser and contains a large amount of noise, the method provided by the invention can directly act on the point cloud and extract the section lines of the annular forging with higher precision.
Drawings
FIG. 1 is a flow chart of a method for extracting a section line of an annular forging based on a normal vector and an L1 median value;
FIG. 2 is a dimensional structure diagram of a third-order annular forging in accordance with an embodiment of the present invention;
FIG. 3 is an initial cloud point of a third order annular forging of the embodiments of the present invention;
FIG. 4 is a third order annular forging sampling point diagram according to an embodiment of the invention;
FIG. 5 is a diagram of the final position of the third-order ring forging sampling point iterative contraction in the embodiment of the invention;
FIG. 6 is a cross-sectional line drawing of a third order ring forging extracted according to an embodiment of the invention.
In the figure:
a first axial height dimension 1; a second axial height dimension 2; a third axial height dimension 3; a fourth axial height dimension 4; a third order annular forging 10.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings 1 to 6 and specific embodiments.
Specifically, as shown in fig. 1, the invention provides a method for extracting a section line of an annular forging based on a normal vector and an L1 median, which comprises the following steps:
s1, down-sampling the annular forging point cloud based on curvature to obtain a sampling point set, wherein the method specifically comprises the following steps;
s11, constructing a local quadric surface of each data point in the annular forging point cloud, and taking the average curvature of the local quadric surface as the curvature of the point;
s12, calculating a curvature threshold value H of the annular forging point cloud, putting points with curvature values larger than the threshold value H into a large curvature value area, and putting points with curvature values smaller than the threshold value H into a small curvature value area;
the curvatures of the point clouds of the annular forging are respectively concentrated in two sections of numerical value ranges, the curvatures at the corners of the annular forging are concentrated in one section of a higher numerical value range and marked as A, and the point clouds curvatures at other places are concentrated in the other section of a lower numerical value range and marked as B. There is a large difference in the two-stage values. And selecting the minimum value in the A value section and the maximum value in the B value section, calculating the average value of the minimum value and the maximum value as a curvature threshold value H, putting the point with the curvature value larger than the threshold value H into a large curvature value area, and putting the point with the curvature value smaller than the threshold value H into a small curvature value area.
S13, curvature sampling is conducted on the large curvature value area, average sampling is conducted on the small curvature value area, and a sampling point set I of the annular forging is obtained.
The down-sampling method selected by the invention is utilized to carry out down-sampling, so that sampling points containing more detailed characteristics of the annular forging can be obtained. The dimensional structure diagram of the third-order annular forging is shown in the attached drawing 2, the complete point cloud of the third-order annular forging is shown in the attached drawing 3, and the sampling point of the third-order annular forging is shown in the attached drawing 4.
S2, accurately selecting the neighborhood of the sampling point in the source input point set, which comprises the following steps;
the accurate selection of the sampling points in the neighborhood of the source input point set is the basis for ensuring the accurate contraction of the sampling points.
S21, obtaining a normal vector of each sampling point according to a principal component analysis method;
s211, constructing a covariance matrix of sampling points:
wherein q isjIs the source input point, k is the neighborhood
The number of points is the neighborhood mean of the sampling points. At the moment, the neighborhood of the sampling point is selected from the source input point set J, and the source input point with the distance from the sampling point less than the neighborhood radius h is selected as the neighborhood point.
S212, calculating the eigenvalue and the eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is the normal vector of the sampling point.
S213, adjusting the directions of the normal vectors of the sampling points according to the minimum spanning tree theory to enable all the normal vectors to be consistent in direction. And then accurately selecting a neighborhood of the sampling point according to two conditions of a normal vector and an Euclidean distance of the sampling point.
S22, selecting the source input points with the distance x smaller than the neighborhood radius h from the source input point set as initial neighborhood points.
S23, the included angle between the initial neighborhood point and the normal vector of the sampling point is beta, the initial neighborhood point with beta being less than or equal to 90 degrees is selected as the final neighborhood point of the sampling point, and the two conditions simultaneously meet the requirement of obtaining the accurate neighborhood of the sampling point.
S3, combining a projection operator based on a normal vector with a local L1 median value to create an iterative shrinkage optimization model, and specifically, the steps are as follows;
s31, obtaining a normal vector of the source input data point according to a principal component analysis method:
(1) constructing a covariance matrix of the points:
wherein q isjIs the source input point, k is
The number of neighborhood points is the neighborhood mean of the source input point. The neighborhood of source input points is selected from a set of source input points J.
