CN118013747A - Large-section positioning hole selection method based on simulated annealing nested principal component analysis - Google Patents
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Abstract
The invention provides a large-section locating hole selection method based on simulated annealing nested principal component analysis, which comprises the following steps: respectively carrying out point cloud scanning on the butt joint end surfaces of the large sections of the aircraft, and extracting the characteristics of the end surface connecting holes after processing the point cloud data; establishing a corresponding relation of the butt end face connecting holes of the large section of the aircraft to form a positioning butt point set; selecting a limited group of positioning pair point sets, and calculating pose transformation of the butt joint end surfaces based on principal component analysis transformation; and taking the average value and the mean square value of the integral positioning errors of the butt joint end surfaces as optimization indexes, optimizing an initial positioning pair point set based on a simulated annealing algorithm, and selecting an optimal initial positioning hole. The method improves the uniformity of end face correction and improves the positioning precision of end face butt joint.
Description
Technical Field
The invention relates to the technical field of large-section butt joint assembly, in particular to a large-section locating hole selection method based on simulated annealing nested principal component analysis.
Background
The accuracy of the butt-joint assembly of a large section of the aerospace vehicle determines the service performance of the aircraft. And the flatness and roundness of the butt joint end surfaces of most sections deviate from theoretical values when in horizontal assembly due to the influences of manufacturing errors, dead weight deformation and the like, so that the circle centers of the positioning pin holes and the butt joint holes distributed circumferentially on the respective end surfaces cannot be completely overlapped. In engineering, in order to realize the butt joint of a large section of an aircraft, the positioning and the bolt connection of uniformly distributed positioning pin holes are finished first. And then manually visually selecting a butt joint hole area with high hole center overlapping ratio to finish bolt fastening. And finally, carrying out end face correction on the butt joint hole area with larger hole center deviation through manual operations such as tilting, pulling, pressing and the like, and further completing the fastening of bolt holes on the butt joint end face. The assembly process is high in randomness, extremely depends on experience of engineers, is time-consuming and labor-consuming, and greatly prolongs manufacturing and assembly cycles of the aircraft. And the end face correction is easy to cause uneven stress and strain distribution, and the running stability of the aircraft is reduced.
In the butt joint assembly of the large sections of the aircraft, the positioning pin holes are used as initial positioning references, and then the assembly mode of manually selecting the bolt connection sequence can influence the positioning precision of the end face bolt holes, the fastening efficiency of the bolts and the correction degree of the end faces. At present, in the butt joint of a large section of an aircraft, a plurality of bolt holes instead of positioning pin holes are not considered to be directly used as initial positioning references for the butt joint of the end faces, and the accuracy and the orthopedic uniformity of the butt joint of the end faces are required to be improved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a large-section locating hole selection method based on simulated annealing nested principal component analysis.
In order to solve the problems, the technical scheme of the invention is as follows:
a large-section locating hole selection method based on simulated annealing nested principal component analysis comprises the following steps:
Respectively carrying out point cloud scanning on the butt joint end surfaces of the large sections of the aircraft, and extracting the characteristics of the end surface connecting holes after processing the point cloud data;
establishing a corresponding relation of the butt end face connecting holes of the large section of the aircraft to form a positioning butt point set;
selecting a limited group of positioning pair point sets, and calculating pose transformation of the butt joint end surfaces based on principal component analysis transformation;
And taking the average value and the mean square value of the integral positioning errors of the butt joint end surfaces as optimization indexes, optimizing an initial positioning pair point set based on a simulated annealing algorithm, and selecting an optimal initial positioning hole.
Preferably, the step of performing point cloud scanning on the butt-joint end surfaces of the large section of the aircraft, and extracting the characteristics of the end surface connecting hole after processing the point cloud data specifically includes: and (3) carrying out point cloud scanning on the butt joint end surfaces of the large sections of the two aircrafts for horizontal assembly, carrying out denoising and deleting treatment on point cloud data, and then carrying out plane fitting and roundness calculation to extract the characteristics of the end surface connecting holes.
Preferably, the step of establishing a correspondence between the connection holes of the butt end surfaces of the large sections of the aircraft to form a positioning butt point set specifically includes: and establishing a corresponding relation of connecting holes of the butt joint end surfaces of two large sections of the aircraft to form a positioning butt point set, wherein the positioning butt point set is marked as C 0 and comprises N p pairs of positioning holes.
