CN115994403A - Pile casing checking method, device and equipment based on three-dimensional circle center fitting - Google Patents
Pile casing checking method, device and equipment based on three-dimensional circle center fitting Download PDFInfo
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Abstract
The invention discloses a pile casing checking method, device and equipment based on three-dimensional circle center fitting, and belongs to the technical field of pile casing checking in pile foundation construction. The method of the invention realizes the non-contact measurement of the pile casing based on the fitting of the three-dimensional circle center, and has the support of the circle center deviation value, so that constructors can conveniently position and correct the pile casing, and the construction efficiency and quality are improved.
Description
Technical Field
The invention belongs to the technical field of pile foundation construction, in particular to the technical field of pile casing checking during pile foundation construction, and particularly relates to a pile casing checking method, device and equipment based on three-dimensional circle center fitting.
Background
In bridge construction sites, drilling machines are often used for drilling pile foundation holes. In order to ensure that the lofting position of the pile position is consistent with the design drawing, so as to achieve accurate lofting of the pile position, a pile casing is often used, and positioning and protection of a pile foundation hole are carried out through the pile casing, wherein one common mode of pile foundation hole positioning through the pile casing is as follows: after the central position of the pile foundation is determined, pile protection is introduced in the longitudinal and transverse directions, the central position of the pile casing is determined by using four pile protection in the orthogonal directions, then the pile casing is buried, and the longitudinal and transverse lines are restored to the pile casing, so that the central position of the drilling machine is adjusted, and the pile position is positioned. In the processes of clay backfill tamping, drilling machine positioning and drilling, the phenomenon of deviation of the pile casing can occur, and the positioning check of the pile casing is an essential ring in bridge construction. However, in the field construction, the pile casing is buried in the pile foundation hole, so that the non-contact measurement cannot be conveniently and accurately performed, and further, the pile position before concrete pouring cannot be well ensured to be vertical and free of offset, so that the time and the labor are consumed for reworking the pile foundation, and the construction cost is increased; in addition, if the deviation of the pile foundation can not be found in the construction stage, the delivery quality of the cast bridge is also directly reduced.
Therefore, an effective method for checking the casing is needed.
Disclosure of Invention
In view of the above, the invention aims to overcome one or more of the shortcomings related in the background art, and provides a pile casing checking method, device and equipment based on three-dimensional circle center fitting.
The aim of the invention is realized by the following technical scheme:
first aspect
The first aspect of the invention provides a pile casing checking method based on three-dimensional circle center fitting, which comprises the following steps:
s100, obtaining three-dimensional coordinates of at least three scattered points, wherein the scattered points are positioned at the edge of the inner wall at the top of the pile casing;
s200, judging whether all scattered points are collinear or not, if so, returning to S100, otherwise, executing S300;
s300, carrying out plane fitting on all scattered points according to an SVD (singular value decomposition) algorithm, and solving an optimal plane and a normal vector of the optimal plane, wherein the sum of squares of distances between all the scattered points and the optimal plane is the minimum value;
s400, judging whether the optimal plane is a 2D plane, if so, jumping to S800, otherwise, executing S500;
s500, projecting each scattered point distributed on the optimal plane to a preset reference 2D plane based on a first transformation relation to obtain coordinates of a projected point corresponding to each scattered point, wherein the first transformation relation is a mapping relation between a direction vector of any scattered point and a first target direction vector obtained by rotating the direction vector of the scattered point to the reference 2D plane, and the first target direction vector is a direction vector of the projected point of the corresponding scattered point on the reference 2D plane;
s600, performing circular fitting on all projection points, calculating the radius of the circle obtained by fitting and the fitting circle center coordinates, and then executing S700;
s700, determining the coordinates of each projection point and the fitting circle center on the optimal plane on the basis of a second transformation relation, wherein the second transformation relation is reciprocal to the first transformation relation, and then executing S900;
s800, performing circular fitting on all scattered points distributed on the optimal plane, calculating the radius of the circle obtained by fitting and the fitting circle center coordinates, and then executing S900;
s900, calculating a circle center deviation value of the protective cylinder according to the coordinate of the fitting circle center on the optimal plane and the coordinate of the design circle center of the top of the protective cylinder.
