Arch bridge cable-stayed buckle hanging buckle cable force multi-target data processing method based on influence matrix

Abstract

The invention relates to an influence matrix-based arch bridge cable-stayed buckle hanging buckle cable force multi-target data processing method and a multi-target optimization system thereof. The method comprises the following steps: establishing a finite element model, and correcting the model according to a construction sequence; extracting a plurality of correlation influence matrixes, wherein the influence matrixes comprise a displacement influence matrix, a cable force influence matrix and an internal force influence matrix; on the basis of a superposition principle, according to the obtained multiple correlation influence matrixes, obtaining an influence matrix relation, and then obtaining initial tension vectors of the buckle cables; and determining a plurality of corresponding constraint conditions based on an optimization theory, establishing an initial cable force multi-objective optimization model of a variable load, and calculating cable force value parameters of a buckle back cable of the cable-stayed buckle-hanging construction arch bridge. According to the method, the axial force of the arch rib rod piece and the arch rib line shape in the cable-stayed buckling construction process of the large-span arch bridge can be effectively controlled, and the optimal arch line shape and the stable stress state of the arch ring of the bridge are achieved.

Description

Technical Field

[0001] The invention relates to an influence matrix-based arch bridge inclined-stayed buckle cable force multi-objective data processing method, belonging to the technical field of bridge construction. Background Art

[0002] The terrain in southwest my country is complex, earthquakes are frequent, and canyon winds are turbulent. Arch bridges have developed rapidly and are widely used due to their advantages of earthquake resistance, wind resistance, and strong bearing capacity. Since this area is mostly high canyon and deep valley, construction conditions and construction space are limited, and the inclined cable hanging method is often used for arch rib construction. Because the cable force and arch rib displacement and internal force will affect each other during the segment assembly process, the determination of the initial tension of the cable is crucial to the overall stability and linear control of the arch rib.

[0003] At present, the main methods for calculating the cable force of the cable in the construction process of the arch bridge cable-stayed buckle hanging include zero displacement method, iteration method, improved iteration algorithm, static static, influence matrix method and optimization method. For example, the zero displacement method is a classic calculation method. It assumes that the displacement of the cable is zero in a certain state, so as to calculate the initial cable force of the cable. The zero displacement method sets reasonable initial conditions so that the cable has no deformation in the initial state, thereby ensuring that the structural deformation during the construction process meets the design requirements. For example, the iteration method repeatedly adjusts the initial cable force of the cable so that the calculation results gradually approach the actual construction state. The iteration method usually needs to set an initial value, and then reduce the calculation error through step-by-step iteration until the predetermined accuracy requirements are met. The improved iteration algorithm is optimized on the basis of the traditional iteration method, usually introducing strategies to accelerate convergence or technologies to reduce the amount of calculation. For example, the improved iteration algorithm can improve the efficiency and accuracy of the calculation, making engineering applications more convenient. The "quiet and motionless" method takes the tensioning of the cable of the new segment of the arch rib as the standard without affecting the linear shape of the previous segment; when calculating, the vertical displacement of the front end point of the previous segment can be used as the target to calculate the cable force, which can better meet the linear shape requirements of the construction process, but manual iteration is required when calculating the cable force, and when optimizing to the ideal bare arch, certain cable adjustment experience is required. For example, the influence matrix method is a calculation method based on matrix theory. By establishing the influence matrix of the structure under various construction conditions, the influence of each cable force on the structural deformation is analyzed to determine the optimal cable force distribution. The influence matrix method can systematically consider various construction conditions and constraints, and is a more accurate and comprehensive analysis method. For example, the optimization method uses the optimization algorithm to find the optimal solution among many possible solutions. It usually sets the objective function and constraints and uses numerical optimization techniques, such as genetic algorithms and particle swarm algorithms, to solve the optimal distribution of cable forces. The optimization method can make full use of the powerful computing power of computers to solve complex engineering problems. However, the existing calculation method of the initial tension of the arch bridge cable cannot fully consider the entire process of arch rib construction and the stress state after the bridge is completed. Summary of the invention

[0004] The present invention provides an arch bridge cable-stayed buckle hook cable force multi-objective data processing method 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 the present invention relates to a multi-objective data processing method for arch bridge cable-stayed buckle cable force based on an influence matrix. The method according to the present invention comprises the following steps:

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

[0007] S200, extracting a plurality of relevant influence matrices, wherein the influence matrices include a displacement influence matrix, a cable force influence matrix, and an internal force influence matrix;

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

[0009] S400. Based on the optimization theory, the corresponding multiple constraint conditions are determined, a multi-objective optimization model of the initial cable force with variable load is established, and the cable force value parameters of the back cable of the cable-stayed arch bridge are calculated.

