Arch bridge arch rib hoisting linear control method

Abstract

This invention discloses a method for controlling the alignment of arch ribs during hoisting, relating to the field of bridge engineering structure construction technology. The method includes: measuring and obtaining the measured coordinates of the alignment control points of the erected arch rib segments; determining the predicted coordinates of the next arch rib segment's alignment control points using rigid body motion transformation formulas based on the measured and theoretical coordinates of the existing arch rib segment's alignment control points, as well as the theoretical coordinates of the next arch rib segment's alignment control points; and hoisting and splicing the next arch rib segment based on the predicted coordinates of the next arch rib segment's alignment control points. This method solves the problem in existing technologies where, to correct the error between the measured and predicted values ​​of the arch rib segment's alignment control points, CAD drawing is typically used to create subsequent arch rib position diagrams for correction, which is time-consuming, inefficient, and cannot guarantee the accuracy of error correction.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering structure construction technology, specifically to a method for controlling the alignment of the arch rib hoisting of an arch bridge. Background Technology

[0002] During the hoisting of arch rib segments in long-span steel-concrete composite arch bridges, the installation alignment of the arch ribs is often controlled by several non-collinear alignment points. However, in actual hoisting, factors such as welding during construction, temporary construction loads, and misalignment between segments, as well as environmental factors like wind direction and temperature, and the dimensional accuracy of the arch rib manufacturing, can cause discrepancies between the measured and predicted values ​​of the arch rib segment alignment control points. If these errors are not corrected in time, and the arch ribs are hoisted at the original assembly angle, the accumulated errors will affect the hoisting accuracy of subsequent arch rib segments, alter the predicted alignment of the entire arch rib, and generate secondary internal forces on the installed arch rib segments, impacting the structural safety of the arch ribs.

[0003] In existing technologies, in order to correct the error between the measured and predicted values ​​of the control points of the arch rib segment alignment, CAD drawing is generally used to create subsequent arch rib position diagrams for correction. This method is time-consuming, inefficient, and cannot guarantee the accuracy of error correction. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for controlling the alignment of arch ribs during hoisting. This method solves the problem that in existing technologies, in order to correct the error between the measured and predicted values ​​of the control points for the alignment of arch rib segments, CAD drawing is generally used to create subsequent arch rib position diagrams for correction. This method is time-consuming, inefficient, and cannot guarantee the accuracy of error correction.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This solution provides a method for controlling the alignment of the arch ribs during hoisting of an arch bridge, including:

[0007] Measure and obtain the actual coordinates of the control points for the alignment of the erected arch rib segments;

[0008] Based on the measured and theoretical coordinates of the control points of the arch rib segments that have already been erected, as well as the theoretical coordinates of the control points of the next arch rib segment, the predicted coordinates of the control points of the next arch rib segment are determined using the rigid body motion transformation formula.

[0009] Based on the predicted coordinates of the control points for the next arch rib section, the next arch rib segment is hoisted and spliced.

[0010] In some alternative schemes, based on the measured and theoretical coordinates of the control points for the existing arch rib segments, and the theoretical coordinates of the control points for the next arch rib segment, the predicted coordinates of the control points for the next arch rib segment are determined using rigid body motion transformation formulas, including:

[0011] Establish the rigid body motion control equations for the linear control points of the arch rib segment;

[0012] Based on the measured and theoretical coordinates of the control points of the erected arch rib segments, determine the rotation matrix and translation parameters in the rigid body motion control equations;

[0013] Based on the rotation matrix, translation parameters, and theoretical coordinates of the control points for the next arch rib section, combined with the rigid body motion control equations, the predicted values ​​of the control points for the next arch rib section are determined.

[0014] In some alternative solutions, the rigid body motion control equations are:

[0015]

[0016] Among them, [X S Y S Z S ] T For the predicted coordinates of the linear control points, [Y] L Y L Z L ] T X represents the theoretical coordinates of the linear control points. S Y is the predicted value on the horizontal axis. S Z is the predicted value of the ordinate. S X is the predicted value of the vertical coordinate. L Y is the theoretical value of the horizontal axis. L Z is the theoretical value of the ordinate. L R is the theoretical value of the vertical coordinate, R is the rotation matrix, and T is the vertical coordinate. X T is the first translation parameter. Y T is the second translation parameter. Z This is the third translation parameter.