(2) And calculating the eigenvalue and the eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is the normal vector of the sampling point.
(3) And adjusting the directions of the normal vectors of the source input points according to the minimum spanning tree theory to enable all the normal vectors to be consistent in orientation.
S32, obtaining a projection operator according to the normal vector of the source input data point:
where x is the sampling point, qjIs the jth neighbor, n, of the sample point in the source input point set JjIs qjThe corresponding consistent outward normal vector,
the projection operator is a projection point of the sampling point on the tangent line of the jth adjacent point in the neighborhood of the source input point, and the point is named as a prediction point of the neighborhood of the sampling point.
S33, adding shape control parameters into the projection operator to obtain the projection operator with controllable shape:
where s is a shape control parameter,
is a neighborhood prediction point with controllable position of the sampling point.
S34, local L1 median definition is carried out according to the L1 median principle:
(1) the definition of the median value of L1 is to calculate the point with the minimum sum of Euclidean distances of all data points in a set of points, and the specific expression is as follows:
where x is the sampling point, qjIs the jth point in the source input point set J.
(2) Local L1 median definition:
wherein the content of the first and second substances,
for the weight function, r is the distance between the sampling point and the source input point, and h is the neighborhood radius. x is the number ofiIs the ith sample point in the set of sample points I, qjIs the jth neighborhood point of the sample point in the neighborhood of the source input point set J.
S35, combining the projection operator with controllable shape based on the normal vector with the local L1 median value to obtain an optimization formula, wherein the optimization formula is as follows:
wherein the content of the first and second substances,
is a weight function. r is the distance between the sampling point and the source input point and h is the neighborhood radius. x is the number ofiIs the ith sampling point in the sampling point set I, s is the shape control parameter,
is the sampling point xiA prediction point whose position on the jth neighborhood point tangent of the neighborhood in its source input point set J is controllable.
And S4, performing iterative shrinkage on the sampling points according to the iterative shrinkage optimization model.
(1) And (4) carrying out iterative contraction on the sampling points by using the optimization formula, wherein the sampling points move step by step.
(2) Setting shrinkage stop conditions: and when the distribution metric value sigma of all the sampling points is greater than 0.9, the sampling points stop moving, and when the condition is not met, the sampling points continue moving.
The concrete solving step of the distribution metric value sigma of the sampling points comprises the following steps:
(2.1) establishing a covariance matrix of the sampling points according to a principal component analysis method:
wherein the content of the first and second substances,
as a function of weight, xiIs the ith sample point, x, in the set of sample points IiIs sample point xiThe average value in the neighborhood of the sampling point set, at the moment, the neighborhood of the sampling point is selected from the sampling point set I, and the distance sampling point x is selectediOther sampling points smaller than the neighborhood radius h are neighborhood points. CiIs the sampling point xiThe covariance matrix of (2).
(2.2) obtaining a distribution metric value of a point according to the characteristic value of the covariance matrix:
wherein λ isi 0，λi 1，λi 2Covariance matrix Ci3 of a characteristic value, and λi 0＜λi 1＜λi 2，σi＝σ(xi) Is the sampling point xiThe distribution metric value of (2).
And carrying out iterative shrinkage on the sampling points by utilizing an optimization formula, wherein the optimization formula has the characteristic of the median of L1, which is insensitive to noise, and the excessive shrinkage capability of the median of L1 is restrained by adding a normal vector, so that the sampling points are shrunk more accurately and more detailed characteristics are reserved. The three-order annular forging sampling point iterative contraction final position graph is shown in FIG. 5.
And S5, connecting the sampling points to obtain a section line of the annular forging.
(1) Connecting sampling points to construct curve branches
And simply connecting the sampling points which show obvious curve distribution to form a curve branch, roughly screening candidate sampling points from the rest sampling points, and screening and connecting the candidate sampling points by using a hard constraint rule to construct the curve branch.
