Multi-objective optimization method for arch control and backstay cable force of auxiliary tower suspension with pier instead of tower

Abstract

The present application relates to a kind of arch control and back cable force multi-objective optimization method of auxiliary tower suspension with pier instead of tower.The method comprises: constructing the displacement influence factor matrix of back cable and cable to arch rib control node, back cable and cable to the top of interface pier tower, back cable and cable to the top of auxiliary tower;Extract the influence matrix corresponding to the maximum cantilever stage and cable removal stage, and construct optimization function combined with constraint condition to optimize the tension of back cable and cable;With arch rib linear deviation, interface pier deviation, auxiliary tower deviation and cable force boundary as constraint condition, with arch rib linear error, interface pier deviation and auxiliary tower deviation penalty weighted as objective function, construct optimization model to iteratively optimize the tension of back cable and cable;When meeting preset trigger condition, with the arch rib linear of auxiliary tower construction stage, interface pier deviation and auxiliary tower deviation as control condition, the tension of back cable and cable is corrected using pre-elevation method.The present application can effectively control the uniformity of arch rib linear, the offset of interface pier and auxiliary tower deviation and the tension of back cable and cable in construction process, realize the cost reduction and efficiency improvement, and ensure the effective control of arch rib construction whole process and stress state after arching.

Description

Technical Field

[0001] This invention relates to a method for controlling and optimizing the cable force of the back-cable structure by using piers instead of towers and auxiliary towers to form an arch, and belongs to the field of bridge construction technology. Background Technology

[0002] As bridge engineering develops towards longer spans, the construction of modern long-span arch bridges faces specific requirements such as high clearance under the bridge, complex foundation conditions, and limitations imposed by deep canyon terrain. Traditional full-span scaffolding and rotation construction methods are no longer applicable. The cable-stayed suspension construction method, due to its advantages of good stability, high strength, and strong adaptability to complex terrain, has become the preferred solution to meet the specific requirements of long-span arch bridge construction. When using this method, it is necessary to calculate the tension of the backstay cables and the stability and load-bearing capacity of the suspension towers; the accuracy of this calculation depends primarily on the tension of the backstay cables.

[0003] Existing methods for calculating cable tension in backstay cables mainly include the zero-displacement method, iterative method, improved iterative algorithm, the "quiet and still" rule, the influence factor matrix method, and optimization method. Among these, the zero-displacement method assumes zero cable displacement under specific working conditions to solve for the initial cable force. While this ensures no initial deformation, it doesn't consider the coupling effect of multiple working conditions. The iterative method approximates the initial cable force by iteratively correcting iteratively, bringing the result closer to the actual state, but requires pre-setting initial parameters and involves significant computation. Improved iterative algorithms introduce convergence acceleration techniques or computation reduction strategies on top of traditional iterative methods, significantly improving efficiency and accuracy. The "quiet and still" rule, which ensures that tensioning newly installed cable segments does not disturb the alignment of already installed segments, effectively meets alignment requirements, but requires manual iteration and a high level of cable adjustment experience. The influence factor matrix method, based on matrix theory, constructs an influence factor matrix system for different working conditions to analyze the sensitivity of cable force to deformation, comprehensively considering various constraints and achieving high accuracy. Optimization algorithms establish objective functions and constraint equations, using methods such as genetic algorithms or particle swarm optimization to search for optimal solutions, efficiently handling complex problems.

[0004] However, when faced with the specific construction scenario of using piers instead of towers and auxiliary towers to form an arch, the above methods fail to fully consider the coupling constraints of the offset of the boundary piers and the offset of the auxiliary towers, making it difficult to meet the multi-objective collaborative control requirements under the condition of limited construction work surface. Summary of the Invention

[0005] This invention provides a data processing method for controlling the arch formation by using piers instead of towers and auxiliary towers, and optimizing the multi-objective force of the back-cable cable, aiming to solve at least one of the technical problems existing in the prior art.

[0006] The technical solution of this invention relates to a data processing method for controlling the arch formation by using piers instead of towers and auxiliary towers, and optimizing the multi-objective optimization of back-cable tension. The method according to this invention includes the following steps: S100. Construct an influence factor matrix, wherein the influence factor matrix includes the displacement influence factor matrix of the cable-stayed arch rib control node, the displacement influence factor matrix based on the junction pier, and the displacement influence factor matrix based on the auxiliary tower. S200. Based on the aforementioned influence factor matrix, solve for the initial tension vector of the back strap. S300. Extract the influence matrices corresponding to the maximum cantilever stage and the cable dismantling stage, and construct an optimization function in combination with the constraint conditions to optimize the tension of the back cable. S400. When the preset triggering conditions are met, the tension of the buckle cable is corrected based on the control conditions.

[0007] Furthermore, in step S100, constructing the displacement influence factor matrix based on the boundary pier includes constructing the displacement influence factor matrix of the back cable force on the top of the boundary pier and the displacement influence factor matrix of the fastening cable force on the top of the boundary pier; constructing the displacement influence factor matrix based on the auxiliary tower includes constructing the displacement influence factor matrix of the back cable force on the top of the auxiliary tower and the displacement influence factor matrix of the fastening cable force on the top of the auxiliary tower.

