CN111524129A - Aircraft skin butt joint gap calculation method based on end face extraction - Google Patents

Aircraft skin butt joint gap calculation method based on end face extraction Download PDF

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CN111524129A
CN111524129A CN202010359793.1A CN202010359793A CN111524129A CN 111524129 A CN111524129 A CN 111524129A CN 202010359793 A CN202010359793 A CN 202010359793A CN 111524129 A CN111524129 A CN 111524129A
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汪俊
黄耀然
陈红华
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses an aircraft skin butt joint gap calculation method based on end face extraction, which specifically comprises the following steps: acquiring actual measurement point cloud data of an aircraft skin; rasterizing the actually measured point cloud data; calculating the flatness of the point cloud data in each grid through principal component analysis, extracting a planar grid in the grids, and fitting the point cloud data in the planar grid into a plane by adopting a weighted least square algorithm; based on the fitted grid plane, extracting point cloud data of a skin plane area by adopting a region growing algorithm; and fitting the plane by adopting an iterative weighted least square algorithm, judging whether the fitted plane is an end face, and calculating the butt joint gap of the skin end face. The method can accurately calculate the aircraft skin butt joint gap, and solves the problem that the aircraft skin butt joint gap is difficult to detect.

Description

Aircraft skin butt joint gap calculation method based on end face extraction
Technical Field
The invention relates to the field of computer vision, in particular to a method for calculating a butt seam gap of an aircraft skin based on end face extraction.
Background
With the rapid development of the three-dimensional measurement technology, the existing measurement equipment can rapidly measure large scene complex parts, and the scanning speed can scan hundreds of thousands of even millions of points per second; the scanning precision is greatly improved. In recent years, three-dimensional measurement technology is gradually applied to the aviation field, and is often used for detecting manufacturing errors of certain key parts and assembly errors of parts in the aircraft manufacturing process. The butt seam clearance in the aircraft skin assembling state directly influences the appearance and the aerodynamic performance of the aircraft, so that the butt seam clearance generated in the aircraft skin assembling process is effectively controlled, and the butt seam clearance has important significance for improving the assembling precision of the aircraft and improving the aerodynamic performance of the aircraft.
At present, in the process of assembling the aircraft skin, the gap clearance of the aircraft skin is still manually measured by a feeler gauge, so that the problems of difficulty in ensuring the measurement precision, low measurement efficiency and the like exist. In view of the defects in the existing measurement process of the skin butt-joint gap of the airplane, the method for the skin butt-joint gap of the airplane based on end face extraction is provided. The problem that the aircraft skin butt joint gap is difficult to extract can be effectively solved.
Disclosure of Invention
The invention aims to provide an aircraft skin butt-joint gap calculation method based on end face extraction, which can accurately extract the butt-joint gap of a skin in an aircraft assembly state and effectively solve the problem of difficult skin butt-joint gap extraction in the aircraft assembly process.
In order to achieve the purpose, the invention adopts the technical scheme that:
an aircraft skin butt joint gap calculation method based on end face extraction comprises the following steps:
s1: acquiring actual measurement point cloud data of an aircraft skin;
s2: combining the actually measured point cloud data to perform rasterization processing;
s3: calculating the flatness of point cloud data in the grids through principal component analysis, and extracting planar grids in the grids;
s4: fitting the point cloud data in the plane grid into a plane by adopting a weighted least square algorithm;
s5: based on the fitted plane, extracting point cloud data of a plane area by adopting a region growing algorithm;
s6: and fitting the plane by adopting an iterative weighted least square algorithm, judging whether the fitted plane is an end face, and calculating the butt joint gap of the end face of the skin.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in step S2, the rasterizing process performed by combining the acquired actually measured point cloud data includes the following steps:
s21: calculating a minimum bounding box size that can include the entire measured point cloud data;
s22: determining the geometric size of the grid according to the size of the minimum bounding box and the actually-measured point cloud resolution;
s23: and judging the grid serial number of each point in the grid point cloud.
Further, in step S21, the minimum bounding box size of the measured point cloud data is calculated, and the formula is as follows:
Xmax＝max(pi(x))Xmin＝min(pi(x))
Ymax＝max(pi(y))Ymin＝min(pi(y))
Zmax＝max(pi(z))Zmin＝min(pi(z))
in the formula, XmaxIs the maximum coordinate of the actually measured point cloud data in the X direction, XminIs the minimum coordinate, p, of the actually measured point cloud data in the x directioni(x) Is a point piX coordinate of (a); y ismaxIs the maximum coordinate of the actually measured point cloud data in the Y direction, YminIs the minimum coordinate, p, of the actually measured point cloud data in the y directioni(y) is the point piY-coordinate of (a); zmaxIs the maximum coordinate of the actually measured point cloud data in the Z direction, ZminIs the minimum coordinate, p, of the actually measured point cloud data in the z directioni(z) is a point piZ coordinate of (a).
