Multi-objective data processing method for arch bridge cable-stayed buckle tension based on influence matrix

Abstract

This invention relates to a multi-objective data processing method and multi-objective optimization system for the cable force of cable-stayed arch bridges based on influence matrices. The method includes: establishing a finite element model and modifying the model according to the construction sequence; extracting multiple relevant influence matrices, including displacement influence matrices, cable force influence matrices, and internal force influence matrices; based on the superposition principle, obtaining the relationship between the multiple relevant influence matrices, and thus obtaining the initial tension vector of each cable; determining multiple corresponding constraints based on optimization theory, establishing a multi-objective optimization model for the initial cable force under variable loads, and calculating the cable force parameters of the back cables in the cable-stayed arch bridge construction. This invention can effectively control the axial force and arch rib shape of the arch rib members during the cable-stayed construction of long-span arch bridges, achieving optimal arch shape and stable stress state of the completed arch ring.

Description

Technical Field

[0001] This invention relates to a multi-objective data processing method for cable tension of cable-stayed arch bridges based on an influence matrix, belonging to the field of bridge construction technology. Background Technology

[0002] Arch bridges have seen rapid development and widespread application due to their advantages such as earthquake resistance, wind resistance, and high load-bearing capacity. Because the southwest region is mostly characterized by high gorges and deep valleys, construction conditions and space are limited, so the cable-stayed method is often used for arch rib construction. Since the cable tension, arch rib displacement, and internal forces interact during segmental assembly, determining the initial cable tension is crucial for the overall stability and alignment control of the arch rib.

[0003] Currently, there are several methods for calculating the cable force of the cable backstays during the construction of cable-stayed arch bridges, including the zero-displacement method, iterative method, improved iterative algorithm, static stabilization method, influence matrix method, and optimization method. For example, the zero-displacement method is a classic calculation method that assumes zero displacement of the cable in a certain state, thus calculating the initial cable force. The zero-displacement method ensures that the cable has no deformation in the initial state by setting reasonable initial conditions, thereby ensuring that the structural deformation during construction meets design requirements. For example, the iterative method gradually approximates the actual construction state by repeatedly adjusting the initial cable force of the cable. The iterative method usually requires setting an initial value and then gradually reducing the calculation error through iteration until the predetermined accuracy requirements are met. Improved iterative algorithms optimize the traditional iterative method, usually introducing strategies to accelerate convergence or techniques to reduce the amount of computation. For example, improved iterative algorithms can improve the efficiency and accuracy of calculations, making engineering applications more convenient. The "quiet and still" method uses the standard that the tensioning of the new arch rib segment's tie cable should not affect the alignment of the previous segment. During calculation, the vertical displacement of the previous segment's front end point can be set as zero as the target to calculate the tie cable force. This method can better meet the alignment requirements during construction, but manual iteration is required when calculating the tie cable force. When optimizing towards an ideal bare arch, certain experience in cable adjustment is needed. For example, the influence matrix method is a calculation method based on matrix theory. By establishing an influence matrix of the structure under various construction states, it analyzes the impact of each tie cable force on structural deformation, thereby determining the optimal tie cable force distribution. The influence matrix method can systematically consider various construction conditions and constraints, making it a relatively accurate and comprehensive analytical tool. For example, optimization methods use optimization algorithms to find the optimal solution among many possible solutions. This is usually achieved by setting an objective function and constraints, and employing numerical optimization techniques such as genetic algorithms and particle swarm optimization to solve for the optimal distribution of tie cable forces. Optimization methods can fully utilize the powerful computing capabilities of computers to solve complex engineering problems. However, existing methods for calculating the initial tension of the cable-stayed anchorage in arch bridges cannot fully consider the stress state during the entire construction process of the arch rib and after the bridge is completed. Summary of the Invention

[0004] This invention provides a multi-objective data processing method for the cable force of cable-stayed arch bridges based on an influence matrix, aiming to solve at least one of the technical problems existing in the prior art.

[0005] The technical solution of this invention relates to a multi-objective data processing method for the cable force of cable-stayed arch bridges based on an influence matrix. The method according to this invention includes the following steps:

[0006] S100. Establish a finite element model and modify the model according to the construction sequence;

[0007] S200. Extract multiple relevant influence matrices, wherein the influence matrices include displacement influence matrix, cable force influence matrix and internal force influence matrix;

[0008] S300. Based on the superposition principle, the influence matrix relationship is obtained according to the multiple relevant influence matrices, and then the initial tension vector of each cable is obtained.

[0009] S400. Based on optimization theory, determine the corresponding multiple constraints, establish a multi-objective optimization model for the initial cable force under variable load, and calculate the cable force parameters of the back cable of the cable-stayed arch bridge.

[0010] Furthermore, in step S100, the largest cantilever element is activated once during the construction phase, and the element load and corresponding constraints are activated one by one according to the construction sequence.