After the iterative shrinkage stops, each sampling point has a corresponding sigma value, the sampling points are smoothed by using a nearest neighbor node algorithm (KNN), K is selected to be 5, and the sampling points with the smoothed sigma values larger than 0.9 are used as candidate feature points. Searching is started from a candidate feature point with the largest sigma value, searching is carried out along the front end and the rear end of a Principal Component Analysis (PCA) direction (the feature vector corresponding to the largest feature value), the searching range is the size of the current neighborhood, and if a candidate point meets an included angle rule (namely, the included angle between two adjacent segments is smaller than 25 degrees) in the searching range, the candidate point is included in the current candidate branch. When a candidate branch contains more than 5 sample points, the branch is trusted and the corresponding sample point is marked as a fixed point. And if not, deleting the corresponding sampling point from the candidate points, after a round of search, if no candidate points remain, terminating the construction of a new curve branch, otherwise, continuously searching from the candidate point with the maximum sigma value.
(2) Connecting the curve branches to form a one-dimensional curve
In the process of connecting the curve branches: only two head and tail points are arranged in a certain area range, and when the directions of the two branches are more than 155 degrees, the two branches are connected into a long branch; in a certain area range, when there are three or more head and tail points, the middle point of the head branch is solved and the nearest branch is moved to the middle point, the middle point of the tail point corresponding branch is solved and the nearest branch is moved to the middle point, and the two branches are connected into a long branch. The multiple connecting curve branches form a continuous one-dimensional curve.
(3) And smoothing the one-dimensional curve according to a quadrilateral subdivision rule and a Laplace smoothing theory to obtain a smooth one-dimensional curve.
In the first step, for each node v1 except the head and tail points of each curve, the corresponding included angle between the node v0 and the front and back nodes v2 can be calculated, and if the included angle is more than 50 degrees, the node is subjected to one-dimensional laplacian smoothing, that is, v1 is v0/4+ v1/4+ v 2/4.
And secondly, carrying out four-point interpolation subdivision on each curve until the longest section of the curve is smaller than a threshold value. The subdivision method is as follows, assuming that v0, v1, v2 and v3 are four points in succession on the curve, the rule for inserting new points is as follows.
(1) v1, new insertion point of v 2: v ═ v0+9v1+9v2-v 3)/16.
(2) If v1 is an endpoint, i.e., v1 has no point before: v ═ 8 (3v1+6v2-v 3).
(3) If v2 is an endpoint, i.e., there is no point after v 2: v (-v0+6v1+3v 2)/8.
And thirdly, down-sampling the subdivided curve, namely, gradually taking out the next point from the first point as a sampling node, wherein the node just meets the condition that the distance between the next point and the previous point is more than a threshold value. A smooth one-dimensional curve with substantially the same segment length is obtained.
(4) And projecting the smooth one-dimensional curve to a two-dimensional plane to obtain the section line of the annular forging.
And selecting the section lines of 10 of the annular forgings, and measuring the section lines to obtain the critical dimensions, wherein the section line of one annular forging is shown in FIG. 6, and the critical dimension data measured by the section lines of 10 annular forgings is shown in Table 1.
TABLE 1 key dimension of each axial height of three-order annular forging
From table 1, the average absolute error value of the first axial height dimension of the key dimension of the annular forging obtained by the algorithm of the invention is 0.338mm, and the maximum error is 0.54 mm; the average absolute error of the second axial height dimension 2 is 0.345mm, and the maximum error is 0.56 mm; the average absolute error value of the third axial height dimension 3 is 0.318mm, the maximum error is 0.56mm, the average absolute error value of the fourth axial height dimension 4 is 0.326mm, the maximum error is 0.57mm, and the errors are all less than 1 mm.
In summary, the method for extracting the section lines of the annular forging based on the normal vectors and the L1 median can directly process point clouds containing a large amount of noise, extract the section lines of the annular forging with high precision, and measure the section lines of the annular forging to obtain the errors of all axial critical dimensions and actual dimensions within 1 mm.