Preferably, the step S300 is specifically:
s301, carrying out average value subtraction on the three-dimensional coordinates of all scattered points, and forming the three-dimensional coordinates of all the scattered points subjected to the average value subtraction
Matrix A of (2), wherein matrix->
，/>
Representing three-dimensional coordinates of scattered points, i is more than or equal to 1 and less than or equal to n, n represents the number of the scattered points, and the average value is +.>
；
S302, the sum of squares of the distances from each scattered point to the pre-solving plane is expressed as
Wherein n represents the pre-solved normal vector +.>
，/>
Representing square of two norms of matrix A and normal vector n after matrix multiplication, and +.>
，/>
Indicating the scatter after mean subtraction +.>
Three-dimensional coordinates of +.>
Indicating the scatter after mean subtraction +.>
Is a three-dimensional coordinate of (2);
s303, carrying out singular value decomposition on the matrix A based on SVD decomposition algorithm, and carrying out singular value decomposition on the matrix A
Wherein->
The matrix is a diagonal matrix with non-main diagonal elements of 0, the elements on the main diagonal are sequentially reduced, and a left singular matrix U and a right singular matrix V are unitary matrices;
s304, the sum of squares of the distances from each scattered point to the pre-solving plane is expressed as
；
S305, according to the diagonal matrix
The value of the last row in +.>
And according to
Derived->
；
S306, determining a third row of the right singular matrix V as a normal vector n, and determining a pre-solution according to the normal vector n obtained by solution
And solving a plane, wherein the normal vector of the plane is a normal vector n, and defining the plane as the optimal plane.
Preferably, in S500, the rotation of the direction vector of each scatter point to the reference 2D plane results in the use of the rodgers rotation.
Preferably, in the step S600, a least square method is adopted when circular fitting is performed on all the projection points; in S800, a least square method is used for performing circular fitting on each scattered point distributed on the optimal plane.
Preferably, the method comprises the steps of,
in S500, the generation process of the first transformation relationship specifically includes:
defining the rotation axis K as a vector product of a normal vector n of the optimal plane and a normal vector of the reference 2D plane;
determining rotation angle from normal vector n of the most suitable plane and normal vector of the reference 2D plane
；
Based on the rotation axis K and rotation angle determined
The expression of the rotdrigas rotation formula is obtained:
wherein->
Direction vector representing the scatter to be rotated, < ->
Representing a first target direction vector obtained by rotating the scatter direction vector,/for>
Representing a dot product symbol;
and generating a coordinate mapping relation between any one scattered point and a projection point of the scattered point on a reference 2D plane according to the determined Rodrigues rotation formula, and defining the coordinate mapping relation as a first transformation relation.
Preferably, the step S900 further includes:
s1000, determining a real-time central axis of the protection barrel according to the coordinates of all scattered points or all projection points on the optimal plane, the coordinates of the fitting circle center on the optimal plane and the preset depth value of the protection barrel, and calculating the offset angle between the real-time central axis of the protection barrel and the design central axis of the protection barrel.
The first aspect of the invention has the following beneficial effects:
(1) Solving the optimal plane of each three-dimensional scattered point through SVD (singularvalue ecomposition, singular value decomposition) algorithm; when the optimal plane is a 3D plane, carrying out rotation projection on the direction vectors of all three-dimensional scattered points, rotating the direction vectors of all three-dimensional scattered points to a reference 2D plane, obtaining projection points of all three-dimensional scattered points, carrying out circular fitting on all projection points on the reference 2D plane, determining the fitting circle center and radius of the circular according to the circular obtained after fitting, and turning all projection points on the circular and the direction vectors corresponding to the fitting circle center back to the optimal plane through the reverse rotation process of rotating the direction vectors of all three-dimensional scattered points to the reference 2D plane, so as to obtain the coordinates of the fitting circle center on the optimal plane; when the optimal plane is a 2D plane, directly carrying out circular fitting on each scattered point, determining the fitting circle center and the radius of the circle according to the circle obtained after fitting, and then calculating the circle center deviation between the fitting circle center and the design circle center;
therefore, the non-contact measurement of the pile casing is realized, the support of the circle center deviation value is provided, and constructors can conveniently and rapidly position and correct the pile casing, so that the construction efficiency and quality are improved.
