A method for determining the position of a push variable-curvature main beam based on a Fréchet algorithm

Abstract

The application provides a method for determining the position of a main beam of a push variable curvature bridge based on a Fréchet algorithm, comprising the following steps: step one, discretizing curve A and curve B; step two, pushing curve A along the connecting line between the centers of the tail and head push piers to obtain curve A', and discretizing curve A' to obtain sequence A'; step three, respectively pushing the permanent pier and the temporary pier to perform transverse correction on sequence A' to obtain the sequence A' corresponding to the center line of the corrected main beam curve i ; step four, respectively calculating the Fréchet distance value sequence δ i between sequence A' F and sequence B; step five, obtaining the minimum value minδ F in sequence δ F , and calculating the construction step correction amount according to minδ F ; and step six, distributing the transverse offset amount to each pushing step to ensure that the main beam can reach the optimal position. The application provides a new method for determining the position of the main beam of the push variable curvature bridge after pushing and construction.

Description

Technical Field

[0001] This invention relates to the field of bridge technology, and specifically to a method for determining the position of a variable curvature main beam based on the Fréchet algorithm. Background Technology

[0002] The incremental launching method is a bridge construction method that uses jacks to longitudinally push the superstructure of a bridge onto the piers. It offers advantages such as eliminating the need for large construction equipment, simplicity, speed, and immunity to external influences. With the development of incremental launching technology, it has evolved from initially being applicable only to straight beam bridges to being suitable for spatial curve bridges with vertical and horizontal curves. However, incremental launching is still affected by factors such as the launching equipment, the flatness of the launching platform, and temperature, leading to lateral displacement. This is especially true for variable-curvature bridges, where the constantly changing curvature directly causes lateral displacement of the main beam during the launching process, and this displacement cannot be completely corrected. Excessive lateral displacement can adversely affect the piers, placing them in a state of bending-torsional coupling under longitudinal stress and lateral pressure. Therefore, minimizing lateral displacement is a crucial problem to be solved in the incremental launching of bridges with variable curvature radii.

[0003] Currently, the main method for controlling the position of the beam in the incremental launching method uses passive guiding devices to control the directional and lateral offset during the launching process. However, passive guiding devices can cause stress concentration in the main beam structure during launching, which is detrimental to the structural integrity. Active correction devices use correction jacks to correct the lateral offset of the main beam as a whole. Current research on the beam centerline and pier top centerline focuses on calculating the lateral offset value using two curves, but lacks the ability to determine the similarity between the two curves, thus making it impossible to determine the position of the main beam after launching. Summary of the Invention

[0004] In view of this, this application provides a method for determining the position of a variable curvature main beam based on the Fréchet algorithm, to solve the problem in the prior art where the beam position cannot be controlled in terms of jacking direction and lateral offset during the jacking process. The specific solution is as follows:

[0005] A method for determining the position of a variable curvature main beam by incremental launching based on the Fréchet algorithm includes the following steps:

[0006] Step 1: Using the centerline of the main beam segment as curve A, and the design centerlines of the permanent and temporary piers where the main beam segment is located as curve B, discretize curves A and B respectively. The discretization points are the intersections of curve A with the vertical centerlines of each permanent and temporary pier. The sequence of curves A is A = {A1, A2, ..., A...}. n The sequence of curve B is B = {B1, B2, ..., B}. n};

[0007] Step 2: The curve A is pushed along the line connecting the center of the tail jacking pier and the head jacking pier of the permanent and temporary piers to obtain curve A'. Curve A' is then discretized, where the discrete points of curve A' are the intersections of curve A' with the vertical center lines of each permanent and temporary pier. Curve A' corresponds to the sequence A', where the sequence A' = {A'1, A'2, ..., A'...} n};

[0008] Step 3: Perform lateral correction on curve A' at each permanent and temporary pier to obtain different correction main beam curves A'. i ;

[0009] Discretize the main beam curve A' of the correction beam i Obtain sequence A' i ={A' i1 ,A' i2 ,...,A' in The discrete point is the main beam curve A' of the correction beam. i The intersection with the vertical centerline of each permanent and temporary pier;

[0010] Step 4: Calculate sequence A' separately. i The Fréchet distance value between sequence B and sequence δ, wherein the Fréchet distance value is the sequence δ. F ={δ F1 ,δ F2 ,...,δ Fi};

[0011] Step 5: Obtain the Fréchet distance value δ F ={δ F1 ,δ F2 ,...,δ Fi The minimum value δ in} Fmin And according to the minimum value δ Fmin Extract the lateral correction amount corresponding to step three, and calculate the step correction amount in the construction process based on the lateral correction amount;

[0012] Step 6: During construction, based on the aforementioned step correction amount, a lateral step correction is performed for each stroke of the jacking, ultimately ensuring that the centerline of the main beam segment is located at the minimum value δ. Fmin The corresponding position.