[0011] Furthermore, in step S200, let the number of back straps be n, and the unknown force of the straps be T = (T1, T2, T3, ... T n ) T The number of control nodes for the arch ribs and towers is m;

[0012] The influence matrix of the tensioning unit cable force on the displacement of the control node during construction is expressed as follows:

[0013]

[0014] In the formula, element δ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the effect of the unit tension force of the j-th cable on the displacement of the i-th control node during construction.

[0015] The influence matrix of the tensioning unit cable force on the cable force of each cable during construction is expressed as follows:

[0016]

[0017] In the formula, element f i,j (i = 1, 2, ..., n; j = 1, 2, ..., n) represents the influence of the unit tension force of the j-th cable on the cable force of the i-th cable during construction.

[0018] The displacement influence matrix of the control node caused by the unit cable force during cable removal is expressed as follows:

[0019]

[0020] In the formula, the element ε i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the effect of the unit tension force of the j-th cable on the displacement of the i-th control node after the arch rib is closed;

[0021] The displacement influence matrix of the control node during the cable removal process is represented as follows:

[0022]

[0023] In the formula, element λ i,j (i = 1, 2, ..., m; j = 1, 2, ..., k) represents the influence of the self-weight of the j-th cable on the displacement of the i-th control node during construction;

[0024] The influence matrix of the tension unit cable force on the cable force during construction is expressed as follows:

[0025]

[0026] In the formula, element φ i,j (i = 1, 2, ..., k; j = 1, 2, ..., n) represents the displacement effect of the j-th fixed load on the i-th control node during construction;

[0027] The influence matrix of the tensioning unit cable force on the internal forces at the arch foot during construction is expressed as follows:

[0028]

[0029] In the formula, the element σ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the effect of the unit tension force of the j-th cable on the displacement of the i-th control node during construction.

[0030] The influence matrix of the unit cable force during cable removal on the internal forces at the arch foot is expressed as follows:

[0031]

[0032] In the formula, element ω i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the effect of the unit tension force of the j-th cable on the displacement of the i-th control node after the arch rib is closed;

[0033] The influence matrix of the removal of wind cables during the cable removal process on the internal forces at the arch foot is represented as follows:

[0034]

[0035] In the formula, element τ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the influence of the self-weight of the j-th cable on the displacement of the i-th control node during construction.

[0036] Furthermore, in step S300, the influence matrix relationship is expressed as follows:

[0037] D=A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0

[0038] N=F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3

[0039] In the formula, D is the target displacement vector; N is the target internal force vector; T is the unknown quantity of the cable force; A is the influence matrix of the tension unit cable force on the vertical displacement of the main truss; B is the influence matrix of the tension unit cable force on the cable force of the cable; C is the influence matrix of the removal of the cable on the vertical displacement of the main arch rib; F is the influence matrix of the tension unit cable force on the internal force of the arch foot; G is the influence matrix of the removal of the wind cable on the displacement of the arch rib; H is the influence matrix of the tension unit cable force on the wind cable; I is the influence matrix of the removal of the cable on the internal force of the arch foot; J is the influence matrix of the removal of the wind cable on the internal force of the arch foot; where b0 is the influence vector of the main arch rib self-weight on the vertical displacement of the arch rib; b1 is the influence vector of the main arch rib self-weight on the cable force; b3 is the influence vector of the cable removal self-weight on the internal force of the arch foot; b5 is the influence vector of the main arch rib self-weight on the internal force of the arch foot; b6 is the influence vector of the main arch rib self-weight on the wind cable force; b7 is the initial value vector of the wind cable force.

[0040] Furthermore, in step S300,

[0041] The initial tension vectors of each sling are:

[0042]

[0043] Furthermore, in step S400,

[0044] The difference between the actual displacement of each control node after closure and the displacement of the target alignment is used as the alignment inequality constraint condition, which is expressed as follows:

[0045] |A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0-b2|≤Δδ

[0046] In the formula, Δδ is the allowable deviation between the control node alignment in the bare arch state and the ideal bare arch;

[0047] The linear inequality constraint condition, which is the difference between the maximum axial tensile force and the minimum axial compressive force at the arch rib section of the lower chord arch foot during construction, is expressed as follows:

[0048] |F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3-b4|≤ΔN i

[0049] In the formula, ΔN i The allowable deviation between the control node alignment in the bare arch state and the ideal bare arch;

[0050] Among them, the magnitude of the axial force of the arch foot rib in the maximum cantilever state is used as a nonlinear inequality constraint condition, which is expressed as follows:

[0051] N Z <ΔN1

[0052] In the formula, N Z ΔN represents the internal force at the arch foot under maximum cantilever condition; ΔN is the design value of the internal force at the arch foot under maximum cantilever condition.