Preferably, the step of selecting a limited set of positioning pairs, calculating pose transformation of the butt end surface based on principal component analysis transformation, specifically comprises the following steps:
selecting n pairs from a positioning pair point set C 0 as an initial positioning hole, and marking the initial positioning hole as a point set pair C, wherein the initial positioning hole comprises a point set Q= { Q 1,q2,…,qn } and a point set P= { P 1,p2,…,pn }, the point set Q is positioned on a target butt joint surface, and the point set P is positioned on a source butt joint surface;
Calculating the center of gravity of the positioning point set, and carrying out point set centering treatment:
Calculating covariance matrix W among the point sets, and carrying out SVD decomposition:
W＝P1·Q1 T＝UΣVH
constructing a rotation matrix R and a displacement matrix t from the source point set P to the target point set Q according to SVD decomposition results:
R＝V·UT
constructing a pose transformation matrix from a source end face to a target end face:
Pose transformation is performed on the butt-joint end face positioning pair point set C 0, and the positioning error epsilon (C 0) and the positioning error mean square value mu (C 0) of all positioning points are calculated:
preferably, the step of optimizing the initial positioning pair point set based on the simulated annealing algorithm by using the average value and the mean square value of the overall positioning error of the butt end surface as optimization indexes, and selecting the optimal initial positioning hole specifically comprises the following steps:
Step 1: initializing parameters of a simulated annealing algorithm: initial temperature T 0, cooling temperature T f, temperature decay parameter α and Markov chain length L k;
Step 2: randomly selecting any pair of the pair of replacement point sets C from the positioning point sets C 0 based on the selected initial positioning holes and positioning precision to form a new point set pair C N, checking the repetition condition, and reconstructing the new point set pair C N if the new point set pair C N exists in the history selection;
Step 3: performing a principal component analysis algorithm on the new point set pair C N to calculate an end-to-end joint pose change T (C N);
step 4: calculating the positioning error of the positioning pin hole after the butt joint pose changes T (C N), and judging whether the positioning precision meets the coordination positioning requirement:
l≤D-d
Wherein l is the center distance of the positioning pin hole pair, D is the diameter of the positioning pin hole, and D is the diameter of the positioning pin;
Step 5: calculating positioning error epsilon N of the butt joint end face, if the positioning error epsilon N is smaller than historical optimal error epsilon best, replacing an optimal point set pair C best with a new point set pair C N, replacing a current point set pair C with a new point set pair C N, and replacing the optimal error epsilon best with a current error epsilon N; otherwise, the current point set pair C is replaced with the probability exp (- (ε N - ε (C))/T as the new point set pair C N.
Preferably, the step of optimizing the initial positioning pair point set based on the simulated annealing algorithm by using the average value and the mean square value of the overall positioning error of the butt end surface as optimization indexes and selecting the optimal initial positioning hole specifically further comprises: judging whether the cycle times are smaller than the Markov chain length, if not, continuing to circularly calculate at the current temperature T N; if yes, annealing and cooling, wherein the current temperature is reduced as follows: t N = αt, determining whether the current temperature T is less than the cooling temperature T f, if not, continuing to circulate at the annealed temperature T N; if yes, the cycle is terminated, and an optimal point set pair C best and an optimal end face positioning error epsilon best are output.
Compared with the prior art, the invention provides a large-section locating hole selection method based on simulated annealing nested principal component analysis, and the locating holes with larger weight on the butt joint precision are efficiently calculated and reserved in the random search process by introducing the principal component analysis transformation algorithm and the simulated annealing algorithm, so that the relative optimal solution is obtained, the priority recommendation of the connection of the connecting holes can be improved, the influence of manufacturing errors and self-weight deformation on the butt joint of the end faces can be considered by the initial locating holes optimized by the method, the uniformity of end face correction is improved, the locating precision of the butt joint of the end faces is improved, and the method has important significance on the butt joint work of large sections of aircrafts in engineering practice.