(2) For redundant observation, when the SVD decomposition algorithm obtains the optimal plane of each three-dimensional scattered point, invalid observation points (invalid scattered points) with overlarge deviation are effectively filtered, and the calibration result of the pile casing is high in accuracy while the non-contact measurement of the pile casing is realized.
(3) The method for rotating the direction vector of each three-dimensional scattered point to the reference 2D plane is introduced, so that the efficiency of rotation projection is improved, and the checking efficiency of the pile casing checking method realized in the first aspect of the invention is further improved;
(4) The circle fitting is carried out by adopting a least square method, the fitting error is small, and the calculated circle center deviation and the calculated offset angle (the inclination of the protection barrel) between the real-time central axis of the protection barrel and the design central axis of the protection barrel are high in accuracy, so that the accuracy of the protection barrel checking method realized in the first aspect of the invention is improved.
Second aspect
The second aspect of the invention provides a casing checking device based on three-dimensional circle center fitting, which comprises a memory and a processor, wherein the memory is used for storing the casing checking method based on the three-dimensional circle center fitting, and the processor is used for calling the method stored in the memory to check the casing.
The second aspect of the present invention brings about the same effective effects as the first aspect, and is not described here again.
Third aspect of the invention
The third aspect of the invention provides a pile casing checking device based on three-dimensional circle center fitting, which comprises the pile casing checking device based on three-dimensional circle center fitting and a total station, wherein the pile casing checking device is in communication connection with the total station, the total station is used for scanning scattered points positioned at the edge of the inner wall of the top of the pile casing, generating three-dimensional coordinates of each scattered point after scanning, and sending the three-dimensional coordinates of each scattered point to the pile casing checking device.
The third aspect of the present invention brings about the same effective effects as the first aspect, and is not described here in detail.
Drawings
Fig. 1 is a flowchart of a three-dimensional circle center fitting-based casing verification method according to an embodiment.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by a person skilled in the art without any inventive effort, are intended to be within the scope of the present invention, based on the embodiments of the present invention.
Example 1
Referring to fig. 1, the embodiment provides a pile casing checking method based on three-dimensional circle center fitting, which is used for checking pile position casings in bridge construction.
Specifically, the pile casing checking method based on three-dimensional circle center fitting provided by the embodiment comprises the following steps:
s100, acquiring point set data, wherein the point set data comprises three or more three-dimensional coordinates of scattered points, and each scattered point is positioned at the edge of the inner wall at the top of the protective cylinder. The point set data can be obtained by scanning the edge of the inner wall at the top of the pile casing through three-dimensional scanning equipment.
S200, judging whether all scattered points are collinear or not, if so, returning to S100, otherwise, executing S300. The three-dimensional coordinates of the scattered points obtained by scanning the edge of the inner wall at the top of the casing through the three-dimensional scanning equipment are not collinear, so that whether invalid scattered points exist in the scattered points is determined through judging whether the three points are collinear, and if the three points are collinear, the process returns to the step S100 to re-obtain the point set data.
S300, carrying out plane fitting on all scattered points according to an SVD (singular value decomposition) algorithm, and solving an optimal plane and a normal vector of the optimal plane, wherein the sum of squares of distances between all the scattered points and the optimal plane is the minimum value. The spatial initial plane direction of the scatter distribution is found by step S300.
Optionally, one specific implementation procedure of step S300 is as follows:
s301, carrying out average value subtraction on three-dimensional coordinates of all scattered points, and forming three-dimensional coordinates of all scattered points subjected to average value subtraction
Matrix A of (2), wherein matrix->
，/>
Representing three-dimensional coordinates of scattered points, i is more than or equal to 1 and less than or equal to n, n represents the number of the scattered points, and the average value is +.>
. As will be appreciated by those skilled in the art, the average C comprises an average C of x-dimensional coordinates x Average C of y-dimensional coordinates y And average value C of z-dimensional coordinates z And the coordinates of each dimension are subjected to average subtraction by using the average value corresponding to the dimension. Through average value subtraction, the operation process of subsequent SVD decomposition is simplified.