[0053] The boundary constraint condition that minimizes the maximum breaking force of the back cable is expressed as follows:

[0054] T L <T<T B

[0055] In the formula, T B T is the lower limit of the cable force. L This represents the upper limit of cable force (maximum breaking force) and the allowable value of cable force.

[0056] Furthermore, in step S400, the sum of the squares of the differences between the actual displacement and the target displacement of the arch rib control points at each hoisting construction stage is used as the optimization objective function, which is expressed as follows:

[0057] min(sum(0.5·(u1(T i )-u2(T i ))-u l ) 2 )

[0058] In the formula, u1(T) i ) represents the actual displacement vector of the control node after the arch rib segment is installed and the cable tensioning is applied; u2(T) i The actual displacement vector of the control node at the cantilever end after installing the arch cross brace; u l The displacement vector of the bare arch during a single frame lowering at the control node.

[0059] Furthermore, in step S100, the load includes a constant load and a variable load, and the variable load includes cable tension and wind cable tension.

[0060] 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.

[0061] The technical solution of the present invention also relates to a multi-objective optimization system for the cable force of the cable-stayed bridge of an arch bridge based on an influence matrix. The system includes a computer device that contains the aforementioned computer-readable storage medium.

[0062] The beneficial effects of this invention are as follows:

[0063] The multi-objective optimization data processing method and its multi-objective optimization system for cable-stayed bridges proposed in this invention can effectively control the axial force and arch rib shape of the arch rib members during the construction of cable-stayed bridges, thereby achieving the optimal arch shape and stable stress state of the completed bridge arch ring.

[0064] The method of this invention uses the sum of squares of the differences between the arch rib shape during construction and the target shape as the optimization objective function, and uses the maximum axial tension of the lower chord arch foot arch rib section, the minimum axial compression of the upper chord, the magnitude of the cable force during construction, the axial force of the arch foot arch rib in the maximum cantilever state, and the deviation of the arch shape after cable loosening as constraints to establish an initial cable force multi-objective optimization model. Based on the actual engineering situation, the cable force of the cable that meets the boundary conditions can be quickly and accurately calculated.

[0065] The initial cable force optimized by the method of this invention can effectively control the uniformity of the arch rib alignment and the axial force distribution of the upper and lower chord arch rib sections at the arch foot during construction. This ensures that the arch rib alignment remains good after closure and cable release, and provides sufficient pressure reserve for the upper chord arch rib in the completed bridge state, offsetting the tensile forces generated by wind loads and vehicle loads on the arch rib during operation, thus ensuring the stability of the arch ring's stress state. The multi-objective optimization data processing method of this invention, utilizing finite element software and numerical analysis software, achieves automated and intelligent solution for cable force optimization, avoiding tedious trial calculations and improving the efficiency of cable force adjustment. It can effectively solve the multi-objective initial cable force optimization problem for cable-stayed arch bridges. Furthermore, this method can also effectively solve construction control problems for other types of large-span arch bridges where internal forces are the optimization objective. It is applicable to the construction control of general arch bridges, ensuring structural safety and stability throughout the entire construction process. Attached Figure Description

[0066] Figure 1 This is a flowchart of the cable force calculation method described in this invention.

[0067] Figure 2 This is a diagram showing the arch bridge fastening arrangement in an embodiment of the present invention.

[0068] Figure 3 This is a schematic diagram of the arch bridge structure and control nodes in an embodiment of the present invention.

[0069] Figure 4 This is a schematic diagram of the model modification of the present invention.

[0070] Figure 5 for Figure 2 The diagram shows the initial tension of the backstay cable during the construction of the arch bridge.

[0071] Figure 6 for Figure 2 The diagram shows the time history of the cable tensions of the left span of the arch bridge on the Wulong side, including the cable tensions of the sling and wind cable.

[0072] Figure 7 for Figure 2 The diagram shows the time history of the backstay force of the left span of the arch bridge on the Wulong side.

[0073] Figure 8 for Figure 2 The diagram shows the time history of the cable tensions of the left span of the arch bridge on both sides of the river.

[0074] Figure 9 for Figure 2 The diagram shows the time history of the backstay force of the arch bridge on the left side of the two banks of the river.

[0075] Figure 10 for Figure 2 The diagram shows the linear relationships of the arch ribs of the arch bridge.

[0076] Figure 11 for Figure 2 The time history curve of the tower deflection of the arch bridge shown is shown.

[0077] Figure 12 for Figure 2 The diagram shows the maximum cantilever state of the arch bridge and the axial force diagram of the arch foot truss members during the second phase of paving. Detailed Implementation

[0078] 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.

[0079] 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.

[0080] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used 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.

[0081] Reference Figures 1 to 12 In some embodiments, the multi-objective data processing method for the cable force of cable-stayed arch bridges based on the influence matrix according to the present invention includes at least the following steps:

[0082] S100. Establish a finite element model and modify the model according to the construction sequence;

[0083] S200. Extract multiple relevant influence matrices, including displacement influence matrix, cable force influence matrix and internal force influence matrix;

[0084] S300. Based on the superposition principle, the influence matrix relationship is obtained according to the multiple relevant influence matrices, and then the initial tension vector of each cable is obtained.