And obtaining the minimum bounding box size comprising the point cloud data according to the maximum coordinates and the minimum coordinates of the bounding box in the y direction and the z direction.
Further, in step S22, the grid geometry is calculated according to the minimum bounding box size and the actually measured point cloud resolution, and the formula is as follows:
Figure BDA0002473259960000021
Figure BDA0002473259960000022
Figure BDA0002473259960000023
in the formula, sx，sy，szThe dimensions of the grid in the X, y, z directions, respectively, are the point cloud resolution, Xmax，Ymax，ZmaxMaximum coordinates of the bounding box in the X, y, z directions, X, respectivelymin，Ymin，ZminThe minimum coordinate of the bounding box in the x, y, z directions, respectively.
Further, in step S23, the serial number of each point in the point cloud in the grid is determined, and the formula is as follows:
Figure BDA0002473259960000031
Figure BDA0002473259960000032
Figure BDA0002473259960000033
wherein i, j, and k are points piGrid number of the grid, sx、sy、szThe dimensions of the grid in the X, y, z directions, X, respectivelymin、Ymin、ZminThe minimum coordinate of the bounding box in the x, y, z directions, p, respectivelyi(x)、pi(y)、pi(z) are each a point piX, y, z coordinate of (2)]Is a floor function.
Further, in step S3, the calculating the flatness of the point cloud data in the grid through principal component analysis includes the following steps:
calculating the gravity center of the point cloud in the grid, wherein the formula is as follows:
Figure BDA0002473259960000034
in the formula, pcIs the barycentric coordinate of the grid point cloud, piIs the point coordinates in the grid point cloud and k is the total number of points in the point cloud in the grid.
The covariance matrix is calculated, the formula is shown below:
Figure BDA0002473259960000035
where M is the covariance matrix, pcIs the barycentric coordinate of the point cloud in the grid, piIs the point coordinates in the grid point cloud and k is the total number of points in the grid.
Performing eigenvalue decomposition on the covariance matrix, wherein the eigenvalue is lambdaiWhere i ═ 1, 2, 3, λ1≤λ2≤λ3The flatness calculation formula is as follows:
Figure BDA0002473259960000036
wherein P is the flatness, λ1、λ2Are all eigenvalues;
setting a flatness threshold PthAnd taking the grid with the grid flatness smaller than the threshold value as a plane grid, taking the grid with the grid flatness larger than the threshold value as a non-plane grid, and extracting the plane grid.
Further, in step S4, fitting a plane to the point cloud data in the planar grid by using a weighted least squares algorithm, includes the following steps:
constructing a driving model, wherein the formula is as follows:
Figure BDA0002473259960000041
in the formula, riIs a point piProjection distance to plane to be fitted, θ (r)i) Is a gaussian weight function; the specific expression is as follows:
Figure BDA0002473259960000042
Figure BDA0002473259960000043
in the formula, piIs the coordinate of the midpoint of the planar grid,
Figure BDA0002473259960000044
the center of gravity of the plane grid point cloud, c is a constant value which is generally set to be 5 times of the resolution ratio of the point cloud, and n is a unit normal vector of a plane to be fitted.
n satisfies the condition | | | n | | | | 1, so the driving model is solved by adopting a lagrange multiplier method, and the following driving model solving function is constructed, and the formula is shown as follows:
Figure BDA0002473259960000045
where f (n) drives the model solution function, n is the unit normal vector of the plane to be fitted, λ is the Lagrange multiplier, θ (r)i) Is a gaussian weight function.
When f (n) is the minimum value, namely n is the unit normal vector of the plane to be fitted, a gradient descent algorithm is adopted to differentiate f (n) from n, and the expression after differentiation is as follows:
Figure BDA0002473259960000046
in the formula (I), the compound is shown in the specification,
Figure BDA0002473259960000047
is the derivative of (n) to n, n is the unit normal vector of the plane to be fitted, λ is the Lagrangian multiplier, θ (r)i) Is a gaussian weight function.
Continuously and iteratively calculating n when f (n) is the minimum value, wherein a specific iterative formula is as follows:
Figure BDA0002473259960000048
in the formula, ni+1Is the normal vector, n, obtained by the (i + 1) th iterative computationiIs the normal vector obtained by the ith iteration calculation, and τ is the iteration step length.
After i +1 times of iteration, the solved normal vector is the normal vector of the fitting plane, and a plane equation is determined by the center of gravity of the grid point cloud and the normal vector obtained by calculation.