[0013] Preferably, in step 6, the step correction specifically includes:

[0014] S1, determine the optimal main beam segment position corresponding to the minimum Fréchet distance through steps 1-5;

[0015] S2, determine the lateral correction distance of each jacking device corresponding to the optimal position of this main beam through step 3;

[0016] S3, each jacking device first jacks the beam longitudinally, and then performs step correction of the transverse correction distance determined in S2.

[0017] S4 distributes the step correction value evenly over each longitudinal jacking process.

[0018] Preferably, during the lateral correction process, the method for determining the lateral offset vector is as follows:

[0019] S1, mark the starting position of the center point of the tail of curve A as point A, and the center line of each jacking pier in the permanent pier and temporary pier is represented as Y1;

[0020] S2, draw curve A along the line connecting the center of the first and last jacking piers among the permanent and temporary piers, according to the sequence d = {d1, d2, ..., d...} n The lengths of the jacking blocks are sequentially pushed to obtain curve A'. The center point of the tail of curve A' is marked as point B. The intersections of curve A' and the center lines Y1 of each jacking block form a sequence D = {D1, D2, ..., D}. n};

[0021] S4, laterally offset curve A' at each jacking pier, causing curve A' to rotate at a certain angle. Different lateral offsets yield curve A. i ', curve A i The intersection points with the centerline Y1 of each jacking pier form a sequence E = {E1, E2, ..., E...} n};

[0022] S3, sequence E = {E1, E2, ..., E n} and the sequence D = {D1, D2, ..., D} n The length of the corresponding connection is the sequence P = {P1, P2, ..., P}. n};

[0023] The sequence P = {P1, P2, ..., P} n} is the distance of the lateral offset vector corresponding to each jacking pier of the main beam segment, and the direction of the lateral offset vector is the radial direction of curve A at each jacking pier.

[0024] Preferably, in step 4, the Fréchet distance value is calculated as follows:

[0025] The sequence A' i The Euclidean distance between A' and the elements in sequence B is denoted as d(A'). i B j );

[0026] A' i Euclidean distance induction with elements in B and Euler matrix D ixj

[0027] The discrete Fréchet distance between position i in sequence A and position j in sequence B is denoted as δ. F (A' i B j );

[0028] First, the Eulerian distance matrix D between points in sequences A' and B is obtained. ixj ;

[0029] Secondly, from i=1, j=1 to i=n, ​​j=m, perform δ F (A' i B j The recursive calculation of sequence A' is performed sequentially. i The corresponding Fréchet distance values ​​δ F ;

[0030] The Fréchet distance values ​​δ F The discrete Fréchet distance matrix D is constructed F ;

[0031] The matrix D F The minimum value of each element is the Fréchet distance δ between sequence A' and sequence B. F (A',B).

[0032] Preferably, the δ F (A' i B j The recursive calculation method for ) is as follows:

[0033] When i = 1 and j = 1, δ F (A' i B j )=d(A'1,B1);

[0034] When j = 1, then δ F (A' i ,B1)=max[d(A' i-1 ,B1),d(A' i ,B1)];

[0035] When i = 1, then δ F (A' i B j )=max[d(A'1,B j-1 ),d(A'1,B j)];

[0036] When i≥2 and j≥2

[0037] Then δ F (A' i B j )=max[d(A' i B j ),min(d(A' i B j-1 ),d(A' i-1 B j ),d(A' i-1 B j-1 )).

[0038] Preferably, the Eulerian distance matrix D between the points corresponding to sequence A' and sequence B is... ixj for:

[0039]

[0040] The matrix D F for:

[0041]

[0042] Preferably, the minimum Fréchet distance δ Fmin Corresponding A' i The sequence represents the optimal position after the variable curvature main beam is pushed.

[0043] Preferably, the different δ values ​​obtained from the different lateral offsets F The curves representing the values ​​are the lateral offset vectors of each jacking pier.