[0085] S400. Based on optimization theory, determine the corresponding multiple constraints, establish a multi-objective optimization model for the initial cable force under variable load, and calculate the cable force parameters of the back cable of the cable-stayed arch bridge.

[0086] This invention presents a multi-objective data processing method and optimization system for cable-stayed arch bridges based on an influence matrix, which considers the stress state throughout the entire arch rib construction process and after bridge completion. It should be noted that this invention can be applied to various arch bridges, including steel-concrete composite arch bridges, steel truss arch bridges, and reinforced concrete arch bridges. The method uses the sum of squares of the differences between the arch rib alignment during construction and the target alignment as the objective function, and uses the maximum axial tensile force at the lower chord arch foot section, the minimum axial compressive force at the upper chord, the cable force during construction, the axial force at the arch foot arch rib in the maximum cantilever state, and the deviation in arch alignment after cable release as constraints. An initial cable force multi-objective optimization model is established, which quickly and accurately calculates the cable force satisfying the boundary conditions based on actual engineering conditions.

[0087] In some embodiments, see Figures 2 to 4 The method of this invention determines the control nodes of the arch rib and the unknown load T according to the construction requirements. iThe number of control nodes is determined, and the deviation values ​​of the target alignment and the allowable values ​​of cable force are determined. A finite element model is established based on the geometric parameters, material parameters, boundary conditions and load conditions of the arch bridge. The construction stage structure group, boundary value and load group are determined according to the construction conditions to establish the construction stage model. The model is then corrected according to the construction sequence.

[0088] Specifically, for bridges constructed with cantilever structures, the elevation of newly constructed beam segments is influenced by existing beam segments. To accurately simulate the coupling effect between the cable-stayed systems and ensure the reliability of the extracted influence matrix, the construction stage model of this invention can activate the largest cantilever element at once. Element loads and corresponding constraints are not applied simultaneously, but are activated sequentially according to the construction order to ensure the tangential assembly relationship between the new and old arch rib elements. It should be noted that loads can be divided into two categories: dead loads and variable loads. Dead loads may include the structure's self-weight, while variable loads may include cable tension and wind cable tension, etc.

[0089] In some embodiments, the method of the present invention combines the principle of influence matrices to determine the number of unknown loads, and extracts multiple influence matrices corresponding to the unknown loads using finite element software. Specifically, let the number of backstay cables be n, and the unknown load (such as the unknown cable force) T = (T1, T2, T3, ... T n ) T The number of control nodes for the arch ribs and towers is m, and the number of wind turbine supports is k. The extracted multiple influence matrices include multiple displacement influence matrices, multiple cable force influence matrices, and multiple internal force influence matrices.

[0090] The influence matrix of the tensioning unit cable force on the displacement of the control node during construction is expressed as follows:

[0091]

[0092] In the formula, element δ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the displacement effect of the unit tension force of the j-th cable on the i-th control node during construction. For example, A is the matrix representing the influence of the unit tension force on the vertical displacement of the main truss.

[0093] The influence matrix of the tensioning unit cable force on the cable force of each cable during construction is expressed as follows:

[0094]

[0095] In the formula, element f i,j (i = 1, 2, ..., n; j = 1, 2, ..., n) represents the influence of the unit tension force of the j-th cable on the cable force of the i-th cable during construction. For example, B is the influence matrix of the unit tension force on the cable force of the tie cable.

[0096] The displacement influence matrix of the control node caused by the unit cable force during cable removal is expressed as follows:

[0097]

[0098] In the formula, the element ε i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the displacement effect of the unit tension force of the j-th cable on the i-th control node after the arch rib is closed. For example, C is the displacement effect matrix of the main arch rib on the vertical displacement of the main arch rib caused by the removal of the fastening cable.

[0099] The displacement influence matrix of the control node during the cable removal process is represented as follows:

[0100]

[0101] In the formula, element λ i,j (i = 1, 2, ..., m; j = 1, 2, ..., k) represents the displacement effect of the j-th cable's self-weight on the i-th control node during construction. For example, G is the displacement effect matrix of the arch rib caused by the removal of the wind cable.

[0102] The influence matrix of the tension unit cable force on the cable force during construction is expressed as follows:

[0103]

[0104] In the formula, element φ i,j (i = 1, 2, ..., k; j = 1, 2, ..., n) represents the displacement effect of the j-th fixed load on the i-th control node during construction.

[0105] The influence matrix of the tensioning unit cable force on the internal forces at the arch foot during construction is expressed as follows:

[0106]

[0107] In the formula, the element σ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the influence of the unit tension force of the j-th cable on the displacement of the i-th control node during construction. For example, F is the matrix representing the influence of the unit tension force on the internal forces at the arch foot.