Further, in step S5, based on the fitted plane, extracting the point cloud data of the skin plane region by using a region growing algorithm, including the following steps:
s51: taking all the planes fitted in the step S4 and the point cloud data corresponding to the planes as algorithm input, and setting relevant parameters, including the following parameters:
ψtotal: all the planes of the input are collected; i istotalIs an input planar raster point cloud set, where Delta theta is the threshold value of the included angle between the normal lines of different planes, Delta theta ∈ [5 deg. °, 10 deg. °](ii) a Delta d is a projection distance threshold value of the gravity centers of different planes along the normal direction of the planes, and is 2 times of the resolution ratio of the point cloud; psi is a plane set to be output, and is initialized to be an empty set; i isoutInitializing a point set corresponding to a plane set to be output into an empty set;
s52: set psi of all planes randomly input fromtotalRandomly selecting partial planes as seed planes, adding the seed planes into a plane set psi to be output, and adding point cloud data corresponding to the seed planes into a point set I corresponding to the plane set to be outputout；
S53: searching unselected planes in the neighborhood of the plane set psi to be output, and judging whether the planes are coplanar with the planes in the plane set psi to be output, wherein the judgment formula is as follows:
θ＜Δθ，d＜Δd
where θ is the angle between the plane normalsD is the projection distance of the gravity centers of different planes along the normal direction; if the non-selected plane near psi and all planes in psi meet the above-mentioned judgment condition of coplanar planes, i.e. coplanar, adding them into psi, and adding the point cloud data corresponding to said plane into point set IoutIf not, continuing to search the next unselected plane in the psi neighborhood range;
s54: repeating the step S53 until the unselected planes near the plane set psi to be output are not coplanar with the mid-plane of psi or no planes are in the neighborhood of psi, stopping growing, and connecting psi and IoutOutput and empty, and from psitotalRemoving psi from ItotalIn which removal of Iout；
S55: and repeating the steps S52, S53 and S54 until all planes and the point cloud data corresponding to the planes are output.
Further, in step S6, an iterative weighted least squares algorithm is applied to the I outputted in step S54outCarrying out plane fitting, judging whether the fitted plane is an end face, and calculating the distance between the end faces, wherein the specific steps are as follows:
s61: set of computation points IoutIncluding the center of gravity and the initial normal line, and setting a reasonable iteration number kiterTerminating the condition gamma of iteration, and fitting the threshold value of the angle difference of the normal line of the plane in two adjacent iterations;
s62: construction IoutThe weighted covariance matrix C "of (a), the formula is as follows:
Figure BDA0002473259960000061
Figure BDA0002473259960000062
Figure BDA0002473259960000063
Figure BDA0002473259960000064
Figure BDA0002473259960000065
wherein p isiIs the coordinates of a point or points of interest,
Figure BDA0002473259960000066
is the coordinate of the center of gravity,
Figure BDA0002473259960000067
for the k iteration center of gravity offset, n is the normal, wiFor the weighting factor, const is a constant value, which can be set according to the resolution of the point cloud.
And decomposing the characteristic value of C, and taking the characteristic vector corresponding to the minimum characteristic value as a point set IoutThe normal vector of (2).
S63: judging the normal angle deviation value of two adjacent iterative calculations, if the deviation is less than gamma, ending the iteration in advance, otherwise, continuing the iterative calculation C until the iteration times is more than kiter；
S64: and judging whether the fitted plane is an end face or not, and calculating the distance between the end faces to obtain the end face butt joint gap of the aircraft skin.
Further, in step S64, determining whether the fitted plane is an end face, and calculating a distance between the end faces to obtain a butt seam gap of the aircraft skin, specifically including the following steps:
setting neighborhood thresholdthAnd angle threshold thetathTaken at the centre of gravity of one of the planesthA neighborhood range including a point on another plane and having an angle greater than θ between the normal vector of the other plane and the normal vector of the other planethJudging that the fitted plane is an end face, and when the included angle of normal vectors of the two end faces is 180 degrees, the two end faces are parallel, otherwise, the two end faces are not parallel;
if the fitted end surfaces are parallel, then a point is arbitrarily selected on each of the two end surfaces, and the projection distance between the two points along the normal direction of the end surfaces is calculated, namelyEnd face butt joint gap d of skiniThe calculation formula is as follows:
di＝||(pi-pj)·n||
in the formula (d)iIs the butt-joint clearance of the end faces of the skins when the end faces of the skins are parallel; p is a radical ofi，pjRespectively are any two points on two end faces, and n is a plane normal vector;
if the fitted end surfaces are not parallel, calculating the distance from all end points of one end surface to the other end surface, wherein the maximum value is dmaxMinimum value of dminThe end face of the skin faces the gap diIn the range of dmin≤di≤dmax。
The invention has the beneficial effects that:
the method for calculating the butt-joint gap of the aircraft skin based on the end face extraction can accurately extract the butt-joint gap of the skin in the aircraft assembly state.