[0017] In some alternative schemes, based on the measured and theoretical coordinates of the control points of the erected arch rib segments, the rotation matrix and translation parameters in the rigid body motion control equations are determined, including:

[0018] By using the Rodrigue matrix to reduce the order of the rotation matrix, the rotation angle parameters of the rotation matrix are converted into alternative parameters;

[0019] The error equation is obtained by comparing the rigid body motion control equation with its first-order Taylor expansion.

[0020] The error equation is solved iteratively using the least squares method to obtain the substitution parameters and translation parameters.

[0021] In some alternative approaches, the rotation matrix is ​​reduced in order using the Rodrigues matrix, converting the rotation angle parameters of the rotation matrix into alternative parameters, including:

[0022] The original rotation matrix is:

[0023]

[0024] The reduced matrix is:

[0025]

[0026] Where α is the first rotation angle parameter, β is the second rotation angle parameter, γ is the third rotation angle parameter, a is the first substitution parameter, b is the second substitution parameter, and c is the third substitution parameter.

[0027] In some alternative schemes, the error equation is: v = AΔx + l;

[0028] In the formula, Δx=(Δa Δb Δc ΔT X ΔT Y ΔT Z ) T ;

[0029]

[0030] l = (l1 l2 l3) T ;

[0031]

[0032]

[0033]

[0034] Where v is the error value, Δx is the parameter increment, parameters with Δ all represent their increments, A is the coefficient of the error equation, i is the linear control point number, l is the constant term matrix, l1 is the first constant term, l2 is the second constant term, and l3 is the third constant term.

[0035] In some alternative solutions, the least squares method is used to iteratively solve the error equation to obtain alternative parameters and translation parameters, including:

[0036] Set initial values ​​for the substitution and translation parameters, and use the least squares method to obtain the parameter increments and error values;

[0037] Continue iterating using the least squares method. When the error value is less than the set value, use the substitution parameter and translation parameter at this time as the result.

[0038] In some alternative solutions, the least squares formula is: Δx=(A T A) -1 (A T l);

[0039] Among them, A T Let A be the transpose of matrix A.

[0040] In some alternative schemes, based on the arch rib design alignment and finite element analysis, the theoretical coordinates of the control points of the already erected arch rib segments and the control points of the next arch rib segment are obtained.

[0041] In some alternative designs, an arch rib includes at least three non-collinear linear control points.

[0042] Compared with existing technologies, the advantages of this invention are as follows: This solution obtains the measured coordinates of the control points of the erected arch rib segments through measurement; based on the measured and theoretical coordinates of the control points of the erected arch rib segments, and the theoretical coordinates of the control points of the next arch rib segment, the predicted coordinates of the control points of the next arch rib segment are determined using rigid body motion transformation formulas; and based on the predicted coordinates of the control points of the next arch rib segment, the next arch rib segment is hoisted and spliced. This solves the problem in existing technologies where, in order to correct the error between the measured and predicted values ​​of the control points of the arch rib segments, CAD drawing methods are generally used to create subsequent arch rib position diagrams for correction, which is time-consuming, inefficient, and cannot guarantee the accuracy of error correction. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart illustrating the method for controlling the hoisting alignment of the arch ribs of an arch bridge in an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram of the assembled arch rib segment in an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the structure of the lower arch rib in an embodiment of the present invention;

[0047] Figure 4This is a cross-sectional schematic diagram of the arrangement of measuring points on the spliced ​​arch rib segments in an embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0049] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0050] like Figure 1 As shown, the present invention provides a method for controlling the alignment of the arch rib hoisting of an arch bridge, comprising:

[0051] S1: Measure and obtain the actual coordinates of the control points of the erected arch rib segment alignment.

[0052] S2: Based on the measured and theoretical coordinates of the control points of the arch rib segments that have been erected, and the theoretical coordinates of the control points of the next arch rib segment, the predicted coordinates of the control points of the next arch rib segment are determined using the rigid body motion transformation formula.

[0053] Step S2 specifically includes:

[0054] S21: Establish the rigid body motion control equations for the control points of the arch rib segment.

[0055] In this embodiment, the rigid body motion control equation is:

[0056] Among them, [X S T S Z S ] T For the predicted coordinates of the linear control points, [X L Y L Z L ] T X represents the theoretical coordinates of the linear control points. S Y is the predicted value on the horizontal axis. S Z is the predicted value of the ordinate. S X is the predicted value of the vertical coordinate. L Y is the theoretical value of the horizontal axis. L Z is the theoretical value of the ordinate. L R is the theoretical value of the vertical coordinate, R is the rotation matrix, and T is the vertical coordinate. X T is the first translation parameter. Y T is the second translation parameter. ZThis is the third translation parameter.