[0108] The influence matrix of the unit cable force during cable removal on the internal forces at the arch foot is expressed as follows:

[0109]

[0110] In the formula, element ω i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the displacement effect of the unit tension force of the j-th cable on the i-th control node after the arch rib is closed. For example, I is the matrix of the influence of removing the fastening cable on the internal forces at the arch foot.

[0111] The influence matrix of the removal of wind cables during the cable removal process on the internal forces at the arch foot is represented as follows:

[0112]

[0113] In the formula, element τ i,j (i = 1, 2, ..., m; j = 1, 2, ..., n) represents the influence of the self-weight of the j-th cable on the displacement of the i-th control node during construction. For example, J is the matrix representing the influence of the removal of the wind cable on the internal forces at the arch foot.

[0114] In some embodiments, the method of the present invention is based on the superposition principle to obtain the influence matrix relationship (i.e., the cable force influence matrix equation), and then solves for the initial tension vector of each cable. Specifically, for the cable-stayed arch bridge construction, the construction stage is mainly divided into the cable installation stage and the cable removal stage. During the construction process, the loads that affect the structure are composed of several parts, including dead load, cable force, and wind-driven cable force. Therefore, according to the superposition principle, the influence matrix relationship can be expressed as follows:

[0115] D=A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0

[0116] N=F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3

[0117] In the formula, D is the target displacement vector; N is the target internal force vector; T is the unknown quantity of the cable tension; A is the influence matrix of the tension unit cable force on the vertical displacement of the main truss; B is the influence matrix of the tension unit cable force on the cable tension; C is the influence matrix of the removal of the cable tension on the vertical displacement of the main arch rib; F is the influence matrix of the tension unit cable force on the internal force of the arch foot; G is the influence matrix of the removal of the wind cable on the displacement of the arch rib; H is the influence matrix of the tension unit cable force on the wind cable; I is the influence matrix of the removal of the cable tension on the internal force of the arch foot; J is... The matrix represents the influence of the removal of the wind cable on the internal forces at the arch foot. Here, b0 is the vector representing the influence of the main arch rib's self-weight (such as high-strength bolts, gusset plates, etc.) on the vertical displacement of the arch rib; b1 is the vector representing the influence of the main arch rib's self-weight (such as high-strength bolts, gusset plates, etc.) on the cable force; b3 is the vector representing the influence of the cable's self-weight on the internal forces at the arch foot; b5 is the vector representing the influence of the main arch rib's self-weight (such as high-strength bolts, gusset plates, etc.) on the internal forces at the arch foot; b6 is the vector representing the influence of the main arch rib's self-weight (such as high-strength bolts, gusset plates, etc.) on the wind cable force; and b7 is the initial value vector of the wind cable force.

[0118] The initial tension vectors of each cable are then obtained as follows:

[0119]

[0120] In some embodiments, the method of the present invention establishes a mathematical model based on optimization theory to calculate the optimal cable force.

[0121] The actual displacement of each control node after closure and cable release, and the displacement difference between the target alignment, are used as the alignment inequality constraint to control the arch rib alignment after closure and cable release. This is expressed as follows:

[0122] |A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0-b2|≤Δδ

[0123] In the formula, Δδ is the allowable deviation between the control node alignment in the bare arch state and the ideal bare arch;

[0124] Among them, the difference between the maximum axial tensile force and the minimum axial compressive force at the arch foot section of the lower chord during construction is used as a linear inequality constraint condition to control the internal forces at the arch foot during construction, as expressed below:

[0125] |F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3-b4|≤ΔN i

[0126] In the formula, ΔN i The allowable deviation between the control node alignment in the bare arch state and the ideal bare arch;

[0127] Among them, the magnitude of the axial force of the arch rib at the arch foot in the maximum cantilever state is used as a nonlinear inequality constraint condition to control the state of the arch rib after the bridge is completed, which is expressed as follows:

[0128] N Z <ΔN1

[0129] In the formula, N Z ΔN represents the internal force at the arch foot under maximum cantilever condition; ΔN is the design value of the internal force at the arch foot under maximum cantilever condition.

[0130] The back strap force value has a safety factor, and the maximum breaking force of the back strap force is used as the boundary constraint condition for minimizing the boundary force, which is expressed as follows:

[0131] T L <T<T B

[0132] In the formula, T B T is the lower limit of the cable force. L The upper limit of cable force (maximum breaking force) and the allowable value of cable force.

[0133] To ensure the stability of the arch rib control node alignment during construction, the sum of the squares of the differences between the actual and target displacements of the arch rib control points at each hoisting stage is used as the optimization objective function, as follows:

[0134] min(sum(0.5·(u1(T i)-u2(T i ))-u l ) 2 )

[0135] In the formula, u1(T) i ) represents the actual displacement vector of the control node after the arch rib segment is installed and the cable tensioning is applied; u2(T) i The actual displacement vector of the control node at the cantilever end after installing the arch cross brace; u l The displacement vector of the bare arch during a single frame lowering at the control node.