Firstly, actual measurement point cloud data can be divided into a plurality of small blocks of grid point cloud data through rasterization processing; calculating the flatness of each small piece of raster point cloud data, setting a reasonable flatness threshold value, extracting raster point cloud data with the shape similar to a plane in the raster point cloud data, and performing plane fitting on each small piece of plane raster point cloud data by using a weighted least square algorithm; aiming at the plane of the last step of fitting, extracting a plane area in the point cloud data by using an area growing algorithm, and performing plane fitting by using an iterative weighted least square algorithm; and finally, judging whether the plane is covered on the butt joint end face or not, and calculating the covered butt joint gap or the range value of the covered butt joint gap aiming at different butt joint end faces. The problem that the skin butt joint gap is difficult to extract in the aircraft assembling process can be effectively solved.
Drawings
FIG. 1 is a flow chart of a method for calculating a skin butt-joint gap of an aircraft based on end face extraction according to the invention;
FIG. 2 is a schematic diagram of the point cloud data of the measured aircraft skin obtained by scanning according to the present invention;
FIG. 3 is a schematic view of the point cloud data of the end surface region after extraction according to the region growing algorithm of the present invention;
FIG. 4 is a schematic end view of the invention after fitting according to an iterative weighted least squares algorithm;
fig. 5 is a schematic diagram of the calculation of the gap of the butt seam of the present invention.
Detailed Description
For a better understanding of the present disclosure, reference will now be made to the embodiments illustrated in the drawings.
The invention provides an aircraft skin butt seam gap calculation method based on end face extraction, which can be directly applied to butt seam gap detection of skin end faces in an aircraft assembly process, and can be specifically realized by programming by utilizing source codes in a PCL (personal computer) library; specifically, fig. 1 is a flow chart of the method, comprising the steps of:
s1: acquiring actual measurement point cloud data of an aircraft skin;
s2: rasterizing the actually measured point cloud data, and dividing the actually measured point cloud data into a plurality of small blocks of raster point cloud data;
s3: calculating the flatness of the grid through principal component analysis, and extracting a planar grid in the grid;
s4: fitting the point cloud data in the plane grid into a plane by adopting a weighted least square algorithm;
s5: based on the fitted plane, extracting point cloud data of a plane area by adopting a region growing algorithm;
s6: and fitting the plane by adopting an iterative weighted least square algorithm, judging whether the fitted plane is an end face, and calculating the butt joint gap of the end face of the skin.
In the above embodiment, an effective method is provided for detecting the end-to-seam gap of the aircraft skin, and the method is realized by the following steps: acquiring actual measurement point cloud data of an aircraft skin; rasterizing the actually measured point cloud data; calculating the flatness of the point cloud in each grid by using a principal component analysis method, setting a reasonable flatness threshold value to extract a plane grid in the point cloud of the grid, and fitting the point cloud data in the plane grid into a plane by using a weighted least square algorithm; extracting point cloud data of a plane area by a region growing algorithm aiming at the fitted plane; and fitting the point cloud data of the plane area by adopting an iterative weighted least square algorithm, judging whether the fitted plane is an end face, and calculating the butt joint gap of the skin end face.
Fig. 2 shows two pieces of skin point cloud data obtained, which are divided into many small pieces of grid point cloud through rasterization.
Specifically, the minimum bounding box of the point cloud data is calculated first, and the specific formula is as follows:
Xmax＝max(pi(x))Xmin＝min(pi(x))
Ymax＝max(pi(y))Ymin＝min(pi(y))
Zmax＝max(pi(z))Zmin＝min(pi(z))
in the formula, XmaxIs the maximum coordinate of the actually measured point cloud data in the X direction, XminIs the minimum coordinate, p, of the actually measured point cloud data in the x directioni(x) Is a point piX coordinate of (a); y ismaxIs the maximum coordinate of the actually measured point cloud data in the Y direction, YminIs the minimum coordinate, p, of the actually measured point cloud data in the y directioni(y) is the point piY-coordinate of (a); zmaxIs the maximum coordinate of the actually measured point cloud data in the Z direction, ZminIs the minimum coordinate, p, of the actually measured point cloud data in the z directioni(z) is a point piZ coordinate of (a).
And obtaining the minimum bounding box size capable of comprising the point cloud data according to the maximum coordinates and the minimum coordinates of the bounding box in the directions of x, y and z.
The grid geometry is determined by the minimum bounding box size and the point cloud resolution, and the specific formula is as follows:
Figure BDA0002473259960000081
Figure BDA0002473259960000082
Figure BDA0002473259960000083
in the formula, sx，sy，szThe dimensions of the grid in the X, y, z directions, respectively, are the point cloud resolution, Xmax，Ymax，ZmaxMaximum coordinates of the bounding box in the X, y, z directions, X, respectivelymin，Ymin，ZminThe minimum coordinate of the bounding box in the x, y, z directions, respectively.
And finally, determining the serial number of the grid where each point in the point cloud is located, wherein the calculation formula is as follows:
Figure BDA0002473259960000091
Figure BDA0002473259960000092
Figure BDA0002473259960000093
wherein i, j, and k are points piGrid number of the grid, sx、sy、szThe dimensions of the grid in the X, y, z directions, X, respectivelymin、Ymin、ZminThe minimum coordinate of the bounding box in the x, y, z directions, p, respectivelyi(x)、pi(y)、pi(z) are each a point piX, y, z coordinate of (2)]Representing a floor function.
