CN114808754A - High-precision real-time prediction method for spatial position of large-scale swivel bridge - Google Patents
High-precision real-time prediction method for spatial position of large-scale swivel bridge Download PDFInfo
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Abstract
The invention discloses a high-precision real-time prediction method for a space position of a large-scale swivel bridge, which comprises the following steps of: arranging reference points on the swivel bridge, establishing a corresponding three-dimensional space coordinate system, and collecting initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 (ii) a Initial coordinate A based on rigid body space position transformation basic theory and the reference point 0 And coordinates A after the rotation change 1 Calculating a rigid transformation matrix H and determining the structure motion characteristics; obtaining an initial coordinate value B of a key position measuring point of a beam body 0 And calculating the coordinate value B of the key position measuring point of the beam body at any moment in the turning process according to the structural motion characteristics 1 And the high-precision real-time prediction of the spatial position of the swivel bridge is realized. The invention has the advantages that: has the advantages of convenient and fast operation, saving a large amount of manpower, material resources and financial resources, and effectively improving the space position of the bridge to turnAccuracy and robustness of real-time prediction.
Description
Technical Field
The invention relates to the technical field of bridges, in particular to a high-precision real-time prediction method for the space position of a large-scale rotating bridge.
Background
With the development of the traffic industry of China, the number of the vertical crossing lines is continuously increased, and how to avoid the interference of construction on the existing lines becomes the research focus in the field of bridge engineering at present. The bridge rotating technology is essentially that the structure of a bridge is used for supporting so as to avoid erecting a support on a river channel or a traffic line and rotate to the position after the construction is finished. The interference of bridge rotation construction to the traffic trunk line is small, and the traffic transportation department clearly stipulates that the place where the bridge spans must be constructed. Therefore, the bridge rotation construction technology is further researched and perfected, and the aim of realizing rotation, stability and accuracy is of great significance for the development of bridge engineering. The existing swivel construction control mainly adopts a traction cable to pull a swivel, and if the swivel exceeds a design angle, a jack can only be used for pushing and returning, so that a higher requirement is provided for accurate swivel. On the other hand, because a gap exists between the supporting foot fixed on the upper structure (the upper rotating disc) and the slideway, the beam body rotates around the vertical shaft and also rotates longitudinally and transversely around the structure in the rotating process, so that the spatial position of the rotating structure has uncertainty in a certain range. Therefore, accurate rotation is ensured, accurate actions such as obstacle crossing and specified space crossing of the bridge with a rotating body are realized, and monitoring of the whole bridge rotating process is an important link. The swivel process monitoring mainly comprises structural deformation monitoring and swivel angle monitoring, and the monitoring equipment and the method comprise a turntable pointer, a total station, satellite positioning and the like.
The turntable pointer method is the most widely used method for monitoring the rotating angle at present, and is divided into a laser demarcation device method and a mechanical turntable pointer method, the two methods have the same principle, the position monitoring in the bridge rotating process is realized by using various pointer alignment, and the excessive rotation can be prevented. However, the method has poor precision control, and a small amount of angle indication errors can cause obvious deviation of the cantilever end of the beam body; on the other hand, the single angle monitoring is omitted for measuring the vertical displacement of the structure, which is not beneficial to the smooth implementation of the bridge rotation. The monitoring of the satellite positioning system can realize full-automatic measurement, but the equipment has higher condition requirements, the communication signal is greatly interfered by the outside world, the stability is poor, and the implementation of accurate rotation is not facilitated, and the method is still in an exploration stage at present. The total station observation method is simple to operate and mature, and for most of rotating bridges, the coordinates of key points can be directly measured only by finding a measuring station capable of monitoring the whole process, so that the total station observation method is widely favored.
Disclosure of Invention
The invention aims to provide a high-precision real-time prediction method for the spatial position of a large-scale swivel bridge according to the defects of the prior art, which can calculate a rigid transformation matrix according to the initial coordinates and the changed coordinates of the rigid body datum points, and combine the rigid transformation matrix with the initial postures of the control points to obtain the target form of the control points, thereby effectively improving the precision and the robustness of the real-time prediction of the spatial position of the swivel bridge.