[0044] Preferably, the formula for calculating the step correction amount is shown in equation (1):

[0045]

[0046] Where TO is the lateral offset vector, PD is the jacking distance of curve A in step 2, and ES is the rated step size of the jacking device.

[0047] The present invention provides a method for determining the position of the incremental launching main beam based on discrete Fréchet distance, the functions and effects of which are as follows:

[0048] According to the present invention, a method for determining the position of the main girder after jacking based on discrete Fréchet distance is used. The sequence of main girder centerlines corresponding to different lateral correction values ​​of the box girder centerline after jacking is compared with the sequence of design centerlines of temporary piers and protective piers based on Fréchet distance curve similarity. The Fréchet distance values ​​of different curves are compared, and the main girder centerline position corresponding to the smaller Fréchet distance value is the more suitable main girder position after jacking of the variable curvature bridge. Based on the calculated lateral offset, the step correction amount is calculated and distributed to each jacking step to ensure that the main girder reaches the optimal position. This method enables the determination and construction of the main girder position after jacking of variable curvature bridges, providing a new approach for this purpose. Attached Figure Description

[0049] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0050] In the attached diagram:

[0051] Figure 1 This is a schematic diagram of the centerline of the main beam segment of the variable curvature radius bridge and the centerlines of the permanent and temporary piers in an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram showing the centerline position of the main beam segment and the centerline of the launching pier after the variable radius of curvature bridge is launched in an embodiment of the present invention.

[0053] Figure 3 This is a schematic diagram of the centerline of the main beam segment obtained under different lateral offsets of each jacking pier for permanent and temporary piers in an embodiment of the present invention.

[0054] Figure 4 This is a diagram illustrating the calculation of the lateral offset of each jacking pier in an embodiment of the present invention;

[0055] Among them, 1-centerline of the main girder segment, 2-centerline of the permanent pier and temporary pier, 3-permanent pier and temporary pier, 4-intersection point, 5-direction, 6-distance, 7-centerline of the main girder segment after jacking, 8-curve of the first main girder, 9-curve of the second main girder, 10-10 # jacking pier, 11-11 # jacking pier, 12-12 # jacking pier, 13-13 # jacking pier. Detailed Implementation

[0056] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0057] According to the appendix Figure 1-4 The method for determining the position of a variable curvature main beam based on the Fréchet algorithm, as shown, includes the following steps:

[0058] A method for determining the position of a variable curvature main beam by incremental launching based on the Fréchet algorithm includes the following steps:

[0059] Step 1: Using the centerline of the main beam segment as curve A, and the design centerlines of the permanent and temporary piers where the main beam segment is located as curve B, discretize curves A and B respectively. The discretization points are the intersections of curve A with the vertical centerlines of each permanent and temporary pier. The sequence of curves A is A = {A1, A2, ..., A...}. n The sequence of curve B is B = {B1, B2, ..., B}. n};

[0060] Step 2: The curve A is pushed along the line connecting the center of the tail jacking pier and the head jacking pier of the permanent and temporary piers to obtain curve A'. Curve A' is then discretized, where the discrete points of curve A' are the intersections of curve A' with the vertical center lines of each permanent and temporary pier. Curve A' corresponds to the sequence A', where the sequence A' = {A'1, A'2, ..., A'...} n};

[0061] Step 3: Perform lateral correction on curve A' at each permanent and temporary pier to obtain different correction main beam curves A'. i ;

[0062] Discretize the main beam curve A' of the correction beam i Obtain sequence A' i ={A' i1 ,A' i2 ,...,A' in The discrete point is the main beam curve A' of the correction beam. i The intersection with the vertical centerline of each permanent and temporary pier;

[0063] Step 4: Calculate sequence A' separately. i The Fréchet distance value between sequence B and sequence δ, wherein the Fréchet distance value is the sequence δ. F ={δ F1 ,δ F2 ,...,δ Fi};

[0064] Step 5: Obtain the Fréchet distance value δ F ={δ F1 ,δ F2 ,...,δ FiThe minimum value δ in} Fmin And according to the minimum value δ Fmin Extract the lateral correction amount corresponding to step three, and calculate the step correction amount in the construction process based on the lateral correction amount;

[0065] Step 6: During construction, based on the aforementioned step correction amount, a lateral step correction is performed for each stroke of the jacking, ultimately ensuring that the centerline of the main beam segment is located at the minimum value δ. Fmin The corresponding position.