[0136] This invention's method extracts the influence matrix using finite element analysis software, substitutes it into the solved initial tension vectors of each cable, and then calculates relevant parameters of the cable force values ​​for the back-cables of a cable-stayed arch bridge based on determined constraints and a multi-objective optimization model of the initial cable force under variable loads. These parameters include the cable force of the arch rib segments, the cable force of the wind cables, the axial force, and the linearity of the arch formation calculation. This invention's method uses operations research theory to establish a mathematical model of functional relationships to calculate the optimal cable force. By considering the influence of each variable and fixed load on the arch rib alignment and the mutual influence between variable and fixed loads, it obtains the corresponding influence matrix. Based on actual engineering conditions, it quickly and accurately obtains the optimal back-cable force values ​​that satisfy the boundary conditions.

[0137] This section uses specific embodiments to verify the multi-objective data processing method for cable force of cable-stayed arch bridges based on influence matrix and its multi-objective optimization system of the present invention.

[0138] For example, see Figure 2 As shown, the main span of a certain Daxi River super-large bridge is a 580m span upper-bearing steel truss arch bridge with a rise of 116m and a rise-to-span ratio of 1 / 5. The centerline of the arch rib is a catenary, and the arch axis coefficient is 2.0. See the elevation layout of the Daxi River super-large bridge for details. Figure 2As shown. The main bridge deck structure adopts a three-span configuration, arranged as [(66.75+53.4+3×40.05)+(40.05+50+40.05)+(3×40.05+53.4+66.75)]m continuous steel-concrete composite beams. The steel-concrete composite beam structure system mainly consists of three main structural units: steel main beams, steel crossbeams (including intermediate crossbeams and reinforcing crossbeams at supports), and bridge deck panels. The main chord members adopt box-shaped welded sections with the same inner width and inner height. To accommodate different stresses in different sections and save steel, the main chord members use two widths and heights. The cross-section of the web members varies depending on their location, employing either box-shaped or I-shaped sections. The inner height of the web members' web plates is the same as that of the corresponding chord members, typically 1800 or 2300 mm. The inner width of the top plate of box-shaped web members is 1000 mm or 1200 mm, while the width of the top plate of I-shaped web members is 700 mm, 760 mm, 800 mm, or 900 mm. The thickness of the web member flanges and web plates ranges from 16 to 42 mm. The main truss web members are bolted to the upper and lower chords via integral node plates. To increase the integrity of the main arch rib, reduce the difficulty of assembling members on site, and enhance the structure's corrosion resistance, this embodiment uses integral nodes. The main truss welded integral nodes are constructed by welding the members and node plates together in the factory. The chord members of the arch rib of this bridge are connected by welding and high-strength bolts, while the web members of the arch rib are connected to the integral node plates of the upper and lower chords via high-strength bolts. Except for the arch crown bracing, the upper and lower chord bracing of the arch ribs all adopt a continuous "K"-shaped bracing arrangement. The bracing rods use welded box-section sections, while the diagonal braces use welded box-section and I-shaped sections. The arch-supported column piers adopt a steel frame structure, with the columns being uniform cross-section steel boxes containing longitudinal stiffening ribs and transverse diaphragms. The transverse width of the column steel box is the same as the width of the arch rib.

[0139] A finite element model is constructed based on the geometric parameters, material parameters, boundary conditions, and load conditions of the arch bridge. A construction stage model is established by determining the structural groups, boundary values, and load groups according to the engineering construction conditions. The number of unknown loads is determined using the influence matrix principle, and multiple influence matrices corresponding to the unknown loads are derived. In this embodiment, finite element software, such as Midas / Civil structural analysis software, is used for calculation, and mathematical engineering optimization software, such as MATLAB, is used for the solution.

[0140] The main purpose of the tie cables is to balance the self-weight of the arch rib during cantilever assembly, while the anchor cables are used to balance the force exerted by the tie cables on the anchor tower, ensuring the safety of the anchor tower during construction. An ideal set of tie and anchor cable forces should meet the following conditions: First, during tangential assembly, after the arch rib is closed and the tie and anchor cables are removed, the error between the bare arch shape and the target bare arch shape should be within the allowable range of the specifications; second, ensure the safety of the arch rib and anchor tower under stress during construction; third, during the cantilever assembly of the arch rib, the post-tensioned tie cables should not have an excessive impact on the displacement of the installed stage; fourth, during construction, the tensile force borne by the lower chord of the arch rib should not be excessive; finally, after the cables are removed, the stress at the arch foot should be basically consistent with the design requirements. Based on the above principles, the number of control nodes, variable loads, and fixed loads (i.e., dead loads) were determined. After considering the required values ​​for parameters such as the arch rib alignment deviation, arch foot stress allowable value, and cable force allowable value, the influence matrix data and parameter values ​​were input into the optimization model constructed by programming software to solve for the cable force. Through iterative computer calculations, the optimization results are as follows: Figures 5-12 .