[0010] Furthermore, in step S100, the model activates the largest cantilever unit once during the construction phase, and the unit loads and corresponding constraints are activated one by one according to the construction sequence.

[0011] Furthermore, in step S200, the number of back-fastening cables is assumed to be n, and the unknown cable force T is T = (T1, T2, T3, ... T n ) T , the number of control nodes of arch ribs and towers is m;

[0012] Among them, the influence matrix of the tension unit cable force on the displacement of the control node during the construction process is expressed as:

[0013]

[0014] In the formula, the element δ i,j (i=1,2,…,m;j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the displacement of the ith control node during the construction process;

[0015] Among them, the influence matrix of the tension unit cable force on the cable force of each cable during the construction process is expressed as:

[0016]

[0017] In the formula, the element f i,j(i=1,2,…,n;j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the force of the ith cable during the construction process;

[0018] Among them, the displacement influence matrix of the control node caused by the removal of the unit cable force during the cable removal process is expressed as:

[0019]

[0020] In the formula, the element ε i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the ith control node after the arch rib is closed;

[0021] Among them, the displacement influence matrix of the control node caused by removing the wind cable during the cable removal process is expressed as:

[0022]

[0023] In the formula, the element λ i,j (i=1,2,…,m;j=1,2,…,k) is the influence of the deadweight of the jth cable on the displacement of the ith control node during the construction process;

[0024] Among them, the influence matrix of the tension unit cable force on the wind cable during the construction process is expressed as:

[0025]

[0026] In the formula, the element φ i,j (i=1,2,…,k;j=1,2,…,n) is the displacement effect of the jth fixed load on the ith control node during the construction process;

[0027] Among them, the influence matrix of the tension unit cable force on the internal force of the arch foot during construction is expressed as:

[0028]

[0029] In the formula, the element σ i,j (i=1,2,…,m;j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the displacement of the ith control node during the construction process;

[0030] Among them, the influence matrix of the unit cable force on the internal force of the arch foot during the cable removal process is expressed as:

[0031]

[0032] In the formula, the element ω i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the ith control node after the arch rib is closed;

[0033] Among them, the internal force influence matrix of the removal of wind cables on the arch foot during the cable removal process is expressed as:

[0034]

[0035] In the formula, the element τ i,j (i=1,2,…,m;j=1,2,…,n) is the influence of the deadweight of the jth cable on the displacement of the i-th control node during the construction process.

[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 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; 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 force; 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; among them, 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 removal of the cable 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] Further, in step S300,

[0041] The initial tension vector of each cable is:

[0042]

[0043] Further, in step S400,

[0044] Among them, the difference between the actual displacement of each control node and the displacement of the target line shape after the closure is completed is taken as the linear inequality constraint condition, which is expressed as follows:

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

[0046] Where Δδ is the allowable deviation between the control node line shape in the bare arch state and the ideal bare arch;

[0047] Among them, the internal force difference of the maximum axial tension of the arch foot and the minimum axial pressure of the arch rib section of the lower chord during the construction period is taken as the linear inequality constraint condition, which is expressed as follows:

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

[0049] Where, ΔN i is the allowable deviation between the linear shape of the control node in the bare arch state and the ideal bare arch;

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

[0051] N Z <ΔN1

[0052] Where N Z is the internal force of the arch foot in the maximum cantilever state; ΔN is the design value of the internal force of the arch foot in the maximum cantilever state;

[0053] Among them, the maximum breaking force of the buckle back cable is taken as the minimization boundary constraint condition, which is expressed as follows:

[0054] T L <T<T B

[0055] Where, T B is the lower limit of the cable force, T L It is the upper limit of cable force (maximum breaking force) and the allowable value of cable force.

[0056] Further, in step S400, the square sum of the difference between the actual displacement and the target displacement of the arch rib control point in each lifting 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 ) is the actual displacement vector of the control node after the arch rib segment is installed and the cable is tensioned; u2(T i ) Actual displacement vector of the cantilever end control node after installing the arch ring cross brace; u l It is the displacement vector of the bare arch when the control node is dropped once.

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

[0060] The technical solution of the present invention also relates to a computer-readable storage medium on which program instructions are stored, and the above-mentioned method is implemented when the program instructions are executed by a processor.