[0057] S22: Determine the rotation matrix and translation parameters in the rigid body motion control equation based on the measured and theoretical coordinates of the control points of the erected arch rib segments.

[0058] Step S22 specifically includes:

[0059] S221: Use the Rodrigue matrix to reduce the order of the rotation matrix, and convert the rotation angle parameter of the rotation matrix into a substitute parameter.

[0060] In this embodiment, the original rotation matrix is:

[0061]

[0062] The reduced matrix is:

[0063]

[0064] Where α is the first rotation angle parameter, β is the second rotation angle parameter, γ is the third rotation angle parameter, a is the first substitution parameter, b is the second substitution parameter, and c is the third substitution parameter.

[0065] S222: Obtain the error equation based on the difference between the rigid body motion control equation and its first-order Taylor expansion.

[0066] In this embodiment, the error equation is: v = AΔx + l;

[0067] In the formula, Δx=(Δa Δb Δc ΔT X ΔT Y ΔT Z ) T ;

[0068]

[0069] l = (l1 l2 l3) T ;

[0070]

[0071]

[0072]

[0073] Where v is the error value, Δx is the parameter increment, parameters with Δ all represent their increments, A is the coefficient of the error equation, i is the linear control point number, l is the constant term matrix, l1 is the first constant term, l2 is the second constant term, and l3 is the third constant term.

[0074] S223: Use the least squares method to iteratively solve the error equation and obtain the substitution parameters and translation parameters.

[0075] In this embodiment, the least squares method is used to iteratively solve the error equation to obtain the substitution parameters and translation parameters, including:

[0076] Set initial values ​​for the substitution and translation parameters, and use the least squares method to obtain the parameter increments and error values;

[0077] Continue iterating using the least squares method. When the error value is less than the set value, use the substitution parameter and translation parameter at this time as the result.

[0078] The least squares formula is: Δx = (A T A) -1 (A T l), where A T Let A be the transpose of matrix A.

[0079] S23: Based on the rotation matrix, translation parameters, and theoretical coordinates of the control points of the next arch rib section, combined with the rigid body motion control equations, determine the predicted values ​​of the control points of the next arch rib section.

[0080] In this embodiment, step S2 can be implemented using MATLAB.

[0081] S3: Based on the predicted coordinates of the control points for the next arch rib section, hoist and splice the next arch rib segment.

[0082] In some optional embodiments, based on the arch rib design alignment and finite element analysis methods, the theoretical coordinates of the control points of the already erected arch rib segment alignment and the next arch rib segment alignment control points are obtained.

[0083] In some alternative embodiments, an arch rib includes at least three non-collinear linear control points.

[0084] In summary, this invention obtains the measured coordinates of the control points of the erected arch rib segments by measurement; based on the measured and theoretical coordinates of the control points of the erected arch rib segments, and the theoretical coordinates of the control points of the next arch rib segment, the predicted coordinates of the control points of the next arch rib segment are determined using rigid body motion transformation formulas; and based on the predicted coordinates of the control points of the next arch rib segment, the next arch rib segment is hoisted and spliced. This solves the problem in existing technologies where, to correct the error between the measured and predicted values ​​of the control points of the arch rib segments, CAD drawing methods are generally used to create subsequent arch rib position diagrams for correction, which is time-consuming, inefficient, and cannot guarantee the accuracy of error correction.

[0085] This invention ensures that the arch rib bridge alignment meets design and specification requirements, satisfies arch rib curvature requirements, and allows for one-time hoisting of the arch rib, reducing the number of adjustments required for each arch rib segment. It also boasts high computational efficiency and enables verification of the alignment of installed arch rib segments.

[0086] The following is a specific example to facilitate understanding of the present invention.

[0087] like Figure 2 , Figure 3 and Figure 4 As shown, in the hoisting and splicing of the arch ribs of a steel-concrete composite arch bridge:

[0088] After the first arch rib section on the right side was assembled, the measured coordinates of the control points for the first arch rib section were obtained 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).

[0089] The theoretical coordinates of the control points of the first arch rib are known to be: 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 theoretical coordinates of the control points for the second arch rib section are: 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).

[0090] According to the above scheme, the predicted coordinates of the control points of the second arch rib are: 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).