The purpose of the invention is realized by the following technical scheme:
a high-precision real-time prediction method for a space position of a large-scale swivel bridge is characterized by comprising the following steps:
(S1) arranging reference points on the swivel bridge, establishing a corresponding three-dimensional space coordinate system, and collecting initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 ；
(S2) transforming the basic theory based on the spatial position of the rigid body and the initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 Calculating rigid transformation matrix H and determining structure operationDynamic characteristics;
(S3) acquiring an initial coordinate value B of a key position measuring point of the beam body 0 And calculating the coordinate value B of the key position measuring point of the beam body at any moment in the turning process according to the structural motion characteristics 1 And the high-precision real-time prediction of the spatial position of the swivel bridge is realized.
In step S1, the position of the reference point is selected on the upper turntable of the swivel bridge.
In step S2, a set of points P = ∑ tone in spacep i |p i ∈R,i=1,2, … n } is spatially transformed into a set of points Q = penq i |q i ∈R,i=1,2, … n }, the coordinate transformation from P to Q is calculated as follows (1):
q i =Hp i （1），
in the formula (I), the compound is shown in the specification,q i andp i for the four-dimensional column vectors in the spatial point sets P and Q, three position coordinates for each point in P and Q are represented,p i =[x i ，y i ，z i ，1] T 、q i =[x i ′，y i ′，z i ′，1] T (ii) a H is a space object coordinate transformation matrix;
calculating a space object coordinate transformation matrix H according to the following formula (2):
wherein R is a rotation transformation matrix,tin order to translate the vector, the vector is translated,vin order to transform the vector for perspective,Sis an integral scale factor;
for the space rigid body, in order to ensure that the shape and size after transformation are kept unchanged, in the formula (2), the space rigid body is providedvIs a vector of 0 s and is a vector,Sto 1, the rotation transformation matrix R and translation vector are calculated by the following equations (3) and (4)t：
In the formula (I), the compound is shown in the specification,α、β、γare respectively wound around the objectx、y、zThe rotation angles of the three shafts are different,t x 、t y 、t z respectively displacement of the object along three-axis directions; at the moment, the space object coordinate transformation matrix H is called a rigid transformation matrix, and when the change of the shape and the size is not considered, the rigid transformation matrix can be formed by three corners and three displacement parameters; for rigid body position transformation, a coordinate transformation matrix H of the space object can be identified by combining the change of coordinate points;
the rotation transformation matrix R is calculated by the following equations (5) and (6):
in the formula (I), the compound is shown in the specification,a i =[x i ，y i ，z i ] T ，i= 1-3 is three non-collinear key points selected from the entity point set P, and the corresponding points after the movement areb i =[x i ′，y i ′，z i ′] T ，i=1~3；η i Andη i ' is the vector direction between corresponding vectors;
the translation vector is calculated as follows (7)t：
In the formula (2)x i ，y i ，z i ] T And 2x i ′，y i ′，z i ′] T Respectively representing coordinates before and after the change of the key points, wherein R is a rotation transformation matrix;
the rigid transformation matrix H is calculated as follows (8):
wherein R is a rotation transformation matrix,tis a translation vector, and O is a 0 vector;
according to the above-mentioned basic theory of rigid body space position transformation and calculation formula the initial coordinate A of said reference point 0 And coordinates A after the rotation change 1 And obtaining a rigid transformation matrix H as the structural motion characteristic.
In step S3, the coordinate value B of the key position measuring point at any time during rotation is calculated according to the following equation (9) 1 ：
B 1 =HB 0 （9），
In the formula, B 0 And H is a rigid transformation matrix.
The invention has the advantages that: calculating a rigid transformation matrix according to the initial coordinates and the changed coordinates of the rigid body reference points, and combining the rigid transformation matrix with the initial posture of the control point to obtain a target form of the control point; the spatial position of the bridge at any moment in the turning process can be predicted only by monitoring the coordinates of the reference point near the center of the turning body without directly monitoring the coordinates of the control point at the cantilever end; the method has the advantages of being convenient and fast to operate, saving a large amount of manpower, material resources and financial resources, and effectively improving the accuracy and robustness of real-time prediction of the spatial position of the turning bridge.