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Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of a large section locating hole selection method based on simulated annealing nested principal component analysis;
FIG. 2 is a pictorial representation of a large section of an aircraft according to the present invention;
FIG. 3 is a graph of real-time point cloud data for a large section of an aircraft according to the present invention;
FIG. 4 is a flow chart of a set of locating points matching calculation based on principal component analysis transformation in accordance with the present invention;
FIG. 5 is a flow chart of the initial positioning point optimization based on the simulated annealing algorithm;
FIG. 6 is a graph showing the distribution of the optimal initial positioning points with the number of 2-10 in the end face;
FIG. 7 is a graph comparing the end face positioning errors given by the preferred initial positioning points of the method and the sequential indexing method;
FIG. 8 is a time comparison of the method of the present invention with a sequential index preferred initial location point algorithm;
FIG. 9 is a graph of end face positioning error for an initial number of positioning points of 2-10 according to the present invention;
FIG. 10 is a graph showing the algorithm calculation time when the initial number of positioning points is 2-10.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.
Specifically, the invention provides a large-section locating hole selection method based on simulated annealing nested principal component analysis, as shown in fig. 1, comprising the following steps:
S1: respectively carrying out point cloud scanning on the butt joint end surfaces of the large sections of the aircraft, and extracting the characteristics of the end surface connecting holes after processing the point cloud data;
Specifically, as shown in fig. 2, the physical model of the large section of the aircraft performs point cloud scanning as shown in fig. 3 on the butt end surfaces of the large section of the two aircraft for horizontal assembly. And then, carrying out preprocessing such as denoising, deleting and the like on the point cloud data, and then carrying out plane fitting and roundness calculation to extract the characteristics of the end face connecting hole.
S2: establishing a corresponding relation of the butt end face connecting holes of the large section of the aircraft to form a positioning butt point set;
Specifically, a corresponding relation of connecting holes of the butt joint end surfaces of two large sections of the aircraft is established, and a positioning butt point set is formed, and is marked as C 0 and comprises N p pairs of positioning holes.
S3: selecting a limited group of positioning pair point sets, and calculating pose transformation of the butt joint end surfaces based on principal component analysis transformation;
Specifically, as shown in fig. 4, fig. 4 shows a locating point set matching flow based on principal component analysis transformation, a principal component analysis algorithm transforms a space point set to obtain a principal component vector of the space point set, then calculates a covariance matrix by using the principal component vector and barycentric coordinates of the point set, and finally calculates a transformation relationship between the covariance matrices. The method realizes the calculation of the end face positioning error and the mean square value of any given initial positioning point group.
First, n pairs are selected from the positioning pair point set C 0 as initial positioning holes, and are denoted as point set pairs C, including point sets q= { Q 1,q2,…,qn } and p= { P 1,p2,…,pn }, where point set Q is located on the target butt-joint surface and point set P is located on the source butt-joint surface.
Calculating the center of gravity of the positioning point set, and carrying out point set centering treatment:
Calculating covariance matrix W among the point sets, and carrying out SVD decomposition:
W＝P1·Q1 T＝UΣVH
constructing a rotation matrix R and a displacement matrix t from the source point set P to the target point set Q according to SVD decomposition results:
R＝V·UT
further, constructing a pose transformation matrix from the source end face to the target end face:
Pose transformation is performed on the butt-joint end face positioning pair point set C 0, and the positioning error epsilon (C 0) and the positioning error mean square value mu (C 0) of all positioning points are calculated:
s4: and taking the average value and the mean square value of the integral positioning errors of the butt joint end surfaces as optimization indexes, optimizing an initial positioning pair point set based on a simulated annealing algorithm, and selecting an optimal initial positioning hole.
Specifically, as shown in fig. 5, the process of selecting the optimal initial positioning hole based on the simulated annealing algorithm includes the following steps:
Step 1: initializing parameters of a simulated annealing algorithm: initial temperature T 0, cooling temperature T f, temperature decay parameter α and Markov chain length L k;
Step 2: randomly selecting any pair of the pair of replacement point sets C from the positioning point sets C 0 based on the selected initial positioning holes and positioning precision to form a new point set pair C N, checking the repetition condition, and reconstructing the new point set pair C N if the new point set pair C N exists in the history selection;
Step 3: performing a principal component analysis algorithm on the new point set pair C N to calculate an end-to-end joint pose change T (C N);
step 4: calculating the positioning error of the positioning pin hole after the butt joint pose changes T (C N), and judging whether the positioning precision meets the coordination positioning requirement:
l≤D-d
wherein l is the center distance of the positioning pin hole pair, D is the diameter of the positioning pin hole, and D is the diameter of the positioning pin. And if the positioning error of the positioning pin hole does not meet the requirement, the step 2 is re-executed.