[0008] Furthermore, the boundary pier bears the backstays installed on the first N arch rib segments, and the auxiliary tower bears the backstays installed on the (N+1)th and subsequent arch rib segments, where N is a segment number threshold determined according to the construction conditions.

[0009] Furthermore, the influence factor matrix includes the displacement influence factor matrix of the cable-stayed arch rib control node, as shown below: In the formula, the element For the corresponding working condition, the first n root cord to the first n Displacement influence factors of each arch rib control node; The matrix representing the influence of the backstay cable force on the displacement of the top of the junction pier is as follows: Elements in the formula For the corresponding working condition, the first n Root back cable to the first m Displacement influence factors of each boundary pier control node; The influence factor matrix of the cable tension on the displacement of the top of the junction pier is expressed as follows: Elements in the formula For the corresponding working condition, the first n root cord to the first m Displacement influence factors of each boundary pier control node; The matrix representing the influence of the backstay cable force on the displacement at the top of the auxiliary tower is as follows: Elements in the formula For the corresponding working condition, the first n Root back cable to the first i Displacement influence factors of each auxiliary tower control node; The influence factor matrix of the cable tension on the displacement of the auxiliary tower top is expressed as follows: Elements in the formula For the corresponding working condition, the first n root cord to the first i Displacement influence factors of each auxiliary tower control node; Furthermore, based on the aforementioned influence factor matrix, the initial tension vector of the back strap is calculated as follows: Calculate the change in cord and backspin change The calculation formula is as follows: The unique solution can be obtained by using MATLAB's least squares method, and the resulting matrix form is as follows: In the formula, The deformation vector of the arch rib control node target; For the vertical displacement of the arch rib control node, The top of the boundary pier is offset. The top of the auxiliary tower is offset.

[0010] Change in the amount of the cleavage and backspin change Each with its own selected initial cable force , Superimpose and combine the initial cable forces ,in It is expressed as follows: Furthermore, the constraints include arch rib alignment deviation constraints, junction pier offset constraints, auxiliary tower offset constraints, and cable force boundary constraints, wherein, The arch rib alignment deviation constraint is expressed as follows: In the formula, The calculated deformation values ​​for the control nodes of the arch rib; The deformation vector of the arch rib control node target; The allowable deformation error value for the control node of the arch rib; The offset constraints of the auxiliary tower and the offset constraints of the boundary pier are expressed as follows: In the formula, Calculated deformation values ​​of the control nodes at the top of the boundary pier; The allowable deformation value for the control node at the top of the boundary pier; Calculated deformation values ​​of the control nodes at the top of the auxiliary tower; The allowable deformation value for the control node at the top of the auxiliary tower; The cable force boundary constraint is represented as follows: In the formula, This is the lower limit of the cable tension. This represents the upper limit of the cable tension.

[0011] Furthermore, the construction of the optimization function is represented as follows: In the formula, The objective function value, To control the shape of the main arch, To control the displacement of the boundary pier, To control the displacement of the auxiliary tower, To control the uniformity of cable force, To satisfy cable force constraints. , which is a weighting coefficient used to adjust the importance of the main arch alignment control, the boundary pier displacement control, the auxiliary tower displacement control, the cable force uniformity control, and the constraint conditions.

[0012] Furthermore, when the triggering conditions are met, the arch rib alignment, boundary pier deviation, and auxiliary tower deviation during the auxiliary tower construction stage are used as control conditions. The pre-lifting method is used to raise the coordinates of the arch rib control nodes to a preset height. After the auxiliary tower construction is completed, the actual deformation value is measured, and the tension of the back-cable is calculated for supplementary tensioning.

[0013] The present invention also relates to a computer-readable storage medium having program instructions stored thereon, which, when executed by a processor, implement the above-described method.

[0014] The technical solution of the present invention also relates to a multi-objective optimization system for arch control and back-cable force optimization using piers instead of towers and auxiliary towers suspended and assembled, the system including a computer device containing the aforementioned computer-readable storage medium.

[0015] The beneficial effects of this invention are as follows: This invention presents a data processing method and system for controlling the arch construction using piers instead of towers and auxiliary towers, and optimizing the multi-objective force of the back-cable cables. By reusing the boundary piers as the supporting structure for the back-cable cables and erecting column-type auxiliary towers on the arch rib segments, it avoids the additional occupation of the construction site by traditional back-cable cables. This effectively solves a series of problems such as limited construction work area, conflicts between the assembly site and the back-cable cables, conflicts between the actual hoisting line and the back-cable cables, and the lack of a proper hanging angle in the integrated cable design. Based on the inclined cable-stayed system, the boundary piers support small-numbered back-cable cables, and auxiliary towers are introduced to support large-numbered back-cable cables for auxiliary construction. By constructing a displacement influence factor matrix of the back-cable cables on the arch rib control nodes, boundary piers, and auxiliary towers, the initial tension vector of the back-cable cables is solved. A multi-objective optimization function is constructed with constraints such as arch rib alignment deviation, boundary pier offset, auxiliary tower offset, and cable force boundaries to iteratively optimize the back-cable cable force. Using the arch rib alignment and offset during the auxiliary tower construction stage as control conditions, a pre-lifting method is used to correct and control individual cable forces. During construction, the deviations of the junction piers and auxiliary towers remained within acceptable limits. After cable removal, the arch rib profile matched the target value well. The cable force distribution under various working conditions was uniform and did not exceed the cable bearing capacity. This effectively controlled the uniformity of the arch rib profile during construction and after cable release, ensuring the stability of the arch ring's stress state. This achieved cost reduction and efficiency improvement while ensuring effective control of the stress state throughout the arch rib construction process and after arch completion. Using finite element software and numerical analysis software, automated and intelligent solutions for cable force optimization were achieved, improving the efficiency of cable force adjustment. It should be noted that this invention can be applied to the control and calculation of cable-stayed suspension construction of large-span arch bridges under limited working conditions, and can also be extended to the construction control and cable force calculation of general arch bridges. Attached Figure Description

