CN116484465A - Linear control method for lifting arch rib of arch bridge - Google Patents
Linear control method for lifting arch rib of arch bridge Download PDFInfo
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Abstract
The invention discloses a linear control method for lifting arch ribs of an arch bridge, which relates to the technical field of bridge engineering structure construction, and comprises the following steps: measuring and obtaining the actual measurement value of the linear control point coordinates of the erected arch rib segment; determining a coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point; and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib. The method solves the problems that in the prior art, in order to correct errors between actual measurement values and predicted values of linear control points of arch rib segments, a CAD drawing method is generally adopted to make subsequent arch rib position diagrams for correction, time is wasted, efficiency is low, and accuracy of error correction cannot be guaranteed.
Description
Technical Field
The invention relates to the technical field of bridge engineering structure construction, in particular to a linear control method for lifting arch ribs of an arch bridge.
Background
In the process of hoisting the arch rib segments of the large-span steel pipe concrete arch bridge, the arch rib installation alignment is often controlled by a plurality of non-collinear alignment points. However, in the actual hoisting process, the arch rib of the leading section is affected by welding in construction, temporary load in construction, butt joint deviation of two sections, wind direction and temperature in the environment, and the like, and the dimensional accuracy of arch rib manufacturing, so that a certain error is generated between the measured value and the predicted value of the linear control point of the arch rib section. If the error is not corrected in time, the arch rib is hoisted according to the original splicing angle, the generated accumulated error influences the hoisting precision of the subsequent arch rib section, the prediction line shape of the whole arch rib is changed, and meanwhile, secondary internal force is generated on the installed arch rib section, so that the stress safety of the arch rib is influenced.
In the prior art, in order to correct errors between actual measurement values and predicted values of linear control points of arch rib segments, a CAD drawing method is generally adopted to make subsequent arch rib position diagrams for correction, and the problems of low time consumption and efficiency and incapability of ensuring the accuracy of error correction exist.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide the arch bridge arch rib hoisting linear control method, which can solve the problems that in the prior art, in order to correct errors between actual measurement values and predicted values of arch rib segment linear control points, a CAD drawing method is generally adopted to make subsequent arch rib position drawings for correction, the time consumption is low, and the accuracy of error correction cannot be ensured.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the scheme provides an arch bridge arch rib hoisting linear control method, which comprises the following steps:
measuring and obtaining the actual measurement value of the linear control point coordinates of the erected arch rib segment;
determining a coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point;
and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib.
In some alternative solutions, determining, according to the actual measurement value and the theoretical coordinate value of the linear control point of the erected arch rib segment and the theoretical coordinate value of the linear control point of the next arch rib segment, the predicted coordinate value of the linear control point of the next arch rib segment through a rigid body motion transformation formula includes:
establishing a rigid motion control equation of the arch rib segment linear control points;
determining a rotation matrix and translation parameters in a rigid body motion control equation according to the actual measurement value and the theoretical coordinate value of the linear control point of the erected arch rib segment;
and determining the predicted value of the next arch rib linear control point according to the rotation matrix, the translation parameter and the theoretical value of the next arch rib linear control point coordinate by combining a rigid motion control equation.
In some alternatives, the rigid motion control equation is:
wherein [ X ] S Y S Z S ] T Is the predicted value of the coordinates of the linear control point, [ Y ] L Y L Z L ] T Is the theoretical value of the coordinates of the linear control point, X S As the abscissa predicted value, Y S As the predicted value of the ordinate, Z S As predicted value of vertical coordinate, X L Is the theoretical value of the abscissa, Y L As the theoretical value of the ordinate, Z L Is a theoretical value of vertical coordinates, R is a rotation matrix, T X For the first translation parameter, T Y For the second translation parameter, T Z Is a third translation parameter.
In some alternatives, determining the rotation matrix and translation parameters in the rigid body motion control equation based on the actual measurement and the theoretical measurement of the linear control point coordinates of the erected rib segment includes:
reducing the rotation matrix by using the Rodrign matrix, and converting the rotation angle parameter of the rotation matrix into a substitution parameter;
obtaining an error equation according to the difference between the rigid motion control equation and the first-order Taylor expansion of the rigid motion control equation;
and (5) iteratively solving an error equation by using a least square method to obtain a substitution parameter and a translation parameter.
In some alternatives, reducing the rotation matrix by the rodgers matrix converts the rotation angle parameter of the rotation matrix into the substitution parameter, including:
the rotation matrix is originally:
the matrix after the reduction is:
wherein, alpha is a first rotation angle parameter, beta is a second rotation angle parameter, gamma is a third rotation angle parameter, a is a first substitution parameter, b is a second substitution parameter, and c is a third substitution parameter.