[0061] The technical solution of the present invention also relates to a multi-objective optimization system for the cable forces of arch bridge cable-stayed buckles based on an influence matrix, wherein the system comprises a computer device which contains the above-mentioned computer-readable storage medium.

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

[0063] The multi-objective optimization data processing method and multi-objective optimization system of the cable-stayed buckle and cable force of a large-span arch bridge proposed in the present invention can effectively control the axial force of the arch rib rods and the arch rib line shape during the construction process of the cable-stayed buckle and cable force of the large-span arch bridge, so as to achieve the optimal arch line shape and the stable stress state of the arch ring of the completed bridge.

[0064] The method of the present invention takes the sum of squares of the differences between the arch rib linear shape during the construction period and the target linear shape as the optimization objective function, takes the maximum axial tension of the arch rib section of the lower chord arch foot, the minimum axial pressure of the upper chord during the construction period, the cable force size during the construction process, the axial force of the arch rib at the arch foot in the maximum cantilever state and the deviation of the arch linear shape after the cables are released as constraints, and establishes a multi-objective optimization model for the initial cable force. According to the actual situation of the project, the cable tension that meets the boundary conditions is quickly and accurately calculated.

[0065] The initial cable force optimized by the method of the present invention can effectively control the uniformity of the arch rib linear shape and the axial force distribution of the upper and lower chord arch rib sections at the arch foot position during the construction process, so as to achieve good arch rib linear shape after the joint is closed and the cables are released, and provide sufficient pressure reserve for the upper chord arch rib in the completed bridge state, offset the tension on the arch rib caused by wind load and vehicle load during the operation period, and ensure the stability of the arch ring stress state. The multi-objective optimization data processing method of the present invention realizes the automation and intelligent solution of cable force optimization with the help of finite element software and numerical analysis software, avoids the tedious trial calculation process, improves the efficiency of cable force adjustment, and can effectively solve the multi-objective initial cable force optimization problem of cable-stayed buckle-hung arch bridges. At the same time, the method of the present invention can also effectively solve the construction control problems of other types of large-span arch bridges with internal force as the optimization target, is suitable for the construction control of general arch bridges, and ensures the structural safety and stability during the entire construction process. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flow chart of the cable force calculation claimed in the present invention.

[0067] Figure 2 It is a diagram of the arch bridge buckle hanging arrangement in an embodiment of the present invention.

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

[0069] Figure 4 It is a schematic diagram of model correction of the present invention.

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

[0071] Figure 6 for Figure 2 The diagram shows the time history of the tension of the left cable and wind cable of the Wulong bank of the arch bridge.

[0072] Figure 7 for Figure 2 The diagram shows the stress history of the left back cable of the Wulong bank of the arch bridge.

[0073] Figure 8 for Figure 2 The diagram shows the time history of the tension of the left-side cables and wind cables on both river banks of the arch bridge.

[0074] Fig. 9 for Figure 2 The diagram shows the time history of the back cable stress on the left side of the arch bridge on both river banks.

[0075] Fig.10 for Figure 2 The linear relationship diagram of the arch ribs of the arch bridge is shown.

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

[0077] Fig.12 for Figure 2 The maximum cantilever state of the arch bridge and the axial force diagram of the arch foot truss members in the second phase paving stage are shown. DETAILED DESCRIPTION

[0078] The concept, specific structure and technical effects of the present invention will be clearly and completely described below in combination with the embodiments and drawings to fully understand the purpose, scheme and effect of the present invention.

[0079] It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to another feature, or it may be indirectly fixed or connected to another feature. The singular forms "a", "said" and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art. The terms used in this specification are intended only to describe specific embodiments and are not intended to limit the invention. The term "and / or" used herein includes any combination of one or more of the related listed items.

[0080] It should be understood that, although the term first, second, third etc. may be adopted to describe various elements in the present disclosure, these elements should not be limited to these terms. These terms are only used to distinguish the same type of elements from each other. For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element. The use of any and all examples or exemplary language ("for example", "such as" etc.) provided herein is only intended to better illustrate embodiments of the present invention, and unless otherwise required, the scope of the present invention will not be limited.

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

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

[0083] S200, extracting a plurality of related influence matrices, wherein the influence matrix includes a displacement influence matrix, a cable force influence matrix and an internal force influence matrix;

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

[0085] S400. Based on the optimization theory, the corresponding multiple constraint conditions are determined, a multi-objective optimization model of the initial cable force with variable load is established, and the cable force value parameters of the back cable of the cable-stayed arch bridge are calculated.