[0016] Figure 1 This is a basic flowchart of the method according to the present invention.

[0017] Figure 2 This is a construction fastening layout diagram for the small-numbered arch segments according to an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the construction of the auxiliary tower according to an embodiment of the present invention.

[0019] Figure 4 This is a construction and fastening layout diagram of the first section of the large-numbered arch segment after the construction of the auxiliary tower according to an embodiment of the present invention.

[0020] Figure 5 This is a diagram showing the arrangement of the arch bridge fastening system according to an embodiment of the present invention.

[0021] Figure 6 This is a schematic diagram of a single-stage dismantling model according to an embodiment of the present invention.

[0022] Figure 7 This is a schematic diagram of a construction model according to an embodiment of the present invention.

[0023] Figure 8 This is a schematic diagram illustrating the theoretical calculation value of the back strap force according to an embodiment of the present invention.

[0024] Figure 9 This is a schematic diagram of the linear theoretical calculation value of the arch rib according to an embodiment of the present invention.

[0025] Figure 10 This is a schematic diagram illustrating the theoretical calculation values ​​of the linear difference between the left and right spans and the upstream and downstream arch ribs according to an embodiment of the present invention.

[0026] Figure 11 This is a schematic diagram illustrating the theoretical calculation values ​​of the boundary pier offset and auxiliary tower offset according to an embodiment of the present invention.

[0027] Figure 12 This is a diagram showing the cable tension error of the back strap according to an embodiment of the present invention.

[0028] Figure 13 This is a linear error diagram of the arch rib according to an embodiment of the present invention. Detailed Implementation

[0029] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with the embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention.

[0030] It should be noted that, unless otherwise specified, when a feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. The singular forms "a," "described," and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this specification is for the purpose of describing particular embodiments only and not for limiting the invention. The term "and / or" as used herein includes any combination of one or more of the associated listed items.

[0031] It should be understood that although the terms first, second, third, etc., may be used to describe various elements in this disclosure, these elements should not be limited to these terms. These terms are used only to distinguish elements of the same type from one another. For example, a first element may also be referred to as a second element without departing from the scope of this disclosure, and similarly, a second element may also be referred to as a first element. Any and all instances or exemplary language (“e.g.,” “such as,” etc.) provided herein are intended only to better illustrate embodiments of the invention and, unless otherwise required, do not impose a limitation on the scope of the invention.

[0032] Reference Figure 1 In some embodiments, the multi-objective data processing method for the cable force of cable-stayed arch bridges based on the influence factor matrix according to the present invention includes at least the following steps: S100. Construct an influence factor matrix, wherein the influence factor matrix includes the displacement influence factor matrix of the cable-stayed arch rib control node, the displacement influence factor matrix based on the junction pier, and the displacement influence factor matrix based on the auxiliary tower. S200. Based on the aforementioned influence factor matrix, solve for the initial tension vector of the back strap. S300. Extract the influence matrices corresponding to the maximum cantilever stage and the cable dismantling stage, and construct an optimization function in combination with the constraint conditions to optimize the tension of the back cable. S400. When the preset triggering conditions are met, the tension of the buckle cable is corrected based on the control conditions.