[0141] Among them, the initial tension of the sling is as follows Figure 5 As shown in the figure, the anchor cable tension is relatively uniform without abrupt changes, indicating that the anchor cable tension is reasonable. Due to space limitations, the time history diagram of the cable tension on the left side of the main bridge is as follows: Figures 6 to 9 During construction, the changes in cable tension were relatively gradual, without significant abrupt changes. Since this bridge is designed primarily for internal force control, meaning the tension cable tension was strictly controlled during arch erection, the calculated arch alignment is based on the initial tension calculations. See the following for the alignment relationships: Figure 10 As shown. Based on the determined anchor cable tension, calculations are performed during the construction phase to obtain the theoretical deflection of the top of the anchor towers on both banks. Figure 11 As shown. From Figure 11 As can be seen from the data, during construction, the maximum tower top deviation was 9.4 cm, which is less than H / 1000 = 14.5 cm. Therefore, the tower top deviation meets the specifications. The axial force calculation results for the arch foot truss members on both banks under the maximum cantilever condition and during the second-phase paving stage are as follows: Figure 12 As shown. From Figure 12 It can be seen that the axial forces of the arch foot truss members in the maximum cantilever state are basically negative, and the axial forces of the arch foot truss members in the second-phase paving stage are all negative. The internal force distribution of the structure tends to be consistent with the ideal internal force state in the design. From the perspective of theoretical calculation, the construction safety of the steel tie rod of the lower chord of the arch is guaranteed, and the compressive stress reserve of the upper chord arch foot after the bridge is completed meets the design requirements.

[0142] Using the sum of squares of the differences between the arch rib alignment during construction and the target alignment as the objective function, and with constraints including the maximum axial tension at the lower chord arch rib section, the minimum axial compression at the upper chord, the magnitude of cable forces during construction, the axial force at the arch rib at the arch foot in the maximum cantilever state, and the deviation in arch alignment after cable release, a multi-objective optimization model for initial cable forces was established. The optimized initial cable forces effectively control the uniformity of the arch rib alignment and the axial force distribution at the arch foot section during construction, ensuring a good arch rib alignment after cable release and providing sufficient pressure reserve for the upper chord arch rib in the completed bridge state. This offsets the tensile forces generated by wind loads and vehicle loads on the arch rib during operation, ensuring the stability of the arch ring's stress state. The automated and intelligent solution of cable force optimization is achieved using finite element method (FEM) and numerical analysis software, avoiding tedious trial calculations and improving the efficiency of cable force adjustment. This effectively solves the multi-objective initial cable force optimization problem for cable-stayed arch bridges. It also effectively solves construction control problems for other types of large-span arch bridges where internal forces are the optimization objective, and is applicable to the construction control of general arch bridges.

[0143] 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).

[0144] 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.

[0145] 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.

[0146] 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.

[0147] 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 multi-objective data processing method for the cable force of cable-stayed arch bridges based on the influence matrix, characterized in that, The method includes the following steps: S100. Establish a finite element model and modify the model according to the construction sequence; S200. Extract multiple relevant influence matrices, wherein the influence matrices include displacement influence matrix, cable force influence matrix and internal force influence matrix; S300. Based on the superposition principle, the influence matrix relationship is obtained according to the multiple relevant influence matrices, and then the initial tension vector of each cable is obtained. S400. Based on optimization theory, determine the corresponding multiple constraints, establish a multi-objective optimization model for the initial cable force of variable load, and calculate the cable force parameters of the back cable of the cable-stayed arch bridge. In step S300, the influence matrix relationship is expressed as follows: D=A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0 N=F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3 In the formula, D is the target displacement vector; N is the target internal force vector; T is the unknown quantity of the cable force; A is the influence matrix of the tension unit cable force on the vertical displacement of the main truss; B is the influence matrix of the tension unit cable force on the cable force of the cable; C is the influence matrix of the removal of the cable on the vertical displacement of the main arch rib; F is the influence matrix of the tension unit cable force on the internal force of the arch foot; G is the influence matrix of the removal of the wind cable on the displacement of the arch rib; H is the influence matrix of the tension unit cable force on the wind cable; I is the influence matrix of the removal of the cable on the internal force of the arch foot; J is the influence matrix of the removal of the wind cable on the internal force of the arch foot; where b0 is the influence vector of the main arch rib self-weight on the vertical displacement of the arch rib; b1 is the influence vector of the main arch rib self-weight on the cable force; b3 is the influence vector of the cable removal self-weight on the internal force of the arch foot; b5 is the influence vector of the main arch rib self-weight on the internal force of the arch foot; b6 is the influence vector of the main arch rib self-weight on the wind cable force; b7 is the initial value vector of the wind cable force. In step S300, the initial tension vector of each sling is: In step S400, the difference between the actual displacement of each control node after closure and the displacement of the target alignment is used as the alignment inequality constraint condition, which is expressed as follows: |A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0-b2|≤Δδ In the formula, Δδ is the allowable deviation between the control node alignment in the bare arch state and the ideal bare arch; The linear inequality constraint condition, which is the difference between the maximum axial tensile force and the minimum axial compressive force at the arch rib section of the lower chord arch foot during construction, is expressed as follows: |F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3-b4|≤ΔN i In the formula, ΔN i The allowable deviation between the control node alignment in the bare arch state and the ideal bare arch; Among them, the magnitude of the axial force of the arch foot rib in the maximum cantilever state is used as a nonlinear inequality constraint condition, which is expressed as follows: N Z <ΔN1 In the formula, N Z ΔN represents the internal force at the arch foot under maximum cantilever condition; ΔN is the design value of the internal force at the arch foot under maximum cantilever condition. The boundary constraint condition that minimizes the maximum breaking force of the back cable is expressed as follows: T L <T<T B In the formula, T B T is the lower limit of the cable force. L This represents the upper limit of the cable tension.