In some alternatives, the error equation is: v=aΔx+l;
wherein Δx= (ΔaΔbΔcΔt) X ΔT Y ΔT Z ) T ；
l＝(l 1 l 2 l 3 ) T ；
Wherein v is an error value, deltax is a parameter increment, parameters with Deltax are all the increment, A is an error equation coefficient, i is a linear control point serial number, l is a constant term matrix, l 1 Is the first constant term, l 2 Is the second constant term, l 3 Is a third constant term.
In some alternatives, iteratively solving the error equation using a least squares method, obtaining the surrogate parameters and the translation parameters, comprising:
setting initial values of replacement parameters and translation parameters, and acquiring parameter increment and error values by using a least square method;
and continuing to iterate through the least square method, and taking the substitution parameter and the translation parameter at the moment as results when the error value is smaller than the set value.
In some alternatives, the minimumThe square formula is: Δx= (a T A) -1 (A T l)；
Wherein A is T Is the transpose of matrix a.
In some alternative schemes, the coordinate theoretical value of the linear control point of the segment of the erected arch rib and the coordinate theoretical value of the linear control point of the next segment of the arch rib are obtained according to arch rib design linearity and finite element analysis means.
In some alternatives, a segment of the rib includes at least three non-collinear linear control points thereon.
Compared with the prior art, the invention has the advantages that: according to the scheme, the actual measurement value of the coordinates of the linear control points of the erected arch rib segments is obtained through measurement; determining a coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point; and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib. The method solves the problems that in the prior art, in order to correct errors between actual measurement values and predicted values of linear control points of arch rib segments, a CAD drawing method is generally adopted to make subsequent arch rib position diagrams for correction, time is wasted, efficiency is low, and accuracy of error correction cannot be guaranteed.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for controlling the lifting line shape of an arch rib of an arch bridge in an embodiment of the invention;
FIG. 2 is a schematic view of a spliced rib segment in accordance with an embodiment of the present invention;
FIG. 3 is a schematic view of a next arch rib according to an embodiment of the present invention;
FIG. 4 is a schematic cross-sectional view of a spliced rib segment station arrangement in accordance with an embodiment of the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present application based on the embodiments herein.
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a linear control method for lifting arch ribs of an arch bridge, which comprises:
s1: and measuring to obtain the actual measurement value of the linear control point coordinates of the erected arch rib segment.
S2: and determining the coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point.
The step S2 specifically comprises the following steps:
s21: and (5) establishing a rigid motion control equation of the arch rib segment linear control points.
In the present embodiment, the rigid body motion control equation is:
wherein [ X ] S T S Z S ] T Is the predicted value of the coordinates of the linear control point, [ X ] L Y L Z L ] T Is the theoretical value of the coordinates of the linear control point, X S As the abscissa predicted value, Y S As the predicted value of the ordinate, Z S As predicted value of vertical coordinate, X L Is the theoretical value of the abscissa, Y L As the theoretical value of the ordinate, Z L Is a theoretical value of vertical coordinates, R is rotationMatrix, T X For the first translation parameter, T Y For the second translation parameter, T Z Is a third translation parameter.
S22: and determining a rotation matrix and translation parameters in the rigid motion control equation according to the actual measurement value and the theoretical coordinate value of the linear control point of the erected arch rib segment.
The step S22 specifically includes:
s221: and reducing the rotation matrix by using the Rodrign matrix, and converting the rotation angle parameter of the rotation matrix into a substitution parameter.
In this embodiment, the rotation matrix is originally:
the matrix after the reduction is:
wherein, alpha is a first rotation angle parameter, beta is a second rotation angle parameter, gamma is a third rotation angle parameter, a is a first substitution parameter, b is a second substitution parameter, and c is a third substitution parameter.
S222: and obtaining an error equation according to the difference between the rigid motion control equation and the first-order Taylor expansion of the rigid motion control equation.
In this embodiment, the error equation is: v=aΔx+l;
wherein Δx= (ΔaΔbΔcΔt) X ΔT Y ΔT Z ) T ；
l＝(l 1 l 2 l 3 ) T ；
Wherein v is an error value, deltax is a parameter increment, parameters with Deltax are all the increment, A is an error equation coefficient, i is a linear control point serial number, l is a constant term matrix, l 1 Is the first constant term, l 2 Is the second constant term, l 3 Is a third constant term.
S223: and (5) iteratively solving an error equation by using a least square method to obtain a substitution parameter and a translation parameter.
In this embodiment, the error equation is iteratively solved by using a least square method, to obtain the substitution parameter and the translation parameter, including:
setting initial values of replacement parameters and translation parameters, and acquiring parameter increment and error values by using a least square method;
and continuing to iterate through the least square method, and taking the substitution parameter and the translation parameter at the moment as results when the error value is smaller than the set value.