Drawings
FIG. 1 is a schematic flow chart of a high-precision real-time prediction method for the spatial position of a large-scale swivel bridge according to the present invention;
FIG. 2 is a local coordinate monitoring point diagram of the turntable on the swivel bridge according to the present invention;
FIG. 3 is a regional view of a swivel bridge observation station location of the present invention;
FIG. 4 is a schematic view of a pivot bridge end layout survey of the present invention;
FIG. 5 is a table of coordinate data of base points of the turntable according to the present invention;
FIG. 6 is a table of coordinates of a formal swivel deck according to the present invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings to facilitate understanding by those skilled in the art:
example (b): as shown in fig. 1, the present embodiment relates to a method for predicting a spatial position of a large-sized swivel bridge in real time with high accuracy, where the prediction method includes the following steps:
s1: arranging reference points on the rotating bridge, establishing a corresponding three-dimensional space coordinate system, and collecting initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 。
The swivel bridge generally comprises an upper rotating disc, a lower rotating disc, a spherical hinge, a beam body and the like. For the actual structure, the points on the upper rotating disc are easy to carry out coordinate monitoring; the key points such as the top plate or the bottom plate at the beam end of the beam body are inconvenient to directly monitor due to the fact that the span distance is large in the rotating process and is influenced by light rays, distance or other factors. Therefore, the position of the reference point is generally selected on the rotary bridge rotary disk.
S2: initial coordinate A based on rigid body space position transformation basic theory and reference point 0 And coordinates A after swivel change 1 And calculating a rigid transformation matrix H and determining the structure motion characteristics.
Wherein, a group of point sets P = &inspacep i |p i ∈R,i=1,2, … n } is spatially transformed into a set of points Q = penq i |q i ∈R,i=1,2, … n }, and the coordinate change from P to Q is calculated by the following equation (1)Changing:
q i =Hp i （1），
in the formula (I), the compound is shown in the specification,q i andp i for the four-dimensional column vectors in the spatial point sets P and Q, three position coordinates for each point in P and Q are represented,p i =[x i ，y i ，z i ，1] T 、q i =[x i ′，y i ′，z i ′，1] T (ii) a H is a space object coordinate transformation matrix;
calculating a space object coordinate transformation matrix H according to the following formula (2):
where R is a rotation transformation matrix (rotation transformation subblock),tin order to translate the vector, the vector is translated,vin order to transform the vector for perspective,Sis an integral scale factor;
for the space rigid body, in order to ensure that the shape and size after transformation are kept unchanged, in the formula (2), the space rigid body is providedvIs a vector of 0 s and is a vector,Sto 1, the rotation transformation matrix R and translation vector are calculated by the following equations (3) and (4)t：
In the formula (I), the compound is shown in the specification,α、β、γare respectively wound around the objectx、y、zThe rotation angles of the three shafts are different,t x 、t y 、t z respectively displacement of the object along the three-axis direction; at the moment, the space object coordinate transformation matrix H is called rigid transformation momentWhen the change of the shape and the size is not considered, the rigid transformation matrix can be formed by three corners and three displacement parameters; for the rigid body position transformation problem, a coordinate transformation matrix H of the space object can be identified by directly combining the change of the coordinate point;
the rotation transformation matrix R is calculated by the following equations (5) and (6):
in the formula (I), the compound is shown in the specification,a i =[x i ，y i ，z i ] T ，i= 1-3 is three non-collinear key points selected from the entity point set P, and the corresponding points after the movement areb i =[x i ′，y i ′，z i ′] T ，i=1~3；η i Andη i ' is the vector direction between corresponding vectors;
the translation vector is calculated as follows (7)t：
In the formula (2)x i ，y i ，z i ] T And 2x i ′，y i ′，z i ′] T Respectively representing coordinates before and after the change of the key points, wherein R is a rotation transformation matrix;
the rigid transformation matrix H is calculated as follows (8):
wherein R is a rotation transformation matrix,tis a translation vector, and O is a 0 vector;
according to the above-mentioned basic theory of rigid body space position transformation and calculation formula, the initial coordinate A of reference point 0 And coordinates A after the rotation change 1 A rigid transformation matrix H can be obtained as the structural motion characteristic.
S3: obtaining an initial coordinate value B of a key position measuring point of a beam body 0 And calculating the coordinate value B of the key position measuring point of the beam body at any moment in the turning process according to the structure motion characteristics 1 And high-precision real-time prediction of the spatial position of the rotating bridge is realized.
Wherein, the coordinate value B of the key position measuring point at any time in the turning process is calculated according to the following formula (9) 1 ：
B 1 =HB 0 （9），
In the formula, B 0 And H is a rigid transformation matrix.