Substep S302 the sum of squares of the distances of the various scatter points to the pre-solved plane is expressed as
Wherein n represents the pre-solved normal vector +.>
，/>
Representing square of two norms of matrix A and normal vector n after matrix multiplication, and +.>
，/>
Representing the scatter after mean subtraction
Three-dimensional coordinates of +.>
Indicating the scatter after mean subtraction +.>
Is a three-dimensional coordinate of (c).
The principle of the step is as follows: to find a plane, the sum of distances from all the scattered points to the plane is satisfied, and the distance is measured in step S302 by using the sum of squares formula of distances from the scattered points to the plane simplified in step S301, and the sum of squares formula is algebraically expressed as
，/>
Representing the matrix bipartite.
S303, carrying out singular value decomposition on the matrix A based on SVD (singular value decomposition) algorithm, and carrying out singular value decomposition on the matrix A
Wherein->
The matrix is a diagonal matrix with non-main diagonal elements of 0, the elements on the main diagonal are sequentially reduced, and a left singular matrix U and a right singular matrix V are unitary matrices;
substep S304, step SThe sum of squares of the distances of the individual scatter points to the pre-solved plane is expressed as
；
Substep S305. According to the diagonal matrix
The value of the last row in +.>
And according to
Derived->
；
And S306, determining a third row of the right singular matrix V as a normal vector n, determining a pre-solved plane according to the solved normal vector n, wherein the normal vector of the plane is the normal vector n, and defining the plane as an optimal plane.
S400, judging whether the optimal plane is a 2D plane, if so, jumping to S800, otherwise executing S500.
S500, projecting each scattered point distributed on the optimal plane to a preset reference 2D plane based on a first transformation relation to obtain coordinates of a projected point corresponding to each scattered point, wherein the first transformation relation is a mapping relation between a direction vector of any scattered point and a first target direction vector obtained by rotating the direction vector of the scattered point to the reference 2D plane, and the first target direction vector is a direction vector of the projected point of the corresponding scattered point on the reference 2D plane. The scattered points distributed in the direction of the initial plane of the space are projected onto a preset reference 2D plane through the step S500, so that curve fitting on the reference 2D plane is convenient to carry out. Preferably, the reference 2D plane is chosen as the XOY plane of the three-dimensional coordinate system.
Optionally, in S500, one generation process of the first transformation relationship is:
step 1) defining a rotation axis as a vector product of a normal vector n of the optimal plane and a normal vector of a reference 2D plane;
step 2) determining a rotation angle according to the normal vector n of the optimal plane and the normal vector of the reference 2D plane
The method specifically comprises the following steps: the angle between the normal vector n of the most suitable plane and the normal vector of the reference 2D plane is defined as the rotation angle +.>
；
Step 3) according to the determined rotation axis K and rotation angle
The expression of the rotdrigas rotation formula is obtained:
wherein->
Direction vector representing the scatter to be rotated, < ->
Representing a first target direction vector obtained by rotating the scatter direction vector,/for>
Representing a dot product symbol;
and 4) generating a coordinate mapping relation between any one scattered point and a projection point of the scattered point on a reference 2D plane according to the determined Rodrigues rotation formula, and defining the coordinate mapping relation as a first transformation relation.
S600, performing circular fitting on all projection points, calculating the radius of the circle obtained by fitting and the fitting center coordinates, and then executing S700. The coordinates of the fitting circle center obtained at this time are two-dimensional coordinates.
Optionally, when all the projection points are circularly fitted in step S600, a least square method is adopted, and the implementation process of the least square method adopts the process in the common embodiment.
S700, determining the coordinates of each projection point and the fitting circle center on the optimal plane on the basis of a second transformation relationship, wherein the second transformation relationship is reciprocal to the first transformation relationship, and then executing S900. At this time, the coordinates of each projection point and the fitting circle center obtained based on the second transformation relation are three-dimensional coordinates.