The least square formula is: Δx= (a T A) -1 (A T l) wherein A T Is the transpose of matrix a.
S23: and determining the predicted value of the next arch rib linear control point according to the rotation matrix, the translation parameter and the theoretical value of the next arch rib linear control point coordinate by combining a rigid motion control equation.
In this embodiment, step S2 may be performed by MATLAB.
S3: and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib.
In some alternative embodiments, the theoretical value of the coordinates of the linear control points of the segment of the erected arch rib and the theoretical value of the coordinates of the linear control points of the next segment of the arch rib are obtained according to arch rib design linearity and finite element analysis means.
In some alternative embodiments, a segment of the rib includes at least three non-collinear linear control points thereon.
In summary, the invention obtains the actual measurement value of the linear control point coordinates of the erected arch rib segment through measurement; determining a coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point; and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib. The method solves the problems that in the prior art, in order to correct errors between actual measurement values and predicted values of linear control points of arch rib segments, a CAD drawing method is generally adopted to make subsequent arch rib position diagrams for correction, time is wasted, efficiency is low, and accuracy of error correction cannot be guaranteed.
The invention ensures that the bridge formation of the arch rib meets the design and specification requirements and the curvature requirement of the arch rib, ensures that the arch rib is hoisted in place at one time and reduces the adjustment times of hoisting arch rib sections. The calculation efficiency is high, and the line shape of the installed arch rib section can be rechecked.
The following provides a specific example for facilitating understanding of the present invention.
As shown in fig. 2, 3 and 4, in the hoisting and splicing of the arch rib of a certain steel tube concrete arch bridge:
after the first section arch rib of the right width is assembled, the measured value of the coordinates of the linear control point of the first section arch rib is measured by using a total station: g1-1 (307.861, 11.749, 632.390), G1-2 (307.860,8.249, 632.391), G1-3: (307.432, 11.751, 631.982), G1-4 (307.430,8.250, 631.980).
The theoretical value of the coordinates of the linear control points of the first arch rib is known as follows: g1-1 '(308.020, 11.750, 632.545), G1-2' (308.020,8.250, 632.545), G1-3 '(307.586, 11.750, 632.131), G1-4' (307.586,8.25, 632.131). The second arch rib linear control point coordinate theoretical value is: g2-1 '(307.861, 11.749, 632.390), G2-2' (308.860,8.249, 632.391), G2-3 '(307.432, 11.751, 631.982), G2-4' (307.430,8.250, 631.980).
According to the scheme, the predicted value of the coordinates of the linear control points of the second arch rib can be obtained as follows: g2-1 "(307.868, 11.754, 632.395), G2-2" (308.865,8.254, 632.398), G2-3 "(307.435, 11.756, 631.991), G2-4" (307.431,8.255, 631.991).
At this time, the deviation between the coordinate predicted value and the theoretical value of the linear control point of the second arch rib is as follows:
(G2-1”)-(G2-1')：(0.007，0.005，0.005)；
(G2-2”)-(G2-2')：(0.005，0.005，0.007)；
(G2-3”)-(G2-3')：(0.003，0.005，0.009)；
(G2-4”)-(G2-4')：(0.001，0.005，0.011)。
according to the deviation between the predicted value and the theoretical value of the coordinates of the control point of the second arch rib, the deviation between the predicted line shape and the theoretical line shape of the second arch rib when no adjustment is performed can be quantitatively described, so that measures can be taken in advance to correct the assembly angle of the second arch rib, and the arch rib line shape after bridge formation is ensured to meet the design requirement. And the coordinate predicted value of the linear control point of the second arch rib can be obtained by only measuring the actual measured value of the linear control point of the first arch rib. And the least square method is adopted to solve the rigid motion parameters, the manufacturing error and the measuring error are comprehensively considered, and the result precision is high.
In the description of the present application, it should be noted that the azimuth or positional relationship indicated by the terms "upper", "lower", etc. are based on the azimuth or positional relationship shown in the drawings, and are merely for convenience of description of the present application and simplification of the description, and are not indicative or implying that the apparatus or element in question must have a specific azimuth, be configured and operated in a specific azimuth, and thus should not be construed as limiting the present application. Unless specifically stated or limited otherwise, the terms "mounted," "connected," and "coupled" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the terms in this application will be understood by those of ordinary skill in the art as the case may be.