In addition, the large-scale rotating bridge has slow rotating speed, and the whole process is quasi-static; the rotation is selected in a time period with small external wind load, and the rail traffic under the bridge is interrupted during the rotation, so that the bridge rotation process is slightly interfered by the outside, and the large-scale rotation bridge structure can be considered to have rigid body properties. The main factors influencing the prediction accuracy of the spatial position of the rigid body structure include: firstly, testing errors by coordinate values; the area of the test net, namely the area of the area enclosed by the three control points. The spatial position prediction bias increases as the test error of the instrument increases. The higher the precision of the measuring instrument, the larger the area of the 'test net' is, the smaller the deviation of the prediction result is.
In the embodiment, the upper structure of the swivel beam is a 2 × 66m variable cross-section box-shaped beam, the bridge width is 34m, the swivel beam is connected with the spherical hinge through the V-shaped pier, the total weight of the swivel bridge is 2.14 ten thousand tons, and the design position of a main line can be reached after the swivel beam rotates clockwise by 70 degrees. The bearing capacity of the swivel spherical hinge is 2.5 ten thousand tons, the radius R of the sphere is = 9.0 m, the horizontal projection radius of the spherical surface is 5.0 m, and the design diameter of the annular slide way is 12.5 m. The V-shaped pier upper rotary table consists of a square upper disc and a circular rotary table, wherein the side length of the square upper disc is 16m, and the height of the square upper disc is 2 m; the diameter phi of the round turntable is 14.5m, and the height is 1 m; 8 pairs of steel supporting feet are uniformly arranged along a circular slideway below the circular turntable. And 2 pairs of steel cables are embedded in the rotary table and used as traction cables in the rotating body construction process. Weighing and actually measuring the frictional resistance moment of the spherical hinge of the rotating body to be 28650 kN.m, the longitudinal unbalanced moment of the bridge to be 4850 kN.m (deviated to a small mileage side) and the transverse unbalanced moment; the ball pivot coefficient of friction μ = 0.015. The longitudinal eccentricity is 0.023m, and the transverse eccentricity is 0.0011 m. The bridge has good integral balance and small eccentric moment, and does not need to be subjected to counterweight treatment. The average value of the measured traction force is 116 tons during the trial rotation of the bridge.
As shown in fig. 2, the triangular points on the turntable are selected as local coordinate monitoring points, so that the observation angle can be conveniently adjusted and the rapid test can be realized in the rotation process of the bridge, and the test points are arranged on the upper turntable according to the principle of maximum area of the test net.
As shown in fig. 3, the three measuring points can be observed in the whole rotating process for observing the position area of the station. In addition, two groups of testing groups are additionally arranged in the turning process to synchronously monitor the coordinates of the measuring points at the beam ends, and the coordinates are used for carrying out comparison and verification on a space position prediction method based on local coordinates.
As shown in fig. 4, a measuring point is arranged for the beam end. The state after the trial rotation is finished is taken as an observation starting point (namely, the initial state), 52 degrees of the accumulated rotation is selected as a state one, and 70 degrees of the accumulated rotation is selected as a state two. The coordinates of the test reference points J1, J2, and J3 in the different states are shown in fig. 5. On the basis, the motion characteristics of the rigid body relative to the initial state are identified and extracted for predicting coordinates of beam end measuring points P1-P6, and the predicted result and the actually measured coordinates are compared as shown in figure 6. As can be seen from the data in fig. 5 and 6: the height coordinate change in the rotation process of the bridge is small, and the height of the end part of the longitudinal bridge facing to the small mileage in the whole rotation process is reduced by about 6cm relative to the initial position; the maximum difference value of the height changes of the transverse bridge direction is about 1-2 cm; the data shows that the swivel process is relatively smooth. The predicted result of the bridge far-end measuring point based on the method is compared with the corresponding actually measured coordinate data, and the following results can be seen: the predicted value and the measured value of the three-dimensional coordinate of the same measuring point are very close, and the predicted deviation of the coordinates of a plurality of measuring points is between 1 and 4 mm. The maximum deviation value is 2.37cm, i.e. the x-coordinate value of point P3 in fig. 6 (among other factors). The data result shows that the method can realize high-precision prediction of the space position of the rotary bridge.
In summary, in the present embodiment, the key of the "turning accuracy" of the turning bridge is to accurately measure and acquire the spatial position or posture of the bridge structure at any time in the turning process, so as to compare the spatial position or posture with the external structure in real time, thereby ensuring the accuracy and safety of the turning bridge. The bridge rotation process is essentially rigid motion, and the motion rules of all parts of the bridge rotation process are consistent. The method provides a high-precision real-time prediction method for the spatial position of a large-scale rotating bridge, and the motion rule of the whole structure can be obtained by observing the local spatial position change of a rigid body. When the bridge rotates, the motion amplitude near the rotating shaft is small, so that the bridge is an ideal total station observation object.