[0033] This invention presents a data processing method and system for controlling the arch construction using piers instead of towers and auxiliary towers, and optimizing the multi-objective force of the back-cable cables. By reusing the boundary piers as the supporting structure for the back-cable cables and erecting column-type auxiliary towers on the arch rib segments, it avoids the additional occupation of the construction site by traditional back-cable cables. This effectively solves a series of problems such as limited construction work area, conflicts between the assembly site and the back-cable cables, conflicts between the actual hoisting line and the back-cable cables, and the lack of a proper hanging angle in the integrated cable design. Based on the inclined cable-stayed system, the boundary piers support small-numbered back-cable cables, and auxiliary towers are introduced to support large-numbered back-cable cables for auxiliary construction. By constructing a displacement influence factor matrix of the back-cable cables on the arch rib control nodes, boundary piers, and auxiliary towers, the initial tension vector of the back-cable cables is solved. A multi-objective optimization function is constructed with constraints such as arch rib alignment deviation, boundary pier offset, auxiliary tower offset, and cable force boundaries to iteratively optimize the back-cable cable force. Using the arch rib alignment and offset during the auxiliary tower construction stage as control conditions, a pre-lifting method is used to correct and control individual cable forces. During construction, the deviations of the junction piers and auxiliary towers remained within acceptable limits. After cable removal, the arch rib profile matched the target value well. The cable force distribution under various working conditions was uniform and did not exceed the cable bearing capacity. This effectively controlled the uniformity of the arch rib profile during construction and after cable release, ensuring the stability of the arch ring's stress state. This achieved cost reduction and efficiency improvement while ensuring effective control of the stress state throughout the arch rib construction process and after arch completion. Using finite element software and numerical analysis software, automated and intelligent solutions for cable force optimization were achieved, improving the efficiency of cable force adjustment. It should be noted that this invention can be applied to the control and calculation of cable-stayed suspension construction of large-span arch bridges under limited working conditions, and can also be extended to the construction control and cable force calculation of general arch bridges.

[0034] In some embodiments of the present invention, two models are established: one for the initial frame removal and the other for the construction process. The initial frame removal model activates all elements, boundary conditions, and loads at once. The construction model sets corresponding construction stages according to the construction conditions, activating the corresponding elements, boundary conditions, and loads for each stage. The deformation values ​​of the control nodes are calculated and extracted using the initial frame removal model. These deformation values ​​are then superimposed with the manufacturing alignment to obtain the ideal bare arch alignment, which is the target alignment for construction control.

[0035] In some embodiments of the present invention, the corresponding influence factor matrix is ​​extracted using finite element software. Here, let the number of anchor cables = the number of back cables = the number of arch rib control nodes = n, and the unknown variables be... .matrix The tension of the tether; matrix The force of the backstays is denoted by N, where the boundary pier bears the backstays installed on the first N arch rib segments (smaller numbers 1-N), and the auxiliary tower bears the backstays installed on the (N+1)th and subsequent arch rib segments (larger numbers N+1-n), where N is a segment numbering threshold determined based on construction conditions. The number of control nodes for the boundary pier is... m The auxiliary tower control node is i .

[0036] In some embodiments of the present invention, the backstays are numbered according to the installation sequence of the arch rib segments. Backstays with numbers less than or equal to a threshold N are defined as low-numbered backstays, and their anchoring system is supported by the boundary pier; backstays with numbers greater than N are defined as high-numbered backstays, and their anchoring system is supported by the auxiliary tower. The threshold N is determined based on the angle between the elevation of the tensioning point of the arch rib segment and the top elevation of the boundary pier. When the angle between the backstay and the horizontal plane is lower than a preset value, the auxiliary tower is used instead of the boundary pier for force conversion.

[0037] It should be noted that the influence factor matrix and the influence matrix are different concepts in this invention. The influence factor matrix is ​​formed by combining the influence factors of the control nodes corresponding to each construction stage, and is used for the whole-process construction control and initial cable force solution; the influence matrix is ​​the control node response matrix extracted under a single working condition, and is used for cable force optimization calculation in the maximum cantilever stage and cable dismantling stage.

[0038] It should be noted that in this invention, the term "fastening and backing cable" is a general term for both fastening cable and backing cable. The fastening cable is used for the control of the arch rib segment suspension, while the backing cable is used for structural reverse balance and auxiliary load bearing.

[0039] Specifically, the influence factor matrix includes the displacement influence factor of the cable tie on the control node of the arch rib, the displacement influence factor matrix of the back cable force on the top of the junction pier, the displacement influence factor matrix of the cable tie force on the top of the junction pier, the displacement influence factor matrix of the back cable force on the top of the auxiliary tower, and the displacement influence factor matrix of the cable tie force on the top of the auxiliary tower.

[0040] The displacement influence factor matrix of the control nodes of the arch rib due to the fastening cable is represented as follows: (1.1) In the formula, the element For the corresponding working condition, the first n root cord to the first n Displacement influence factors of each arch rib control node; The displacement influence factor matrix of the backstay force on the control node at the top of the junction pier under the action of the unit's self-weight under all working conditions is expressed as follows: (1.2) Elements in the formula For the corresponding working condition, the first n Root back cable to the first m Displacement influence factors of each boundary pier control node; The displacement influence factor matrix of the control node at the top of the junction pier under the action of the cable force and the self-weight of the unit under all working conditions is expressed as follows: (1.3) Elements in the formula For the corresponding working condition, the first n root cord to the first m Displacement influence factors of each boundary pier control node; The displacement influence factor matrix of the backstay cable force on the control node at the top of the auxiliary tower under the action of the unit's self-weight under all working conditions is expressed as follows: (1.4) Elements in the formula For the corresponding working condition, the first n Root back cable to the first i Displacement influence factors of each auxiliary tower control node; The displacement influence factor matrix of the auxiliary tower top control node under the action of the cable tension and the element's self-weight under all working conditions is expressed as follows: (1.5) Elements in the formula For the corresponding working condition, the first n root cord to the first i Displacement influence factors of each auxiliary tower control node; In some embodiments, the influence factor matrix is ​​used to characterize the cumulative impact of cable force changes on the deformation of control nodes throughout the construction process. Based on the influence factor matrix, the specific steps for solving the initial tension vector of the backstay cable are as follows: Calculate the change in cord and backspin change The calculation formula is as follows: (1.10) The least squares method is implemented using MATLAB to obtain a unique solution. The resulting matrix form is as follows: (1.11) In the formula, The deformation vector of the arch rib control node target; For the vertical displacement of the arch rib control node, The top of the boundary pier is offset. The top of the auxiliary tower is offset.