[0086] The multi-objective data processing method of the arch bridge cable-stayed buckle and hanging buckle cable force based on the influence matrix of the present invention and its multi-objective optimization system can consider the whole process of arch rib construction and the stress state after the bridge is completed. It should be noted that the present invention can be applied to multiple arch bridges such as steel tube concrete arch bridges, steel truss arches and rigid skeleton concrete arch bridges. The method of the present invention takes the sum of the squares of the difference between the arch rib linear shape and the target linear shape during the construction period as the optimization objective function, and takes the maximum axial tension of the arch foot and arch rib section of the lower chord during the construction period, the minimum axial pressure of the upper chord, the size of the cable force during the construction process, the axial force of the arch foot and arch rib in the maximum cantilever state, and the deviation of the arch linear shape after the cable is released as constraints, and establishes a multi-objective optimization model for the initial cable force. According to the actual situation of the project, the cable force that meets the boundary conditions is quickly and accurately calculated.

[0087] In some embodiments, see Figures 2 to 4 The method of the present invention determines the arch rib control node and the unknown load T according to the construction requirements. i The number of nodes is determined, and the deviation value of the target linear shape of the control node and the allowable value of the cable force are determined at the same time. A finite element model is established based on the geometric parameters, material parameters, boundary conditions and load conditions of the arch bridge. According to the construction conditions of the project, the construction stage structure group, boundary value and load group are determined to establish a construction stage model, and the model is modified according to the construction sequence.

[0088] Specifically, for cantilever bridges, the elevation of the newly constructed beam section is affected by the existing beam section. In order to accurately simulate the coupling between the cable-stayed buckle systems and ensure the reliability of the extracted influence matrix, the construction phase model of the method of the present invention can activate the largest cantilever unit at one time. The unit load and the corresponding constraints are not applied at the same time, but are activated one by one according to the construction sequence to ensure the tangent assembly relationship between the new and old units of the arch rib. It should be noted that loads can be divided into two categories: constant loads and variable loads. Constant loads can include the deadweight of the structure, and variable loads can include cable forces and wind cable forces.

[0089] In some embodiments, the method of the present invention combines the influence matrix principle to determine the number of unknown loads, and extracts multiple influence matrices corresponding to the unknown loads through finite element software. Specifically, assuming that the number of back-hook cables is n, the unknown load (such as the unknown amount of the cable force) T = (T1, T2, T3, ... T n ) T , the number of control nodes of arch ribs and towers is m, the number of wind rails is k, and the extracted multiple influence matrices include multiple displacement influence matrices, multiple cable force influence matrices and multiple internal force influence matrices.

[0090] Among them, the influence matrix of the tension unit cable force on the displacement of the control node during the construction process is expressed as:

[0091]

[0092] In the formula, the element δ i,j(i=1,2,…,m;j=1,2,…,n) is the displacement influence of the jth cable tensioning unit force on the ith control node during the construction process. For example, A is the displacement influence matrix of the tensioning unit cable force on the vertical direction of the main truss.

[0093] Among them, the influence matrix of the tension unit cable force on the cable force of each cable during the construction process is expressed as:

[0094]

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

[0096] Among them, the displacement influence matrix of the control node caused by the removal of the unit cable force during the cable removal process is expressed as:

[0097]

[0098] In the formula, the element ε i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the ith control node after the arch rib is closed. For example, C is the displacement effect matrix of the main arch rib vertically after the removal of the cable.

[0099] Among them, the displacement influence matrix of the control node caused by removing the wind cable during the cable removal process is expressed as:

[0100]

[0101] In the formula, the element λ i,j (i=1,2,…,m;j=1,2,…,k) is the displacement effect of the deadweight of the jth cable on the ith control node during the construction process. For example, G is the displacement effect matrix of the arch rib due to the removal of the wind cable.

[0102] Among them, the influence matrix of the tension unit cable force on the wind cable during the construction process is expressed as:

[0103]

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

[0105] Among them, the influence matrix of the tension unit cable force on the internal force of the arch foot during construction is expressed as:

[0106]

[0107] In the formula, the element σ i,j (i=1,2,…,m;j=1,2,…,n) is the displacement influence of the jth cable tensioning unit force on the ith control node during construction. For example, F is the influence matrix of the tensioning unit cable force on the internal force of the arch foot.