It should be noted that in this application, relational terms such as "first" and "second" and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The foregoing is merely a specific embodiment of the application to enable one skilled in the art to understand or practice the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. The linear control method for lifting the arch rib of the arch bridge is characterized by comprising the following steps of:
measuring and obtaining the actual measurement value of the linear control point coordinates of the erected arch rib segment;
determining a coordinate predicted value of the next arch rib linear control point through a rigid body motion transformation formula according to the actual measurement value and the coordinate theoretical value of the erected arch rib section linear control point and the coordinate theoretical value of the next arch rib linear control point;
and hoisting and splicing the next arch rib section according to the coordinate predicted value of the linear control point of the next arch rib.
2. A method of controlling arch bridge arch rib lifting linearity as recited in claim 1, wherein determining a next arch rib linear control point coordinate prediction value from the erected arch rib segment linear control point coordinate actual measurement value and coordinate theoretical value, and the next arch rib linear control point coordinate theoretical value by a rigid body motion transformation formula, comprises:
establishing a rigid motion control equation of the arch rib segment linear control points;
determining a rotation matrix and translation parameters in a rigid body motion control equation according to the actual measurement value and the theoretical coordinate value of the linear control point of the erected arch rib segment;
and determining the predicted value of the next arch rib linear control point according to the rotation matrix, the translation parameter and the theoretical value of the next arch rib linear control point coordinate by combining a rigid motion control equation.
3. An arch bridge rib lifting line shape control method according to claim 2, wherein the rigid body motion control equation is:
wherein [ X ] S Y S Z S ] T Is the predicted value of the coordinates of the linear control point, [ X ] L Y L Z L ] T Is the theoretical value of the coordinates of the linear control point, X S As the abscissa predicted value, Y S As the predicted value of the ordinate, Z S As predicted value of vertical coordinate, X L Is the theoretical value of the abscissa, Y L As the theoretical value of the ordinate, Z L Is a theoretical value of vertical coordinates, R is a rotation matrix, T X For the first translation parameter, T Y For the second translation parameter, T Z Is a third translation parameter.
4. A method of controlling arch bridge rib lifting linearity as claimed in claim 2 wherein determining rotation matrix and translation parameters in rigid motion control equations based on actual and theoretical coordinates of the erected arch rib segment linear control points comprises:
reducing the rotation matrix by using the Rodrign matrix, and converting the rotation angle parameter of the rotation matrix into a substitution parameter;
obtaining an error equation according to the difference between the rigid motion control equation and the first-order Taylor expansion of the rigid motion control equation;
and (5) iteratively solving an error equation by using a least square method to obtain a substitution parameter and a translation parameter.
5. An arch bridge rib lifting line shape control method as recited in claim 4, wherein the reducing the rotation matrix by the rode matrix, converting the rotation angle parameter of the rotation matrix into the substitution parameter, comprises:
the rotation matrix is originally:
the matrix after the reduction is:
wherein, alpha is a first rotation angle parameter, beta is a second rotation angle parameter, gamma is a third rotation angle parameter, a is a first substitution parameter, b is a second substitution parameter, and c is a third substitution parameter.
6. An arch bridge rib lifting line shape control method as recited in claim 4, wherein the error equation is: v=aΔx+l;
wherein Δx= (ΔaΔbΔcΔt) X ΔT Y ΔT Z ) T ；
l＝(l 1 l 2 l 3 ) T ；
Wherein v is an error value, deltax is a parameter increment, parameters with Deltax are all the increment, A is an error equation coefficient, i is a linear control point serial number, l is a constant term matrix, l 1 Is the first constant term, l 2 Is the second constant term, l 3 Is a third constant term.
7. An arch bridge rib hoisting line control method as recited in claim 4, wherein iteratively solving the error equation using a least squares method to obtain the substitution parameter and the translation parameter comprises:
setting initial values of replacement parameters and translation parameters, and acquiring parameter increment and error values by using a least square method;
and continuing to iterate through the least square method, and taking the substitution parameter and the translation parameter at the moment as results when the error value is smaller than the set value.
8. An arch bridge rib lifting linear control method as recited in claim 7, wherein the least square method formula is: Δx= (a T A) -1 (A T l)；
Wherein A is T Is the transpose of matrix a.
9. A method for controlling the lifting line shape of arch rib of arch bridge according to claim 1, wherein the theoretical value of the line shape control point coordinates of the segment of the erected arch rib and the theoretical value of the line shape control point coordinates of the next segment of the arch rib are obtained according to the analysis means of the design line shape of the arch rib and the finite element.
10. A method of controlling the lifting alignment of arch ribs of an arch bridge as recited in claim 1, wherein a segment of the arch rib includes at least three alignment control points that are not collinear.
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| CN117217048A (en) * | 2023-09-07 | 2023-12-12 | 重庆中环建设有限公司 | Cantilever beam construction monitoring system and monitoring method |
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| CN117217048A (en) * | 2023-09-07 | 2023-12-12 | 重庆中环建设有限公司 | Cantilever beam construction monitoring system and monitoring method |
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