Step 5: calculating positioning error epsilon N of the butt joint end face, if the positioning error epsilon N is smaller than historical optimal error epsilon best, replacing an optimal point set pair C best with a new point set pair C N, replacing a current point set pair C with a new point set pair C N, and replacing the optimal error epsilon best with a current error epsilon N; otherwise, replace the current point set pair C with the probability exp (- (epsilon N -epsilon (C))/T as the new point set pair C N;
Preferably, judging whether the cycle number is smaller than the Markov chain length, if not, continuing to calculate at the current temperature T N; if yes, annealing and cooling, wherein the current temperature is reduced as follows:
TN＝αT
Judging whether the current temperature T is smaller than the cooling temperature T f, if not, continuing to circulate at the annealed temperature T N; if yes, the cycle is terminated, and an optimal point set pair C best and an optimal end face positioning error epsilon best are output.
Further, as shown in fig. 6, initial positioning point positions are drawn on the butt end surfaces of a large section, and 2-10 initial positioning point positions are shown in fig. 6. According to roundness analysis in the end face point cloud data processing process, the initial positioning holes are selected from the positions with poor roundness of the butt joint end faces, so that the uniformity of end face correction is improved, and all the butt joint holes are easier to connect.
The existing initial positioning hole selection method based on the sequential index strategy is a method for sequentially calculating the end face pose transformation and the positioning error for the arrangement and combination of the butt joint end face connecting hole pairs of a large section of the aircraft, and selecting the combination corresponding to the minimum positioning error. Compared with the end face positioning error and the calculation time calculated by the method and the sequential indexing method, as shown in fig. 7 and 8, the calculation magnitude of the sequential indexing method shows exponential increase. When the initial positioning hole exceeds 5 pairs, the computing power used by the computing example cannot meet the computing requirement, and the positioning Kong Xunyou fails to solve. The algorithm provided by the invention has robustness, and the initial positioning logarithm can finish calculation when the initial positioning logarithm is increased by 2-10 pairs. The method only compares the end face positioning errors and algorithm calculation time of the initial positioning hole pairs in 2-5 pairs, and under the condition that the accuracy of the results is the same, the algorithm efficiency provided by the invention is far higher than that of a sequential guiding method, and the method has the capability of guiding the butt joint of large sections in engineering practice efficiently.
Figures 9 and 10 show the average positioning error and algorithmic calculation time of the end face abutment for initial pilot hole at 2-10 pairs of increments. The algorithm provides the initial positioning hole combination condition under the working condition of the butt joint of the aircraft end face under the minimum positioning error and the mean square value of the minimum positioning error, so that the selection of the initial positioning hole logarithm has little influence on the end face positioning precision. When the number of the positioning holes is increased, the distribution positions of the positioning holes are known, and the initial positioning holes are firstly distributed at the position with poor roundness of the end face, so that the correction uniformity of the end face is facilitated. The invention provides a guiding scheme for connecting priorities of end face butt joint holes of a large section of an aircraft, which can effectively improve the uniformity of end face correction, reduce the accident of end face butt joint, reduce the labor cost and improve the butt joint efficiency.
The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.
Claims (6)
1. A large-section locating hole selection method based on simulated annealing nested principal component analysis, characterized by comprising the following steps:
Respectively carrying out point cloud scanning on the butt joint end surfaces of the large sections of the aircraft, and extracting the characteristics of the end surface connecting holes after processing the point cloud data;
establishing a corresponding relation of the butt end face connecting holes of the large section of the aircraft to form a positioning butt point set;
selecting a limited group of positioning pair point sets, and calculating pose transformation of the butt joint end surfaces based on principal component analysis transformation;
And taking the average value and the mean square value of the integral positioning errors of the butt joint end surfaces as optimization indexes, optimizing an initial positioning pair point set based on a simulated annealing algorithm, and selecting an optimal initial positioning hole.
2. The method for selecting the positioning holes of the large section based on the simulated annealing nesting principal component analysis according to claim 1, wherein the step of respectively performing point cloud scanning on the butt joint end surfaces of the large section of the aircraft and extracting the characteristics of the end surface connecting holes after processing the point cloud data specifically comprises the following steps: and (3) carrying out point cloud scanning on the butt joint end surfaces of the large sections of the two aircrafts for horizontal assembly, carrying out denoising and deleting treatment on point cloud data, and then carrying out plane fitting and roundness calculation to extract the characteristics of the end surface connecting holes.