Further, calculating the grid flatness through principal component analysis, and extracting the planar grid comprises the following steps:
calculating the gravity center of the grid point cloud by the following calculation formula:
Figure BDA0002473259960000094
in the formula, pcIs the barycentric coordinate of the grid point cloud, piIs the point coordinates in the grid point cloud, k is the total number of points in the point cloud in the grid;
the covariance matrix formula is calculated as follows:
Figure BDA0002473259960000095
where M is the covariance matrix, pcIs the barycentric coordinate of the grid point cloud, piIs the point coordinates in the grid point cloud, k is the total number of points in the grid point cloud;
performing eigenvalue decomposition on the covariance matrix, wherein the eigenvalue is lambdaiWhere i ═ 1, 2, 3, λ1≤λ2≤λ3The flatness calculation formula is as follows:
Figure BDA0002473259960000096
wherein P is the flatness, λ1、λ2Are all characteristic values.
Setting the flatness threshold value to be 0.01, and extracting the grids smaller than the flatness in the grid point cloud to be used as plane grids.
Further, fitting the point cloud data in the plane grid into a plane by adopting a weighted least square algorithm, and specifically comprising the following steps of:
constructing a driving model, wherein the formula is as follows:
Figure BDA0002473259960000101
in the formula, riIs a point piProjection distance to plane to be fitted, θ (r)i) Is a gaussian weight function; the specific expression is as follows:
Figure BDA0002473259960000102
Figure BDA0002473259960000103
in the formula, piIs the coordinate of the midpoint of the planar grid,
Figure BDA0002473259960000104
the method comprises the following steps that the center of gravity of a planar grid point cloud is determined, c is a constant value and is set to be 5 times of the resolution of the point cloud, n is a unit normal vector of a plane to be fitted, and n meets the condition that n is equal to 1;
a driving model is solved by adopting a Lagrange multiplier method, and the following driving model solving function is constructed, wherein the formula is as follows:
Figure BDA0002473259960000105
wherein f (n) drives the model solving function, n is the unit normal vector of the plane to be fitted, lambda is Lagrange multiplier, and theta (r)i) Is a gaussian weight function;
determining a unit normal vector of a plane to be fitted by calculating n when the minimum value of f (n) is obtained, and deriving f (n) from n by adopting a gradient descent algorithm, wherein an expression after derivation is as follows:
Figure BDA0002473259960000106
in the formula (I), the compound is shown in the specification,
Figure BDA0002473259960000107
is the derivative of (n) to n, n is the unit normal vector of the plane to be fitted, λ is the Lagrangian multiplier, θ (r)i) Is a gaussian weight function.
Iteratively calculating n when f (n) is the minimum value, wherein a specific iterative formula is as follows:
Figure BDA0002473259960000108
in the formula, ni+1Is the normal vector, n, obtained by the (i + 1) th iterative computationiIs the normal direction obtained by the ith iterative calculationQuantity, τ is the iteration step; specifically, the number of iterations is set to 200, and the iteration step size is set to 0.001.
After i +1 iterations, the solved normal vector is the normal vector of the fitting plane, and the plane passes through the center of gravity of the grid point cloud, so that a plane equation can be determined by the center of gravity and the normal vector obtained by calculation.
Further, for all the fitted planes, a region growing algorithm is adopted to further extract point cloud data of the plane region, and the specific algorithm implementation process comprises the following steps:
(1) set ψ of all planes to be fittedtotalPoint cloud set I corresponding to planetotalAs the input of the algorithm, initializing relevant parameters, wherein delta theta is a threshold value of a normal included angle of two different planes, and is initialized to 5 degrees, and delta d is a threshold value of a projection distance between the gravity centers of the two planes along the normal direction, and is initialized to 4 times of the resolution ratio of the point cloud; psi is the set of planes to be output, initialized to the empty set; i isoutThe method comprises the steps that a point set corresponding to a plane set to be output is initialized to be an empty set;
(2) set psi of all planes randomly input fromtotalRandomly selecting partial planes as seed planes, adding the seed planes into a plane set psi to be output, and adding point cloud data corresponding to the seed planes into a point set I corresponding to the plane set to be outputout。
(3) Searching unselected planes in the neighborhood of the plane set psi, judging whether the searched planes are coplanar with the planes in the psi, if so, adding the planes into the psi, and adding the point cloud corresponding to the planes into the point set IoutIf not, the next unselected plane is searched for, where is the maximum of the dimensions of the grid in the three directions.