Finally, it should be noted that the above-mentioned preferred examples are only intended to illustrate the technical solution of the present invention and are not to be limiting, and that, although the present invention has been described in detail by the above-mentioned specific examples, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (8)
1. A method for extracting section lines of an annular forging based on normal vectors and L1 median values is characterized by comprising the following steps:
s1, down-sampling the annular forging point cloud based on curvature to obtain a sampling point set, wherein the method specifically comprises the following steps;
s11, constructing a local quadric surface of each data point in the annular forging point cloud, and taking the average curvature of the local quadric surface as the curvature of the point;
s12, calculating a curvature threshold value H of the annular forging point cloud, putting points with curvature values larger than the threshold value H into a large curvature value area, and putting points with curvature values smaller than the threshold value H into a small curvature value area;
s13, curvature sampling is conducted on the sampling points in the large curvature value area, average sampling is conducted on the sampling points in the small curvature value area, and a sampling point set I of the annular forging is obtained;
s2, accurately selecting the neighborhood of the sampling point in the source input point set, which comprises the following steps;
s21, obtaining a normal vector of each sampling point according to a principal component analysis method;
s22, selecting a source input point with the distance x from the sampling point in the source input point set smaller than the neighborhood radius h as an initial neighborhood point;
s23, calculating an included angle beta between the initial neighborhood point and a normal vector of the sampling point, selecting the initial neighborhood point with beta being less than or equal to 90 degrees as a final neighborhood point of the sampling point, and obtaining an accurate neighborhood of the sampling point;
s3, combining a projection operator based on a normal vector with a local L1 median value to create an iterative shrinkage optimization model, and specifically, the steps are as follows;
s31, obtaining a normal vector of the source input data point according to a principal component analysis method;
s32, obtaining a projection operator according to the normal vector of the source input data point:
where x is the sampling point, qjIs the jth neighbor, n, of the sample point in the source input point set JjIs qjThe corresponding consistent outward normal vector,
the projection operator is a projection point of a sampling point on the tangent line of the jth adjacent point in the neighborhood of the source input point of the sampling point, and the point is named as a prediction point of the neighborhood of the sampling point;
s33, adding shape control parameters into the projection operator to obtain the projection operator with controllable shape:
where s is a shape control parameter,
the neighborhood prediction points with controllable positions of sampling points;
s34, local L1 median definition is carried out according to the expression of L1 median:
the median of local L1 is defined as:
wherein the content of the first and second substances,
as a weight function, r is the distance between the sampling point and the source input point, and h is the neighborhood radius; x is the number ofiIs the ith sample point in the set of sample points I, qjIs the jth neighborhood point of the sampling point in the neighborhood of the source input point set J;
s35, combining the projection operator with the controllable shape with the local L1 median value to create an iterative shrinkage optimization model, wherein the expression is as follows:
wherein the content of the first and second substances,
as a weight function, r is the distance between the sampling point and the source input point, and h is the neighborhood radius; x is the number ofiIs the ith sampling point in the sampling point set I, s is the shape control parameter,
is the sampling point xiThe jth of the neighborhood in its source input point set JControllable prediction points in positions on the tangent line of the neighborhood points;
s4, performing iterative shrinkage on the sampling points obtained in the step S2 according to an iterative shrinkage optimization model, wherein the specific steps are as follows;
s41, setting an iterative contraction stopping condition, and beginning to contract each point in the sampling point set;
s42, calculating a distribution metric value sigma of the contracted sampling points;
s43, judging whether the distribution metric value sigma of the sampling points meets the iterative contraction stopping condition, and if the distribution metric value sigma of the sampling points does not meet the iterative contraction stopping condition, performing the step S44; when the condition is satisfied, proceed to step S45;
s44, continuously shrinking each point in the sampling point set, and repeating the steps S42 and S43;
s45, stopping contraction of the sampling points, and finishing iterative contraction of the sampling points;
s5, connecting sampling points after iterative contraction to obtain section lines of the annular forging, and specifically comprising the following steps:
s51, connecting the sampling points after iterative contraction to construct a curve branch;
simply connecting sampling points which are obviously distributed in a curve to form a curve branch, roughly screening candidate sampling points from the rest sampling points, and screening and connecting the candidate sampling points by using a hard constraint rule to construct the curve branch;
s52, connecting the curve branches according to a connection rule to form a one-dimensional curve;
s53, smoothing the one-dimensional curve according to a quadrilateral subdivision rule and a Laplace smoothing theory to obtain a smooth one-dimensional curve;
and S54, projecting the smooth one-dimensional curve to a two-dimensional plane to obtain a section line of the annular forging.