[0066] Furthermore, in step 6, the step correction specifically includes:

[0067] S1, determine the optimal main beam segment position corresponding to the minimum Fréchet distance through steps 1-5;

[0068] S2, determine the lateral correction distance of each jacking device corresponding to the optimal position of this main beam through step 3;

[0069] S3, each jacking device first jacks the beam longitudinally, and then performs step correction of the transverse correction distance determined in S2.

[0070] S4 distributes the step correction value evenly over each longitudinal jacking process.

[0071] Furthermore, in the lateral correction process, the method for determining the lateral offset vector is as follows:

[0072] S1, mark the starting position of the center point of the tail of curve A as point A, and the center line of each jacking pier in the permanent pier and temporary pier is represented as Y1;

[0073] S2. The curve A is drawn along the line connecting the center of the first and last jacking piers of the permanent and temporary piers, according to the sequence d = {d1, d2, ..., d...} n The lengths of the jacking blocks are sequentially pushed to obtain curve A'. The center point of the tail of curve A' is marked as point B. The intersections of curve A' and the center lines Y1 of each jacking block form a sequence D = {D1, D2, ..., D}. n};

[0074] S4, laterally offset curve A' at each jacking pier, causing curve A' to rotate at a certain angle. Different lateral offsets yield curve A. i ', curve A i The intersection points with the centerline Y1 of each jacking pier form a sequence E = {E1, E2, ..., E...} n};

[0075] S3, sequence E = {E1, E2, ..., E n} and the sequence D = {D1, D2, ..., D}n The length of the corresponding connection is the sequence P = {P1, P2, ..., P}. n};

[0076] The sequence P = {P1, P2, ..., P} n} is the distance of the lateral offset vector corresponding to each jacking pier of the main beam segment, and the direction of the lateral offset vector is the radial direction of curve A at each jacking pier.

[0077] Furthermore, in step 4, the method for calculating the Fréchet distance value is as follows:

[0078] The sequence A' i The Euclidean distance between A' and the elements in sequence B is denoted as d(A'). i B j );

[0079] A' i Euclidean distance induction with elements in B and Euler matrix D ixj

[0080] The discrete Fréchet distance between position i in sequence A and position j in sequence B is denoted as δ. F (A' i B j );

[0081] First, the Eulerian distance matrix D between points in sequences A' and B is obtained. ixj ;

[0082] Secondly, from i=1, j=1 to i=n, ​​j=m, perform δ F (A' i B j The recursive calculation of sequence A' is performed sequentially. i The corresponding Fréchet distance values ​​δ F ;

[0083] The Fréchet distance values ​​δ F The discrete Fréchet distance matrix D is constructed F ;

[0084] The matrix D F The minimum value of each element is the Fréchet distance δ between sequence A' and sequence B. F (A',B).

[0085] Furthermore, the δ F (A' i B j The recursive calculation method for ) is as follows:

[0086] When i = 1 and j = 1, δ F (A' i B j )=d(A'1,B1);

[0087] When j = 1, then δ F (A' i ,B1)=max[d(A' i-1 ,B1),d(A' i ,B1)];

[0088] When i = 1, then δ F (A' i B j )=max[d(A'1,B j-1 ),d(A'1,B j )];

[0089] When i≥2 and j≥2

[0090] Then δ F (A' i B j )=max[d(A' i B j ),min(d(A' i B j-1 ),d(A' i-1 B j ),d(A' i-1 B j-1 )).

[0091] Furthermore, the Eulerian distance matrix D between the points corresponding to sequence A' and sequence B... ixj for:

[0092]

[0093] The matrix D F for:

[0094]

[0095] Furthermore, the minimum Fréchet distance δ Fmin Corresponding A' i The sequence represents the optimal position after the variable curvature main beam is pushed.

[0096] Furthermore, the different δ values ​​obtained from the different lateral offsets F The curves representing the values ​​are the lateral offset vectors of each jacking pier.

[0097] Furthermore, the formula for calculating the step correction amount is shown in equation (1):

[0098]

[0099] Where TO is the lateral offset vector, PD is the jacking distance of curve A in step 2, and ES is the rated step size of the jacking device.

[0100] It should be noted that:

[0101] In this application: the arrangement of the centerline of the main beam segment and the jacking of permanent or temporary piers can be realized by computer-aided software. At intersection 4, the sequence A formed by the centerline of the main beam segment and the sequence B formed by the centerlines of the permanent and temporary piers can also be obtained by computer-aided software.