(4) Repeating the step (3) until the unselected planes near the plane set psi to be output are not coplanar with the mid-plane of psi or no planes exist in the neighborhood of psi, stopping growing, and enabling psi and IoutOutput and empty, and from psitotalRemoving psi from ItotalIn which removal of Iout(ii) a Wherein fig. 3 is a schematic view of point cloud data for the skin end face region.
(5) And (5) repeating the steps (2), (3) and (4) until all the planes and the point cloud data corresponding to the planes are output.
Further, an iterative weighted least square algorithm is applied to output a point set IoutPerforming a plane fit, comprising:
(1) set of computation points IoutThe principal component analysis method is applied to the initial normal direction, and the specific formula is as follows:
Figure BDA0002473259960000111
Figure BDA0002473259960000112
wherein p iscAs barycentric coordinates, M as a covariance matrix, piAre the coordinates of the points. And carrying out eigenvalue decomposition on the covariance matrix, and taking the eigenvector corresponding to the minimum eigenvalue as the initial normal direction.
(2) Constructing a set of points IoutThe weighted covariance matrix C of (a) is specifically defined as follows:
Figure BDA0002473259960000113
Figure BDA0002473259960000121
Figure BDA0002473259960000122
Figure BDA0002473259960000123
Figure BDA0002473259960000124
wherein p isiIs the coordinates of a point or points of interest,
Figure BDA0002473259960000125
is the coordinate of the center of gravity,
Figure BDA0002473259960000126
for the k iteration center of gravity offset, n is the normal, wiFor the weighting factor const is a constant value set to 5 times the resolution of the point cloud.
(3) Performing eigenvalue decomposition on the weighted covariance matrix, taking the eigenvector corresponding to the minimum eigenvalue as a new normal vector, judging the normal angle deviation value of two adjacent calculations, and if the deviation is less than gamma, ending the iteration in advance; otherwise, continuing to iteratively calculate C until the iteration number is more than kiterThe resulting output fitted plane is shown in fig. 4.
Further, judging whether the fitted plane is an end face specifically comprises the following steps:
the end face satisfies the following two conditions:
a) the gaps between the end faces of different skins of the airplane are generally very small;
b) the end faces are approximately parallel to each other, so that the normal vector included angle between the end faces is large.
Setting neighborhood thresholdthAnd angle threshold thetathTaken at the centre of gravity of one of the planesthA neighborhood range including a point on another plane and having an angle greater than θ between the normal vector of the other plane and the normal vector of the other planethThen the two planes that satisfy the above relationship are end faces. WhereinthTake 6mm, thetathTake 150 deg.
And further, calculating the distance between the end faces to obtain the butt seam gap of the aircraft skin. The following two cases are specifically distinguished:
when the fitted end surfaces are parallel, any point is taken on each of the two end surfaces, the projection distance between the two points along the normal direction of the end surface is calculated, namely the end surface butt seam gap of the skin, and the calculation formula is as follows:
d＝||(pi-pj)·n||
when the fitted end face is notWhen the two end faces are parallel, the range of the end-to-seam clearance of the skins is calculated, the distance from all end points of one end face to the other end face is calculated, and the maximum value is dmaxMinimum value of dminThus the distance d from any point on the end face to another end faceiSatisfy dmin≤di≤dmaxSo that the range of the butt joint clearance of the end face of the skin can be determined as [ d ]min，dmax]。

Claims (10)

1. An aircraft skin butt joint gap calculation method based on end face extraction. The method for extracting the aircraft skin butt joint gap is characterized by comprising the following steps:
s1: acquiring actual measurement point cloud data of an aircraft skin;
s2: rasterizing the actually measured point cloud data, and dividing the actually measured point cloud data into a plurality of small blocks of raster point cloud data;
s3: calculating the flatness of the grid through principal component analysis, and extracting a planar grid in the grid;
s4: fitting the point cloud data in the plane grid into a plane by adopting a weighted least square algorithm;
s5: based on the fitted plane, extracting point cloud data of a plane area by adopting a region growing algorithm;
s6: and fitting the plane by adopting an iterative weighted least square algorithm, judging whether the fitted plane is an end face, and calculating the butt joint gap of the end face of the skin.
2. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 1, wherein in step S2, the combining the actually measured point cloud data, performing rasterization processing to divide the actually measured point cloud data into a plurality of small pieces of raster point cloud data specifically includes the following steps:
s21: calculating a minimum bounding box size that can include the entire measured point cloud data;
s22: determining the geometric size of the grid according to the size of the minimum bounding box and the actually-measured point cloud resolution;
s23: and judging the grid serial number of each point in the grid point cloud.