[0108] Among them, the influence matrix of the unit cable force on the internal force of the arch foot during the cable removal process is expressed as:

[0109]

[0110] In the formula, the element ω i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the ith control node after the arch rib is closed. For example, I is the internal force effect matrix of the arch foot after the removal of the cable.

[0111] Among them, the internal force influence matrix of the removal of wind cables on the arch foot during the cable removal process is expressed as:

[0112]

[0113] In the formula, the element τ i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable deadweight on the ith control node during construction. For example, J is the internal force effect matrix of the removed wind cable on 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 solve the initial tension vector of each cable. Specifically, for the construction of the arch bridge cable-stayed buckle, the construction stage is mainly divided into the cable installation stage and the cable removal stage. During the construction process, the loads that have an effect on the structure are composed of several parts such as the dead load, the cable force and the wind-drawn 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 cable force; A is the displacement influence matrix of the tension unit cable force on the vertical direction of the main truss; B is the cable force influence matrix of the tension unit cable force on the cable; C is the displacement influence matrix of the removal of the cable on the vertical direction of the main arch rib; F is the internal force influence matrix of the tension unit cable force on the arch foot; G is the displacement influence matrix of the removal of the wind cable on the arch rib; H is the cable force influence matrix of the tension unit cable force on the wind cable; I is the internal force influence matrix of the removal of the cable on the arch foot; J is The influence matrix of the removed wind cable on the internal force of the arch foot; among them, b0 is the influence vector of the main arch rib self-weight (such as high-strength bolts, node plates, etc.) on the vertical displacement of the arch rib; b1 is the influence vector of the main arch rib self-weight (such as high-strength bolts, node plates, etc.) on the cable force; b3 is the influence vector of the removed cable self-weight on the internal force of the arch foot; b5 is the influence vector of the main arch rib self-weight (such as high-strength bolts, node plates, etc.) on the internal force of the arch foot; b6 is the influence vector of the main arch rib self-weight (such as high-strength bolts, node plates, etc.) on the wind cable force; b7 is the initial value vector of the wind cable force.

[0118] Then the initial tension vector of each cable is solved as:

[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] Among them, the displacement difference between the actual displacement of each control node and the target line shape after the closure and release of the cable is used as the linear inequality constraint condition to control the line shape of the arch rib after the closure and release of the hook, which is expressed as follows:

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

[0123] Where Δδ is the allowable deviation between the control node line shape in the bare arch state and the ideal bare arch;

[0124] Among them, the internal force difference of the maximum axial tension of the arch rib section of the lower chord arch foot and the minimum axial pressure of the upper chord during the construction period is used as the linear inequality constraint condition to control the internal force of the arch foot during the construction process, which is expressed as follows:

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

[0126] Where, ΔN i is the allowable deviation between the linear shape of the control node in the bare arch state and the ideal bare arch;

[0127] Among them, the axial force of the arch foot and arch rib in the maximum cantilever state is used as the 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] Where N Z is the internal force of the arch foot in the maximum cantilever state; ΔN is the design value of the internal force of the arch foot in the maximum cantilever state;

[0130] Among them, there is a safety factor for the back cable force value, and the maximum breaking force of the back cable force is used as the minimization boundary constraint condition, which is expressed as follows:

[0131] T L <T<T B

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

[0133] In order to ensure the stability of the linear shape of the arch rib control nodes during the construction process, 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:

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

[0135] In the formula, u1(T i ) is the actual displacement vector of the control node after the arch rib segment is installed and the cable is tensioned; u2(T i ) Actual displacement vector of the cantilever end control node after installing the arch ring cross brace; u l It is the displacement vector of the bare arch when the control node is dropped once.

[0136] The method of the present invention substitutes the influence matrix extracted by finite element software into the solved initial tension vector of each cable, and then calculates the relevant parameters of the back cable force value of the cable-stayed and hook-hung arch bridge based on the determined constraint conditions and the initial cable force multi-objective optimization model of the variable load, such as the arch rib segment tension cable force, wind cable force, axial force and arch calculation linearity. The method of the present invention establishes a functional relationship mathematical model based on operations research theory to calculate the optimal cable force. By considering the influence of each variable load and fixed load on the arch rib line shape and the mutual influence between the variable load and the fixed load, the corresponding influence matrix is ​​obtained, and the optimal back cable force value that meets the boundary conditions is quickly and accurately obtained according to the actual engineering situation.