[0102] It should be noted that, in order to ensure the effectiveness of the jacking of the variable curvature bridge, the jacking direction of all jacking equipment should be consistent during the jacking process. The jacking direction is controlled by the direction 5 of the line connecting the center of the front jacking pier and the center of the rear jacking pier.

[0103] Computer-aided software can be used to translate the curve A sequence along the pushing direction to obtain the sequence A' corresponding to the curve A'.

[0104] To make the technical means and effects of the present invention easy to understand, the present invention will be specifically described below in conjunction with embodiments and accompanying drawings.

[0105] Example 1

[0106] As attached Figure 1 As shown, in Figure 1 In the design, the centerline 1 of the main beam segment is taken as curve A, and the design centerline 2 of the permanent pier and temporary pier 3 is taken as curve B.

[0107] Step 1: Discretize curves A and B respectively. The discretization point is the intersection point 4 of curve A and the vertical centerlines of the permanent pier and temporary pier 3. At intersection point 4, the centerlines 1 of the main beam segment form sequence A, and the permanent pier and temporary pier 3 form sequence B, where A = {A1, A2, ..., A...} n};B={B1,B2...,B n}

[0108] Step 2: Push the centerline 1 of the main girder segment a distance 6 along the line connecting the centers of the first and last jacking piers of the permanent and temporary piers 3. After the jacking, the centerline 1 of the main girder segment becomes the centerline 7 of the main girder segment, as shown in the attached figure. Figure 2 As shown, the sequence corresponding to the centerline 7 of the main beam segment after the jacking is sequence A', where sequence A' = {A'1, A'2, ..., A'}. nAt this time, the centerline 2 of the permanent pier and the temporary pier 3 has not changed, so sequence B remains unchanged. The element data in sequence A' is the intersection point 9 of the centerline 7 of the main beam segment after the jacking and the centerlines of each jacking pier in the permanent pier and the temporary pier 3.

[0109] Step 3: For the deviation where the centerline 7 of the main beam segment does not coincide with the centerline 2 after jacking, the centerline 7 of the main beam segment is laterally corrected at different jacking locations of the permanent and temporary piers 3 to obtain different first main beam curves 8 and second main beam curves 9.

[0110] As attached Figure 3 After the jacking, the centerline of the main beam segment 7 is at 10. # jacking piers 10 and 11 # jacking piers 11 and 12 # jacking piers 12 and 13 # At each of the 13 jacking piers, the corresponding lateral correction value is applied to the centerline 7 of the main beam segment, causing the main beam segment to rotate as a whole. Based on the A' sequence corresponding to the centerline 7 of the main beam segment after jacking, the first main beam curve 8 and the second main beam curve 9 are obtained based on the rotation angles corresponding to different lateral corrections.

[0111] The specific lateral correction process is as follows: Assume 10 # The jacking pier 10 is adjusted to correct the deviation at distance D1, 11. # The jacking pier 11 is pushed through D2, and so on, until 13. # If the jacking pier 13 is adjusted by a distance of D4, the main beam segment will have an overall rotational effect. Therefore, the corresponding jacking piers should be adjusted laterally by distances D1, D2, D3, and D4 to make the main beam segment rotate.

[0112] In this embodiment, the lateral correction process is a standard procedure in the industry, namely, lateral correction devices are arranged on both sides of each jacking pier of the permanent and temporary piers 3; the correction device consists of jacks and guide steel components. When correction is required during the jacking process, the extension and retraction of the jacks are used to move the beam back to its original position laterally, and PTFE sliding plate pads are placed close to the box girder to reduce the friction between the box girder and the limiting device.

[0113] The method for determining the lateral correction distance is as follows:

[0114] As attached Figure 4 As shown, assuming only longitudinal jacking without lateral correction, the initial location of the main beam's tail center point is marked as point A. After jacking the main beam along the line connecting the centerlines of piers #1 and #4 for a length d in direction 5, the tail center point of the main beam is pushed from point A to point B. At this point, the centerline 7 of the main beam and the centerline 2 of the permanent and temporary piers 3 are respectively aligned with point 1. #The centerline Y1 of the jacking pier intersects at points C and D. The length P1 of the line connecting points C and D is the correction distance. After jacking, the centerline of the main beam segment is at 1. # Bridge piers and 4 # The radial direction at the bridge pier is the correction direction;

[0115] According to 1 # jacking pier and 4 # The method for obtaining the correction distance and direction of the jacking pier can be obtained similarly. # jacking pier, 3 # The correction values ​​P2, P3, and P4 corresponding to the jacking pier and jacking pier No. 4.