[0041] Change in the amount of the cleavage and backspin change Each with its own selected initial cable force , Superimpose and combine the initial cable forces ,in It is expressed as follows: (1.12) In some embodiments, the constraints include arch rib alignment deviation constraints, junction pier offset constraints, auxiliary tower offset constraints, and cable force boundary constraints, wherein... The arch rib alignment deviation constraint is expressed as follows: (1.13) In the formula, The calculated deformation values ​​for the control nodes of the arch rib; The deformation vector of the arch rib control node target; The allowable deformation error value for the control node of the arch rib; The offset constraints of the auxiliary tower and the offset constraints of the boundary pier are expressed as follows: (1.14) In the formula, Calculated deformation values ​​of the control nodes at the top of the boundary pier; The allowable deformation value for the control node at the top of the boundary pier; Calculated deformation values ​​of the control nodes at the top of the auxiliary tower; The allowable deformation value for the control node at the top of the auxiliary tower; The cable force boundary constraints are expressed as follows: (1.15) In the formula, This is the lower limit of the cable tension. This represents the upper limit of the cable tension.

[0042] In some embodiments of the present invention, the influence matrix includes the influence matrix of cable force on the displacement of the arch rib control node, the influence matrix of cable force on the displacement of the boundary pier control node, and the influence matrix of cable force on the displacement of the auxiliary tower control node corresponding to the maximum cantilever stage and the cable removal stage, and is obtained by finite element analysis.

[0043] Specifically, the influence matrix is ​​extracted from the construction model. The influence matrix of cable force on cable force during the maximum cantilever stage is expressed as follows: (1.6) Elements in the formula For the 2nd n Root cable tensioning for the 2nd n The influence value of the cable force generated by the root cable; The influence matrix of cable force on cable force during cable dismantling is expressed as follows: (1.7) Elements in the formula For the 2nd n The root cable releases a 1kN force on the second n The influence value of the cable force generated by the root cable; The influence matrix of cable force on the displacement of the control node of the arch rib during the maximum cantilever stage is expressed as follows: (1.8) Elements in the formula For the first n Root cable tensioning on the first n Displacement influence value generated by each arch rib control node; The influence matrix of cable force on the displacement of the control node of the arch rib during cable removal is expressed as follows: (1.9) Elements in the formula For the first n The displacement effect of the 1KN force released from the root cable on the control node of the nth arch rib; The influence matrix of the backstay force during the maximum cantilever stage on the displacement of the control node at the top of the junction pier under the action of the element's self-weight is expressed as follows: (1.10) Elements in the formula For the first n The force of 1 kN applied to the back cable tensioning the first m Displacement impact value generated by each boundary pier control node; The displacement influence matrix of the back cable force on the control node at the top of the junction pier under the self-weight of the unit during the cable removal process is expressed as follows: (1.11) Elements in the formula For the firstn The root back cable releases a force of 1 kN on the first m Displacement impact value generated by each boundary pier control node; The influence matrix of the cable force during the maximum cantilever stage on the displacement of the control node at the top of the junction pier under the self-weight of the unit is expressed as follows: (1.12) Elements in the formula For the first n The force of 1 kN applied to the tension of the first cable m Displacement impact value generated by each boundary pier control node; The influence matrix of the cable force on the displacement of the control node at the top of the junction pier under the self-weight of the unit during the cable removal process is expressed as follows: (1.13) Elements in the formula For the first n The root of the rope releases a 1kN force on the first m Displacement influence value of each boundary pier control node The influence matrix of the backstay cable force on the displacement of the control node at the top of the auxiliary tower under the action of the element's self-weight during the maximum cantilever stage is expressed as follows: (1.14) Elements in the formula For the first n The force of 1 kN applied to the back cable tensioning the first i Displacement impact value generated by each auxiliary tower control node; The influence matrix of the back cable force on the displacement of the control node at the top of the auxiliary tower under the action of the unit's self-weight during the cable dismantling process is expressed as follows: (1.15) Elements in the formula For the first n The root back cable releases a force of 1 kN on the first i Displacement impact value generated by each auxiliary tower control node; The influence matrix of the cable force on the displacement of the control node at the top of the auxiliary tower under the action of the element's self-weight during the maximum cantilever stage is expressed as follows: (1.16) Elements in the formula Representing the first n The force of 1 kN applied to the tension of the first cable i Displacement impact value generated by each auxiliary tower control node; The influence matrix of the cable force during the cable removal process on the displacement of the control node at the top of the auxiliary tower under the action of the unit's self-weight is expressed as follows: (1.17) In the formula, the element Representing the first n The root of the rope releases a 1kN force on the first i Displacement impact value generated by each auxiliary tower control node; In some embodiments, the influence matrices corresponding to the maximum cantilever stage and the cable dismantling stage are superimposed to form a cumulative influence matrix for the entire process, which is used to characterize the comprehensive influence of cable force changes on the displacement of the control nodes of the junction pier and auxiliary tower throughout the entire process. The cumulative influence factor matrix for the entire process is expressed as follows: (1.18) In some embodiments, the optimization function is constructed as follows: (1.19) In the formula, The objective function value, To control the shape of the main arch, To control the displacement of the boundary pier, To control the displacement of the auxiliary tower, To control the uniformity of cable force, To satisfy cable force constraints. These are weighting coefficients used to adjust the relative importance of the main arch alignment control, junction pier displacement control, auxiliary tower displacement control, cable tension uniformity control, and constraint conditions. The above terms are expressed as follows: (1.20) In the formula, The initial backstay cable force vector is obtained by solving based on the target arch alignment. For cable force adjustment vector; The matrix representing the comprehensive influence of backstay cable force on the displacement of the main arch control point; This is the displacement vector of the control points corresponding to the target alignment.