[0137] Here, some specific embodiments are used to verify the multi-objective data processing method of the arch bridge cable-stayed buckle and hook cable force based on the influence matrix and the multi-objective optimization system thereof.

[0138] For example, see Figure 2 As shown in the figure, the main bridge of a Daxi River Bridge is a 580m-span steel truss arch bridge with a rise of 116m and a rise-span ratio of 1 / 5: the center line of the arch rib is the catenary, and the arch axis coefficient is 2.0. Figure 2 As shown. The main bridge deck structure adopts a triple setting, arranged as [(66.75+53.4+3×40.05)+(40.05+50+40.05)+(3×40.05+53.4+66.75)]m steel plate continuous steel-concrete composite beam. The steel-concrete composite beam structure system is mainly composed of three main structural units: steel main beam, steel cross beam (including middle cross beam and reinforced cross beam at the support), and bridge deck. The main truss chord adopts a box-shaped welded section with the same inner width and inner height. In order to adapt to the stress of different sections and save steel, the main chord members adopt two widths and heights. The cross section of the web member is box-shaped or I-shaped according to different positions. The inner height of the web member web plate is the same as the corresponding chord, which is 1800 and 2300mm. The inner width of the top plate of the box-type web member is 1000mm and 1200mm, and the width of the top plate of the I-type web member is 700mm, 760mm, 800mm, and 900mm; the thickness of the web member wing plate is 16-42mm, and the thickness of the web plate is 16-42mm. The web member of the main truss is bolted to the upper and lower chords through an integral node plate. In order to increase the integrity of the main arch rib, reduce the difficulty of assembling the rods on the construction site, and enhance the corrosion resistance of the structure, this embodiment adopts an integral node. The main truss welded integral node welds the rods and the node plate into one in the factory. The arch rib chords of this bridge are connected by welding and high-strength bolts, and the arch rib web member is connected to the integral node plates of the upper and lower chords by high-strength bolts. The upper and lower chord parallel joints of the arch ribs are arranged with continuous "K" braces except for the arch top, and the parallel joint braces are welded box sections, and the diagonal bars are welded box sections and I-sections. The column piers on the arches are made of steel frame structure, and the columns are made of equal-section steel boxes. The columns are equipped with 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] Based on the geometric parameters, material parameters, boundary conditions and load conditions of the arch bridge, a finite element model is constructed, and the construction stage structure group, boundary value and load group are determined according to the engineering construction conditions to establish a construction stage model; the number of unknown loads is determined in combination with 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 calculation, is combined with mathematical engineering optimization software, such as MATLAB calculation.

[0140] The main purpose of the cable is to balance the deadweight of the arch rib during the cantilever assembly of the arch rib, while the anchor cable is to balance the force of the cable on the tower to ensure the safety of the tower during construction. An ideal set of cable force should meet the following conditions: First, during the tangent assembly, the cable is removed after the arch rib is closed, and the error between the bare arch line shape and the target bare arch line shape should be within the allowable range of the specification; second, the force safety of the arch rib and the tower should be ensured during the construction process; third, during the cantilever assembly of the arch rib, the post-tensioned cable should not have too much influence on the displacement of the installed stage; fourth, during the construction process, the tension on the lower chord of the arch rib should not be too large; finally, after the cable is removed, the force on the arch foot should basically meet the design requirements. Based on the above principles, the number of control nodes, variable loads, fixed loads (i.e., constant loads), and the values ​​of various parameters such as the arch rib linear deviation value, arch foot stress allowable value, and cable force allowable value required by the specification are determined. The influence matrix data and various parameter values ​​are then brought into the optimization model constructed by the programming software to solve the cable force. After computer iterative calculation, the optimization calculation results are as follows: Figure 5-Figure 12 .

[0141] Among them, the initial tension of the cable is Figure 5 As can be seen from the figure, the cable force of the anchor cable is relatively uniform, without sudden changes, and the tension force of the anchor cable is reasonable. Due to space constraints, the cable force time history diagram of the left span of the main bridge is shown in Figures 6 to 9 During the construction process, the tension of the back cables changes slowly without major mutations. Since the bridge is mainly controlled by internal forces according to the design requirements, that is, the tension cable force is strictly controlled during the arch erection process, the arch calculation line shape is calculated according to the initial tension calculation of this group. Fig.10 Based on the determined anchor cable tension force, the construction phase calculations are performed and the theoretical deviation of the tower tops on both sides is obtained as follows: Fig.11 As shown. Fig.11 It can be seen that during the construction process, the maximum tower top deviation is 9.4cm, which is less than H / 1000=14.5cm. The tower top deviation meets the specification requirements. The calculation results of the axial force of the arch foot truss members on both sides of the maximum cantilever state and the second phase paving stage are as follows Fig.12 As shown. Fig.12 It can be seen that the axial force of the arch foot truss rods in the maximum cantilever state is basically negative, and the axial force of the arch foot truss rods in the second phase paving stage is all negative, and the internal force distribution of the structure is consistent with the ideal internal force state of the design. From the perspective of theoretical calculation, the safety of the construction of the lower chord steel tie rods at the arch foot is guaranteed, and the compressive stress reserve of the upper chord arch foot after the bridge is completed meets the design requirements.