[0116] Step 4: Using the sequence values ​​in sequence A' corresponding to the first main beam curve 8 and the second main beam curve 9, respectively, and the sequence values ​​in the corresponding sequence B, the discrete curves required for calculating the discrete Fréchet distances between sequences A8' and A9' corresponding to the first main beam curve 8 and the second main beam curve 9 and sequence B are calculated. The Fréchet distance values ​​δ between sequences A8' and A9' and sequence B are then calculated respectively. F8 and δ F9 The specific calculation process is as follows:

[0117] Step 4-1, the Euclidean distances between sequences A8' and A9' and elements in sequence B are expressed as d(A8',B) and d(A9',B), respectively;

[0118] Where d(A8',B) and d(A9',B) represent sequence A i The Euclidean distance between ' and elements in sequence B, δ F (A' i B j ) represents the discrete Fréchet distance value between position i in sequence A and position j in sequence B.

[0119] Step 4-2 introduces the method for calculating the Fréchet distance using sequence A' as an example. Based on sequences A' and B, the Eulerian distance matrix D between points in the two sequences is obtained. ixj :

[0120]

[0121] Step 4-3: When i = 1, j = 1, δ F (A'1,B1)=d(A'1,B1);

[0122] When j = 1, then

[0123] δ F (A' i ,B1)=max[d(A'i-1 ,B1),d(A' i ,B1)]

[0124] When i = 1, then

[0125] δ F (A'1,B j )=max[d(A'1,B j-1 ),d(A'1,B j )]

[0126] Step 4-4, when i≥2 and j≥2, then

[0127] δ F (A' i B j )=max[d(A' i B j ),min(d(A' i B j-1 ),d(A' i-1 B j ),d(A' i-1 B j-1 ))]

[0128] Steps 4-5, according to the above δ F (A' i B j The calculation method for ) starts recursively from i=1, j=1 until i=n, ​​j=m, resulting in the discrete Fréchet distance matrix D. F :

[0129]

[0130] Step 5: First, compare the Fréchet distance values ​​δF8 and δF9 between the sequence values ​​corresponding to the first main beam curve 8 and the second main beam curve 9 calculated in Step 4 and the corresponding sequence values ​​in Sequence B, and obtain the minimum Fréchet distance value as δF8 or δF9.

[0131] Then, the lateral correction amount is extracted according to the minimum value δF8 or δF9, and according to equation (1) Calculate the actual step correction amount during construction;

[0132] Finally, based on the actual step correction amount, rotate or adjust the angle of the main beam as much as possible to determine the position of the main beam after jacking.

[0133] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for determining the position of a variable curvature main beam by incremental launching based on the Fréchet algorithm, characterized in that, Includes the following steps: Step 1: Using the centerline of the main beam segment as curve A, and the design centerlines of the permanent and temporary piers where the main beam segment is located as curve B, discretize curves A and B respectively. The discretization points are the intersections of curve A with the vertical centerlines of each permanent and temporary pier. The sequence of curves A is A = {A1, A2, ..., A...}. n The sequence of curve B is B = {B1, B2, ..., B}. n }; Step 2: The curve A is pushed along the line connecting the center of the tail jacking pier and the head jacking pier of the permanent and temporary piers to obtain curve A'. Curve A' is then discretized, where the discrete points of curve A' are the intersections of curve A' with the vertical center lines of each permanent and temporary pier. Curve A' corresponds to the sequence A', where the sequence A' = {A'1, A'2, ..., A'...} n }; Step 3: Perform lateral correction on curve A' at each permanent and temporary pier to obtain different correction main beam curves A'. i ; Discretize the main beam curve A' of the correction beam i Obtain sequence A' i ={A' i1 ,A' i2 ,...,A' in The discrete point is the main beam curve A' of the correction beam. i The intersection with the vertical centerline of each permanent and temporary pier; Step 4: Calculate sequence A' separately. i The Fréchet distance value between sequence B and sequence δ, wherein the Fréchet distance value is the sequence δ. F ={δ F1 ,δ F2 ,...,δ Fi }; Step 5: Obtain the Fréchet distance value δ F ={δ F1 ,δ F2 ,...,δ Fi The minimum value δ in} Fmin And according to the minimum value δ Fmin Extract the lateral correction amount corresponding to step 3, and calculate the step correction amount in the construction process based on the lateral correction amount; Step 6: During construction, based on the aforementioned step correction amount, a lateral step correction is performed for each stroke of the jacking, ultimately ensuring that the centerline of the main beam segment is located at the minimum value δ. Fmin The corresponding position.

2. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 1, characterized in that, In step 6, the step correction specifically includes: S1, determine the optimal main beam segment position corresponding to the minimum Fréchet distance through steps 1-5; S2, determine the lateral correction distance of each jacking device corresponding to the optimal position of this main beam through step 3; S3, each jacking device first jacks the beam longitudinally, and then performs step correction of the transverse correction distance determined in S2. S4 distributes the step correction value evenly over each longitudinal jacking process.

3. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 1, characterized in that, In the lateral correction process, the method for determining the lateral offset vector is as follows: S1, mark the starting position of the center point of the tail of curve A as point A, and the center line of each jacking pier in the permanent pier and temporary pier is represented as Y1; S2, draw curve A along the line connecting the center of the first and last jacking piers among the permanent and temporary piers, according to the sequence d = {d1, d2, ..., d...} n The lengths of the jacking blocks are sequentially pushed to obtain curve A'. The center point of the tail of curve A' is marked as point B. The intersections of curve A' and the center lines Y1 of each jacking block form a sequence D = {D1, D2, ..., D}. n }; S4, laterally offset curve A' at each jacking pier, causing curve A' to rotate at a certain angle. Different lateral offsets yield curve A. i ', curve A i The intersection points with the centerline Y1 of each jacking pier form a sequence E = {E1, E2, ..., E...} n }; S3, sequence E = {E1, E2, ..., E n } and the sequence D = {D1, D2, ..., D} n The length of the corresponding connection is the sequence P = {P1, P2, ..., P}. n }; The sequence P = {P1, P2, ..., P} n } is the distance of the lateral offset vector corresponding to each jacking pier of the main beam segment, and the direction of the lateral offset vector is the radial direction of curve A at each jacking pier.

4. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 1, characterized in that, In step 4, the Fréchet distance value is calculated as follows: The sequence A' i The Euclidean distance between A' and the elements in sequence B is denoted as d(A'). i B j ); A' i Euclidean distance induction with elements in B and Euler matrix D ixj The discrete Fréchet distance between position i in sequence A and position j in sequence B is denoted as δ. F (A' i B j ); First, the Eulerian distance matrix D between points in sequences A' and B is obtained. ixj ; Secondly, from i=1, j=1 to i=n, ​​j=m, perform δ F (A' i B j The recursive calculation of sequence A' is performed sequentially. i The corresponding Fréchet distance values ​​δ F ; The Fréchet distance values ​​δ F The discrete Fréchet distance matrix D is constructed F ; The matrix D F The minimum value of each element is the Fréchet distance δ between sequence A' and sequence B. F (A',B).

5. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 4, characterized in that, The δ F (A' i B j The recursive calculation method for ) is as follows: When i = 1 and j = 1, δ F (A' i B j )=d(A'1,B1); When j = 1, then δ F (A' i ,B1)=max[d(A' i-1 ,B1),d(A' i ,B1)]; When i = 1, then δ F (A' i B j )=max[d(A'1,B j-1 ),d(A'1,B j )]; When i≥2 and j≥2 Then δ F (A' i ,B j ) = max[d(A' i ,B j ), min(d(A' i ,B j-1 ), d(A' i-1 ,B j ), d(A' i-1 ,B j-1 )].

6. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 4, characterized in that, The Eulerian distance matrix D between the points corresponding to sequence A' and sequence B ixj for: The matrix D F for:

7. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 2, characterized in that, The minimum Fréchet distance δ Fmin Corresponding A' i The sequence represents the optimal position after the variable curvature main beam is pushed.

8. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 2, characterized in that, Different δ values ​​obtained from different lateral offsets F The curves representing the values ​​are the lateral offset vectors of each jacking pier.

9. The method for determining the position of a variable curvature main beam based on the Fréchet algorithm according to claim 2, characterized in that, The formula for calculating the step correction amount is shown in equation (1): Where TO is the lateral offset vector, PD is the jacking distance of curve A in step 2, and ES is the rated step size of the jacking device.

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