[0091] At this point, the deviation between the predicted and theoretical coordinates of the control points for the second arch rib is:

[0092] (G2-1”)-(G2-1’): (0.007, 0.005, 0.005);

[0093] (G2-2”)-(G2-2’): (0.005, 0.005, 0.007);

[0094] (G2-3”)-(G2-3’): (0.003, 0.005, 0.009);

[0095] (G2-4”)-(G2-4’): (0.001, 0.005, 0.011).

[0096] Based on the deviation between the predicted and theoretical coordinates of the control points for the second arch rib, the deviation between the predicted and theoretical alignments of the second arch rib without adjustment can be quantitatively described. This allows for proactive measures to correct the assembly angle of the second arch rib, ensuring that the arch rib alignment of the completed bridge meets design requirements. The predicted coordinates of the control points for the second arch rib can be obtained simply by measuring the actual coordinates of the control points for the first arch rib. The least squares method is used to solve for the rigid body motion parameters, comprehensively considering manufacturing and measurement errors, resulting in high accuracy.

[0097] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0098] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0099] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for controlling the line shape of an arch rib of an arch bridge, characterized by, include: Measure and obtain the actual coordinates of the control points for the alignment of the erected arch rib segments; Based on the measured and theoretical coordinates of the control points of the arch rib segments that have already been erected, as well as the theoretical coordinates of the control points of the next arch rib segment, the predicted coordinates of the control points of the next arch rib segment are determined using the rigid body motion transformation formula. Based on the predicted coordinates of the control points for the next arch rib section, the next arch rib segment is hoisted and spliced. Based on the measured and theoretical coordinates of the control points for the existing arch rib segments, and the theoretical coordinates of the control points for the next arch rib segment, the predicted coordinates of the control points for the next arch rib segment are determined using rigid body motion transformation formulas, including: Establish the rigid body motion control equations for the linear control points of the arch rib segment; Based on the measured and theoretical coordinates of the control points of the erected arch rib segments, determine the rotation matrix and translation parameters in the rigid body motion control equations; Based on the rotation matrix, translation parameters, and theoretical coordinates of the control points of the next arch rib, combined with the rigid body motion control equations, the predicted values ​​of the control points of the next arch rib are determined. Based on the measured and theoretical coordinates of the control points of the erected arch rib segments, the rotation matrix and translation parameters in the rigid body motion control equations are determined, including: By using the Rodrigue matrix to reduce the order of the rotation matrix, the rotation angle parameters of the rotation matrix are converted into alternative parameters; The error equation is obtained by comparing the rigid body motion control equation with its first-order Taylor expansion. The error equation is solved iteratively using the least squares method to obtain the substitution parameters and translation parameters.

2. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, The rigid body motion control equation is as follows: ; in, These are the predicted coordinates of the linear control points. These are the theoretical values ​​of the coordinates of the linear control points. The predicted value for the horizontal axis. The predicted value for the ordinate is... The vertical coordinate is the predicted value. The theoretical value of the horizontal axis. The theoretical value for the ordinate is... This is the theoretical value of the vertical coordinate. Let be a rotation matrix. The first translation parameter is... This is the second translation parameter. This is the third translation parameter.

3. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, By using the Rodrigues matrix to reduce the order of the rotation matrix, the rotation angle parameters of the rotation matrix are converted into alternative parameters, including: The original rotation matrix is: ； The reduced matrix is: ； in, The first rotation angle parameter, This is the second rotation angle parameter. This is the third rotation angle parameter. As the first alternative parameter, As the second alternative parameter, This is the third alternative parameter.

4. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, The error equation is: ; In the formula, ; ； ； ； ； ； in, This is the error value. For parameter increments, with The parameters all represent their increments. These are the coefficients of the error equation. This refers to the linear control point number. A matrix of constant terms, This is the first constant term. This is the second constant term. This is the third constant term.

5. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, The error equation is solved iteratively using the least squares method to obtain the substitution parameters and translation parameters, including: Set initial values ​​for the substitution and translation parameters, and use the least squares method to obtain the parameter increments and error values; Continue iterating using the least squares method. When the error value is less than the set value, use the substitution parameter and translation parameter at this time as the result.

6. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 5, characterized in that, The least squares formula is: ; in, For matrix The transpose of .

7. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, Based on the arch rib design alignment and finite element analysis, the theoretical coordinates of the control points of the erected arch rib segments and the control points of the next arch rib segment are obtained.

8. The method for controlling the alignment of the arch rib hoisting of an arch bridge as described in claim 1, characterized in that, A section of the arch rib includes at least three non-collinear linear control points.

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