[0142] The sum of squares of the difference between the arch rib linear shape and the target linear shape during the construction period was used as the optimization objective function, and the maximum axial tension of the arch rib section at the arch foot of the lower chord during the construction period, the minimum axial pressure of the upper chord, the cable force during the construction process, the axial force of the arch rib at the arch foot in the maximum cantilever state, and the deviation of the arch linear shape after the cable was released were used as constraints. The optimized initial cable force can effectively control the uniformity of the arch rib linear shape and the axial force distribution of the upper and lower chord arch rib sections at the arch foot during the construction process, so as to achieve a good arch rib linear shape after the closure and cable release, and provide sufficient pressure reserve for the upper chord arch rib in the completed bridge state, offset the tension of the arch rib caused by wind load and vehicle load during the operation period, and ensure the stability of the arch ring stress state. With the help of finite element software and numerical analysis software, the automatic and intelligent solution of cable force optimization is realized, which avoids the tedious trial calculation process, improves the efficiency of cable force adjustment, and can effectively solve the multi-objective initial cable force optimization problem of cable-stayed buckle arch bridge. It can effectively solve the construction control problem of other types of large-span arch bridges with internal force as the optimization target, and is also suitable for the construction control of general arch bridges.

[0143] It should be appreciated that the method steps in the embodiments of the present invention can be implemented or implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level process or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in an assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, the program can be run on a programmed ASIC for this purpose.

[0144] Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.

[0145] Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Various aspects of the present invention can be implemented in 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, an optical read and / or write storage medium, an RSM, a ROM, etc., so 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 process described herein. In addition, the machine-readable code, or portions thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention can also include the computer itself.

[0146] The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a 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 present invention, the converted data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on the display.

[0147] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the present invention. Within the scope of protection of the present invention, its technical scheme and / or implementation method may have various modifications and changes.

Claims

1. A multi-objective data processing method for arch bridge cable-stayed buckle cable force based on influence matrix, characterized in that: The method comprises the following steps: S100, establish a finite element model and modify the model according to the construction sequence; S200, extracting a plurality of relevant influence matrices, wherein the influence matrices include a displacement influence matrix, a cable force influence matrix, and an internal force influence matrix; S300, based on the superposition principle, according to the obtained multiple related influence matrices, the influence matrix relationship is obtained, and then the initial tension vector of each cable is obtained; S400. Based on the optimization theory, the corresponding multiple constraint conditions are determined, a multi-objective optimization model of the initial cable force with variable load is established, and the cable force value parameters of the back cable of the cable-stayed arch bridge are calculated.

2. The method according to claim 1, characterized in that In the step S100, the model activates the largest cantilever unit once in the construction phase, and the unit loads 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, the number of back-fastening cables is assumed to be n, and the unknown cable force T is T = (T1, T2, T3, ... T n ) T , the number of control nodes of arch ribs and towers is m; Among them, the influence matrix of the tension unit cable force on the displacement of the control node during the construction process is expressed as: In the formula, the element δ i,j (i=1,2, … ,m; j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the displacement of the i-th control node during the construction process; Among them, the influence matrix of the tension unit cable force on the cable force of each cable during the construction process is expressed as: In the formula, the element f i,j (i=1,2,…,n;j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the force of the ith cable during the construction process; Among them, the displacement influence matrix of the control node caused by the removal of the unit cable force during the cable removal process is expressed as: In the formula, the element ε i,j (i=1,2, … ,m; j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the i-th control node after the arch rib is closed; Among them, the displacement influence matrix of the control node caused by removing the wind cable during the cable removal process is expressed as: In the formula, the element λ i,j (i=1,2, … ,m; j=1,2,…,k) is the influence of the deadweight of the jth cable on the displacement of the i-th control node during the construction process; Among them, the influence matrix of the tension unit cable force on the wind cable during the construction process is expressed as: In the formula, the element φ i,j (i=1,2, … ,k; j=1,2,…,n) is the displacement influence of the jth fixed load on the ith control node during the construction process; Among them, the influence matrix of the tension unit cable force on the internal force of the arch foot during construction is expressed as: In the formula, the element σ i,j (i=1,2, … ,m; j=1,2,…,n) is the influence of the tensioning unit force of the jth cable on the displacement of the i-th control node during the construction process; Among them, the influence matrix of the unit cable force on the internal force of the arch foot during the cable removal process is expressed as: In the formula, the element ω i,j (i=1,2,…,m;j=1,2,…,n) is the displacement effect of the jth cable tensioning unit force on the ith control node after the arch rib is closed; Among them, the internal force influence matrix of the removal of wind cables on the arch foot during the cable removal process is expressed as: In the formula, the element τ i,j (i=1,2, … ,m; j=1,2,…,n) is the influence of the deadweight of the jth cable on the displacement of the ith control node during the construction process.