The principle of the step is as follows: after fitting the circle on the reference 2D plane, the obtained circle needs to be rotated back to the position of the optimal plane, so that a secondary rotation is also needed, and it can be seen that the secondary rotation is a reverse rotation of the primary rotation, and therefore the second transformation relationship is reciprocal to the first transformation relationship.
S800, performing circular fitting on all scattered points distributed on the optimal plane, calculating the radius of the circle obtained by fitting and the fitting circle center coordinates, and executing S900. The coordinates of the fitting circle center obtained at this time are three-dimensional coordinates.
Optionally, when the circular fitting is performed on each scattered point distributed on the optimal plane in step S800, a least square method is adopted, and the implementation process of the least square method adopts the process in the common embodiment.
S900, calculating a circle center deviation value of the protective cylinder according to the coordinate of the fitting circle center on the optimal plane and the coordinate of the design circle center of the top of the protective cylinder.
Example two
The difference between this embodiment and the first embodiment is that the following steps are further included after step S900:
s1000, determining a real-time central axis of the protection barrel according to the coordinates of all scattered points or all projection points on the optimal plane, the coordinates of the fitting circle center on the optimal plane and the preset depth value of the protection barrel, and calculating the offset angle between the real-time central axis of the protection barrel and the design central axis of the protection barrel.
Example III
The embodiment provides a pile casing checking device based on three-dimensional circle center fitting, which comprises a memory and a processor, wherein the memory is used for storing the pile casing checking method based on the three-dimensional circle center fitting realized in the first embodiment or the second embodiment, and the processor is used for calling the pile casing checking method stored in the memory to check the pile casing.
Example IV
The embodiment provides a pile casing checking device based on three-dimensional circle center fitting, which comprises a pile casing checking device based on three-dimensional circle center fitting and a total station, wherein the pile casing checking device is in communication connection with the total station, the total station is used for scanning scattered points positioned at the edge of the inner wall of the top of the pile casing, generating three-dimensional coordinates of the scattered points after scanning, and sending the three-dimensional coordinates of the scattered points to the pile casing checking device.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and environments and is capable of modifications within the scope of the inventive concept, either as taught or as a matter of routine skill or knowledge in the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (8)
1. A pile casing checking method based on three-dimensional circle center fitting is characterized by comprising the following steps:
s100, obtaining three-dimensional coordinates of at least three scattered points, wherein the scattered points are positioned at the edge of the inner wall at the top of the pile casing;
s200, judging whether all scattered points are collinear or not, if so, returning to S100, otherwise, executing S300;
s300, carrying out plane fitting on all scattered points according to an SVD (singular value decomposition) algorithm, and solving an optimal plane and a normal vector of the optimal plane, wherein the sum of squares of distances between all the scattered points and the optimal plane is the minimum value;
s400, judging whether the optimal plane is a 2D plane, if so, jumping to S800, otherwise, executing S500;
s500, projecting each scattered point distributed on the optimal plane to a preset reference 2D plane based on a first transformation relation to obtain coordinates of a projected point corresponding to each scattered point, wherein the first transformation relation is a mapping relation between a direction vector of any scattered point and a first target direction vector obtained by rotating the direction vector of the scattered point to the reference 2D plane, and the first target direction vector is a direction vector of the projected point of the corresponding scattered point on the reference 2D plane;
s600, performing circular fitting on all projection points, calculating the radius of the circle obtained by fitting and the fitting circle center coordinates, and then executing S700;
s700, determining the coordinates of each projection point and the fitting circle center on the optimal plane on the basis of a second transformation relation, wherein the second transformation relation is reciprocal to the first transformation relation, and then executing S900;
s800, performing circular fitting on all scattered points distributed on the optimal plane, calculating the radius of the circle obtained by fitting and the fitting circle center coordinates, and then executing S900;
s900, calculating a circle center deviation value of the protective cylinder according to the coordinate of the fitting circle center on the optimal plane and the coordinate of the design circle center of the top of the protective cylinder.