3. The method for selecting a large-section positioning hole based on simulated annealing nesting principal component analysis according to claim 1, wherein the step of establishing a correspondence of large-section butt-joint end face connecting holes of an aircraft to form a positioning butt-joint point set specifically comprises: and establishing a corresponding relation of connecting holes of the butt joint end surfaces of two large sections of the aircraft to form a positioning butt point set, wherein the positioning butt point set is marked as C 0 and comprises N p pairs of positioning holes.
4. The method for selecting a large-section positioning hole based on simulated annealing nesting principal component analysis according to claim 3, wherein said selecting a finite set of positioning pairs, calculating a pose transformation of a butt end face based on a principal component analysis transformation, specifically comprises the steps of:
selecting n pairs from a positioning pair point set C 0 as an initial positioning hole, and marking the initial positioning hole as a point set pair C, wherein the initial positioning hole comprises a point set Q= { Q 1,q2,…,qn } and a point set P= { P 1,p2,…,pn }, the point set Q is positioned on a target butt joint surface, and the point set P is positioned on a source butt joint surface;
Calculating the center of gravity of the positioning point set, and carrying out point set centering treatment:
Calculating covariance matrix W among the point sets, and carrying out SVD decomposition:
W＝P1·Q1 T＝UΣVH
constructing a rotation matrix R and a displacement matrix t from the source point set P to the target point set Q according to SVD decomposition results:
R＝V·UT
constructing a pose transformation matrix from a source end face to a target end face:
Pose transformation is performed on the butt-joint end face positioning pair point set C 0, and the positioning error epsilon (C 0) and the positioning error mean square value mu (C 0) of all positioning points are calculated:
5. The method for selecting the positioning holes of the large section based on the simulated annealing nesting principal component analysis according to claim 1, wherein the step of optimizing the initial positioning pair point set based on the simulated annealing algorithm by using the average value and the mean square value of the overall positioning error of the butt end surface as optimization indexes, and selecting the optimal initial positioning holes specifically comprises the following steps:
Step 1: initializing parameters of a simulated annealing algorithm: initial temperature T 0, cooling temperature T f, temperature decay parameter α and Markov chain length L k;
Step 2: randomly selecting any pair of the pair of replacement point sets C from the positioning point sets C 0 based on the selected initial positioning holes and positioning precision to form a new point set pair C N, checking the repetition condition, and reconstructing the new point set pair C N if the new point set pair C N exists in the history selection;
Step 3: performing a principal component analysis algorithm on the new point set pair C N to calculate an end-to-end joint pose change T (C N);
step 4: calculating the positioning error of the positioning pin hole after the butt joint pose changes T (C N), and judging whether the positioning precision meets the coordination positioning requirement:
l≤D-d
Wherein l is the center distance of the positioning pin hole pair, D is the diameter of the positioning pin hole, and D is the diameter of the positioning pin;
Step 5: calculating positioning error epsilon N of the butt joint end face, if the positioning error epsilon N is smaller than historical optimal error epsilon best, replacing an optimal point set pair C best with a new point set pair C N, replacing a current point set pair C with a new point set pair C N, and replacing the optimal error epsilon best with a current error epsilon N; otherwise, the current point set pair C is replaced with the probability exp (- (ε N - ε (C))/T as the new point set pair C N.
6. The method for selecting a large-section positioning hole based on simulated annealing nesting principal component analysis according to claim 5, wherein the step of optimizing the initial positioning pair point set based on the simulated annealing algorithm by using the average value and the mean square value of the overall positioning error of the butt end surface as optimization indexes, and selecting the optimal initial positioning hole specifically further comprises: judging whether the cycle times are smaller than the Markov chain length, if not, continuing to circularly calculate at the current temperature T N; if yes, annealing and cooling, wherein the current temperature is reduced as follows: t N = αt, determining whether the current temperature T is less than the cooling temperature T f, if not, continuing to circulate at the annealed temperature T N; if yes, the cycle is terminated, and an optimal point set pair C best and an optimal end face positioning error epsilon best are output.
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