4. The method according to claim 3, characterized in that 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 Where D is the target displacement vector; N is the target internal force vector; T is the unknown cable force; A is the influence matrix of the tension unit cable force on the vertical displacement of the main truss; B is the cable force influence matrix of the tension unit cable force on the cable; C is the influence matrix of the vertical displacement of the main arch rib caused by the removal of the cable; 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 tensioning unit cable force on wind cable force; I is the influence matrix of removing cable on internal force of arch foot; J is the influence matrix of removing wind cable on internal force of arch foot; among them, b0 is the influence vector of main arch rib self-weight on vertical displacement of arch rib; b1 is the influence vector of main arch rib self-weight on cable force; b3 is the influence vector of removing cable self-weight on internal force of arch foot; b5 is the influence vector of main arch rib self-weight on internal force of arch foot; b6 is the influence vector of main arch rib self-weight on wind cable force; b7 is the initial value vector of wind cable force.

5. The method according to claim 4, characterized in that In step S300, The initial tension vector of each cable is:

6. The method according to claim 5, characterized in that In the step S400, Among them, the difference between the actual displacement of each control node and the displacement of the target line shape after the closure is completed is taken as the linear inequality constraint condition, which is expressed as follows: |A·T+C·(B·T+b1)+G·(H·T+b6+b7)+b0-b2|≤Δδ Where Δδ is the allowable deviation between the control node line shape in the bare arch state and the ideal bare arch; Among them, the internal force difference of the maximum axial tension of the arch foot and the minimum axial pressure of the arch rib section of the lower chord during the construction period is taken as the linear inequality constraint condition, which is expressed as follows: |F·T+I·(B·T+b1)+J·(H·T+b6+b7)+b5-b3-b4|≤ΔN i Where, ΔN i is the allowable deviation between the linear shape of the control node in the bare arch state and the ideal bare arch; Among them, the axial force of the arch foot and arch rib in the maximum cantilever state is taken as the nonlinear inequality constraint condition, which is expressed as follows: N Z <ΔN1 Where N Z is the internal force of the arch foot in the maximum cantilever state; ΔN is the design value of the internal force of the arch foot in the maximum cantilever state; Among them, the maximum breaking force of the buckle back cable is taken as the minimization boundary constraint condition, which is expressed as follows: T L <T<T B Where, T B is the lower limit of the cable force, T L is the upper limit of the cable force.

7. The method according to claim 6, characterized in that In the step S400, Among them, the sum of the squares of the differences between the actual displacement and the target displacement of the arch rib control point at each lifting construction stage is taken as the optimization objective function, which is expressed as follows: min(sum(0.5·(u1(T i )-u2(T i ))-u l ) 2 ) In the formula, u1(T i ) is the actual displacement vector of the control node after the arch rib segment is installed and the cable is tensioned; u2(T i ) Actual displacement vector of the cantilever end control node after installing the arch ring cross brace; u l It is the displacement vector of the bare arch when the control node is dropped once.

8. The method according to claim 2, characterized in that: In the step S100, the load includes a constant load and a variable load, and the variable load includes the cable force and the wind cable force. 9 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions, when executed by a processor, implement the method according to any one of claims 1 to 8.

10. Multi-objective optimization of cable forces of arch bridge cable-stayed buckles based on influence matrix The system is characterized in that include: A computer device comprising a computer readable storage medium according to claim 9.

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