[0044] (1.21) L The displacement influence matrix of the boundary pier. (1.22) T Auxiliary tower displacement influence matrix (1.23) The objective function for cable force uniformity is used to reduce the dispersion of cable force and improve the force coordination of each back cable. This is the average value of the tension of all back straps.

[0045] Penalty function output It is expressed as follows: (1.24) Soli's violation penalty It is expressed as follows: (1.25) Penalty for exceeding the limit of boundary pier deviation It is expressed as follows: (1.26) Penalty for excessive deviation of auxiliary tower It is expressed as follows: (1.27) When all variables are within the feasible region =0, no penalty.

[0046] In some embodiments, for Regarding decision vectors Differentiate and let The unconstrained optimal total cable force is expressed as follows: (1.28) In some embodiments, the present invention employs a step-by-step approximation of the final output through a cutting iteration. The cable force is represented by the unilateral segmentation iterative solution as follows: (1.29) In the formula The cutting coefficient is... k This represents the number of cuts.

[0047] In some embodiments, the cable forces obtained at the final stage generally meet the construction requirements. However, there are certain construction conditions where the upstream and downstream alignment deviations are too large, the tower deflection is too large, or special control is required. Therefore, individual cable forces are optimized during the construction process. During the construction of the auxiliary tower on the arch, a pre-lifting method is used for control. That is, when tensioning the corresponding arch segment, the coordinates of the control nodes are pre-lifted by 80% of the theoretical deformation value after the auxiliary tower construction. After the auxiliary tower construction is completed, additional tensioning is performed. Therefore, the control cable forces for tensioning the corresponding arch segment are corrected based on the completion of the auxiliary tower construction.

[0048] A specific embodiment is described here. See [link to documentation]. Figures 2 to 5As shown, a certain bridge is a 520m steel box girder arch bridge, constructed using a cable-stayed, suspended assembly method. The centerline of the truss arch and the centerlines of the upper and lower chords are all catenaries, with an arch axis coefficient of 1.55. The calculated span L = 520m, the calculated rise f = 130m, and the rise-to-span ratio is 1 / 4. The radial height of the arch crown section is 9.0m, and the radial height of the arch foot section is 14.0m. The truss arch has four main arch ribs arranged transversely, forming two ribs spaced 8.0m apart, with a spacing of 14.0m between any two main arch ribs. The entire bridge consists of 21 main segments and one closure segment, totaling 88 segments. The maximum lifting weight per segment is 284.8t, and the minimum is 122.02t. Construction of the first bank (NS1-NS8) was carried out using the boundary piers as anchor towers. After KS8 and BS8 were fully tensioned, LZ4 columns were assembled on arch segment NS8 as auxiliary towers to provide support for the assembly of the first bank (NS9-NS11) and subsequent tensioning of the anchor cables. Construction of the second bank (NS1'-NS8') was carried out using the boundary piers as anchor towers. A temporary tower was then built on top of the boundary piers to provide support for the assembly of the second bank (NS9'-NS10') and subsequent tensioning of the anchor cables.

[0049] Furthermore, a finite element model is constructed based on the geometric parameters, material parameters, boundary conditions, and load conditions of the arch bridge. The structural groups, boundary values, and load groups for each construction stage are determined according to the engineering construction conditions, establishing a construction stage model. The number of unknown loads is determined using the principle of the influence factor matrix, and the influence factor matrix corresponding to each unknown load is derived. In this embodiment, the calculation is performed using the finite element software MIDAS Civil, and the solution is obtained using the mathematical engineering optimization software MATLAB.