2. The pile casing checking method based on three-dimensional circle center fitting according to claim 1, wherein the step S300 is specifically:
s301, carrying out average value subtraction on the three-dimensional coordinates of all scattered points, and forming the three-dimensional coordinates of all the scattered points subjected to the average value subtraction
Matrix A of (2), wherein matrix->
，/>
Representing three-dimensional coordinates of scattered points, i is more than or equal to 1 and less than or equal to n, n represents the number of the scattered points, and the average value is +.>
；
S302, the sum of squares of the distances from each scattered point to the pre-solving plane is expressed as
Wherein n represents the pre-solved normal vector +.>
，/>
Represents the square of the two norms of the matrix A and the normal vector n after matrix multiplication, and
， />
indicating the scatter after mean subtraction +.>
Three-dimensional coordinates of +.>
Indicating the scatter after mean subtraction +.>
Is a three-dimensional coordinate of (2);
s303, carrying out singular value decomposition on the matrix A based on SVD decomposition algorithm, and carrying out singular value decomposition on the matrix A
Wherein, the method comprises the steps of, wherein,
the matrix is a diagonal matrix with non-main diagonal elements of 0, the elements on the main diagonal are sequentially reduced, and a left singular matrix U and a right singular matrix V are unitary matrices;
s304, the sum of squares of the distances from each scattered point to the pre-solving plane is expressed as
；
S305, according to the diagonal matrix
The value of the last row in +.>
And according to
Derived->
；
S306, determining a third row of the right singular matrix V as a normal vector n, determining a pre-solved plane according to the solved normal vector n, wherein the normal vector of the plane is the normal vector n, and defining the plane as an optimal plane.
3. The method for checking a casing based on three-dimensional circle center fitting according to claim 1, wherein in S500, the rotation of the direction vector of each scattered point to the reference 2D plane is performed by using the rotation of rodgers when obtaining the first target direction vector.
4. The method for checking the pile casing based on the three-dimensional circle center fitting according to claim 1, wherein in the step S600, a least square method is adopted when all projection points are circularly fitted; in S800, a least square method is used for performing circular fitting on each scattered point distributed on the optimal plane.
5. The method for checking the pile casing based on the three-dimensional circle center fitting according to claim 3, wherein,
in S500, the generation process of the first transformation relationship specifically includes:
defining the rotation axis K as a vector product of a normal vector n of the optimal plane and a normal vector of the reference 2D plane;
normal vector n according to the most suitable plane and normal vector of the reference 2D planeDetermining rotation angle
；
Based on the rotation axis K and rotation angle determined
The expression of the rotdrigas rotation formula is obtained:
wherein->
Direction vector representing the scatter to be rotated, < ->
Representing a first target direction vector obtained by rotating the scatter direction vector,/for>
Representing a dot product symbol;
and generating a coordinate mapping relation between any one scattered point and a projection point of the scattered point on a reference 2D plane according to the determined Rodrigues rotation formula, and defining the coordinate mapping relation as a first transformation relation.
6. The method for checking the casing based on the three-dimensional circle center fitting according to claim 1, wherein the step S900 further comprises:
s1000, determining a real-time central axis of the protection barrel according to the coordinates of all scattered points or all projection points on the optimal plane, the coordinates of the fitting circle center on the optimal plane and the preset depth value of the protection barrel, and calculating the offset angle between the real-time central axis of the protection barrel and the design central axis of the protection barrel.
7. The pile casing checking device based on the three-dimensional circle center fitting is characterized by comprising a memory and a processor, wherein the memory is used for storing the pile casing checking method based on the three-dimensional circle center fitting, and the processor is used for calling the method stored in the memory to check the pile casing.
8. The pile casing checking device based on the three-dimensional circle center fitting is characterized by comprising the pile casing checking device based on the three-dimensional circle center fitting and a total station, wherein the pile casing checking device is in communication connection with the total station, the total station is used for scanning scattered points positioned on the edge of the inner wall of the top of the pile casing, generating three-dimensional coordinates of each scattered point after scanning, and sending the three-dimensional coordinates of each scattered point to the pile casing checking device.
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