Although the conception and the embodiments of the present invention have been described in detail with reference to the drawings, those skilled in the art will recognize that various changes and modifications can be made therein without departing from the scope of the appended claims, and therefore, they are not to be considered repeated herein.
Claims (4)
1. A high-precision real-time prediction method for a space position of a large-scale swivel bridge is characterized by comprising the following steps:
(S1) arranging reference points on the swivel bridge, establishing a corresponding three-dimensional space coordinate system, and collecting initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 ；
(S2) transforming the basic theory based on the spatial position of the rigid body and the initial coordinates A of the reference points 0 And coordinates A after the rotation change 1 Calculating a rigid transformation matrix H and determining the structure motion characteristics;
(S3) acquiring an initial coordinate value B of a key position measuring point of the beam body 0 And calculating the coordinate value B of the key position measuring point of the beam body at any moment in the turning process according to the structural motion characteristics 1 And the high-precision real-time prediction of the spatial position of the swivel bridge is realized.
2. The method for predicting the spatial position of a large-scale swivel bridge in real time with high accuracy according to claim 1, wherein in step S1, the position of the reference point is selected on the upper rotary disk of the swivel bridge.
3. The method as claimed in claim 2, wherein in step S2, a set of points in space P = last leaf in spacep i |p i ∈R,i=1,2, … n } is spatially transformed into a set of points Q = penq i |q i ∈R,i=1,2, … n }, the coordinate transformation from P to Q is calculated as follows (1):
q i =Hp i （1），
in the formula (I), the compound is shown in the specification,q i andp i for the four-dimensional column vectors in the spatial point sets P and Q, three position coordinates for each point in P and Q are represented,p i =[x i ，y i ，z i ，1] T 、q i =[x i ′，y i ′，z i ′，1] T (ii) a H is a space object coordinate transformation matrix;
calculating a space object coordinate transformation matrix H according to the following formula (2):
wherein R is a rotation transformation matrix,tin order to translate the vector, the vector is translated,vin order to transform the vector for perspective,Sis an integral scale factor;
for the space rigid body, in order to ensure that the shape and size after transformation are kept unchanged, in the formula (2), the following equation is setvIs a vector of 0 s and is a vector,Sto 1, the rotation transformation matrix R and translation vector are calculated by the following equations (3) and (4)t：
In the formula (I), the compound is shown in the specification,α、β、γare respectively wound around the objectx、y、zThe rotation angle of the three shafts is changed,t x 、t y 、t z respectively displacement of the object along three-axis directions; at the moment, the space object coordinate transformation matrix H is called a rigid transformation matrix, and when the change of the shape and the size is not considered, the rigid transformation matrix can be formed by three corners and three displacement parameters; for rigid body position transformation, a coordinate transformation matrix H of the space object can be identified by combining the change of coordinate points;
the rotation transformation matrix R is calculated by the following equations (5) and (6):
in the formula (I), the compound is shown in the specification,a i =[x i ，y i ，z i ] T ，i= 1-3 is three non-collinear key points selected from the entity point set P, and the corresponding points after the movement areb i =[x i ′，y i ′，z i ′] T ，i=1~3；η i Andη i ' is the vector direction between corresponding vectors;
the translation vector is calculated as follows (7)t：
In the formula (2)x i ，y i ，z i ] T And 2x i ′，y i ′，z i ′] T Respectively representing coordinates before and after the change of the key points, wherein R is a rotation transformation matrix;
the rigid transformation matrix H is calculated as follows (8):
wherein R is a rotation transformation matrix,tis a translation vector, and O is a 0 vector;
according to the above-mentioned basic theory of rigid body space position transformation and calculation formula the initial coordinate A of said reference point 0 And coordinates A after the rotation change 1 A rigid transformation matrix H can be obtained as the structural motion characteristic.
4. The method for predicting the space position of the large-scale swivel bridge in real time with high accuracy according to claim 3, wherein in step S3, the coordinate value B of the key position measuring point at any time in the swivel process is calculated according to the following formula (9) 1 ：
B 1 =HB 0 （9），
In the formula, B 0 And H is a rigid transformation matrix.
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