[0050] In this embodiment, the correspondence between the symbols of the above method and specific engineering parameters is as follows: the number of first bank cable anchors n=11 (corresponding to arch segments NS1~NS11, cable anchors KS1~KS11, and back cables BS1~BS11), and the number of second bank cable anchors n=10 (corresponding to arch segments NS1'~NS10', cable anchors KS1'~KS10', and back cables BS1'~BS10'). The number of control nodes m of the junction pier and the number of control nodes i of the auxiliary tower are determined based on the monitoring nodes at the top of the tower in the finite element model; the allowable deformation error value of the arch rib control node is taken according to the "Technical Specifications for Construction of Highway Bridges and Culverts"; the allowable deviation value of the junction pier and auxiliary tower is determined according to the design requirements; and the upper and lower limits of cable force are determined based on the cable breaking force and safety factor.

[0051] In some embodiments of the present invention, see Figure 6As shown, the single-stage dismantling model is used to solve the overall initial state of the arch bridge structure. This model activates all structural elements, boundary constraints, and load conditions at once to simulate the overall stress and deformation response of the structure under ideal bare arch conditions. The displacement response of each control node under its own weight and initial constraints is calculated using this model, and this response is superimposed with the manufacturing alignment to obtain the construction control target alignment, providing benchmark data for subsequent calculation of the backstay cable forces.

[0052] In some embodiments of the present invention, see Figure 7 As shown, the construction model is used to simulate the phased construction behavior of the entire cantilever arch bridge construction process. The model divides the construction into phases according to the actual construction sequence, activating corresponding structural units, boundary conditions, and load cases in each phase, and simultaneously updating the backstay cable force state. This model enables dynamic simulation of the structural response during the maximum cantilever stage and the cable removal stage, thus providing a comprehensive analytical basis for influence matrix extraction and multi-objective optimization calculations.

[0053] It should be noted that the main function of the back-clip cable is to provide temporary support during the cantilever assembly of the arch rib segments, ensuring that the arch rib alignment meets the closure accuracy requirements. A reasonable back-clip cable force should meet the following conditions: First, the deviation of the junction pier and auxiliary tower during construction should be within the allowable range; second, the error between the arch rib alignment and the target alignment after cable removal should be less than the allowable value specified in the code; third, the back-clip cable force distribution under each working condition should be uniform and not exceed the cable's bearing capacity. Based on the above principles, after determining the values ​​of parameters such as arch rib alignment deviation constraints, junction pier deviation constraints, auxiliary tower deviation constraints, and cable force boundary constraints, the influence factor matrix data and parameter values ​​are substituted into the optimization model to solve for the back-clip cable force adjustment value. The optimization calculation results are obtained through computer iterative calculation, as shown in the figure below. Figures 8-11 The initial tension of the back strap is shown in the figure. Figure 8 As shown, the cable tension on the second bank changes gradually, while the cable tension on the first bank, except for KS7 and KS8, changes uniformly. Deformation values ​​for each control node are shown in [reference needed]. Figure 9 After cable removal, the arch rib deformation was largely in line with the target value, with the largest difference being 48mm (outer left side of the connection between arch segments NS7 and NS8); the largest deformation difference between the four arch segments was 10mm. For the offset of the junction piers and auxiliary towers at each key construction stage, please refer to... Figure 11 The maximum deviation of the junction pier was 39mm, and the maximum deviation of the auxiliary tower was 38mm, both within a reasonable range. For the error between the actual cable force and the theoretical cable force after construction, please refer to [reference needed]. Figure 12 The maximum error in the tension of the tie cables was 9.8%, and the maximum error in the tension of the back cables was 9.9%. The actual tension did not exceed the bearing capacity of the cable body. For the differences between the actual and theoretical elevations of the arch rib control nodes during the closure but before cable removal and after cable removal, please refer to [reference needed]. Figure 13The maximum error during the closure but before cable removal stage was -43mm, and the maximum error after cable removal was 29mm. The overall line shape was smooth and highly consistent with the theoretical value.

[0054] It should be understood that the method steps in the embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit (ASIC).

[0055] Furthermore, the procedures described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by the context. The procedures described herein (or variations and / or combinations thereof) may be executed under the control of one or more computer systems configured with executable instructions, and may be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors. The computer program comprises a plurality of instructions executable by one or more processors.

[0056] Furthermore, the method can be implemented in any suitable type of computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or in communication with charged particle tools or other imaging devices, etc. Aspects of the invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage medium, RSM, ROM, etc., such that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the processes described herein. Furthermore, the machine-readable code, or portions thereof, can be transmitted via wired or wireless networks. The invention described herein includes these and other different types of non-transitory computer-readable storage media when such media comprises instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. When programmed according to the methods and techniques described in the invention, the invention may also include the computer itself.

[0057] A computer program can be applied to input data to perform the functions described herein, thereby transforming the input data to generate output data stored in non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects generated on the display.

[0058] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, as long as they achieve the technical effects of the present invention by the same means, should be included within the scope of protection of the present invention. Within the scope of protection of the present invention, the technical solutions and / or implementation methods can have various modifications and variations.