3. The method for calculating the aircraft skin butt-seam gap based on the end face extraction as claimed in claim 2, wherein in step S21, the calculation formula for calculating the minimum bounding box size including the whole measured point cloud data is as follows:
Xmax＝max(pi(x)) Xmin＝min(pi(x))
Ymax＝max(pi(y)) Ymin＝min(pi(y))
Zmax＝max(pi(z)) Zmin＝min(pi(z))
in the formula, XmaxIs the maximum coordinate of the actually measured point cloud data in the X direction, XminIs the minimum coordinate, p, of the actually measured point cloud data in the x directioni(x) Is a point piX coordinate of (a); y ismaxIs the maximum coordinate of the actually measured point cloud data in the Y direction, YminIs the minimum coordinate, p, of the actually measured point cloud data in the y directioni(y) is the point piY-coordinate of (a); zmaxIs the maximum coordinate of the actually measured point cloud data in the Z direction, ZminIs the minimum coordinate, p, of the actually measured point cloud data in the z directioni(z) is a point piZ-coordinate of (a);
and obtaining the minimum bounding box size capable of comprising the point cloud data according to the maximum coordinates and the minimum coordinates of the bounding box in the directions of x, y and z.
4. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 3, wherein in step S22, the grid geometric dimension is calculated according to the minimum bounding box dimension and the resolution of the measured point cloud:
Figure FDA0002473259950000021
Figure FDA0002473259950000022
Figure FDA0002473259950000023
in the formula, sx，sy，szThe dimensions of the grid in the X, y, z directions, respectively, are the point cloud resolution, Xmax，Ymax，ZmaxMaximum coordinates of the bounding box in the X, y, z directions, X, respectivelymin，Ymin，ZminThe minimum coordinate of the bounding box in the x, y, z directions, respectively.
5. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 4, wherein in step S23, the serial number of the grid where each point is located is determined to be calculated according to the following formula:
Figure FDA0002473259950000024
Figure FDA0002473259950000025
Figure FDA0002473259950000026
wherein i, j, and k are points piGrid number of the grid, sx、sy、szThe dimensions of the grid in the X, y, z directions, X, respectivelymin、Ymin、ZminThe minimum coordinate of the bounding box in the x, y, z directions, p, respectivelyi(x)、pi(y)、pi(z) are each a point piX, y, z coordinate of (2)]Representing a floor function.
6. The aircraft skin butt-seam gap calculation method based on the end face extraction as claimed in claim 5, wherein in step S3, the flatness of point cloud data in the grid is calculated through principal component analysis, and a planar grid in the grid is extracted, and the method comprises the following steps:
calculating the gravity center of the point cloud in the grid, wherein the formula is as follows:
Figure FDA0002473259950000027
in the formula, pcIs the barycentric coordinate of the grid point cloud, piIs the point coordinates in the grid point cloud, k is the total number of points in the point cloud in the grid;
the covariance matrix is calculated, the formula is shown below:
Figure FDA0002473259950000031
where M is the covariance matrix, pcIs the barycentric coordinate of the point cloud in the grid, piIs the point coordinates in the grid point cloud, k is the total number of points in the grid;
decomposing the eigenvalue of the covariance matrix M to obtain the eigenvalue of lambdaiWhere i ═ 1, 2, 3, λ1≤λ2≤λ3The flatness calculation formula is as follows:
Figure FDA0002473259950000032
wherein P is the flatness, λ1、λ2Are all eigenvalues;
setting a flatness threshold PthAnd taking the grid with the grid flatness smaller than the threshold value as a plane grid, taking the grid with the grid flatness larger than the threshold value as a non-plane grid, and extracting the plane grid.
7. The aircraft skin butt-joint gap calculation method based on end face extraction as claimed in claim 6, wherein in step S4, a weighted least squares algorithm is adopted to fit point cloud data in a planar grid to a plane, specifically comprising the following steps:
constructing a driving model, wherein the formula is as follows:
Figure FDA0002473259950000033
in the formula, riIs a point piProjection distance to plane to be fitted, θ (r)i) Is a gaussian weight function; the specific expression is as follows:
Figure FDA0002473259950000034
Figure FDA0002473259950000035
in the formula, piIs the coordinate of the midpoint of the planar grid,
Figure FDA0002473259950000036
the method comprises the following steps of (1) obtaining a planar grid point cloud barycentric coordinate, c is a constant value, n is a unit normal vector of a plane to be fitted, and n meets the condition of 1;
a driving model solving function is constructed by adopting a Lagrange multiplier method, and the formula is as follows:
Figure FDA0002473259950000037
where f (n) drives the model solution function, n is the unit normal vector of the plane to be fitted, λ is the Lagrange multiplier, θ (r)i) Is a gaussian weight function;
n when f (n) takes the minimum value, i.e. the unit normal vector of the plane to be fitted.
Continuously and iteratively calculating n when f (n) is the minimum value, wherein a specific iterative formula is as follows:
Figure FDA0002473259950000041
in the formula, ni+1Is the normal vector, n, obtained by the (i + 1) th iterative computationiIs the normal vector obtained by the ith iteration calculation, and τ is the iteration step length.
After i +1 times of iteration, the solved normal vector is the normal vector of the fitting plane, and a plane equation is determined by the center of gravity of the grid point cloud and the normal vector obtained by calculation.
8. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 7, wherein in step S5, based on the fitted plane, a region growing algorithm is used to extract point cloud data of the skin plane region, and the method comprises the following steps:
s51: taking all the planes fitted in the step S4 and the point cloud data corresponding to the planes as algorithm input, and setting relevant parameters, including the following parameters:
ψtotal: all the planes of the input are collected; i istotal: inputting a planar grid point cloud set; Δ θ: thresholds of different plane normal included angles; Δ d: a distance threshold between the centers of gravity of the planes; psi: initializing a plane set to be output into an empty set; i isout: initializing a point set corresponding to a plane set to be output into an empty set;
s52: set psi of all planes randomly input fromtotalRandomly selecting partial planes as seed planes, adding the seed planes into a plane set psi to be output, and adding point cloud data corresponding to the seed planes into a point set I corresponding to the plane set to be outputout；
S53: searching unselected planes in the neighborhood of the plane set psi to be output, and judging whether the planes are coplanar with the planes in the plane set psi to be output, wherein the judgment formula is as follows:
θ＜Δθ，d＜Δd
wherein theta is an included angle between normal lines of the planes, and d is a projection distance of the gravity centers of different planes along the normal line direction; if the non-selected plane near psi and all planes in psi meet the above-mentioned judgment condition of coplanar planes, i.e. coplanar, adding them into psi, and adding the point cloud data corresponding to said plane into point set IoutIf not, continuing to search the next unselected plane in the psi neighborhood range;
s54: repeating the step S53 until the unselected planes near the plane set psi to be output are not coplanar with the mid-plane of psi or no planes are in the neighborhood of psi, stopping growing, and connecting psi and IoutOutput and empty, and from psitotalRemoving psi from ItotalIn which removal of Iout；
S55: and repeating the steps S52, S53 and S54 until all planes and the point cloud data corresponding to the planes are output.
9. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 8, wherein in step S6, the I outputted in step S54 is processed by using an iterative weighted least squares algorithmoutCarrying out plane fitting, judging whether the fitted plane is an end face, and calculating the distance between the end faces, wherein the specific steps are as follows:
s61: set of computation points IoutThe basic parameters of (2) include: center of gravity, initial normal, and set iteration number kiterTerminating the condition gamma of iteration and the threshold value of the angle difference of the normal line of the fitted plane;
s62: construction IoutThe weighted covariance matrix C of (a), the formula is as follows:
Figure FDA0002473259950000051
Figure FDA0002473259950000052
Figure FDA0002473259950000053
Figure FDA0002473259950000054
Figure FDA0002473259950000055
wherein p isiIs the coordinates of a point or points of interest,
Figure FDA0002473259950000056
is the coordinate of the center of gravity,
Figure FDA0002473259950000057
for the k iteration center of gravity offset, n is the normal, wiFor the weighting factor, const is a constant value, which can be set according to the resolution of the point cloud.
Performing eigenvalue decomposition on the weighted covariance matrix C, and taking the eigenvector corresponding to the minimum eigenvalue as a point set IoutThe normal vector of (a);
s63: judging the normal angle deviation value of two adjacent iterative calculations, if the deviation is less than gamma, ending the iteration in advance, otherwise, continuing the iterative calculation C until the iteration times is more than kiterFinally outputting a fitted plane;
s64: and judging whether the fitted plane is an end face or not, and calculating the distance between the end faces to obtain the end face butt joint gap of the aircraft skin.
10. The method for calculating the aircraft skin butt-joint gap based on the end face extraction as claimed in claim 9, wherein in step S64, it is first determined whether the fitted plane is an end face, and then the distance between the end faces is calculated to obtain the aircraft skin butt-joint gap, which specifically includes the following steps:
setting neighborhood thresholdthAnd angle threshold thetathTaken at the centre of gravity of one of the planesthA neighborhood range including a point on another plane and having an angle greater than θ between the normal vector of the other plane and the normal vector of the other planethJudging that the fitted plane is an end face; when the included angle of the normal vectors of the two end surfaces is 180 degrees, the two end surfaces are parallel, otherwise, the two end surfaces are not parallel;
if the fitted end surfaces are parallel, then respectively selecting one point on the two end surfaces, and calculating the projection distance between the two points along the normal direction of the end surfaces, namely the end surface butt joint gap d of the skiniThe calculation formula is as follows:
di＝||(pi-pj)·n||
in the formula (d)iIs the butt-joint clearance of the end faces of the skins when the end faces of the skins are parallel; p is a radical ofi，pjRespectively are any two points on two end faces, and n is a plane normal vector;
if the fitted end surfaces are not parallel, calculating the distance from all end points of one end surface to the other end surface, wherein the maximum value is dmaxMinimum value of dminThe end face of the skin faces the gap diIn the range of dmin≤di≤dmax。
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