2. The method for extracting section lines of annular forgings based on normal vectors and L1 median values as claimed in claim 1, wherein the step S21 comprises the following steps:
s211, constructing a covariance matrix of sampling points:
wherein q isjIs the source input point, k is the neighborhood number,
is the neighborhood mean of the sampling point; selecting a neighborhood of the sampling point from a source input point set J, and selecting a source input point with a distance sampling point less than a neighborhood radius h as a neighborhood point;
s212, calculating an eigenvalue and an eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is a normal vector of a sampling point;
s213, adjusting the directions of the normal vectors of the sampling points according to the minimum spanning tree theory to enable all the normal vectors to be consistent in direction.
3. The method for extracting section lines of annular forgings based on normal vectors and L1 median values as claimed in claim 1, wherein the step S31 comprises the following steps:
s311, constructing a covariance matrix of the source input data points:
wherein q isjIs the source input point, k is the number of neighborhood points,
is the source input point neighborhood mean; selecting a neighborhood of the source input point from a source input point set J;
s312, calculating an eigenvalue and an eigenvector of the covariance matrix, wherein the eigenvector corresponding to the minimum eigenvalue is a normal vector of a sampling point;
s313, the directions of the normal vectors of the source input points are adjusted according to the minimum spanning tree theory, and the directions of all the normal vectors are consistent.
4. The method for extracting the section line of the annular forging based on the normal vector and the L1 median as claimed in claim 1, wherein the specific solving step of the distribution metric σ of the sampling points in the step S41 is:
p1, establishing a covariance matrix of the sampling points according to a principal component analysis method:
wherein the content of the first and second substances,
as a function of weight, xiIs the ith sampling point, x 'in sampling point set I'iIs the sampling point xiThe average value in the neighborhood of the sampling point set, at the moment, the neighborhood of the sampling point is selected from the sampling point set I, and the distance sampling point x is selectediOther sampling points smaller than the neighborhood radius h are neighborhood points; ciIs the sampling point xiThe covariance matrix of (a);
p2, obtaining a distribution metric value sigma of the sampling point according to the eigenvalue of the covariance matrix:
wherein the content of the first and second substances,
covariance matrix CiAnd 3 characteristic values of
σi＝σ(xi) Is the sampling point xiThe distribution metric value of (2).
5. The method for extracting the section line of the annular forging based on the normal vector and the L1 median as claimed in claim 1, wherein the step S53 is implemented as follows:
s531, for each node v1 except the head and tail points of each curve, calculating a corresponding included angle between the node v0 and the front node v2 and the corresponding included angle between the node v1 and the rear node v0 and the corresponding included angle v2, and if the included angle is larger than 50 degrees, performing one-dimensional Laplace smoothing on the node, namely v 1-v 0/4+ v1/4+ v 2/4;
s532, four-point interpolation subdivision is carried out on each curve until the longest subsection of the curve is smaller than a threshold value;
s533, carrying out down-sampling on the subdivided curve, namely, gradually taking out the next point from the first point as a sampling node, wherein the node just meets the condition that the distance between the node and the previous point is more than a threshold value; a smooth one-dimensional curve with substantially the same segment length is obtained.
6. The method for extracting the section line of the annular forging based on the normal vector and the L1 median as claimed in claim 5, wherein the interpolation subdivision method in step S532 is as follows: assuming that v0, v1, v2 and v3 are four points in succession on the curve, the rule for inserting new points is as follows:
if neither v1 nor v2 is an endpoint, the new insertion point is v ═ v0+9v1+9v2-v 3)/16;
if v1 is an endpoint, i.e., v1 has no point before: the new insertion point is v ═ 3v1+6v2-v 3)/8;
if v2 is an endpoint, i.e., there is no point after v 2: the new insertion point is v ═ v0+6v1+3v 2)/8.
7. The method for extracting section lines of annular forgings based on normal vectors and median values of L1 as claimed in claim 1, wherein the iterative shrinkage stop condition set in step S41 is that the distribution metric value σ of all sampling points is > 0.9.
8. The method for extracting section lines of annular forgings based on normal vectors and L1 median values as claimed in claim 1, wherein the connection rules in step S52 are: when only two head and tail points exist in a certain area range and the directions of the two branches are more than 155 degrees, the two branches are connected into a long branch; when there are three or more head and tail points in a certain area, the middle point of the head branch is solved and the nearest branch is moved to the middle point, the middle point of the tail point corresponding branch is solved and the nearest branch is moved to the middle point, and the two branches are connected into a long branch.
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