Claims

1. A data processing method for controlling and optimizing the multi-objective stress of the back-cable tension in the arch-forming system using piers instead of towers and auxiliary towers, characterized in that... The method includes the following steps: S100. Construct an influence factor matrix, wherein the influence factor matrix includes the displacement influence factor matrix of the cable-stayed arch rib control node, the displacement influence factor matrix based on the junction pier, and the displacement influence factor matrix based on the auxiliary tower. S200. Based on the aforementioned influence factor matrix, solve for the initial tension vector of the back strap. S300. Extract the influence matrices corresponding to the maximum cantilever stage and the cable dismantling stage, and construct an optimization function in combination with the constraint conditions to optimize the tension of the back cable. S400. When the preset triggering conditions are met, the tension of the buckle cable is corrected based on the control conditions.

2. The method according to claim 1, characterized in that, In step S100, constructing the displacement influence factor matrix based on the junction pier includes constructing the displacement influence factor matrix of the back cable force on the top of the junction pier and the displacement influence factor matrix of the fastening cable force on the top of the junction pier; constructing the displacement influence factor matrix based on the auxiliary tower includes constructing the displacement influence factor matrix of the back cable force on the top of the auxiliary tower and the displacement influence factor matrix of the fastening cable force on the top of the auxiliary tower.

3. The method according to claim 2, characterized in that, The boundary pier supports the backstays installed on the first N arch rib segments, and the auxiliary tower supports the backstays installed on the (N+1)th and subsequent arch rib segments, where N is a segment number threshold determined according to the construction conditions.

4. The method according to claim 2, characterized in that, The influence factor matrix includes the displacement influence factor matrix of the control node of the rib, which is represented as follows: In the formula, the element For the corresponding working condition, the first n root cord to the first n Displacement influence factors of each arch rib control node; The matrix representing the influence of the backstay cable force on the displacement of the top of the junction pier is as follows: Elements in the formula For the corresponding working condition, the first n Root back cable to the first m Displacement influence factors of each boundary pier control node; The influence factor matrix of the cable tension on the displacement of the top of the junction pier is expressed as follows: Elements in the formula For the corresponding working condition, the first n root cord to the first m Displacement influence factors of each boundary pier control node; The matrix representing the influence of the backstay cable force on the displacement at the top of the auxiliary tower is as follows: Elements in the formula For the corresponding working condition, the first n Root back cable to the first i Displacement influence factors of each auxiliary tower control node; The influence factor matrix of the cable tension on the displacement of the auxiliary tower top is expressed as follows: Elements in the formula For the corresponding working condition, the first n root cord to the first i Displacement influence factor of each auxiliary tower control node.

5. The method according to claim 1, characterized in that, Based on the aforementioned influence factor matrix, the initial tension vector of the back strap is calculated as follows: Calculate the change in cord and backspin change The calculation formula is as follows: The unique solution can be obtained by using MATLAB's least squares method, and the resulting matrix form is as follows: In the formula, The deformation vector of the arch rib control node target; For the vertical displacement of the arch rib control node, The top of the boundary pier is offset. The top of the auxiliary tower is offset. Change in the amount of the cleavage and backspin change Each with its own selected initial cable force , Superimpose and combine the initial cable forces ,in It is expressed as follows: 。 6. The method according to claim 3, characterized in that, In step S300, the constraints include arch rib alignment deviation constraints, junction pier misalignment constraints, auxiliary tower misalignment constraints, and cable force boundary constraints, wherein... The arch rib alignment deviation constraint is expressed as follows: In the formula, The calculated deformation values ​​for the control nodes of the arch rib; The deformation vector of the arch rib control node target; The allowable deformation error value for the control node of the arch rib; The offset constraints of the auxiliary tower and the offset constraints of the boundary pier are expressed as follows: In the formula, Calculated deformation values ​​of the control nodes at the top of the boundary pier; The allowable deformation value for the control node at the top of the boundary pier; Calculated deformation values ​​of the control nodes at the top of the auxiliary tower; The allowable deformation value for the control node at the top of the auxiliary tower; The cable force boundary constraint is expressed as follows: In the formula, This is the lower limit of the cable tension. This represents the upper limit of the cable tension.

7. The method according to claim 1, characterized in that, The optimization function is constructed as follows: In the formula, The objective function value, To control the shape of the main arch, To control the displacement of the boundary pier, To control the displacement of the auxiliary tower, To control the uniformity of cable force, To satisfy cable force constraints. , which is a weighting coefficient used to adjust the importance of the main arch alignment control, the boundary pier displacement control, the auxiliary tower displacement control, the cable force uniformity control, and the constraint conditions.

8. The method according to claim 1, characterized in that, When the triggering conditions are met, the arch rib alignment, boundary pier deviation, and auxiliary tower deviation during the auxiliary tower construction stage are used as control conditions. The pre-lifting method is used to raise the coordinates of the arch rib control nodes to a preset height. After the auxiliary tower construction is completed, the actual deformation value is measured, and the tension of the back-cable is calculated for supplementary tensioning.

9. A computer-readable storage medium having stored thereon program instructions that, when executed by a processor, perform the method as described in any one of claims 1 to 8.

10. A multi-objective optimization control system for arch construction using piers instead of towers and auxiliary towers, and for back-cable tension, characterized in that... include: A computer device, the computer device comprising the computer-readable storage medium according to claim 9.

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