2. The method according to claim 1, characterized in that, In step S100, the largest cantilever element is activated once during the construction phase, and the element load and corresponding constraints are activated one by one according to the construction sequence.

3. The method according to claim 2, characterized in that, In step S200, let the number of back straps be n, and the unknown force of the straps be T = (T1, T2, T3, ... T n ) T The number of control nodes for the arch ribs and towers is m; The influence matrix of the tensioning unit cable force on the displacement of the control node during construction is expressed as follows: In the formula, element δ i,j Let represent the effect of the unit tension force of the j-th cable on the displacement of the i-th control node during construction, where i = 1, 2, ..., m; j = 1, 2, ..., n; The influence matrix of the tensioning unit cable force on the cable force of each cable during construction is expressed as follows: In the formula, element f i,j Let i = 1, 2, ..., n; j = 1, 2, ..., n. The displacement influence matrix of the control node caused by the unit cable force during cable removal is expressed as follows: In the formula, the element ε i,j The effect of the unit tension force of the j-th cable on the displacement of the i-th control node after the arch rib is closed; i = 1, 2, ..., m; j = 1, 2, ..., n; The displacement influence matrix of the control node during the cable removal process is represented as follows: In the formula, element λ i,j Let represent the effect of the self-weight of the j-th cable on the displacement of the i-th control node during construction; i = 1, 2, ..., m; j = 1, 2, ..., k; The influence matrix of the tension unit cable force on the cable force during construction is expressed as follows: In the formula, element φ i,j Let represent the displacement effect of the j-th fixed load on the i-th control node during construction; i = 1, 2, ..., k; j = 1, 2, ..., n; The influence matrix of the tensioning unit cable force on the internal forces at the arch foot during construction is expressed as follows: In the formula, the element σ i,j The effect of the unit tension force of the j-th cable on the displacement of the i-th control node during construction; i = 1, 2, ..., m; j = 1, 2, ..., n; The influence matrix of the unit cable force during cable removal on the internal forces at the arch foot is expressed as follows: In the formula, element ω i,j The effect of the unit tension force of the j-th cable on the displacement of the i-th control node after the arch rib is closed; i = 1, 2, ..., m; j = 1, 2, ..., n The influence matrix of the removal of wind cables during the cable removal process on the internal forces at the arch foot is represented as follows: In the formula, element τ i,j Let represent the effect of the self-weight of the j-th cable on the displacement of the i-th control node during construction; i = 1, 2, ..., m; j = 1, 2, ..., n.

4. The method according to claim 3, characterized in that, In step S400 The objective function is the sum of the squares of the differences between the actual displacement and the target displacement of the arch rib control points at each hoisting stage, as expressed below: min(sum(0.5·(u1(T i )-u2(T i ))-u l ) 2 ) In the formula, u1(T) i ) represents the actual displacement vector of the control node after the arch rib segment is installed and the cable tensioning is applied; u2(T) i The actual displacement vector of the control node at the cantilever end after installing the arch cross brace; u l The displacement vector of the bare arch during a single frame lowering at the control node.

5. The method according to claim 2, characterized in that, In step S100, the load includes a constant load and a variable load, and the variable load includes cable tension and wind cable tension.

6. A computer-readable storage medium having program instructions stored thereon, which, when executed by a processor, perform the method as described in any one of claims 1 to 5.

7. Multi-objective optimization of cable force in cable-stayed arch bridges based on influence matrix The system is characterized in that, include: A computer device, the computer device comprising the computer-readable storage medium according to claim 6.

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